diff --git a/include/xsf/polygamma.h b/include/xsf/polygamma.h new file mode 100644 index 0000000000..15ba4093b7 --- /dev/null +++ b/include/xsf/polygamma.h @@ -0,0 +1,324 @@ +/* + * Calculation of the polygamma function for positive integer orders and real and complex inputs + * Author: Lorenzo Peri + */ + +#pragma once + +#include "cephes/psi.h" +#include "cephes/zeta.h" +#include "config.h" +#include "digamma.h" +#include "error.h" +#include "gamma.h" +#include "trig.h" +#include "trigamma.h" + +namespace xsf { + +constexpr int MAX_ORDER_BERNOULLI_SERIES = 6; + +namespace detail { + + XSF_HOST_DEVICE inline std::complex + polygamma_forward_recurrence(int n, std::complex const z, std::complex const psiz, int m) { + /* Compute polygamma(n, z + m) using polygamma(n, z) using the recurrence relation + * polygamma(n, z + 1) = polygamma(n, z) + (-1)^n * n! / z^(n+1). + * See https://dlmf.nist.gov/5.15#E5 */ + + std::complex zk, res = psiz; + + for (int k = 0; k < m; k++) { + zk = (z + static_cast(k)); + res += std::pow(zk, -(n + 1)); + } + + return res; + } + + XSF_HOST_DEVICE inline std::complex + polygamma_backward_recurrence(int n, std::complex const z, std::complex const psiz, int m) { + /* Compute polygamma(n, z + m) using polygamma(n, z) using the recurrence relation + * polygamma(n, z + 1) = polygamma(n, z) + (-1)^n * n! / z^(n+1). + * See https://dlmf.nist.gov/5.15#E5 */ + + std::complex zk, res = psiz; + + for (int k = 1; k < m + 1; k++) { + zk = (z - static_cast(k)); + res -= std::pow(zk, -(n + 1)); + } + + return res; + } + + XSF_HOST_DEVICE inline std::complex polygamma_asymptotic_series(int n, std::complex z) { + /* Evaluate digamma using an asymptotic series. See + * http://dlmf.nist.gov/5.15.E8 + * Higher order converge slower, so we need slightly more Bernoulli + * numbers than the digamma (Bernoulli numbers calculated via sympy). + */ + static constexpr std::array bernoulli2k = { + 1.66666666666666666670e-1, -3.33333333333333333330e-2, 2.38095238095238095240e-2, + -3.33333333333333333330e-2, 7.57575757575757575760e-2, -2.53113553113553113550e-1, + 1.16666666666666666670e+0, -7.09215686274509803920e+0, 5.49711779448621553880e+1, + -5.29124242424242424240e+2, 6.19212318840579710140e+3, -8.65802531135531135530e+4, + 1.42551716666666666670e+6, -2.72982310678160919540e+7, 6.01580873900642368380e+8, + -1.51163157670921568630e+10, 4.29614643061166666670e+11, -1.37116552050883327720e+13, + 4.88332318973593166670e+14, -1.92965793419400681490e+16, 8.41693047573682615000e+17, + -4.03380718540594554130e+19, 2.11507486380819916060e+21, -1.20866265222965259350e+23, + 7.50086674607696436690e+24, -5.03877810148106891410e+26, 3.65287764848181233350e+28, + -2.84987693024508822260e+30, 2.38654274996836276450e+32, -2.13999492572253336660e+34, + 2.05009757234780975700e+36, -2.09380059113463784090e+38, 2.27526964884635155600e+40, + -2.62577102862395760470e+42, 3.21250821027180325180e+44, -4.15982781667947109140e+46, + }; + + std::complex res, term, fac_coeff; + std::complex const zn_inv = std::pow(z, -n); + std::complex const rzz = 1. / z / z; + std::complex zfac = zn_inv; + + if (!(std::isfinite(z.real()) && std::isfinite(z.imag()))) { + /* Check for infinity (or nan) and return early. + * Result of division by complex infinity is implementation dependent. + * and has been observed to vary between C++ stdlib and CUDA stdlib. + */ + return 0.; // Asymptotically psi(n, z) ~ 1/z, so just return zero? + } + + res = zn_inv * (1. / n + 0.5 / z); + + fac_coeff = (0.5 * static_cast>(n + 1)); + + for (int k = 1; k < bernoulli2k.size() + 1; k++) { + + zfac *= rzz; + term = bernoulli2k[k - 1] * fac_coeff * zfac; + res += term; + + if (std::abs(term) < std::numeric_limits::epsilon() * std::abs(res)) { + break; + } + + double const num_coeff = (2. * k + n) * (2. * k + n + 1.); + double const den_coeff = (2. * k + 2) * (2. * k + 1.); + fac_coeff *= num_coeff / den_coeff; + } + + return -res; + } + + XSF_HOST_DEVICE inline std::complex polygamma_reflection_rhs(int n, std::complex z) { + /* The reflection formula for the polygamma of arbitrary positive order + * reads (http://dlmf.nist.gov/5.15.E6) + * psi(n, 1-z) + (-1)**(n-1) * psi(n, z) = (-1)**(n-1) * pi * d^n/dz^n cot(pi z) + * To calculate this derivative we can leverage the fact that, if y = cot(z), then + * d/dz cot(z) = - (1 + y **2). Therefore, the derivatives of y = cot(z)) are all + * polynomials in cot(z) + * P_n(y) = sum_{m=1}^{n+1} c_{n, m} y**m + * that satisfy the recurrence relation + * c_{n+1, m} = -(m+1) c_{n, m+1} - (m-1) c_{n, m-1} + * This allows fast calculation of the coefficients of P_n(y). + * However, this requires us to loop through the calculation n times, + * and the coefficients blow up, leading to loss of precision. + * For larger n, there is little point using this strategy. + */ + + if (n > MAX_ORDER_BERNOULLI_SERIES) { + // We are not going to use it for n>MAX_ORDER_BERNOULLI_SERIES. + // Statically allocate the memory and check against misuse + return std::numeric_limits::quiet_NaN(); + } + + std::array coefficient_array{}; // all zeros at the start + std::array next_coeffs; + + coefficient_array[1] = 1.; // P_0(y) = y + + /* The coefficients blow up very rapidly roughly O(n!). So we compute the + * normalized RHS (-1)**(n-1) * pi * d^n/dz^n cot(pi z) / n!, and let the + * general prefactor in the main polygamma driver handle the n! scaling + */ + for (int k = 0; k < n; k++) { + std::fill(next_coeffs.begin(), next_coeffs.end(), 0.); + for (int m = 0; m < k + 3; m++) { + double const term1 = (m + 1 <= k + 1) ? (-static_cast(m + 1) * coefficient_array[m + 1]) : 0.; + double const term2 = (m - 1 >= 0) ? (-static_cast(m - 1) * coefficient_array[m - 1]) : 0.; + next_coeffs[m] = (term1 + term2) / static_cast(k + 1); + } + std::copy(next_coeffs.begin(), next_coeffs.end(), coefficient_array.begin()); + } + + std::complex result = 0.0; + std::complex cot_piz = cospi(z) / sinpi(z); + // Evaluate from highest degree down to 0 + for (int m = n + 1; m >= 0; m--) { + result = result * cot_piz + coefficient_array[m]; + } + + double const sign = (n & 1) ? -1.0 : 1.0; + return sign * std::pow(M_PI, n + 1) * result; + } + + XSF_HOST_DEVICE inline std::complex polygamma_Hurwitz_series(int n, std::complex z) { + /* Evaluate the sum for the Hurwitz zeta function: + * zeta(n+1, z) = sum_{k=0}^\infty 1 / (z+k)^{n+1} + * For n > 8, the terms decay exponentially fast, making direct + * summation far more stable than the asymptotic Bernoulli series. + */ + std::complex res = 0.0; + for (int k = 0; k < 10000; k++) { + std::complex const zk = z + static_cast(k); + std::complex const term = std::pow(zk, -(n + 1)); + res += term; + + if (std::abs(term) < std::numeric_limits::epsilon() * std::abs(res)) { + break; + } + } + return -res; + } + +} // namespace detail + +XSF_HOST_DEVICE inline double polygamma(int n, double z) { + if (n < 0) { + /* Although it is formally possible to extend the polygamma function to negative orders + * this is not implemented yet. For more information see: + * O. Espinosa, and V.H. Moll (2003), "A GENERALIZED POLYGAMMA FUNCTION" + * https://arxiv.org/pdf/math.CA/0305079 + */ + set_error("polygamma", SF_ERROR_DOMAIN, NULL); + return std::numeric_limits::quiet_NaN(); + } + /* To compute the polygamma for real inputs we can leverage Cehpes via the identity + * psi(n, x) = (-1)**(n+1) * n! * zeta(n+1, x) + * where n is a positive integer and zeta is the Hurwitz zeta function + */ + if (n == 0) { + return digamma(z); + } else if (n == 1) { + return trigamma(z); + } + + /* (-1)^(n+1) */ + const double sign = n & 1 ? 1. : -1.; + const double np1 = static_cast(n + 1); + + double const factorial = gamma(np1); + + const double Hur_zeta = cephes::zeta(np1, z); + + return sign * factorial * Hur_zeta; +} + +XSF_HOST_DEVICE inline float polygamma(int n, float z) { + return static_cast(polygamma(n, static_cast(z))); +} + +XSF_HOST_DEVICE inline std::complex polygamma(int n, std::complex z) { + /* + * Compute the polygamma function for complex arguments. The strategy is: + * - For small orders (n <= (MAX_ORDER_BERNOULLI_SERIES = 6)): + * - If close to the origin, use a reflection relation to step away + * from the origin. + * - If close to the negative real axis, use the recurrence + * formula to move to the right halfplane. + * - If |z| is large (> 16), use the asymptotic series. + * - If |z| is small, use a recurrence relation to make |z| large + * enough to use the asymptotic series. + * - For large orders (n > (MAX_ORDER_BERNOULLI_SERIES = 6)): + * - Use the recurrence relation to move in the positive half plane + * - Evaluate the Hurwitz zeta, which converges faster and to higher accuracy + * than the Bernoulli asymptotic series for large n. + */ + if (n < 0) { + /* Although it is formally possible to extend the polygamma function to negative orders + * this is not implemented yet. For more information see: + * O. Espinosa, and V.H. Moll (2003), "A GENERALIZED POLYGAMMA FUNCTION" + * https://arxiv.org/pdf/math.CA/0305079 + */ + set_error("polygamma", SF_ERROR_DOMAIN, NULL); + return {std::numeric_limits::quiet_NaN(), std::numeric_limits::quiet_NaN()}; + } + // Fall back to digamma and trigamma + if (n == 0) { + return digamma(z); + } else if (n == 1) { + return trigamma(z); + } + + if (std::abs(z.imag()) < std::numeric_limits::epsilon()) { + // use the real zeta, because it evaluates to better precision + return static_cast>(polygamma(n, z.real())); + } + + double absz = std::abs(z); + std::complex res = 0.; + /* The reflection formula flips the sign for odd polygammas. + * We must keep track of that. */ + std::complex sign = 1.; + std::complex const prefactor_sign = (n & 1) ? -1. : 1.; + std::complex const prefactor = prefactor_sign * gamma(static_cast(n + 1)); + /* Use the asymptotic series for z away from the negative real axis + * with abs(z) > smallabsz. */ + double const smallabsz = 16.; + + if (z.real() <= 0.0 && std::ceil(z.real()) == z) { + // Poles + set_error("polygamma", SF_ERROR_SINGULAR, NULL); + return {std::numeric_limits::quiet_NaN(), std::numeric_limits::quiet_NaN()}; + } + + if (n <= MAX_ORDER_BERNOULLI_SERIES) { + /* For small orders, the Hurwitz series converges slowly, best take the approaches + * of the di- and trigamma with the Bernoulli series + */ + if (z.real() < 0 && std::abs(z.imag()) < smallabsz) { + std::complex const reflection_rhs = detail::polygamma_reflection_rhs(n, z); + res -= reflection_rhs; + sign *= (n & 1) ? -1. : 1.; + z = 1. - z; + absz = std::abs(z); + } + if (absz < 0.5) { + res -= sign * std::pow(z, -(n + 1)); + z += 1; + absz = std::abs(z); + } + + if (absz > smallabsz) { + res += sign * detail::polygamma_asymptotic_series(n, z); + } else if (z.real() >= 0.0) { + double m = std::trunc(smallabsz - z.real()) + 1; + std::complex init = detail::polygamma_asymptotic_series(n, z + m); + res += sign * detail::polygamma_backward_recurrence(n, z + m, init, m); + } else { + double m = std::trunc(smallabsz + z.real()) + 1; + std::complex init = detail::polygamma_asymptotic_series(n, z - m); + res += sign * detail::polygamma_forward_recurrence(n, z - m, init, m); + } + } else { + /* For large n, Hurwitz series converges converges very fast, so we can use it directly. + * However, we need to make sure that Re[z] is negative-enough that + * sum_{k=0}^\infty 1 / (z+k)^{n+1} converges quickly. + * The reflection is very expensive to calculate and its coefficients blow up like n!. + * We can however use the recurrence formula to step away towards + * the positive real semi-plane */ + while ((absz < 0.5) || (z.real() < 0)) { + res -= std::pow(z, -(n + 1)); + z += 1; + absz = std::abs(z); + } + + res += detail::polygamma_Hurwitz_series(n, z); + } + + return prefactor * res; +} + +XSF_HOST_DEVICE inline std::complex polygamma(int n, std::complex z) { + return static_cast>(polygamma(n, static_cast>(z))); +} + +} // namespace xsf diff --git a/include/xsf/trigamma.h b/include/xsf/trigamma.h new file mode 100644 index 0000000000..f63469dec3 --- /dev/null +++ b/include/xsf/trigamma.h @@ -0,0 +1,395 @@ +/* + * Calculation of the trigamma function for real and complex inputs + * Author: Lorenzo Peri + */ + +#pragma once + +#include "cephes/psi.h" +#include "cephes/zeta.h" +#include "config.h" +#include "error.h" +#include "trig.h" + +namespace xsf { +namespace detail { + + /* There exist no real roots of the trigamma function. + * All the roots of the trigamma function lay in the negative real semi-plane (Re[z] < 0) + * and come in an infinite number of complex pairs (z_n, \bar{z}_n). + * This is the location of the two roots closer to the origin. + */ + + constexpr double firstroot_re = -0.41213454795193723424; + constexpr double firstroot_im = +0.59781194232059657221; + + constexpr double secondroot_re = -1.4455692007504016647; + constexpr double secondroot_im = +0.69926087106525701723; + + /* NOTE: + * For better accuracy, one may be able to use the fact that + * trigamma(z) + trigamma(1-z) = pi**2 / sin(pi * z)**2 + * So for large negative Re[z], the roots must asymptotically approach + * real part -n + 1/2, with slowly-growing imaginary part. Hence, for values around + * z = -n + 1/2 +- 0.75j we could use the Taylor expansion via the polygamma, + * if more precision is needed for root-finding. + * However, testing suggests this is not the case, so this has not been implemented. + */ + + XSF_HOST_DEVICE inline std::complex + trigamma_root_series(std::complex const z, int const root_index, double const imsign) { + + /********************************** Series expansion constants **********************************/ + /* Because the trigamma does not have roots in the real axis, we cannot piggy-back on cephes::zeta. + * However, psi(n+1, z)/(n)! can still be evaluated via mpmath and stored as a constant array + */ + + static constexpr std::array roots_location_re = {firstroot_re, secondroot_re}; + + static constexpr std::array roots_location_im = {firstroot_im, secondroot_im}; + + static constexpr std::array, 2> taylor_coeffs_re = { + {{// First root + 9.1080172479838895865e-17, -2.9833604957805599511e+0, -14.018950391053259352e+0, + 9.0244567682892409266e+0, 30.874956766351548509e+0, 34.541752961058271865e+0, + 39.009566174081896861e+0, -132.61045192741005394e+0, -218.62357592235318293e+0, + -64.411882496106031226e+0, 203.10382610710644258e+0, 843.63339672989093287e+0, + 662.46913770761409523e+0, -772.94967564645764924e+0, -2195.3718826638200881e+0, + -2930.2957335752762447e+0, 645.15496382139008347e+0, 7427.2379542621074506e+0, + 9439.1355798311033141e+0, 2265.3656112362482418e+0, -17976.059265797157423e+0, + -34557.165315543585166e+0, -15488.046929912889027e+0, 40467.071329236867314e+0, + 102237.07007987287943e+0, 84308.324421938203159e+0, -81451.135771210465464e+0, + -290705.554540852434e+0, -314668.7054179974366e+0, 78288.649124173025484e+0, + 785651.99318701238371e+0, 1078335.3382942241151e+0, 173941.59359342456446e+0, + -1883168.9550851269159e+0, -3430120.4253031355329e+0, -1663440.5002393615432e+0, + 4158107.3425906528719e+0, 9981119.5116241183132e+0, 7815988.8380806706846e+0, + -7551943.8107375940308e+0, -27587495.006474528462e+0, -29076752.908828314394e+0, + 8077666.9182099932805e+0, 71044589.308923915029e+0, 97353898.125684320927e+0, + 14547456.322059284896e+0, -169035489.75971624255e+0, -299438887.83402949572e+0, + -143212831.15478402376e+0, 363534700.00453239679e+0, 861125488.17706620693e+0, + 657213911.34497916698e+0, -650972657.23167860508e+0, -2332338481.4032406807e+0, + -2429691855.3164582253e+0, 716433626.61413443089e+0, 5917764178.0552072525e+0, + 8008883489.7560710907e+0, 1112483090.8655650616e+0, -13937926524.107784271e+0, + -24338541099.401115417e+0, -11362293924.424409866e+0, 29639987087.049156189e+0, + 69304135290.439422607e+0, 52046135316.926963806e+0, -52924464353.45640564e+0, + -185777990501.79312134e+0, -191320182474.67971802e+0, 59363105651.442115784e+0, + 467673151063.63690186e+0, 625806128716.41210938e+0, 79708654667.238372803e+0, + -1094025457975.3127441e+0, -1889131923265.0839844e+0, -861612477677.46520996e+0, + 2315097770655.0478516e+0, 5344755178877.3457031e+0, 3957704192960.6518555e+0, + -4133617154330.4306641e+0, -14243561160457.984375e+0, -14507740357232.351563e+0, + 4730156227368.0966797e+0, 35680709502628.15625e+0, 47264902566753.390625e+0, + 5466706316509.2929688e+0, -83134951089908.90625e+0, -142094372390481.15625e+0, + -63354475700337.945313e+0, 175532075173260.25e+0, 400403810133614.4375e+0, + 292525586156113.625e+0, -313960697597505.6875e+0, -1063201394869874.0e+0, + -1071636435602862.75e+0, 366735533339498.3125e+0, 2655187226255846.5e+0, + 3484089660964081.0e+0, 362143126064491.1875e+0, -6172561211494055.0e+0, + -10448437646105654.0e+0 + }, + {// Second root + 5.4524533247549979198e-17, -1.1129516609162204421e+0, -8.4123458270441080487e+0, + 4.4344884179193835294e+0, 20.732204861034905008e+0, 3.0429402875860867006e+0, + 4.8856876287330912589e+0, -34.394886945411350609e+0, -73.718725710581068711e+0, + 34.397533695264762343e+0, 82.019204983273539256e+0, 87.311394512730743145e+0, + 79.813123929215834096e+0, -229.88961911997415655e+0, -307.25357348392651602e+0, + 17.768513154646232266e+0, 233.9103567437451261e+0, 644.57447585988916217e+0, + 400.31597610602159421e+0, -838.99527370542307381e+0, -1142.667274602767975e+0, + -672.50854221176700776e+0, 699.33343286998206167e+0, 2952.2729899380997267e+0, + 1804.4156337893034561e+0, -1939.0222428852139274e+0, -4390.9776154142909945e+0, + -4765.9689718843501396e+0, 1782.0073007910705201e+0, 10472.703050074791463e+0, + 8540.7804724000234273e+0, -1795.7734006212097029e+0, -16338.586309481521312e+0, + -22056.889110903408437e+0, 1042.6133896764329165e+0, 31820.13958963152254e+0, + 38860.710514671307465e+0, 10325.776471356321053e+0, -53936.772552904549229e+0, + -85802.932425871578744e+0, -23282.380866077233804e+0, 86119.543405023272499e+0, + 158925.90507253524265e+0, 84995.099389624680043e+0, -148968.3693368526001e+0, + -305690.65955470677e+0, -182464.18278398935217e+0, 200570.45908379976754e+0, + 578305.62896160327364e+0, 438149.73490933538415e+0, -311083.99629818135872e+0, + -1022984.1769126829458e+0, -934179.80446570529602e+0, 320098.97928918036632e+0, + 1889408.096175869694e+0, 1919098.4924058187753e+0, -260137.09258919744752e+0, + -3194477.7004772522487e+0, -3949612.7951777679846e+0, -268240.58420638204552e+0, + 5568022.6676272731274e+0, 7594112.9608210055158e+0, 1866021.784239478875e+0, + -9080501.0774496924132e+0, -14858851.839382385835e+0, -5612890.7087618308142e+0, + 14571131.499402185902e+0, 27616979.832255661488e+0, 14860656.240491846576e+0, + -22371271.646269556135e+0, -51332035.234632596374e+0, -33734206.887385599315e+0, + 31637528.883603923023e+0, 92778118.069112360477e+0, 74537842.063162609935e+0, + -41599123.161676205695e+0, -164575435.80708390474e+0, -154751889.32015013695e+0, + 41749336.101391732693e+0, 287615800.32811558247e+0, 313345749.76099699736e+0, + -17522700.13627949357e+0, -487787122.48196721077e+0, -617073974.94401979446e+0, + -81001990.910296738148e+0, 814449173.36699914932e+0, 1183835029.963737011e+0, + 344342132.1734226346e+0, -1310270797.1101074219e+0, -2235174639.0448431969e+0, + -972870005.92697286606e+0, 2044440891.2078654766e+0, 4120640100.7729520798e+0, + 2371630467.9593176842e+0, -3026173792.9559259415e+0, -7486827096.7126846313e+0, + -5297885493.9058942795e+0, 4160137914.0421552658e+0, 13321713752.551465988e+0, + 11278342754.757139206e+0 + }} + }; + + static constexpr std::array, 2> taylor_coeffs_im = { + {{ + // First root + 1.9689476472890448436e-16, 4.044337981596503262e+0, -7.3941432193042802012e+0, + -26.4623069876907131e+0, -1.5657568234258929518e+0, 12.808397661710225535e+0, + 88.027833394290681213e+0, 123.62940643728001078e+0, -106.32109009482918793e+0, + -272.45867815419285307e+0, -410.27930694666247291e+0, -86.782597941426899979e+0, + 1102.1387232076265263e+0, 1466.0506454643184497e+0, 545.1882812919824346e+0, + -2217.9064686095880461e+0, -5754.8727812528886716e+0, -3283.4424631773640613e+0, + 5543.4392134415256805e+0, 15833.635370604708442e+0, 16682.880006384319131e+0, + -9435.5858181943276577e+0, -47167.297127159035881e+0, -56722.714163294331229e+0, + -854.28115876288268282e+0, 124033.47128391949809e+0, 196500.84514077924541e+0, + 63124.484428748924984e+0, -284327.58732096874155e+0, -608727.64227164373733e+0, + -392247.35741802095436e+0, 604454.0479207362514e+0, 1734042.636362915393e+0, + 1621968.5883482831996e+0, -909822.08165691560134e+0, -4736249.7619706066325e+0, + -5710757.7356921844184e+0, 207452.20227611850714e+0, 11818016.939825890586e+0, + 18576645.04214990139e+0, 6031726.6782435318455e+0, -27102249.135446421802e+0, + -55521819.735950939357e+0, -35071050.387607783079e+0, 54519628.983876109123e+0, + 156158894.62619554996e+0, 141738560.80960172415e+0, -82503555.349761158228e+0, + -412818986.95092844963e+0, -494446402.06373292208e+0, 25868788.41499729827e+0, + 1015950908.8245180845e+0, 1569817888.5925683975e+0, 497068007.28298789263e+0, + -2297081599.2161045074e+0, -4632770027.5792331696e+0, -2861134230.4570889473e+0, + 4554388755.4394798279e+0, 12857647166.110887527e+0, 11502606847.624053955e+0, + -6921551638.6264343262e+0, -33553555348.813869476e+0, -39739817902.058311462e+0, + 2586764571.5984015465e+0, 81853762473.440658569e+0, 124901288496.36500549e+0, + 38189522192.376235962e+0, -183499975705.06417847e+0, -365651105247.84295654e+0, + -221707664548.28396606e+0, 362081755311.74279785e+0, 1006612243979.449707e+0, + 889379762919.08422852e+0, -552674484944.32897949e+0, -2608847120879.1108398e+0, + -3056520000009.1757813e+0, 238946410783.76174927e+0, 6328034955998.734375e+0, + 9555065868385.1386719e+0, 2817455991885.3300781e+0, -14122437331019.056641e+0, + -27828358863467.332031e+0, -16589801973106.900391e+0, 27819982471996.28125e+0, + 76235974161174.5e+0, 66565105419682.960938e+0, -42721272861724.007813e+0, + -196745977498914.03125e+0, -228195034186489.65625e+0, 20884379691198.875e+0, + 475554441415672.3125e+0, 711150412786520.875e+0, 202086534694355.9375e+0, + -1058822981010458.0e+0, -2064494960700603.5e+0, -1210578706349626.5e+0, + 2085822266866922.5e+0, 5638495776870608.0e+0, 4867352096330547.0e+0, + -3226346588093619.5e+0, + }, + {// Second root + -2.0886187184514818594e-16, 2.6352910681361323419e+0, -2.7465273316761171785e+0, + -16.081603936774637731e+0, 3.6349150477985818775e+0, 15.326822302901804917e+0, + 16.963613417604033629e+0, 38.030023581648258357e+0, -45.080272523330833678e+0, + -94.683126434869024024e+0, -9.8547858644971260134e+0, 23.13494927816051927e+0, + 175.86022148586815206e+0, 204.21597173963738214e+0, -191.75729307902071241e+0, + -334.08125960690273359e+0, -287.7192524549465702e+0, -18.440040361671922398e+0, + 894.44902390096001454e+0, 825.34530871214099079e+0, -320.73324130858628678e+0, + -1160.3663328222710334e+0, -1920.3364016438486033e+0, -324.32309629687068764e+0, + 3144.1574371753281412e+0, 3371.5495145367981422e+0, 851.25003006116332926e+0, + -4081.6620591933688047e+0, -8578.2344898673782154e+0, -2668.3694373718035422e+0, + 8579.661814979142946e+0, 14009.367669937275423e+0, 9337.3016036521203205e+0, + -12620.991744398463197e+0, -31502.710372905752592e+0, -17620.59367900545476e+0, + 18235.149970555630716e+0, 54404.217666152544552e+0, 48932.207386342364771e+0, + -28758.606484943069518e+0, -103989.97488247773435e+0, -93196.077915846719407e+0, + 21679.049627542692178e+0, 188424.71855478230282e+0, 209095.51932349728304e+0, + -21708.310137294363813e+0, -318917.72407036350342e+0, -412294.83355757704703e+0, + -65133.869098773830046e+0, 573262.05199860793073e+0, 811407.75078429805581e+0, + 223905.47458710509818e+0, -898392.3956043071812e+0, -1594942.9401338619646e+0, + -692055.71907006460242e+0, 1502419.6342246450949e+0, 2936510.239670007024e+0, + 1722814.7067913736682e+0, -2194149.2624233397655e+0, -5568379.2814786368981e+0, + -3861876.4619128271006e+0, 3140539.447914307937e+0, 9908628.1384462881833e+0, + 8556352.4623205848038e+0, -3885309.5242206109688e+0, -17843844.457143317908e+0, + -17440540.353781145066e+0, 3359989.4226588201709e+0, 30885963.191879630089e+0, + 35667011.386512152851e+0, 106318.61343497049529e+0, -52540829.694197170436e+0, + -69449093.001229658723e+0, -13246966.086865155026e+0, 87453795.719745591283e+0, + 133842334.35044507682e+0, 44941680.012016184628e+0, -139416689.22975465655e+0, + -251742409.82044029236e+0, -121905667.62976655364e+0, 216799719.98306891322e+0, + 463634394.69740325212e+0, 287096515.37800866365e+0, -313586151.84701472521e+0, + -842334206.9316624403e+0, -633756729.02875030041e+0, 421789259.77867001295e+0, + 1492942912.7488236427e+0, 1335806458.6442694664e+0, -474527237.98944181204e+0, + -2610230524.3749175072e+0, -2706852540.8357629776e+0, 324012012.95333015919e+0, + 4450062790.8111820221e+0, 5356330811.5707168579e+0, 390413362.75755184889e+0, + -7433131911.5818634033e+0, -10309588508.552108765e+0, -2484592309.8536400795e+0, + 12070922242.493497849e+0 + }} + }; + + /************************************************ Series evaluation + * ************************************************/ + + std::complex const root(roots_location_re[root_index], imsign * roots_location_im[root_index]); + std::complex const zr = z - root; + + std::complex res(taylor_coeffs_re[root_index][0], imsign * taylor_coeffs_im[root_index][0]); + std::complex coeff = 1.; + std::complex term; + for (int n = 1; n < 100; n++) { + coeff *= zr; + term = + coeff * std::complex(taylor_coeffs_re[root_index][n], imsign * taylor_coeffs_im[root_index][n]); + res += term; + if (std::abs(term) < std::numeric_limits::epsilon() * std::abs(res)) { + break; + } + } + return res; + } + + XSF_HOST_DEVICE inline std::complex + trigamma_forward_recurrence(std::complex const z, std::complex const psiz, int const n) { + /* Compute trigamma(z + n) using trigamma(z) using the recurrence relation + * trigamma(z + 1) = trigamma(z) - 1/z^2. + * See http://dlmf.nist.gov/5.15.E5 */ + + std::complex zk, res = psiz; + + for (int k = 0; k < n; k++) { + zk = (z + static_cast(k)); + res -= 1. / (zk * zk); + } + return res; + } + + XSF_HOST_DEVICE inline std::complex + trigamma_backward_recurrence(std::complex const z, std::complex const psiz, int const n) { + /* Compute trigamma(z + n) using trigamma(z) using the recurrence relation + * trigamma(z + 1) = trigamma(z) - 1/z^2. + * See http://dlmf.nist.gov/5.15.E5 */ + + std::complex zk, res = psiz; + + for (int k = 1; k < n + 1; k++) { + zk = (z - static_cast(k)); + res += 1. / (zk * zk); + } + return res; + } + + XSF_HOST_DEVICE inline std::complex trigamma_asymptotic_series(std::complex z) { + /* Evaluate digamma using an asymptotic series. See + * http://dlmf.nist.gov/5.15.E8 + * Higher order converge slower, so we need slightly more Bernoulli + * numbers than the digamma (Bernoulli numbers calculated via sympy). + */ + static constexpr std::array bernoulli2k = { + 0.16666666666666665741e+0, -0.033333333333333332871e+0, 0.023809523809523808202e+0, + -0.033333333333333332871e+0, 0.075757575757575759678e+0, -0.25311355311355310249e+0, + 1.1666666666666667407e+0, -7.0921568627450977118e+0, 54.971177944862155584e+0, + -529.12424242424242493e+0, 6192.1231884057970092e+0, -86580.253113553117146e+0, + 1425517.1666666667443e+0, -27298231.067816093564e+0, 601580873.90064239502e+0, + -15116315767.092157364e+0, 429614643061.16668701e+0, -13711655205088.332031e+0, + 488332318973593.1875e+0, -19296579341940068.0e+0, 841693047573682560.0e+0, + -40338071854059454464.0e+0, 2.1150748638081992622e+21, -1.2086626522296526202e+23, + }; + + std::complex const rz = 1.0 / z; + std::complex const rzz = rz * rz; + std::complex zfac = rz; + + std::complex term; + std::complex res; + + if (!(std::isfinite(z.real()) && std::isfinite(z.imag()))) { + /* Check for infinity (or nan) and return early. + * Result of division by complex infinity is implementation dependent. + * and has been observed to vary between C++ stdlib and CUDA stdlib. + */ + return 0.; // Asymptotically psi(1, z) ~ 1/z, so just return zero? + } + + res = rz + 0.5 * rzz; + + for (int k = 1; k < bernoulli2k.size() + 1; k++) { + zfac *= rzz; + term = bernoulli2k[k - 1] * zfac; + res += term; + if (std::abs(term) < std::numeric_limits::epsilon() * std::abs(res)) { + break; + } + } + return res; + } + +} // namespace detail + +XSF_HOST_DEVICE inline double trigamma(double z) { + /* To compute the trigamma for real inputs we can leverage Cehpes via the identity + * psi(n, x) = (-1)**(n+1) * n! * zeta(n+1, x) + * where n is a positive integer and zeta is the Hurwitz zeta function + */ + return cephes::zeta(2., z); +} + +XSF_HOST_DEVICE inline float trigamma(float z) { return static_cast(trigamma(static_cast(z))); } + +XSF_HOST_DEVICE inline std::complex trigamma(std::complex z) { + /* + * Compute the trigamma function for complex arguments. The strategy is: + * + * - Around the two zeros closest to the origin + * use a Taylor series with precomputed coefficient. + * - If close to the origin, use a recurrence relation to step away + * from the origin. + * - If close to the negative real axis, use the reflection formula + * to move to the right halfplane. + * - If |z| is large (> 16), use the asymptotic series. + * - If |z| is small, use a recurrence relation to make |z| large + * enough to use the asymptotic series. + */ + + int n; + double absz = std::abs(z); + std::complex res = 0.; + /* The reflection formula flips the sign for odd polygammas. + * We must keep track of that. */ + std::complex sign = 1.; + /* Use the asymptotic series for z away from the negative real axis + * with abs(z) > smallabsz. */ + int const smallabsz = 16; + + if (z.real() <= 0.0 && std::ceil(z.real()) == z) { + // Poles + set_error("trigamma", SF_ERROR_SINGULAR, NULL); + return {std::numeric_limits::quiet_NaN(), std::numeric_limits::quiet_NaN()}; + } + + if (std::abs(z.imag()) < std::numeric_limits::epsilon()) { + // use the zeta, because it evaluates to better precision + return static_cast>(cephes::zeta(2., z.real())); + } + // Near the first two roots, use the asymptotic series + if (std::abs(z - std::complex(detail::firstroot_re, +detail::firstroot_im)) < 0.1) { + return detail::trigamma_root_series(z, 0, +1.); + } else if (std::abs(z - std::complex(detail::firstroot_re, -detail::firstroot_im)) < 0.1) { + return detail::trigamma_root_series(z, 0, -1.); + } else if (std::abs(z - std::complex(detail::secondroot_re, +detail::secondroot_im)) < 0.2) { + return detail::trigamma_root_series(z, 1, +1.); + } else if (std::abs(z - std::complex(detail::secondroot_re, -detail::secondroot_im)) < 0.2) { + return detail::trigamma_root_series(z, 1, -1.); + } + + if (z.real() < 0 && std::abs(z.imag()) < smallabsz) { + /* Reflection formula. + * trigamma(z) + trigamma(1-z) = pi**2 / sin(pi * z)**2 + * https://dlmf.nist.gov/5.15#E5 + * NOTE: sign change */ + std::complex const ssp = sinpi(z); + res += (M_PI * M_PI) / (ssp * ssp); + sign *= -1; + z = 1. - z; + absz = std::abs(z); + } + + if (absz < 0.5) { + // Use one step of the recurrence relation to step away from the pole + res += sign / (z * z); + z += 1; + absz = std::abs(z); + } + + // At this point we are sure to be far away from any root + if (absz > smallabsz) { + res += sign * detail::trigamma_asymptotic_series(z); + } else if (z.real() >= 0.0) { + double n = std::trunc(smallabsz - absz) + 1; + std::complex init = detail::trigamma_asymptotic_series(z + n); + res += sign * detail::trigamma_backward_recurrence(z + n, init, n); + } else { + double n = std::trunc(smallabsz - absz) - 1; + std::complex init = detail::trigamma_asymptotic_series(z - n); + res += sign * detail::trigamma_forward_recurrence(z - n, init, n); + } + + return res; +} + +XSF_HOST_DEVICE inline std::complex trigamma(std::complex z) { + return static_cast>(trigamma(static_cast>(z))); +} + +} // namespace xsf diff --git a/tests/xsf_tests/test_polygamma.cpp b/tests/xsf_tests/test_polygamma.cpp new file mode 100644 index 0000000000..37f61499df --- /dev/null +++ b/tests/xsf_tests/test_polygamma.cpp @@ -0,0 +1,16532 @@ +#include +#include +#include + +#include "../testing_utils.h" + +#include + +#include + +#define REQUIRE_dCLOSE(a, b, rtol, atol) \ + CAPTURE(a, b, rtol, atol); \ + REQUIRE_THAT(a, Catch::Matchers::WithinRel(b, rtol) || Catch::Matchers::WithinAbs(b, atol)); + +#define REQUIRE_zCLOSE(a, b, rtol, atol) \ + CAPTURE(a, b, rtol, atol); \ + REQUIRE_THAT( \ + std::real(a), Catch::Matchers::WithinRel(std::real(b), rtol) || Catch::Matchers::WithinAbs(std::real(b), atol) \ + ); \ + REQUIRE_THAT( \ + std::imag(a), Catch::Matchers::WithinRel(std::imag(b), rtol) || Catch::Matchers::WithinAbs(std::imag(b), atol) \ + ); + +using namespace std::literals::complex_literals; + +// Raw input-output pairs calculated via mpmath + +typedef std::pair ArgResPair; +typedef std::pair, std::complex> CArgResPair; + +const std::vector gamma_2_r = { + {115.57609680702209687, -0.000075512970653153507305}, {-46.229512195544998576, 161.89712003976262622}, + {-86.868954415374588507, -886.9188191511379955}, {-142.7911850226261663, -216.53831258378977509}, + {-141.23058138214864243, 159.58470025725904406}, {-204.93052367711760553, -5962.8351469940998868}, + {30.981732763262314734, -0.0010759792612248144771}, {140.71608327767904711, -0.000050862630194118537091}, + {202.96841664160359642, -0.000024393986454421262436}, {-75.919871023302718527, -3886.355932931740881}, + {51.610641516579661925, -0.00038276813904703003945}, {-24.189557063237458578, 290.87379102082036297}, + {80.049044151021192306, -0.00015802031112115475344}, {-95.987090387630331634, -929587.5765532538062}, + {-31.134126836043268582, 827.01839527375045691}, {46.834190866381938179, -0.00046574292980255531686}, + {-3.0735676287015416541, 5022.0269810839927231}, {-35.660875643800615364, -44.821523460167526309}, + {-24.273890854215832036, 92.797567608322694355}, {54.059944320057219613, -0.00034856351319522235104}, + {104.81608664087127636, -0.000091894062223527367612}, {-58.405133182494161304, 20.846361598879660448}, + {-33.465333453989025259, 6.8606995834894721753}, {13.664689017276105076, -0.005761744063869302275}, + {-1.3441194715546924687, 42.169541516194236408}, {-282.85235346611011664, -619.32950416295818741}, + {92.55740093183128181, -0.00011799667524708536506}, {132.05388715453631221, -0.000057781173290096046215}, + {73.505381273471385839, -0.0001876160048782475056}, {-49.496617871477937456, 0.65859930882861683621}, + {-28.061572998851264771, 8566.7874366709547758}, {94.057311668797424886, -0.00011424366534218061207}, + {-149.59800695976980478, -21.715115353821129673}, {-76.408205028573590312, 20.014883945571433799}, + {-102.14438341870324223, 662.47076261626500582}, {-26.135123323836019438, 808.79985331434534146}, + {-6.6724094066166808048, -50.836177711488225839}, {-29.718077447123853574, -84.510923030145420398}, + {-25.39243334807805752, 24.481411773696329703}, {-130.5130003186291674, -2.5383975696413925149}, + {-111.64322625671607625, -36.940046258023549797}, {-60.528598742039818603, -5.6322036896429903408}, + {88.851357268058947625, -0.00012810310031951125981}, {31.205424393666014282, -0.0010603633028830813934}, + {60.245752060292723229, -0.00028012735641346229792}, {44.12782151034411271, -0.00052531029966857995927}, + {163.6875147109174975, -0.000037551048367531964563}, {22.694126635254935564, -0.0020291010081091988108}, + {4.8169754558768342889, -0.052960277761528014306}, {61.914218954223386504, -0.0002651144204854854569}, + {108.11004380188478535, -0.000086354506777903760435}, {-21.408860227080019456, 19.837811077615533861}, + {77.423025605093030777, -0.00016899308592617363315}, {-54.412800201857102422, 18.80200057324096008}, + {-109.83832550290453867, -470.98469993152014013}, {-129.79621938091298716, -233.31938325099059739}, + {-85.907098641743289136, -2493.1471517564959868}, {-140.90047403838534024, -2027.3805670426902452}, + {107.34354927293226467, -0.000087597936576205934905}, {33.424331015018175606, -0.00092228673958185682872}, + {-131.41797912303135831, 17.477402931296037281}, {26.465517632692787231, -0.0014826720505314006614}, + {-203.68366820144396456, -57.465637357152722586}, {21.503814029732527757, -0.002265467400009838362}, + {-115.90124424579273921, -2075.2292287977397791}, {63.830120969520379504, -0.0002493172322162496863}, + {-141.16698630415589832, 427.15417550543918424}, {31.456162772493538426, -0.0010432598910623039606}, + {43.852979399381304404, -0.00053199107629715934164}, {233.71121618731683611, -0.00001838650296618477348}, + {-87.816921836355561481, -323.28123653882835242}, {98.759719510471981607, -0.00010357089162302859616}, + {-161.75989756253818541, -140.73460863754453953}, {-79.08956701526031452, 2782.2713431261208825}, + {23.247540786165178162, -0.0019316189463613735611}, {80.242333080342760354, -0.0001572552128654708262}, + {37.829803538862996959, -0.00071748149344682328899}, {40.391591009044184091, -0.00062830291739645292848}, + {-104.82024100234745845, -341.72897425376822866}, {98.250154699408426495, -0.00010465349362437244534}, + {-40.79270462075383108, -221.43410021195506943}, {-33.6605510490657025, -44.663415126685514167}, + {-163.88247703277951928, -1230.5504819960315217}, {-217.17777044774297224, 353.44774306999767077}, + {6.913525591766192413, -0.024165479472237093306}, {23.675302999484415523, -0.001861003459320795337}, + {-65.606992823334380205, -24.311380633714541943}, {85.188254976267359098, -0.00013942430690022295284}, + {51.293212789930841211, -0.00038756679020663400937}, {99.021897960884572854, -0.00010302041040053835474}, + {-3.5128139132467977035, -2.5629548463476723441}, {4.5415390340377586043, -0.060316236662743709374}, + {-53.212532744361304538, 205.13933566430276301}, {-20.190728661688780221, 285.47396708778671837}, + {200.99661382058070558, -0.00002487615273561319607}, {82.408456307261047868, -0.0001490480627640740081}, + {-35.976456951985483101, -153264.32075769666699}, {91.268638862060797123, -0.00012137106889991484038}, + {-10.549711599748503588, -10.014488514350201598}, {-91.619182695480532175, -28.131567788341186542}, +}; + +const std::vector gamma_3_r = { + {119.80816526189539672, 1.1776174703063896182e-6}, {-34.553301566933797062, 217.56123107514977733}, + {-30.72677905044704616, 1101.642783666387686}, {-99.986072837028544313, 159477954.03110399842}, + {12.655980763787248122, 0.0011096770920505172678}, {-10.292019469131826526, 852.3068896723261787}, + {139.51650797183975783, 7.4442274604328121308e-7}, {116.4147011580185449, 1.2840983129966398589e-6}, + {66.336571816849414063, 7.0077448215458175567e-6}, {2.6503972415437040411, 0.1825833931428672563}, + {31.808298038645617112, 0.000065137371133366738342}, {75.090616357557806282, 4.8187942526404274615e-6}, + {27.770857726950872291, 0.000098546649939913820004}, {-162.56009046587217881, 224.04185724186118023}, + {203.66896137128316013, 2.3848037932199406957e-7}, {145.14700285506495447, 6.6083235679899193047e-7}, + {-42.495521550471373473, 194.97245707553821603}, {69.06864592127232072, 6.2030759258276339576e-6}, + {90.723313433196565825, 2.7229960080278821432e-6}, {-89.500251304829617993, 194.81866505062976103}, + {-118.42927056024312549, 236.11992294401343884}, {-41.800470431411845595, 3804.0763897569067922}, + {-222.12811001940724509, 22290.168667773479683}, {90.702617581996335616, 2.7248706324042762627e-6}, + {-11.937273755569940192, 387587.00163394142874}, {-99.969901542935573957, 7310971.5972377937287}, + {-13.545773788539236193, 211.41393095668095725}, {181.15300386193734994, 3.3922494451547008304e-7}, + {-110.31846755971201901, 614.31139847152201128}, {-72.102647301126765456, 54060.017699545649521}, + {-24.540174423080756583, 207.51591365924059573}, {22.262362060681919473, 0.00019384473139787407824}, + {-67.383910905110809608, 320.82107144884525951}, {241.33092273949063156, 1.4318235550586266948e-7}, + {125.140791991240377, 1.0328456358558631952e-6}, {-106.73676121423395102, 1273.4044821056611454}, + {190.92690753312436414, 2.8962701181700196673e-7}, {98.057942455356439382, 2.1538689965780402844e-6}, + {27.537432562998031216, 0.00010111995219562587383}, {-8.5884077946530918979, 262.02293565059517277}, + {39.900008471390023601, 0.000032688969081563953574}, {65.649750775220738319, 7.2317027600614323325e-6}, + {81.360809240657516739, 3.7825313661757820561e-6}, {-270.07921863543447216, 152363.54731488585821}, + {-63.692453596367172963, 700.02011988703827683}, {-144.24977988085007041, 1563.9462652096256079}, + {66.979186081878708592, 6.8064990393452933813e-6}, {-56.447207363811912728, 217.11194482724539512}, + {-32.481881547254531029, 197.35457774052929381}, {-59.309064506269933759, 687.16265294294657906}, + {3.5154289999511716402, 0.069267015666734516044}, {74.593541874934217617, 4.9164245498701959747e-6}, + {-32.781364957426674778, 2645.7721430064216293}, {165.47699643708244821, 4.4540166872298695106e-7}, + {156.10303447130326049, 5.3084391226265444523e-7}, {69.305545331203632031, 6.1392286716616605805e-6}, + {0.61330549731263594992, 43.485081266645110531}, {9.6095428271272762544, 0.0026299220028015834333}, + {-153.83456191784011935, 8026.2388437551971947}, {122.19941581675817588, 1.1095576044248398382e-6}, + {34.457570285342811189, 0.0000510542569091702777}, {98.328737220615934689, 2.1360330340981293403e-6}, + {35.797951979475165274, 0.000045457680937223858889}, {-13.721247162845548573, 1019.319099495735145}, + {-28.823174857319340703, 6154.5193701821517607}, {75.280546136017377989, 4.7821728716328116296e-6}, + {119.37476250903384312, 1.1905445271280071419e-6}, {240.45539793423719743, 1.4475535946405126854e-7}, + {150.574574432088923, 5.9169649004611359586e-7}, {-47.797315847802316569, 3574.0566195126598359}, + {6.0621175917711811465, 0.011439997700283643933}, {-97.860187618812702226, 15718.040296736729942}, + {118.36167320830980998, 1.2215086814959309254e-6}, {7.6089897565165127702, 0.0055126602656839574293}, + {-136.67538172089800241, 572.34394941820107761}, {83.186435491040725765, 3.5374916780767213851e-6}, + {-24.258432255857083959, 1368.4977288605405192}, {-13.289524421379026009, 880.79885707470759826}, + {25.069664655813184595, 0.00013473268588986862045}, {-93.611049734981349957, 308.16025466291409884}, + {11.464752942481336362, 0.0015109029070828558245}, {-48.584931717154525188, 256.30321650754655138}, + {74.858127684897652898, 4.864132417090298695e-6}, {-50.373142865360442499, 351.35199146599433107}, + {-11.185140584287598386, 5124.461789784974826}, {-12.336305768593401666, 503.09461162844269211}, + {-33.916497805782675812, 123426.51601913913328}, {130.27284818328271854, 9.1509375803290135101e-7}, + {-70.038523784161668573, 2724191.2027251762338}, {42.518214538545024084, 0.000026952202687465473573}, + {-0.75579196958867866929, 1708.2055601882257179}, {44.477680016922739981, 0.000023508277583224644554}, + {40.425973413489792563, 0.000031414292890265508738}, {67.460177177597529408, 6.6608827549720278557e-6}, + {15.460581080519503416, 0.0005959599965954955449}, {-75.05158408768619438, 847412.87589565711096}, + {12.490017912726749216, 0.0011562893364143373744}, {-109.08055106227291731, 142530.63074599191896}, + {112.74134340268075505, 1.4143411974054886465e-6}, {-140.18219381389616274, 5462.7808822620718274}, +}; + +const std::vector gamma_4_r = { + {-4.6571969759031954794, -4877.7748756829641934}, {54.257386509034965627, -7.182464087730526223e-7}, + {-132.32087057483619219, 6894.3072966533200088}, {18.930073042381241777, -0.000051877621629545261255}, + {73.362041510691739177, -2.1285200605766420411e-7}, {-142.61889883274201907, -2723.8982221929345542}, + {96.522027348436992611, -7.0571364931183659512e-8}, {-50.728603322434736356, -16189.102148796671827}, + {72.61271847690586867, -2.2183710808981886864e-7}, {9.0401310025476000476, -0.0011152816160503911235}, + {-7.7659903104738496893, -34117.565882854418305}, {21.574349673505764713, -0.000030361352791762305004}, + {220.41082844667960217, -2.565413102064784144e-9}, {-16.838545881714324537, -218711.60424262436572}, + {-99.844575387744669115, -264568.80365353572415}, {-86.550353660123093391, -831.52807015032021809}, + {16.691576578410181497, -0.000087019876064583901831}, {116.60819097891656781, -3.3012086298063250019e-8}, + {51.987915093274786216, -8.5348039240537724572e-7}, {-25.71342592411457062, -12292.872115426243909}, + {89.783992397498053606, -9.4408576144983657396e-8}, {-206.2149754011894629, 52199.393071151826007}, + {-27.85799311677126866, -415549.33794501126977}, {114.27950714861493964, -3.5798687415009832211e-8}, + {-0.91869520685548999861, -6755060.2801012033597}, {4.481618100347835032, -0.022705441088841826075}, + {25.754323500280921877, -0.000014731316313013347632}, {-40.015267525263404025, 28931303760.902900696}, + {34.232868312624006535, -4.6304195331669927382e-6}, {-159.32065900061883212, 6917.8810485984458865}, + {19.38664991919713998, -0.000047045622546301430302}, {-138.26205151755277711, 19317.885723682673415}, + {-104.15085646736648073, 307135.90930620627478}, {5.737206998562794702, -0.0077432272247756521802}, + {111.87158083022390542, -3.8996401907838708902e-8}, {92.378181739648965731, -8.418967135346477018e-8}, + {-176.37156711362084138, 3146.7762932543882926}, {84.131680893824679401, -1.2263550098118298129e-7}, + {-7.6249265856414298881, -2984.2850270867202198}, {-146.00114196048772897, 