/*
  This code can be loaded, or copied and pasted, into Magma.
  It will load the data associated to the HMF, including
  the field, level, and Hecke and Atkin-Lehner eigenvalue data.
  At the *bottom* of the file, there is code to recreate the
  Hilbert modular form in Magma, by creating the HMF space
  and cutting out the corresponding Hecke irreducible subspace.
  From there, you can ask for more eigenvalues or modify as desired.
  It is commented out, as this computation may be lengthy.
*/

P<x> := PolynomialRing(Rationals());
g := P![1, 7, 11, -2, -7, 0, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {41, 41, w^4 - w^3 - 5*w^2 + 3*w + 3}>;

primesArray := [
[5, 5, -2*w^5 + w^4 + 13*w^3 - 2*w^2 - 19*w - 5],
[9, 3, 2*w^5 - w^4 - 14*w^3 + 2*w^2 + 23*w + 6],
[11, 11, w - 1],
[25, 5, w^3 + w^2 - 4*w - 3],
[29, 29, w^5 - w^4 - 7*w^3 + 4*w^2 + 11*w],
[41, 41, w^4 - w^3 - 5*w^2 + 3*w + 3],
[49, 7, w^5 - w^4 - 7*w^3 + 4*w^2 + 11*w + 1],
[59, 59, 2*w^5 - w^4 - 14*w^3 + 2*w^2 + 24*w + 7],
[59, 59, -w^5 + 8*w^3 + 2*w^2 - 15*w - 8],
[61, 61, w^5 - 7*w^3 - 2*w^2 + 12*w + 4],
[61, 61, -w^5 + 7*w^3 - 11*w - 1],
[64, 2, 2],
[71, 71, w^3 + w^2 - 5*w - 3],
[71, 71, -3*w^5 + w^4 + 21*w^3 - w^2 - 33*w - 9],
[79, 79, -2*w^5 + w^4 + 13*w^3 - 3*w^2 - 19*w - 5],
[81, 3, 2*w^5 - w^4 - 13*w^3 + w^2 + 19*w + 8],
[89, 89, 2*w^5 - w^4 - 13*w^3 + 2*w^2 + 20*w + 7],
[89, 89, -w^5 + 8*w^3 + w^2 - 16*w - 5],
[89, 89, -3*w^5 + w^4 + 20*w^3 - 30*w - 11],
[89, 89, -w^5 + 7*w^3 + 2*w^2 - 11*w - 4],
[89, 89, -2*w^5 + 14*w^3 + 3*w^2 - 22*w - 8],
[89, 89, 2*w^5 - w^4 - 14*w^3 + 3*w^2 + 22*w + 6],
[101, 101, 3*w^5 - 2*w^4 - 18*w^3 + 6*w^2 + 22*w + 6],
[101, 101, w^2 - w - 4],
[101, 101, -3*w^5 + w^4 + 20*w^3 - 2*w^2 - 29*w - 7],
[109, 109, w^4 - w^3 - 5*w^2 + 4*w + 5],
[121, 11, w^5 - 7*w^3 - 2*w^2 + 10*w + 6],
[131, 131, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 4*w - 3],
[131, 131, -2*w^5 + w^4 + 13*w^3 - 3*w^2 - 20*w - 6],
[131, 131, 3*w^5 - w^4 - 21*w^3 + w^2 + 35*w + 11],
[131, 131, -w^5 + w^4 + 6*w^3 - 4*w^2 - 7*w + 2],
[139, 139, -w^5 + 6*w^3 + w^2 - 8*w - 1],
[151, 151, -w^3 + w^2 + 4*w - 2],
[179, 179, w^4 - 6*w^2 + 6],
[181, 181, w^3 + w^2 - 3*w],
[191, 191, 3*w^5 - w^4 - 20*w^3 + 2*w^2 + 28*w + 5],
[199, 199, -2*w^5 + w^4 + 12*w^3 - 3*w^2 - 15*w - 2],
[199, 199, 5*w^5 - w^4 - 34*w^3 - w^2 + 52*w + 15],
[211, 211, 3*w^5 - w^4 - 19*w^3 + w^2 + 26*w + 9],
[229, 229, -w^5 + w^4 + 7*w^3 - 3*w^2 - 11*w],
[229, 229, -w^4 + 2*w^3 + 6*w^2 - 7*w - 6],
[239, 239, -w^5 + w^4 + 7*w^3 - 3*w^2 - 13*w - 6],
[239, 239, 3*w^5 - w^4 - 21*w^3 + w^2 + 35*w + 10],
[239, 239, w^3 - w^2 - 4*w + 1],
[239, 239, 5*w^5 - 2*w^4 - 34*w^3 + 2*w^2 + 53*w + 17],