12358218076946246.0}, + {22.145559078335331549, -0.000027283803062001276346}, {33.778115801797319762, -4.8886592958193829655e-6}, + {35.139977604439366132, -4.1642752860307053842e-6}, {-134.7710693679279359, -38086.793444512622955}, + {162.44727155037460875, -8.7225387901690692422e-9}, {-10.74568258067577986, -22462.018645104530151}, + {85.487825491728159477, -1.1499376147979539122e-7}, {8.5904459261123395919, -0.0013829250766127271395}, + {94.404670083409854442, -7.7154533065388261856e-8}, {2.4895904642399795392, -0.31985072033481576348}, + {62.016124298312583107, -4.1888978594927620499e-7}, {-143.74759576912350667, -23331.465032544128917}, + {259.14302959664030368, -1.3407343169096989261e-9}, {99.924738953857143997, -6.1395537324488585154e-8}, + {-104.04841819507117862, 90192038.893978998065}, {-53.190561803317969236, 95446.410149971037754}, + {-159.2284150423886615, 38519.82287105260184}, {138.34077958726524571, -1.6619628835885371429e-8}, + {-77.339399845281889156, 5142.174157981738972}, {-56.441581592313006865, 988.7304256165454035}, + {-91.632409287389577912, -3341.771396737613486}, {212.47867314154009932, -2.9714916812056927542e-9}, + {42.201667967817392935, -1.9830311266679294697e-6}, {68.829596869290398331, -2.7519359073026491996e-7}, + {4.7682605846738042032, -0.017301513256749979919}, {-1.1945062186520343239, 86144.903925559803611}, + {-68.085933528817406568, 5121487.7473599035293}, {21.630208197070935228, -0.000030041874503789623422}, + {0.89206014019558643735, -43.636224649621603078}, {-77.11086978372958356, 1432637.4681010905188}, + {-105.46297191940028881, 591.84957624735409354}, {104.38168259001857052, -5.1518334477703870263e-8}, + {168.13680583091777976, -7.597327773495070586e-9}, {44.484980540887939071, -1.6023103796705643837e-6}, + {-15.228211437136282669, 38692.444740701394039}, {9.2322581231461740003, -0.0010208169114729391362}, + {98.351769480220212927, -6.5439311550454522924e-8}, {73.083214202370854196, -2.161413105476304007e-7}, + {121.40118490033707133, -2.8080462940640069362e-8}, {83.436552371229367964, -1.2679867908370858322e-7}, + {-26.260266291448953524, 19994.541561121313862}, {39.189557779654947467, -2.6762984364302274569e-6}, + {88.865265082944006281, -9.8396254648255157508e-8}, {-181.14129900637325932, 426064.47130601934623}, + {118.5293497931246236, -3.091471265563646604e-8}, {162.73125497315271559, -8.6616252284632068349e-9}, + {22.331260319272910664, -0.000026368045782306394743}, {135.11763237987310049, -1.8269366498622644064e-8}, + {89.242424017345271636, -9.6734223474091936869e-8}, {-174.36914896684106679, 3263.9472241258122267}, + {107.81596536936240227, -4.5233738294493446304e-8}, {186.67097224571566016, -4.9945106278360765614e-9}, + {-62.111098139794215456, 1417973.9635864007287}, {123.17480008154748816, -2.6491452283334817706e-8}, + {265.37040650816737752, -1.2190242342931261285e-9}, {-28.913357312376060548, -4915296.2185868397355}, + {-209.38781748470282196, 2459.1963590022114658}, {-61.232948924417343051, 34904.058924402677803}, + {-97.752704308695740565, -25856.949314456313004}, {133.88501331200842515, -1.8954082371241026489e-8}, +}; + +const std::vector gamma_5_r = { + {-198.99100529185807318, 226599417888325.65625}, {-22.726635628703125036, 288410.12488883733749}, + {36.047034136708653307, 4.2244006867964690001e-7}, {-65.860628673267910926, 16373821.419399280101}, + {-161.02224143030915116, 991299690992.90905762}, {-102.84438489379085979, 8450658.8629077877849}, + {-145.02940343711111382, 185691765574.65188599}, {-74.013868415104326459, 16866316749479.660156}, + {34.111104563356974495, 5.588782467681059167e-7}, {-76.965676156065981672, 73384735928.218811035}, + {292.59699987671638155, 1.1286762778472782344e-11}, {18.212380979272804638, 0.000013712027060443809345}, + {-43.802060569552402569, 1995700.56292242161}, {-61.556793303642741932, 19882.484960620193306}, + {-69.02475739199790894, 521136974533.55999756}, {139.74416792631495809, 4.5845654025667810435e-10}, + {-29.242641739858843408, 588688.64297408645507}, {101.46595592753928372, 2.287089640137233666e-9}, + {109.41978502916360583, 1.5654226328886196359e-9}, {-104.13863485737047654, 16902684.596285738051}, + {-58.034287591662881312, 73851506290.138580322}, {62.858434603389810036, 2.5444601267105165303e-8}, + {35.925891443095082423, 4.2970962836745493791e-7}, {-6.1234377045003665074, 33923326.583244591951}, + {-113.24220203834786957, 595120.64337851700839}, {5.6898138808680780443, 0.0060952800893278877639}, + {39.746197477918975949, 2.5755565911054533099e-7}, {-56.784428483771634433, 1196287.0662857533898}, + {-61.967847715425861566, 108620106596.61207581}, {-18.918465200751938937, 408435521.49049550295}, + {83.915916720360698378, 5.9413973745061481188e-9}, {97.258700252051781376, 2.8294572305552798666e-9}, + {-68.849274986085745809, 10234937.879023466259}, {-41.860662447045285717, 16397648.203502897173}, + {71.507946208774086472, 1.329134218345446167e-8}, {105.19152840193891052, 1.908112669335592447e-9}, + {-110.68269726253461727, 118796.10781093091646}, {86.746611440323079023, 5.028379712568692461e-9}, + {31.990895073639315171, 7.739971259740189313e-7}, {42.949641562943241979, 1.7399629843686961796e-7}, + {191.90737094884008229, 9.3412099665942503148e-11}, {109.17951979702216647, 1.5828025074143917768e-9}, + {95.321534344670439509, 3.1305163590077935244e-9}, {248.8492532207414456, 2.5403183655047473963e-11}, + {128.48129257064408648, 6.9894924413690465065e-10}, {169.3962467569368755, 1.7461929004630653117e-10}, + {-127.52101257829563963, 15958.069243848312908}, {27.382221252830170499, 1.7066140466508578067e-6}, + {-34.386000039717082188, 38543.677824488790066}, {48.481362002307207604, 9.4321931025299646923e-8}, + {-61.384254482762138139, 39506.071395097736968}, {-29.702635053044158298, 174585.83561920319335}, + {-31.531630147452290203, 16704.724041712586768}, {-89.317098320731275862, 119249.52330891479505}, + {63.992159246694200192, 2.3252846587154874961e-8}, {39.099935006369349821, 2.7984288457648191796e-7}, + {-15.500715909819565042, 15382.888467852853864}, {97.654013075917774245, 2.7723624749312704852e-9}, + {-55.997215661649114793, 257542667844804384.0}, {-36.037327902967028592, 44358790233.658340454}, + {14.837676969503132085, 0.000039372164045360657798}, {-136.88691919297301069, 57391850.363057918847}, + {225.62711230878670676, 4.1501283393024246739e-11}, {-124.04389382768081873, 16778785672.105596542}, + {-92.864163519374969269, 19102519.219136040658}, {-25.797516978685607114, 1741714.7915923641995}, + {127.15111984414613744, 7.3643128431044812312e-10}, {-33.884214591770991376, 49803633.607086390257}, + {5.8578047596378342021, 0.0052117278133778470461}, {61.355089978028097164, 2.8746180513824359636e-8}, + {40.143976610529648497, 2.4489504205170245803e-7}, {-94.374151609781080197, 45764.168243082036497}, + {32.928046007239167636, 6.6848488477919529235e-7}, {-38.458363617515608723, 17714.795750544846669}, + {87.812048743694532504, 4.7289981688318923713e-9}, {25.064600663616303677, 2.6777161911233341103e-6}, + {-31.199197545219970351, 1921279.1918988353573}, {28.170128317107913318, 1.4772270955768672862e-6}, + {-33.038200843571772225, 38613887665.650535583}, {-80.519482195139630676, 15876.507357217044046}, + {-209.03311475239112838, 91002259371.916519165}, {-83.780535952203848638, 1074564.1096888608299}, + {-55.471146903031467446, 16478.246065127936163}, {-20.816017786330323958, 3094496.8941283179447}, + {-90.843628239338116259, 8208273.2399392360821}, {68.383536972364112216, 1.6644515174956089985e-8}, + {-9.9814492425961116595, 2944498721257.3686523}, {24.934562626637003291, 2.7496705937216285131e-6}, + {-147.49342065097027898, 15438.145521329499388}, {12.321510048422394945, 0.00010303610116405110208}, + {-86.165587889107413844, 5821572.0435359571129}, {-88.975799688536667986, 597386650390.39099121}, + {-19.339588746177479806, 79720.049038025550544}, {51.862242279032741976, 6.7109756529427010053e-8}, + {-46.360968541493200235, 56034.145865228805633}, {46.578552067082959809, 1.1546797895455308444e-7}, + {4.4548870033227965237, 0.023003654626253866589}, {-5.7109626758279397052, 206767.27398566587362}, + {-79.060670657296611807, 2406074626.638323307}, {50.598238684405480114, 7.6012102332934193273e-8}, +}; + +const std::vector gamma_6_r = { + {81.995946986718479366, -4.0949704347560379147e-10}, {-145.64617818026334817, -1021906.0732937159482}, + {72.136026531387514638, -8.8765509074080388977e-10}, {76.806467270058831787, -6.0769079893301460358e-10}, + {-72.150569561324843448, 410364790.49345594645}, {126.70577325033838179, -2.9693281903140973573e-11}, + {120.79348377496263822, -3.959826099818770737e-11}, {45.514452931663221591, -1.4411013947071700676e-8}, + {22.920417099121692672, -9.4147944408578684039e-7}, {-22.510856318551326183, -28177.759998252557125}, + {59.274500852477707724, -2.9095619984207962475e-9}, {-161.49477632028086305, 13499.358844557906195}, + {32.730002235589822135, -1.0687803132286577777e-7}, {231.35167724065630068, -7.9280937985411805251e-13}, + {-110.68857484197079089, -2524572.7823727875948}, {-2.032183888909872671, 20130884306798.457031}, + {-86.037411870087467491, 7018859892122.3583984}, {-85.616776338916423583, -571997.61703642143402}, + {44.121026185122921959, -1.7402306490485384136e-8}, {291.95718698103314637, -1.9575987791293287932e-13}, + {68.012705288437970808, -1.2667808258111586386e-9}, {-19.847493144452556635, -375236068.12005352974}, + {-32.557515001316403414, -173808.38104794808896}, {82.277050512729786647, -4.0112429217766306954e-10}, + {-70.569568253377951805, -226030.39709008671343}, {-3.2047152889402443776, 47780392.446002334356}, + {-65.926165784447064766, -60190622507.570884705}, {124.86292142380696646, -3.2432962207971283114e-11}, + {-150.42798023701419652, 237857.593408335204}, {3.6087252424798141881, -0.11296823387674867489}, + {-90.776616957735242863, -25936603.292255986482}, {14.156624492432040796, -0.000018326196347229853784}, + {25.796605741789701227, -4.5669086134555772673e-7}, {163.00304742910185496, -6.5160349996023467665e-12}, + {114.15072632550860021, -5.56787039365586431e-11}, {-31.305116987812535712, 2915500.5255847838707}, + {89.150506088333401067, -2.471708426642107219e-10}, {-83.372193918640775223, 709017.04778903559782}, + {-51.652810344278243804, -1169855.2972456689458}, {47.967163575051984026, -1.048297205532716771e-8}, + {45.239040924213433925, -1.4951396255162312535e-8}, {70.945763223571930212, -9.8151934365734443451e-10}, + {-18.405589849674676373, 371348.25698671553982}, {86.498132436307855642, -2.9658171889803053985e-10}, + {93.142108275461836797, -1.8977636606383538782e-10}, {118.06414701880842699, -4.5444034317757867588e-11}, + {7.1507778466213434143, -0.0013341748516638215344}, {133.56762931807176642, -2.1612440413323572785e-11}, + {67.848674123831301586, -1.2854033630342599969e-9}, {-154.78534218052348592, -34281373.256838575006}, + {-28.403899998311764818, 383715.71428318973631}, {-43.059500919360012006, 272688461967.9649353}, + {-219.21948706674498908, 29336754.132263530046}, {71.762148175025501473, -9.1596349014094738347e-10}, + {53.626926325460523515, -5.3336430477394207886e-9}, {83.676476683171259197, -3.6229996382849726757e-10}, + {-90.449706207022202875, 146470.77214847717551}, {-5.9176952805081937115, -28142281881.651443481}, + {154.14649449303445294, -9.1203838514985234671e-12}, {80.143551432486901831, -4.7006481561125087554e-10}, + {106.71894237110919335, -8.3541458674432424233e-11}, {171.5025190583168353, -4.7988835117069804253e-12}, + {-127.25375368957165279, 10622411.308797221631}, {-55.502021998628748634, -5219.5607759645090482}, + {-65.780129872513086298, -28980780.511430811137}, {-20.1906666832907149, 78594552.591358155012}, + {-188.85412166541522083, -512147797.46855300665}, {-85.92265425649027577, -43478800862.242584229}, + {0.49090469881114551232, -104843.12536395799543}, {98.771405252697846322, -1.3321083756742760831e-10}, + {-78.204429270736170565, 48250352.715441934764}, {-116.72876049835647905, -6659473.189712244086}, + {-101.91079246965017546, -16014812369.304113388}, {-209.97399712000861882, -89574075613895.875}, + {153.5295530246775968, -9.3432277432935789374e-12}, {-21.705488556963462798, -3738252.1078928713687}, + {27.254846807433875, -3.2636720030614061443e-7}, {96.219794434211834755, -1.559867692173627845e-10}, + {162.95784823732125801, -6.5269197157872012711e-12}, {66.994971628628306348, -1.3876392502278034173e-9}, + {-101.59416209029579647, -369564.7304840334109}, {5.3295049858473078075, -0.0088047511000581626939}, + {52.345886137656663095, -6.1746567500895915745e-9}, {239.30410359223918704, -6.4701925713546037227e-13}, + {-97.300285676522179301, 3261650.2509702597745}, {7.9195205562050574599, -0.00069728896669377278279}, + {152.80745266290008999, -9.6121725278079397847e-12}, {-42.182630807585894672, 106243659.3227057308}, + {-0.62813424376151005823, -713617.39982908719685}, {-42.173439662347725232, 152505824.03894391656}, + {-47.38849471241280753, 516589.1154414837365}, {-66.861683850808873331, -743397753.66830635071}, + {21.079528482153989444, -1.5731833790745371897e-6}, {61.139281821912391024, -2.4124056262120336276e-9}, + {-184.39758216485984121, 433542.305992960406}, {-136.30584979906805643, 2866731.7593800481409}, + {38.858954826600808019, -3.7623964944447303162e-8}, {134.61400538936896965, -2.0620262773934380954e-11}, + {-42.69905123488081955, -3211484.499795676209}, {45.01688192782485487, -1.5404568939135146808e-8}, +}; + +const std::vector gamma_7_r = { + {-41.321548083812395191, 44215395.822613872588}, {-87.77045656686550501, 653941945.91981434822}, + {-146.54503257223669266, 3392920.956463333685}, {118.92799714734383087, 2.2033300602583063086e-12}, + {108.05118348505222059, 4.3245263358532395651e-12}, {72.742685561845874531, 7.0077921071455093004e-11}, + {-253.24488951897558309, 389693480.42310583591}, {180.5394777898232519, 1.1741593021808248465e-13}, + {-156.41665824048760669, 5925016.3464180836454}, {34.961575259387963399, 1.2448997643742851398e-8}, + {-7.7516959734792498793, 348837483.26866000891}, {-135.42758937273725905, 4948126.4924334269017}, + {106.30930950641727861, 4.8481364320871590229e-12}, {-89.745145325612952547, 283251606.6663081646}, + {-110.7471636335408931, 301849300.67939025164}, {88.297130443649422205, 1.7899413768707597621e-11}, + {46.630270034012795577, 1.6179110627565415647e-9}, {42.325347142820710644, 3.2112700410551064961e-9}, + {114.05692729408498565, 2.9563680046536546235e-12}, {-6.0323911397721623473, 4159304302823555.5}, + {-77.474117829712312755, 2836007.5346678616479}, {114.26691434861955088, 2.9183834762110949231e-12}, + {194.9226398990546727, 6.8561109821475251098e-14}, {54.303887407082953587, 5.5117185571722417833e-10}, + {-118.65737575356220646, 26684167.157869298011}, {-55.221577387536235904, 867453678.04508912563}, + {110.60453170859285876, 3.6695478759027055093e-12}, {21.812782371034675322, 3.5861433979008567464e-7}, + {22.148224504418788428, 3.2152955030228827452e-7}, {112.73376321434680847, 3.2091305295408523799e-12}, + {43.500444509083500577, 2.6452959614152656511e-9}, {-31.783337489831115619, 1037948277.3086758852}, + {-93.347340509329484348, 23943244.030900605023}, {79.392256055145921323, 3.7838079997933158642e-11}, + {35.955800013997674114, 1.0202728025111605044e-8}, {-60.588273863893704174, 6455121.65206114389}, + {67.925420389520610343, 1.1359102687366842452e-10}, {16.445418878068863933, 2.7221871451383312987e-6}, + {41.990795094933673681, 3.3968943681348442753e-9}, {8.0063879017823111894, 0.00051495737355344633687}, + {12.57443689072729498, 0.000018940071568160924748}, {100.26630492888735091, 7.3171757872315820317e-12}, + {-50.375846926333800013, 12876673.676976660267}, {204.34083929101842614, 4.9234521043631292983e-14}, + {37.763334900711349462, 7.2049576694760919932e-9}, {-45.011773997146562465, 13647060807499943936.0}, + {-39.978303443355848401, 102637016709666656.0}, {107.57771894406340607, 4.460159084997841785e-12}, + {-61.097469596879840026, 618695827419.48254395}, {159.77622367373146517, 2.7684450115908141344e-13}, + {-47.843232884587621356, 13816290932.025421143}, {42.380120547201663328, 3.1819969375283392375e-9}, + {-135.59875299183096331, 7806861.5681851031259}, {19.401828885993189999, 8.2981421205409625856e-7}, + {-59.530927758057238464, 2949038.904166251421}, {-89.287095237623248067, 109276284.15326744318}, + {-126.21887944888348443, 956770218.07148122787}, {-104.14307379102633888, 28704510627.380126953}, + {-86.392812824617990941, 9164170.7766983415931}, {-75.757425329130143155, 420451567.64839589596}, + {-36.671243359768688208, 37057573.551121816039}, {150.52569600130027538, 4.2085057534217393111e-13}, + {112.63232768609998402, 3.229505659094547056e-12}, {-165.80201640321143941, 2135025663.2037861347}, + {-81.459565823490351022, 3226098.851854483597}, {93.110704805374140847, 1.2319300233703116143e-11}, + {-62.990902084055775845, 1.0737302188252990669e+20}, {94.46371802455864497, 1.1130031453415800347e-11}, + {61.872726085539277108, 2.1939951519142295554e-10}, {-22.822647098656272391, 5149040434.608045578}, + {149.88286751386752371, 4.3369213477440480811e-13}, {-225.79211892207155188, 1445176793.8419349194}, + {120.61333772246172202, 1.9958303244148777333e-12}, {11.481817928166924148, 0.000036669853385047765024}, + {117.94042064113770607, 2.3363389255263925228e-12}, {-102.25486062113240848, 283198750.79230672121}, + {30.383825689079852594, 3.3740091880796959944e-8}, {123.06387204235554123, 1.7327173947248507515e-12}, + {-97.223750344191756767, 802309825.71143591404}, {-103.73843443201084824, 230088640.68694877625}, + {220.89547463590787402, 2.8503154344731078219e-14}, {76.827253701732715285, 4.768712537184905371e-11}, + {-35.392276756917190994, 9259917.6970435362309}, {146.33483157090546456, 5.131637871804702589e-13}, + {43.83951045076726416, 2.5038332534409917618e-9}, {-58.73790400507683529, 226390970.66034758091}, + {16.330155095751010208, 2.8636222330700412233e-6}, {-9.9764466673835805466, 53212249064159552.0}, + {30.699785491645243951, 3.1347012623365321228e-8}, {-136.70686643166203567, 92531409.184560135007}, + {8.0228522204676888663, 0.00050720728597673629418}, {49.293636655619778253, 1.0923575362046028806e-9}, + {115.39743168414268837, 2.7232248234188072426e-12}, {61.868235147944425023, 2.1951190983031219885e-10}, + {-68.100967489670225063, 466635827958.72186279}, {-74.830731014628497633, 7478470516.9300374985}, + {-22.324834428647761797, 40774227.4554996714}, {52.683331706495629021, 6.8271262994130310215e-10}, + {-1.9497891355243646139, 124752410899386.5}, {-14.059665716495475252, 31378462133449.582031}, +}; + +const std::vector gamma_8_r = { + {139.73108883584964701, -3.5684003770909786322e-14}, {-104.83019774322201556, -343581001855.01123047}, + {-12.908090734996996218, -86156269365691.53125}, {68.320153934304727272, -1.1253230388521683495e-11}, + {46.164833304115568069, -2.6616517582316882228e-10}, {-127.84198043785966092, -656330699224.53686523}, + {-22.866432504856266661, -2979980830348.5966797}, {65.207254008838006598, -1.6386859569872603104e-11}, + {4.3869119334158526158, -0.080774174785457023007}, {-78.041743235066135753, 104772086294694544.0}, + {209.69270447403937396, -1.3741321116794408101e-15}, {74.93940231538523733, -5.3428436283735450103e-12}, + {-84.122024948332239092, 6721757245629.0927734}, {-72.499018755482012466, 729303.49315318325534}, + {54.562164414283095937, -6.8998172293660515995e-11}, {-188.12196841716135509, 6749848505954.2900391}, + {-21.171947353487020393, 306874472493.11572266}, {-77.012249594378417328, 6.492697218301724459e+21}, + {-35.223818269324269181, 28605848493.079738617}, {20.114205392099520964, -2.2829325212448700862e-7}, + {85.551738909803759725, -1.83986047519931869e-12}, {-3.2912271881144752328, 2674784961.2919435501}, + {-66.6627949963596933, -713646372.47956156731}, {3.6910117387942769085, -0.36237061216384641726}, + {17.305944912820987014, -7.8368515512378258825e-7}, {257.80389044507614926, -2.6232521351963840511e-16}, + {-46.392910643739440957, 177067927.3137383759}, {-2.0731147952886024299, 675263239791737.375}, + {-78.135371259480933759, 2641084369028.8056641}, {-21.235545546449792198, 18064906387.911491394}, + {10.682027418020787479, -0.000042402267695198661384}, {-249.7340552220365737, -6058302319.1876268387}, + {-17.329842988328330478, 871003308.2897361517}, {100.86053666393655703, -4.8955039422004063148e-13}, + {52.304360253389738489, -9.705431405065756111e-11}, {142.48016298389481449, -3.0517190342741357842e-14}, + {-17.679871320204483709, -1140528009.0327188969}, {81.455300602075325855, -2.7306715838251449372e-12}, + {-12.706577127386676551, -2499861446.3763394356}, {25.016359071404746572, -3.8425647842889036502e-8}, + {-11.244384892254361219, 12966856249.444293976}, {222.12034534239234063, -8.6601814629970637949e-16}, + {-55.583340367496802514, -101380058.15146252513}, {-8.7944126864922580467, -61454191680.946166992}, + {-26.870190282380377766, -3852615454333.1279297}, {-9.8478153791392806227, -920838660874.04919434}, + {-52.47437115795676732, 19983622.867470856756}, {-21.931207795949063666, -1168604370265250.75}, + {-121.19756547358331034, 87926476404.812576294}, {-62.449584975019334365, 45034583.729208044708}, + {110.92720011770657607, -2.2788472754423710526e-13}, {-59.639691631963799523, -391713456.65386980772}, + {-52.452633451315556101, 41418395.696842834353}, {168.47715066218498237, -7.9502847326692617617e-15}, + {-141.20321342940917475, 68225533897.533790588}, {-94.259008958990520455, 7685177229.7525310516}, + {-178.20760754577312923, 56276857997.752388}, {1.3911077747677920158, -2083.2221406637122527}, + {84.230048238653964177, -2.0854222786312719116e-12}, {-102.65438026120867221, -571142222.36456561089}, + {51.360972403001603936, -1.1242164530348303886e-10}, {-90.191294402111935824, 117543655969.83139038}, + {-112.83701141725057937, -496713206290.8503418}, {-0.6897643023981839816, -1513451072.9958946705}, + {-252.59439855021085464, -131362082.23704789579}, {53.226599992047326282, -8.4279905189635377395e-11}, + {66.087533676747213462, -1.4708127309156739041e-11}, {175.48029233698298412, -5.7342270354163748242e-15}, + {18.21457966694939401, -5.148185431492101036e-7}, {115.53181660120412744, -1.6435702084163521991e-13}, + {24.964405370862746025, -3.9082515357042678762e-8}, {42.351644993829388852, -5.3454855090385966876e-10}, + {106.23425711235216795, -3.2254348062877438188e-13}, {107.82731622404062932, -2.8617737088945832071e-13}, + {-9.0158260389411104541, 6.4739665834995770982e+20}, {276.76813106786522667, -1.4851391562110340316e-16}, + {-65.541189422934422737, -34628703.914530910552}, {61.999132350197072583, -2.4611285580496456142e-11}, + {20.703474780776197406, -1.8023672274544844331e-7}, {64.968526730344677844, -1.6878553330082247878e-11}, + {137.5061142036164199, -4.0592101944948395771e-14}, {64.461235046786214298, -1.7979494127333928993e-11}, + {-66.268600785105249429, 5539908660.1491298676}, {-93.907756150969319719, -83384201837097.4375}, + {-5.4338181297005698767, 67345454.2355337888}, {-105.12363574963880808, 5973431900856.2763672}, + {-90.7612838664500714, -16016661693.838327408}, {-284.6502778612634188, -513306395.23599630594}, + {51.143647289499519104, -1.1633839824374528687e-10}, {111.79029605719033214, -2.1412480233817354444e-13}, + {-51.092249231821554645, 83340422450557.0625}, {-149.56340205864137261, -62901010.755727410316}, + {53.036864971091759458, -8.6745221657521938183e-11}, {7.5462674725305642909, -0.00078226914083204409332}, + {-46.442744547411471956, 53899410.797286212444}, {-34.446621569630430315, 48739894.059609726071}, + {-79.651481779027321295, -529580229.56283116341}, {-66.364211259231424833, 355179594.87237000465}, + {57.373019318584340454, -4.6002100821114406028e-11}, {92.586619368564143429, -9.7432688627864820628e-13}, +}; + +const std::vector gamma_9_r = { + {-34.551131653970884372, 1233244426.6552183628}, {4.9371708351271834658, 0.050783751504430776902}, + {-212.03059748541411977, 5.0455169396591558656e+20}, {-10.571878968492240958, 1851277047.5938651562}, + {130.11432518571629657, 3.9043304271442249176e-15}, {-87.733249069526209496, 198939633551.17703247}, + {-19.033001646814582841, 2.3681374807518802739e+20}, {57.996620481876192343, 5.8647203510554968761e-12}, + {88.274424281954139815, 1.3031586278563694494e-13}, {-41.068633361211873023, 156462530468741728.0}, + {-73.171558008236871729, 16430589402720.554688}, {-216.98873672082288522, 1.1043698562413921261e+25}, + {156.21508494990209215, 7.4899199986900974854e-16}, {68.221111471654850789, 1.3447726455586466113e-12}, + {-110.49350654801166627, 750099982.11990225315}, {-104.0341335043303701, 1.6902628915819770675e+20}, + {22.308199747466151308, 3.5853531040858530796e-8}, {130.49294578793336541, 3.8031730584780341595e-15}, + {80.931378421370709475, 2.8604821914277024453e-13}, {-55.034631752795569071, 1.4622388048955831091e+20}, + {193.49902696593966311, 1.0851273959743756177e-16}, {-16.463897911199449453, 971273163.9979391098}, + {40.26065525573632442, 1.6196077308499045813e-10}, {-78.061687987143713485, 454733591266090624.0}, + {-39.270319499981440003, 174184902929.41864014}, {-10.981912401936988033, 9.6817540530758941147e+22}, + {-95.432482044084082418, 1689912278.3294978142}, {55.380456489461082015, 8.9170399374173862482e-12}, + {88.507028330948813277, 1.2724891696898201432e-13}, {-24.567051173362145278, 1673769326.4313097}, + {-36.718094487528631475, 114489386286.92904663}, {-49.784584504717130926, 1686532465869.0310059}, + {107.5983836567594949, 2.1743643175184437519e-14}, {226.54238132952252727, 2.6168557632553206452e-17}, + {20.482969703354907409, 7.8617956797407201456e-8}, {-83.051260759339243123, 2896761106168936960.0}, + {-179.85534712810664359, 90467468415563.40625}, {-128.48680352002813265, 771922971.80468654633}, + {-43.753087974228364487, 430870620453.66448975}, {-41.112225290510266973, 1145132262098756.0}, + {93.125278061308918609, 8.0309147920072388429e-14}, {-68.948826555165084073, 2946568216459205632.0}, + {170.7404748228048561, 3.3565949433769231009e-16}, {41.992347886918594213, 1.1037317518489247679e-10}, + {45.974482682472419981, 4.8397598841941552177e-11}, {-21.973539785316098971, 2.1568969578706519982e+21}, + {-2.419350050318450851, 2241034504.077665329}, {-183.14668157889121858, 78705898701030.46875}, + {61.718883899104007185, 3.3351665700513575096e-12}, {-25.005186248414197792, 2.5776852263632901585e+28}, + {20.094194963303895207, 9.3789316250830716981e-8}, {83.228786740180964898, 2.2201010180300083267e-13}, + {126.00632380922299092, 5.2170700126419237552e-15}, {-141.65314022975522334, 14421106252.048843384}, + {-121.05439881349555264, 1599074728378411008.0}, {-29.987662566084299698, 4.4413463140311380053e+24}, + {-45.072000039582263753, 96924971285902032.0}, {107.4561629118183248, 2.2005227158291835444e-14}, + {17.069452386299111879, 4.2252961385764546083e-7}, {10.689065123674348357, 0.000032878402729791206076}, + {144.80840786331162917, 1.4853117253400341103e-15}, {-6.8302453933044668943, 18261960659705.925781}, + {18.50466259283836834, 2.0047576799993229706e-7}, {-141.69335984339471679, 49385252291.149131775}, + {-63.846287633035295528, 49280482228753.117188}, {-74.97646078225361066, 6.9477273942807302636e+21}, + {88.402332928577322946, 1.2861931483374100304e-13}, {-49.947454418256484132, 2261522886767990528.0}, + {-149.07826902670200298, 42059460739343176.0}, {3.3317268351761337719, 2.3333369423013694544}, + {90.261984771647320258, 1.0653355528567719089e-13}, {-81.300127322696951637, 61206735951.119728088}, + {-4.0354332878276570895, 1.1631842481139975782e+20}, {-82.880017159286154538, 586910167408021.0}, + {-18.137705975764305322, 147990953619408.375}, {-48.682575378139134159, 34959291886.743629456}, + {-178.4330459877528483, 1670435445.458589077}, {-37.464858366272629553, 958527420.84631729126}, + {-198.03325505299449105, 2.1937472548357773722e+20}, {-13.041781559988027794, 22382908633003683840.0}, + {164.70396203133518043, 4.6452323232875891883e-16}, {-13.428752763108962043, 1826677892.2082898617}, + {96.880915865732191605, 5.6159831983429392262e-14}, {-73.979582028904516733, 2.881623161027663233e+22}, + {-83.853376066769286012, 79015881431583.625}, {-22.502155479730546972, 743950722.2781162262}, + {177.76562161132548567, 2.332641710242683949e-16}, {-33.304401415844928636, 53138393258.842658997}, + {-78.22426423371152282, 1127624898980.130127}, {-154.15002102281508201, 62840817403134.460938}, + {26.521983696544193521, 7.3292372472670392686e-9}, {-119.24441991351721981, 476872918486.24432373}, + {199.16444069693818619, 8.3636916082007955662e-17}, {-36.363772566402090547, 8976006404.129617691}, + {-186.72810475556940446, 164350075552.72445679}, {64.124935350006012413, 2.3576114007815609641e-12}, + {13.132092131695113579, 4.8101620187394963861e-6}, {68.476712327524452917, 1.2999505126420075063e-12}, + {-175.61350926979454812, 4927516335.4767684937}, {-6.1157698758175307319, 839087708287885.625}, +}; + +const std::map> polygamma_mr = { + {2, gamma_2_r}, {3, gamma_3_r}, {4, gamma_4_r}, {5, gamma_5_r}, + {6, gamma_6_r}, {7, gamma_7_r}, {8, gamma_8_r}, {9, gamma_9_r}, +}; + +const std::vector gamma_2_c = { + {(-57.453569383931139214 - 51.404416292641343489i), (-0.000019894419201663138003 + 0.00016544538967054500298i)}, + {(-14.127632864397615009 + 10.491691277527667836i), (-0.00099129817238566807214 - 0.0029216513799464475035i)}, + {(13.509235577240430004 + 36.375027550378788987i), (0.00051811597497931482104 + 0.00042504718008693788672i)}, + {(115.38990944157514207 + 59.933530620400844668i), (-0.000034074644665891198479 + 0.000048840939581206654571i)}, + {(164.38616971093037478 - 120.94202241744412163i), (-7.1071994672320313154e-6 - 0.000023033089679497373623i)}, + {(39.028315814387191551 + 80.608466994287141461i), (0.000078682501149447708509 + 0.000097491631588999353992i)}, + {(231.40090291903314323 - 56.306283572934312076i), (-0.000015716254057654586513 - 8.1495420970969117855e-6i)}, + {(83.809846676580150415 + 78.116453039825188398i), (-4.9296742596016495221e-6 + 0.000076512439176994943672i)}, + {(-22.392120681632420087 + 44.860379962577631829i), (0.0002313276399908824766 - 0.00031927027495399053561i)}, + {(-181.28991133354020349 - 106.27435373184468403i), (-0.000011063730105699080741 + 0.000019651649418801533231i)}, + {(8.1223457699022016953 + 83.907224160669798607i), (0.00013857296321056054747 + 0.00002538704604001932371i)}, + {(25.077868730788221541 - 98.776316364563299999i), (0.000085264072224868435717 - 0.000045233091234063745989i)}, + {(138.83262786965667601 - 48.10143044879814056i), (-0.000036562806171472582168 - 0.000028924356555728430177i)}, + {(-102.29714432788018996 + 64.865111704636220225i), (-0.0000291348462387696704 - 0.000061090890304463018939i)}, + {(36.853737261337428777 + 18.649112202429247276i), (-0.00034945818426756667351 + 0.00048646215666567967518i)}, + {(-79.778223496410163307 + 85.511691843207429997i), (4.5833815987745095405e-6 - 0.000072546540290646335412i)}, + {(-85.222178484256076558 + 79.802910491829308626i), (-5.2087812077134085405e-6 - 0.000072716908923417745069i)}, + {(-201.04984792661429083 - 207.67021861380774794i), (3.5705030420641046975e-7 + 0.000011935065371079997329i)}, + {(-131.21290651686067008 + 77.608143140377407576i), (-0.000020734198094458630766 - 0.000037427849344342171273i)}, + {(35.692010936690977019 + 108.19100233679537837i), (0.000062473543399005340899 + 0.000045452437048504074502i)}, + {(54.553445036798521528 + 63.617842013958835423i), (0.000023168351032498224143 + 0.00014161061798311554843i)}, + {(-124.12950696630926473 - 288.31928484988702621i), (6.9443375884759648889e-6 + 7.3831082661007111634e-6i)}, + {(125.5087849840800942 - 127.82078080012990995i), (6.9555432493939741004e-7 - 0.00003127614834012389962i)}, + {(269.04919346049689466 + 77.688616553505653428i), (-0.000010818959132884289342 + 6.8313155848319099387e-6i)}, + {(73.382428914534713726 + 15.60650796964731768i), (-0.00016421557615683296267 + 0.000073703895517674699613i)}, + {(-146.43132997164255471 - 36.229800893332466671i), (-0.000038659772374307398786 + 0.000020299126723314445548i)}, + {(172.30572575719151018 - 221.23057345370912685i), (3.1555463479059290473e-6 - 0.000012348520446623991665i)}, + {(-65.961257751417463169 - 0.69666303451649846945i), (0.8269385100317673265 + 3.165270996995691366i)}, + {(44.850655427870428582 - 168.39679050988050335i), (0.000028698788729941000742 - 0.000016243661731575788641i)}, + {(3.5809316424563872872 - 68.618413627272616395i), (0.00021111335255529883447 - 0.000018997069110234267027i)}, + {(-94.872795497106835683 + 139.19749280634553656i), (0.00001268092252941484782 - 0.000032753325829191762199i)}, + {(74.552863323450424105 - 109.85818094225616903i), (0.000021372645438900881389 - 0.000052810913960717760626i)}, + {(-101.55276185614954443 + 130.6979628039889576i), (8.8179299767316858999e-6 - 0.000035282844639686926152i)}, + {(-105.79353380548499786 + 133.67084645667026166i), (7.7225856545013065227e-6 - 0.000033405286752336396975i)}, + {(-201.19560925033104581 + 37.170991619012049512i), (-0.000022212010590321981559 - 8.4747984079865820392e-6i)}, + {(-135.65222582724686617 + 0.53133077152780538999i), (6.047088760578009925 + 5.4026955879602809318i)}, + {(-17.350355024399963355 + 129.97517159308605983i), (0.000055948055890996360197 - 0.000015663096505243092883i)}, + {(142.00458124387094472 + 125.552200752856848i), (-3.3266390001121260533e-6 + 0.00002774443623864443137i)}, + {(11.891800450980493764 + 27.790003589548394558i), (0.00078961379912166574854 + 0.00077842022556081844065i)}, + {(-143.35435102592850853 + 56.497214689460030002i), (-0.000030676334697844284834 - 0.000028489588082840289413i)}, + {(-57.349021089050225441 - 144.24335023788970034i), (0.000029929932780298223625 + 0.000028608732334043831386i)}, + {(-96.093803737755976613 - 86.20654848831806305i), (-6.7590458988771952081e-6 + 0.000059274774249919204869i)}, + {(8.3363340546841975254 - 110.01502398852144893i), (0.000081376647909620541737 - 0.000011652224040289117725i)}, + {(74.655097103543269554 + 67.084376796523386588i), (-9.9905127791939563362e-6 + 0.000099506561400919491607i)}, + {(-97.387608893666637755 - 179.05464119157755931i), (0.000012962604413710928316 + 0.000020214896058502310113i)}, + {(134.15057260803516215 - 70.408655346835132605i), (-0.0000247821261795141173 - 0.000036140632903143694551i)}, + {(0.67695794919736784756 + 52.384140596783232979i), (0.00036443917531506784049 + 2.4624637054174187713e-6i)}, + {(-156.37672136286451519 - 49.510807605706865786i), (-0.000030258015227251524839 + 0.000021211636294831220603i)}, + {(-150.70720650475280422 + 28.303287898738805239i), (-0.000039395816110261751828 - 0.000015283716817568992059i)}, + {(184.58293521885315158 - 12.677874158592878473i), (-0.000029093429796038041172 - 4.0264232479070217774e-6i)}, + {(135.10389135103616809 - 24.497346135365720698i), (-0.000049997460965277826012 - 0.000018821824013263304971i)}, + {(-91.377834600420626998 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0.000019164374686441959479i)}, + {(-119.67396848238523432 - 6.7389056717738000657i), (-0.000068592557777628456925 + 7.7169597856356136271e-6i)}, + {(-87.022006248593186228 + 92.401490267080703234i), (3.3450967749179519525e-6 - 0.000061644853866872994608i)}, + {(-2.6302978308820437192 - 94.359397920174970409i), (0.00011194589731518988411 + 7.4358239982221005545e-6i)}, + {(-0.12569587373765098159 - 73.889839198163187461i), (0.0001831289525519583304 + 3.1018201289374760074e-6i)}, + {(-75.96385597325725314 + 19.950033561403053284i), (-0.0001397195636947027675 - 0.000078229910244544736075i)}, + {(-9.5728027711094192398 + 47.246314149205034028i), (0.00039127862879180579049 - 0.000174804368611333245i)}, + {(40.599935650153845756 + 10.225276586882738883i), (-0.00051257487521003868101 + 0.00027954085660081512497i)}, + {(90.576450483139907988 + 15.156446288320912785i), (-0.00011325138962281018813 + 0.000039221039125756870271i)}, + {(31.649404373512641797 - 187.29420074573422994i), (0.000026246609677492081081 - 8.9787032391045320194e-6i)}, + {(20.483301757277210697 - 75.175730730860209405i), (0.00014345823497078038946 - 0.000082071341729642556463i)}, + {(27.271209447001464099 - 29.331616266077404021i), (0.000057658524961811985802 - 0.00063148105797977379435i)}, + {(14.080416679556165604 + 0.1660748005592994625i), (-0.0054124304769261107756 + 0.00013221831964087596943i)}, + {(-83.476200547193499801 - 43.155436180641736144i), (-0.000065306719127844500123 + 0.000091206103657173346949i)}, + {(-188.87489237533063147 + 1.9303256914697717317i), (0.00092043392931207533309 - 0.00094756674030931618315i)}, + {(-167.8224449693196334 + 75.077393170896783658i), (-0.000019668875109431641291 - 0.000021903316087995580941i)}, + {(-54.279428287741438908 - 43.922212006436481602i), (-0.000044101176684812881657 + 0.00019798747215796057026i)}, + {(51.683187407475216446 - 42.555095726973043213i), (-0.000041211761449771388774 - 0.00022190347720839234246i)}, + {(69.846983656344988844 - 46.388798896333064192i), (-0.00005484035589936025871 - 0.00013277762802776596094i)}, + {(-0.018851753390831671453 + 1.5588076414659961522i), (0.29832875617036097582 - 0.27520924132118151917i)}, + {(89.322814550103657893 - 52.251498542135557557i), (-0.000045748220540020581777 - 0.000082303424637809400048i)}, + {(-89.156992800874135696 - 34.155278634703250873i), (-0.000081100684527890391264 + 0.000072278749433974352756i)}, +}; + +const std::vector gamma_3_c = { + {(-102.71881640848181405 - 26.346115676131802275i), (-1.2107804641272995052e-6 + 1.1272956555051113733e-6i)}, + {(56.279566233817050147 + 47.576727748051091282i), (-2.642915185560251793e-6 - 4.3329373925070091024e-6i)}, + {(-24.840059724185099554 + 57.886605135002497491i), (7.4921847066452140361e-6 + 2.5900142453399919139e-6i)}, + {(83.146078971636839583 + 83.173484941299307138i), (-8.8559538876062567498e-7 - 8.6891753069157689916e-7i)}, + {(46.094610660205162844 + 32.924713364170280272i), (-3.3794353540646484326e-6 - 0.000010722996907183234802i)}, + {(47.557765018425314452 - 41.652143606157146394i), (-4.5678728515148501424e-6 + 6.6384449716306655981e-6i)}, + {(95.708643438014945559 + 10.145395486835806054i), (2.163797000696988323e-6 - 7.1337634393826069362e-7i)}, + {(-51.13050870145201543 - 79.158052728555333033i), (2.3379487687764610988e-6 + 3.8476599303842654323e-7i)}, + {(-129.96209808647074624 - 96.84685390667698357i), (1.5765390583194529487e-7 + 4.387998298428186409e-7i)}, + {(49.370831285401258981 - 108.42891092304998324i), (-1.1356050118016837002e-6 - 3.5180394234780440011e-7i)}, + {(-14.986151184582796603 + 112.29658225060983057i), (5.4871718839265823915e-7 + 1.2585984224276647121e-6i)}, + {(101.38385604827379893 - 195.43194467485741939i), (-1.8612677157390841695e-7 - 2.6456150807973482336e-8i)}, + {(114.74610923767332338 + 175.44309620066570687i), (-2.1512776002524710939e-7 - 3.4902617866612509486e-8i)}, + {(-10.360678917929398324 + 26.049503103726202369i), (0.000082479745113174036042 + 0.000033453077843841994932i)}, + {(5.1557502363008165247 + 118.20360239936407254i), (-1.4236377278078473715e-7 + 1.1997962479936259499e-6i)}, + {(-163.41624833017175433 - 65.98083579865638626i), (-1.4873388760722132398e-7 + 3.3060559380485480452e-7i)}, + {(102.55913965386372411 + 86.521206537674174797i), (-4.2839421371988792471e-7 - 7.167079164296697189e-7i)}, + {(89.438252125447448293 + 19.491617515303925501i), (2.1137510489048783905e-6 - 1.5976259499338311286e-6i)}, + {(-18.776004190036900354 + 33.113626825940919218i), (0.000035559336515623197496 - 3.9114108192636091563e-7i)}, + {(-106.99598864067453974 - 39.594798184813896569i), (-6.5184201668918115748e-7 + 1.1596951626685816487e-6i)}, + {(-20.921916811237672107 - 30.888344615551567074i), (0.000036501496285074154578 + 9.2675627716444910158e-6i)}, + {(-22.398643178411798971 + 280.13100857395915i), (2.1821050797464509737e-8 + 8.7393312141644847014e-8i)}, + {(-81.411869978596101305 - 95.375458631941171461i), (8.5377739648525177161e-7 + 5.3294623066157783672e-7i)}, + {(-10.509790971698688367 + 85.580798040351126588i), (1.1659565412466531806e-6 + 2.8868407318306903854e-6i)}, + {(134.3397452131362968 - 49.094060971354899436i), (3.4064724394765900652e-7 + 6.0038077546065297781e-7i)}, + {(19.093191203074567852 - 64.823195432835518659i), (-4.8479964417342514711e-6 - 4.3626028399882852042e-6i)}, + {(-33.15506221666053932 + 95.970201117543652458i), (1.6120874721993768051e-6 + 1.008269750235867026e-6i)}, + {(33.060506466419987248 + 96.808751133526158128i), (-1.5519791789544377711e-6 + 1.0558736541674576307e-6i)}, + {(227.77584142316928251 - 103.95548215676511461i), (3.5878444811919091849e-8 + 1.2299282415595694213e-7i)}, + {(-65.769080689868090417 + 180.60112753326427537i), (2.4438125610482802853e-7 + 1.3854459253137087598e-7i)}, + {(-5.5385821515957038841 + 45.97046017558815123i), (7.665440629841853567e-6 + 0.000018548424771476875643i)}, + {(-81.781473659347341254 - 32.367638589102988078i), (-1.249273265915835264e-6 + 2.6095505564993333037e-6i)}, + {(94.821090315858185704 - 116.6327610835718076i), (-5.2853909694535763988e-7 + 2.6801336797375756008e-7i)}, + {(59.199458948133511171 + 51.628377852925822822i), (-2.3406553613815350361e-6 - 3.4709648103454415603e-6i)}, + {(9.2972145055083785792 - 135.07127057188327512i), (-1.5636316122659175274e-7 - 7.9117982931623798703e-7i)}, + {(83.890346016765803938 + 284.87141925244964114i), (-5.7672761814560612013e-8 + 5.022409994019868551e-8i)}, + {(127.21695857745207547 - 40.923547573519961418i), (5.0152163169813185486e-7 + 6.8256462214545305663e-7i)}, + {(-92.980081427571420249 - 93.184916682128886123i), (6.1205024619221525147e-7 + 6.1792027197469510013e-7i)}, + {(-6.239645274349396864 + 87.984978697430932471i), (6.6180077506508613313e-7 + 2.8346258890245840016e-6i)}, + {(97.105402616477533684 - 83.159388768361566235i), (-5.1408357134207858854e-7 + 8.1744660528344705295e-7i)}, + {(-20.379807613107143283 - 65.63670993913399343i), (4.8848678357847767875e-6 - 3.688647152953223434e-6i)}, + {(125.06728118351307444 - 64.403864721274359795i), (1.0070310092615756781e-7 + 7.1822351421648046893e-7i)}, + {(142.5710365499366219 - 73.733055507589611466i), (6.5466798863778571879e-8 + 4.8326878838311666453e-7i)}, + {(86.291005532548496149 - 38.373701991388799115i), (7.3274709207291315823e-7 + 2.2950955428784646253e-6i)}, + {(-16.980673305082095936 - 113.38052767779542762i), (5.8683843654741433565e-7 - 1.1876539924986919704e-6i)}, + {(61.645084826891341834 + 214.88606037191425457i), (-1.325459362692601874e-7 + 1.2081548349101387427e-7i)}, + {(-22.24138602821423305 + 63.967370753192213328i), (5.4629525934219481072e-6 + 3.3192846008538347986e-6i)}, + {(-60.302472106400017537 + 32.83664081910678334i), (-5.1669632535091132169e-7 - 6.0385910939657190625e-6i)}, + {(-219.61298795625575053 - 149.80317379550882606i), (2.3320634464653935632e-8 + 1.0336255271013249121e-7i)}, + {(168.40767777323694077 + 85.452451973850713784i), (4.7210627871156182788e-8 - 2.9532073051556643041e-7i)}, + {(-114.97426430177814893 - 29.083719065164743256i), (-8.7449214228406544794e-7 + 7.9877480265005157134e-7i)}, + {(8.9071067094014342302 - 138.47108072006338375i), (-1.355352729030041264e-7 - 7.3678451020392361771e-7i)}, + {(-129.87533023892927986 - 104.47378025684639624i), (1.8879850086776223383e-7 + 3.8508244307233086881e-7i)}, + {(57.930575540057873241 + 51.585915561394990902i), (-2.5423212392319140856e-6 - 3.5264806113052614656e-6i)}, + {(234.71762349792862778 - 16.695494240957682308i), (1.5097084358328575577e-7 + 3.2728510395024903233e-8i)}, + {(-196.10843992590309881 - 74.109898293602839203i), (-1.0135605087030629636e-7 + 1.9030326198026522184e-7i)}, + {(52.917186632631462828 + 45.479255816346707775i), (-3.2445523873846978032e-6 - 5.028241390543973868e-6i)}, + {(25.753437218025389654 + 71.553032465437212295i), (-3.896155972784942913e-6 + 2.4042486574856154213e-6i)}, + {(80.14867599646969154 + 43.730250740139879895i), (1.7191438890958743352e-7 - 2.6603391770076824732e-6i)}, + {(160.73463365396170843 - 160.50664374895495712i), (-1.2153262879722781457e-7 + 1.209181408808335616e-7i)}, + {(65.234865616183014936 + 131.84542410817309133i), (-6.1839430251818760784e-7 + 1.2634361208747529444e-7i)}, + {(123.36177526762541845 - 255.88603309127330476i), (-8.5187193941071702177e-8 - 1.9755969887325819892e-8i)}, + {(-6.0565863314087788893 + 127.33339131808283184i), (1.4833651169038287224e-7 + 9.5345027680231172501e-7i)}, + {(122.69796151750298918 + 161.88306300116940406i), (-2.2355959870905236109e-7 - 8.6457374073673785543e-8i)}, + {(79.997665901467556182 - 94.654764806758706186i), (-9.163366689883238083e-7 + 5.30743618215616467e-7i)}, + {(-7.7938640002839880694 - 40.625606146473899116i), (0.00001594481476687519911 - 0.000023094111622435794758i)}, + {(-52.669910213407611366 + 123.95579030929131648i), (7.6423697823364865433e-7 + 2.8344620786568844319e-7i)}, + {(33.771591475364083124 + 67.043358033074667901i), (-4.685741780878110825e-6 + 8.9508059678949869421e-7i)}, + {(-240.39678309128126443 + 23.159260035126315813i), (-1.3531161921766812654e-7 - 4.0014677133782558429e-8i)}, + {(-38.076239418384304258 - 62.778552625327236569i), (4.9826875704082480406e-6 + 4.1092409742101742401e-7i)}, + {(182.13531305112417158 - 367.74428284274989664i), (-2.8439406415211968524e-8 - 5.6018391315894025403e-9i)}, + {(-93.15437963051184056 - 41.640845708877840536i), (-5.7672504958565016365e-7 + 1.7656403182260360512e-6i)}, + {(44.941987241895162697 - 8.0074514191855499234i), (0.000018682987227839399522 + 0.000011065199047814426405i)}, + {(-165.86850434323221748 - 78.188918830400425009i), (-8.0524293471949041035e-8 + 3.1173017327141343556e-7i)}, + {(16.318351772576054515 + 68.004603213471938261i), (-3.7210557993663892929e-6 + 4.5484679345219659365e-6i)}, + {(52.631357734820070959 - 154.03673222790069985i), (-3.8598682336187216241e-7 - 2.5943643939482879004e-7i)}, + {(114.46661044018962627 + 110.33064575041764499i), (-3.3668729108172427919e-7 - 3.7114858771119744432e-7i)}, + {(23.354817591722490278 - 75.958676951957826873i), (-3.0806442473331713935e-6 - 2.5630769775663858301e-6i)}, + {(-21.790331721122857545 + 42.815180273332806848i), (0.000017633371948789919114 + 2.3161874063607854288e-6i)}, + {(82.555667629275589547 + 55.42560272982031222i), (-4.3214220762463429824e-7 - 2.0140392757111916973e-6i)}, + {(-102.74442989859684872 + 38.980057536249901773i), (-6.9741677945595145273e-7 - 1.3144555393827412041e-6i)}, + {(98.288619513731205757 + 11.631427401455402659i), (1.9633868869788721305e-6 - 7.2817933392452393057e-7i)}, + {(-54.973433383137717101 + 77.863851576852383118i), (2.1956356746918927383e-6 - 6.4645643856898710563e-7i)}, + {(77.847984316903591662 - 147.83930175324283596i), (-4.2723271214310323761e-7 - 5.3554416673689267181e-8i)}, + {(67.111927383618265708 - 19.559266764925965276i), (3.9141033342344502032e-6 + 4.5166951423489545443e-6i)}, + {(111.17965560712657691 - 109.63540711127393479i), (-3.6867143187333774868e-7 + 3.793235122183725772e-7i)}, + {(142.04263208498295512 - 106.00973418904867174i), (-1.2661838639937704041e-7 + 3.387586154453386389e-7i)}, + {(77.7900235861026772 + 19.70353448606358171i), (2.8868389550989135451e-6 - 2.6829148031130968845e-6i)}, + {(-43.373963303522877766 - 205.18251481827488192i), (1.2790402311643728723e-7 - 1.7469811604027773115e-7i)}, + {(110.69640133101894719 - 74.333837345428008803i), (-1.7711231794258399753e-7 + 8.3293957565998455364e-7i)}, + {(-36.858119171396651836 + 174.62225308603862572i), (2.0756967835459877121e-7 + 2.8332478017891776384e-7i)}, + {(-113.22524856973490159 - 36.151791816593750184i), (-7.0985542115003350784e-7 + 9.3870639483886407033e-7i)}, + {(160.11882661103547321 - 107.17906599773235143i), (-5.6775272912309135542e-8 + 2.7561857121448873369e-7i)}, + {(-85.347556401535001669 + 34.730983994219826627i), (-1.0211149250364189106e-6 - 2.3018241856364509099e-6i)}, + {(161.52327266696426022 - 7.4092568789576764843i), 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81.816097916189121975i), (1.0881179249886437455e-6 - 3.4262889182026419951e-6i)}, + {(11.595504197775326816 + 127.81436959691710342i), (-2.4329166379595003212e-7 + 9.1535737101916348971e-7i)}, + {(113.47769481381266132 - 154.2415398198533012i), (-2.7111629069609050843e-7 + 9.1588554237518941182e-8i)}, + {(-48.443030169401986029 + 41.104598227704187252i), (3.8379317900313923557e-6 - 6.6292225474210750467e-6i)}, + {(-34.944242878039602829 - 1.3205072774398620705i), (0.36544213480262355276 - 0.13382924193128092893i)}, + {(309.66870378767725924 + 124.56299219330517758i), (2.2110503425514788784e-8 - 4.927357402693141742e-8i)}, + {(82.635871741004379487 + 70.87123709356086465i), (-8.3855431661446182781e-7 - 1.3230975572014996235e-6i)}, + {(-104.30011564701055704 - 121.71638176274457521i), (4.0848760751446931163e-7 + 2.5712214638569488222e-7i)}, + {(-69.154277353607497503 - 20.359242730387695275i), (-3.4416401014679991451e-6 + 3.9419469566227818014e-6i)}, + {(-11.781409802086667327 - 26.516338701445658188i), (0.000077290674483581088333 - 0.000021316666872398604891i)}, + {(104.92857445241723724 + 22.353007892253941691i), (1.3242654743768719364e-6 - 9.7080030108299887021e-7i)}, + {(-129.6575691156622554 - 60.00572520045105307i), (-1.8437668044069815426e-7 + 6.5381177769211849934e-7i)}, + {(-1.2779192528638472215 + 216.04380482915752282i), (4.8955977824626969732e-9 + 1.982589106433762826e-7i)}, + {(-66.651637904015387903 + 61.12219395194111371i), (1.6047526344685712074e-6 - 2.1355431472536364498e-6i)}, + {(122.6690997521960611 + 37.096904813846506954i), (6.0897862414301365403e-7 - 7.4328757689763445944e-7i)}, + {(33.133178782450244171 + 70.52238001630452402i), (-4.1075737762724405441e-6 + 1.1392449693778918925e-6i)}, + {(92.030020194896522412 + 7.2637292721291828457i), (2.5110269451519365234e-6 - 6.080260154997856191e-7i)}, + {(98.198706591215866979 - 20.538326232796993764i), (1.6339462971132138455e-6 + 1.1704193278914314117e-6i)}, + {(70.828642824435675607 + 132.71160022716375693i), (-5.8680311962150632079e-7 + 6.4128382701940451372e-8i)}, + {(-18.57533551691244611 + 106.25064766938562855i), (8.0779828003667274296e-7 + 1.3694685992575351731e-6i)}, +}; + +const std::vector gamma_4_c = { + {(-125.84007495368484797 + 17.717725968116045721i), (-1.9221826282770986774e-8 - 1.1979066463171876608e-8i)}, + {(-60.926962301902655383 - 188.6161760212682168i), (-1.1873982310162091966e-9 - 3.6887064258284402757e-9i)}, + {(15.426892880500448157 + 144.43927422852232212i), (-1.2366950653088863616e-8 - 5.4033272190230883395e-9i)}, + {(108.36040598197010354 - 137.08270561083440953i), (5.7641618329830872524e-9 + 2.9638961304650210861e-9i)}, + {(-181.52361094710161638 - 31.043729526038958966i), (-4.0269599227811801297e-9 + 3.2277879331681573313e-9i)}, + {(-66.892613536979553146 + 69.099190755603871139i), (6.9041269161489133284e-8 + 3.4494451185762105008e-9i)}, + {(-62.204622366486162832 + 191.39928110439885245i), (-1.0929037101007799674e-9 + 3.4785811926660067572e-9i)}, + {(-151.33344901950204076 - 12.649640841954601811i), (-1.0524432085709858591e-8 + 3.6340280583809285271e-9i)}, + {(102.3940974883262669 + 176.75333706093167052i), (1.7237283854852110616e-9 - 3.0036332881784170506e-9i)}, + {(-9.4103856084753640943 - 95.755972241038165294i), (-6.4005609328499105504e-8 - 2.8011936338804671262e-8i)}, + {(205.60589998432178049 + 129.73560531471471791i), (1.0944433541423044374e-9 + 1.3391707472655318389e-9i)}, + {(-139.61765018796450022 + 15.973017586296938575i), (-1.3631947185872167688e-8 - 6.6526892359485880956e-9i)}, + {(56.03301641516302567 + 132.05958343908309871i), (3.0616623152295546415e-10 - 1.4241445426987412327e-8i)}, + {(23.893023013995492221 + 97.66029069427571585i), (-3.4775676242920773298e-8 - 4.7661785176107514594e-8i)}, + {(-52.93457316393392631 - 30.762289493792177808i), (2.05709707289429864e-7 + 3.6057005970590143693e-7i)}, + {(-65.623814389284490289 - 77.736320282689590044i), (5.2466674843353017131e-8 - 1.7509596973050283462e-8i)}, + {(-102.61647221987024636 - 25.307412323873180071i), (-2.6972020019789539787e-8 + 3.8743017637301951811e-8i)}, + {(42.967092397804670156 + 120.37113788259303249i), (-4.8024264297195935782e-9 - 2.2087896520007411961e-8i)}, + {(1.6955492638111395731 - 175.87779296665632955i), (-6.2678446698746987414e-9 + 1.7046722526660902386e-10i)}, + {(8.7334953790321652178 + 0.63985498339412283375i), (-0.0012145426519367709395 + 0.00038689085472194440244i)}, + {(48.480724542491465456 - 217.08751124752353689i), (-1.5833732712994982308e-9 + 1.8771921200515918144e-9i)}, + {(80.718201738646286003 + 6.3218520074887054605i), (-1.3607422393472512315e-7 + 4.4273859006297340547e-8i)}, + {(-23.693652414435341313 - 76.41291262334416956i), (-4.9062136961515693503e-8 - 1.368674256933073303e-7i)}, + {(61.61143696765357447 - 40.036541391363691389i), (1.433909441753946611e-7 - 1.5423450615413671529e-7i)}, + {(-23.84664475290873753 + 87.370106166031035855i), (-4.1235251406737209787e-8 + 7.8499403718186000855e-8i)}, + {(81.757186425034845456 + 52.433699314833468463i), (4.530206143676256067e-8 + 5.1513921103045229268e-8i)}, + {(14.15447614954314659 - 32.606882473608436612i), (6.1404176006545131102e-8 + 3.8434372811721225418e-6i)}, + {(-24.469504839702320709 - 49.521461907287665838i), (1.8591896652230306204e-7 - 6.0643453974009563223e-7i)}, + {(-73.433215242282884105 + 100.18843934221204961i), (2.0621943373166253771e-8 + 1.4065449523799714933e-8i)}, + {(-111.33826636825826029 + 41.786001004501734712i), (-4.137189458028117156e-9 - 2.9238969882678854485e-8i)}, + {(-2.1910904875227905642 + 99.748288418826462021i), (-6.0172911241277480917e-8 + 6.5175819490544092562e-9i)}, + {(-81.078607609672488366 + 51.095788507784824617i), (4.3251192296881437829e-8 - 5.4888919834430360943e-8i)}, + {(75.66412998685200364 - 65.099887528257966096i), (5.8867339964254974209e-8 - 1.7349073749145037591e-8i)}, + {(-75.004232553177288878 + 119.05615314092818835i), (9.6680400100553552224e-9 + 1.1714919147014706047e-8i)}, + {(36.377344446258256028 - 60.929812979681038598i), (1.2711002219435698226e-7 + 2.0364085491554337083e-7i)}, + {(-66.405559007777853253 + 42.275761824505657671i), (9.6536816730950900474e-8 - 1.1860346357790992556e-7i)}, + {(-10.621718083606094041 - 95.895876787056494095i), (-6.1846519374302205087e-8 - 3.0785589015383832108e-8i)}, + {(-66.450796107114925348 - 34.36842897443742828i), (5.9923035313156770506e-8 + 1.7717881375215875667e-7i)}, + {(60.980184405332671815 - 25.015174106941547194i), (-7.1943194212509195252e-10 - 3.2694162382575579649e-7i)}, + {(30.45368211126173108 - 114.1971387204511359i), (-1.6003596215070369728e-8 + 2.6416322874992280459e-8i)}, + {(192.18903843938471709 + 72.148991642193678331i), (-4.4491477002315063228e-10 + 3.380241255754673072e-9i)}, + {(67.366539272612911304 - 14.662197920193676737i), (-1.7753839898446605379e-7 - 2.0762865989354235483e-7i)}, + {(144.28231199054934564 - 80.284781228069206804i), (3.6669918260560153032e-9 - 7.2876737650690791378e-9i)}, + {(78.682881781439462543 + 49.635068826920928586i), (5.2033533275552365704e-8 + 6.2821700758668553103e-8i)}, + {(150.14547708825000427 + 279.18917232916788862i), (2.3060660419865362469e-10 - 5.4951256483407289259e-10i)}, + {(-126.83745164756388135 + 162.75498172617469095i), (2.9092749477313597187e-9 + 1.5366259540677632827e-9i)}, + {(-2.9902094628934783316 + 21.013261795537207632i), (-0.000023081599946841414389 + 0.000017875588917221664216i)}, + {(69.784987337013816955 + 85.704916194472176016i), (3.7102997724974818434e-8 - 1.6663872927543003807e-8i)}, + {(4.5058842474868789907 + 127.98654426248351967i), (-2.2143947189194112178e-8 - 2.7860854401688976627e-9i)}, + {(131.86079239403312613 + 77.155983932971068384i), (5.8550187107887507876e-9 + 9.4759491407308418153e-9i)}, + {(98.133890116434912443 - 150.42065665483738712i), (3.8781482440442195117e-9 + 4.3150938865329225016e-9i)}, + {(-146.47588680540030737 - 73.699077734360344039i), (2.3347730514998533307e-9 + 7.8709524921201761227e-9i)}, + {(-20.270272170557692704 - 138.77928125263397874i), (-1.2821986963561560541e-8 - 8.6643313995204937736e-9i)}, + {(-36.962530309929626071 + 4.2006397328040936401i), (-2.6860980462279606046e-6 - 1.249428921893836218e-6i)}, + {(137.06633816396180237 - 94.317564499566358904i), (5.9239665554240241808e-9 - 5.2374482281278761555e-9i)}, + {(173.7174637727726747 + 60.043015982662872432i), (-1.2425407952974926714e-9 + 5.1641529787245439884e-9i)}, + {(-18.810392147438506072 - 248.19192651504380365i), (-1.4875470562190101844e-9 - 4.774757962394291005e-10i)}, + {(184.89242478353122578 + 110.95883175743344395i), (1.5703214614239158425e-9 + 2.315051156102559026e-9i)}, + {(-41.612732194712762634 + 17.960688872779719816i), (5.657089894910309552e-8 - 1.3641044451538924628e-6i)}, + {(58.631652144487745204 - 181.14645895719496593i), (-1.4784841175737049314e-9 + 4.3352099227303164273e-9i)}, + {(50.026089569057759832 - 104.94751261261401964i), (6.3445727111101169316e-9 + 3.2471546076915331753e-8i)}, + {(-22.843005173866622215 - 13.189469954154562359i), (5.4144182233090331144e-6 + 0.000010263293203316384243i)}, + {(-40.513596112145656036 + 129.04969206126347103i), (-5.9500189801909042897e-9 + 1.6825772898217041959e-8i)}, + {(-12.312235190435467658 + 90.203409891628055561i), (-7.3580415724467171636e-8 + 4.6583616209987010306e-8i)}, + {(-55.763052857217317637 - 10.105837711656020517i), (-4.2574641001789797607e-7 + 3.6653504036130683271e-7i)}, + {(84.509039583147654184 - 104.55041927898295739i), (1.6823722861183390031e-8 + 7.7972519430562575099e-9i)}, + {(127.62700809252625334 + 51.937149290350717479i), (-3.2762795071085632554e-10 + 1.6866699898013724332e-8i)}, + {(142.54501323349671793 - 30.185503010292730863i), (-9.029790592274227258e-9 - 1.0024419188499564593e-8i)}, + {(99.19995337729841367 + 41.733631490110134621i), (1.3323381375700423436e-9 + 4.5478253069683378851e-8i)}, + {(170.07638267898533968 - 120.06739658038362961i), (2.5087674626717467144e-9 - 2.0171354721984084695e-9i)}, + {(188.01240815953201491 - 25.226131084272658711i), (-4.0281039465329351161e-9 - 2.3867472119821617697e-9i)}, + {(43.486645183552134597 - 98.270580033925568841i), (3.5625071384428031457e-9 + 4.5191548961992960428e-8i)}, + {(-124.52224028206342155 - 123.14745461667320114i), (6.3236503617591279164e-9 + 1.9131261216130424403e-10i)}, + {(-136.49557324154420712 + 27.270428694081282117i), (-1.113777933621487811e-8 - 1.1150131492394699102e-8i)}, + {(-135.40054296872153827 + 63.966549400477731524i), (2.2131379981246891698e-9 - 1.1578290741625618897e-8i)}, + {(-135.17524508150879115 - 45.111313942003903321i), (-4.0618239773642467644e-9 + 1.3770181916602873425e-8i)}, + {(-221.86113009892386572 - 138.74613554673086924i), (7.8016877700275359779e-10 + 1.0039525933071979466e-9i)}, + {(-105.33034895602312986 - 48.745922322178969921i), (5.0480901546939883119e-9 + 3.2158044537267515854e-8i)}, + {(-56.167521552596497258 + 180.52540629872729028i), (-1.6234070030414781335e-9 + 4.3909341652590916811e-9i)}, + {(61.990894424531582274 + 140.57789829301424334i), (8.4982199095773870725e-10 - 1.0791590778232922715e-8i)}, + {(22.995608099356822152 - 34.014831427101370309i), (1.5056511632657881618e-6 + 1.5623864416063497101e-6i)}, + {(-40.669231690702936532 + 57.157285917260246322i), (1.9481184530467897327e-7 + 1.4644501156380630448e-7i)}, + {(103.25983152703754797 + 14.734657636760584154i), (-4.3501652877607888192e-8 + 2.7861855931436192185e-8i)}, + {(198.42553234782570826 + 16.73516621164166196i), (-3.6369972611991802244e-9 + 1.2759319399443563003e-9i)}, + {(41.373896246190490444 + 187.09790882405502543i), (-2.90907462842376548e-9 - 3.3813985004211398436e-9i)}, + {(-98.213519352287121933 + 149.48502986480443155i), (4.0297068120507960032e-9 + 4.2083643069277814135e-9i)}, + {(-32.053848571489979236 + 38.471432395375451563i), (8.7934690709020858476e-7 + 3.033365274257270342e-7i)}, + {(69.955436081702828233 + 31.591628585144665209i), (2.4103137997231683067e-8 + 1.7534275876812786384e-7i)}, + {(-153.10035052564228408 + 57.424180294449797657i), (-1.1558070684508178292e-9 - 8.2164655130648877164e-9i)}, + {(55.061771119546122577 + 52.305365647179002053i), (1.8318465607086603717e-7 + 1.5532594404129878477e-8i)}, + {(-34.825426671726106065 - 57.144503172521844192i), (1.7687641682815361717e-7 - 2.3555069141248572915e-7i)}, + {(64.957485766321639176 - 218.84036924981685956i), (-9.1335965217413063686e-10 + 2.017979635811515282e-9i)}, + {(-31.368873101599959341 + 141.18315470870032868i), (-8.6268296835250160136e-9 + 1.0608164425211731419e-8i)}, + {(56.009677107375168248 - 181.03146340739272091i), (-1.7342048689103262858e-9 + 4.3334498862547547864e-9i)}, + {(10.209677686634199389 + 47.323705596010498198i), (-7.6010522872667946103e-7 - 7.978327986933740534e-7i)}, + {(137.03876913478234201 - 75.815631412671820044i), (4.4474232421178258607e-9 - 9.0517463974512770184e-9i)}, + {(-53.471408521466237573 - 69.955603688624719894i), (8.5780205148894939188e-8 - 4.8318848811305754594e-8i)}, + {(24.222264131895940409 - 167.58888153644147678i), (-6.1842953941846978005e-9 + 3.8985769840843856158e-9i)}, + {(234.9401491272735143 + 9.858887388055311618i), (-1.9512640277996144782e-9 + 3.3115498936928361043e-10i)}, + {(117.84125858737735371 + 15.038875143421931213i), (-2.6735789634085814559e-8 + 1.4949972348978261695e-8i)}, + {(51.417422612175343488 - 24.496009513325688545i), (1.2994911385494551291e-7 - 5.740214331989189754e-7i)}, + {(54.01074705236864304 - 36.642080907715630644i), (2.5042315690688450897e-7 - 2.2869397900254925106e-7i)}, + {(-88.143649096410612742 + 50.015690704738034356i), (2.6013165420599148943e-8 - 4.9487756194536814051e-8i)}, + {(63.918692357182180785 + 18.342207975616105387i), (-1.3586899457408239206e-7 + 2.8509478281651218248e-7i)}, + {(241.61714883664052422 + 130.62360815739202735i), (4.2790097214783931142e-10 + 9.7088037547723107739e-10i)}, + {(-49.72946747690173197 - 61.490079146603385141i), (1.3896455486708409387e-7 - 5.902991728316473871e-8i)}, + {(-164.33430853091510926 + 180.6576861964107934i), (1.6493858477793188216e-9 + 3.0534897619537712782e-10i)}, + {(104.82893684757247854 - 7.5856025240195856796i), (-4.8012602045320689796e-8 - 1.4343899254594413654e-8i)}, + {(-111.55984208894520293 + 87.031185538229209442i), (1.2989813431396861987e-8 - 7.1009964899811585443e-9i)}, + {(-68.265560854933639234 - 158.76889543119182235i), (4.2905519757459755106e-10 - 6.6814496631469942224e-9i)}, + {(-98.442315213660151585 - 232.75891312381205012i), (5.4220302101503437422e-11 - 1.4653984499754360942e-9i)}, + {(43.318321274101208473 - 226.88087216217866171i), (-1.5504288454888489715e-9 + 1.4332179799379980947e-9i)}, + {(63.629834618483641862 - 71.184387626866538312i), (7.1126945010378480873e-8 + 1.7367781612818454265e-8i)}, + {(-125.43511060359617204 - 18.192880153059128645i), (-1.9221302083905919924e-8 + 1.2425311568019196226e-8i)}, + {(130.76855341490042406 + 135.98738975712686283i), (4.7534657835117997827e-9 - 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(-1.0646737193472391382e-9 + 2.1977420916662513533e-8i)}, + {(-84.509243912933783349 - 19.477999293753899934i), (-6.4389933982204282806e-8 + 8.1293744182097800911e-8i)}, + {(45.693208859072683481 - 205.20027335817508174i), (-1.9917059460319048891e-9 + 2.3470841201473037811e-9i)}, + {(89.301860293449777828 - 120.82436160711364437i), (9.7530029511162800678e-9 + 6.7632289926992014602e-9i)}, + {(45.373365543477447659 + 97.904577352840590265i), (6.5909469158266167666e-9 - 4.4110440944715066993e-8i)}, +}; + +const std::vector gamma_5_c = { + {(115.57609680702209687 - 46.229512195544998576i), (-2.7216297035800724812e-10 + 7.7152451873154635784e-10i)}, + {(-86.868954415374588507 - 142.7911850226261663i), (-7.0436116133822777029e-11 - 1.6844353946421119707e-10i)}, + {(-141.23058138214864243 - 204.93052367711760553i), (-2.8981067918282203546e-12 - 2.482123833791823271e-11i)}, + {(30.981732763262314734 + 140.71608327767904711i), (3.3964530409679454414e-10 - 1.8738668397078569701e-10i)}, + {(202.96841664160359642 - 75.919871023302718527i), (-1.1223136715697670523e-11 + 4.9510632309374068271e-11i)}, + {(51.610641516579661925 - 24.189557063237458578i), (-2.4757099732328426864e-8 + 3.3312897510676692145e-8i)}, + {(80.049044151021192306 - 95.987090387630331634i), (-2.496739555025274386e-10 - 7.5692562849186596837e-10i)}, + {(-31.134126836043268582 + 46.834190866381938179i), (-7.08115760058573449e-9 + 4.102107817368629512e-8i)}, + {(-3.0735676287015416541 - 35.660875643800615364i), (-1.9462577311188107043e-7 + 3.5662021006028676984e-7i)}, + {(-24.273890854215832036 + 54.059944320057219613i), (-2.703797177376109768e-8 + 1.7637586251778339195e-8i)}, + {(104.81608664087127636 - 58.405133182494161304i), (-8.1667948617807920803e-10 + 5.4640903546875221091e-10i)}, + {(-33.465333453989025259 + 13.664689017276105076i), (1.2196272364549656443e-7 - 3.4363402611983875755e-7i)}, + {(-1.3441194715546924687 - 282.85235346611011664i), (-4.3200800539003256535e-13 + 1.3247749266366148831e-11i)}, + {(92.55740093183128181 + 132.05388715453631221i), (2.1635737712011771536e-11 + 2.2098423547004726142e-10i)}, + {(73.505381273471385839 - 49.496617871477937456i), (-4.4360944411946916444e-9 + 7.2842347330890794861e-10i)}, + {(-28.061572998851264771 + 94.057311668797424886i), (-2.6031394526715568034e-9 - 2.5241145497892388114e-10i)}, + {(-149.59800695976980478 - 76.408205028573590312i), (1.2496835210039210738e-10 + 1.2544456781181657438e-10i)}, + {(-102.14438341870324223 - 26.135123323836019438i), (-5.7349743875458922391e-10 + 1.7062786806458979206e-9i)}, + {(-6.6724094066166808048 - 29.718077447123853574i), (-8.3358304110060035321e-7 + 3.3884205261092099221e-7i)}, + {(-25.39243334807805752 - 130.5130003186291674i), (-4.7772722973776971427e-10 + 3.2092870476393792285e-10i)}, + {(-111.64322625671607625 - 60.528598742039818603i), (5.6103809706457658377e-10 + 4.4173626436568396625e-10i)}, + {(88.851357268058947625 + 31.205424393666014282i), (-4.1987622708056814284e-10 - 3.295815511156676382e-9i)}, + {(60.245752060292723229 + 44.12782151034411271i), (-1.0607915877792165359e-8 + 4.1386678310026271609e-10i)}, + {(163.6875147109174975 + 22.694126635254935564i), (1.523462107848964763e-10 - 1.2596625158470654207e-10i)}, + {(4.8169754558768342889 + 61.914218954223386504i), (8.8928183033072390899e-9 - 2.4505882662210937166e-8i)}, + {(108.11004380188478535 - 21.408860227080019456i), (8.3832407853772327984e-10 + 1.2550052172478888294e-9i)}, + {(77.423025605093030777 - 54.412800201857102422i), (-3.2250733816906625344e-9 + 2.0493831043057174164e-10i)}, + {(-109.83832550290453867 - 129.79621938091298716i), (6.2225792322085029743e-11 - 1.5526189371766393129e-10i)}, + {(-85.907098641743289136 - 140.90047403838534024i), (-7.4154464382733822029e-11 - 1.7987391535709667485e-10i)}, + {(107.34354927293226467 + 33.424331015018175606i), (7.4896757988316652723e-11 - 1.3627195639912330295e-9i)}, + {(-131.41797912303135831 + 26.465517632692787231i), (-2.9866861532583316053e-10 - 4.5501134901127181988e-10i)}, + {(-203.68366820144396456 + 21.503814029732527757i), (-5.6935975595206917476e-11 - 3.2951092237857572227e-11i)}, + {(-115.90124424579273921 + 63.830120969520379504i), (4.6903373929656653309e-10 - 3.4466286969122174059e-10i)}, + {(-141.16698630415589832 + 31.456162772493538426i), (-1.7164500978517199081e-10 - 3.3104727798349164858e-10i)}, + {(43.852979399381304404 + 233.71121618731683611i), (2.5108247587926269021e-11 - 1.923527332501831489e-11i)}, + {(-87.816921836355561481 + 98.759719510471981607i), (2.8528765877420727767e-10 + 5.1405651728641630742e-10i)}, + {(-161.75989756253818541 - 79.08956701526031452i), (8.0374301832697336036e-11 + 9.6034150763761419672e-11i)}, + {(23.247540786165178162 + 80.242333080342760354i), (5.8410195085778402091e-9 - 1.1203912145921021747e-9i)}, + {(37.829803538862996959 + 40.391591009044184091i), (-2.6490003832747645872e-8 + 3.9654421091530060118e-8i)}, + {(-104.82024100234745845 + 98.250154699408426495i), (3.1695379640747720452e-10 + 2.2235431285307629756e-10i)}, + {(-40.79270462075383108 - 33.6605510490657025i), (5.3782869561306149313e-8 - 1.5325144692422795352e-8i)}, + {(-163.88247703277951928 - 217.17777044774297224i), (1.5655637473280476773e-12 - 1.5932934135300964182e-11i)}, + {(6.913525591766192413 + 23.675302999484415523i), (2.6256613066289030577e-6 - 6.6209793690417379982e-7i)}, + {(-65.606992823334380205 + 85.188254976267359098i), (2.5940483357142086046e-10 + 1.6258439162201224322e-9i)}, + {(51.293212789930841211 + 99.021897960884572854i), (9.8049433312967677401e-10 + 1.0076419929472695657e-9i)}, + {(-3.5128139132467977035 + 4.5415390340377586043i), (0.00143964929074019048 + 0.0025694933204425418095i)}, + {(-53.212532744361304538 - 20.190728661688780221i), (8.6707453778102549767e-9 + 3.7578793810214389154e-8i)}, + {(200.99661382058070558 + 82.408456307261047868i), (-1.8553547193867007319e-11 - 4.6581456738194069407e-11i)}, + {(-35.976456951985483101 + 91.268638862060797123i), (-2.4751997678323193373e-9 + 8.4881490272406540178e-10i)}, + {(-10.549711599748503588 - 91.619182695480532175i), (-2.0255247461793099457e-9 + 2.9596830884571801224e-9i)}, + {(119.80816526189539672 - 34.553301566933797062i), (1.3038281359982855584e-10 + 8.0113324865612557287e-10i)}, + {(-30.72677905044704616 - 99.986072837028544313i), (-1.9001815071019593374e-9 + 1.0874579552475034777e-10i)}, + {(12.655980763787248122 - 10.292019469131826526i), (-0.000021840440564836535996 - 8.3788219046432232479e-6i)}, + {(139.51650797183975783 + 116.4147011580185449i), (-1.1526906176084415302e-10 + 4.1305543463067956114e-11i)}, + {(66.336571816849414063 + 2.6503972415437040411i), (1.8929802308875012313e-8 - 3.8600152846013010756e-9i)}, + {(31.808298038645617112 + 75.090616357557806282i), (6.191326958014016757e-9 + 2.6502531266870946099e-9i)}, + {(27.770857726950872291 - 162.56009046587217881i), (1.4570252979821329456e-10 + 1.3296643258949966228e-10i)}, + {(203.66896137128316013 + 145.14700285506495447i), (-2.4708880890280012002e-11 - 9.8728326994275615236e-13i)}, + {(-42.495521550471373473 + 69.06864592127232072i), (-2.3557675672930189311e-9 + 6.3081340636747264031e-9i)}, + {(90.723313433196565825 - 89.500251304829617993i), (-5.2218371582501955705e-10 - 5.0150923042964540705e-10i)}, + {(-118.42927056024312549 - 41.800470431411845595i), (8.956084235607077104e-11 + 7.4849487342645615105e-10i)}, + {(-222.12811001940724509 + 90.702617581996335616i), (1.0631458663407833604e-11 - 2.7938476685778256699e-11i)}, + {(-11.937273755569940192 - 99.969901542935573957i), (-1.3420658403946945814e-9 + 1.884258259975948864e-9i)}, + {(-13.545773788539236193 + 181.15300386193734994i), (-4.573100007742227863e-11 - 1.1223817767771630658e-10i)}, + {(-110.31846755971201901 - 72.102647301126765456i), (5.7452591333967922893e-10 + 1.5132508015303336273e-10i)}, + {(-24.540174423080756583 + 22.262362060681919473i), (5.0115038872219764394e-7 + 2.6795657638026463442e-7i)}, + {(-67.383910905110809608 + 241.33092273949063156i), (-2.3754819981749997298e-11 - 4.8095190236990300133e-12i)}, + {(125.140791991240377 - 106.73676121423395102i), (-1.8583461882043258591e-10 - 7.8399025034369685399e-11i)}, + {(190.92690753312436414 + 98.057942455356439382i), (-3.8440326080545541815e-11 - 3.6828320398025794689e-11i)}, + {(27.537432562998031216 - 8.5884077946530918979i), (4.4147417662012379535e-8 + 1.3038094682486826816e-6i)}, + {(39.900008471390023601 + 65.649750775220738319i), (3.8750362846595210706e-9 + 8.2581133165007559721e-9i)}, + {(81.360809240657516739 - 270.07921863543447216i), (1.3384830479053037074e-11 + 1.5633310069449411091e-12i)}, + {(-63.692453596367172963 - 144.24977988085007041i), (-2.1194782342198041782e-10 - 1.2211973326718363695e-10i)}, + {(66.979186081878708592 - 56.447207363811912728i), (-4.4211073967133639401e-9 - 1.7560629490419095176e-9i)}, + {(-32.481881547254531029 - 59.309064506269933759i), (-9.4684149096520304843e-9 - 1.3728222524832198922e-8i)}, + {(3.5154289999511716402 + 74.593541874934217617i), (2.077262253859382182e-9 - 1.0141568415867774741e-8i)}, + {(-32.781364957426674778 + 165.47699643708244821i), (-1.4668573773355010116e-10 - 9.5768730771463832818e-11i)}, + {(156.10303447130326049 + 69.305545331203632031i), (-8.3772891963355511973e-11 - 1.448707894477684749e-10i)}, + {(0.61330549731263594992 + 9.6095428271272762544i), (0.000017584510974329051278 - 0.00029629568675206100241i)}, + {(-153.83456191784011935 + 122.19941581675817588i), (7.9453258999849719785e-11 + 1.6679767678105775618e-11i)}, + {(34.457570285342811189 + 98.328737220615934689i), (1.9619140514808145442e-9 + 1.8079859449524677293e-10i)}, + {(35.797951979475165274 - 13.721247162845548573i), (-8.5786868951107035241e-8 + 2.9569621595904200539e-7i)}, + {(-28.823174857319340703 + 75.280546136017377989i), (-6.6897609800691523901e-9 + 1.9710131291948603234e-9i)}, + {(119.37476250903384312 + 240.45539793423719743i), (1.2938060148624073091e-11 + 1.1460175746156550233e-11i)}, + {(150.574574432088923 - 47.797315847802316569i), (7.2192585012595436574e-12 + 2.4749976604049576971e-10i)}, + {(6.0621175917711811465 - 97.860187618812702226i), (7.4309693978940536315e-10 + 2.5467930319504378131e-9i)}, + {(118.36167320830980998 + 7.6089897565165127702i), (9.9044542083640046602e-10 - 3.3079108236623157318e-10i)}, + {(-136.67538172089800241 + 83.186435491040725765i), (2.065812273037131038e-10 - 9.1261115800973327825e-11i)}, + {(-24.258432255857083959 - 13.289524421379026009i), (1.0644990593917048914e-6 + 8.6042125906678345137e-7i)}, + {(25.069664655813184595 - 93.611049734981349957i), (2.7108985844350195323e-9 + 8.0115177808275461178e-10i)}, + {(11.464752942481336362 - 48.584931717154525188i), (7.0167076695701068122e-8 + 3.4830765900593981027e-8i)}, + {(74.858127684897652898 - 50.373142865360442499i), (-4.0508932176711512891e-9 + 6.7293825099048458917e-10i)}, + {(-11.185140584287598386 - 12.336305768593401666i), (0.000010312794124369343673 - 0.000013447715039634634392i)}, + {(-33.916497805782675812 + 130.27284818328271854i), (-5.1945535932353520295e-10 - 1.4899429593392219449e-10i)}, + {(-70.038523784161668573 + 42.518214538545024084i), (5.7569023014527799489e-9 - 2.6367661969409837449e-9i)}, + {(-0.75579196958867866929 + 44.477680016922739981i), (-1.9373399111336156923e-8 - 1.3632246097421883114e-7i)}, + {(40.425973413489792563 + 67.460177177597529408i), (3.6680671608538843756e-9 + 7.2317239568691025472e-9i)}, + {(15.460581080519503416 - 75.05158408768619438i), (7.6146908940555887161e-9 + 5.0645952838578112794e-9i)}, + {(12.490017912726749216 - 109.08055106227291731i), (7.850331827831446354e-10 + 1.2878673725087073682e-9i)}, + {(112.74134340268075505 - 140.18219381389616274i), (-2.9824921459747615219e-11 - 1.2499562746871537731e-10i)}, + {(-4.6571969759031954794 + 54.257386509034965627i), (-2.27848527285385612e-8 - 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18.109024405578288963i), (1.8119833678318360041e-10 - 1.1345010483947830844e-10i)}, + {(40.263761553472889432 - 62.611508341521158627i), (3.2851075715390797229e-9 - 1.0175323656784753654e-8i)}, + {(-248.14736281881442892 - 98.447565808110681473i), (5.4221068419738814659e-12 + 1.6687112142979460857e-11i)}, + {(-3.7373904724171986835 + 214.64598712383863699i), (-5.1853112618835640121e-12 - 5.2368181715634214095e-11i)}, + {(-44.514893690102013579 + 151.15535619416530722i), (-2.4407852569852584535e-10 - 3.0312149316256218525e-11i)}, + {(31.571630709946500559 - 36.083415200624266106i), (-3.9392170149284905769e-8 - 8.9776751247561214898e-8i)}, + {(41.025313762187458622 + 94.576926348879922557i), (1.8708759338319107972e-9 + 9.1160866772925706445e-10i)}, + {(-84.546575823163507835 - 10.897929895082141272i), (-4.1620314401568455962e-9 + 3.0806620430190293015e-9i)}, + {(-109.27044902179510188 - 10.620328028918970986i), (-1.3032858087409120997e-9 + 6.822047379625268719e-10i)}, +}; + +const std::vector gamma_6_c = { + {(110.00829016856795306 + 108.84004115557112868i), (1.6330747225268511161e-13 - 8.8569819213022223482e-12i)}, + {(-135.91268273942191058 - 82.976410935945352776i), (7.1742456559683807129e-12 - 9.9080052342362142813e-13i)}, + {(-65.920356963035828812 - 156.8419642776384535i), (-3.6359866526565953729e-12 + 3.3068334619015331465e-12i)}, + {(-28.089855858079822326 - 15.730636065641856902i), (9.8527464197772857719e-8 + 1.2372331633750010942e-8i)}, + {(-48.640474581116414754 + 130.77081247761447003i), (-8.9285361722047960133e-12 - 1.3452102253127729526e-11i)}, + {(114.26807799821179401 - 48.326959583439723644i), (2.5034949026118703125e-11 - 2.2473945654573958902e-11i)}, + {(-24.490593169708102295 + 19.865531777716093131i), (7.1622802673322876482e-8 + 8.7804559409487979605e-8i)}, + {(-138.08109438803518287 + 35.78775797788431845i), (-7.6033288629002146839e-13 - 1.3936855679029153927e-11i)}, + {(50.037968385336959898 - 36.241839813581421481i), (1.7893293502379613155e-9 + 1.3537123903748190779e-9i)}, + {(-108.12645672815396836 + 59.052402517225367262i), (3.3191133406615692494e-11 - 5.1542814819091627537e-12i)}, + {(131.16154366439204182 - 84.593100221927088i), (8.0459028957635871569e-12 + 2.5392666704980158409e-12i)}, + {(-230.54223987322416178 - 82.22689725544934447i), (2.550651705576943085e-13 + 4.8911150937422672537e-13i)}, + {(69.706307597028299483 + 85.997745072910063868i), (-3.9955461424526597314e-11 - 5.2944504609595368876e-11i)}, + {(-70.068947203295380177 + 177.30306071503466114i), (-1.6045907526966776215e-12 - 1.8973573870692877131e-12i)}, + {(51.579836684350823361 - 22.44952159659138502i), (3.146966714286700949e-9 - 2.4297228010211100306e-9i)}, + {(77.400472527778362064 - 115.67921339377349454i), (-1.5521465313882414915e-11 + 6.1749298034034811885e-12i)}, + {(-105.91765976344839828 - 83.424234773935722842i), (1.2992538120679403843e-11 - 1.4715861119518222084e-11i)}, + {(10.232330875014779892 - 149.40997104882191593i), (9.8507267890873775034e-12 - 4.0525218763425319608e-12i)}, + {(12.091286878999532917 - 101.32826131355710686i), (8.2691910364992041338e-11 - 6.7339892007799692071e-11i)}, + {(-21.495823523882510386 - 24.845388620889902853i), (-3.1920997405987180516e-8 - 8.4044857123867523941e-8i)}, + {(-80.089955770221067155 - 49.744152451996384912i), (1.6371799558022559881e-10 - 2.9161938205238321772e-11i)}, + {(-28.647282084680270486 - 48.501820298321433711i), (-3.6358513258609957773e-9 - 3.8540455611715002444e-10i)}, + {(27.912530399949879722 - 74.259144444264052254i), (-2.5550129297811216749e-10 - 4.156494308347872115e-10i)}, + {(-74.198113270098119187 - 42.770676608230992599i), (2.9493324266787589551e-10 + 6.4046990989572259974e-12i)}, + {(29.715633485857779306 + 32.083221877706883163i), (-4.9606509760000743144e-9 - 1.7280272342746300856e-8i)}, + {(49.78164422675553169 + 87.176217636271204015i), (-1.1881957610253288585e-10 + 6.4595844928364151583e-12i)}, + {(29.497595346389232418 + 76.002297352189813751i), (-2.3943682870260132527e-10 + 3.3801926343791637688e-10i)}, + {(-62.037760531138715692 - 109.84147424194257781i), (-2.941096086068532751e-11 + 1.0607729334869314528e-12i)}, + {(-87.42845261198645801 - 91.77062021500213973i), (-3.6388331893099943463e-12 - 2.823750719793352805e-11i)}, + {(-192.76738030599790363 - 12.801064403523520596i), (-2.0959233756263342016e-12 + 8.7830662422774924007e-13i)}, + {(85.505593950634491307 - 138.98920418294952128i), (-6.3426166146730409831e-12 + 9.7086626980168598217e-13i)}, + {(-182.1464541652603657 + 94.374289596331735197i), (1.5273085375523137674e-12 - 4.3934108602133755696e-13i)}, + {(57.819462848253564857 - 173.93947979620921274i), (-1.0582896593628500096e-12 - 2.9992429576661577873e-12i)}, + {(85.883278903669548754 + 291.32149703156574105i), (-2.1370134281557510439e-14 + 1.5181729341048212338e-13i)}, + {(6.1882900865983323513 - 165.74893271977231279i), (5.6455320849806219909e-12 - 1.1787473728824894246e-12i)}, + {(-2.9403107135619048762 - 147.68981701713119037i), (1.1432772692091021532e-11 + 1.6081366869839135724e-12i)}, + {(-24.277620253688215968 - 99.359964391051661892i), (1.0845499138665739912e-11 + 1.0351508086588153545e-10i)}, + {(6.7318185393483744861 - 71.75426043222691419i), (7.4630313763311421049e-10 - 4.2715669582108539e-10i)}, + {(97.827292500748001203 - 165.36045829729545176i), (-2.4016368703679619088e-12 + 1.2093893643994669424e-13i)}, + {(27.788211428850505769 + 107.16479176722972966i), (4.8972675140658839702e-12 + 6.544204111826895706e-11i)}, + {(-50.756135941297365832 + 68.453432838373558411i), (-2.3170666314902024489e-10 + 2.0115412491161843464e-10i)}, + {(81.369043329751747251 - 159.67560812806539161i), (-3.4544065397267363222e-12 - 1.1783709202126102998e-12i)}, + {(126.6470621937634462 - 107.2956855173477777i), (2.7045027321960549067e-12 + 5.1503156098758701797e-12i)}, + {(-69.851787341894691963 + 67.406537529483429694i), (1.7967308576703570486e-11 + 1.3911467181712740831e-10i)}, + {(-36.899505336729006899 - 93.038460875399337624i), (-7.8077175116303165554e-11 + 8.8556671500249844284e-11i)}, + {(11.492398521152294322 - 48.370727848549293526i), (1.8355626834196320302e-9 - 7.8486405346699957821e-9i)}, + {(67.799407815845782466 - 263.1211576023397356i), (2.0423099840309646954e-14 - 2.9831677322907814298e-13i)}, + {(-108.6141522808501918 + 117.10143108175554971i), (-1.4995942566876905326e-12 + 6.9776651779069478771e-12i)}, + {(-38.120808198635522501 - 188.99833999513055005i), (8.2337937570279273633e-13 + 2.17850373851441524e-12i)}, + {(104.44438815893224159 - 74.825515952126664843i), (2.2409886135166089845e-11 + 1.5393864507458916364e-11i)}, + {(28.117521017333974243 + 163.09369646070797444i), (3.133064321096512125e-12 + 4.9497738521615909843e-12i)}, + {(-84.019282367008457868 + 42.054127549512784867i), (1.5794395985452592774e-10 - 6.1541807253134732908e-11i)}, + {(-37.458446015790819672 - 112.98454620381161817i), (-1.5290908757535734132e-11 + 3.8964885223919384308e-11i)}, + {(-124.39795664840906397 + 16.614344114388789109i), (-2.1033347983118185073e-11 - 2.1374941752260546479e-11i)}, + {(57.753946295654024823 - 99.848308715439003436i), (-5.1608495538949076156e-11 - 9.1102172184273831423e-13i)}, + {(-12.801734378692147587 + 7.9671852826231068789i), (8.571409251552456485e-6 + 7.7299988739205381895e-7i)}, + {(-99.522822113892488005 - 6.9556647859050579896i), (-1.0798965667865126228e-10 + 4.774154734757935727e-11i)}, + {(5.3431536002127089091 + 123.42877409188237436i), (3.285419191987487019e-11 + 7.8771531638091898445e-12i)}, + {(106.51107366836059498 + 4.250149180874554844i), (-8.170356724467587361e-11 + 2.0029575651052887703e-11i)}, + {(-53.043975021762548749 + 154.27623947834555906i), (-2.6583694860422898764e-12 - 5.7418909814459903524e-12i)}, + {(-163.0181339268600027 - 163.84749318341926028i), (-4.6827478667696400388e-15 - 7.7994441351980002794e-13i)}, + {(-132.08077261309335881 - 42.479246913840356115i), (4.7054089279310345552e-12 + 1.5793434059379379559e-11i)}, + {(11.813890149328033274 + 15.712525045870368245i), (-1.8732257210899397997e-6 - 1.3014443025094320055e-6i)}, + {(35.630128260142477359 + 11.210035855795757342i), (1.3257326313595296346e-8 + 4.5796785368415607976e-8i)}, + {(-107.8908900868438252 + 49.144252574058825189i), (3.5145527272656481035e-11 - 2.3411293216069634457e-11i)}, + {(-141.73732828385320204 - 96.060547793253775239i), (4.2813194469039367417e-12 - 1.9237897627760239595e-12i)}, + {(43.502664951326622145 - 158.9438824128481258i), (-8.7889563649302905304e-14 - 6.0208239065790767419e-12i)}, + {(-39.590641444993657672 + 134.42166604580427247i), (-2.6392621980367626096e-12 - 1.5530719773721718134e-11i)}, + {(-125.30511865035700225 - 69.846380956079357816i), (1.3449349225570233794e-11 + 1.3593051326152502994e-12i)}, + {(37.794108908919419321 - 222.72706294084278511i), (4.9231121493391174671e-13 - 7.5908563223190796933e-13i)}, + {(-18.636895873040643323 - 39.867051988251013483i), (-1.4415804563644074127e-8 + 7.0650211319615202067e-9i)}, + {(-63.000218812322970052 - 64.096486772203419946i), (-6.1881164377983549734e-12 - 2.2235082679048978714e-10i)}, + {(-33.849760915319635046 - 111.40730046692975463i), (-1.0605820092759277937e-11 + 4.6608331182943969417e-11i)}, + {(58.568020180426735521 + 63.155262497748701378i), (-7.4863496493766430953e-11 - 2.9147325586612774071e-10i)}, + {(3.1259194260365203988 + 42.794618455560055281i), (1.8042418754962035475e-8 + 6.9528062483790930051e-9i)}, + {(0.10698904396331232469 + 117.56877070733710866i), (4.5434153860428709085e-11 - 9.1142583290679157462e-13i)}, + {(-103.50554591384195646 + 20.837991608965118928i), (-3.1591966120060226943e-11 - 7.8088365011494041293e-11i)}, + {(-19.117835740246885479 - 55.117601770923585036i), (-1.3855972146294153864e-9 + 2.6537204904328629159e-9i)}, + {(-65.600858522038322462 - 28.707406768176202405i), (6.6407131983781164719e-10 + 5.4089204127722235872e-10i)}, + {(-146.29432297846170741 - 15.799620441833518214i), (-9.2692190067931599809e-12 + 6.948892656009179378e-12i)}, + {(-113.92032460776049163 + 66.405349010517326747i), (2.2381083115675724863e-11 + 3.0112913697517077126e-13i)}, + {(86.79752773672340993 - 169.14003793424961941i), (-2.4375101984618001918e-12 - 7.8306927379563936649e-13i)}, + {(236.78661541068001384 - 132.10584180535894916i), (3.0385667004542696391e-13 - 2.5227470851609367302e-14i)}, + {(-68.651100968277845027 - 55.216279716307511194i), (1.5512182804021346148e-10 - 1.9591902257916231715e-10i)}, + {(102.40659978114582884 - 26.367059893177792418i), (-4.5635057137688843142e-12 - 8.8084423297965909854e-11i)}, + {(111.47804369294831872 + 40.402710639401675508i), (2.2122032590589861564e-11 + 3.8281376065151726121e-11i)}, + {(22.664036782475378118 + 30.735966973186123141i), (-3.3276791326249520038e-8 - 2.316327501981776054e-8i)}, + {(118.64193548487030228 - 60.076075592505496559i), (2.1018101484900242749e-11 - 6.9439554337912363859e-12i)}, + {(196.79859757517098728 + 53.892707552743722488i), (6.2113473082320487375e-14 + 1.6853422051489967829e-12i)}, + {(27.031104492160306307 + 100.82429562455736516i), (2.5103879132180337429e-12 + 9.3425215074091928971e-11i)}, + {(18.709491700963912564 + 59.370386662397336863i), (-4.4669163775761293203e-10 + 2.0448733888248747516e-9i)}, + {(-117.5224788469385544 + 185.83793283145590181i), (-1.0205009351123739383e-12 + 2.6421302376173790768e-13i)}, + {(47.349880238912007258 - 203.21806561328600083i), (3.0591485635429829909e-13 - 1.4262204355719340862e-12i)}, + {(-121.93753356094256901 - 7.3602497371847190877i), (-3.2969837882975405242e-11 + 1.2422319151335567349e-11i)}, + {(-74.270662215873954892 + 67.435512772328380038i), (3.5062143341803574942e-11 + 1.0968963521732817444e-10i)}, + {(-178.78402008711918825 + 13.391637967697011646i), (-3.2038745433414411941e-12 - 1.5371182107663982605e-12i)}, + 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53.677580320647585665i), (-1.2923090279302918244e-9 + 3.4215669790160661723e-9i)}, + {(-53.030054105991034419 + 29.654034765307208943i), (2.2714445778248130821e-9 - 2.4322501940691588625e-10i)}, + {(84.68932061597701022 - 67.902779161881170467i), (4.4771343693567263018e-11 + 6.0106527090801261963e-11i)}, + {(-24.640052637857010609 - 56.823877656970687156i), (-1.6702504101035237869e-9 + 1.2489281747149738116e-9i)}, + {(64.49451992685209234 + 64.987459273920961778i), (-9.5812506711288736737e-12 - 2.082389569698476981e-10i)}, + {(3.2991578348331787041 + 170.08212169864418684i), (4.9292648600261494888e-12 + 4.882994885947144268e-13i)}, + {(-10.038286828536163497 + 52.954882478364773135i), (1.8510604015837124933e-9 - 4.4785384018246678196e-9i)}, + {(-135.83253795135200903 + 96.723270911130555305i), (4.6584192300785692897e-12 + 2.9248266996494211077e-12i)}, + {(135.30437087466935964 + 116.47369078890430671i), (1.5884571281604966071e-12 - 3.40071127929387021e-12i)}, + {(79.739719884637764835 + 40.365857033479350946i), (2.3066186053459496097e-10 + 7.5127121636390126788e-11i)}, + {(17.584130275664278997 + 183.66247278223895023i), (2.5870992341785827879e-12 + 1.6094770780852292467e-12i)}, + {(-133.84935986748996584 + 48.549331689155174274i), (6.889718819722978642e-12 - 1.2324796761548668281e-11i)}, + {(-57.620846247790659334 - 42.769160467625425781i), (6.6901004016713052031e-10 - 5.2400863378400402157e-10i)}, + {(95.819710814147896372 + 62.595481699438515477i), (5.1356983011778329007e-11 - 1.8436927108677929007e-11i)}, + {(-75.93855956358109438 + 101.8089488277477983i), (-2.1140932051613671896e-11 + 1.8639640373743909826e-11i)}, + {(-133.40438081139186011 + 58.796321949623056469i), (9.6957931787854628695e-12 - 7.5121946736976828802e-12i)}, + {(61.098237511859942117 + 30.671269552452791629i), (1.1560838454385879819e-9 + 3.9677162754758948697e-10i)}, + {(76.159474499370347189 - 23.575444277594876041i), (1.1580693677084171647e-10 - 4.7031399168913599358e-10i)}, + {(8.1690040174319822341 + 209.57173234673879847i), (1.3769386992355559117e-12 + 3.0713993753698155302e-13i)}, + {(109.49755694217645896 - 77.849836235573405929i), (1.7385235051574785394e-11 + 1.1380551302335317018e-11i)}, + {(92.486909727751836385 + 119.4336188291938754i), (-7.1503793538254882912e-12 - 7.3077183980839053503e-12i)}, + {(-120.29875195091386786 + 79.418675276698138532i), (1.2357238680016192471e-11 + 4.4811120910933110223e-12i)}, + {(13.729283611369744733 + 6.1038847031107161811i), (0.000010611861926131334308 + 6.5661511384621169455e-6i)}, + {(-77.831299766592962897 + 55.997163604407894866i), (1.2576634712911230855e-10 + 8.2770747740349409004e-11i)}, + {(41.733230003853556411 - 74.883446258733769696i), (-3.0526971241914871254e-10 - 3.7249059769304749891e-11i)}, + {(-48.136958400144116865 + 53.414415399029365972i), (-2.3362048030186796722e-10 + 8.1138048931582315265e-10i)}, + {(-93.581946469108686415 - 67.910273997101413102i), (4.0314627336040543534e-11 - 2.8153238583482233612e-11i)}, + {(20.367637301547194539 - 185.10835334786813178i), (2.3091552338162544435e-12 - 1.7247775956790773496e-12i)}, + {(-55.666667609920104098 - 50.250813852562636441i), (2.1438043032130452149e-10 - 6.1879089188625016851e-10i)}, + {(-174.97215601856657941 - 37.885315631526779612i), (-1.0423537733359986215e-12 + 3.4306420954998664646e-12i)}, + {(-102.35283703045440973 - 47.209062216273906643i), (4.8396967228322137005e-11 + 3.0331440986548490684e-11i)}, + {(-129.22615690937232102 - 50.039096221691750088i), (9.8904868759048305864e-12 + 1.3339497396522251564e-11i)}, + {(12.740663869991777801 + 20.22990389619068452i), (-6.8221643827901532606e-7 - 8.64546664070692064e-8i)}, + {(-131.79137321502952318 + 124.37020985694522324i), (6.1651746699067381146e-13 + 3.2913639997428095441e-12i)}, + {(-112.74341560283151864 - 109.61601901685315852i), (7.6390173301033889044e-13 - 7.7922344610907992349e-12i)}, + {(-16.827379720976907151 - 184.83844846888069924i), (2.4822032466029468614e-12 + 1.5590901650476307279e-12i)}, + {(-93.382136922741082685 - 72.974368698815780476i), (2.887636508787036251e-11 - 3.1118396553811640175e-11i)}, + {(11.540714526065579904 - 118.69088281652717853i), (3.5518581676837258672e-11 - 2.2097809857418385793e-11i)}, + {(66.803313601291051782 + 60.306481030169358348i), (6.4906763553226146177e-11 - 2.2220791356844570769e-10i)}, + {(-76.630193071773774705 + 8.2491053229414674774i), (-4.4195103823172725672e-10 - 3.2851017593160812184e-10i)}, + {(-93.72798239358940009 - 31.182560458795560265i), (4.2632107364679304537e-11 + 1.1803697198539061752e-10i)}, + {(-223.22905761149067416 - 34.353844424544767833i), (-5.446612955667382972e-13 + 7.0667769603238261109e-13i)}, + {(-149.43774353654376341 - 48.013659953541690584i), (2.2426065489879795596e-12 + 7.5537135675967995293e-12i)}, + {(-29.839350037024175322 + 62.781581547043515457i), (-9.44692205111613312e-10 - 4.4514739799460762832e-10i)}, + {(-3.1182256036866018434 - 26.794018138526030981i), (2.1318952812304241496e-7 + 2.2215828729165594835e-7i)}, + {(-17.900438941474828169 - 39.676675717020536638i), (-1.4754762451550680738e-8 + 8.7538291399307067163e-9i)}, + {(-41.26596151686467806 + 22.066344259948277085i), (1.0522701851163174178e-8 - 2.4183742745565343207e-9i)}, + {(21.316778328041181112 - 174.31226418771805697i), (3.1008222362481402848e-12 - 2.6823836015876122175e-12i)}, + {(-103.5287778805948733 - 18.326081999918901744i), (-4.3261591240900587108e-11 + 7.4757759579679346667e-11i)}, + {(170.64514524789439065 + 60.103298639988786078i), (1.5634097051873073059e-12 + 3.1041981850476746464e-12i)}, + {(98.839611209044335283 + 48.508854522438596746i), (6.3786563683892942509e-11 + 2.6381762782554738328e-11i)}, + {(3.6285389911689556186 + 69.111456219544947999i), (1.054800578522373374e-9 + 2.9357861077454146982e-10i)}, + {(60.628040646590399376 + 199.6755931976147167i), (-2.6726006946496587175e-13 + 1.4346559378848283572e-12i)}, + {(117.20799431607706254 - 25.262121989062407579i), (-1.1908022195472295692e-11 - 3.9637671973395543656e-11i)}, + {(-17.329894880509947086 - 16.212801888201074263i), (1.7383487109008828328e-7 - 5.8725232447163390797e-7i)}, + {(-157.43534729194152533 + 0.25234140583314290662i), (-55407.930010143849358 - 40779.821475009863207i)}, + {(112.84787607799825082 - 150.6340950256593203i), (-2.0783034298663533217e-12 + 1.7627453985935965704e-12i)}, + {(-63.528110653894145798 + 56.454350440694987867i), (1.1415297456321589154e-10 + 2.8838229653202651517e-10i)}, + {(97.761802252158176429 - 42.576632329046411485i), (6.5865485829200948518e-11 - 5.1751612555814961069e-11i)}, + {(-140.45107443876793241 - 52.598031379459172285i), (5.6029447851369407699e-12 + 8.7007258308429512478e-12i)}, + {(-75.219326514730667554 + 26.528160649021316431i), (1.9602461686463818217e-10 - 4.0482340926264633741e-10i)}, + {(114.28727454728939961 - 103.2622327918497831i), (2.6139877860473147254e-12 + 8.7343014986988369291e-12i)}, + {(-121.48479229609334595 - 16.740433258031885089i), (-2.3535492914420268268e-11 + 2.5135491865007728716e-11i)}, + {(28.05133263271152444 - 146.71174011975523399i), (4.7857311579012089184e-12 - 9.7330184799943549694e-12i)}, + {(129.29528436854255347 - 139.85653840710801887i), (-6.2078819172613641846e-13 + 2.4635352186334976779e-12i)}, + {(-81.379092028264608416 - 131.32281314567617869i), (-8.5550842792447427226e-12 - 1.766022518005120447e-12i)}, + {(53.504673092976361204 + 63.033206547931442287i), (-1.9009511861288960765e-10 - 3.3432351631961822265e-10i)}, + {(60.756920491224740033 - 126.89975187954409819i), (-1.3838350028311797632e-11 - 7.2329718251287948787e-12i)}, + {(-37.058300359516103128 - 38.92198816796509675i), (-5.0884623914426310303e-10 - 4.7654875988772213409e-9i)}, + {(35.8390284941181676 - 102.68295940833650093i), (-2.9710258714983676363e-11 - 6.6878857769334139119e-11i)}, + {(-122.61420039329624387 + 9.6895902648149743186i), (-3.0138335035082778886e-11 - 1.5356105288788884912e-11i)}, + {(63.603208792145530026 + 117.28021489864362081i), (-2.1160924894392806239e-11 + 3.8452498669526671121e-12i)}, + {(-64.511649801285841477 + 137.34866715754691313i), (-8.6045009739369655744e-12 - 4.5786055827650399473e-12i)}, + {(-102.07293965080607734 + 76.228944286849468881i), (2.1191538251693905336e-11 + 1.7596967212530516318e-11i)}, + {(-13.241458266055646575 - 167.52559335564697562i), (4.6921188250252925537e-12 + 2.509154379693563925e-12i)}, + {(-36.366001794466221497 - 19.295187585942574771i), (2.2391975674246797165e-8 + 5.701684438033848791e-9i)}, + {(-116.26896439323120092 + 101.26840395213727675i), (3.6359219676556625126e-12 + 8.0144172148739826098e-12i)}, + {(176.20747957595369826 + 224.14125597521686473i), (-1.4881881265902634326e-13 - 1.6857377944263782087e-13i)}, + {(15.152961321528794159 - 64.901054157683560675i), (3.2665823437440163067e-10 - 1.3446159029944854187e-9i)}, + {(72.179463484541130924 + 60.700745796471743176i), (8.3261199438841667529e-11 - 1.5362636246442763489e-10i)}, + {(68.879174921510539775 + 127.32251694077743309i), (-1.29467861379734779e-11 + 2.4151080206597112973e-12i)}, + {(173.32189568962053272 + 104.82766704197297258i), (1.7447387625976278988e-12 - 2.2768467696473845273e-13i)}, + {(77.989876915497731602 + 4.4830336426559371787i), (-5.1593057193184428826e-10 + 1.8640162390441659616e-10i)}, + {(-29.440759243504967202 - 18.974064268192844196i), (5.8637102189156251509e-8 - 1.4736744582907207178e-8i)}, + {(-51.404844893237900294 - 49.278452834018942497i), (1.3874712942488305612e-10 - 8.8190889982690880534e-10i)}, + {(-73.169025940732026925 - 57.405384809997869411i), (1.2204013436059487281e-10 - 1.3341878844744754675e-10i)}, + {(38.338443797602245411 - 44.842428544816783642i), (-1.4270973768974273739e-9 + 2.5720691492985276059e-9i)}, + {(71.036421525343996564 + 5.9830041079980151864i), (-8.3304071612719812145e-10 + 4.6340707649674253174e-10i)}, + {(-139.89777010213242647 + 176.9964337415419493i), (-5.7365921505337584085e-13 + 6.96786537771864059e-13i)}, + {(-171.24245608304860866 - 13.537856072187997469i), (-4.0882503903666096543e-12 + 2.0868534060167050638e-12i)}, + {(67.563071422626890694 + 79.413746134144460598i), (-4.6000564395753305373e-11 - 8.3299154608595165051e-11i)}, + {(-138.54925683447808638 - 57.50293439768374526i), (7.2848393753709847787e-12 + 7.3358121272124731063e-12i)}, + {(96.126907726167260648 - 41.439961491634107915i), (7.2322942785475607924e-11 - 5.9469397736854425246e-11i)}, + {(105.1847028745204824 + 62.601709904884849323i), (3.6282318220942348931e-11 - 3.3474335023022181343e-12i)}, + {(-59.166410718672210578 - 58.999949526764105201i), (1.1667154917938551402e-11 - 3.4356815757529824653e-10i)}, + {(-88.860525328720967764 + 179.38378930560307367i), (-1.727824379879136863e-12 - 6.6727014150895065168e-13i)}, + {(126.91136087109786956 + 166.15513079737874591i), (-1.0496525040504604196e-12 - 9.9908810924486744122e-13i)}, + {(55.398779962669578936 + 56.128449617018482343i), (-3.3872999227108790662e-11 - 5.1119402279140420084e-10i)}, + {(296.76949933319167485 - 7.9906402327141456965i), (-1.7474102801014178494e-13 - 2.8519706382083041243e-14i)}, + {(14.333122797590178266 + 19.180841230172216427i), (-5.6275839042201402346e-7 - 3.9352139277359737416e-7i)}, + {(-5.7652685344120886413 + 69.385839487204449938i), (9.0026914612996888745e-10 - 5.4010793066543991011e-10i)}, + {(-60.801038511347293536 - 86.407590690604735073i), (-7.1871743389026038372e-11 - 4.5135795301163278983e-11i)}, + {(92.957203675623517825 + 72.67762217997713492i), (2.9751579870234110715e-11 - 3.4239062648245895284e-11i)}, + {(-99.454421556768309642 + 84.089538187696817317i), (1.1921175029148536808e-11 + 2.101354039614755369e-11i)}, + {(135.48914663322250362 - 47.233394103225485594i), (6.0835084274971598141e-12 - 1.2635989017167203831e-11i)}, + {(-196.98362107817726496 + 6.3932346874960552796i), (-1.8362981276700476246e-12 - 1.7675742621571976001e-12i)}, + {(-124.28336626538700216 - 6.7732156258555287209i), (-2.9975389273795597114e-11 + 1.0043240579572241497e-11i)}, +}; + +const std::vector gamma_7_c = { + {(114.18996928663671042 + 124.38374084968427269i), (1.662538673981549264e-13 + 8.471623053190111645e-14i)}, + {(32.995518838571328502 + 108.94684857172900649i), (-2.6304384198324788658e-12 - 1.2979488657747340183e-12i)}, + {(-20.661281036088922747 - 147.17540966976528694i), (3.7702442504222071691e-13 - 2.4226686461454985347e-13i)}, + {(-43.835924679575306584 + 89.45693915112144623i), (-5.7836174018748220857e-13 - 7.258693332534169776e-12i)}, + {(-68.188509627014099124 - 54.488113237884135742i), (3.3160235252709848088e-13 - 1.8074541851983115539e-11i)}, + {(80.876705611949390118 - 40.586874860848148217i), (-1.4871455913970159441e-11 - 1.9657330782149865934e-12i)}, + {(-88.460412368176477571 - 155.21101584318728328i), (-5.9035567499197633609e-14 + 1.07651182944095481e-13i)}, + {(12.391140567444983489 + 138.25275230647849867i), (-4.1079702740873477305e-13 + 5.9967034643664749556e-13i)}, + {(35.199512097480322836 - 33.99332498334013053i), (7.374949553273370318e-10 - 8.5378282046219354893e-10i)}, + {(-22.514547886767317664 + 40.517627541860868234i), (-6.9105650890335760399e-10 - 1.3427504694350393282e-9i)}, + {(138.87377248682838626 + 100.06792385139905832i), (-5.5048909007880446271e-14 + 1.6086929594945635719e-13i)}, + {(-74.298015795863122435 + 144.23065773630270314i), (-4.9611584645457631408e-14 - 2.3577225333875086379e-13i)}, + {(-91.491458493312336486 - 31.289555127314898186i), (5.8311835554368035381e-12 + 6.5941326310125458484e-12i)}, + {(22.191535033033872537 - 45.648219306642097592i), (-3.0500083839361927036e-11 + 8.5480178056406113291e-10i)}, + {(6.5357175950037982304 + 63.866920317129952878i), (-9.8739561219300829865e-11 + 1.2730870850597679212e-10i)}, + {(-24.183497597308196703 + 156.0480469233667975i), (2.6096052017583347388e-13 + 1.3341839738998448864e-13i)}, + {(-132.46530550057732967 - 27.093082096093400679i), (-1.3855031283443610804e-13 + 8.3835507971045598994e-13i)}, + {(-179.04964463844211764 + 11.250363247563978319i), (-1.0690169967563718351e-13 - 5.0070186148386610145e-14i)}, + {(-84.17308232976591853 - 145.47639876858158914i), (-9.8022232231150050814e-14 + 1.6051108872827951352e-13i)}, + {(-79.614490249542370748 + 24.686450416439353006i), (1.2320960209631963433e-11 - 2.1450819704625770793e-11i)}, + {(52.86026068991226623 - 92.423232267220711833i), (2.1230036813900884143e-12 + 4.2139289595310947004e-12i)}, + {(110.33689149399974383 + 58.016299701814531886i), (-1.5246395359302896738e-12 + 4.0553954816072998004e-13i)}, + {(-69.684981925843374029 + 169.80732079002493151i), (3.94696651173603562e-14 - 9.3881989388338201197e-14i)}, + {(71.735699043774133088 - 192.70944365251278896i), (-2.8679991533616463951e-14 + 3.6723359836579285778e-14i)}, + {(-4.8843870621761986683 + 24.867303639049758601i), (1.0433690859199602551e-7 + 8.014963820900658092e-9i)}, + {(32.246496920842716349 + 72.339839097255534739i), (-9.1515580425962616838e-12 - 3.6370428873279550666e-11i)}, + {(-54.99551990249165101 + 21.564048494846229431i), (2.3167528829500283942e-10 - 1.4131559192256855142e-10i)}, + {(-87.483828183630791386 - 70.398423064892938328i), (-3.4863554008265993748e-14 - 3.1212097780125857901e-12i)}, + {(107.5485191310676214 + 128.51099516182657112i), (1.944486612428833327e-13 + 2.9278075996722821129e-14i)}, + {(-9.5402157820119359855 - 58.132897303419859725i), (2.697536934540532466e-10 - 1.0568454815108166204e-10i)}, + {(55.584293334653068541 - 20.800179283836865096i), (-2.3961409058577553364e-10 + 1.6913868609090893397e-10i)}, + {(135.13298747810159739 - 78.480454924552716989i), (-2.7453781362711714972e-13 - 1.6933959242731611863e-13i)}, + {(-75.507724328083398291 - 105.63491484221545136i), (-1.0713960121137122874e-12 + 3.8654802290668523967e-13i)}, + {(-36.82831200873387445 + 11.733302129514624923i), (2.7206382250046029277e-9 - 4.3378145795441106424e-9i)}, + {(-232.12099607888995934 - 201.30861118479836591i), (-7.6607978497202280674e-16 - 2.6528575842059337181e-15i)}, + {(-58.371723436276070629 + 54.384953594028040413i), (-1.6482145065636631299e-11 + 2.961406085096950578e-11i)}, + {(-58.208332400312656318 + 26.627152550629716643i), (1.5354843687184051155e-10 - 2.5000297406758535462e-11i)}, + {(165.3506073055347656 - 58.315684152103926863i), (-1.042423642263188134e-13 + 9.9388726732871365645e-14i)}, + {(47.775742635960170901 - 114.69074722668469235i), (-6.2701574146821031962e-13 + 1.4641345978805265591e-12i)}, + {(7.1832603271017525515 - 75.315784986386233868i), (-2.960361676694537845e-11 - 4.1501605397270570423e-11i)}, + {(-204.02925786962123311 + 97.754110060579421315i), (2.339961880903576033e-14 - 4.8393637187309440116e-16i)}, + {(33.631233837497894967 - 54.301641837988377404i), (1.092776105690844413e-10 + 1.3138898423417137376e-10i)}, + {(-104.57573571290204484 - 26.71546134830834518i), (6.9941087610926227333e-13 + 4.0278683367757207074e-12i)}, + {(-67.534157047571341081 + 52.321256566207296146i), (2.5883966149803764142e-12 + 2.0826901495353670458e-11i)}, + {(-144.33471621619065672 + 69.217732087154871579i), (2.6207100481486575829e-13 - 5.4865634647021883666e-15i)}, + {(-11.695732700367900136 - 7.0169726572070771908i), (5.7435242999002718194e-6 - 3.1604282960529797905e-6i)}, + {(-51.520147580423561351 - 40.141820210635060562i), (1.5266193104074781133e-11 - 1.3527740932385588648e-10i)}, + {(-41.169625309287553705 - 23.232906724657585329i), (1.1690510881312950886e-9 - 5.1910425883194751076e-10i)}, + {(-154.50058064860144214 - 70.387804326658908849i), (1.7161582045350697109e-13 + 2.7302580651266240365e-14i)}, + {(-234.68639479089992506 + 120.61966481803629847i), (7.8660222573208551694e-15 + 1.3956876390314151198e-15i)}, + {(114.33392111985551765 + 73.763180375439901582i), (-5.4096578702540932194e-13 + 6.5841971886412343404e-13i)}, + {(-6.7203844511702763853 - 67.352657542243704825i), (7.4844906679942022585e-11 - 8.0716509998189064299e-11i)}, + {(-135.66371809995726494 - 149.21482115720718298i), (-4.6875482261456458695e-14 - 2.3549304736620154066e-14i)}, + {(-154.53270649501885714 - 112.60808287264070771i), (2.3527674109929591813e-14 - 7.2179719998813453569e-14i)}, + {(-31.048243115479294829 + 25.898140005946245878i), (-3.7220125035475434756e-10 + 3.7954908159713467185e-9i)}, + {(-93.895900445911422594 - 24.807677652019968662i), (1.9287909793343864857e-12 + 8.3111426978996272792e-12i)}, + {(26.728168979160766838 + 75.761253616770090957i), (-2.446324163051276943e-11 - 2.3362928021969426888e-11i)}, + {(94.198574897634429703 + 22.288951539452959594i), (-5.9756442167274965332e-13 - 9.3443708413994265198e-12i)}, + {(-108.9295320405306029 - 33.803605852332061943i), (1.3990482968168753224e-12 + 2.4078214392054313026e-12i)}, + {(228.57068934962137519 + 87.059446255491735656i), (-1.158541476240915101e-14 - 7.741430927232346084e-15i)}, + {(20.830800147648819376 - 7.0349570383748378788i), (-2.3114652258529027544e-7 + 2.4417004495551531171e-7i)}, + {(-119.99278223600042281 + 38.48708906816298736i), (7.7693490926379450194e-13 - 1.1520854563943575507e-12i)}, + {(-9.4574827959190219673 - 117.19359165796730338i), (1.2932299365149128077e-12 - 1.9174818107717097708e-12i)}, + {(181.69801371789000655 - 2.2825419071196111354i), (1.1176248991801163019e-13 + 9.879959095929120255e-15i)}, + {(157.90227874665009722 + 141.01158212145102766i), (1.4938987728668880661e-14 + 3.5211273306591731324e-14i)}, + {(-193.0797862244970986 + 17.89933891317378567i), (-5.4804108334647811594e-14 - 4.1266595042839184324e-14i)}, + {(21.574488586582489802 + 41.834935862153493247i), (1.8262066651787241853e-10 - 1.4442069344641809522e-9i)}, + {(44.446275315220944435 - 64.843651647543978811i), (3.407517991087955092e-11 + 2.0550565247574755953e-11i)}, + {(-80.390272464826679766 - 9.1852059366927321093i), (-2.1345298908681224689e-11 + 2.1602681838569540538e-11i)}, + {(-117.1545052733825969 + 59.086923440800688923i), (1.0428636384232492202e-12 + 1.2170934068896610945e-13i)}, + {(-125.8271742739560608 - 70.847522721957247427i), (4.8803977054400659556e-13 - 2.2745592887713971459e-13i)}, + {(51.743577645013431265 + 55.541973627895657728i), (4.4791176280756992141e-11 + 2.4713735459018191899e-11i)}, + {(81.060297705185547557 - 1.9496137013313805664i), (3.2150021845741071412e-11 + 5.4974020332708165169e-12i)}, + {(-65.211798062520927033 - 8.0536672190805216331i), (-8.4863236838823385162e-11 + 9.729487582997370165e-11i)}, + {(-31.167289350646054658 + 40.659267324549944078i), (-7.4345504973520595009e-10 - 5.928942894374931068e-11i)}, + {(-65.99386539338370028 + 9.2580320277076744162i), (-6.6350570656967950211e-11 - 9.6456966285992709898e-11i)}, + {(-19.804239193418936793 + 74.400510361186150021i), (4.2478533625238894464e-11 - 1.2876360670551017417e-11i)}, + {(0.7381108741451698485 - 47.999473978216698811i), (-4.263394531172444368e-11 - 1.2269243469550192072e-9i)}, + {(44.37007060261864666 + 213.56451016376593088i), (-3.0391331521352085974e-14 + 4.6733281781943810912e-15i)}, + {(170.77176673478928137 + 117.23909750356322945i), (-2.1055893383410335668e-14 + 3.9335187412429874383e-14i)}, + {(155.26486285431340661 - 94.268152774995002119i), (-8.66747540189072547e-14 - 7.1239018221206046452e-14i)}, + {(15.642811106431084411 + 0.89821966845757639231i), (3.5314740852187152349e-6 - 1.5498005580067928668e-6i)}, + {(-21.650453667208889641 + 150.51862380829743415i), (3.2577578041662667979e-13 + 1.9883149498633103388e-13i)}, + {(26.637434532967013467 - 55.293621367580669812i), (-1.1270245250915953541e-11 + 2.2474233898119242391e-10i)}, + {(108.72886284449651839 + 21.727988338934626i), (6.5937340093687442529e-13 - 3.5432339683374777056e-12i)}, + {(15.008537162021029943 - 4.8171523310760004932i), (-2.2653184775379050364e-6 + 2.8753685264194325025e-6i)}, + {(-66.347615334802441112 + 85.400102892347504735i), (-4.0721965271236884484e-12 - 2.5780850540700025e-13i)}, + {(-112.14032186419042603 + 79.230768332220691264i), (3.1354899918150972167e-13 + 6.9931644119471313244e-13i)}, + {(-122.96428032006909348 + 29.777768959723449171i), (1.1573779896701573715e-13 - 1.3456817422916383468e-12i)}, + {(-181.3220543407385037 + 63.909753689102323904i), (5.2049773485392507485e-14 - 5.1037858255581085322e-14i)}, + {(-43.913894983530674665 + 173.69280752646679389i), (1.1896329574054391818e-13 - 2.1846341153412265678e-14i)}, + {(-69.988998109518263391 - 108.31190969979689953i), (-9.3490492872501906729e-13 + 7.4635560175069944014e-13i)}, + {(230.43282154502676917 - 44.208854583086434786i), (4.4567188799911069481e-15 + 1.8120824134304003921e-14i)}, + {(-6.2723527317225649114 + 51.554405610412466388i), (5.5552615805899432606e-10 + 4.2783226369836328961e-10i)}, + {(-27.45633768017619758 + 103.22214368390551442i), (4.3256925208509106791e-12 - 1.2473701068169875036e-12i)}, + {(-60.916252526595030758 - 96.070247467618472115i), (-2.1400504852277912341e-12 + 1.917429655933596391e-12i)}, + {(10.465741993435184298 + 125.59173981528326181i), (-7.5233295938321049267e-13 + 1.2152897984105668491e-12i)}, + {(56.95474141296100612 - 28.617095159775722379i), (-1.7509391051382728537e-10 - 2.5035866791301427042e-11i)}, + {(102.7656060357765142 - 281.53299701790029985i), (-2.1508576432260411878e-15 + 2.5401781226171475542e-15i)}, + {(-37.165618537358078299 + 179.30093491300866049i), (1.0314223793260418349e-13 + 1.2579003694060220944e-14i)}, + {(-5.1994005457205965115 - 123.64678901337286732i), (5.126209515878167399e-13 - 1.5343092119495301867e-12i)}, + {(98.438574018753115524 - 93.816580723586184831i), (5.059214860142623291e-13 - 6.8690259939463608573e-13i)}, + {(6.8971070824424609569 + 26.698762505860596406i), (-6.122954903847487503e-8 - 4.7116532708800426725e-9i)}, + {(-68.698810581416481114 - 114.0320087017106232i), (-6.0011704433781086219e-13 + 7.4738117947859642138e-13i)}, + {(-38.533012127504953526 - 116.22640838740203151i), (1.3254596825363691556e-12 + 1.110329477839922357e-12i)}, + {(67.997011164062342914 + 101.47404850396229392i), (1.4846066518556653579e-12 - 1.0233358200856589649e-12i)}, + {(-44.053802341521198116 + 83.499832793905198969i), (-3.0240564137768226344e-12 - 1.014614336393459588e-11i)}, + {(8.4189229451604088439 + 26.290035689254587226i), (-5.4459444825749465089e-8 - 2.8276704065156041404e-8i)}, + {(99.97992642450329015 + 199.63564284505389423i), (2.4734538588502246646e-15 - 2.6098012811615883869e-14i)}, + {(11.979152295353005186 - 26.084914129693419937i), (-1.1116626534977846318e-8 + 4.591971297735459541e-8i)}, + {(-158.90230078408748682 - 184.27278103907400464i), (-1.3575106319531140213e-14 - 3.8999761031460055224e-15i)}, + {(44.969883808024221139 + 6.9032355351412331146i), (9.1075053532008786563e-10 - 1.6947600190315854675e-9i)}, + {(189.81388802996895038 + 19.926968159531295299i), (5.901181020149406617e-14 - 5.3247554601289262579e-14i)}, + {(-3.2583568548516428365 - 108.93643747154459334i), (9.4177091478432394208e-13 - 3.8248649719194783899e-12i)}, + {(41.421559893560370824 + 41.445817056417197932i), (2.3351581068962614736e-10 + 2.1387798499376890891e-10i)}, + {(145.11420527644105505 - 64.143998285388619252i), (-2.8333626613491978749e-13 + 6.3153254816498421924e-14i)}, + {(-70.920112402229889881 - 24.923085762741152394i), (3.5691194726611650564e-11 + 3.6135356826553233355e-11i)}, + {(-115.71976404837339203 + 91.164472371482190738i), (2.6426195050500108878e-14 + 4.6857591962019953314e-13i)}, + {(-61.234869458402549469 - 21.111590554168120804i), (9.593311047185012049e-11 + 1.0603910580348879954e-10i)}, + {(-31.509876785733766269 - 35.129509212373704941i), (-1.1773064512291033777e-9 - 5.8535743167747581612e-10i)}, + {(-6.2297580825340022059 - 127.64780422185366149i), (4.654743077145150922e-13 - 1.2046608117819130223e-12i)}, + {(-4.8150464499706764343 + 52.323451859477401626i), (4.2144799447194417102e-10 + 4.9151335587252060064e-10i)}, + {(10.739915950712552117 - 7.717348657404309975i), (-2.5630668953885047378e-6 - 0.000012319931491375437588i)}, + {(-106.50788805550719474 - 133.11354978858096842i), (-1.6978685740931418101e-13 - 4.6573227994491944428e-15i)}, + {(5.4929227178667181519 + 108.9857760565513729i), (-1.2330637258528522196e-12 + 3.7148915526136361016e-12i)}, + {(-168.32419282966498031 - 32.345088492154914661i), (-3.9498069590551089722e-14 + 1.5747570084422007693e-13i)}, + {(37.985506046745520337 - 20.719538091389107848i), (-2.5148616031749005837e-9 - 1.0393759364436441703e-9i)}, + {(55.645206604589183996 + 126.70785426746155622i), (-1.98200944173161189e-13 - 7.215822291983902502e-13i)}, + {(-43.939643789136844987 - 107.49384507214105611i), (9.6726289174201675535e-13 + 2.3048289239890897398e-12i)}, + {(-33.176289313662842062 + 95.024305206431876059i), (4.6739059198368584666e-12 - 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(1.1566425709707485882e-12 + 1.6744523424417037376e-12i)}, + {(-18.376437184952919779 + 151.14302428104895171i), (2.8928389585883737805e-13 + 2.4417340874611958931e-13i)}, + {(10.492577287437434563 + 37.371200437128962335i), (-5.3761565871367102581e-9 - 1.4238855104501833159e-9i)}, + {(-42.15372600766787059 + 52.876916429213913773i), (-1.0772962912031140212e-10 + 4.2714572187971830877e-12i)}, + {(-49.346738141427564983 - 117.36979052965732251i), (4.2584960690240470291e-13 + 1.2425185440624452703e-12i)}, + {(59.343878004122899483 + 128.65727135849635943i), (-8.7786929485348074323e-14 - 6.2864407441390938098e-13i)}, + {(175.53393137582582995 - 92.797984554165509508i), (-5.7918897089234011945e-14 - 1.6079721914246189519e-14i)}, + {(35.101840283628575889 + 87.074969744798053739i), (-5.3823018192945451918e-12 - 1.0001702876128073343e-11i)}, + {(91.436785887826204089 - 90.542063268785810237i), (8.7469273512527194526e-13 - 9.0199710858448265457e-13i)}, + {(-201.68367678117564878 - 133.79492839559199524i), (8.5000064968342306662e-15 - 1.1898959697057756727e-14i)}, + {(-113.91321985522293403 + 66.480837170096990008i), (8.6770317189452279706e-13 + 5.2358050681573768536e-13i)}, + {(-62.379618543968447852 - 12.366797088022476458i), (-3.4056698624584141094e-11 + 1.5850669361777389624e-10i)}, + {(1.3814444057246637598 - 39.851644327706345905i), (-6.9554308676203248217e-10 - 4.4552708083639924146e-9i)}, + {(-114.80941001521665612 + 1.2926098532937295715i), (242.8477670128804391 + 690.36549304145637507i)}, + {(-199.17609153470638716 + 120.7649491635982173i), (1.5024289970719366434e-14 + 1.1805091524691012671e-14i)}, + {(76.259657716626293222 - 72.985344323859251858i), (3.0749439460910664118e-12 - 4.0061518657931438626e-12i)}, + {(36.233095492570541296 + 160.20487264806456551i), (-2.2416959944166761605e-13 + 7.7551305108692925361e-15i)}, + {(-71.678014740594335308 + 46.477616471550291521i), (1.3623809159559623547e-11 + 1.5914553296147714635e-11i)}, + {(64.393568635915642062 + 52.29807265072457767i), (2.440240968546114988e-12 + 2.7409807995153317324e-11i)}, + {(-0.98786283406579522559 - 11.285067494688476586i), (0.000023589690177705392846 - 0.00001787392475335521723i)}, + {(-140.97082401100558968 + 52.022341816698350669i), (3.179287504245715275e-13 - 2.5448761256595825734e-13i)}, + {(-106.70556078869890371 - 63.627087708149552725i), (1.2630172140423012849e-12 - 8.7840814047881322174e-13i)}, + {(-151.88754785796376723 + 68.384518076577990087i), (1.9497661934050046508e-13 - 3.7282461748412685695e-14i)}, + {(38.536030764080031474 + 52.172538919329959128i), (1.4698112338914275201e-10 - 4.5818429809569447091e-11i)}, + {(97.640399570204380097 + 30.665372105970128302i), (-3.410668928385885549e-12 - 5.3265582628851673636e-12i)}, + {(17.972901701759251836 - 53.564056973036556997i), (-3.2136426925312653895e-10 + 2.3772074613170781862e-10i)}, + {(-115.5070674710327836 - 256.71027571106714049i), (8.6799137297686669216e-16 + 5.0399967340545553813e-15i)}, + {(-89.39769024049381585 + 133.09966720600868939i), (-2.2205992070605858523e-13 - 1.3738831611161009417e-13i)}, + {(34.163900501000824761 + 60.596023681676236095i), (3.7194559992544018721e-11 - 8.593904169809698243e-11i)}, + {(60.696736990251984878 + 181.28551957942136141i), (-6.0653516446173275383e-14 - 4.8393372788505590967e-14i)}, + {(-0.83818890764139197813 + 123.68294693191981537i), (1.2301112085410366351e-13 + 1.6210830244594755618e-12i)}, + {(-264.60974911635480566 + 32.649591836263738287i), (-4.8542794112955460403e-15 - 5.6130143342972180961e-15i)}, + {(-106.33233627358704609 + 63.592065348672434766i), (1.2791668083129253036e-12 + 9.0688377859431647962e-13i)}, + {(244.15922351874272067 + 13.02448696699719477i), (1.3014293332976187304e-14 - 5.1049828858280860762e-15i)}, + {(70.905559232453313712 - 28.827769468171986489i), (-4.4523483165428864632e-11 + 1.9961684204213562136e-11i)}, + {(145.04925430090770533 - 53.376397376090331193i), (-2.7455773700114900116e-13 + 2.1553715539500953656e-13i)}, + {(167.14924035798441082 + 69.103663992399177118i), (-1.0705297074825697598e-13 - 4.4011022708203884121e-14i)}, + {(3.2918116625261673036 - 26.563535456323698725i), (-4.9871131807041513286e-8 - 5.531523918358131798e-8i)}, + {(-121.24278657787115776 - 97.584254441135399816i), (-5.5527948568505422182e-15 - 3.1980602504173274111e-13i)}, + {(-46.47003501959453331 + 157.98605622517985125i), (1.9601840787793672806e-13 - 9.520258559572931127e-14i)}, + {(-194.21719112672101915 - 25.798337740748529257i), (-3.8565254311705426629e-14 + 5.0862677054678853666e-14i)}, + {(-32.071136112796779116 + 45.66758310298452983i), (-3.8355418568386346946e-10 - 1.5092087041670880839e-10i)}, + {(108.47686009025183296 + 80.933900237889375262i), (-1.8423338659069280797e-13 + 8.6425260995239223181e-13i)}, + {(11.350307181909712995 + 173.58265641024931369i), (-6.3308318909848322768e-14 + 1.3552980374202765494e-13i)}, + {(64.534245796933419115 - 62.373757322401068848i), (1.0086281422348306674e-11 - 1.2142454985401275044e-11i)}, + {(-56.614603583291447819 - 49.844579606454594511i), (-1.5264315911375401704e-11 - 4.7662713031915499627e-11i)}, + {(21.957797884354533835 - 49.868529664651262578i), (-1.5149989694421985632e-10 + 4.9566222832774233989e-10i)}, + {(-52.760038206195304156 - 71.670571217704420519i), (-1.5458354138904269374e-11 + 3.7585552365655704213e-12i)}, + {(47.093597229102066137 - 4.748848453785478263i), (1.102745393725439376e-9 + 9.4932817406286589355e-10i)}, + {(8.7148200541096567662 - 42.549542300972014175i), (-2.4423415733690733711e-9 - 5.8554189188235915676e-10i)}, + {(131.63311057990497943 + 25.823082042833846117i), (1.9682571659030869902e-13 - 9.2434475912876220376e-13i)}, + {(-100.09208949933281474 - 14.209075891330719799i), (-3.578435670015093554e-12 + 5.3609816346431925912e-12i)}, + {(35.603835322909269223 + 54.007817702300044971i), (1.2196895297983279679e-10 - 9.8100533980536918917e-11i)}, + {(7.3132122772655545617 + 99.976552426528840556i), (-3.2543408633321078888e-12 + 6.3073838416604360798e-12i)}, + {(-99.359506297031586541 + 145.22267988012583828i), (-1.1991377102046645961e-13 - 6.4839438213221281813e-14i)}, + {(140.9385524853004199 + 158.79464163194393223i), (3.5070878552549784915e-14 + 1.3064050157544891038e-14i)}, + {(-5.5849869874157480609 - 67.409302600020595264i), (6.5246488517669165696e-11 - 8.9436906600626144711e-11i)}, + {(-3.8490974747071144968 + 238.15576248342682675i), (2.1097237367809742008e-15 + 1.6415666317387392316e-14i)}, + {(1.6166024758519248472 - 85.660105262256053038i), (-1.9381710157123391359e-12 - 2.1181244167773636988e-11i)}, + {(128.7153998202097398 - 193.35933195079076086i), (1.6268467914864914121e-14 + 1.1459521458119284822e-14i)}, + {(-13.233601660492983143 + 68.947092106861049388i), (8.3275324345718441575e-11 + 1.6386806964254636669e-11i)}, + {(97.017964626247007232 + 10.733074780256227854i), (6.3119916531979826261e-12 - 6.1843066280205384604e-12i)}, + {(-88.152971357914850614 - 54.862813995432745173i), (3.9807361347389915285e-12 - 3.6155666172458705852e-12i)}, + {(16.926738207944939774 - 72.323828487987412927i), (-5.83524742896305617e-11 - 4.2264020613087258485e-13i)}, + {(120.86201242354547958 + 85.438838578325757567i), (-1.7991371473033324527e-13 + 4.3601016725590135679e-13i)}, + {(-21.293193762253924461 + 6.2670780065505731216i), (8.7768411262707735933e-8 - 2.1544232976903966897e-7i)}, + {(83.421756640951016948 - 71.484841081216771386i), (1.010026071482400556e-12 - 3.6829952719720803835e-12i)}, + {(-42.597350374339171708 - 39.835617902392897349i), (-1.4645606131329592205e-10 - 2.6210130965764721033e-10i)}, + {(30.805959066783817235 + 95.932580977850591353i), (-5.8072249511577083315e-12 - 3.73248652781804965e-12i)}, + {(53.787438033382258595 - 9.9414881750592396514i), (1.4456747396054273558e-10 + 5.0278430712259264458e-10i)}, + {(36.803860346551026339 - 37.318191120510860515i), (5.3562445324994271575e-10 - 4.4190993282037717005e-10i)}, + {(-100.60396841147796465 + 145.2486572208659652i), (-1.1892100676941402765e-13 - 5.8285307556221964586e-14i)}, + {(132.95855241192694507 - 172.70436480993745931i), (3.0845369633809382293e-14 + 4.1091630548355297393e-15i)}, + {(-19.166232623690792281 + 217.00579501119867132i), (1.825669751222772336e-14 + 2.4900223714475437352e-14i)}, +}; + +const std::vector gamma_8_c = { + {(-74.047652863206522511 + 37.526521218651240019i), (1.7798128640689579599e-12 + 1.1888685741928443349e-12i)}, + {(-49.669237381357945083 - 1.0001244363624699485i), (-13313.892971660714466 + 20374.064327880252677i)}, + {(69.658510213512187192 + 201.36571253197325859i), (1.0503867407241529037e-15 - 5.6695924758534260564e-16i)}, + {(-138.3477752065399784 - 64.374390880226854961i), (1.5832430682303418482e-14 - 5.4473115349062031356e-15i)}, + {(42.124530089672425959 - 50.817970998503078306i), (-1.0209399076735322303e-11 - 1.035159265026913282e-11i)}, + {(15.791373295728789117 - 22.682278719489502805i), (-5.9040281206018705014e-10 - 1.6086361963909109482e-8i)}, + {(-81.217967395475227477 - 0.10848676466802488483i), (-7078227765.0090560913 + 11390686987.944555283i)}, + {(-54.993353404776314619 - 74.280596301184957042i), (-3.7705842141326409513e-13 + 8.4214416795611266746e-13i)}, + {(99.634537833023671283 - 197.00352916155225103i), (7.4927914886733869593e-16 - 4.9969852866652913182e-16i)}, + {(2.6166141094858668126 - 9.5836734565760384186i), (0.00001088500722122876561 + 0.000059245702685834255891i)}, + {(-203.94295344729124508 - 140.42306974597960334i), (-3.5966433626170762673e-17 - 3.5010910390301648085e-16i)}, + {(-112.54392924630842288 + 0.93908598465148940271i), (2508.6061620449531802 - 16631.214273261903145i)}, + {(10.118222853257391236 + 25.447790626939049474i), (1.6334060828966977066e-8 - 4.1360451266633598114e-9i)}, + {(60.279577272653796172 - 123.8584897418155748i), (3.535983068910471624e-14 - 1.7337288178872759651e-14i)}, + {(-212.05418976437258038 + 7.1054766300692184799i), (2.0690566203059582237e-13 + 5.869743917729524917e-13i)}, + {(-159.40996960864541165 + 116.87825472383302383i), (-7.0318856380281498304e-16 + 2.0079364233765328331e-15i)}, + {(-118.68478113139440211 + 146.09974961793125203i), (-2.1784612562349756244e-15 - 2.2829084350026254665e-15i)}, + {(-36.230417255622604955 + 239.55404211617064902i), (-1.4666269969814075529e-16 + 3.9729645192232900656e-16i)}, + {(-114.2433981348797829 - 114.63957126894801775i), (-1.0521016992231747919e-14 - 3.9297400803927259646e-17i)}, + {(180.49503009793258457 + 64.890763791616436151i), (2.6122595767477596431e-15 + 1.0239105539680259743e-15i)}, + {(-123.58603019120180022 + 159.11541849404403592i), (-1.0148294575268323782e-15 - 1.5277326561725941992e-15i)}, + {(-29.819073026733537546 + 48.57964430922325505i), (1.0698466782348186582e-11 - 4.2270356681010681803e-11i)}, + {(-50.501457283583384594 + 9.3657100809327893387i), (-1.1366812942572414687e-11 - 9.564365185557929946e-11i)}, + {(100.8494172078352733 - 44.202391008196883604i), (2.3730253351727485224e-13 + 4.2575797996333525267e-14i)}, + {(38.709445660323765992 + 152.72291937192480304i), (5.0851806732274471045e-15 - 1.2353282182589921703e-14i)}, + {(235.59515037683587479 + 166.89923139407031272i), (-2.3695987843534518306e-17 - 1.0286540394589379542e-16i)}, + {(34.839285483052648829 + 155.7523453110112257i), (1.9804340808056468518e-15 - 1.1873757901200164573e-14i)}, + {(-177.17454035958422764 - 63.944969452102981222i), (2.8975641528426813095e-15 + 1.1503203962760953724e-15i)}, + {(-141.35074322129705138 + 19.134143857904813757i), (-1.3667076291307866188e-14 - 2.512508333433480903e-14i)}, + {(174.28512236456171536 + 33.223502473336218088i), (-3.1286482587902606841e-16 + 5.2379312869070831326e-15i)}, + {(18.47738144287605877 + 80.758775094718814103i), (4.1490580556745401637e-13 - 2.2587117129476201799e-12i)}, + {(9.6306371356427007413 - 103.70908580114381436i), 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6.4312693006452440496e-16i)}, + {(143.53262741286090431 + 55.845160559265828226i), (1.6090972235008478706e-14 + 2.6595232163983365038e-15i)}, + {(57.290871591586210343 - 53.307059335138887946i), (-3.6012463957207274832e-12 + 9.3318662968242312671e-13i)}, + {(119.44355086939614807 - 167.36195277230751799i), (-3.6474875839382110431e-16 - 1.553401439872392179e-15i)}, + {(75.23364529178151372 + 85.715975031728348199i), (-1.5394706587370069426e-13 + 9.3644958335273214248e-14i)}, + {(47.765787855680784446 + 21.504920199224862642i), (9.1718290271992962907e-11 - 2.5725797750746824957e-11i)}, + {(-29.129506296115909691 + 116.74661571961166828i), (4.6157991059519509024e-14 + 1.040115868496957204e-13i)}, + {(86.445989164285663264 + 39.121532129426896063i), (7.6689077133675747106e-13 - 2.1673228642569022725e-13i)}, + {(59.491933393429661692 - 55.453346412023165612i), (-2.6462433904147588798e-12 + 6.6931241530123490814e-13i)}, + {(-16.05797911564123126 - 147.42697385530573229i), (-1.344166880663051315e-14 - 1.6758409064100791124e-14i)}, + {(80.368347147226543825 - 239.76254670996587492i), (2.5520866560164799472e-16 + 1.6327008478426394467e-16i)}, + {(53.207707505671443471 + 78.305387889533193402i), (-2.1987861504571243471e-14 + 7.9954426933695934979e-13i)}, + {(46.222419369593090721 + 38.349712851366419386i), (-2.39504756242213236e-11 - 2.0197756916711859078e-11i)}, + {(57.850166937295512071 + 22.741404577433151246i), (2.3821483047780425348e-11 + 2.9207196891200186088e-12i)}, + {(90.556349777104756527 + 77.87382660276966817i), (-1.0446280913287845373e-13 - 6.837444708682779061e-14i)}, + {(10.802580859416478276 - 38.119868619381136909i), (4.404518949064500378e-10 + 7.3168275007810688935e-10i)}, + {(64.616668068025063576 - 14.782049338710010034i), (3.4302528726713782235e-12 - 1.391951961299386946e-11i)}, + {(90.237265141904259735 + 95.663191367174150059i), (-5.566334928376827109e-14 + 1.4536292344037508994e-14i)}, + {(-16.741322923140891987 + 115.17558203863632116i), (-5.5536644385582923947e-14 + 1.3824620483748557797e-13i)}, + {(188.74697389662543401 + 176.94331209172327135i), (-2.461969421812148941e-16 - 6.2232302689331160182e-17i)}, + {(21.211090667191903947 + 51.459334078206410368i), (5.6083392481317187638e-11 - 4.4856538070977788961e-12i)}, + {(-65.257233580388444238 + 8.6574834585033606515i), (-6.7267983819757221929e-12 - 1.1647696628881611878e-11i)}, + {(-96.277346231939162635 - 45.358068950064357239i), (2.7650138583274838524e-13 - 1.0548944105102024801e-13i)}, + {(222.59283087782861799 - 26.764704615183315894i), (-4.6128695333075297304e-16 - 6.5811135587075670862e-16i)}, + {(160.49321055762109722 - 73.327518275002532278i), (5.2362354366667164597e-15 + 1.5986710777040680663e-15i)}, + {(81.56781734085089397 - 165.31184587739596736i), (3.3382919440731808336e-15 - 1.8495453151559036691e-15i)}, + {(33.407304754923416112 - 39.475836675597072656i), (-7.767846550277730387e-11 - 6.8525149775397741958e-11i)}, + {(-59.217269244693213182 + 53.445812344625821311i), (-2.6754717029862224611e-12 + 1.2705864326801097549e-12i)}, + {(-78.967840901367111428 + 68.296194161475838769i), (-2.8545033027636409115e-13 + 1.9695051889052046751e-13i)}, + {(-88.724930061776305479 - 35.777829135621395551i), (6.880601377110500816e-13 + 6.2771160370333503283e-14i)}, + {(-24.739110681217979959 + 178.96886118944698296i), (-1.9251241478449811548e-15 + 3.9857070491313185712e-15i)}, + {(-75.330110728535061071 - 5.9809093264316883776i), (6.3563980246460027652e-10 + 3.5466911643167072493e-10i)}, + {(-25.111778638274667941 + 73.883627701393933762i), (3.2124856896029105258e-12 + 1.6390683520412538116e-12i)}, + {(-173.00560528515725878 - 166.9539934850435543i), (-4.4077078586325361251e-16 - 6.8411497338049851755e-17i)}, + {(-31.9103350137875168 + 45.24416618852959715i), (-1.415489099594902053e-11 - 5.2908974918468048833e-11i)}, + {(-110.28123712676176638 + 97.740188273958267473i), (-1.94934721845809851e-14 + 1.0644527743885693584e-14i)}, + {(36.955499406584820576 + 274.99527094475126887i), (-7.0971570468481662316e-17 - 1.2499806916902103425e-16i)}, + {(-86.552983633416474163 - 87.347478954799385065i), (-9.4216356521977498642e-14 + 1.2542487637353445857e-15i)}, + {(-80.993237057209896079 + 173.6709221535219001i), (2.5631541774319641833e-15 - 9.8935476633563412806e-16i)}, + {(-1.6162465485119432707 - 136.75154458021486903i), (-4.0859199586923748021e-14 - 5.0842063450120251028e-15i)}, + {(-144.08063692646123855 - 51.695469947312055581i), (1.5058723344711601591e-14 + 6.2704006418690199132e-15i)}, + {(48.297791659417249832 + 118.74612333513276496i), (6.9707677501864430533e-14 - 5.5916746714132430785e-15i)}, + {(69.649707277362622904 + 30.38109530266521574i), (4.6887894446252545672e-12 - 8.0357965729048092571e-13i)}, + {(-127.97729300813213626 + 32.811463897455361405i), (2.1952548182053277983e-14 - 4.7934416455782283242e-14i)}, + {(61.004192381917334842 + 207.55435987446549007i), (6.7911058203673009212e-16 - 8.0883141204333405508e-16i)}, + {(-65.734498631960946113 + 35.15039619566379514i), (3.6501955175329329499e-12 + 3.4775490735297932224e-12i)}, + {(3.459029162410983016 - 46.761347646983672632i), (-1.9006392764229167006e-10 + 1.0525181380335941816e-10i)}, + {(-118.63980478200826951 - 118.66713429353654874i), (-7.8830021596776770627e-15 - 1.2619444114334482189e-16i)}, + {(88.766289531989130523 + 3.9042747091289369266i), (-1.2728406269533761255e-12 + 4.6982106116242756198e-13i)}, + {(-53.316400111178616328 - 8.6564374202896487986i), (-1.8799940267088163774e-11 + 6.1817907561441848272e-11i)}, +}; + +const std::vector gamma_9_c = { + {(-13.619663456486552633 - 138.29523485764644875i), (-1.6495102035594244372e-15 + 1.2671552916096808586e-15i)}, + {(-88.818528479030803169 - 83.166523471259608868i), (-6.002156125119464701e-15 + 3.0058321614892697757e-15i)}, + {(73.288874707911688233 - 12.492426147526696667i), (2.5453064539518276025e-14 + 6.1595620794785653027e-13i)}, + {(2.8920459108755371957 - 87.232069486003481984i), (3.3576677163507117077e-14 + 1.3329717625205537334e-13i)}, + {(-63.820988568821512388 - 6.1750190110103018171i), (-5.8554805451523145317e-10 + 1.2233130657935169387e-9i)}, + {(39.164919825206659709 + 207.63251747479256437i), (4.8046111263846237555e-17 + 4.1526901350774575807e-18i)}, + {(-38.769278971027823388 - 107.27360626919593756i), (2.0492000412374961019e-16 - 1.2171706909981151444e-14i)}, + {(-48.99612034835819685 + 13.911457095654297333i), (1.2510312618698739371e-11 - 1.0042239126654111748e-11i)}, + {(-88.735107659275641367 + 38.44181570929138303i), (4.5348261135249932041e-14 + 2.590565216642102525e-14i)}, + {(15.338451663393781743 + 103.16211817001598661i), (2.6673575040713649276e-14 - 7.8144464251681792833e-15i)}, + {(-7.182916832327769896 - 100.44554777524193412i), (-2.3944353745810801869e-14 + 2.9182799522539509807e-14i)}, + {(9.2515419735668000811 + 71.912833600830282421i), (6.5101662913964037754e-13 - 3.3951862508154379716e-13i)}, + {(-111.23368668430948958 + 158.92303121751930917i), (7.1071877162735631184e-17 - 7.3581056633225187984e-17i)}, + {(-68.578455540110212496 - 33.007488375358867927i), (2.8772289359819278293e-13 - 3.4082002260295061291e-13i)}, + {(107.21478236797108252 + 134.18259995251722216i), (-7.3755767608206041004e-17 - 3.0633590707549270814e-16i)}, + {(11.833666093767181593 - 58.333370665534388877i), (4.3144423188245834458e-12 - 6.8168690647055230939e-13i)}, + {(-1.6692492919781698468 - 3.4883172751890456631i), (0.12813452122364285546 + 0.089253223092200073552i)}, + {(-14.765940913765868814 - 1.9967514044012262264i), (-33.519497964767495546 + 339.73004629878903415i)}, + {(191.93087893340126016 - 126.47454389389460516i), (1.1807822384585301836e-17 - 1.9602114239158117051e-17i)}, + {(197.11380866703942161 + 127.22728955813475693i), (8.3886147685491385009e-18 + 1.7081170507126776858e-17i)}, + {(-88.962503509911599053 - 77.152845821482813449i), (-8.9300940907538938335e-15 + 1.0895796233502837017e-15i)}, + {(42.348847928804332241 + 90.31800787658202978i), (-2.9070750726332596664e-14 + 3.0354576369052255568e-14i)}, + {(114.80063951186059512 - 258.2730756164221475i), (-2.0148453965302291687e-18 - 2.8934596924983756032e-18i)}, + {(124.74344915817137291 + 44.655408757108261852i), (-3.3056927146462205202e-15 - 1.2025572323871147598e-16i)}, + {(-95.190150591936387059 - 109.41239017824709379i), (-2.5517337601949419904e-16 + 1.3686033129691537124e-15i)}, + {(-34.490027543320877612 - 50.528848090074006905i), (2.3812886963874105515e-12 + 2.1720081518032281825e-12i)}, + {(65.003082111791556486 + 30.748586957988059964i), (-5.4046680233334038352e-13 + 6.2949103303304795681e-13i)}, + {(13.987194476391007214 - 104.89989808113600134i), (2.224233643613377761e-14 + 9.9295293017723712436e-15i)}, + {(29.010540572717850694 - 148.06245961404050604i), (9.910111504659622835e-16 - 1.4099733481762439127e-16i)}, + {(38.761699401190099934 - 241.92935005481666622i), (1.2547260222300251726e-17 + 2.0132588966527305436e-18i)}, + {(262.15556241187977093 - 71.867682370509072598i), (-3.7704237087476983446e-18 + 3.3682761671327288439e-18i)}, + {(41.464894658313063758 - 167.89554464032119085i), (2.4477547771660535973e-16 - 1.614533564267684227e-16i)}, + {(-88.137781301716984217 + 57.949937963667522922i), (-1.1507510655683179364e-14 + 2.1135659443310364145e-14i)}, + {(-39.877762480674903145 - 79.201592312112424565i), (1.0373575076624079513e-13 - 5.2540585890476449526e-14i)}, + {(36.330007630896730575 - 12.919953926426726909i), (-2.3842988503993361981e-10 + 6.8057385902471189481e-12i)}, + {(-22.836680360594765915 - 29.731086399230495232i), (7.3614257844895305838e-11 + 2.4551804803897587802e-10i)}, + {(-163.09300041083318433 + 5.1261817642613873858i), (-8.2209586739317413775e-7 + 5.4372384674097232827e-7i)}, + {(-106.15775109991747627 - 113.31253380590058555i), (-3.7005811823334283292e-16 + 6.5639266540328671388e-16i)}, + {(-13.985474215511223051 + 70.885374256110651459i), (-7.2081189895417957891e-13 + 1.7919596111651366792e-13i)}, + {(-87.382701500347252477 + 196.65407106291434047i), (2.4153720467175985754e-17 + 3.2383603975082323362e-17i)}, + {(252.75861729244780918 - 137.07993310827748701i), (-7.0103057499056720536e-19 - 2.9606811441318935322e-18i)}, + {(-76.451939303990059216 - 84.65631834389080268i), (-4.1966571310755711824e-15 + 1.1253383572891731367e-14i)}, + {(-35.077746331706684657 - 95.198944822607842298i), (2.698920584300493346e-15 - 3.4765249406698814275e-14i)}, + {(134.52742706211503787 + 85.584463768400453887i), (2.4262308283184269507e-16 + 5.7052886957339539189e-16i)}, + {(-27.060451095735881921 + 95.63569973915952005i), (-2.4323785409931141131e-14 + 3.4348158739381785713e-14i)}, + {(271.73203533425424894 + 45.872952360023262486i), (2.8111199315694846956e-19 - 4.4612169250733525628e-18i)}, + {(-50.245830426471037811 - 239.11070651083048233i), (-1.232128982079855531e-17 - 3.9651924172581739437e-18i)}, + {(4.4902716827772080066 - 61.332947846467043007i), (1.7800751716241564331e-12 + 2.6885116709472245289e-12i)}, + {(-61.735156994445397061 + 135.45222958142468883i), (7.4392151619584449185e-16 + 8.233084068685470705e-16i)}, + {(-164.38873755059211135 - 145.26116797813054404i), (-3.2955986888104241687e-17 + 7.2493527960989486699e-18i)}, + {(-12.704645755891075254 + 156.09515741836713687i), (-4.8878053240407898014e-16 - 5.1471535793600377495e-16i)}, + {(135.60519874408578289 + 18.179298949094587101i), (8.8975863995591858524e-16 - 2.3140873378770382248e-15i)}, + {(-82.666774268722264196 - 147.70663139171179523i), (3.4731564211802032348e-16 - 3.3791186780926764128e-17i)}, + {(-40.305163542068598304 + 89.616234200577565616i), (3.0000859133144942207e-14 + 3.5315192231103752732e-14i)}, + {(-22.142456436821728261 + 37.922475153849688922i), (6.2527585693901664332e-11 - 8.4088581042047463517e-12i)}, + {(-44.165207822549312766 - 97.520090939250252404i), (1.4215574468192503476e-14 - 1.6074250538309824032e-14i)}, + {(-127.40550233791219625 - 150.93783636438124063i), (-3.7999100667325194584e-18 + 8.6739127699864642453e-17i)}, + {(143.7501276411165918 - 21.115253500542984i), (3.6163486636877862156e-16 + 1.3946091818407110217e-15i)}, + {(-107.55955029391468258 + 32.971912971590199959i), (1.1945660938639870445e-14 - 6.1640346624354274421e-15i)}, + {(-25.913044440854871908 + 46.650685450205628513i), (1.100160612025403972e-11 + 8.2215526438006207394e-13i)}, + {(40.427029906512856883 + 75.210922858647137446i), (-1.626753181185489736e-13 + 5.3843990161606021684e-14i)}, + {(62.69317780426703024 + 110.78625602675380435i), (-4.6479456530367414692e-15 + 5.0557086764642529532e-16i)}, + {(-17.072313405299595956 - 37.317983411046910192i), (8.5472589429331907191e-11 - 7.9618054092589873681e-11i)}, + {(-62.384545001018501864 + 115.55776999900588464i), (3.3279385954322832065e-15 + 7.6838530721572746955e-16i)}, + {(48.802991288934862268 - 62.337940336368532712i), (-1.1708120180156522261e-13 + 3.2112947512225169624e-13i)}, + {(-90.438877769636704329 + 39.406747526978477936i), (3.7509203939230750835e-14 + 2.2397082362521596485e-14i)}, + {(-21.655371430376490594 - 101.80067373702419786i), (-2.6122589484800172095e-14 - 9.7726007265880576123e-15i)}, + {(-75.982837476218293205 - 142.1754100565962915i), (5.2159930562362231569e-16 - 1.4457432232125887168e-16i)}, + {(29.191802211276890233 + 78.843542884731746767i), (2.965037759576765687e-17 + 1.9577309790110783447e-13i)}, + {(68.576420974055267266 + 175.8292222787388539i), (-2.4376750654888895849e-17 + 1.3165558310277005751e-16i)}, + {(-175.77200275361917647 - 102.75141532169989489i), (-2.4592242121465946712e-18 - 6.5748249655238809067e-17i)}, + {(42.568056387782156946 + 51.681054484440295482i), (-2.0701735505537875575e-13 - 1.5424367466328702187e-12i)}, + {(29.198268688326251663 + 80.959438278650893039i), (1.1930238298114548957e-14 + 1.5802590914279221209e-13i)}, + {(40.833350629897047668 - 43.668416306950959438i), (1.8108289888215317878e-12 + 3.955488805924931811e-12i)}, + {(15.086910187298421704 + 95.241233939803109365i), (5.5201231240120891381e-14 - 1.1355829799190532282e-14i)}, + {(-69.220910371588956878 + 194.53307214782859091i), (-2.5972045638360080918e-18 + 5.861516626704857745e-17i)}, + {(-137.57635281920158832 - 205.55920869748155155i), (9.432801571834906267e-18 + 6.6074762373488590612e-18i)}, + {(-139.81450565746942516 - 6.0440494505276509685i), (-1.2159191780792423038e-9 + 2.8339378704020358966e-9i)}, + {(161.74447675159086657 + 196.42029259301847333i), (-8.8198038009700340691e-19 - 9.0786839865097707349e-18i)}, + {(2.2250843390960479695 + 237.95987526695620318i), (1.074367107489120143e-18 - 1.6443260815213836491e-17i)}, + {(0.6301446780148244331 + 60.49238880361274795i), (7.2059213493961128431e-14 - 3.7202206527312833828e-12i)}, + {(140.53766946981866681 + 66.732296861002993182i), 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{(-106.99482514235896247 + 98.522901369135595928i), (-1.2495997201604752948e-15 - 5.188128090084326376e-16i)}, + {(-58.003332913282378058 + 69.080363137829749576i), (-4.0908451929108918893e-15 - 9.8689952193954166296e-14i)}, + {(-173.59423315623635631 + 3.2244937107946118893i), (0.12644892043870556431 - 0.08504676592718919681i)}, + {(-40.790716998601503462 - 48.691664771009399715i), (-1.0920499619967858105e-13 + 2.2862943627444319105e-12i)}, + {(-121.25950471508724604 - 4.811526547074906901i), (4.2480867341596560579e-7 - 7.1048952808904274755e-6i)}, + {(-37.144561106617132396 - 6.5817445434800756487i), (-6.7887813516848459505e-11 + 1.4843366334326444413e-10i)}, + {(4.3392679630529613632 + 135.81690356910485207i), (6.4300030056078784741e-16 - 2.4732059984935037898e-15i)}, + {(-56.465181155300513183 + 45.39821958174631078i), (-6.8014617206228117923e-13 + 1.5780740776190193558e-13i)}, + {(-159.68212632030622444 - 99.807698970793921944i), (-3.9537441193639569845e-17 - 1.2667723807878628367e-16i)}, + {(-89.275078236434552537 - 90.435565969939673892i), (-3.1109238158672359871e-15 + 3.3216978282377919379e-15i)}, + {(168.12794432241952336 + 131.80512659619535043i), (4.2425522577510124782e-17 + 1.2489922873009490046e-17i)}, + {(28.954767649396341511 + 28.675367677153069224i), (9.622063816547773832e-11 - 1.0267800948975077251e-10i)}, + {(-46.491764895088991238 - 4.9989462980375112267i), (2.1893988000495569782e-6 - 1.1335969279877964917e-7i)}, + {(149.67852651088827542 + 67.978239679244978788i), (-3.5858700671412973699e-16 + 3.0600087518519459613e-16i)}, + {(-136.45120141020242954 - 189.70972824934685264i), (1.1696983670590905564e-17 + 1.5206918409203708878e-17i)}, + {(-139.66155230463948556 + 97.831484719675160022i), (-2.2579964816752651041e-16 + 2.3198981708541319697e-16i)}, + {(96.954069922759941846 - 73.169558676538883901i), (6.5201377243146438534e-15 - 3.0904435661560594177e-15i)}, + {(102.35720589190538021 + 8.0606095225879208499i), (2.5168574998547583373e-14 - 2.1663309504735011238e-14i)}, + {(3.6384716910117709254 + 12.529753691530665094i), (3.2741949831156098749e-6 + 2.4834476891599934077e-6i)}, + {(138.99264454963744697 + 387.12434484696433401i), (5.9469396143013205959e-21 + 1.1994410038890397862e-19i)}, + {(26.5946377718778173 + 38.654487970279816977i), (-3.1151907455093071828e-11 - 2.2876675467764202484e-11i)}, + {(47.702839855516693035 + 9.0031818706499961991i), (-3.6689139173353196129e-12 - 2.9236443490185333378e-11i)}, + {(-48.891847604229262458 + 16.795436705026940416i), (1.3810736561978750413e-11 - 2.69081519420930485e-12i)}, + {(-137.47440137094088186 - 94.702791376037538384i), (-2.5267481198676294666e-16 - 2.992441831415214032e-16i)}, + {(-93.084492277346399192 - 32.387930399598317877i), (4.3551352356826176643e-14 + 6.2797920097131416402e-15i)}, + {(-65.785946961116621878 + 68.283344952178552489i), (-3.8227867620247728083e-14 - 5.0053620785373146264e-14i)}, + {(74.143671981617103484 - 313.54768135673072038i), (9.4591009332128293116e-19 - 5.2345254569376464884e-19i)}, + {(128.19474358628352206 - 10.189190096455781998i), (3.2723777141073365901e-15 + 2.850387642807235475e-15i)}, + {(150.77706292756391804 + 36.650864033269542119i), (-4.372126264881588124e-16 - 6.6428344845495822046e-16i)}, + {(-87.717409691726302867 + 4.00688945098222149i), (0.00022710006709694715676 - 0.0010934996781148725777i)}, + {(-23.951629507867661317 + 228.09523478574772071i), (-1.8789075026100744481e-17 - 1.3122496820994408202e-17i)}, + {(120.45478461545009452 - 183.93931557566901347i), (-2.9981416800225920741e-17 + 1.5938089511633930809e-17i)}, + {(113.48451112120952189 - 19.802196768192917631i), (1.0986901634621913032e-16 + 1.1724276171392242836e-14i)}, + {(-5.2573579752975057033 + 51.070512445528159162i), (-1.3673648474005753068e-11 - 8.5754283409913926394e-12i)}, + {(17.569666881278141801 - 50.051718325813865818i), (2.2676731815126930425e-12 - 1.227127662664381413e-11i)}, + {(-34.846365743433310058 + 12.96084471041581665i), (2.6479703343561506843e-10 + 5.2485327101687065575e-12i)}, + {(-76.32560004359798711 + 8.0740444167765446082i), (-2.3779221907298465378e-13 - 3.2483463667425326292e-13i)}, + {(-1.8143862951580567167 + 214.01359972294608269i), (-4.1581226625811172211e-18 - 4.2588764579067228678e-17i)}, + {(204.65714250734049529 - 4.1202093962880610434i), (6.4239639496441069231e-17 + 1.1796256565661382698e-17i)}, + {(138.62520614181934775 + 56.056251324456681573i), (-1.0501323179493956612e-15 + 3.5739713739560828334e-16i)}, + {(39.590137309374320296 - 59.283151438080196272i), (-7.5582912017104915524e-13 + 4.4770486446195253703e-13i)}, + {(-48.178327850786040187 + 14.730357962855435972i), (1.5543750079273137016e-11 - 8.4468718880102668515e-12i)}, + {(-24.922241238339346125 + 62.319231530218942794i), (4.8133665331286716994e-13 + 1.339610182774092484e-12i)}, + {(-197.54141235609253613 - 29.640846656506720791i), (-1.8034972692725903909e-17 + 7.5754855431405065153e-17i)}, + {(-74.055445168416397905 - 164.23971783602934238i), (1.27590422266524823e-16 - 1.5344907886689242471e-16i)}, + {(234.71926967180780821 - 32.581624032346624631i), (5.5975323446424066246e-18 + 1.6512459732776150974e-17i)}, + {(-118.67195810724753358 + 60.992762730886106226i), (1.2831132552667269512e-15 + 2.6217629107076461921e-15i)}, + {(-64.438843659102573724 + 39.647285723244841904i), (-1.0303110078494586563e-13 + 4.6033618546788436806e-13i)}, + {(76.852016512601906584 - 117.96595171254699608i), (-1.6934526406807436271e-15 + 8.3409508069159226836e-16i)}, + {(82.199806220952211788 - 103.85638335629852236i), (-9.1975835100755669743e-16 + 3.1512125083562344823e-15i)}, + {(105.87982787556417463 - 136.80579707353297181i), (-1.0837289316499171831e-16 + 2.7465017556677738512e-16i)}, + {(-68.525063196171899449 + 83.150140423723641447i), (9.4825426746218476611e-16 - 2.0037080796697286336e-14i)}, + {(-65.12827057058767366 - 27.733007158862140074i), (7.6474720226282662725e-13 - 3.7530701611964990379e-13i)}, + {(1.3457642288346898241 + 24.821362537722219344i), (3.4096581111599115819e-9 - 1.0756576887782215548e-8i)}, + {(-147.46588526737093616 + 60.406066431119953108i), (5.5735967794918568988e-16 + 2.0132967078804768324e-16i)}, + {(119.24704789341511457 + 69.98633281155959196i), (1.8065303340224204233e-16 + 2.2376141261186676102e-15i)}, + {(-15.360314185562758738 - 16.827593475713307214i), (-1.071565440846803039e-8 + 1.8450874732773880885e-8i)}, + {(-97.643505456301511458 + 141.5074332888640356i), (2.2245776698262367957e-16 - 2.052672726647062966e-16i)}, + {(155.67764077096754249 + 141.30222792785167485i), (4.7689260616933640245e-17 - 1.8191198009549466462e-17i)}, + {(-55.853217555558451579 + 141.70473445660499578i), (2.3682436333431257974e-16 + 8.7243294311565675238e-16i)}, + {(-6.7327429207996782878 + 69.888730089734863782i), (-7.7403804221305791429e-13 - 5.7936691217966241201e-13i)}, + {(39.79629594493967204 - 146.42865393341051572i), (6.7137217871191725028e-16 - 6.7618460549044955068e-16i)}, + {(102.44006094071420421 + 89.667826593430177695i), (2.5166207852608539328e-15 - 5.3520031459226594262e-16i)}, + {(-10.603047761270152805 - 89.016531128757748093i), (-9.6371987188914414621e-14 + 4.7014778381545221742e-14i)}, + {(38.445399273995221279 - 50.334300182048643535i), (-1.1591421804251095767e-12 + 2.2902519191112508945e-12i)}, + {(82.696377960873206803 + 8.8183955913864728871i), (1.278496561797214891e-13 - 1.8330271964265976919e-13i)}, + {(81.367441277429605861 - 79.278939959232772594i), (1.0101705307218518923e-14 + 8.436915374301559005e-15i)}, + {(63.893448309570274546 + 121.64258580146662325i), (-2.1707519554113740651e-15 + 8.8834938443604850711e-16i)}, + {(210.54854875969431305 + 51.127174884200186966i), (-2.1360984299938610988e-17 - 3.2743800822242574224e-17i)}, + {(-98.709179147172733337 - 31.962210604479889042i), (2.6201748738827600103e-14 + 9.1732276156272948962e-15i)}, + {(-24.749622054451339892 + 131.28579007697226189i), (-2.9270654594774503337e-15 + 4.1049300428105055314e-16i)}, + {(-5.0430057841930677753 + 105.4954480822199514i), (-1.1201620700284768383e-14 - 2.1916901339082484341e-14i)}, + {(-105.71654073700398158 - 29.741938910538490148i), (1.2920602467545070094e-14 + 1.0546449805700630815e-14i)}, + {(-46.560621829392857762 + 21.090366700741451922i), (1.2437365924828605607e-11 + 9.4394314903996771417e-12i)}, + {(94.707853732390404389 + 59.554833777205054446i), (5.3652858941601384573e-15 + 1.4213173779819050971e-14i)}, + {(-201.27622911270046302 - 50.348744696728033432i), (3.2644859281281610291e-17 + 4.4776175809868470366e-17i)}, + {(-34.235020292945527842 - 89.732978807134500698i), (1.0361547732709967685e-14 - 5.609528190821415253e-14i)}, + {(-61.277348160269063726 - 30.669326892383015348i), (6.1168183077339838427e-13 - 9.6321297953897467817e-13i)}, + {(7.8716619163817060922 + 139.83840274570002293i), (8.8910295908986321923e-16 - 1.7330242357581256349e-15i)}, + {(-79.877520682680753339 - 69.205705602546274235i), (-2.3576637653279058203e-14 + 2.7027286425625234268e-15i)}, + {(75.603175495831877129 - 149.51898183308659895i), (-3.3985652485384606274e-16 - 1.9590803798645060456e-16i)}, + {(98.594247721240549254 - 6.6011740183894840328i), (3.8633439165424877566e-14 + 2.669707509423479824e-14i)}, + {(-1.2864683544292832007 - 81.152142371173397351i), (-5.1903739724523278376e-14 + 2.5854806339174900263e-13i)}, + {(55.837990145149909438 - 87.307240810995537572i), (-2.7881553961640809878e-14 + 1.088632307424382318e-14i)}, + {(-52.923371855902999528 + 24.661850590860744603i), (3.4869632369588826853e-12 + 3.2480222642274292037e-12i)}, + {(53.114357938144571847 + 134.54425808131119879i), (-3.1170433859281243811e-16 + 1.4378524733792995014e-15i)}, + {(232.10272268952266472 - 67.119143213642090018i), (-1.20489775528871169e-17 + 8.2953755740740284064e-18i)}, + {(114.91912323970463206 - 5.4771754558590117767i), (1.0786744192318752367e-14 + 4.9531486339871584897e-15i)}, + {(277.42311978435975561 - 122.99143689163723536i), (-1.5239457611357824454e-18 - 1.0881316307255845926e-18i)}, + {(168.199682499256852 - 189.62228710865747416i), (2.1901703735460636047e-18 + 9.189269411326465578e-18i)}, + {(-17.609976730449439231 + 26.065559362250233733i), (8.9858852315479873758e-10 - 8.4735935900302402384e-10i)}, + {(25.719505903003884839 + 176.68404984070988917i), (2.1000627622898480919e-16 - 6.3754599110782427253e-17i)}, + {(-20.041718833945822098 - 100.48191243965678154i), (-3.117265327518558505e-14 - 7.768195210877836098e-15i)}, + {(154.53866913768473523 + 46.555011074649769398i), (-4.8890459358306241658e-16 - 2.6719474819929446847e-16i)}, + {(34.076715763861450625 + 133.5270323073615657i), (1.8103702821352403999e-15 + 1.3661904809492885218e-15i)}, + {(-68.657729236215672586 - 35.368576662314929138i), (1.7318022897861970167e-13 - 3.5110875785204451947e-13i)}, + {(51.099736279129437833 + 64.808330492975102288i), (-7.309151118291813229e-14 - 2.2312789549147083112e-13i)}, + {(69.07859925152637004 - 0.16081048527561633832i), (1.2005201695022891767e-12 + 2.5335209031649765642e-14i)}, + {(-124.93640045185540544 - 46.551314779795802679i), (2.929378257333970223e-15 - 1.6572284322329225591e-16i)}, + {(177.92780093697581378 + 30.047401869580188105i), (1.2420618923816146306e-17 - 2.0333353521655900506e-16i)}, + {(-134.59795419822867757 - 44.018036031403759978i), (1.6279842142183699019e-15 + 5.1595821012856187778e-16i)}, + {(52.263472927817353764 + 42.141401505911396441i), (1.5189406289887274627e-12 + 2.0540538246958869305e-13i)}, + {(-149.82434886885093306 + 71.582537498100435869i), (2.6812064635883153477e-16 + 3.1021258309585158389e-16i)}, + {(-51.58066715321940876 - 203.25748649727390216i), (-3.9556383466453691203e-17 - 3.2431533254843182154e-17i)}, + {(29.539791353621584591 - 102.55003472954784627i), (1.3893413953021795161e-14 - 1.798112996090031549e-14i)}, + {(74.800013790892066368 + 6.9174197941326527328i), (3.7681003262571899842e-13 - 4.1649223276779392917e-13i)}, + {(22.926647915558557855 - 37.767259417810464583i), (-6.5898155903142043985e-11 + 7.4137645173047204785e-12i)}, + {(-22.331203873109220837 + 110.64794688008782941i), (-1.2993753632339973953e-14 + 3.4661679830843203606e-15i)}, + {(-73.995451963509168536 + 34.235346302514983563i), (1.7866405098121130426e-13 + 1.6150086943847840819e-13i)}, + {(-36.500147852483031841 + 116.28412456191578883i), (-2.4237838461618235052e-15 + 6.269029323917060576e-15i)}, + {(-152.67377722389900896 - 114.26214452013591938i), (-1.032460206348833331e-16 - 5.8440132193591973298e-17i)}, + {(103.7952276280616104 + 42.712862651681618331i), (-1.370419404058260533e-14 + 5.5855834231800344971e-15i)}, + {(-139.83875016006658143 + 115.7015954098384185i), (-1.8451591494721606897e-16 + 1.4434224269908928629e-17i)}, + {(94.911769343725666204 + 99.637413356741220127i), (1.2050079673885487474e-15 - 1.9953409638276048038e-15i)}, + {(43.433887213138625327 - 50.43826686608235832i), (1.058398608761039295e-13 + 1.6397292767208593035e-12i)}, + {(49.476264811477676631 + 11.052730003115856405i), (-8.2101405835141437115e-12 - 1.8083829625855204874e-11i)}, + {(15.401645142803726429 + 41.961686597679189958i), (4.0620028850489805508e-12 + 5.8521811560498203847e-11i)}, + {(93.154824217209281301 + 34.527433425570315251i), (-4.4507941166815950094e-14 + 3.0536915725871646336e-15i)}, + {(81.468964525204967231 + 28.535061700410036423i), (-1.5842615933984829927e-13 - 1.4688648641902734485e-14i)}, + {(-23.480824687482602542 - 12.170431671213471247i), (2.5708586628523844619e-9 - 4.8216562142568967834e-9i)}, + {(-145.33843331693202572 + 41.446877520907328574i), (7.5840937814898200777e-16 - 5.7607918655701680892e-16i)}, + {(-51.742504112538753702 - 19.760448487696329778i), (7.5657443710567614912e-12 - 8.5186690579821157497e-13i)}, + {(44.137240070926061719 + 91.304162027687283398i), (-2.7725422875003890923e-14 + 2.333188069936553403e-14i)}, + {(-167.6026505446445185 - 121.39925566255915612i), (-4.5147993389491356729e-17 - 3.462127868560260343e-17i)}, + {(-71.764950311584115639 + 10.707578355015998639i), (-1.6629072060983243203e-13 - 6.5923737905132952529e-13i)}, + {(-148.21232872241208156 - 136.90259582862890397i), (-6.5549714320347336685e-17 + 2.8753950916280389726e-17i)}, + {(-162.33202538711759644 + 8.0760869632968681486i), (3.8869612547099706806e-15 + 7.4374247694051901969e-15i)}, + {(-58.322271622344544539 + 35.328647226643369095i), (-1.8413893151417313404e-13 + 1.181157145956200104e-12i)}, + {(130.74805828823372167 - 99.574563533577247654i), (4.322523135858481041e-16 - 1.8729142292098691027e-16i)}, + {(16.431490087784496268 + 18.199101930985925435i), (2.7554350407606198499e-9 - 1.3974296852152533487e-8i)}, +}; + +const std::vector gamma_10_c = { + {(91.375317406275385679 + 123.62125824345883984i), (5.0121495146519589002e-17 + 2.8116277738547994602e-18i)}, + {(36.439820282486138581 + 89.256171353892170828i), (-4.1268548594465899242e-15 - 3.3833302014061256888e-15i)}, + {(-119.67773254719162423 + 133.53649637879269108i), (5.2018370272547475056e-18 - 8.9621333276117017202e-18i)}, + {(106.06672596117702767 + 51.005991743401601468i), (1.5538714095929873505e-16 - 7.2274984734068657003e-16i)}, + {(14.404707913089872307 - 130.89279271174393671i), (1.1397142314218257011e-16 - 2.0260499700695319873e-16i)}, + {(-122.99177118976774636 - 131.0821944323175785i), (2.9683896956250722864e-18 + 9.6667459998892669556e-18i)}, + {(30.171353874743644496 + 23.088423378640900552i), (-6.0875188391703483792e-11 + 2.0603512546338664732e-11i)}, + {(-98.146244096188766548 + 91.254305019828422019i), (-7.1717223474245465694e-17 - 1.7481418539052059719e-16i)}, + {(-56.083506895743582277 + 102.39315443711495845i), (2.4946805045934398733e-16 + 7.1352062665903995109e-16i)}, + {(59.74638772222886729 + 50.825767092175190953i), (-2.9890119299977501657e-14 + 3.1180914742042975005e-14i)}, + {(144.63953248826783238 + 36.078767563278617558i), (5.3386772895154447053e-17 + 4.3975804202178484327e-17i)}, + {(28.121354015976017138 - 88.66586700788840858i), (-7.5519411574309206255e-15 - 9.2099801249481613848e-16i)}, + {(93.906669268667485539 + 164.10111373723074735i), (2.8097296498603799503e-18 - 5.6372974283453578272e-18i)}, + {(-130.91432404628119457 - 8.0618938068160677091i), (3.0778939012491389323e-14 + 5.1994280876282401787e-14i)}, + {(-37.702231260066639607 + 136.43496616939683008i), (-1.0206052178866261833e-16 - 4.4523452970817661064e-17i)}, + {(-78.693385116191151951 - 165.71058252055871662i), (-2.0893996517866350659e-18 - 8.0433385547894142218e-18i)}, + {(-39.819649790252711341 - 57.347311617326091948i), (1.2512786750801680975e-13 - 1.9477048447271313475e-14i)}, + {(-133.87655280602700714 - 45.782026803798189007i), (1.0804188320148766498e-16 - 1.5437369154305533827e-17i)}, + {(75.785160992883035647 - 62.797064421007952717i), (-3.4720104672714102995e-15 - 2.7416014468047409457e-15i)}, + {(93.391574950436663016 + 126.21198554316836749i), (4.0547630544101465724e-17 + 2.5081147430825460211e-18i)}, + {(-24.891254408856745783 - 29.537782981662630277i), (3.0798028341261225016e-11 + 3.3028190493160160173e-11i)}, + {(19.085348790017462761 - 74.669270954650983185i), (-3.8109769788701869466e-14 - 3.2215384246625205821e-14i)}, + {(-8.4731072703203871299 - 77.809158882181009176i), (1.7135253784861023443e-14 + 3.8116615668154726246e-14i)}, + {(-155.82153096748749022 + 15.71639309342734947i), (-2.1327906028905766889e-17 - 3.3361704703708715144e-17i)}, + {(-91.474661697129121762 - 22.256168510589240839i), (4.5328796511849318654e-15 + 4.3747614629132032199e-15i)}, + {(-125.53222077255794886 + 55.271310229916934986i), (8.1559928879943572875e-17 + 1.2457911275026351595e-16i)}, + {(-129.20958301497390153 - 16.555248057487876423i), (-7.3685549862258693705e-17 + 2.3703333392074605302e-16i)}, + {(-27.911846007030931105 + 90.313745420049755808i), (-6.2457587650847143646e-15 - 5.8516555271915099565e-16i)}, + {(-44.039488913637022449 - 121.28979158535970839i), (-2.6010681486433193012e-16 - 1.0324805937223109158e-16i)}, + {(-66.929932732179480581 + 85.297915884145808718i), (1.4431961813458698314e-15 - 6.2133838083478518309e-16i)}, + {(52.54779003129331727 - 48.921587715565912902i), (-3.2052273673532944143e-14 - 9.9917683901696210931e-14i)}, + {(-40.169457961573847626 - 84.371848873584383455i), (-1.5268692656927839906e-15 - 6.8176079594568924716e-15i)}, + {(-5.841517115061798826 - 94.255952122082860001i), (5.0195790383906712783e-15 + 3.9919518670042251505e-15i)}, + {(-108.27218689516750771 + 95.184635092579696902i), (-5.6294741257650923208e-17 - 7.1727146802050400828e-17i)}, + {(-7.004825994153629054 - 87.942091740856369597i), (8.3391199623179412702e-15 + 9.5199197849124422812e-15i)}, + {(10.032764528860463216 - 65.966374988578550642i), (2.8327030294031316539e-14 - 2.0801612931422583108e-13i)}, + {(27.476556175270300031 + 65.379318269417851184i), (-8.3042616028648576702e-14 - 8.0911621882040282207e-14i)}, + {(96.682957916711416146 - 35.641519927509321519i), (2.5837778894593963184e-15 + 1.1133094404635778997e-15i)}, + {(0.55665029229253504273 - 13.789740592718278123i), (1.4941360681192247459e-6 - 6.1719245686498578256e-8i)}, + {(-10.868210641161498486 - 74.342694510916771833i), (3.3326162877889648608e-15 + 6.2648484491099649919e-14i)}, + {(47.483869970372523994 + 60.031818549438177968i), (5.1284191474214437065e-14 + 1.9203740862125618618e-14i)}, + {(105.37872971548011947 - 240.7756436277025216i), (-1.3209837268430786736e-19 + 1.913154186112586917e-19i)}, + {(110.01073826200833139 + 97.440551478472286817i), (-4.360035832718273824e-17 + 6.6145007413664781365e-17i)}, + {(-4.7881962710001673145 + 36.370053788008519291i), (1.0170715465326427191e-11 - 8.0325941300465135687e-11i)}, + {(173.03417853834352513 + 9.3693987472018065432i), (-1.3099031682931852112e-17 + 7.8964656452919980572e-18i)}, + {(141.28313305929555099 + 195.64842241807744472i), (5.4765497832733006397e-19 - 2.5044768549564813847e-20i)}, + {(77.387464082387666053 - 111.18717317145478773i), (1.7326765745031796517e-16 + 4.1094866001767313103e-17i)}, + {(84.027111303576646151 - 27.389955008384553992i), (1.3162823666758638881e-14 + 3.5199653899598653452e-16i)}, + {(62.00552061857621311 + 113.64772831066242986i), (6.8725068281238324897e-17 - 2.7093795325543730708e-16i)}, + {(131.24031531933792394 - 93.116617470797393707i), (-3.1823732794831184219e-17 + 3.0167201265066945694e-18i)}, + {(60.947537490884130307 + 126.62450309272747972i), (-3.1349311705894298458e-17 - 1.1863067733754814143e-16i)}, + {(108.13914741689343657 + 61.596109502875961539i), (-1.9653503028078894249e-16 - 3.7296398713782431644e-16i)}, + {(-33.206662182801402139 - 108.31474027232614787i), (-1.0207633463656965432e-15 + 1.277085239505768861e-16i)}, + {(255.24962804382863624 - 66.295794089882093658i), (1.8802140764718750051e-19 - 1.2745046606659719214e-19i)}, + {(46.731445086666667521 + 297.72376178669946967i), (1.7808656342785266843e-21 + 5.8845215034163297678e-20i)}, + {(184.92650115874658923 + 11.835270312930031622i), (-6.2589689921719584502e-18 + 4.668232378577540943e-18i)}, + {(43.635547596244947499 + 58.439949299306746866i), (8.8537817238387848325e-14 + 6.7572852523212814565e-15i)}, + {(-23.20640342808688672 + 8.4740172078498332553i), (3.3841139880459632341e-9 + 9.9834730441735016846e-10i)}, + {(-160.1724703466944959 + 260.59016879887354889i), (3.6442923959633945664e-20 + 3.4497911321561777535e-20i)}, + {(135.10680239535025748 - 34.106353347292049705i), (1.0751177025315052795e-16 - 8.3467122457997659585e-17i)}, + {(-0.36623094902539288231 + 30.2660993344993976i), (5.4017092263957300892e-10 - 1.5908676128674676168e-10i)}, + {(31.066857830446810596 - 60.804337534590288783i), (-9.1063287238345866326e-15 + 1.7013343536253734576e-13i)}, + {(-92.802355177507820372 - 68.509512266540625092i), (-8.3913241069349023472e-16 + 4.206927592327640619e-17i)}, + {(-91.421745223982213702 + 186.07170138212214283i), (-3.023865545685960019e-19 + 2.4291961397289370448e-18i)}, + {(-54.640352496019183093 - 115.93743553326621054i), (-8.0385635940453441031e-17 - 2.8736702548518891622e-16i)}, + {(-109.48374578803404233 + 73.491732649331495963i), (-2.0438529733741126866e-16 + 8.4672806591960864278e-17i)}, + {(-174.49575660970918989 - 85.52277884729292623i), (7.6616113368417991901e-19 - 4.5531826046979196322e-18i)}, + {(-50.240947298428785928 + 4.2069067048712778245i), (-0.0019937356404964054306 - 0.0001135257396690248497i)}, + {(-73.000166672515959476 + 94.137237230773308738i), (5.7810943733081225546e-16 - 2.0855138348798865501e-16i)}, + {(98.140894732994738092 + 197.00911058483848137i), (-1.5215397756851426522e-19 - 1.3654968596922465393e-18i)}, + {(-157.73461735679740059 - 32.797522423537756708i), (1.360830156779286219e-17 + 2.6597901516798041944e-17i)}, + {(183.6679743095107824 - 108.5085854468117077i), (-1.1262486526636675025e-18 + 1.5265107433735665426e-18i)}, + {(7.2777994490028863339 - 13.661104444158480575i), (-4.9036590043479212955e-8 + 5.3752840842202428464e-7i)}, + {(-56.019751866407183627 - 80.540077549858636985i), (4.2106198339694421754e-15 - 6.9542638622090789614e-16i)}, + {(-92.368813632504767952 - 135.49110271733789546i), (2.4425253937610204983e-17 - 6.8722017562776593911e-18i)}, + {(-92.153405012018225761 - 47.560972980466367233i), (-7.1867487176327886734e-17 - 2.415326349258826141e-15i)}, + {(10.171841689891708782 - 128.40518456880610643i), (2.1151813350023507502e-16 - 1.977817385854890375e-16i)}, + {(-144.46347007235073079 - 89.25535133222355455i), (-1.281082518044717557e-17 - 1.2284354576927278562e-17i)}, + {(40.208287662028673992 + 134.44472850638186401i), (-1.1934938480895558294e-16 + 3.2980857669252086916e-17i)}, + {(112.16772495653010822 - 121.86659825465268625i), (1.0073224327405383747e-17 - 2.1605391748061463316e-17i)}, + {(61.046106601317752904 + 122.01247430976647479i), (-1.7457517065160059373e-17 - 1.6418390274253195726e-16i)}, + {(-44.722433199785690761 - 51.866158145834916127i), (9.6132051147696628315e-14 + 1.1832738825643414597e-13i)}, + {(-134.45795281794607945 + 120.11609852802284593i), (-5.3776914767805161614e-18 - 8.1840056915467246661e-18i)}, + {(8.4452300576408259047 - 141.10098547045478767i), (9.6608108883702507718e-17 - 6.0908088489331488734e-17i)}, + {(106.11424613481884194 - 37.755662765162398387i), (1.1029295075505681996e-15 + 3.3088610586578544363e-16i)}, + {(-100.62947065663918522 + 56.121136193345954268i), (-2.9335018136908884923e-16 + 7.9467713775589962444e-16i)}, + {(-33.295235072107523422 - 53.083595657496296383i), (3.0497381845261609464e-13 - 2.1445487888651181591e-13i)}, + {(-52.652842510624743966 + 32.931509126929661591i), (-2.9387283588705572541e-13 + 2.6695473398304300636e-13i)}, + {(5.1404350963531308949 + 21.82626694225080044i), (-6.0227511356556993511e-9 + 1.0329675113380430094e-8i)}, + {(-141.04135886657937249 - 185.98748257357999591i), (7.2778415991888939176e-19 + 1.6435377905727242379e-19i)}, + {(2.6924158766271801824 - 79.398024267567720358i), (3.4958927219418493522e-14 - 9.9051324260830764839e-15i)}, + {(46.04349276663470647 + 127.65335893171001658i), (-1.6649418183565159933e-16 - 4.8876282579186340832e-17i)}, + {(-179.87899696083590584 - 143.96185935008281831i), (-7.6137144871092875284e-19 + 3.7022032373401755763e-19i)}, + {(34.50210794185978358 + 93.111938284904269381i), (-3.7090944678180490661e-15 - 1.3960992962098231904e-15i)}, + {(103.71210866696858943 + 85.596520677022539303i), (-1.5488116087826603924e-16 + 1.1537660651368598524e-16i)}, + {(39.953392229071333475 + 122.23563407232684597i), (-2.9689806351604659057e-16 + 5.7423405250124182393e-18i)}, + {(22.337193558213890299 - 8.3725052909364876541i), (6.4146816590639855512e-9 + 3.6221737930763850374e-9i)}, + {(53.726770569507820596 + 127.32975534548273799i), (-9.9005108769376209742e-17 - 1.0568938957306222541e-16i)}, + {(276.49987549106685947 + 196.81407237429345969i), (-1.8039662171751162087e-20 - 1.6028452986611582261e-21i)}, + {(121.74549849628616016 - 74.069293501073374841i), (-7.5457733895386151499e-17 + 7.7601810127373192636e-17i)}, + {(136.01798845808636429 + 129.14401389759620997i), (-1.638310456445097058e-18 + 6.6681868753906484418e-18i)}, + {(34.73655014653691353 - 68.83031603276569399i), (-4.8312628888399167424e-15 + 5.0131630843622222004e-14i)}, + {(72.905813583315278947 - 77.401502580363967354i), (6.6297674443176255698e-16 - 1.9171305162653722956e-15i)}, + {(-21.257157175711263619 + 71.099899249095955156i), (-6.9275067834113268064e-14 - 1.2000700175431953711e-14i)}, + {(45.601804943738699194 + 67.661644039268153961i), (2.6414169060921220725e-14 - 1.1265282267131786448e-14i)}, + {(-50.708451904614307182 - 72.627359589485891433i), (1.1699684891035976254e-14 - 1.6646591205443624175e-15i)}, + 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58.507999644080001644i), (-1.4510638773595405526e-16 + 4.7958003250017028447e-16i)}, + {(113.88250180589398042 + 157.7111188685790637i), (4.7412969186926860823e-18 - 2.3688974689518644206e-19i)}, + {(-56.596607326635393065 + 24.906066264702417357i), (2.3272047322717616485e-13 + 3.4017468646665475085e-13i)}, + {(43.890683395655130994 - 71.355932982056259561i), (1.5020168656516497446e-14 + 1.6069867610206632437e-14i)}, + {(44.911385539326381888 + 112.64700452715960921i), (-4.378581227383179089e-16 - 3.0866836315641248402e-16i)}, + {(84.739541770387930342 + 80.968749600906747332i), (-1.5072588461843001361e-16 + 7.5014178744662002196e-16i)}, + {(-104.11425054255067835 + 158.39440969743566257i), (5.3896647740307937475e-18 + 2.5775446908761001133e-18i)}, + {(-75.077489934035497754 + 16.202217621990079977i), (2.4522076448431267392e-14 - 4.0842906143663996984e-14i)}, + {(-35.406850858753955436 - 194.75913572580827804i), (-9.7670219810686133917e-19 + 3.7867197140541415622e-18i)}, + {(-10.625474713682388384 + 39.788276856877246246i), (-2.2986538145730720182e-11 - 1.0090918954712237702e-11i)}, + {(-33.595974812078068794 + 109.69731375193012468i), (-8.9972439552056275578e-16 - 1.1568044868400999193e-16i)}, + {(81.585242995108615105 + 32.26186234383953888i), (1.131691429126441736e-14 - 8.5094899213238491807e-15i)}, + {(-88.176779254713039791 + 18.976970516267314792i), (4.9345105278743571892e-15 - 8.2846709066763432427e-15i)}, + {(-75.902984636917992134 + 23.252595764531921674i), (3.3756431701385354763e-14 - 6.4095497002867393492e-15i)}, + {(-116.8923339885822088 + 10.083843806823802325i), (-4.6056081893446544335e-16 - 5.3182224106326984204e-16i)}, + {(65.331046017868175113 - 16.670139336414020903i), (1.6271615720515875654e-13 - 1.1746827910278869348e-13i)}, + {(-147.41983729546163318 + 1.3753180694730255951i), (-35288.988839361460123 + 82944.911225040283171i)}, + {(-165.02982466720516186 + 42.558902469236400634i), (1.3832842268193998891e-17 - 9.982357074920019459e-18i)}, + {(29.35616645063958785 - 59.488051929979988586i), (-4.4117220387242005956e-14 + 2.2313209661174717318e-13i)}, + {(28.099769229401882598 + 10.783688021148151392i), (5.7953593070780719193e-10 - 3.7941293942949291347e-10i)}, + {(80.685831290852036091 + 204.79681695260171637i), (-1.1384266576526678572e-18 - 7.628651045292432248e-19i)}, + {(-71.853835488283564814 + 160.5049017640450586i), (-5.8248925392938491609e-18 + 1.1266025306879769778e-17i)}, + {(129.14537663552840741 - 90.779832208445355946i), (-3.8382945533099831147e-17 + 5.3392394037564543371e-18i)}, + {(94.285660229972734214 - 17.623485641204258201i), (1.6367561066059493313e-15 - 5.5560935009171558043e-15i)}, + {(-20.184098872470904951 + 114.8365817547690142i), (-1.6278498806995643524e-16 - 7.5856328167528136793e-16i)}, + {(81.124962331056622133 + 31.274583944808409086i), (1.3151224098397834541e-14 - 8.2146238234907957455e-15i)}, + {(114.6044869713096972 - 178.225193100869717i), (1.675762442998696117e-18 + 1.1180256242286931289e-18i)}, + {(-19.519097748187647312 + 168.71711586789626836i), (6.8801258014171728687e-18 - 1.6750449856059558262e-17i)}, + {(205.78003151756018951 - 243.86426238312654391i), (2.5322826544172795201e-20 - 2.1937276695107538202e-20i)}, + {(33.321128764841880354 - 69.413950394228081109i), (-1.4821198427470767381e-14 + 4.8773787896212621664e-14i)}, + {(-149.47264353394581349 - 242.09119367626934149i), (7.660174121275055859e-20 - 6.9506538230456067751e-20i)}, + {(-37.052111598416828997 - 19.452150598629046385i), (-1.2857725759559592198e-12 - 1.975607313815102996e-11i)}, + {(184.42746589343974506 + 4.770106708103091897i), (-7.888848700067678942e-18 + 2.0925400378925857197e-18i)}, + {(-42.725535648293103463 - 143.78839199445707209i), (-6.0814803578662067866e-17 + 1.3678179709629026681e-17i)}, + {(154.60077540367899473 - 63.804336712463275205i), (1.5425763306627708148e-17 + 1.5377310818562409191e-17i)}, + {(-98.560979586835983923 - 59.412407524824949689i), (-5.45895837217640961e-16 - 6.618159649449739056e-16i)}, + {(-119.26785282899557217 - 60.822108159687815032i), (2.588952385691292602e-18 - 1.8968519334527926059e-16i)}, + {(-23.47696467787549679 + 12.273379881036676764i), (-2.4431346129492383052e-11 + 1.7981961936103803715e-9i)}, + {(210.09610542950380818 + 171.73736133750148269i), (-1.4212511242695051974e-19 + 9.3355551050211603583e-20i)}, + {(14.653623185679940377 + 171.24994103447218663i), (1.0977360477550284997e-17 + 1.1874585301321188771e-17i)}, + {(31.772876618163554241 + 151.56301954514549379i), (-2.0618778835813707517e-17 + 4.1192887196389243473e-17i)}, + {(58.544986575024140052 - 175.73015830119436487i), (-7.6907959653696745226e-18 + 3.7511021318924205744e-19i)}, + {(-54.005030400045249905 + 1.2658946384101550375i), (-11646.813801730444538 - 289107.06508566788398i)}, + {(2.3959685649158255494 - 79.011731659174671449i), (3.7092950140168455085e-14 - 9.0752816351531170371e-15i)}, + {(29.398653874226926774 - 274.28581177417095205i), (7.0931318875531905968e-20 - 1.2358009955998596786e-19i)}, + {(-7.1144894413125392418 - 196.90239794773046356i), (3.8086801476695130494e-18 + 1.5501512916448596208e-18i)}, + {(180.90398868977072766 + 16.07919964416480596i), (-6.0197198124526430011e-18 + 7.4154756602672409718e-18i)}, + {(-39.69052345396667647 + 118.0782522644503274i), (-3.9436878716606005057e-16 + 5.5296003807145211846e-17i)}, + {(91.877258261504664461 + 41.769967756044067642i), (1.4276060319065555838e-15 - 3.1528596902148022648e-15i)}, + {(16.644723049462438524 + 37.850321737815875167i), (-1.63947660223206119e-11 - 2.0328861137463786338e-11i)}, + {(-3.411966753186221446 - 13.748341012883887657i), (-9.7316185658108066533e-7 + 3.6342498466151069076e-7i)}, + {(-75.585987341982459498 - 161.77864578185628375i), (-3.3829114426905233575e-18 - 1.0341880610196928867e-17i)}, + {(123.82663226664591605 + 99.897870555490797528i), (-3.0966745865857897131e-17 + 1.7931867100686716176e-17i)}, + {(72.729688716630192857 - 13.321225713176950478i), (1.9842287072279158545e-14 - 7.6844568082058840361e-14i)}, + {(51.240708453613983409 - 229.08892200600283218i), (-4.1034975531363082043e-19 - 5.8844644777789264872e-19i)}, + {(-13.538238988489309733 + 147.40351211186387559i), (4.1699487940292703841e-17 - 5.8255639555948081435e-17i)}, + {(88.273979340319712605 - 140.67713188305771155i), (1.759678325794154702e-17 + 1.4962725373998119942e-17i)}, + {(114.44217105520586131 - 1.3237396789915822914i), (-9.7619161072479307227e-16 - 1.1391019393809959413e-16i)}, + {(72.335242543720440267 + 43.925674499712492604i), (-1.4173797070246346097e-14 - 1.4465849698998641882e-14i)}, + {(117.07501470359449058 - 144.17284746690651787i), (6.5741198356070101026e-18 - 3.7330931854073553482e-18i)}, + {(-39.301264713245487314 - 74.341214581846486453i), (4.0392617955537564514e-15 - 1.9555399086989035441e-14i)}, + {(78.795873367726201764 + 70.580108564590858578i), (-1.0610066122116769368e-15 + 1.8607819501420429645e-15i)}, + {(-17.159839777271056249 + 56.269980725860044402i), (-7.1007919397901137312e-13 - 7.1084817039945678053e-14i)}, + {(68.640744279265788919 + 23.887064493766366979i), (9.1657639546688634694e-14 - 2.1417394599372900426e-14i)}, + {(-88.067713264241149318 + 4.0437030784805481076i), (-0.0022981818819652771214 - 0.0050717774458542861857i)}, + {(-77.240758366650538846 - 25.329641937784092676i), (2.7160145934953417092e-14 - 2.1062352037647939622e-16i)}, + {(11.192755063452898057 + 34.700288590256434418i), (-9.0316019980172061783e-11 + 1.3695860502937197239e-11i)}, + {(53.974376042316542623 - 56.745056251337722131i), (1.2741845355646960022e-14 - 4.1796711956540997532e-14i)}, + {(28.313027906099186737 + 66.032161549750483687i), (-6.7538778462010173003e-14 - 7.6196435580630540554e-14i)}, + {(18.639548492806447655 - 74.772779952043535445i), (-3.6154982866957347631e-14 - 3.4450357573474015245e-14i)}, + {(-263.05897422418411224 - 171.58265482079224284i), (-3.3420655349473085039e-20 - 1.8794974046116122118e-20i)}, + {(170.7508910860441631 + 121.24506918373924691i), (-2.2703404688019259609e-18 - 2.1612921820377637926e-19i)}, + {(80.360421699746581226 - 81.364358602329147629i), (9.0766243914288102712e-17 - 9.7393754290258062236e-16i)}, + {(-149.49485946620237087 + 5.367648901619456403i), (-4.3863638340642080511e-8 + 1.3575802331007944944e-6i)}, + {(213.48390200478058887 + 81.683091419373752728i), (8.2525265813416259374e-19 - 4.7307900139419123705e-19i)}, + {(34.205214642868355668 + 88.554291539677663536i), (-5.4749458434050040184e-15 - 2.9597865487599068603e-15i)}, + {(145.39207485985113522 + 0.95168319861666328396i), (-8.875460062971681875e-17 + 5.837656491261839949e-18i)}, + {(-161.34177034912110571 - 16.716672634350434379i), (-1.4386629812711781761e-17 + 2.3914795904806836146e-17i)}, + {(41.69789931373344416 + 115.35430574629732803i), (-4.5758741602947184177e-16 - 1.3596965453109755924e-16i)}, + {(174.08016467208301492 + 93.487482108166062744i), (-9.2383471131289575281e-19 - 3.9837158831292828754e-18i)}, + {(10.480603756688736894 - 19.102349473372523647i), (1.8600023090728109148e-9 + 1.6771141366867926263e-8i)}, + {(30.138557832215838062 - 109.6564868824291068i), (-8.8990585328348901481e-16 - 4.8804816995517420831e-16i)}, + {(-137.32245921846956094 + 119.91477053434833522i), (-5.6040811044246235185e-18 - 6.7373952311253685423e-18i)}, + {(117.47734549733554843 - 84.080650100118319301i), (-9.4130715783887403555e-17 + 4.8257762226347000492e-18i)}, + {(-29.906739517752644275 - 15.748054241535186293i), (-1.0312626104274964748e-11 - 1.6301191449992854382e-10i)}, + {(33.641878639308885113 + 48.104245699726092766i), (7.6040966008082638417e-13 - 1.9347782211869393069e-13i)}, + {(124.13562096103130727 - 2.7572474000636759683i), (-4.2289399635424385183e-16 - 9.5884182755107759273e-17i)}, + {(-72.380000340384668789 + 52.524429958211463543i), (-1.0590223433026440917e-14 + 4.1218548957468167089e-16i)}, + {(-45.570864910574343298 - 14.998459590051258061i), (5.0823587027286691357e-12 - 2.3226645049050860467e-14i)}, + {(10.322140289892782761 + 53.897363377800331818i), (-3.4353786453106065566e-13 + 1.4518955195010611556e-12i)}, + {(-112.81005771001197502 + 10.379216136092729528i), (-6.0933133230515819952e-16 - 7.8937464336050130658e-16i)}, + {(147.70394429738897202 + 50.441738409258633169i), (4.3039819339615663302e-17 - 6.9259339604593122369e-18i)}, + {(-26.734090414184173312 - 88.9227915583732198i), (-7.3939776116582841636e-15 + 1.2641633284966833607e-15i)}, + {(-99.512583102593083595 + 98.079907743418175414i), (-1.2179997039382986886e-17 - 1.2414925836492658767e-16i)}, + {(112.94073609490924071 - 112.94442439653042243i), (7.6090179517765309122e-19 - 3.4319631170406468514e-17i)}, + {(25.574122635987656338 - 91.704546101230278055i), (-5.3594859407199521157e-15 - 2.738235651991468403e-15i)}, + {(55.232379783189642808 - 48.323610602633735311i), (-4.9104842259614565118e-14 - 6.8503692347346553771e-14i)}, +}; + +const std::vector gamma_15_c = { + {(-91.040308126645939524 + 26.972882201580837602i), (7.0783253803657950007e-20 + 1.60750221484895012e-19i)}, + {(7.3687951582146364871 - 105.64972229774869561i), (-3.0661807290379553559e-20 - 2.0834460606901961289e-20i)}, + {(-44.249474370666035838 + 142.13395004094621754i), (-2.1785508155825345335e-22 - 3.0012068778834097719e-23i)}, + {(-61.791108359787529025 - 57.24833169457885873i), (-1.6168588420434082045e-19 - 1.0583081338133495777e-18i)}, + {(123.82992152892195747 - 70.537345283322551381i), (2.7579102674810958494e-23 + 4.4837010205815909705e-22i)}, + {(-55.876203109877799591 + 86.073263279565367156i), (3.7744450217377684639e-20 - 4.252625986665546238e-20i)}, + {(-143.49123773415840333 + 66.522661429433554758i), (-8.4264744444077033741e-23 - 1.7804022600011423405e-23i)}, + {(-161.43332343303421794 + 226.57253218697493935i), (2.1596680822595531158e-27 - 1.8419702115808178645e-26i)}, + {(-111.26236111414340257 - 28.02132290249135238i), (8.906061488454665727e-21 - 5.3740711129994063067e-21i)}, + {(181.29216127985432649 - 66.201229074446516165i), (2.4708979317917510904e-24 - 4.0068841942305503627e-24i)}, + {(-3.4053093472491662297 + 56.657394100932265246i), (3.6416297483698834458e-16 + 2.1733834515661319615e-16i)}, + {(-17.776751305575754003 - 104.43626330148842385i), (1.873535866753129857e-20 + 3.1075417932661055042e-20i)}, + {(21.041767831135839373 - 10.24149428839618281i), (2.6742844843196690875e-10 + 1.9883258417793191878e-10i)}, + {(275.83075558230223123 + 23.141633604181816253i), (6.4277422410369271293e-27 - 1.9859515399073443355e-26i)}, + {(121.74109016017349916 - 296.9912273547336099i), (1.0062049233551062782e-27 - 1.9838646031813834068e-27i)}, + {(151.82054204514358275 + 34.478946335119985633i), (-1.1653307900223264958e-22 + 2.5895411550063007016e-23i)}, + {(70.736180019953891929 - 26.872040638090467723i), (4.3459934479959301723e-18 - 4.5032746984388573016e-18i)}, + 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7.8089963737487439428e-24i)}, + {(35.372040353130124402 - 36.656327306001394106i), (2.1900413132177878367e-15 - 9.6543221513920691818e-16i)}, + {(179.25268346085945836 - 41.306650589984066357i), (-9.3682388848736654076e-24 - 2.5395963600737461674e-24i)}, + {(-101.78865867200612172 - 9.6454054446491852559i), (6.7935827111887571258e-15 - 2.7416437858529776893e-14i)}, + {(-15.675615800722750848 - 10.183543921075594696i), (2.7091231574204048574e-9 + 4.4220746729952765557e-9i)}, + {(-42.86497913707842855 + 238.92350998339034618i), (6.2801656539431872474e-26 - 1.3056597774760065552e-25i)}, + {(-28.822372144090063983 + 68.777685426529771462i), (-1.6058510766673214887e-18 + 6.6520903573742790593e-18i)}, + {(14.65377916346237086 + 101.07176195838351873i), (-5.5900214745552007538e-20 - 3.1743360494075002151e-20i)}, + {(-1.3008625622207721229 - 30.886971477459045587i), (2.9667610768402405703e-12 - 2.4785867405810070375e-12i)}, + {(58.636060739366094197 + 31.457896231529346665i), 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{(-62.638125251988554965 + 74.580704155793142718i), (-1.106303219593592567e-19 - 5.4400365012615132297e-20i)}, + {(-4.937814896122365127 + 128.84445969687016031i), (1.1369377622061749865e-21 + 1.5503899958647937091e-21i)}, + {(-179.6222703490931849 - 98.324182504753949274i), (-6.3562815220994912625e-25 + 1.6931849780878689521e-24i)}, + {(-74.020707093851839886 + 17.674865910173373607i), (4.4672289212985338424e-18 + 1.6347378163082038578e-18i)}, + {(-105.55065414699220128 + 49.770975514179141896i), (-7.7539019410933933042e-21 - 2.3835154545849866684e-21i)}, + {(-93.091023837031926291 + 0.52489691537300464663i), (-28688222091472784.0 - 11937573973183296.0i)}, + {(9.217126100894633467 + 17.223222573041681471i), (-3.1911373873663118955e-9 + 3.312354366054188284e-9i)}, + {(204.1937640503222724 - 53.630341844004846052i), (-9.1929440374066444968e-25 - 8.0627098829498779744e-25i)}, + {(-194.35670061835136835 + 70.747311457687288794i), (-7.6042617720537237165e-25 + 1.3544682002375821008e-24i)}, + {(-23.61748144102029201 + 12.997313463991361004i), (-1.0250577393138325826e-11 - 2.1186031023388773875e-11i)}, + {(-117.55085725890846504 + 22.904510532236788123i), (5.2848475984857625829e-21 - 1.4468842751268305301e-21i)}, + {(180.93326239317107706 - 55.535186690920291142i), (-1.4639925837773780478e-24 - 6.1485276784794546692e-24i)}, + {(126.09926892127691644 - 5.3961519254605807561i), (2.2503453283804376481e-21 + 1.6895079488810060335e-21i)}, + {(-101.92468417963893046 - 16.981556245767482238i), (3.8662604184005670365e-20 + 3.1097590254397673742e-20i)}, + {(-27.386415270604537398 + 43.735569545760284882i), (1.2995058516613188265e-15 - 1.0162237939357379721e-15i)}, + {(64.961818350430419855 - 90.833005925477564801i), (-2.8633563101378858503e-21 + 1.7071480923586527117e-20i)}, + {(130.39086026963266818 - 56.644234741273656653i), (4.6410352562868627821e-22 - 5.3675355957933124746e-23i)}, + {(-135.34545685032520623 - 76.322475221045451121i), (-1.9704441781383063683e-23 + 1.1073917158651150755e-22i)}, + {(-24.87277625756304289 + 78.826996685559919342i), (-1.4768514999777807416e-18 - 5.9751588293827120243e-20i)}, + {(-113.66804633641061173 + 69.90243732845127056i), (4.1343243245841391295e-22 - 1.0159217557485637656e-21i)}, + {(-42.029151089607871938 - 51.434906947346888728i), (-3.0355571254392769893e-17 + 2.2125105599052622242e-17i)}, + {(-192.75999430477830288 - 17.062952613910304933i), (-1.0378496864913453726e-24 + 4.0659967617023517458e-24i)}, + {(125.3451756714338643 - 93.648879032457230664i), (-1.0698393168161756093e-22 - 2.4880103220114570879e-23i)}, + {(106.98047557158183452 + 164.94941383925493028i), (-2.5824821654601298606e-24 - 2.3803675974275777557e-24i)}, + {(-47.971431942683246064 - 165.63621633898361551i), (-2.196405131283682015e-23 + 1.0390567129692142416e-23i)}, + {(-3.8244631224895289101 - 34.639953260809349445i), (6.036268303991315602e-13 + 1.82894744720606686e-13i)}, + {(158.33206399215265492 - 114.33004465971039565i), (-3.9211275118539116546e-24 + 8.441310798040185363e-26i)}, + {(29.195886530773641709 + 41.13182311834225402i), (-7.651158519076113655e-16 - 2.6234816784272971958e-15i)}, + {(40.839939464812289316 + 18.177587768252958966i), (1.7779085840486728661e-14 - 1.1290114507805253217e-15i)}, + {(117.91576704211171034 - 111.97080674409365031i), (2.5518338351972925003e-23 - 5.5784212279269426668e-23i)}, + {(-118.18584420397996837 + 109.23052754418117161i), (-1.0873465962670533929e-23 + 6.608219642019397375e-23i)}, + {(141.22579645075254007 - 61.69059652032539276i), (1.3820223919975925577e-22 - 1.1961273123533689103e-23i)}, + {(109.10079914539498702 + 22.420189112254522712i), (-1.8405814969434581971e-20 - 1.626275781601588842e-21i)}, + {(-97.023044012893009835 + 46.269967565262142273i), (-2.5900211485860811179e-20 - 9.7833056337297395836e-21i)}, + {(29.958159206458244483 + 45.511825681057551662i), (-6.1262991327389559596e-16 - 5.8915321882355736547e-16i)}, + {(40.757104382959020938 - 119.82029621555150811i), (2.5668536812113702151e-21 - 3.8777295762012156762e-22i)}, + {(-57.37470329777640643 - 180.81373730824236645i), (-5.7997076058039683695e-24 + 3.8104852329880064502e-25i)}, + {(216.43834993733958072 - 171.48273145340775159i), (-1.7227761430284078308e-26 - 1.288982091233588394e-26i)}, + {(45.251085855259830737 - 131.29008617999724606i), (6.2939995773034161289e-22 - 1.3778832380963583869e-22i)}, + {(14.116964872488397376 + 30.404696231188871991i), (-5.0276749478782004724e-14 + 1.2680555707385856292e-12i)}, + {(-79.544511169601122447 - 1.3153718740600484072i), (8447975917.6543607712 + 5330230727.2805957794i)}, + {(-48.511719461866661618 - 128.10769393428182639i), (-5.4766491129348655728e-22 - 5.2997825400538690591e-22i)}, + {(-113.75637300059125323 + 179.05925430438239232i), (8.4847719069678986749e-25 - 6.6615644910349834903e-25i)}, + {(-194.83834512588293819 - 33.758011449902014078i), (2.5501454232335073229e-24 + 1.6517413604495227119e-24i)}, + {(35.068471755663402689 - 60.333588647744640809i), (-2.0291388690543490629e-17 - 9.6960205454278073416e-19i)}, + {(-76.031799313635033855 - 107.42232743051877719i), (1.8974101641671201935e-22 + 1.3576663908375478503e-21i)}, + {(-18.146775016078318998 - 79.035172439772708231i), (-6.5087613390517105924e-19 + 1.8727965199592331704e-18i)}, + {(-92.470076091692803288 - 29.279164699875209976i), (1.7406519201199245572e-20 - 1.2670840794305577003e-19i)}, + {(-13.729884082058477546 - 105.43092336757142391i), (3.1161309638224639893e-20 + 1.4739068653290380829e-20i)}, + {(-82.884469137130992067 - 140.74632224335948649i), (5.3432107255865868889e-23 + 9.1188995568774408769e-24i)}, + {(-60.619726062103907793 - 83.48952940674887202i), (-2.8716434338650913589e-21 + 5.2195489004197769839e-20i)}, + {(2.9466058117695195229 + 32.037773186031202499i), (-1.995440712820859073e-12 + 9.0560199914952983238e-13i)}, + {(-47.824362085577014625 - 42.173275223925998034i), (1.5865676691079931655e-17 - 6.6269694079155918838e-17i)}, + {(15.778743821808191683 + 61.207579745896175893i), (4.4193872240358261911e-17 - 7.561223524901294454e-17i)}, + {(42.829742052311218004 - 36.352240324277872219i), (-1.9155192385417428435e-16 - 5.1649011744643300734e-16i)}, + {(-129.62972261519323069 - 145.73029119720223434i), (-3.7721279985231646916e-24 + 2.3313515784840716578e-25i)}, + {(-46.060998326962966587 + 3.0602170927965923752i), (24414.149254939515231 - 9845.3885667687100067i)}, + {(106.65472343204444883 + 145.22253359137081929i), (5.7086653345081899745e-25 - 1.3035547056089949791e-23i)}, + {(100.23630751032153796 + 51.837658828709898273i), (9.3059863562787071724e-21 - 1.1871898124551658063e-20i)}, + {(-49.118235749456147232 + 16.716817077491537447i), (-2.271328341487381631e-16 + 1.4084931029352243924e-15i)}, + {(-54.368400022209804945 - 76.892713417339322746i), (2.5979157421628944081e-20 + 2.0333278433386245231e-19i)}, + {(158.17938958414629269 - 77.088009773151171089i), (1.6204947046885920519e-23 + 9.6559131199001793353e-24i)}, + {(-42.782005037846410289 + 65.584358521111425944i), (2.0228792568218102225e-18 - 2.536196320180647525e-18i)}, +}; + +const std::vector gamma_20_c = { + {(68.164869992727929571 + 102.78009410031252457i), (-1.161996718330474182e-25 + 1.528885895106512948e-25i)}, + {(65.679862173210082688 + 92.238620354467997231i), (-1.0303392253267510694e-24 + 2.7591963376922116076e-25i)}, + {(-103.72989230685919892 + 140.05790685846554311i), (-1.7117896092300973439e-28 + 4.0016179994754787335e-29i)}, + {(-164.90055035605200828 + 13.71135959966833795i), (-1.3002044480358496668e-21 + 1.8026538914885195051e-21i)}, + {(61.572057986187964218 - 44.958974138739932869i), (-3.0473568255262516174e-21 - 3.750297733473472345e-22i)}, + {(-5.4435570484445561235 - 0.39510124336097257602i), (-1.3148566516921600783e+23 - 5.9541628481180518056e+22i)}, + {(-42.801672377237792944 + 9.2802935277230851341i), (-2.5992503850980585939e-9 + 8.7484837391994948033e-10i)}, + {(16.982247412265884634 + 93.681881497557043303i), (3.1220450077198489555e-23 + 1.1120830609814386755e-23i)}, + {(-120.26964458266635916 + 113.67514978228194877i), (4.0320637086481576905e-28 - 2.7921587134428841149e-28i)}, + {(-92.845011509179158793 + 6.4560062934170092674i), (-0.1154673123604697399 + 0.07848371144867526128i)}, + {(-22.752370321676909981 + 111.47516486082832898i), (5.1084060211634933666e-25 - 7.4819871265315360466e-25i)}, + {(-93.443458649115669346 - 36.600719263463723507i), (-4.2522577569638997251e-24 + 9.3979214524153895117e-24i)}, + {(26.493475215788684807 + 74.842286301353098565i), (-1.1804299301122888335e-21 - 5.0475503780789070644e-22i)}, + {(-180.24261913112275124 - 124.40307505691976075i), (-1.5864968897643821479e-30 - 8.8795816761287178708e-31i)}, + {(-3.3231553834872751274 + 29.576934691509670472i), (3.3796784843288779434e-13 + 2.1451142132458556853e-13i)}, + {(-94.234980209384062277 - 121.0364063396069696i), (-1.6944121624472991163e-27 - 1.4753031597902088188e-27i)}, + {(-55.77348028133501856 - 24.555386596977331948i), (7.5994457580958204233e-20 + 1.9497425512901811276e-19i)}, + {(-21.828068998122532207 - 11.225900316316540284i), (1.3121354249656198669e-11 + 1.7076759211867679774e-12i)}, + {(-56.895720229577086968 + 116.68720810476767724i), (6.1159153836662770773e-26 + 1.7679329360251395251e-26i)}, + {(-10.557918771835932858 + 211.07437665059202914i), (-1.9225391327369268589e-30 + 3.327330198066021724e-30i)}, + {(13.726145089011531297 - 9.3883378997799038501i), (-7.1910296895787265477e-8 + 2.0857796301613303432e-8i)}, + {(-14.917992145209094446 + 15.066068238294342052i), (2.4941684537146066418e-10 - 6.8623632391519855287e-11i)}, + {(-54.510168708856497233 - 95.257353230816462997i), (8.9942766998747876229e-25 + 1.5699738025738809915e-24i)}, + {(74.340455308229394404 + 17.897947236241236624i), (-1.246373634397873971e-22 - 2.9492425138693334079e-21i)}, + {(36.111635589447722339 - 140.14156922077941658i), (-1.9967581438713033773e-27 - 7.3603835171230439963e-27i)}, + {(-79.770862386925742271 - 47.15115320658287601i), (1.8631678794581281239e-23 - 4.7296989050459533884e-23i)}, + {(51.664583673700747113 + 122.80214468379217863i), (1.7004921907259350182e-27 - 4.0338993925856772901e-26i)}, + {(-0.97691212359968437884 - 68.433829463510861046i), (-2.1751084409963869738e-20 - 1.0020998753451077455e-20i)}, + {(6.7632501168042331585 + 62.395902141987249934i), (5.7709946578869701662e-20 - 1.2551142360653655311e-19i)}, + {(-126.16253355124815982 + 118.85461580929748493i), (1.565801586634315593e-28 - 1.1570770044087953695e-28i)}, + {(135.7856096648466746 - 135.29975259570230151i), (2.813898983614273596e-29 + 1.5963910528074058818e-32i)}, + {(-118.14810511223629419 + 9.5304029076448379953i), (4.5689680218724644142e-10 + 3.4033912528757007985e-10i)}, + {(11.19134628322604641 + 249.11381331649994308i), (-9.2233857209726598132e-32 - 1.0666965846791841447e-31i)}, + {(139.48085772205087096 + 189.64290874572259327i), (-4.5494651028972281618e-31 - 3.7706688376541713569e-32i)}, + {(-44.343234095826552732 + 50.333883680641690717i), (1.3273037287675019477e-20 + 2.9553181139371900626e-20i)}, + {(46.049253646691937547 + 11.193487193047605643i), (-4.6906291657756656576e-18 - 4.5230630303853025435e-17i)}, + {(24.638224500627362801 + 115.78078281234223823i), (2.4020078306350507426e-25 + 3.5025149415320148495e-25i)}, + {(207.53795244655296415 - 36.875505174690367483i), (3.9404955925146468551e-30 + 1.5899052395371872749e-30i)}, + {(-128.39664599733734462 - 57.794443940917261671i), (6.6098718853736848572e-27 + 1.0189611080225792397e-26i)}, + {(52.073280621914911137 - 27.497430247975827911i), (5.2330623894861624748e-19 + 2.0153440571953380053e-19i)}, + {(50.322790983486889616 - 124.49188457109865169i), (-8.1781516817817343084e-27 + 3.3480248557217415965e-26i)}, + {(194.67748824304493382 - 101.44573800829401478i), (1.8359984545434018816e-30 + 3.791670824812002054e-31i)}, + {(-90.416191080030230864 + 130.89843524254831664i), (-9.9191641581132253047e-28 - 4.4829982530303388198e-28i)}, + {(78.532570129772253154 - 11.098200967737783529i), (1.3466629741792145343e-21 - 4.4152502050579018848e-22i)}, + {(123.58611940414827757 - 95.31475398561018153i), (-1.424940785920914204e-27 - 9.9870723074579038252e-28i)}, + {(-239.88496659393535992 + 154.0059560120865001i), (-3.6614793373869165241e-33 + 8.6623743425925885921e-33i)}, + {(-125.5263113292312056 - 9.3134741678592849468i), (-3.6639707394335984177e-10 + 2.1960763686335281205e-9i)}, + {(46.238141497648804545 - 210.71905629456023235i), (1.0918543924930875649e-30 - 2.3350052136311410459e-30i)}, + {(107.59652562172638568 - 24.718815954396625045i), (3.2181287546644223351e-25 + 1.8064637970375755717e-24i)}, + {(-86.425510919263160758 - 35.26359896919771586i), (-6.4161533270446751967e-24 + 4.3163506644876515619e-23i)}, + {(-0.093175744272001578827 + 21.87015236270903884i), (-1.7105044848249343682e-10 + 1.0354746737141227508e-10i)}, + {(-73.004818461508079963 + 150.97968262044227572i), (3.5799160072891199051e-28 + 1.3589600027200779093e-28i)}, + {(8.194935558793501329 - 30.597652064816383444i), (-2.8679201906980421035e-14 - 1.2612460284715622537e-13i)}, + {(158.43129059986080165 + 180.09121158381120154i), (8.1452946899355300671e-32 - 3.0395950890602620344e-31i)}, + {(84.096440619643161085 - 109.83024817092530157i), (-1.7427001424659944395e-26 + 8.3408866938876959989e-27i)}, + {(0.41827578551189520395 - 86.392437936588720504i), (-2.2725711114857319773e-22 - 4.3010669218064132297e-24i)}, + {(0.52216328238143472351 - 74.029471782636818489i), (-4.9932320649750593728e-21 + 2.9907858610434848821e-23i)}, + {(107.54660669256767846 - 225.07086958885733452i), (1.216242770400778496e-31 + 7.3833109857033275761e-32i)}, + {(219.32570089022124193 + 99.512886606378387455i), (1.8457853502665192302e-31 + 2.2737911405809613857e-31i)}, + {(-161.59746119917645046 + 25.676077988978484257i), (6.0489650564126677377e-28 + 5.1754044972393578982e-32i)}, + {(-55.328845530951141996 + 19.279864793469375428i), (-4.2409606230287482703e-19 - 1.6159618238262226146e-19i)}, + {(-12.564802209800809862 - 12.278479460888922503i), (8.0300312558541580096e-9 + 6.4209749353952167305e-9i)}, + {(-36.941464224953691087 + 150.12146014428512331i), (-3.4564623582939495583e-28 - 1.9393148865654164963e-27i)}, + {(75.241966615235256199 + 142.08060631700465137i), (9.0903000043013771783e-28 + 2.4301751146699117066e-28i)}, + {(180.37761987890280579 - 289.58172156188311419i), (-3.2754267272052317329e-35 - 2.6875401115286598097e-34i)}, + {(-302.84962486841789087 - 59.239263087193727131i), (1.4502166004117801716e-33 - 1.2603652076835648284e-33i)}, + {(45.752825939755574325 - 14.07955494221022974i), (-3.5797692817507097327e-17 + 9.3255759972372643384e-18i)}, + {(-124.16112335144975987 + 107.1378825962791268i), (3.581693407833895273e-29 - 5.8554626116092811669e-28i)}, + 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63.302363255482639204i), (1.421813667420073088e-26 + 7.4200005652876307075e-28i)}, + {(-14.212084234648870051 - 34.737400963796737585i), (5.9947580598331541088e-16 - 3.5501905879595813917e-15i)}, + {(99.420991375957015634 + 182.71997390117877558i), (4.7485368909516761448e-30 + 2.5915959116914474985e-30i)}, + {(30.552197610333731603 - 34.978880035632833767i), (4.2866881914398247837e-18 + 6.4222071164584404812e-17i)}, + {(37.183876287185860576 + 22.779838179360993422i), (-2.6188075586077749185e-17 - 2.3698577431955402661e-16i)}, + {(-112.88169093729412396 - 1.3416510807786734549i), (-4562687556910661.0 + 1175793559616221.75i)}, + {(-170.0093041186326559 - 113.55916904846093018i), (-4.915130952536887856e-30 - 5.224913683539070356e-30i)}, + {(49.244464474544571431 - 262.93904981012263988i), (3.0105131354997665447e-32 - 1.741896495954425651e-32i)}, + {(-106.22849849815092682 + 27.37591940110941735i), (-5.3061803721440895242e-25 + 1.6641234981267231245e-24i)}, + {(-110.11762620268810053 - 125.26404580584696191i), (1.3705991606520898543e-28 - 3.9862934874547747132e-28i)}, + {(4.04112731048492968 - 50.798393764877260992i), (-1.5771720583957549232e-18 + 8.7708329335659205913e-18i)}, + {(89.293985444588969358 - 12.088730257322275463i), (9.8652313590111624842e-23 - 4.595536264075157201e-23i)}, + {(-203.60180110385655894 - 23.649494094021115131i), (4.5439306450516335901e-30 + 5.0030922744253921505e-30i)}, + {(167.44703196685333069 + 350.14442225108354023i), (1.7675412588132447376e-35 - 1.0272297994503239933e-35i)}, + {(53.378006257181354499 + 97.205574890867325166i), (1.3772606982077175469e-24 + 8.2675610546227429642e-25i)}, + {(-140.19573563992364029 - 135.82257672198295495i), (1.705843879872092347e-29 + 6.2826729232049793151e-30i)}, + {(-10.600188527558767504 - 178.53584886711757918i), (-3.4931603415004577501e-29 - 1.0236378953717290952e-28i)}, + {(110.01121234717341224 + 154.62270587790948184i), (-3.3217372448440022909e-29 + 8.1679129566051994994e-30i)}, + {(-107.690595102215255 - 138.58752798220916702i), (-1.176965088828217286e-28 - 9.733434062840601074e-29i)}, + {(-56.703706766239712067 + 96.342556452937358813i), (3.4360834325029289891e-25 - 1.2036440693749804984e-24i)}, + {(77.924796668263070387 - 115.89007310411302853i), (-1.1243811175467505541e-26 - 1.1253199040019577743e-26i)}, + {(25.956416440536489887 + 45.884753134391004892i), (3.6926505389890587934e-18 + 3.1797088987270322652e-18i)}, + {(95.137653288774401972 - 68.177313629638845782i), (-5.580311592967268552e-25 + 4.5756453772531937915e-26i)}, + {(-7.152030317677654736 + 115.92351011924262139i), (-1.5161012395168981634e-25 + 5.8798052505100047548e-25i)}, + {(-90.88025069786588972 - 154.95975487752957633i), (3.2089980841517491094e-29 + 9.1057605171993476156e-29i)}, + {(36.702471007401541669 + 51.976141890385896716i), (-1.040579398471371191e-19 + 4.33257147857451067e-20i)}, + {(25.587434207967895361 - 18.356046813470850765i), (-1.7017927725422481353e-13 - 8.5039938878465095703e-15i)}, + {(-103.29643954259128691 - 113.86510887557952287i), (1.2902952140811548274e-27 - 1.7078332170192060939e-27i)}, + {(80.379241525404182767 + 5.9239427368197397072i), (-9.2973359212868895544e-23 + 1.0224379378042536138e-21i)}, +}; + +const std::vector gamma_25_c = { + {(-57.453569383931139214 - 51.404416292641343489i), (-2.7723238258045389153e-24 - 2.404558117349797718e-24i)}, + {(-14.127632864397615009 + 10.491691277527667836i), (1.509312961210668808e-8 + 3.8404701678155688313e-9i)}, + {(13.509235577240430004 + 36.375027550378788987i), (9.815843327535420162e-17 + 9.0403052518901173699e-17i)}, + {(115.38990944157514207 + 59.933530620400844668i), (8.1302430206573076064e-30 + 4.9518134019037190356e-30i)}, + {(164.38616971093037478 - 120.94202241744412163i), (-1.1518713934503068791e-34 - 2.1585021646011332053e-35i)}, + {(39.028315814387191551 + 80.608466994287141461i), (-1.0279544834777372323e-25 - 1.5931679174111119152e-26i)}, + {(231.40090291903314323 - 56.306283572934312076i), (2.3601906581306393606e-36 - 7.3977839264502418856e-37i)}, + {(83.809846676580150415 + 78.116453039825188398i), (2.2410720255188019175e-28 + 4.6384492249948651077e-30i)}, + {(-22.392120681632420087 + 44.860379962577631829i), (1.2058465473425082239e-19 - 1.2651366376024291391e-19i)}, + {(-181.28991133354020349 - 106.27435373184468403i), (-4.0319215166167403242e-35 + 3.1199623617648604281e-35i)}, + {(8.1223457699022016953 + 83.907224160669798607i), (3.4691544099074498088e-25 + 2.8909719794312601879e-25i)}, + {(25.077868730788221541 - 98.776316364563299999i), (-7.3517318000630949578e-28 + 3.9245201759882294484e-27i)}, + {(138.83262786965667601 - 48.10143044879814056i), (-2.1834766707438231886e-31 + 3.8911387333303323272e-31i)}, + {(-102.29714432788018996 + 64.865111704636220225i), (-3.1202734186550687717e-30 - 4.7034078973730148587e-29i)}, + {(36.853737261337428777 + 18.649112202429247276i), (2.3930834692011340395e-17 + 2.1408674615028853061e-17i)}, + {(-79.778223496410163307 + 85.511691843207429997i), (1.780966132092733653e-31 - 1.1515265200325344473e-28i)}, + {(-85.222178484256076558 + 79.802910491829308626i), (-1.1867046483599557627e-28 + 1.3131161536347449048e-29i)}, + {(-201.04984792661429083 - 207.67021861380774794i), (-7.2083130117647076973e-39 + 1.6501561640307602872e-38i)}, + {(-131.21290651686067008 + 77.608143140377407576i), (-1.1236926986797755922e-31 - 1.0343799052157021093e-31i)}, + {(35.692010936690977019 + 108.19100233679537837i), (2.4697999206568943198e-28 + 2.2979646407373017882e-30i)}, + {(54.553445036798521528 + 63.617842013958835423i), (-5.356524078402690086e-25 - 1.8495534783525333404e-25i)}, + {(-124.12950696630926473 - 288.31928484988702621i), (1.6261692720394616258e-39 - 1.6584770813529895646e-39i)}, + {(125.5087849840800942 - 127.82078080012990995i), (1.4838876995120245493e-33 + 2.6640550528925482885e-33i)}, + {(269.04919346049689466 + 77.688616553505653428i), (3.1065348786003903545e-38 - 2.9331055343961808837e-38i)}, + {(73.382428914534713726 + 15.60650796964731768i), (5.0884006749448672604e-24 + 8.1288533662331132116e-24i)}, + {(-146.43132997164255471 - 36.229800893332466671i), (-1.9114137000695357748e-31 - 4.675286415272411824e-32i)}, + {(172.30572575719151018 - 221.23057345370912685i), (-2.9197365720545289371e-38 - 2.8359336413991969313e-38i)}, + {(-65.961257751417463169 - 0.69666303451649846945i), (-2.2656464566383036865e+28 + 1.7829632046402942066e+29i)}, + {(44.850655427870428582 - 168.39679050988050335i), (9.1215752134675177536e-34 + 5.8260088735278677367e-33i)}, + {(3.5809316424563872872 - 68.618413627272616395i), (6.7298581087999641273e-23 + 3.238833688302598906e-23i)}, + {(-94.872795497106835683 + 139.19749280634553656i), (-8.2466208745806468688e-33 + 9.9993590315253768794e-33i)}, + {(74.552863323450424105 - 109.85818094225616903i), (4.2179039112140501934e-30 - 3.4964251585326305863e-30i)}, + {(-101.55276185614954443 + 130.6979628039889576i), (1.5268696891894571064e-32 + 1.2972394505283163636e-32i)}, + {(-105.79353380548499786 + 133.67084645667026166i), (8.4931988686222400102e-33 + 4.4524415733782972767e-33i)}, + {(-201.19560925033104581 + 37.170991619012049512i), (1.543462398099804977e-35 + 9.7328597689497508753e-35i)}, + {(-135.65222582724686617 + 0.53133077152780538999i), (1.6695797131833411113e+30 - 1.2425201038703073054e+30i)}, + {(-17.350355024399963355 + 129.97517159308605983i), (1.8745807704924368392e-30 + 6.7496380019281014602e-30i)}, + {(142.00458124387094472 + 125.552200752856848i), (5.6511063615379172606e-34 + 4.8272190105821314195e-34i)}, + {(11.891800450980493764 + 27.790003589548394558i), (-2.3035929149434208194e-14 + 6.8959432589183503698e-14i)}, + {(-143.35435102592850853 + 56.497214689460030002i), (1.1600908881897474192e-31 - 8.1068136699517331429e-33i)}, + {(-57.349021089050225441 - 144.24335023788970034i), (1.1262628199341231023e-32 - 1.0076298842022345616e-31i)}, + {(-96.093803737755976613 - 86.20654848831806305i), (-7.8402143699189567132e-30 - 5.7797591473039585898e-30i)}, + {(8.3363340546841975254 - 110.01502398852144893i), (5.2540529688736340454e-28 - 1.1048147281749582159e-28i)}, + {(74.655097103543269554 + 67.084376796523386588i), (5.5412794689113188835e-27 + 2.7994656756973957121e-27i)}, + {(-97.387608893666637755 - 179.05464119157755931i), (6.5215800138592718535e-36 + 1.1166122798139761342e-34i)}, + {(134.15057260803516215 - 70.408655346835132605i), (1.8572008870445464488e-31 - 8.8729833391636812241e-32i)}, + {(0.67695794919736784756 + 52.384140596783232979i), (5.5383965465626373903e-21 - 6.5372437949040162823e-20i)}, + {(-156.37672136286451519 - 49.510807605706865786i), (-5.1361151579199568875e-33 + 2.388415613106267293e-32i)}, + {(-150.70720650475280422 + 28.303287898738805239i), (1.1305215505622366401e-32 + 1.3017154665017023402e-31i)}, + {(184.58293521885315158 - 12.677874158592878473i), (-2.0437321341558891273e-34 + 1.3694751383115887884e-33i)}, + {(135.10389135103616809 - 24.497346135365720698i), (-5.1568670994734519534e-31 - 2.3928848829598137284e-30i)}, + {(-91.377834600420626998 - 124.3362978193898698i), (2.3271419686478845398e-32 - 1.1314635812043076891e-31i)}, + {(-4.0028613488723312486 - 115.85891425242603248i), (-1.2703595959249947841e-28 + 8.6817233314931107484e-29i)}, + {(-22.156938842513369536 - 103.96222898714187011i), (1.0466378269635040448e-27 + 8.0076799474401303686e-28i)}, + {(-183.94810076856091996 - 34.005087697568967542i), (1.4226304574302697515e-34 - 9.09062238643090827e-34i)}, + {(-86.695856201436996002 - 101.23324608908103528i), (3.8951867691806555829e-30 + 2.1214090022529777915e-30i)}, + {(19.279441178180938721 + 4.7272239714102752828i), (3.8450124613476868461e-9 + 5.8538415042702411068e-10i)}, + {(193.31994001170454567 - 11.46749433768116333i), (3.7798148685816368579e-35 + 4.3936520481180541885e-34i)}, + {(-17.882380860702127734 + 186.91443563678711826i), (-5.6738683987744742357e-34 + 6.8653591487198023735e-34i)}, + {(32.686303600176394468 + 128.77248865575688797i), (-8.2977143115041706381e-31 - 5.1666790223776756277e-30i)}, + {(18.513119043136804009 + 148.8430904508350352i), (3.2373976174851458487e-32 + 2.4680874229085072652e-31i)}, + {(-82.523538940261929042 - 145.65865304059951768i), (-5.7273491521800228076e-33 + 1.4096313857948416796e-32i)}, + {(-62.28063179669809557 + 113.75268270134498039i), (-3.8002019549007702161e-31 - 8.9161996909649448056e-30i)}, + {(76.909342381910988706 - 99.268321962166339745i), (-1.4208993112801968302e-29 - 1.7081197129896186307e-29i)}, + {(-24.341005817991323568 - 145.29465316746998838i), (3.379016673539376297e-31 - 1.7533976213169377725e-31i)}, + {(2.8095811360982825278 + 58.436687293605380944i), (3.485223399720913065e-21 - 2.2964436892489609332e-21i)}, + {(-7.9801926800644764626 + 60.776360985080820853i), (4.0136341213186073809e-22 + 1.1861331889594436977e-21i)}, + {(61.374201627077916044 + 57.030001461099985249i), (5.7706858948105696841e-25 + 1.9227861466060467911e-26i)}, + {(158.77490586095805725 - 22.939605945447777202i), (-4.4381953572528358411e-32 - 2.1792046197187686297e-32i)}, + {(-71.788024633041473521 + 88.032833029956947257i), (2.3832589662520262136e-28 + 2.1294175333472835291e-29i)}, + {(-136.83890554639273773 - 65.702054734569088623i), (-2.6787998345956910601e-32 - 1.6721014593215136218e-31i)}, + {(-64.058899573916619374 + 46.050570465335098902i), (1.992809949407681523e-24 - 4.496886574019851467e-25i)}, + {(29.753326027708489221 - 16.513836634501437572i), (4.1324640303338027116e-15 + 1.1043860183613979593e-15i)}, + {(177.1009714167507525 - 39.419593020873392675i), (1.5836488960842716859e-33 - 1.6086178991956292574e-33i)}, + {(-92.064271942427382101 + 57.293885674682023534i), (-2.0724907174487523358e-28 - 7.1254557965474167138e-28i)}, + {(104.1064533741520961 + 127.78642682898100702i), (-2.3697722550560043234e-32 + 5.9455214360321052494e-33i)}, + {(-90.589066546995709928 - 6.5592448372069442897i), (605.6708150896809002 + 379.40585707271782212i)}, + {(-15.605713906309134131 - 78.971193134882227582i), (1.3000633623277374582e-24 + 4.2920605528474919543e-25i)}, + {(-8.2773474863070628516 - 147.52856764351091101i), (-3.5529103549769685516e-31 + 3.0273590048725648269e-32i)}, + {(-86.742218002872419902 - 187.7267360554829736i), (7.7639670813943067608e-35 - 9.2989559317261296619e-36i)}, + {(-59.974173883582459155 - 18.274466269258631712i), (-2.976982189341844287e-22 + 5.1850578189396739391e-22i)}, + {(-131.62164339595150864 - 193.03248849433481382i), (-2.3785477616316095629e-36 - 2.81179166708272355e-36i)}, + {(37.931919495227361949 - 146.4487835081895355i), (-5.4031737599564378971e-33 + 2.0291181411288898924e-31i)}, + {(114.66113352198330233 + 19.977007810957907452i), (-5.7787603973402938929e-29 + 1.4376900856507857209e-28i)}, + {(131.94780948891639127 + 22.20164575139067864i), (-2.3669253127047993767e-30 + 4.0411105215126121899e-30i)}, + 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2.6243404673029308319e-39i)}, + {(20.351884350086415054 + 43.924688756287146418i), (-4.8760099213521268158e-19 + 1.9185736050589056726e-19i)}, + {(32.395286408710873616 + 117.50871281341694896i), (1.5257356934763798597e-29 - 4.2612999496427531055e-29i)}, + {(-66.530620650942168481 - 26.391183573286404851i), (2.2454480331293962455e-23 + 1.1538598397468244935e-24i)}, + {(31.489005410974392873 - 48.037669142384189058i), (7.2042294801754757873e-21 - 1.411205870814367788e-21i)}, + {(-188.38908552131755414 + 27.221013414170418088i), (5.0084523129359038576e-34 + 3.0857650558167691352e-34i)}, + {(-241.94607139665828299 - 80.692495280578427241i), (7.1664038935706769587e-38 + 3.9804922181014612399e-37i)}, + {(26.341443222419115955 + 128.03299468636711822i), (-7.5481469938801926232e-30 - 2.0662201560604705917e-30i)}, + {(151.05951115535791018 - 94.175250168691576391i), (5.8883178345560012159e-34 + 3.5595958078852458785e-33i)}, + {(48.130827122988527833 + 158.95160349688146084i), (1.6539521817321221355e-32 - 1.0716191574483548071e-32i)}, + {(170.06443577293856606 - 47.311440291982428619i), (3.8972381348390816262e-33 + 2.2251876067847431548e-33i)}, + {(18.989910192581128001 - 99.63705368893253933i), (-4.4267791877423754833e-27 - 5.5312945209769365091e-28i)}, + {(110.95432347049323596 + 111.48073542991477325i), (4.9360953113765860646e-32 - 6.2192193067266454129e-32i)}, + {(-21.250540593607915696 - 128.09421809422732963i), (7.8063109444458360029e-30 - 4.3351967278231563142e-30i)}, + {(98.201048971087928408 + 141.7808640369409261i), (4.559661612367046337e-33 + 6.349204739458197147e-33i)}, + {(27.357924940711054518 + 81.015787749149353658i), (3.2264667211047196402e-25 + 4.9115075025086749596e-26i)}, + {(206.31088123271555901 - 30.27614268136474962i), (-6.0321318240656234475e-35 - 3.3717752792515663006e-35i)}, + {(174.90528160660818457 - 16.772297007711717498i), (-3.71308507990380808e-33 + 3.4240205794341991546e-33i)}, + {(186.50021214337050424 + 56.805625143324931514i), (1.5983080429051964376e-34 - 3.3587705898626983613e-34i)}, + {(-190.44675063288610772 + 36.503001683895647034i), (-3.5046049212653793261e-36 + 3.7554182254546855667e-34i)}, + {(-59.972552488874619314 - 25.486258868834294589i), (1.981605519412997786e-22 - 1.1939473761253408529e-22i)}, + {(-82.321659391834472785 + 30.380673978078647224i), (1.1419626540952562059e-25 - 8.4584214677314230362e-26i)}, + {(-91.057637296157153628 + 23.811618568294882436i), (-2.4696305260455356776e-26 - 1.886522784445092217e-27i)}, + {(54.650437196993365774 - 87.250807745340722477i), (3.1014913986496940778e-27 + 7.8732905448042781515e-28i)}, + {(-63.842092199025536559 - 74.893037043571681011i), (7.6125122096223253237e-27 + 3.8487942611826242121e-27i)}, + {(138.40633072479181465 - 95.321820742493230227i), (-1.2670067619118802021e-32 + 8.4623993856520773423e-33i)}, + {(79.820509443569278574 + 12.610696962374520425i), (-1.0338275248256877945e-24 + 1.0617497683855219953e-24i)}, + {(-10.709086687612025202 - 112.72833431981274543i), (-1.6937065262748539531e-28 - 2.1668039454995356646e-28i)}, + {(-144.87805436938094772 - 86.75617071495514665i), (-7.5611686993455452506e-33 + 9.2154643543900183483e-33i)}, + {(48.644721891713601281 - 31.86411494490170071i), (-2.5878900004756716407e-21 + 5.0730635978517281061e-21i)}, + {(89.697510139958708919 + 269.90313092719759425i), (2.7956163609697926695e-38 + 3.5333043383570507097e-39i)}, + {(-202.3247214412017172 + 113.26997081974199943i), (-4.3139119975810233923e-36 - 7.233238327883914626e-37i)}, + {(94.303967624084023669 - 21.538177097099236335i), (1.2902833572132219737e-26 - 9.6478675290713439155e-27i)}, + {(-38.168057750235490744 + 181.22352650743698632i), (1.0675890660341794832e-33 - 6.4492726804759323713e-34i)}, + {(110.16857863231057024 + 26.118011416876175446i), (2.7992204028349976252e-28 + 1.3149976284133384962e-28i)}, + {(-76.08316362719868664 - 69.199531388244452046i), (-2.4906960201931700064e-27 - 1.3038297817557629109e-27i)}, + {(134.64648183211272681 + 11.259926977004305115i), (-1.8306359607164188393e-30 - 3.1789182285351443157e-30i)}, + {(-121.82453564669035018 - 30.819733804401483468i), (-1.8505162186813680203e-29 - 2.1122215715377203851e-30i)}, + {(93.482630142021520214 - 6.8239420724055994683i), (-9.1740486343929195138e-27 + 3.4458090916743168985e-26i)}, + {(35.305483094535681232 - 101.42762558276967866i), (9.9402380682679714122e-28 - 4.3390426224688298227e-28i)}, + {(-323.63826077102368117 - 99.691341357116257882i), (-1.3141609800593392913e-40 + 3.1547405678100254317e-40i)}, + {(105.54111936023633689 + 28.656571878163468625i), (6.8715738084596765643e-28 - 2.6965004581984047498e-28i)}, + {(0.93990680644921109632 + 54.929732457246984723i), (3.9807687038668663144e-21 - 1.9602135578564705629e-20i)}, + {(-87.339148217720847356 - 124.24810504538432099i), (-5.4427938269619947333e-32 - 1.6302917003881931326e-31i)}, + {(-42.48616756767236069 + 50.150173820476950937i), (1.7859613509787392792e-22 - 8.4761952441701259824e-23i)}, + {(28.221245725933936654 - 0.35168171538250758701i), (4.8337930186530076919e-13 + 1.5818672609729886309e-13i)}, + {(-36.909583077815625529 - 123.19773793793413574i), (-9.9238353237486604359e-30 + 5.2032386901366922884e-30i)}, + {(135.92333195425143799 - 24.038605585499595918i), (-6.7659513125820471224e-31 - 2.035214108910871155e-30i)}, + {(74.854580883444100436 - 79.964734784736066331i), (-8.2975821646500180727e-29 + 6.8359420961761571592e-28i)}, + {(-65.447473462018763257 + 156.05509388578764174i), (6.3419957051686334265e-33 + 9.8594358103354296267e-33i)}, + {(-14.677123478338071294 + 37.082737619820477448i), (1.5747369605413792706e-17 + 5.1069842614505460001e-17i)}, + {(-12.087591221417785192 - 64.273008909717802339i), (2.4367352134878211603e-22 + 3.060591534621962558e-23i)}, + {(86.17330375115952279 - 284.8656172754739373i), (7.716060911200513397e-39 + 4.7328499463015807297e-39i)}, + {(194.6404735179456793 + 159.99536847683134511i), (-2.8203482114613052035e-38 + 5.9645638932773329049e-37i)}, + {(14.869114807305031434 - 34.365914960432498049i), (-1.5611894965536927865e-16 - 2.9270610101717351118e-16i)}, + {(84.647366993861623996 - 22.181458245692038389i), (1.9731970142683163839e-25 + 3.1548363805877227982e-26i)}, + {(-111.71467167530553866 - 49.891963468800554438i), (1.8671014736595105776e-29 - 3.1303543771988142029e-29i)}, + {(-64.746627386811681504 - 3.8656325241923403802i), (354365813.46065944433 + 16003182992.506046295i)}, + {(12.079163155992821643 - 84.370561995625834584i), (-9.1821951438258287913e-26 - 3.3286694404805712665e-25i)}, + {(-57.197592529808090944 + 66.897749218261964188i), (1.1965136654045196037e-25 - 6.8026451722517306997e-26i)}, + {(128.31157072158458732 - 32.503403809862341234i), (6.1224082970499169438e-30 - 3.5684415594010185803e-31i)}, + {(54.317916153377801436 - 25.856650919141692668i), (4.7705988759388254676e-22 - 2.4078923598891844484e-21i)}, + {(84.339919757971244962 + 27.065399753076192724i), (7.2677717199113288635e-27 - 1.4672577837941257709e-25i)}, + {(-31.928695952273400849 - 47.142742828683466882i), (-4.2608142464895785365e-21 - 5.7642733572108104345e-21i)}, + {(106.95828018239159007 + 25.079040432061482591i), (5.7857752869845266119e-28 + 3.162628289748159753e-28i)}, + {(-115.79195096164423262 + 146.02928757338625587i), (9.2627171623120442393e-34 + 4.6476983548774331968e-34i)}, + {(-141.20856314209905236 - 2.808178299556676194i), (4618446377004.2773438 - 16342935534368.839844i)}, + {(-45.376769592932355124 + 132.92284004810196052i), (-1.1106144918608170889e-30 + 5.4375714132732331872e-31i)}, + {(43.335589309028662797 - 63.301585168064768538i), (3.8003707134987732057e-24 - 3.4693561529270979776e-24i)}, + {(94.290066319284491669 + 124.87362706812102431i), (-3.4749248481449836564e-32 + 8.2673333931563212162e-32i)}, + {(13.489743211330276651 + 37.815581132373019102i), (5.1300999054929833585e-17 + 2.3427347511383887691e-17i)}, + {(-200.05736216110440751 + 105.33477805345678746i), (-7.2918858727801221075e-36 + 3.7639494241781732103e-36i)}, + {(-68.712486323853411818 + 79.552983452047214996i), (1.3378936868002273764e-27 - 9.625864575966151241e-28i)}, + {(-96.001739720845918669 - 185.49360055944558212i), (3.2998336087852548993e-35 + 5.1132365811109138319e-35i)}, + {(167.43934708035152426 - 1.8421876778275021458i), (1.6252436765913899039e-32 + 4.600418041283787659e-33i)}, + {(11.583108093986565379 + 17.078417189511426955i), (1.1557297117562378747e-9 + 3.759187354339135968e-10i)}, + {(-38.208434007656592257 + 71.295089402978689463i), (1.4804738741028792657e-25 - 1.1513142742573810783e-24i)}, + {(250.75597500403543449 - 79.117217811645375036i), (4.0936509295151564814e-38 + 2.0283083935026814373e-37i)}, + {(121.30854455840311346 + 48.397293965784086822i), (-8.5030216013127354784e-30 + 8.527584158109854349e-31i)}, + {(3.3688442045404811687 - 20.257033322915564355i), (-4.2904052841251677462e-10 - 1.0311689460185778212e-9i)}, + {(96.825562090029166029 + 71.454219169184000293i), (-6.3910540965964488035e-29 + 1.6049188935891898775e-29i)}, + {(58.010366236911835358 - 97.008672318413445623i), (2.2355238140516621372e-28 + 2.1115715877740495607e-28i)}, + {(-101.72913952727802211 - 149.65076930839404667i), (-1.4393377427036602017e-33 - 1.6260862363191942967e-33i)}, + {(27.074186967159274531 - 4.1803553404371172064i), (-7.9132017108756626705e-13 - 7.3412397096351217085e-13i)}, + {(159.97663261586160388 - 138.96917898554562498i), (2.7208632708775971233e-35 - 3.6510714668435730493e-35i)}, + {(-1.2225937727210267614 - 92.577718802884390925i), (-1.9117518974572223711e-26 + 3.8083391906459770446e-26i)}, + {(-43.255170955593392534 - 170.73407502725484619i), (4.7245864004878539851e-35 + 4.3619759303817539518e-33i)}, + {(-82.485137270635433993 - 31.509412564446055427i), (1.1415348829588003104e-25 + 4.2310308299878458048e-26i)}, + {(42.788785834467830682 + 86.139379363780534504i), (-1.5940879950084181765e-26 - 7.0419815980573921269e-27i)}, + {(221.5740009848251475 + 52.255916480510265387i), (6.7873910670776026204e-36 + 3.5387970634131824454e-36i)}, + {(-105.75067440663008256 + 134.9568180194520437i), (6.8378632267928654424e-33 + 4.7207077119913927555e-33i)}, + {(-34.57496393758287212 + 2.7662259060431897417i), (5328712893700.6669922 + 5015042802955.5986328i)}, + {(43.924942121529291228 + 98.120432086391645043i), (-8.9443739116924153745e-28 + 5.8272495969276051684e-28i)}, + {(48.476529473726458264 - 81.490928718842368994i), (1.6916049954114254637e-26 + 1.8576340640757704413e-26i)}, + {(-111.71949478896907237 - 104.05276325027995199i), (-1.4697725837287094622e-31 - 2.3619622300310872696e-32i)}, + {(136.18047173930091276 + 63.472231142572631768i), (-1.4587262948798541867e-32 + 2.5373011082310111288e-31i)}, + {(-98.487859697241390222 + 202.09603475320471944i), (8.9616429717130984396e-36 - 3.6976607327983044032e-36i)}, + {(30.020382038754128473 - 179.43684747276378744i), (-1.6064873970006087871e-33 - 1.1854491443090815496e-33i)}, + {(-9.8168540726917203898 + 42.167056816149553811i), (1.9782076397028684486e-18 - 6.9398150110168826551e-18i)}, + {(-31.044806856733707434 + 159.59061101897992785i), (3.190191931521900704e-32 - 5.3656823069604006653e-33i)}, + {(-6.5090660749134245933 - 133.65766549215288705i), (-4.1082847611133406399e-30 + 1.0965308460975204116e-30i)}, + {(-146.38679200179012696 + 22.237130485009469538i), (2.4573734312155423473e-31 + 1.864145814472108176e-31i)}, + {(181.51662048147073847 - 20.207885290173088322i), (-1.7905947934551902644e-33 + 6.7888008292771525609e-34i)}, + {(39.876907251691832812 - 153.51321699907472862i), (-3.3423053981629372032e-34 + 6.216495243343269675e-32i)}, + {(-119.67396848238523432 - 6.7389056717738000657i), (106.26656179686202108 + 205.26015738948677836i)}, + {(-87.022006248593186228 + 92.401490267080703234i), (-1.6290994274466181179e-30 - 1.4853706953318142627e-29i)}, + {(-2.6302978308820437192 - 94.359397920174970409i), (-1.9326019978269951917e-26 + 1.7701164617788880062e-26i)}, + {(-0.12569587373765098159 - 73.889839198163187461i), (-2.526303067745126953e-24 + 1.175013636852760089e-23i)}, + {(-75.96385597325725314 + 19.950033561403053284i), (-2.2140004740455465751e-24 - 2.113243890672943675e-25i)}, + {(-9.5728027711094192398 + 47.246314149205034028i), (4.257821711598715339e-19 - 2.5737044545081987394e-19i)}, + {(40.599935650153845756 + 10.225276586882738883i), (2.3206007295209141941e-17 + 1.1342729317056504665e-18i)}, + {(90.576450483139907988 + 15.156446288320912785i), (-3.0894512772187885547e-26 + 5.085283825112925104e-26i)}, + {(31.649404373512641797 - 187.29420074573422994i), (-5.6333172828264381697e-34 - 3.7884798345315553124e-34i)}, + {(20.483301757277210697 - 75.175730730860209405i), (7.0733556274211309688e-25 + 3.2489862896119099326e-24i)}, + {(27.271209447001464099 - 29.331616266077404021i), (-2.190146648513687632e-17 + 6.2383131260997626466e-17i)}, + {(14.080416679556165604 + 0.1660748005592994625i), (0.000024425013442320882534 - 7.6200572909370411817e-6i)}, + {(-83.476200547193499801 - 43.155436180641736144i), (-1.9903470908282876375e-26 - 1.6804670354627857088e-26i)}, + {(-188.87489237533063147 + 1.9303256914697717317i), (52703483326713792.0 - 609710619890839680.0i)}, + {(-167.8224449693196334 + 75.077393170896783658i), (6.9261546437125878953e-34 + 1.245787692505798895e-33i)}, + {(-54.279428287741438908 - 43.922212006436481602i), (1.6207143351619173544e-23 - 3.9635312089716058296e-23i)}, + {(51.683187407475216446 - 42.555095726973043213i), (9.0316729441547787884e-24 - 1.6244154105446672714e-22i)}, + {(69.846983656344988844 - 46.388798896333064192i), (-3.2328465748817774441e-25 + 4.7399967638060299561e-25i)}, + {(-0.018851753390831671453 + 1.5588076414659961522i), (-1.4212665363351660134e+20 + 44755771590157598720.0i)}, + {(89.322814550103657893 - 52.251498542135557557i), (2.1873414087088876675e-27 + 1.9382173206236729559e-27i)}, + {(-89.156992800874135696 - 34.155278634703250873i), (1.6512137569495848095e-26 + 5.6042467007619041543e-27i)}, +}; + +const std::vector gamma_30_c = { + {(-102.71881640848181405 - 26.346115676131802275i), (-4.6403797959662442608e-31 + 1.2374990113616868579e-30i)}, + {(56.279566233817050147 + 47.576727748051091282i), (6.7292763299721839122e-26 + 7.1011252975026833624e-26i)}, + {(-24.840059724185099554 + 57.886605135002497491i), (8.3719902418444647541e-24 + 1.527934394986417533e-24i)}, + {(83.146078971636839583 + 83.173484941299307138i), (-6.8999032890101086259e-33 - 7.430053535959817199e-32i)}, + {(46.094610660205162844 + 32.924713364170280272i), (-2.7633789889757188297e-22 - 2.7350108961938517487e-23i)}, + {(47.557765018425314452 - 41.652143606157146394i), (9.6105589801391606047e-24 - 2.6056239336395514929e-24i)}, + {(95.708643438014945559 + 10.145395486835806054i), (3.2397581877983936478e-29 - 1.3708770701815218186e-30i)}, + {(-51.13050870145201543 - 79.158052728555333033i), (3.0740651663879179149e-30 - 4.8127770818845017013e-29i)}, + {(-129.96209808647074624 - 96.84685390667698357i), (-3.9963407194858414066e-36 + 1.264305342598204564e-36i)}, + {(49.370831285401258981 - 108.42891092304998324i), (4.8303090702967459166e-32 - 6.767689762688923836e-33i)}, + {(-14.986151184582796603 + 112.29658225060983057i), (-1.1643808263914040807e-31 + 1.700579290391230229e-31i)}, + {(101.38385604827379893 - 195.43194467485741939i), (-7.5619827750132734028e-41 - 4.7032227216678950967e-40i)}, + {(114.74610923767332338 + 175.44309620066570687i), (7.9970400387804558101e-41 - 2.0865971165542118347e-39i)}, + {(-10.360678917929398324 + 26.049503103726202369i), (2.1568937012950262489e-13 + 1.7469573582395228525e-13i)}, + {(5.1557502363008165247 + 118.20360239936407254i), (2.1789878315593255595e-32 + 5.3075725659271318006e-32i)}, + {(-163.41624833017175433 - 65.98083579865638626i), (-1.574175290160405188e-37 - 2.9938738711140235303e-37i)}, + {(102.55913965386372411 + 86.521206537674174797i), (8.865369965559223118e-34 + 1.1116749222204082103e-33i)}, + {(89.438252125447448293 + 19.491617515303925501i), (-1.4413386330757527615e-28 + 2.7317051467449198436e-29i)}, + {(-18.776004190036900354 + 33.113626825940919218i), (-2.8004788816774862684e-17 + 3.6657748601039918286e-18i)}, + {(-106.99598864067453974 - 39.594798184813896569i), (5.9638973650772975207e-32 - 1.3722345254652507454e-31i)}, + {(-20.921916811237672107 - 30.888344615551567074i), (4.0284721178825042077e-17 - 2.9536849378583766039e-17i)}, + {(-22.398643178411798971 + 280.13100857395915i), (-2.3336693447073635736e-43 - 1.944472032269805576e-43i)}, + {(-81.411869978596101305 - 95.375458631941171461i), (-7.0417144287823292711e-33 + 5.9393542917975618611e-33i)}, + {(-10.509790971698688367 + 85.580798040351126588i), (-5.6856121683358082109e-28 + 4.7703264177571459471e-28i)}, + {(134.3397452131362968 - 49.094060971354899436i), (9.2065798424115376485e-35 + 1.9077964173561073888e-34i)}, + {(19.093191203074567852 - 64.823195432835518659i), (-6.1209384526156988958e-25 - 1.0435748688250530775e-24i)}, + {(-33.15506221666053932 + 95.970201117543652458i), (-4.1035611799101920969e-30 + 3.4287305787841945016e-30i)}, + {(33.060506466419987248 + 96.808751133526158128i), (-4.4758738589408625387e-30 - 1.4389415525466598496e-30i)}, + {(227.77584142316928251 - 103.95548215676511461i), (-9.8174322494919085135e-42 - 3.0673342275533644602e-42i)}, + {(-65.769080689868090417 + 180.60112753326427537i), (-1.1370961442880399624e-38 + 2.387851512223126196e-38i)}, + {(-5.5385821515957038841 + 45.97046017558815123i), (-6.5998518376682317271e-20 + 6.5474659558564759569e-20i)}, + {(-81.781473659347341254 - 32.367638589102988078i), (-8.5639993245810970668e-29 - 3.4315253237794871492e-28i)}, + {(94.821090315858185704 - 116.6327610835718076i), (8.2764765133570574441e-37 - 4.6129962798491575565e-35i)}, + {(59.199458948133511171 + 51.628377852925822822i), (1.3375665580457957677e-26 + 4.9677050898583535629e-27i)}, + {(9.2972145055083785792 - 135.07127057188327512i), (-3.7406568629230242033e-34 - 9.3483553960798450471e-34i)}, + {(83.890346016765803938 + 284.87141925244964114i), (-3.7599545616330205772e-44 + 4.5606489920031795955e-44i)}, + {(127.21695857745207547 - 40.923547573519961418i), (1.635992665298650468e-33 - 8.9562429001183152802e-35i)}, + {(-92.980081427571420249 - 93.184916682128886123i), (1.0615137746542024959e-34 - 2.1357297772886536864e-33i)}, + {(-6.239645274349396864 + 87.984978697430932471i), (-2.5070768926973144722e-28 - 2.8384673051651950255e-28i)}, + {(97.105402616477533684 - 83.159388768361566235i), (4.7655260700984829048e-33 - 3.7857986298946322601e-33i)}, + {(-20.379807613107143283 - 65.63670993913399343i), (-6.3090811315933146365e-25 + 1.1504466259429072267e-25i)}, + {(125.06728118351307444 - 64.403864721274359795i), (6.0930819682586839164e-35 - 3.418925801917289847e-34i)}, + {(142.5710365499366219 - 73.733055507589611466i), (1.4536590387244411886e-36 - 6.4028158204682865745e-36i)}, + {(86.291005532548496149 - 38.373701991388799115i), (-5.667662259904938368e-29 - 2.7439070374751358955e-30i)}, + {(-16.980673305082095936 - 113.38052767779542762i), (-1.7579034528907398121e-32 - 1.4299075327737398249e-31i)}, + {(61.645084826891341834 + 214.88606037191425457i), (-1.328499704203823104e-40 + 2.6611829616218365624e-40i)}, + {(-22.24138602821423305 + 63.967370753192213328i), (-6.6907734257692496822e-25 + 7.2857945435072506607e-25i)}, + {(-60.302472106400017537 + 32.83664081910678334i), (3.7545235035424637788e-25 - 4.3564216409473164128e-25i)}, + {(-219.61298795625575053 - 149.80317379550882606i), (-9.2948521487490260458e-43 - 1.2282686456508787398e-42i)}, + {(168.40767777323694077 + 85.452451973850713784i), (-7.4993311251349467116e-40 + 4.9394866938709393606e-38i)}, + {(-114.97426430177814893 - 29.083719065164743256i), (-2.0495460475859482269e-32 + 4.205966810506486014e-32i)}, + {(8.9071067094014342302 - 138.47108072006338375i), (-1.1850413552797716058e-34 - 4.6676897777074430203e-34i)}, + {(-129.87533023892927986 - 104.47378025684639624i), (-2.8082215234685029041e-37 + 1.7954720933616569161e-36i)}, + {(57.930575540057873241 + 51.585915561394990902i), (2.0788611654309780504e-26 + 8.8418142621520198017e-28i)}, + {(234.71762349792862778 - 16.695494240957682308i), (3.5694846695682178141e-41 - 5.6437303094295744202e-41i)}, + {(-196.10843992590309881 - 74.109898293602839203i), (3.3914186810930186133e-40 - 1.8428023383244926031e-39i)}, + {(52.917186632631462828 + 45.479255816346707775i), (4.3046152084855020348e-25 + 2.6970875048750100084e-25i)}, + {(25.753437218025389654 + 71.553032465437212295i), (-2.5484609292565074603e-26 - 2.4126212405761292775e-26i)}, + {(80.14867599646969154 + 43.730250740139879895i), (1.2447211858081417165e-28 + 9.4380593875895138721e-29i)}, + {(160.73463365396170843 - 160.50664374895495712i), (-4.6751158568218698194e-42 + 1.8932438092128901265e-40i)}, + {(65.234865616183014936 + 131.84542410817309133i), (3.7196999468949057198e-35 + 7.8335389627450514599e-35i)}, + {(123.36177526762541845 - 255.88603309127330476i), (1.4683611350230440776e-43 - 1.7162453679400166963e-43i)}, + {(-6.0565863314087788893 + 127.33339131808283184i), (1.6446682455394113274e-34 - 6.0518821428619313536e-33i)}, + {(122.69796151750298918 + 161.88306300116940406i), (4.6111482657191081238e-39 + 2.8229937222009299869e-39i)}, + {(79.997665901467556182 - 94.654764806758706186i), (-7.8696538973455741399e-33 - 1.313904020026511216e-32i)}, + {(-7.7938640002839880694 - 40.625606146473899116i), (2.5925421845213051206e-18 - 6.1429028243205130415e-19i)}, + {(-52.669910213407611366 + 123.95579030929131648i), (1.0271159174022609019e-33 + 4.4479112859686344816e-34i)}, + {(33.771591475364083124 + 67.043358033074667901i), (1.6230995431151156737e-26 + 5.0344843643336104311e-26i)}, + {(-240.39678309128126443 + 23.159260035126315813i), (-8.4869148411797999324e-34 - 1.5877675881836984023e-32i)}, + {(-38.076239418384304258 - 62.778552625327236569i), (-5.7120639337658586296e-26 - 6.2257182986386384252e-26i)}, + {(182.13531305112417158 - 367.74428284274989664i), (1.3204887938679842689e-48 - 3.3656089743750561135e-48i)}, + {(-93.15437963051184056 - 41.640845708877840536i), (-4.2110575887062042526e-30 - 7.5448530391530122603e-32i)}, + {(44.941987241895162697 - 8.0074514191855499234i), (-1.165563230954286634e-19 + 1.6019748124528839025e-19i)}, + {(-165.86850434323221748 - 78.188918830400425009i), (-8.4478630957591515525e-38 + 5.9414370048406049488e-38i)}, + {(16.318351772576054515 + 68.004603213471938261i), (3.5779122284580887705e-25 + 2.3269377157442271207e-25i)}, + {(52.631357734820070959 - 154.03673222790069985i), (-3.8203708432885919994e-36 + 1.4648920462017498038e-36i)}, + {(114.46661044018962627 + 110.33064575041764499i), (4.0404054388694320711e-36 - 7.615081409351066272e-36i)}, + {(23.354817591722490278 - 75.958676951957826873i), (-7.35757997438747122e-27 - 5.6318687894690045456e-27i)}, + {(-21.790331721122857545 + 42.815180273332806848i), (-7.5296176591723751518e-21 - 2.6515085288926380674e-20i)}, + {(82.555667629275589547 + 55.42560272982031222i), (-6.093912521650493754e-30 - 1.0175031238820318342e-29i)}, + {(-102.74442989859684872 + 38.980057536249901773i), (7.6456261919791034634e-32 + 4.521495248532003408e-31i)}, + {(98.288619513731205757 + 11.631427401455402659i), (1.2801982349240186449e-29 - 5.5508026332451445528e-30i)}, + {(-54.973433383137717101 + 77.863851576852383118i), (3.2831272284374162381e-29 + 9.2537134131824776351e-30i)}, + {(77.847984316903591662 - 147.83930175324283596i), (-6.0389923068480937999e-37 - 1.7935765509738371545e-36i)}, + {(67.111927383618265708 - 19.559266764925965276i), (3.2531640334779439867e-25 - 3.7865969360409602954e-25i)}, + {(111.17965560712657691 - 109.63540711127393479i), (2.1219687431950016451e-36 + 1.4655634822498551438e-35i)}, + {(142.04263208498295512 - 106.00973418904867174i), (-2.9968031716285445914e-37 - 1.3900452948753995242e-37i)}, + {(77.7900235861026772 + 19.70353448606358171i), (-2.7983080225592264536e-27 + 7.2470113549424950507e-27i)}, + {(-43.373963303522877766 - 205.18251481827488192i), (1.9549388104622730356e-39 + 7.2116132057532442553e-41i)}, + {(110.69640133101894719 - 74.333837345428008803i), (-8.6355932633990265512e-34 + 1.499248616140692703e-33i)}, + {(-36.858119171396651836 + 174.62225308603862572i), (2.4668769665717143162e-37 - 9.8980932556315050228e-39i)}, + {(-113.22524856973490159 - 36.151791816593750184i), (4.3114824660916844872e-32 + 8.4167892268076316106e-33i)}, + {(160.11882661103547321 - 107.17906599773235143i), (-1.1929639292034897702e-38 + 2.4086646209342475093e-38i)}, + {(-85.347556401535001669 + 34.730983994219826627i), (-4.4957320453872865257e-29 + 7.5965799977475983113e-29i)}, + {(161.52327266696426022 - 7.4092568789576764843i), (-1.0114980813328792442e-36 - 5.2172817261637772717e-36i)}, + {(23.313296386015117889 + 161.9634793336883547i), (-1.69158883585714043e-36 - 2.9961838967591297539e-36i)}, + {(-47.883141357656690218 - 125.47978778734290017i), (5.6697320096360474997e-35 - 1.2206315690178756206e-33i)}, + {(-48.316878447013237974 - 109.16123684110732484i), (4.1404344211253963634e-32 + 2.1273785894812345096e-33i)}, + {(85.216467296377757634 + 9.8872412103680051843i), (9.7971838844177097399e-28 - 3.495522041158420087e-28i)}, + {(55.581498649600561635 - 17.153023054790807578i), (1.1968539502487036371e-22 - 4.7050374737183302011e-23i)}, + {(-42.504311535704665914 - 3.1088472096404253797i), (-2983274474816881.0 + 45920138380187496.0i)}, + {(6.219618165106239438 - 19.457025553286865005i), (-4.1199695557330697659e-9 - 4.1916008537456993683e-9i)}, + {(-2.6182178665741226986 - 160.33400126197651048i), (5.1930995828800059091e-36 + 3.427892956515854678e-36i)}, + {(27.138454077433827649 + 76.59915202614369889i), (-3.8802142993933340442e-27 - 2.7662588046356921145e-27i)}, + {(5.8921616117326793827 - 56.693409245415423925i), (-1.8530641184894918064e-22 - 5.6218232426919176323e-23i)}, + {(31.666817006967374226 + 30.478179573613111586i), (2.0213357604022165943e-19 - 5.4443883672787542458e-19i)}, + {(4.0194287117188416403 + 56.283740257429784037i), (-7.7863391113068939424e-23 + 2.4801955446948156167e-22i)}, + {(-213.22678216407012997 + 1.7338374764844455278i), (6.4355453034544593025e+24 + 4.4188888414249608376e+24i)}, + {(82.012366925570958642 - 76.753378907217012284i), (2.3444194283021024421e-31 + 1.841761100985363287e-31i)}, + {(89.088810167035063614 + 2.478201868626816573i), (-2.2028303943773752459e-28 + 2.4512901338933054576e-28i)}, + {(175.24124159392670208 - 157.71745800508878688i), (6.2015154196972300116e-41 + 2.1881760865113243858e-42i)}, + {(17.296698026195208797 + 64.423635354019168631i), (3.5047544276054468104e-25 + 1.7437193569110054905e-24i)}, + {(132.96869039443080851 + 127.34394115952554216i), (5.8452516899195919927e-38 - 8.6771355791152014573e-38i)}, + {(241.41723042013120448 - 62.299323971486650464i), (-3.0425172724297630166e-42 - 1.1308848290864301868e-41i)}, + {(55.639239570151289627 + 128.2913412349079465i), (3.6606358986631667205e-34 - 1.4924328914149344285e-34i)}, + {(273.7829228442141698 + 114.27387850370318745i), (-4.867019551714404532e-44 - 3.9761491789358047139e-44i)}, + {(52.910673239952245694 - 35.650925528035187995i), (-4.5348284292096951457e-24 + 6.1915610091045118037e-24i)}, + {(4.0329608605054625414 + 18.817772066401634135i), (2.6317452436749949112e-8 - 2.1058163721437447612e-8i)}, + {(-156.62881127261400138 + 22.341603187832717481i), (5.0575858569298571924e-33 - 1.0252088936309904286e-32i)}, + {(-83.421547000980226017 + 18.394112143862457742i), (-1.7651331623740840831e-26 + 3.1130291247968081065e-26i)}, + {(-23.136336259460087206 - 126.23793699771334786i), (3.6288179612707259301e-33 - 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9.5099839305206172532e-35i)}, + {(-19.277286002281268651 - 117.15425090682349207i), (1.5145679606179538217e-32 - 4.8002429350812699806e-32i)}, + {(30.195237098132576392 - 38.441047119299923907i), (1.4134234406999746543e-20 - 1.7757728601928680379e-20i)}, + {(-20.774632897329617265 - 152.73268507403429339i), (-1.0696092644334911361e-35 - 1.7065772967616630793e-35i)}, + {(-27.590509920466089966 - 72.291174724809366126i), (2.3106805382631068539e-27 - 1.8048452060208409259e-26i)}, + {(93.059907868856257096 - 128.02614148570404495i), (9.7178685599171390313e-36 + 6.6829306270446765991e-37i)}, + {(28.567789119406683085 + 153.45279740965443693i), (9.3418110314320860621e-36 - 1.074986994562053871e-35i)}, + {(90.695768743983776972 + 93.816540750017153982i), (-1.8118304800872402354e-33 - 2.7181064900546759569e-33i)}, + {(-138.9299753762620071 - 52.799646897101503384i), (7.5386450903306799843e-36 - 5.4730829904177993007e-35i)}, + {(26.933392607330041812 - 65.950311784975752971i), (1.0879746423430768566e-25 + 2.2765323344389149081e-25i)}, + {(-93.367750623296856816 + 4.9466227138964580234i), (-129968380998.16429138 + 118642784048.42480469i)}, + {(54.415890737718207504 - 16.998574750019955104i), (2.2774577849053434846e-22 - 6.2844129343383206889e-23i)}, + {(62.149717238321933621 - 137.42894112185996391i), (4.0613886063341731494e-35 - 3.4774380273493915137e-36i)}, + {(54.001751164049849763 + 68.044432394414670284i), (2.777779670719853127e-28 + 6.1242947198420650506e-28i)}, + {(-51.495615760322998256 - 59.635502464716324766i), (-8.8681673711002148893e-27 + 4.5386064837935218119e-27i)}, + {(-32.437500193910409507 + 35.094109077620323944i), (-2.3977306072055390223e-20 + 1.7733758309440405381e-20i)}, + {(-176.65820197669435743 - 98.493011361050506025i), (4.8681638629000872332e-39 + 2.5749070442251467688e-39i)}, + {(-7.5049821682183548432 + 17.942264302512882068i), (1.493998945814921553e-8 - 1.5122589285595477821e-9i)}, + {(48.162783094920179394 + 72.173904703120001614i), (1.6062316496959348074e-28 - 6.6996390693949767476e-28i)}, + {(72.76516252816183794 + 76.006107145880861253i), (-1.4496562754486050542e-30 - 1.5460473515303719935e-30i)}, + {(120.03516078379101373 - 46.542413107621719348i), (-7.1101273484979446599e-34 + 4.9772502688109218734e-33i)}, + {(19.401740357710554719 + 118.62258569507193329i), (1.0474333382690815978e-33 - 3.6233204474818825607e-32i)}, + {(-172.01627632296504089 - 46.402667192766649862i), (6.8399140282795646184e-39 + 2.4321375709560962346e-37i)}, + {(-8.0023825460602804327 - 154.34606287163836669i), (-1.5028871455730364483e-36 + 1.8673783658048944312e-35i)}, + {(20.081172087390775971 + 90.272643584100080716i), (9.5199897302328075388e-29 + 1.2134015706353886131e-29i)}, + {(-18.596458648400197688 + 84.197982122671206184i), (6.6863056874598541598e-28 - 2.9060437137723919371e-28i)}, + {(-168.54276053256955947 - 142.39497287161086092i), (2.2498974313988799646e-40 + 3.4330657711433611081e-40i)}, + {(-39.995919769504361341 - 101.08296915836925223i), (2.9173797613763644682e-31 - 6.2304466517020698905e-31i)}, + {(228.39410158819043772 + 38.291729551953984867i), (-2.9959565896153222085e-41 - 1.036209454806795859e-40i)}, + {(41.928736337397943146 + 49.483042477920967883i), (-2.1564783994989350881e-24 + 3.9489164848521409132e-24i)}, + {(17.657587316194209848 - 81.765972068680113694i), (1.948113799177037785e-27 + 1.4803541913209607987e-28i)}, + {(16.039826493231956306 - 132.10464870882327659i), (-1.5836851469214864543e-33 + 6.1745035538337529112e-34i)}, + {(-19.992181787539877291 + 49.676061047399848292i), (7.5290802171466456582e-22 + 8.0588704795387093415e-22i)}, + {(-20.235309924136924309 - 93.130322872682697266i), (3.4806353219560652841e-29 + 1.0419778576616564152e-29i)}, + {(49.035085438654014922 + 43.190140531353307551i), (3.6085823131149198289e-24 + 6.7336456180988926883e-25i)}, + {(62.962792420502601942 - 4.700519284557826083i), (6.854376774680430502e-24 - 8.4575006776480472138e-24i)}, + {(18.864735868849425771 + 130.96097922232297606i), (-1.0272147252498239246e-33 - 1.7447003875809059736e-33i)}, + {(70.836282275891875315 - 6.1143394641857726768i), (2.580635054872620145e-25 - 1.5524036990986697965e-25i)}, + {(-92.261252077061939758 + 134.97566557020553546i), (2.3381900757938091178e-36 + 2.3353792978265640825e-36i)}, + {(-92.886987568121455183 - 48.408233189669878982i), (3.973954794305764655e-31 + 1.8938064677500694892e-30i)}, + {(-113.81125492807437638 + 139.47487391385345745i), (-3.2517949054915538754e-38 - 1.8089023687385434042e-37i)}, + {(-129.08918596410626378 + 90.970867408235136509i), (-8.036707552966752501e-36 + 4.2775488848209864856e-36i)}, + {(104.71023907823516197 - 58.088302612978615969i), (3.9761142764577264602e-32 - 1.943975012256636833e-32i)}, + {(29.321251534063048183 + 82.445275473163277979i), (-4.0485755622647454508e-28 - 3.1905540390076474337e-28i)}, + {(68.588945144400383924 - 3.4467041272897924742i), (-4.6628230460709766541e-26 - 8.5769881581936311077e-25i)}, + {(96.576252720592151491 - 66.666389456457906704i), (-6.410213183783271911e-32 + 4.9115721412481478086e-32i)}, + {(88.213979086111294237 - 1.8165537373516253972i), (-3.6286751345168802372e-28 - 2.5960391957527109864e-28i)}, + {(61.342547076485217872 + 174.05753047196651551i), (-7.4359466346549846779e-38 - 5.8220235663487001475e-38i)}, + {(-122.12320011503150852 + 35.512087006773725761i), (3.2850811556145352843e-33 - 4.7864121508217539216e-33i)}, + {(16.956922780058309996 - 61.126574834077892717i), (-3.2823024479371108397e-25 - 8.0734465912737026796e-24i)}, + {(136.3373940924030876 - 243.41850281385512744i), (-3.5235000648148361265e-43 - 1.6488049724422237811e-43i)}, + {(-9.0792280553855917447 - 16.962966189665309003i), (-1.8711757552459403548e-8 + 3.7096373516568812367e-9i)}, + {(-229.36454261959485734 + 1.7436020892379850977i), (-1.7200170903443546665e+24 - 4.2469015726692133461e+24i)}, + {(-130.75322564231157685 - 22.791478812124012165i), (-3.3684199091206858651e-32 - 1.9904634782214625918e-32i)}, + {(-179.72058222610883149 + 77.479275018354414328i), (-1.3615609248818096822e-38 + 5.5387162335233878226e-39i)}, + {(41.880993210310414554 - 92.566542055076979523i), (5.8428829034435209165e-30 - 2.8152044367736582128e-31i)}, + {(-49.83710602386143762 - 126.96500994384894057i), (2.4865460086021727422e-34 - 7.2715002814917865447e-34i)}, + {(97.462542644708676676 - 26.437591136978262796i), (9.8073548226251841477e-31 - 7.5193710671458515806e-30i)}, + {(151.87354982629398137 + 113.04713450986787393i), (-4.1985167530890755622e-38 + 1.7409375407098823794e-38i)}, + {(124.57028237910832047 - 204.30862036339635779i), (-3.0831915251780227433e-41 + 2.417947786407684677e-41i)}, + {(1.4438869933802729317 - 60.251446869601934964i), (3.1670685403337484869e-23 - 1.6098462761175036736e-23i)}, + {(-7.9153776989968172018 - 81.816097916189121975i), (-3.1212220930025026928e-27 + 2.0479241257629176588e-28i)}, + {(11.595504197775326816 + 127.81436959691710342i), (-4.3022541158778774315e-33 + 2.5989005830258472799e-33i)}, + {(113.47769481381266132 - 154.2415398198533012i), (3.1593302543107850956e-38 - 3.7172349058482204204e-39i)}, + {(-48.443030169401986029 + 41.104598227704187252i), (3.01811686681594078e-24 - 5.1819898880639048302e-24i)}, + {(-34.944242878039602829 - 1.3205072774398620705i), (4.502455712756920878e+28 + 1.2170065661147013756e+28i)}, + {(309.66870378767725924 + 124.56299219330517758i), (-8.6443702965632006999e-46 - 1.6043499003315599996e-45i)}, + {(82.635871741004379487 + 70.87123709356086465i), (6.1711620715441729073e-31 + 4.5672449153381435791e-31i)}, + {(-104.30011564701055704 - 121.71638176274457521i), (-4.6680892260285643411e-36 + 3.6527052271356582068e-36i)}, + {(-69.154277353607497503 - 20.359242730387695275i), (8.2443524228621480085e-26 + 1.0339557820648513064e-25i)}, + {(-11.781409802086667327 - 26.516338701445658188i), (8.6176893004336314192e-14 + 4.500206265743732711e-14i)}, + {(104.92857445241723724 + 22.353007892253941691i), (-1.2257430163130371389e-30 + 5.0878848452307150288e-32i)}, + {(-129.6575691156622554 - 60.00572520045105307i), (-1.6682567521812902166e-34 + 6.8905488194826805385e-35i)}, + {(-1.2779192528638472215 + 216.04380482915752282i), (7.8855272835137662345e-40 - 1.9874139367708121782e-40i)}, + {(-66.651637904015387903 + 61.12219395194111371i), (1.5772450943499584239e-28 + 2.4971718554397034919e-29i)}, + {(122.6690997521960611 + 37.096904813846506954i), (4.8323910558722957474e-33 + 3.1797153679981043399e-33i)}, + {(33.133178782450244171 + 70.52238001630452402i), (1.5525556570728727645e-26 + 7.3157141671162495996e-27i)}, + {(92.030020194896522412 + 7.2637292721291828457i), (8.2090682881487897531e-29 + 7.9049154656565097588e-29i)}, + {(98.198706591215866979 - 20.538326232796993764i), (-9.2383738213001998787e-30 + 6.3502763994984311933e-31i)}, + {(70.828642824435675607 + 132.71160022716375693i), (-2.0637606046814733013e-35 + 3.9303555214224154387e-35i)}, + {(-18.57533551691244611 + 106.25064766938562855i), (5.1788966659468509238e-31 + 7.2859385773380477595e-31i)}, +}; + +const std::vector gamma_35_c = { + {(-125.84007495368484797 + 17.717725968116045721i), (1.3077634345044438537e-20 + 2.0585614368630916872e-20i)}, + {(-60.926962301902655383 - 188.6161760212682168i), (-1.1457701342152092313e-42 - 2.8179749989666637568e-44i)}, + {(15.426892880500448157 + 144.43927422852232212i), (2.8286863838035328811e-38 - 5.6643749641747473072e-38i)}, + {(108.36040598197010354 - 137.08270561083440953i), (1.005442881042425472e-40 + 2.3252695789667599808e-41i)}, + {(-181.52361094710161638 - 31.043729526038958966i), (-3.9183407233578715514e-36 - 1.3979898491531097973e-36i)}, + {(-66.892613536979553146 + 69.099190755603871139i), (9.5635171233665016248e-32 - 3.5283356658468532607e-32i)}, + {(-62.204622366486162832 + 191.39928110439885245i), (-6.702827522067740636e-43 + 5.7731525587361370779e-44i)}, + {(-151.33344901950204076 - 12.649640841954601811i), (-8.2461243568965582925e-7 + 1.4258760801146249732e-6i)}, + {(102.3940974883262669 + 176.75333706093167052i), (2.2228179765268352062e-43 + 3.662729619594504296e-43i)}, + {(-9.4103856084753640943 - 95.755972241038165294i), (-5.0816486292382822964e-32 + 1.0026519695738224461e-31i)}, + {(205.60589998432178049 + 129.73560531471471791i), (6.1975637740962634776e-46 - 7.64352524781581983e-46i)}, + {(-139.61765018796450022 + 15.973017586296938575i), (-1.0392072480072526308e-15 + 9.4739999425463666119e-16i)}, + {(56.03301641516302567 + 132.05958343908309871i), (-9.9419599081628865852e-38 + 2.0468437567086032735e-38i)}, + {(23.893023013995492221 + 97.66029069427571585i), (-2.3790177476137067679e-32 - 9.4209695154807067076e-33i)}, + {(-52.93457316393392631 - 30.762289493792177808i), (-5.5025060903177159009e-25 - 3.5959734707054348534e-25i)}, + {(-65.623814389284490289 - 77.736320282689590044i), (-6.4089331123065743994e-33 - 1.3002758257877887925e-32i)}, + {(-102.61647221987024636 - 25.307412323873180071i), (-4.6173069941899265498e-34 + 3.4511518503027716975e-33i)}, + {(42.967092397804670156 + 120.37113788259303249i), (3.6900264520074465471e-36 + 4.4395745879700805422e-36i)}, + {(1.6955492638111395731 - 175.87779296665632955i), (-1.8218806159410558943e-41 - 7.5119774695705129294e-41i)}, + {(8.7334953790321652178 + 0.63985498339412283375i), (-1091912.6015309258364 - 617161.08893492666539i)}, + {(48.480724542491465456 - 217.08751124752353689i), (-2.0569640936434367613e-44 - 5.0385729428249727873e-45i)}, + {(80.718201738646286003 + 6.3218520074887054605i), (-5.4467600903580642781e-29 - 2.240568336429049376e-29i)}, + {(-23.693652414435341313 - 76.41291262334416956i), (-6.6290986705427872508e-29 + 1.754622982354269989e-29i)}, + {(61.61143696765357447 - 40.036541391363691389i), (2.2535772697610878173e-28 + 1.7230922370292910148e-27i)}, + {(-23.84664475290873753 + 87.370106166031035855i), (-8.1635115153460863464e-32 - 9.0092578759016696182e-31i)}, + {(81.757186425034845456 + 52.433699314833468463i), (3.4283948762543688692e-32 - 8.8735638424671655908e-32i)}, + {(14.15447614954314659 - 32.606882473608436612i), (-1.8962236241670218648e-16 - 4.372703988890992699e-17i)}, + {(-24.469504839702320709 - 49.521461907287665838i), (-1.6513026240990301527e-23 + 2.1661110088194706976e-23i)}, + {(-73.433215242282884105 + 100.18843934221204961i), (-3.5708217049617501702e-36 - 1.326530521905586624e-35i)}, + {(-111.33826636825826029 + 41.786001004501734712i), (-5.9498207523888532601e-35 + 3.210014488378258951e-36i)}, + {(-2.1910904875227905642 + 99.748288418826462021i), (2.5928060114585043906e-32 + 1.8765170117728632039e-32i)}, + {(-81.078607609672488366 + 51.095788507784824617i), (-8.3341262166954015627e-32 - 7.4581563580616819362e-32i)}, + {(75.66412998685200364 - 65.099887528257966096i), (3.551382217082753812e-32 - 5.5886949541548310498e-33i)}, + {(-75.004232553177288878 + 119.05615314092818835i), (1.4305047006658848207e-37 + 1.0576186837445183595e-37i)}, + {(36.377344446258256028 - 60.929812979681038598i), (1.1724870839842649468e-27 - 5.3813597297174351579e-27i)}, + {(-66.405559007777853253 + 42.275761824505657671i), (-6.8474195621956700283e-29 - 8.0556588926100796289e-29i)}, + {(-10.621718083606094041 - 95.895876787056494095i), (-7.984343797005380253e-32 + 6.3250333249770705628e-32i)}, + {(-66.450796107114925348 - 34.36842897443742828i), (3.8994186848365029334e-28 - 4.7524821777547697075e-28i)}, + {(60.980184405332671815 - 25.015174106941547194i), (3.3075707569737363184e-26 + 7.4191878153291769499e-26i)}, + {(30.45368211126173108 - 114.1971387204511359i), (-3.8165411480604356119e-35 + 8.0079423369197683283e-35i)}, + {(192.18903843938471709 + 72.148991642193678331i), (3.729843204292402054e-43 - 1.2042408955669828666e-44i)}, + {(67.366539272612911304 - 14.662197920193676737i), (5.0361557052215605176e-27 + 1.607696215396156556e-26i)}, + 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{(69.980734906027592501 + 169.16186127479750212i), (-1.7360256656071082572e-41 + 9.3858096513084499107e-42i)}, + {(-110.18848446224743043 + 90.978169068497621197i), (-4.961217787828032174e-38 + 8.7762502174651159628e-38i)}, + {(-108.82781610210643919 - 43.125348451552326878i), (-8.6368286253210033294e-35 + 5.6741421702843357712e-35i)}, + {(-117.39816176235216005 - 117.51611635653709698i), (3.5192831537244755556e-40 + 3.9587070374662262852e-40i)}, + {(21.021746795484023806 + 8.5645426626574465701i), (7.0839198321288220414e-10 - 1.8164424719933181546e-9i)}, + {(-38.320448409855444538 - 153.24455482991970712i), (2.1811447466239898913e-39 + 2.3881328666266897315e-39i)}, + {(65.954151846935360481 - 96.90960718165878518i), (-1.1494194652984857089e-34 + 4.5166459125773810839e-35i)}, + {(7.3050240853413050957 + 17.71215068716933061i), (-2.2202559493833522619e-7 + 5.6227779396800621026e-7i)}, + {(-8.9662573858911169822 + 1.7390768372338045733i), (1.7777558076209589845e+31 + 1.4869357448310560293e+31i)}, + {(-110.87311043197212257 + 84.764272102870435788i), (1.6341253759260378688e-37 + 1.6029494889269604641e-37i)}, + {(139.9048771097060353 + 2.5408471149735536443i), (2.0974457848650700177e-37 - 1.5543322373521962442e-37i)}, + {(183.97410221868011604 - 18.702962134034976316i), (-1.3414023268242875983e-41 - 5.8883039571830285348e-42i)}, + {(148.69852897799799507 + 72.800871700822426646i), (-6.7750093374769168329e-40 + 1.8896964901520233713e-40i)}, + {(-70.998249299791055478 + 84.416192394521203823i), (-4.3782962164865712396e-34 + 7.4246234264662881056e-34i)}, + {(-105.62364727502585993 + 70.323403651208622023i), (3.7404562592868894874e-37 - 6.2916907816224553136e-36i)}, + {(-188.8375520903512097 + 74.522436216583002988i), (-3.9875664966207114917e-43 - 2.4824184341424707758e-43i)}, + {(-35.884572440777155578 - 34.977360025353661399i), (5.4521382418178007643e-23 + 7.282584127620203991e-22i)}, + {(105.40586116302306152 + 289.59380859303655598i), (9.181682727109706756e-50 + 2.1605075981473379811e-49i)}, + {(-9.2549386334223751049 - 65.03496282633552994i), (-6.1482201658242102346e-26 - 3.3762386467984675838e-26i)}, + {(-25.661999945306167348 - 62.636786933562305535i), (2.2134766525715933551e-26 - 6.3935057183054954301e-27i)}, + {(-44.938176358327254434 - 55.49061718134523602i), (-2.987431474638715063e-27 - 1.4893953437657634441e-27i)}, + {(-7.9396355929351836167 - 38.298344445255267487i), (4.9949856846996354174e-18 - 1.2643378205300626519e-18i)}, + {(122.03822834049850599 + 47.255337167119080277i), (2.4924080584763396517e-36 - 1.0843387826898468999e-36i)}, + {(44.407814799042668596 + 151.61152681985956292i), (1.4621964341532507161e-39 - 3.0844085760788360789e-39i)}, + {(119.80703842924373248 + 47.736637928583114387i), (3.3149639361958107922e-36 - 3.1047068929897390011e-36i)}, + {(-84.509243912933783349 - 19.477999293753899934i), (-3.828853339632828916e-25 - 2.2238232073669504801e-26i)}, + {(45.693208859072683481 - 205.20027335817508174i), (-1.475172242245890654e-43 - 4.0227754962799914057e-44i)}, + {(89.301860293449777828 - 120.82436160711364437i), (3.9683320341406177961e-39 + 2.0151975373200491696e-38i)}, + {(45.373365543477447659 + 97.904577352840590265i), (-1.3589337701639851805e-33 - 1.7411655935285782537e-33i)}, +}; + +const std::vector gamma_40_c = { + {(115.57609680702209687 - 46.229512195544998576i), (3.3694919305393100713e-38 - 1.5500511000351721889e-38i)}, + {(-86.868954415374588507 - 142.7911850226261663i), (2.2895196460483273965e-43 - 5.7355463663769100896e-45i)}, + {(-141.23058138214864243 - 204.93052367711760553i), (-1.6877996368474347698e-50 + 2.258333169522722467e-50i)}, + {(30.981732763262314734 + 140.71608327767904711i), (5.9911004829482831839e-41 - 7.4041639987926396432e-41i)}, + {(202.96841664160359642 - 75.919871023302718527i), (1.7162790549438811415e-48 - 7.9857496000489234606e-48i)}, + {(51.610641516579661925 - 24.189557063237458578i), (-6.0811809369264717405e-25 + 1.49409146877073612e-24i)}, + {(80.049044151021192306 - 95.987090387630331634i), (2.51132818223027475e-38 + 1.6777845771781659005e-38i)}, + {(-31.134126836043268582 + 46.834190866381938179i), (-3.6763590086832076935e-25 - 1.6415583367772978431e-24i)}, + {(-3.0735676287015416541 - 35.660875643800615364i), (9.3416208858294494407e-17 + 1.0946282997045351413e-16i)}, + {(-24.273890854215832036 + 54.059944320057219613i), (1.6713655431292937534e-26 - 2.2030154139748713343e-25i)}, + {(104.81608664087127636 - 58.405133182494161304i), (-1.342889000172444304e-39 - 1.6069864861293013787e-37i)}, + {(-33.465333453989025259 + 13.664689017276105076i), (5.9219990479750270836e-6 - 0.000026756703967861959016i)}, + {(-1.3441194715546924687 - 282.85235346611011664i), (-1.707085367830779211e-52 - 4.5557758470538583006e-53i)}, + {(92.55740093183128181 + 132.05388715453631221i), (-7.7999613982021154814e-43 + 7.6953679125601824036e-43i)}, + {(73.505381273471385839 - 49.496617871477937456i), (-7.9792240618858885841e-33 + 2.9774756115377125857e-32i)}, + {(-28.061572998851264771 + 94.057311668797424886i), (-2.9269402312789737991e-34 - 2.8377473393487228775e-34i)}, + {(-149.59800695976980478 - 76.408205028573590312i), (-1.7883305344243858241e-43 - 3.0180938400086282634e-45i)}, + {(-102.14438341870324223 - 26.135123323836019438i), (-7.3128244029572709023e-33 + 8.6514733720205926902e-33i)}, + {(-6.6724094066166808048 - 29.718077447123853574i), (8.3973901317455556571e-14 + 6.9511693186944949868e-15i)}, + {(-25.39243334807805752 - 130.5130003186291674i), (-4.1689974395746568357e-41 - 2.2366708922874281869e-39i)}, + {(-111.64322625671607625 - 60.528598742039818603i), (-7.3294894790519956245e-39 + 1.0127419991126116991e-38i)}, + {(88.851357268058947625 + 31.205424393666014282i), (-1.4568899158808057328e-33 + 2.3173864907394312057e-33i)}, + {(60.245752060292723229 + 44.12782151034411271i), (-2.8452214498669954785e-29 + 8.8598851897457070859e-30i)}, + {(163.6875147109174975 + 22.694126635254935564i), (-3.1355309101817071334e-43 - 2.9600030984393948557e-43i)}, + {(4.8169754558768342889 + 61.914218954223386504i), (3.7636724412345404309e-26 - 1.393540588184477113e-26i)}, + {(108.11004380188478535 - 21.408860227080019456i), (-3.8486535416896024236e-39 - 4.9663252899037349189e-36i)}, + {(77.423025605093030777 - 54.412800201857102422i), (-1.9151410829594125367e-33 + 1.0809911977577228045e-33i)}, + {(-109.83832550290453867 - 129.79621938091298716i), (1.1312334241929667475e-43 - 1.0229505176007568364e-44i)}, + {(-85.907098641743289136 - 140.90047403838534024i), (3.8079319815235758566e-43 + 5.8140269716758859389e-45i)}, + {(107.34354927293226467 + 33.424331015018175606i), (-2.0084835851751926935e-36 - 9.502040991030867166e-37i)}, + {(-131.41797912303135831 + 26.465517632692787231i), (-4.9243431480607691458e-33 - 4.1355328549845648308e-34i)}, + {(-203.68366820144396456 + 21.503814029732527757i), (-1.018586145742235112e-26 - 4.4845164259819402204e-27i)}, + {(-115.90124424579273921 + 63.830120969520379504i), (-8.5887753900733897619e-40 - 2.280416400987942742e-39i)}, + {(-141.16698630415589832 + 31.456162772493538426i), (1.7445001587393463273e-36 - 1.4511144879371456603e-36i)}, + {(43.852979399381304404 + 233.71121618731683611i), (-9.1838072268577337971e-50 - 1.6151463653347789185e-49i)}, + {(-87.816921836355561481 + 98.759719510471981607i), (1.6135453415596296393e-39 - 2.0969059460714107555e-39i)}, + {(-161.75989756253818541 - 79.08956701526031452i), (-8.493162266551204736e-45 - 7.2959183429861195682e-45i)}, + {(23.247540786165178162 + 80.242333080342760354i), (-1.726487440958117153e-32 + 2.9168752934819923252e-31i)}, + {(37.829803538862996959 + 40.391591009044184091i), (-9.1199614732822121271e-26 + 4.9628513047923745334e-24i)}, + {(-104.82024100234745845 + 98.250154699408426495i), (-1.6641974312174151286e-41 + 9.2054613680164587561e-41i)}, + {(-40.79270462075383108 - 33.6605510490657025i), (1.0397433645007258281e-23 + 1.4265164054939925198e-23i)}, + {(-163.88247703277951928 - 217.17777044774297224i), (-5.6623827290310885476e-52 - 5.650167701841219666e-52i)}, + {(6.913525591766192413 + 23.675302999484415523i), (2.0176262328502731553e-10 + 5.4741687638046445102e-10i)}, + {(-65.606992823334380205 + 85.188254976267359098i), (-2.962040165133733862e-36 + 9.5689151909894634144e-36i)}, + {(51.293212789930841211 + 99.021897960884572854i), (-2.8188930520044728674e-36 - 3.2008310827563909439e-37i)}, + {(-3.5128139132467977035 + 4.5415390340377586043i), (-1949695715970860032.0 - 1.1989982166307982541e+20i)}, + {(-53.212532744361304538 - 20.190728661688780221i), (4.1674530074325415698e-23 - 9.0759564213562528211e-24i)}, + {(200.99661382058070558 + 82.408456307261047868i), (7.3515688825428367717e-48 + 8.1286090363522929236e-49i)}, + {(-35.976456951985483101 + 91.268638862060797123i), (3.6008007193013317912e-34 + 1.9416391929638809737e-34i)}, + {(-10.549711599748503588 - 91.619182695480532175i), (-4.6162446382205454403e-34 + 5.0851916262140124112e-33i)}, + {(119.80816526189539672 - 34.553301566933797062i), (-9.5536117698583096766e-39 + 3.3461333132160123908e-38i)}, + {(-30.72677905044704616 - 99.986072837028544313i), (-2.8799673599748080474e-35 + 1.4064847768646872621e-35i)}, + {(12.655980763787248122 - 10.292019469131826526i), (0.014304991062675109434 - 0.0065482463341049049546i)}, + {(139.51650797183975783 + 116.4147011580185449i), (8.655807894757491925e-45 + 3.5646432099212320801e-45i)}, + {(66.336571816849414063 + 2.6503972415437040411i), (1.3257260886573398559e-28 + 3.5460356216972651964e-27i)}, + {(31.808298038645617112 + 75.090616357557806282i), (7.8514689978953748626e-31 + 7.9068645178701556646e-32i)}, + {(27.770857726950872291 - 162.56009046587217881i), (-3.9738974447446844353e-43 + 1.5234070998018509141e-43i)}, + {(203.66896137128316013 + 145.14700285506495447i), (-2.4585560643204915588e-50 - 8.157434107614013471e-51i)}, + {(-42.495521550471373473 + 69.06864592127232072i), (7.5341129465894547198e-31 - 2.2502462718332798569e-31i)}, + {(90.723313433196565825 - 89.500251304829617993i), (-1.379991129842595337e-38 + 2.3001110223755737604e-39i)}, + {(-118.42927056024312549 - 41.800470431411845595i), (-1.1218101556611902995e-38 + 1.5791394662351116078e-38i)}, + {(-222.12811001940724509 + 90.702617581996335616i), (1.1486350342779610876e-49 - 2.7309855440533625629e-50i)}, + {(-11.937273755569940192 - 99.969901542935573957i), (-3.6366022293684832253e-35 + 1.4845340789886215612e-34i)}, + {(-13.545773788539236193 + 181.15300386193734994i), (8.6323795443414753352e-45 + 3.977953331199990882e-46i)}, + {(-110.31846755971201901 - 72.102647301126765456i), (1.3585617126693737716e-39 - 2.5312499043301681714e-39i)}, + {(-24.540174423080756583 + 22.262362060681919473i), (1.4847346386098946761e-15 + 1.3424829396437710613e-15i)}, + {(-67.383910905110809608 + 241.33092273949063156i), (5.925344776243405737e-52 - 2.2074272917667337612e-50i)}, + {(125.140791991240377 - 106.73676121423395102i), (5.0672063185531752084e-43 + 2.5375050277903023333e-44i)}, + {(190.92690753312436414 + 98.057942455356439382i), (-1.177165243551930079e-47 + 2.0239918482848638438e-48i)}, + {(27.537432562998031216 - 8.5884077946530918979i), (-1.3958810401632260196e-12 + 4.4847338754978976318e-13i)}, + {(39.900008471390023601 + 65.649750775220738319i), (8.3556345994525435127e-30 - 3.1403259720472729623e-30i)}, + {(81.360809240657516739 - 270.07921863543447216i), (-1.2059138202164788574e-52 - 1.6162082308717908683e-52i)}, + {(-63.692453596367172963 - 144.24977988085007041i), (1.200407069917371138e-42 + 2.0539718774356207858e-42i)}, + {(66.979186081878708592 - 56.447207363811912728i), (4.816254664863121516e-32 - 6.0241399477964844124e-33i)}, + {(-32.481881547254531029 - 59.309064506269933759i), (-1.1925522725612818854e-28 - 1.1096592751542666682e-27i)}, + {(3.5154289999511716402 + 74.593541874934217617i), (1.1434487432330146737e-30 - 2.4672459731222443807e-29i)}, + {(-32.781364957426674778 + 165.47699643708244821i), (1.4141317677931864458e-44 + 1.6406001968958561435e-43i)}, + {(156.10303447130326049 + 69.305545331203632031i), (5.6527359568355019647e-44 - 9.8809736811385342394e-44i)}, + {(0.61330549731263594992 + 9.6095428271272762544i), (-23852767.64160708338 - 15082911.082305219024i)}, + {(-153.83456191784011935 + 122.19941581675817588i), (2.9036356824297117243e-47 - 3.4838236302669370731e-46i)}, + {(34.457570285342811189 + 98.328737220615934689i), (-3.1246187195107160381e-35 - 2.8444393171118103779e-35i)}, + {(35.797951979475165274 - 13.721247162845548573i), (8.9186093678997321501e-18 - 1.1461646836888172892e-17i)}, + {(-28.823174857319340703 + 75.280546136017377989i), (6.9416264539981851757e-31 + 7.7962999115893105552e-31i)}, + {(119.37476250903384312 + 240.45539793423719743i), (-1.3073108799957027362e-51 + 6.8617897501368755731e-52i)}, + {(150.574574432088923 - 47.797315847802316569i), 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{(72.591980994881211586 + 1.7223196608861819357i), (-5.5618003225559523314e-29 + 7.8572694963236638823e-29i)}, + {(-57.042527658975586746 - 27.151531823617336414i), (-4.8587160980513561043e-27 - 1.3590753818490435878e-26i)}, + {(36.030130557010309644 - 41.009894204985592125i), (8.1467744093098541383e-24 - 2.5714666447164755795e-24i)}, + {(-112.73816061853905524 - 207.47012025663610757i), (-9.7993313532456643542e-50 - 2.1106695002608758825e-49i)}, + {(-69.282957862154148643 - 56.448186348447585203i), (7.2851485926703187614e-33 + 1.3520977191956229872e-32i)}, + {(144.34462314015763695 - 194.33318819868338778i), (-8.8082549779515140566e-50 + 3.2778164158898326358e-50i)}, + {(140.20713126521576442 + 202.27331072979092141i), (-2.7970520716557223689e-50 + 3.9430075424057655371e-50i)}, + {(-201.48966523353854541 + 3.4864501091214812334i), (-7.0581097662383474858e+24 + 5.4052947023526098274e+25i)}, + {(70.836354126106442664 - 236.82226095902322527i), (-2.0859644426272509415e-50 - 3.3783764389686527887e-50i)}, + {(-118.98981771729214074 + 10.460936210595885854i), (-967.82158784151295094 + 15106.963694358581051i)}, + {(169.4543474319212919 + 107.246372909512516i), (1.4619093572154634157e-46 - 1.0680076521612935339e-46i)}, + {(54.655173461762650788 - 60.5959266602198241i), (5.0299606730503199942e-31 - 6.4585458918483992619e-31i)}, + {(-108.60327270713972325 + 3.6075712558502996963i), (1.1466733586175730165e+25 + 3.1751469281286456628e+24i)}, + {(26.911213986066425008 + 151.55658514712143869i), (-5.4795512265217092178e-42 - 3.9048092975369979977e-42i)}, + {(-44.893066604509748174 + 109.00469687243612782i), (2.6477367010389605249e-37 - 2.1007375788004284412e-38i)}, + {(-56.035397365948703907 + 12.049393019429439633i), (0.15457001212430243609 + 0.6834862116951814226i)}, + {(-5.4233584309354219144 + 246.19584804770067876i), (-2.5761309479322113587e-50 + 3.6973156494498144672e-50i)}, + {(112.68284201720877036 - 26.496493891310123558i), (6.8256589759692383717e-37 - 1.028025642434323437e-37i)}, + {(-19.01900684663046448 - 172.62319289712863224i), (1.0748631298736557275e-44 + 5.0904596142316384551e-44i)}, + {(4.3849950350477628902 + 29.546919301479572795i), (-1.2094424164981428803e-13 + 2.0278497817195099801e-13i)}, + {(62.978639328000554087 + 205.80189667658621033i), (-7.2442784369305979351e-48 + 7.10652464212332251e-48i)}, + {(-190.05675750079953445 - 132.75762376177323176i), (-3.2917438136153981935e-49 - 3.3494082052601734131e-49i)}, + {(240.09329533206931728 - 44.319722940633916153i), (-3.5275681802495308124e-50 - 5.9125203455647691823e-50i)}, + {(-35.950090360806527201 - 75.291814734979084278i), (-1.7910229582955978834e-31 + 1.8717173598074251241e-31i)}, + {(171.73245775306793348 - 51.918423022537915301i), (-1.1172241315389639343e-44 + 1.131613798392908688e-44i)}, + {(-97.531580156509463109 + 34.632370637000001068i), (-2.2605363727401641452e-35 - 3.6107553408834036056e-35i)}, + {(-95.039728409455932479 + 157.29585945981762052i), (5.1100491090906121911e-45 + 8.0354420071112795563e-46i)}, + {(98.017510755492196495 + 60.309605529526386647i), (8.4444727812932563993e-37 - 1.3557544067239807853e-37i)}, + {(0.32894030388492784267 + 118.91812868221221322i), (-1.9999820187284879492e-37 + 1.1523130434975194605e-38i)}, + {(-60.428883253360453409 - 45.500874468419127084i), (-1.0129111764275114669e-29 + 5.7138273707475304216e-30i)}, + {(55.461087136894548166 + 27.133063896017066696i), (-5.576298252564807189e-26 - 3.1989182377473527849e-26i)}, + {(-23.408722078965986668 - 20.658244030864608476i), (2.0559940379762616854e-14 - 3.3611910896647691164e-15i)}, + {(-150.28930654632029018 - 220.80523659061239528i), (-6.6140160602916553974e-52 + 1.5411031509828572666e-51i)}, + {(144.62812019523184404 + 8.3196959857309806807i), (5.7003216250389556702e-41 + 6.3028866210034272428e-41i)}, + {(74.806480597363588458 - 30.525362836014725332i), (1.2805521898574706389e-30 - 1.5958174284342937866e-31i)}, + {(-63.819230880040421994 - 11.375668331675829137i), (-43.806224458020366797 - 20.355658889874778339i)}, + {(-59.821959544904203199 + 91.67305775518025257i), (1.3595234709879968967e-36 - 4.7772542292277905392e-36i)}, + {(-36.689673919036799532 + 110.3724009690613741i), (-4.1691825147781699593e-37 + 1.9458127830430940574e-37i)}, + {(-61.139709844328230304 + 108.53326014366268737i), (6.9567136923560998572e-39 + 2.7975813481318612388e-38i)}, + {(54.152381490278770571 + 133.4416257656754965i), (9.0998200346894300954e-41 - 4.0007765280842974702e-41i)}, + {(194.15916635514568611 + 64.689739048390251241i), (-7.6711313265148247583e-47 + 2.6110247514933635481e-47i)}, + {(17.942978543623826937 - 64.961864523447459874i), (7.6028838366654546399e-28 - 1.4083457227051764447e-27i)}, + {(313.95123504464919506 - 40.682831745226032183i), (-9.0367485404296780639e-55 + 1.8699111423020042651e-54i)}, + {(3.1126786709422740174 - 94.007678526104939465i), (-1.0620032459652455571e-33 + 2.1491111440770492622e-33i)}, + {(53.901985419565178859 + 31.288805484771437193i), (3.0203469687039022508e-26 + 3.1525906554172158764e-26i)}, + {(209.25164349135357611 - 14.559777816650107951i), (2.8403572850106405863e-47 - 1.0576034834844569628e-47i)}, + {(-154.31852969017296573 - 16.114955483840699202i), (5.1295250396570538051e-12 + 2.3561393329166852398e-12i)}, + {(-19.447255320059934292 - 89.836977609669659728i), (4.4333889014194766003e-33 - 3.5968591970692413226e-33i)}, + {(-10.723836029728101238 + 48.180643707849327484i), (3.4044820617135083667e-22 + 8.9623595547746989705e-23i)}, + {(-130.15809439759783572 - 175.58523383303074183i), (-4.5239207067998398346e-48 - 2.2298467506586694008e-48i)}, + {(13.758979245326120378 - 61.677796306239976332i), (1.2159963948226544538e-26 + 1.6921820547619475403e-26i)}, + {(19.59435881658251688 + 25.387428651085393483i), (-1.2936089524061799072e-14 - 1.1511037867739642703e-14i)}, + {(-38.266725221039003202 - 22.344834398152034538i), (8.4013026821161106916e-21 + 1.6721634530193920296e-20i)}, + {(40.071820157647763949 - 84.471557016109656502i), (-8.2357739602336250157e-34 - 3.2073455240783709135e-33i)}, + {(109.38252307822011744 + 134.00812867708651765i), (3.6970467331749669173e-44 - 5.5033642284891729043e-44i)}, + {(-56.381474897817398073 - 39.534794085872704272i), (-3.1957201281899031429e-28 - 3.6416787755600874951e-28i)}, + {(-84.637804104431410224 + 80.342816454833894113i), (-1.4808717350473027699e-37 + 3.4344204288299301515e-37i)}, + {(-124.62681524525780219 - 75.821622156269015136i), (4.8912595098577285743e-41 + 1.0038105221027388336e-41i)}, + {(-65.287951081879810999 - 35.691002603650176184i), (-1.1385707094110840275e-29 + 1.8680211470309836124e-29i)}, + {(-170.54070882246989527 + 11.845603817143702585i), (-0.63793085271962302052 - 2.4394213134895430528i)}, + {(69.905264472794399921 + 83.597061514240792235i), (6.2862673122876659528e-36 - 3.8744650637315062706e-36i)}, + {(62.990825158440486575 + 34.395802594858089662i), (-4.4985476025672916412e-29 + 1.4277886302690647114e-28i)}, + {(81.319683287252345849 + 93.399249289537706886i), (4.2296721700162251653e-38 + 1.1379226165292880948e-38i)}, + {(-137.28346120434758859 + 268.37205867377832647i), (-1.3331301749752535979e-53 + 1.6562382659226920252e-54i)}, + {(78.863987123708142235 + 152.43134147867357342i), (-8.8219073574789260405e-44 - 1.3034649058350175353e-44i)}, + {(146.22974183452566876 - 245.83695864780673901i), (9.7457773707639470716e-53 + 6.4741113924774141761e-53i)}, + {(79.437592310453965183 - 10.813538718721629195i), (-1.1925441120372797566e-30 + 1.3315685712531726832e-30i)}, + {(-30.987327218042477028 + 14.366466666490570248i), (-2.6511396145166811486e-8 + 3.3224738455632098319e-7i)}, + {(-76.045943847831225071 - 203.2414753866117394i), (1.8449044743435675795e-48 - 6.6250475180996941521e-48i)}, + {(39.816844210199057841 - 33.877671616938222598i), (4.9731844746458619939e-23 + 7.4938571379243017312e-24i)}, + {(-2.6840717915519127779 + 54.647549183073770962i), (4.2201745165082789369e-24 + 4.4412739069636436356e-24i)}, + {(78.980326074945722326 + 142.51654161090678485i), (-2.0049234543348706244e-43 - 6.8761554735820062265e-43i)}, + {(-67.905033533775920773 - 167.39757901442908405i), (1.0259685678575281263e-44 - 1.965344823591405558e-45i)}, + {(-74.349384614764986168 + 203.64303713034547627i), (-3.3783561710197430102e-49 + 7.1475746320801929213e-48i)}, + {(-159.70727425556810886 + 68.449875497623963838i), (4.1823219985868000728e-44 + 1.977578404747457472e-44i)}, + {(253.03458128889496948 + 10.030538980143880678i), (2.7203551028316374475e-52 + 1.5941609450753219149e-50i)}, + {(-131.4154327137368341 - 119.89593555543753212i), (6.157273715370153987e-45 - 1.7451764355852578683e-44i)}, + {(-138.85791389729567413 - 186.92944075477925026i), (-3.5358189699511273264e-49 - 1.901143322824011953e-49i)}, + {(-143.77328868928290717 - 181.2880893265076736i), (9.5221499698947372136e-50 - 5.0808698305315587534e-49i)}, + {(11.584108782464049625 + 126.73827151395144597i), (1.2646465223374093908e-38 + 4.5952761460805840805e-39i)}, + {(-87.641667212479788418 + 188.18683003477835314i), (-9.6833452654176314095e-48 - 3.8968192566317146392e-47i)}, + {(17.534603397925064172 + 98.071183019851886797i), (-2.0402635966426992767e-34 - 1.3909318346451632537e-34i)}, + {(-37.156681137847314744 + 97.043619111739687355i), (2.5672457535980350229e-35 + 3.2192069065844314867e-35i)}, + {(-2.9460282847995391542 - 0.47611503697262336221i), (1.0238358636864944381e+61 + 8.6662689639720823952e+59i)}, + {(-2.5006312147732341344 + 27.418276105302325618i), (1.7233509349138737942e-12 - 5.0026710386356098494e-12i)}, + {(-26.471014108480389382 + 99.285382777086852002i), (2.4542792268519544245e-35 - 6.1042385697997942655e-35i)}, + {(43.259422344431960994 - 49.155064928409260006i), (5.2709655333857608837e-27 - 2.0975502936542628119e-27i)}, + {(140.85146386983592492 + 132.02695867522064077i), (-2.7958606526406097734e-46 - 7.7348793291087294535e-46i)}, + {(100.35716562632156013 - 19.502856893788933945i), (-1.4296355190333216702e-35 - 1.0052037040837151563e-34i)}, + {(-62.170627447852936598 + 42.273263037788382235i), (-2.4041928804981965107e-30 + 