[241, 241, -w^5 + 7*w^3 + w^2 - 13*w - 4],
[241, 241, -3*w^5 + w^4 + 21*w^3 - 35*w - 10],
[241, 241, -w^5 + 7*w^3 - 11*w],
[251, 251, 3*w^5 - w^4 - 21*w^3 + 35*w + 11],
[251, 251, w^5 - 2*w^4 - 6*w^3 + 9*w^2 + 8*w - 3],
[269, 269, -w^5 + 8*w^3 + 3*w^2 - 16*w - 8],
[269, 269, -2*w^5 + w^4 + 13*w^3 - w^2 - 21*w - 9],
[269, 269, 3*w^5 - 21*w^3 - 3*w^2 + 32*w + 12],
[271, 271, -5*w^5 + 3*w^4 + 34*w^3 - 8*w^2 - 53*w - 14],
[281, 281, -w^5 + 8*w^3 + 3*w^2 - 16*w - 11],
[281, 281, 4*w^5 - w^4 - 29*w^3 + 49*w + 13],
[281, 281, w^5 - w^4 - 7*w^3 + 3*w^2 + 11*w + 5],
[281, 281, -5*w^5 + 3*w^4 + 33*w^3 - 8*w^2 - 50*w - 12],
[311, 311, 2*w^5 - w^4 - 14*w^3 + w^2 + 21*w + 9],
[311, 311, -3*w^5 + 20*w^3 + 3*w^2 - 30*w - 10],
[311, 311, 5*w^5 - 2*w^4 - 35*w^3 + 2*w^2 + 57*w + 19],
[331, 331, -w^5 - w^4 + 7*w^3 + 6*w^2 - 11*w - 7],
[349, 349, -6*w^5 + 3*w^4 + 41*w^3 - 7*w^2 - 64*w - 17],
[349, 349, 4*w^5 - w^4 - 29*w^3 - w^2 + 50*w + 17],
[349, 349, 5*w^5 - w^4 - 34*w^3 - w^2 + 52*w + 17],
[359, 359, w^5 - 6*w^3 - w^2 + 5*w + 3],
[379, 379, -w^5 + w^4 + 8*w^3 - 3*w^2 - 17*w - 3],
[379, 379, 2*w^5 - 14*w^3 - 4*w^2 + 22*w + 11],
[379, 379, -5*w^5 + 3*w^4 + 34*w^3 - 8*w^2 - 53*w - 13],
[379, 379, 4*w^5 - 2*w^4 - 27*w^3 + 3*w^2 + 43*w + 14],
[389, 389, 4*w^5 - 2*w^4 - 28*w^3 + 4*w^2 + 44*w + 13],
[401, 401, -2*w^5 + 2*w^4 + 13*w^3 - 6*w^2 - 20*w - 6],
[409, 409, -w^5 + 2*w^4 + 6*w^3 - 8*w^2 - 9*w],
[419, 419, -5*w^5 + w^4 + 34*w^3 + 2*w^2 - 53*w - 19],
[419, 419, 2*w^5 - w^4 - 14*w^3 + 4*w^2 + 23*w + 3],
[421, 421, -w^5 - w^4 + 8*w^3 + 6*w^2 - 13*w - 7],
[421, 421, 2*w^5 - 2*w^4 - 13*w^3 + 8*w^2 + 18*w + 2],
[421, 421, 4*w^5 - w^4 - 26*w^3 + 37*w + 11],
[431, 431, 2*w^5 - w^4 - 13*w^3 + 2*w^2 + 20*w + 9],
[431, 431, w^5 - 8*w^3 - w^2 + 14*w + 2],
[449, 449, 4*w^5 - 2*w^4 - 26*w^3 + 4*w^2 + 38*w + 9],
[449, 449, -3*w^5 + w^4 + 20*w^3 - 31*w - 14],
[461, 461, 3*w^5 - 2*w^4 - 18*w^3 + 6*w^2 + 23*w + 4],
[461, 461, -4*w^5 + 2*w^4 + 26*w^3 - 5*w^2 - 36*w - 9],
[461, 461, -4*w^5 + 2*w^4 + 27*w^3 - 3*w^2 - 42*w - 15],
[491, 491, -3*w^5 + w^4 + 20*w^3 - 29*w - 10],
[491, 491, -5*w^5 + w^4 + 35*w^3 + 2*w^2 - 56*w - 18],
[491, 491, 2*w^5 - 14*w^3 - 4*w^2 + 24*w + 13],
[491, 491, -3*w^5 + w^4 + 21*w^3 - 2*w^2 - 33*w - 10],
[499, 499, 6*w^5 - 3*w^4 - 40*w^3 + 6*w^2 + 61*w + 18],
[499, 499, -4*w^5 + w^4 + 29*w^3 + w^2 - 49*w - 17],
[499, 499, -w^5 - w^4 + 8*w^3 + 5*w^2 - 14*w - 4],
[499, 499, -3*w^5 + w^4 + 19*w^3 - 2*w^2 - 26*w - 8],
[509, 509, -4*w^5 + 2*w^4 + 27*w^3 - 5*w^2 - 43*w - 11],
[509, 509, -2*w^5 + 16*w^3 + 2*w^2 - 30*w - 9],
[521, 521, 3*w^5 - 21*w^3 - 3*w^2 + 34*w + 10],
[521, 521, -3*w^5 + w^4 + 19*w^3 - 26*w - 9],