1.4520553873738089404e-29i)}, + {(-15.545416924351565413 - 42.918421601738373283i), (1.4655956196743042452e-21 - 7.4104144967177207524e-21i)}, + {(-55.469371916566643677 - 5.6835862798136069785i), (31448399156463752.0 + 161451304744251552.0i)}, + {(-66.495797327364030593 - 98.336690037648537555i), (-6.9574248349035321516e-38 + 1.8213958983322130288e-37i)}, + {(-6.7443523176470678848 + 94.779898671397731391i), (1.5554949395738899095e-33 + 1.3885989265420722724e-34i)}, + {(-1.3369372738127911493 - 74.264193100194191288i), (-1.6516881007556821923e-29 - 2.5156588239678309431e-29i)}, + {(-6.1054780739612555251 + 99.558709185584845613i), (1.980168539809210509e-34 + 1.0578872583218879293e-34i)}, + {(-131.63278058777967772 - 3.9733233664024889542i), (1.1457132853864692082e+23 + 1.6911442492172739281e+22i)}, + {(71.018485643667517593 - 125.26153668789498852i), (9.3557187340145978268e-42 + 1.0103640663385940504e-40i)}, + {(-77.100042722706518816 - 38.93994049589833395i), (-5.5966827059540486579e-32 - 1.4484054791191802136e-32i)}, + {(161.68298784486518116 + 18.109024405578288963i), (1.8997722775092025977e-43 - 7.8411188632702796506e-43i)}, + {(40.263761553472889432 - 62.611508341521158627i), (2.5261417335057952101e-29 - 1.9320897457887679337e-29i)}, + {(-248.14736281881442892 - 98.447565808110681473i), (1.3453442450597462682e-51 + 9.7852971974441415478e-52i)}, + {(-3.7373904724171986835 + 214.64598712383863699i), (-7.6839117950535807018e-48 + 7.7488807521856414297e-48i)}, + {(-44.514893690102013579 + 151.15535619416530722i), (-1.3701346635376181746e-42 - 2.0748423536245343925e-42i)}, + {(31.571630709946500559 - 36.083415200624266106i), (1.5581140509463036472e-21 - 3.0254208337500203758e-22i)}, + {(41.025313762187458622 + 94.576926348879922557i), (5.7768747973470653964e-35 + 3.0787761752710919203e-35i)}, + {(-84.546575823163507835 - 10.897929895082141272i), (-280.3771512872235121 + 930.57324637060980876i)}, + {(-109.27044902179510188 - 10.620328028918970986i), (5514.8166543630495653 + 712.49622529605517229i)}, +}; + +const std::vector gamma_45_c = { + {(110.00829016856795306 + 108.84004115557112868i), (-6.8997792319223890847e-45 + 5.1808549525606794012e-45i)}, + {(-135.91268273942191058 - 82.976410935945352776i), (-1.6275538678060190822e-45 - 9.8461474442729003934e-46i)}, + {(-65.920356963035828812 - 156.8419642776384535i), (7.6245914698568978505e-47 + 7.100396596477724924e-47i)}, + {(-28.089855858079822326 - 15.730636065641856902i), (-5.2241867117537482197e-7 - 3.3087368029932180888e-7i)}, + {(-48.640474581116414754 + 130.77081247761447003i), (3.5361768254955610408e-43 + 6.9576211720722408732e-43i)}, + {(114.26807799821179401 - 48.326959583439723644i), (1.3608301077840417787e-40 - 1.3398535744204064898e-40i)}, + {(-24.490593169708102295 + 19.865531777716093131i), (-1.5711692352909991016e-14 + 5.1360221925982234607e-14i)}, + {(-138.08109438803518287 + 35.78775797788431845i), (-6.1863960895899192977e-38 + 4.4882923948159859717e-38i)}, + {(50.037968385336959898 - 36.241839813581421481i), (-9.0550698986911887662e-27 - 1.1541841958986909347e-27i)}, + {(-108.12645672815396836 + 59.052402517225367262i), (1.7308380809937618334e-40 + 7.5502827911112676085e-41i)}, + {(131.16154366439204182 - 84.593100221927088i), (4.4982474154201869543e-45 + 3.939179859525201908e-45i)}, + {(-230.54223987322416178 - 82.22689725544934447i), (1.318595759294911929e-54 + 7.0310802462954709363e-54i)}, + {(69.706307597028299483 + 85.997745072910063868i), (-2.4737786854343493869e-38 - 1.9003496540848402127e-38i)}, + {(-70.068947203295380177 + 177.30306071503466114i), (6.087469358821658256e-49 + 1.4348023964555332517e-49i)}, + {(51.579836684350823361 - 22.44952159659138502i), 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1.9305226249506264939e-29i)}, + {(60.628040646590399376 + 199.6755931976147167i), (6.4907037776934338813e-51 - 9.5516103908062115816e-51i)}, + {(117.20799431607706254 - 25.262121989062407579i), (-8.8980844622035753549e-40 - 1.4839655542679643037e-40i)}, + {(-17.329894880509947086 - 16.212801888201074263i), (1.5625622403539908678e-8 - 9.4165582572074081659e-9i)}, + {(-157.43534729194152533 + 0.25234140583314290662i), (3.558473929729224312e+69 - 5.1759257848814184926e+69i)}, + {(112.84787607799825082 - 150.6340950256593203i), (-6.6890419777281126062e-49 - 1.0544417933591430187e-48i)}, + {(-63.528110653894145798 + 56.454350440694987867i), (-1.5203626291816162155e-33 - 2.9160051178249856432e-33i)}, + {(97.761802252158176429 - 42.576632329046411485i), (1.7124695052352919573e-37 - 5.056980031810117851e-38i)}, + {(-140.45107443876793241 - 52.598031379459172285i), (2.7828230801146187088e-44 - 8.6409396321288281502e-45i)}, + {(-75.219326514730667554 + 26.528160649021316431i), (8.8764022985007279717e-33 - 6.9246263509076171723e-33i)}, + {(114.28727454728939961 - 103.2622327918497831i), (-1.833536148918363319e-45 + 1.0545211662838903281e-44i)}, + {(-121.48479229609334595 - 16.740433258031885089i), (1.0809004830423774564e-9 - 1.0359858007541873903e-10i)}, + {(28.05133263271152444 - 146.71174011975523399i), (3.4648178321812219631e-44 - 1.8963869165392929299e-44i)}, + {(129.29528436854255347 - 139.85653840710801887i), (6.4479642834065932414e-49 - 3.5798930594330385188e-49i)}, + {(-81.379092028264608416 - 131.32281314567617869i), (3.2102673567399641593e-46 + 7.7731474204046490343e-45i)}, + {(53.504673092976361204 + 63.033206547931442287i), (9.9390332519330868822e-34 - 1.6527796967950871855e-32i)}, + {(60.756920491224740033 - 126.89975187954409819i), (5.4187355027624280199e-43 + 2.7369116012398796069e-43i)}, + {(-37.058300359516103128 - 38.92198816796509675i), (3.4281537768736434972e-26 - 2.7243487902174782727e-24i)}, + {(35.8390284941181676 - 102.68295940833650093i), (4.6383825966735575548e-38 - 4.6165278294342551811e-38i)}, + {(-122.61420039329624387 + 9.6895902648149743186i), (14217320835.259284973 - 12407865996.408294678i)}, + {(63.603208792145530026 + 117.28021489864362081i), (-1.502187673788334884e-42 + 6.530514212875854206e-42i)}, + {(-64.511649801285841477 + 137.34866715754691313i), (-1.5333482778398847261e-44 - 8.8514174257484322538e-45i)}, + {(-102.07293965080607734 + 76.228944286849468881i), (3.7867138692883682231e-41 + 1.975067540848274777e-41i)}, + {(-13.241458266055646575 - 167.52559335564697562i), (9.7528663251968027263e-47 - 1.6202874852225002679e-46i)}, + {(-36.366001794466221497 - 19.295187585942574771i), (7.7595914455707695804e-17 - 8.6416802629921869229e-17i)}, + {(-116.26896439323120092 + 101.26840395213727675i), (-6.1203925484972921877e-45 - 5.4737464922827403592e-45i)}, + {(176.20747957595369826 + 224.14125597521686473i), (-9.3119612073635634819e-57 - 6.9395787691137953139e-58i)}, + {(15.152961321528794159 - 64.901054157683560675i), (-1.3527935462878493195e-28 - 2.0831066306548455016e-28i)}, + {(72.179463484541130924 + 60.700745796471743176i), (4.3634901928229773934e-35 - 8.5676635968997899448e-36i)}, + {(68.879174921510539775 + 127.32251694077743309i), (-3.2055103911714027355e-44 + 1.661759788601246592e-43i)}, + {(173.32189568962053272 + 104.82766704197297258i), (3.8702863631753931487e-50 + 2.6429699059883169299e-50i)}, + {(77.989876915497731602 + 4.4830336426559371787i), (-2.006301937291635202e-31 - 1.2101167231488535958e-31i)}, + {(-29.440759243504967202 - 18.974064268192844196i), (3.4534106991831647206e-16 - 2.107250554648586501e-16i)}, + {(-51.404844893237900294 - 49.278452834018942497i), (8.4201319324017338558e-30 + 3.5520467133425538058e-30i)}, + {(-73.169025940732026925 - 57.405384809997869411i), (3.8430930991297152616e-36 - 5.7297980396937268675e-35i)}, + {(38.338443797602245411 - 44.842428544816783642i), (1.0411194502902883814e-26 + 6.9440297890417314968e-26i)}, + {(71.036421525343996564 + 5.9830041079980151864i), (-1.1616740805490906369e-29 + 9.0790054676556102498e-30i)}, + {(-139.89777010213242647 + 176.9964337415419493i), (2.9670948082470424958e-52 - 1.0272830625033561863e-52i)}, + {(-171.24245608304860866 - 13.537856072187997469i), (-0.028211531396468425559 - 0.594736337788428715i)}, + {(67.563071422626890694 + 79.413746134144460598i), (6.9588333713970537993e-38 - 4.6200851559637103145e-37i)}, + {(-138.54925683447808638 - 57.50293439768374526i), (-9.7171726435425401999e-45 - 2.5599959431913114538e-44i)}, + {(96.126907726167260648 - 41.439961491634107915i), (3.6993204062593497641e-37 - 1.8044986837771449663e-37i)}, + {(105.1847028745204824 + 62.601709904884849323i), (2.2018360022324206815e-40 + 2.69140731781252428e-40i)}, + {(-59.166410718672210578 - 58.999949526764105201i), (6.1797451642554200515e-33 - 3.5417454353181029656e-33i)}, + {(-88.860525328720967764 + 179.38378930560307367i), (-6.4107152981815011082e-50 + 2.5527551880654236564e-50i)}, + {(126.91136087109786956 + 166.15513079737874591i), (-9.1781073369449061231e-51 + 5.9628235277392809498e-51i)}, + {(55.398779962669578936 + 56.128449617018482343i), (-4.2108711594797339561e-32 + 1.3563752774886402009e-31i)}, + {(296.76949933319167485 - 7.9906402327141456965i), (5.4336148093889236467e-58 + 1.4547822677600780618e-57i)}, + {(14.333122797590178266 + 19.180841230172216427i), (3.4246636634890151592e-10 + 4.1886138525085206445e-8i)}, + {(-5.7652685344120886413 + 69.385839487204449938i), (2.4795494084239984846e-29 + 1.9118764103863081649e-29i)}, + {(-60.801038511347293536 - 86.407590690604735073i), (-9.5160462684863440193e-38 - 1.7396176288163051994e-37i)}, + {(92.957203675623517825 + 72.67762217997713492i), (2.2841274444372143946e-40 + 1.7851225374485555005e-39i)}, + {(-99.454421556768309642 + 84.089538187696817317i), (-1.5958224130662910421e-41 - 8.3867570340812251283e-43i)}, + {(135.48914663322250362 - 47.233394103225485594i), (-2.2804379970263041297e-43 + 1.442537394582540136e-43i)}, + {(-196.98362107817726496 + 6.3932346874960552796i), (-18555281095434072064.0 - 1916570295096061696.0i)}, + {(-124.28336626538700216 - 6.7732156258555287209i), (356588240817577024.0 - 1675817242725332224.0i)}, +}; + +const std::map> polygamma_mc = { + {2, gamma_2_c}, {3, gamma_3_c}, {4, gamma_4_c}, {5, gamma_5_c}, {6, gamma_6_c}, {7, gamma_7_c}, + {8, gamma_8_c}, {9, gamma_9_c}, {10, gamma_10_c}, {15, gamma_15_c}, {20, gamma_20_c}, {25, gamma_25_c}, + {30, gamma_30_c}, {35, gamma_35_c}, {40, gamma_40_c}, {45, gamma_45_c}, +}; + +TEST_CASE("polygamma id->d", "[polygamma][id->d][xsf_tests]") { + SET_FP_FORMAT() + for (auto const &[nord, resvec] : polygamma_mr) { + for (auto const &argres : resvec) { + double const res = xsf::polygamma(nord, argres.first); + REQUIRE_dCLOSE(res, argres.second, 1e-10, 1e-8) + } + } +} + +TEST_CASE("polygamma iD->D", "[polygamma][iD->D][xsf_tests]") { + SET_FP_FORMAT() + for (auto const &[nord, resvec] : polygamma_mc) { + for (auto const &argres : resvec) { + std::complex const res = xsf::polygamma(nord, argres.first); + REQUIRE_zCLOSE(res, argres.second, 1e-10, 1e-8) + } + } +} diff --git a/tests/xsf_tests/test_trigamma.cpp b/tests/xsf_tests/test_trigamma.cpp new file mode 100644 index 0000000000..0de0ebf2a2 --- /dev/null +++ b/tests/xsf_tests/test_trigamma.cpp @@ -0,0 +1,1551 @@ +#include +#include +#include + +#include "../testing_utils.h" + +#include + +#include + +#define REQUIRE_dCLOSE(a, b, rtol, atol) \ + CAPTURE(a, b, rtol, atol); \ + REQUIRE_THAT(a, Catch::Matchers::WithinRel(b, rtol) || Catch::Matchers::WithinAbs(b, atol)); + +#define REQUIRE_zCLOSE(a, b, rtol, atol) \ + CAPTURE(a, b, rtol, atol); \ + REQUIRE_THAT( \ + std::real(a), Catch::Matchers::WithinRel(std::real(b), rtol) || Catch::Matchers::WithinAbs(std::real(b), atol) \ + ); \ + REQUIRE_THAT( \ + std::imag(a), Catch::Matchers::WithinRel(std::imag(b), rtol) || Catch::Matchers::WithinAbs(std::imag(b), atol) \ + ); + +using namespace std::literals::complex_literals; + +// Raw input-output pairs calculated via mpmath + +typedef std::pair ArgResPair; +typedef std::pair, std::complex> CArgResPair; + +const std::vector trigamma_r = { + {139.73422519724257995, 0.0071821112952925860937}, {-22.443413683574426898, 10.144621789153926983}, + {-111.50045809961454779, 9.8606963673307408413}, {-94.907160944282225046, 119.35764892501813961}, + {-2.3440293144269976899, 12.329351561072801502}, {-43.990537622177974697, 11171.885796008868056}, + {202.44760971937091654, 0.0049517692141240656628}, {-87.864395766629698414, 57.783285607259124106}, + {-27.469581100258860573, 9.9245402468284975583}, {-139.62965805126191299, 11.699803724245127157}, + {136.50258767282213057, 0.0073527681486744555367}, {18.355599587916536564, 0.055990217679220265212}, + {98.295895305537783315, 0.010225288944881488068}, {-17.639302205172132432, 11.97514836491987289}, + {105.53438781769612831, 0.0095206195550429275481}, {86.085413223149288342, 0.011684101134840901154}, + {80.295083576858829133, 0.012531936406346049287}, {-23.687837255430721939, 14.254928241075431217}, + {45.529073236262398439, 0.022206961771225702112}, {-177.09443486865797013, 115.47643317472622471}, + {43.038621009685947172, 0.023506966911567186984}, {42.087127834361439227, 0.024044743603015280436}, + {-26.966189375706822062, 878.03037642549315933}, {43.025134568376714128, 0.023514421235447786895}, + {53.13411261348250747, 0.018998513961949566736}, {-25.951884828879652645, 435.2195958148175805}, + {-11.679356016160397758, 13.727019396125779593}, {-32.924670017920838916, 179.5208153446783399}, + {5.0559095779948268756, 0.21862822811895946118}, {23.739510027882797516, 0.043023531866322600736}, + {67.301950926139227249, 0.014969343162393775049}, {-104.16636239940342534, 39.599949146663171007}, + {-36.741429926773975012, 18.704226931251124455}, {-65.607177149266377114, 11.06375342740279244}, + {82.055318124613705777, 0.012261462461534748669}, {-28.811025566150060939, 31.503619108181478481}, + {95.582639261940073538, 0.010517070103987011601}, {51.054913445176751452, 0.019779826148095546595}, + {-160.60523914140824786, 11.026009919621287736}, {-156.10534816231628952, 93.461241548483343422}, + {-145.60301011618520306, 10.973070247703926583}, {-70.933538833692210801, 229.69832096387494857}, + {-135.53602748538907008, 9.9897761558446358521}, {-57.308397422565860779, 14.510244145806730387}, + {-78.321201322546528445, 13.765934044403891789}, {-25.058129511602047046, 299.21483889441191195}, + {34.96259041130598888, 0.029014936002890994587}, {23.081710129510792484, 0.044276393873570296655}, + {89.47581754821393929, 0.011238890540643923371}, {125.85454287069499912, 0.007977331128257417539}, + {76.338839639013471583, 0.01318566471668204676}, {60.290769521491363037, 0.016724599797672934365}, + {77.084437676499078407, 0.013057297579390803391}, {136.31224035524024885, 0.0073630733100727577614}, + {19.128796639549253911, 0.053667455256011589726}, {-10.236898311995872746, 21.414663938375586127}, + {55.712488931236691769, 0.018111349187826419893}, {-102.38495985110580477, 11.270187900537163017}, + {-41.442915055125176593, 10.170121913186694229}, {-44.203165498731195271, 27.780945649590222502}, + {-203.86447646183518145, 57.85433919246265333}, {22.863494626803131382, 0.044708285015191834288}, + {55.926140837564673802, 0.018041538915514077068}, {-2.6252781039759160997, 11.254010872456776227}, + {157.17923057969116485, 0.0063824452142865039511}, {77.711296237288735256, 0.01295129173016515943}, + {-62.263298917277069222, 18.202705761233637816}, {-121.6662676075720384, 13.13227832293284969}, + {-148.00697595373102899, 20552.383997872908367}, {-15.278531927964255743, 16.688741231742973525}, + {142.8449739333189541, 0.0070251576832558153968}, {-12.423046035403123355, 10.392354365386564652}, + {27.251219043176767798, 0.037377123165580707076}, {-93.66204759009258396, 12.93380141299572017}, + {-23.6953271889661643, 14.724657923610667609}, {-43.424031335891214667, 10.431067368781699045}, + {-71.566695806867954843, 10.302041750611355297}, {85.376569199845008029, 0.01178167829346643547}, + {104.88296593343085306, 0.0095800338982411411409}, {-176.27336032136267363, 17.215015160445659603}, + {-49.530279104858038863, 9.9394656984707907554}, {71.217491708121926308, 0.014140537419485571177}, + {64.967431590186379253, 0.015511397397582128363}, {-184.6245073749569201, 11.542776109728077216}, + {-80.508624393635699334, 9.8645090448403394134}, {-110.98090338143920519, 2745.4070346569587855}, + {161.11032481242716585, 0.0062262296692082060023}, {-36.161842866743207026, 41.61790489546311278}, + {12.255901703672007486, 0.085012494841868346818}, {24.700781333224774983, 0.041315104081382551804}, + {100.91052215557674288, 0.0099590333113247705987}, {-58.250207355812456456, 19.696504139406997069}, + 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{-49.644104108513808171, 12.18475598969442153}, + {-48.157115343095661331, 43.946091196073268748}, {-96.60303443529029721, 10.970179272603234111}, + {29.342339865128185039, 0.034667779110375669671}, {-51.843039755659226842, 44.027295002960109116}, + {28.873963408533136032, 0.035239931813820825346}, {-84.432965714684357295, 10.308822360642265537}, + {73.815489876642047307, 0.013639470994198583595}, {4.7975663906713457152, 0.23165902791813303141}, + {-124.51283810772793004, 9.8776773670250825887}, {-108.18521942236600353, 32.665237566654063528}, + {11.707960139860665194, 0.089163276763376833611}, {78.945021198693481779, 0.012747609004730897989}, + {81.462186688354549347, 0.012351288032091626429}, {-118.02482459227221057, 1625.976153494847722}, + {198.01654458317591434, 0.0050628562082108584039}, {-55.808327105659408574, 30.744552638138610945}, + {29.209426078237715529, 0.034828245463427817685}, {-6.4816147205107155216, 9.7596136521857790314}, + {-10.800106454976591053, 28.504735046501071594}, {-145.80424393956263884, 29.643391716443002082}, + {112.1339837631880556, 0.0089577857885327124426}, {-9.9418401440382737633, 298.84955855831475446}, + {-146.30961353677267311, 14.444981089106809335}, {178.57138089287613525, 0.00561571077274612869}, + {3.7309829856033758233, 0.30710993814684112158}, {63.201629541750435237, 0.015948210801602510922}, + {-116.91746512544878556, 150.12571110436422828}, {-18.715054479268065535, 16.156755693724576872}, + {-55.68761953239940965, 14.265386375902359362}, {-69.106095051706944332, 92.190151915827982521}, + {51.602583157185264895, 0.019567858061910775591}, {-59.32986491112693983, 13.311496656437958208}, + {-27.282473240546750048, 16.377478300982851067}, {81.873552935211932891, 0.012288850365068137646}, + {-42.437161635389259118, 10.2411695195709882}, {1.7117713477935063704, 0.78618300321647305307}, + {-139.76879419643793767, 22.368186341203820433}, {132.19757386016505052, 0.0075931178238158678756}, + {50.302573455495583232, 0.020078609140491854995}, {-71.990890227331178153, 12053.217630028520944}, + {205.33519739935192661, 0.0048819637766071861257}, {5.0288844266174281827, 0.21992257489275582327}, + {-56.211946585987071501, 25.846960398263512104}, {9.1872354266580753546, 0.11498489443761342188}, + {44.211872180446363245, 0.022876082508164887613}, {-24.006467696450080496, 23908.909551151911728}, + {110.35505522452726268, 0.0091028409472670972907}, {58.507287804307409829, 0.017238786272448982512}, + {49.276568020088880928, 0.020500929427363139002}, {18.225782037799458379, 0.056400054538805803606}, + {73.31132832841956315, 0.013733910713376280138}, {-56.385370873961640825, 11.25134371388735488}, + {99.462238062843979947, 0.010104778457468509278}, {-238.82691245725771978, 36.868387769347002347}, + {-27.889582617524467878, 85.356368248850813529}, {-103.67391265400102895, 13.509784410842067714}, + {-96.725551465367715309, 17.109416805387169802}, {-16.816133901626933778, 33.04376681346671063}, + {-132.27015833497699759, 17.517865747658575515}, {-255.13729882468805954, 56.459760913181632702}, + {-23.100974613831255056, 101.39369005703368032}, {-21.666511554345021295, 13.106968687832646125}, + {-74.4264787577635758, 10.402099563213141664}, {68.778377468879227763, 0.0146456632853860097}, + {27.978514425923208364, 0.03638805469541210591}, {70.733199046579755986, 0.014238040139426050984}, + {-37.793186196306301383, 26.941097830015241499}, {94.84686376492919635, 0.010599087225236189166}, + {33.535475910625081042, 0.030268178022791417808}, {117.4572413420334982, 0.0085500811802370207948}, + {-89.307999856391987237, 14.541392679148257727}, {6.9276841663797643633, 0.15526583561728277139}, + {-34.446186855896030465, 10.128536633873720163}, {-63.83645890636435638, 40.844768639051039827}, + {-90.222544859861471878, 23.818569845473721358}, {14.553919189429715075, 0.07112456086352719753}, + {56.182489732821629502, 0.01795848444977542549}, {-97.764709509632368167, 21.736010825991581186}, + {-295.37752096144498637, 11.484807067029553451}, {-38.576668376707750951, 10.439485134726819382}, + {-239.13256630345540543, 60.305847633571339372}, {-76.953871683796961634, 473.25504260780024879}, + {-159.24744831494146524, 20.054564544293267403}, {-39.262265469539023854, 18.302978967054563952}, + {-0.45695283285538768059, 9.0805000646120586083}, {-32.738556144708155671, 18.386073463567914388}, + {-23.437019044170540383, 10.224529802789495747}, {-54.607513873838506413, 11.068955922894431865}, + {21.787681199171839097, 0.046966893235762197101}, {38.869794268381220093, 0.026060692517860896411}, + {-29.42970685586787738, 10.333598213980559777}, {-160.01638137248383487, 3729.7708236065109304}, + {10.572808985734489795, 0.099195912791354923232}, {80.566793830301548951, 0.012489409825892361372}, + {84.829021388861292507, 0.011858174870367920936}, {77.759306117570190509, 0.012943243863423227122}, + {-131.54702549330943384, 10.080615067780138716}, {38.567813591608548052, 0.026267400591184524722}, + {30.56325054615642145, 0.033260137015169631558}, {38.536522391164332646, 0.026289007295436792738}, + {-21.824417474316021526, 35.892138946604454475}, {67.995712337111740453, 0.014815484933205644996}, + {89.002935906994395054, 0.011298939986157947868}, {43.674705363050925655, 0.023160674626069650134}, + {-36.680564001092669457, 13.848842346583422724}, {-41.637512353464266823, 11.943857597690378469}, + {-67.729044871111995008, 17.43383024978592033}, {-66.975036750924189732, 1607.9936103579475457}, + {49.065157144662329358, 0.020590166530020839741}, {45.557860581875786465, 0.022192774967993246504}, + {-17.508489680778989595, 9.8211133491576028121}, {-48.293677717754910361, 15.509921197845240926}, + {71.622679453240493785, 0.014059981073482935923}, {-100.66877875155415722, 13.251581048468333179}, + {-116.56133770649242365, 10.236812507772464542}, {-63.468304706913023949, 9.9524788109018746951}, + {-185.04272320278701613, 551.15990011076507926}, {92.56239852577033389, 0.010862091191848666227}, + {14.588657678392683792, 0.070949335581907427284}, {224.30954122507893089, 0.0044680773254322670579}, + {17.375763216984843496, 0.059239261295330900015}, {93.528679392410410287, 0.010749269771806365878}, + {41.504760675458172159, 0.024386203740349304825}, {48.390400604488483793, 0.020880252789732808849}, + {250.17670637799898259, 0.0040051740417668523636}, {54.287449240217114266, 0.018591162312772777782}, + {20.596329017470448974, 0.049750073096352862012}, {48.29522976519443489, 0.020921826946646925049}, + {27.168624845906709453, 0.037492855109078918052}, {-12.871985490169402411, 64.345656823908484512}, + {217.93967865607021395, 0.0045989685214994028423}, {49.280596571251528815, 0.020499236474314265488}, + {-67.310983583209960557, 14.35291674292392905}, {-27.320092656770672335, 13.803451380183053843}, + {164.24827252570361225, 0.0061069156744601648876}, {10.872591916789865252, 0.0963334881777197366}, + {-162.52802852749437079, 9.9403922293068696092}, {124.03317052083286853, 0.0080949475769797486074}, + {18.33879989047848369, 0.056042918940640923386}, {0.3243859369808750337, 10.609058710604797326}, + {-20.324943350572336698, 13.530837641438893115}, {-96.896102726464889088, 95.98944319515911161}, + {-58.05312868097285417, 357.56736457978456656}, {181.62090228090005439, 0.0055211598835572112121}, + {202.37967922499854012, 0.00495343542816149493}, {30.891930949487111491, 0.032900502964272645978}, + {101.43110288155772025, 0.0099076676211911941794}, {-37.454440414458474606, 10.048242030387633861}, + {13.935553514603721936, 0.074395092516953434392}, {-30.245758044876879467, 20.247136396559529459}, + {-77.994910361410390465, 38606.72653234932659}, {-74.95317534773212742, 459.38124689439479198}, + {-119.37861900252696046, 11.44795122538568144}, {-38.184694222256020169, 32.813197062891624967}, + {-33.125776650139997059, 66.57752796295501696}, {15.606481765292535613, 0.066172614258095271977}, + {13.08562773739547147, 0.079414001172868731171}, {91.084776072988361761, 0.011039270483634006439}, + {4.7246299729850527171, 0.23562267387489932435}, {-130.54575913526602449, 10.068781611060328984}, + {6.8081549204146263321, 0.15819584304541689512}, {-34.758551784596050993, 20.83114159873546356}, + {1.1830374420677496339, 1.2929237695878423864}, {84.998960890256981315, 0.0118343269410991353}, + {-157.24253313151822908, 20.704160975031236092}, {124.8834345320990451, 0.0080396124897565059836}, + {-91.508856447674219226, 9.8663803783082126841}, {-81.98618659704580125, 5244.0916765194315303}, + {52.422530917944321516, 0.019258866541380949972}, {-148.89132286700302643, 88.030163756931600005}, + {-115.68147735606927995, 13.918116323368654008}, {25.695152008544035027, 0.039684967811124176318}, + {76.462950702440068085, 0.013164122115265540491}, {-88.416831553771018548, 10.564030710070225538}, + {188.61774117581157384, 0.0053158072117208019988}, {-26.841255332876031048, 43.106382218995548783}, + {46.443349503457078242, 0.021765076723560063815}, {-5.5734495025127550605, 10.250059758454735714}, + {133.15595862650454251, 0.0075382611904856568555}, {180.20192221004219846, 0.0055647563875416521106}, + {154.04058037185404828, 0.0065129131514884107401}, {-103.76833977425110334, 22.294029392318179816}, + {38.142547021388622852, 0.0265641217809845058}, {103.79742805173523834, 0.0096807075386084687901}, + {-80.808044916265771462, 30.670832829059985869}, {89.238245739011674118, 0.011268978887603791489}, + {130.8045743323472152, 0.0076742900031163902366}, {-110.97732861895812562, 1948.8416342812206494}, + {-22.991350168323172909, 13368.731700729742442}, {-26.223871641053701609, 23.558071800349896563}, + {83.983914774330031605, 0.011978212168819519362}, {155.33487811912783627, 0.006458470702384074523}, + {-50.780627813760382594, 24.387699082344944657}, {-82.181686509020721587, 33.797613820388349382}, + {116.84257930100407918, 0.0085952524824616342858}, {-59.265817705812381178, 17.940703776339937292}, + {111.71836738177198356, 0.0089912600476393777366}, {12.586821494992090464, 0.082687656134416864795}, + {89.978460973884082819, 0.011175757620599875014}, {-18.223645496526888365, 23.58169116790574904}, + {37.470810679805651944, 0.027046716838947219147}, {-166.99537418653684995, 46736.295575034120702}, + {-123.85397006195115921, 50.318957931666474792}, {34.592219066240176062, 0.029330103782323178191}, + {-159.09148662016917797, 122.81582023198045306}, {-242.47113034909267526, 9.9471222590707224498}, + {-44.348065260099254203, 12.487441921109924792}, {-72.803350380493355942, 29.402545342990269006}, + {-65.097622640406797245, 108.26726202703449076}, {74.159384302430311209, 0.013575794197484197801}, + {146.21743780054450212, 0.0068625697140704431873}, {47.402825447603952114, 0.021319869656939206132}, + {-12.302879441887791145, 14.80628195818552939}, {-15.924327001490762967, 177.89622721294054486}, + {-13.17463186234096284, 36.215566761497143489}, {170.4639962770169177, 0.0058835820362624939237}, + {-224.13637950234635809, 57.175077503409788449}, {65.604946615534444732, 0.015359514035076106409}, + {100.96292257278453519, 0.0099538388687606931676}, {-19.581461212172147413, 10.495525275234307117}, + {-10.257015105643631614, 18.813252517518346707}, {15.514944076454348476, 0.066575735031617441773}, + {58.251070504113108939, 0.017315263730714850615}, {-95.379543411400234731, 11.419326247921382844}, + {69.980734906027592501, 0.014392230316073539517}, {169.16186127479750212, 0.0059290053070401929625}, + {-110.18848446224743043, 31.673127874134323179}, {90.978169068497621197, 0.011052277373870794674}, + {-108.82781610210643919, 37.21246232034243917}, {-43.125348451552326878, 67.016220261133085501}, + {-117.39816176235216005, 10.944514831061248117}, {-117.51611635653709698, 9.8864750746999821018}, + {21.021746795484023806, 0.048719161164966898192}, {8.5645426626574465701, 0.1238415531231433081}, + {-38.320448409855444538, 13.794053539384947271}, {-153.24455482991970712, 20.431824936462753328}, + {65.954151846935360481, 0.01527757250325072029}, {-96.90960718165878518, 125.71946431031824432}, + {7.3050240853413050957, 0.14668777532985835532}, {17.71215068716933061, 0.058082169007675710226}, + {-8.9662573858911169822, 881.4910607119334145}, {1.7390768372338045733, 0.77028762423176766472}, + {-110.87311043197212257, 65.496233678607438833}, {84.764272102870435788, 0.011867286565311092536}, + {139.9048771097060353, 0.0071733194184509822475}, {2.5408471149735536443, 0.48089279601097428829}, + {183.97410221868011604, 0.0054503470102720812801}, {-18.702962134034976316, 15.23467270164017151}, + {148.69852897799799507, 0.0067476797014295649552}, {72.800871700822426646, 0.013830871412079105004}, + {-70.998249299791055478, 326272.74242819607025}, {84.416192394521203823, 0.011916510248765190688}, + {-105.62364727502585993, 11.513144714524765178}, {70.323403651208622023, 0.014321600724077100664}, + {-188.8375520903512097, 41.357422304844924099}, {74.522436216583002988, 0.01350921211710138202}, + {-35.884572440777155578, 78.405980213014245805}, {-34.977360025353661399, 1954.2239469256232951}, + {105.40586116302306152, 0.0095322836779933323853}, {289.59380859303655598, 0.0034590813541297790214}, + {-9.2549386334223751049, 19.042798508277122949}, {-65.03496282633552994, 821.34590844281501631}, + {-25.661999945306167348, 12.904040231999834631}, {-62.636786933562305535, 11.926702202863205926}, + {-44.938176358327254434, 264.92481476263964169}, {-55.49061718134523602, 9.8603253424495669321}, + {-7.9396355929351836167, 277.62944658774307527}, {-38.298344445255267487, 15.168666463082422169}, + {122.03822834049850599, 0.0082278174719926256558}, {47.255337167119080277, 0.021387117415532407722}, + {44.407814799042668596, 0.022774004750868673264}, {151.61152681985956292, 0.0066176047035140864172}, + {119.80703842924373248, 0.00838168610043877986}, {47.736637928583114387, 0.021169217418303711703}, + {-84.509243912933783349, 9.8661693918795929648}, {-19.477999293753899934, 9.8668593753854345607}, + {45.693208859072683481, 0.022126315680705097022}, {-205.20027335817508174, 28.494597891221765451}, + {89.301860293449777828, 0.011260906354966066303}, {-120.82436160711364437, 35.908191970243365176}, + {45.373365543477447659, 0.022284012135525554932}, {97.904577352840590265, 0.010266367804820779666}, +}; + +const std::vector trigamma_c = { + {(68.164869992727929571 + 102.78009410031252457i), (0.004468648456511850435 - 0.0067876145127985744107i)}, + {(65.679862173210082688 + 92.238620354467997231i), (0.0051096459198046589867 - 0.0072307690840583190711i)}, + {(-103.72989230685919892 + 140.05790685846554311i), (-0.003419620766003501032 - 0.0045950571111115770181i)}, + {(-164.90055035605200828 + 13.71135959966833795i), (-0.0060046469920930602496 - 0.00049776966190124118453i)}, + {(61.572057986187964218 - 44.958974138739932869i), (0.010619248034588800109 + 0.0078172682922338244255i)}, + {(-5.4435570484445561235 - 0.39510124336097257602i), (2.5396043275170621101 - 0.82876355136326307349i)}, + {(-42.801672377237792944 + 9.2802935277230851341i), (-0.022078864016599159675 - 0.0047314784766371888181i)}, + {(16.982247412265884634 + 93.681881497557043303i), (0.0018217018766301345915 - 0.010354007635576135266i)}, + {(-120.26964458266635916 + 113.67514978228194877i), (-0.0043904622057975781213 - 0.0041325237532688074982i)}, + {(-92.845011509179158793 + 6.4560062934170092674i), (-0.010661844331801966293 - 0.00073738941937206796667i)}, + {(-22.752370321676909981 + 111.47516486082832898i), (-0.0017931752247653779016 - 0.0085966261402016311277i)}, + {(-93.443458649115669346 - 36.600719263463723507i), (-0.0092418320882560692914 + 0.0036005929602873631978i)}, + {(26.493475215788684807 + 74.842286301353098565i), (0.0041411890441961337131 - 0.011923293199096024128i)}, + {(-180.24261913112275124 - 124.40307505691976075i), (-0.0037542089463421688886 + 0.0025839700829100556607i)}, + {(-3.3231553834872751274 + 29.576934691509670472i), (-0.0042997046592488288169 - 0.033257408812859490244i)}, + {(-94.234980209384062277 - 121.0364063396069696i), (-0.0040100472857847657346 + 0.0051233270699707683313i)}, + {(-55.77348028133501856 - 24.555386596977331948i), (-0.014927834094810412194 + 0.006513592741276275945i)}, + {(-21.828068998122532207 - 11.225900316316540284i), (-0.03574895573680258315 + 0.017968736590188733732i)}, + {(-56.895720229577086968 + 116.68720810476767724i), (-0.0033941904421779986976 - 0.0069004222140595155785i)}, + {(-10.557918771835932858 + 211.07437665059202914i), (-0.00024752237488649551011 - 0.004724707890412212577i)}, + {(13.726145089011531297 - 9.3883378997799038501i), (0.050281190854112978172 + 0.035668596908575378457i)}, + {(-14.917992145209094446 + 15.066068238294342052i), (-0.033183984298737360941 - 0.032414914639604407165i)}, + {(-54.510168708856497233 - 95.257353230816462997i), (-0.0045463267328314776322 + 0.007872455155848463032i)}, + {(74.340455308229394404 + 17.897947236241236624i), (0.012791067384449903918 - 0.0031002956199452768454i)}, + {(36.111635589447722339 - 140.14156922077941658i), (0.0017032851470502518784 + 0.0067028415446064920288i)}, + {(-79.770862386925742271 - 47.15115320658287601i), (-0.0092620506278434273917 + 0.0054404295293718051701i)}, + {(51.664583673700747113 + 122.80214468379217863i), (0.0028909842678367402881 - 0.006938700552588255438i)}, + {(-0.97691212359968437884 - 68.433829463510861046i), (-0.00031523461311633711691 + 0.014606112278623557474i)}, + {(6.7632501168042331585 + 62.395902141987249934i), (0.0015927984325668667447 - 0.015867142569537761448i)}, + {(-126.16253355124815982 + 118.85461580929748493i), (-0.0041983296917849008412 - 0.0039395083298169259259i)}, + {(135.7856096648466746 - 135.29975259570230151i), (0.0036955066515689878777 + 0.0036958761582692968226i)}, + {(-118.14810511223629419 + 9.5304029076448379953i), (-0.008374205137179671285 - 0.00067264968217858010779i)}, + {(11.19134628322604641 + 249.11381331649994308i), (0.00017196470609628602315 - 0.0040068544892648853481i)}, + {(139.48085772205087096 + 189.64290874572259327i), (0.0025141264964664853179 - 0.0034305790888863822025i)}, + {(-44.343234095826552732 + 50.333883680641690717i), (-0.009867989751653699973 - 0.011075829880200312519i)}, + {(46.049253646691937547 + 11.193487193047605643i), (0.020703330923374153871 - 0.0050873482967878393135i)}, + {(24.638224500627362801 + 115.78078281234223823i), (0.0017256864421051247918 - 0.0082772842893627362332i)}, + {(207.53795244655296415 - 36.875505174690367483i), (0.0046815121126582157421 + 0.00083382042524430882366i)}, + {(-128.39664599733734462 - 57.794443940917261671i), (-0.0064595048593508166621 + 0.002896276862315826095i)}, + {(52.073280621914911137 - 27.497430247975827911i), (0.015097911526757443537 + 0.0080493912830408801545i)}, + {(50.322790983486889616 - 124.49188457109865169i), (0.0027709599765555628995 + 0.0069237155353897841467i)}, + {(194.67748824304493382 - 101.44573800829401478i), (0.0040456891261861395448 + 0.0021136152172228873589i)}, + {(-90.416191080030230864 + 130.89843524254831664i), (-0.0035793758226227881218 - 0.0051534453257668037113i)}, + {(78.532570129772253154 - 11.098200967737783529i), (0.012560920839736632384 + 0.0017864320491742006428i)}, + {(123.58611940414827757 - 95.31475398561018153i), (0.0050788466144384347353 + 0.0039329023357028087063i)}, + {(-239.88496659393535992 + 154.0059560120865001i), (-0.0029494091646653673375 - 0.0018895759400324877234i)}, + {(-125.5263113292312056 - 9.3134741678592849468i), (-0.0078917109823160962179 + 0.00058319948066876418826i)}, + {(46.238141497648804545 - 210.71905629456023235i), (0.00098373731038784253435 + 0.0045321354961526142888i)}, + {(107.59652562172638568 - 24.718815954396625045i), (0.0088650544617596294811 + 0.0020461039733931252887i)}, + {(-86.425510919263160758 - 35.26359896919771586i), (-0.0098783456375255325466 + 0.0040073324610735861634i)}, + {(-0.093175744272001578827 + 21.87015236270903884i), (-0.0012399016169597806402 - 0.04569874381590296325i)}, + {(-73.004818461508079963 + 150.97968262044227572i), (-0.0026067723001118674707 - 0.0053543065136485712419i)}, + {(8.194935558793501329 - 30.597652064816383444i), (0.0077320640567534260415 + 0.030740137712026799344i)}, + {(158.43129059986080165 + 180.09121158381120154i), (0.0027526135539533819717 - 0.0031388337806271256018i)}, + {(84.096440619643161085 - 109.83024817092530157i), (0.004388052551004535326 + 0.0057650383300391688443i)}, + {(0.41827578551189520395 - 86.392437936588720504i), (-0.000010949983249140952097 + 0.0115752060564505415i)}, + {(0.52216328238143472351 - 74.029471782636818489i), (4.0443110753699696089e-6 + 0.013508337869469425746i)}, + {(107.54660669256767846 - 225.07086958885733452i), (0.0017233426420701011827 + 0.0036234047794934521984i)}, + {(219.32570089022124193 + 99.512886606378387455i), (0.0037867288630045537259 - 0.0017220428478308524162i)}, + {(-161.59746119917645046 + 25.676077988978484257i), (-0.0060181148728237670101 - 0.00095325756217847672832i)}, + {(-55.328845530951141996 + 19.279864793469375428i), (-0.016003127187854515601 - 0.0055262362534791182461i)}, + {(-12.564802209800809862 - 12.278479460888922503i), (-0.040652544585542738087 + 0.038186014460082483291i)}, + {(-36.941464224953691087 + 150.12146014428512331i), (-0.00156409601492896763 - 0.0062711955211518918482i)}, + {(75.241966615235256199 + 142.08060631700465137i), (0.0029000010601285927843 - 0.0055127161232218814535i)}, + {(180.37761987890280579 - 289.58172156188311419i), (0.0015478220196623742894 + 0.0024918070553400051108i)}, + {(-302.84962486841789087 - 59.239263087193727131i), (-0.0031754264995776460348 + 0.00062010822568383595129i)}, + {(45.752825939755574325 - 14.07955494221022974i), (0.020147234900192254048 + 0.0062679633951462062139i)}, + {(-124.16112335144975987 + 107.1378825962791268i), (-0.0046138552177655773115 - 0.0039652749482216144775i)}, + {(28.939930236723192536 + 9.1905943414372615052i), (0.031835203263578852606 - 0.010285886046105675862i)}, + {(71.01629036502330905 + 248.91229738546516614i), (0.0010535881541707181261 - 0.0037190044107871193108i)}, + {(7.7912247803183145578 + 93.209089199841443474i), (0.00083415528350381325153 - 0.010663417192142383289i)}, + {(-232.28873583362999966 - 44.174310163342518365i), (-0.0041464248262585183188 + 0.00078682893283905691768i)}, + {(-15.660652919735179367 + 35.456110598995500993i), (-0.010645246392983616704 - 0.023352867977130729871i)}, + {(-34.355363843526035339 + 146.67460555718346882i), (-0.0015335799088709532994 - 0.0064533992456040061708i)}, + {(-46.400955076339464256 + 66.237606238811565618i), (-0.007120250134272582479 - 0.010055581825244462243i)}, + {(1.8945110527434732006 - 55.756562117566410564i), (0.00044832533565842657818 + 0.017924375639987950859i)}, + {(-96.953372200400650627 + 143.9203030142973887i), (-0.0032258574086717994693 - 0.0047639584340117566499i)}, + {(-96.376706803196796614 + 56.982303312882088164i), (-0.0076691036498171480384 - 0.0045108616828802980056i)}, + {(6.1759844777703882812 + 82.955007328467516459i), (0.00082099995354333943961 - 0.011998696529519767978i)}, + {(55.28180839352710052 + 77.395013019722057379i), (0.0060930311513863960951 - 0.008607994104948899286i)}, + {(-9.3523630085264066736 - 82.824723245252869219i), (-0.0014162289866380896493 + 0.011905363566540386189i)}, + {(124.12273445243951642 - 78.591445162381106115i), (0.0057608313315298757123 + 0.0036623404696411124976i)}, + {(-16.993294219086021002 + 67.382640921980296866i), (-0.0036096880281638633881 - 0.013903724704918728541i)}, + {(126.27244159499511511 + 15.096078220062688402i), (0.0078379118436080804505 - 0.00094075061181759242826i)}, + {(-141.37178879240804008 - 121.37781923513162496i), (-0.0040697444811749914836 + 0.0034818363289865514147i)}, + {(210.20031070507477011 - 70.273436510705082014i), (0.004287242955862784026 + 0.0014367087395882956365i)}, + {(-85.065463487640514018 + 9.3894315718325813691i), (-0.011547780164045009024 - 0.0012671543932783672741i)}, + {(-24.69283546140898622 - 88.196800387383859743i), (-0.0029944665505465188453 + 0.010483025501091279563i)}, + {(116.56116794530717584 + 98.277561926181590479i), (0.0050180762141103941315 - 0.0042491450919101931769i)}, + {(-49.091919122783849616 + 6.3547893789585678803i), (-0.01983819812888898762 - 0.002541929605443146202i)}, + {(-42.334450455565161064 - 124.78080659947885067i), (-0.0024610675780810204946 + 0.0071692540351059605777i)}, + {(14.490037926033883409 + 150.82799746828686693i), (0.00060973226964018624636 - 0.0065735368039097291995i)}, + {(59.838553238330028705 + 89.760118994129840075i), (0.0051252036466695582301 - 0.0077526707624346428982i)}, + {(-84.827983758631049227 + 123.19999870298086364i), (-0.0037992842969390735845 - 0.005485519829590946618i)}, + {(-203.14584121458813115 - 106.38969783524083823i), (-0.0038576295906937426231 + 0.0020153161407455671798i)}, + {(-209.03093458499716917 + 77.571950827614571722i), (-0.0041972786600737253121 - 0.0015538994633662282785i)}, + {(137.27071840289556803 + 8.3638727004236521623i), (0.0072842342218058329234 - 0.00044544525089312901438i)}, + {(-28.577414815417810701 + 125.25640049471942916i), (-0.0017585980676232640819 - 0.0075754135940301363036i)}, + {(73.471163226417900205 - 57.505730706374613703i), (0.0084539013873297895463 + 0.0066620616756163522978i)}, + {(39.287597778309759633 - 103.97080992006890199i), (0.0031498274169446862508 + 0.0084430512315081703012i)}, + {(28.357124399376825608 - 2.8654731293919537549i), (0.035517996208893808097 + 0.0036527191138433822218i)}, + {(7.2780807185649400992 + 3.4080918194796647747i), (0.1177283130417006024 - 0.059024840622765209486i)}, + {(-22.933323031112937684 - 31.859445151874616897i), (-0.014982829033804786686 + 0.020368163470532978793i)}, + {(30.735029296604469806 + 50.671840634635969991i), (0.0086841593583178132432 - 0.014553360267343187079i)}, + {(118.22636349460644567 - 63.069020206765856074i), (0.0066000447084512909104 + 0.0035357795092551980859i)}, + {(78.277609456815085309 - 76.581225371794729995i), (0.0065282752615861971979 + 0.0064277666655794514841i)}, + {(-97.79102635588077419 + 57.054899084740817727i), (-0.007609792788700111936 - 0.0044171922246733410361i)}, + {(10.442372175938107404 - 84.435915154360827728i), (0.0013755301847302801432 + 0.01168146492086362398i)}, + {(20.528918217783882483 - 45.171988347536881747i), (0.0082036278267430141203 + 0.018500693774340885162i)}, + {(-50.814740347984631796 - 57.491113289827154631i), (-0.0086412768152256905912 + 0.0096810912041099227154i)}, + {(56.328593896353254422 - 67.457652483215824191i), (0.0072814343200322765443 + 0.0087979609480058271198i)}, + {(77.307257534602982219 - 42.477654613744803669i), (0.0099701631312836738047 + 0.0055138016576629107074i)}, + {(40.60335628596695301 - 40.985406106549419292i), (0.01219690027649427376 + 0.012464532128896197924i)}, + {(57.758781192331774434 - 125.34288908245719085i), (0.0030153315940362971498 + 0.006600682872007519221i)}, + {(33.173593848458644118 + 23.153781489626904744i), (0.020374729521158090051 - 0.01443682677643103561i)}, + {(79.501604112790829504 - 62.298576927609985887i), (0.0078046921137859453024 + 0.0061544725825211496137i)}, + {(74.11608835148896901 + 107.33129371115919071i), (0.0043459032510634980351 - 0.0063362077402563388162i)}, + {(79.906432084870317567 + 39.207530299524066209i), (0.010124975068059764022 - 0.0049991772768168667856i)}, + {(-62.943224433586472344 - 166.21576835173590325i), (-0.0020043658743241344992 + 0.0052512378206554946938i)}, + {(-86.978539122552646745 - 43.207581025431444743i), (-0.0091894937892671290508 + 0.0045388143201760509926i)}, + {(-67.931039613272901079 + 368.60308661370891059i), (-0.00048687761142555052371 - 0.0026225581048813476244i)}, + {(-86.578789889445431527 - 137.34139140066298523i), (-0.0032927989679618191975 + 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115.92351011924262139i), (-0.00056696131205591024111 - 0.0085890059290487531102i)}, + {(-90.88025069786588972 - 154.95975487752957633i), (-0.0028236277325008416611 + 0.00478819443581538981i)}, + {(36.702471007401541669 + 51.976141890385896716i), (0.0090235535782229956553 - 0.012954641068780364463i)}, + {(25.587434207967895361 - 18.356046813470850765i), (0.025962609025543221392 + 0.018993121696199096599i)}, + {(-103.29643954259128691 - 113.86510887557952287i), (-0.0043724263494569941615 + 0.0047965354987512167501i)}, + {(80.379241525404182767 + 5.9239427368197397072i), (0.012450262946272409523 - 0.00092330282008335688541i)}, +}; + +TEST_CASE("trigamma d->d", "[trigamma][d->d][xsf_tests]") { + SET_FP_FORMAT() + for (auto const &argres : trigamma_r) { + double const res = xsf::trigamma(argres.first); + REQUIRE_dCLOSE(res, argres.second, 1e-10, 1e-8) + } +} + +TEST_CASE("trigamma D->D", "[trigamma][D->D][xsf_tests]") { + SET_FP_FORMAT() + for (auto const &argres : trigamma_c) { + std::complex const res = xsf::trigamma(argres.first); + REQUIRE_zCLOSE(res, argres.second, 1e-10, 1e-8) + } +}