[521, 521, 4*w^5 - w^4 - 27*w^3 + 40*w + 15],
[521, 521, -3*w^5 + 22*w^3 + 3*w^2 - 37*w - 11],
[541, 541, -4*w^5 + w^4 + 29*w^3 + w^2 - 49*w - 18],
[569, 569, -6*w^5 + 2*w^4 + 40*w^3 - 2*w^2 - 60*w - 19],
[569, 569, -w^5 + w^4 + 7*w^3 - 2*w^2 - 12*w - 6],
[571, 571, 4*w^5 - w^4 - 28*w^3 + 43*w + 14],
[571, 571, -4*w^5 + 2*w^4 + 28*w^3 - 4*w^2 - 45*w - 14],
[599, 599, -w^5 + w^4 + 7*w^3 - 2*w^2 - 13*w - 7],
[601, 601, 4*w^5 - w^4 - 26*w^3 + 38*w + 13],
[601, 601, 4*w^5 - 2*w^4 - 28*w^3 + 5*w^2 + 44*w + 11],
[601, 601, 3*w^5 - w^4 - 21*w^3 + 2*w^2 + 35*w + 9],
[619, 619, 4*w^5 - 2*w^4 - 27*w^3 + 4*w^2 + 40*w + 13],
[619, 619, -4*w^5 + w^4 + 26*w^3 - 36*w - 12],
[619, 619, w^4 - w^3 - 6*w^2 + 4*w + 4],
[631, 631, -3*w^5 + w^4 + 20*w^3 - 30*w - 9],
[631, 631, -5*w^5 + 2*w^4 + 35*w^3 - 3*w^2 - 57*w - 15],
[641, 641, 5*w^5 - w^4 - 34*w^3 - w^2 + 52*w + 16],
[641, 641, -5*w^5 + 2*w^4 + 34*w^3 - 2*w^2 - 52*w - 18],
[659, 659, 3*w^5 - w^4 - 20*w^3 + w^2 + 32*w + 9],
[659, 659, -4*w^5 + w^4 + 27*w^3 - w^2 - 40*w - 11],
[661, 661, 4*w^5 - w^4 - 26*w^3 + 38*w + 12],
[661, 661, -w^5 + 6*w^3 - 8*w + 1],
[691, 691, 3*w^5 - 20*w^3 - 3*w^2 + 29*w + 9],
[691, 691, w^5 + w^4 - 8*w^3 - 7*w^2 + 14*w + 9],
[691, 691, -w^5 + w^4 + 6*w^3 - 3*w^2 - 7*w + 2],
[701, 701, -2*w^5 + w^4 + 13*w^3 - 2*w^2 - 19*w - 9],
[701, 701, 5*w^5 - 2*w^4 - 33*w^3 + 3*w^2 + 48*w + 14],
[701, 701, w^4 + 3*w^3 - 3*w^2 - 10*w - 1],
[701, 701, -2*w^5 + w^4 + 14*w^3 - 3*w^2 - 24*w - 3],
[709, 709, -2*w^5 + 2*w^4 + 14*w^3 - 7*w^2 - 22*w - 5],
[709, 709, -3*w^5 + 21*w^3 + 4*w^2 - 34*w - 11],
[719, 719, 5*w^5 - 2*w^4 - 35*w^3 + 3*w^2 + 58*w + 17],
[719, 719, 4*w^5 - 2*w^4 - 26*w^3 + 4*w^2 + 37*w + 11],
[719, 719, 4*w^5 - 2*w^4 - 27*w^3 + 4*w^2 + 40*w + 12],
[719, 719, 2*w^5 - 16*w^3 - 3*w^2 + 30*w + 10],
[739, 739, -5*w^5 + w^4 + 34*w^3 + w^2 - 51*w - 17],
[751, 751, -w^5 - w^4 + 9*w^3 + 7*w^2 - 18*w - 10],
[761, 761, 4*w^5 - 2*w^4 - 28*w^3 + 3*w^2 + 46*w + 16],
[761, 761, -4*w^5 + 2*w^4 + 27*w^3 - 5*w^2 - 43*w - 12],
[769, 769, -4*w^5 + w^4 + 28*w^3 - 44*w - 12],
[769, 769, -w^4 + w^3 + 3*w^2 - 3*w + 1],
[809, 809, 2*w^5 - 2*w^4 - 13*w^3 + 7*w^2 + 20*w + 1],
[811, 811, -2*w^5 + 15*w^3 + 2*w^2 - 24*w - 8],
[811, 811, -w^5 + 9*w^3 + w^2 - 18*w - 6],
[821, 821, -w^5 + 8*w^3 + 3*w^2 - 17*w - 9],
[821, 821, w^5 + w^4 - 7*w^3 - 6*w^2 + 11*w + 8],
[821, 821, 4*w^5 - 2*w^4 - 28*w^3 + 4*w^2 + 46*w + 11],
[821, 821, 5*w^5 - 2*w^4 - 34*w^3 + 4*w^2 + 51*w + 13],
[829, 829, -2*w^5 + w^4 + 15*w^3 - w^2 - 28*w - 10],
[829, 829, -6*w^5 + 3*w^4 + 42*w^3 - 7*w^2 - 68*w - 21],
[829, 829, 4*w^5 - 2*w^4 - 26*w^3 + 5*w^2 + 38*w + 12],
[829, 829, w^5 - 7*w^3 - 3*w^2 + 11*w + 6],
[839, 839, 3*w^5 - 2*w^4 - 20*w^3 + 5*w^2 + 32*w + 11],
[839, 839, -w^4 + w^3 + 6*w^2 - 3*w - 4],
[841, 29, -3*w^5 + w^4 + 22*w^3 - 38*w - 11],
[911, 911, 3*w^5 - w^4 - 21*w^3 + 36*w + 12],
[919, 919, -w^5 - w^4 + 7*w^3 + 6*w^2 - 12*w - 5],
[941, 941, -w^5 + w^4 + 7*w^3 - 5*w^2 - 11*w],
[941, 941, 4*w^5 - w^4 - 29*w^3 + 48*w + 15],
[971, 971, -4*w^5 + w^4 + 27*w^3 + w^2 - 41*w - 13],
[991, 991, w^5 - w^4 - 8*w^3 + 3*w^2 + 16*w + 2],
[991, 991, -4*w^5 + 3*w^4 + 27*w^3 - 9*w^2 - 42*w - 10]];
primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x^13 + 9*x^12 + 8*x^11 - 127*x^10 - 303*x^9 + 428*x^8 + 1644*x^7 - 149*x^6 - 3203*x^5 - 1013*x^4 + 2239*x^3 + 940*x^2 - 484*x - 222;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [e, 17504196/89816329*e^12 + 148865431/89816329*e^11 + 64737411/89816329*e^10 - 2266094877/89816329*e^9 - 4177425359/89816329*e^8 + 9707116435/89816329*e^7 + 24089813559/89816329*e^6 - 15022384745/89816329*e^5 - 48811570830/89816329*e^4 + 7358759046/89816329*e^3 + 35153705032/89816329*e^2 - 2359229089/89816329*e - 7300008286/89816329, -75225301/269448987*e^12 - 640043765/269448987*e^11 - 94514708/89816329*e^10 + 9712462696/269448987*e^9 + 17952566537/269448987*e^8 - 41443847650/269448987*e^7 - 102987762248/269448987*e^6 + 64730048539/269448987*e^5 + 209300180191/269448987*e^4 - 33668065031/269448987*e^3 - 153461300297/269448987*e^2 + 10557421246/269448987*e + 10446259982/89816329, 86989232/269448987*e^12 + 726208402/269448987*e^11 + 73101704/89816329*e^10 - 11243528282/269448987*e^9 - 19241436247/269448987*e^8 + 50121154349/269448987*e^7 + 113773682263/269448987*e^6 - 84324291476/269448987*e^5 - 236049544136/269448987*e^4 + 50115989638/269448987*e^3 + 176441068978/269448987*e^2 - 14447898182/269448987*e - 12543171834/89816329, -30474616/89816329*e^12 - 260920482/89816329*e^11 - 134058386/89816329*e^10 + 3890314863/89816329*e^9 + 7493863249/89816329*e^8 - 15875929296/89816329*e^7 - 42015264575/89816329*e^6 + 22342508342/89816329*e^5 + 83477956096/89816329*e^4 - 8199890596/89816329*e^3 - 59313195968/89816329*e^2 + 2046591465/89816329*e + 11493313566/89816329, 1, 253787890/269448987*e^12 + 2151078953/269448987*e^11 + 312077037/89816329*e^10 - 32450242612/269448987*e^9 - 59775002483/269448987*e^8 + 136245438022/269448987*e^7 + 339035142551/269448987*e^6 - 203779843975/269448987*e^5 - 674766314335/269448987*e^4 + 89676263084/269448987*e^3 + 475751914568/269448987*e^2 - 21541560286/269448987*e - 31610072542/89816329, 177632617/269448987*e^12 + 1519247423/269448987*e^11 + 247924805/89816329*e^10 - 22813733443/269448987*e^9 - 43174119860/269448987*e^8 + 94958457763/269448987*e^7 + 242953123745/269448987*e^6 - 140811477007/269448987*e^5 - 482066950267/269448987*e^4 + 62365158971/269448987*e^3 + 340698469700/269448987*e^2 - 16149845980/269448987*e - 23011074674/89816329, 126741538/269448987*e^12 + 1075148921/269448987*e^11 + 142679946/89816329*e^10 - 16564824478/269448987*e^9 - 29930844371/269448987*e^8 + 73219732732/269448987*e^7 + 176507850245/269448987*e^6 - 122761269712/269448987*e^5 - 370616832973/269448987*e^4 + 77375180651/269448987*e^3 + 285033000077/269448987*e^2 - 27167675614/269448987*e - 20784979862/89816329, -103199375/269448987*e^12 - 837864511/269448987*e^11 - 15691044/89816329*e^10 + 13586630129/269448987*e^9 + 20305044412/269448987*e^8 - 66285790502/269448987*e^7 - 130713077956/269448987*e^6 + 126455093048/269448987*e^5 + 288417843176/269448987*e^4 - 91052259919/269448987*e^3 - 226920993178/269448987*e^2 + 26656782596/269448987*e + 16694394368/89816329, 56815439/89816329*e^12 + 478370560/89816329*e^11 + 185958750/89816329*e^10 - 7254122827/89816329*e^9 - 13011564137/89816329*e^8 + 30821467507/89816329*e^7 + 74098053379/89816329*e^6 - 47221165626/89816329*e^5 - 146706105333/89816329*e^4 + 22621718457/89816329*e^3 + 101418697668/89816329*e^2 - 6403399372/89816329*e - 19910762540/89816329, -56659181/269448987*e^12 - 490851469/269448987*e^11 - 95325446/89816329*e^10 + 7273310315/269448987*e^9 + 14459216776/269448987*e^8 - 29312913008/269448987*e^7 - 79846263121/269448987*e^6 + 40667332727/269448987*e^5 + 155000208065/269448987*e^4 - 15496791553/269448987*e^3 - 104214054217/269448987*e^2 + 4971624590/269448987*e + 6477534537/89816329, -57829197/89816329*e^12 - 498815922/89816329*e^11 - 265656539/89816329*e^10 + 7508561954/89816329*e^9 + 14611126304/89816329*e^8 - 31286058856/89816329*e^7 - 83329952394/89816329*e^6 + 45276340624/89816329*e^5 + 168523082068/89816329*e^4 - 17177920968/89816329*e^3 - 122116784734/89816329*e^2 + 4130316726/89816329*e + 25076907828/89816329, -47755180/89816329*e^12 - 400116700/89816329*e^11 - 140878252/89816329*e^10 + 6102113774/89816329*e^9 + 10756706450/89816329*e^8 - 26122901503/89816329*e^7 - 61864633264/89816329*e^6 + 39392745903/89816329*e^5 + 122229230986/89816329*e^4 - 15679992090/89816329*e^3 - 82372389527/89816329*e^2 + 2662831918/89816329*e + 15428099592/89816329, 122651483/269448987*e^12 + 1035875758/269448987*e^11 + 131554178/89816329*e^10 - 15866825306/269448987*e^9 - 28181990644/269448987*e^8 + 69555669821/269448987*e^7 + 162746657113/269448987*e^6 - 117162700538/269448987*e^5 - 332406008714/269448987*e^4 + 74419882792/269448987*e^3 + 244920686989/269448987*e^2 - 21555018830/269448987*e - 16331082684/89816329, -199819435/269448987*e^12 - 1658419040/269448987*e^11 - 135771726/89816329*e^10 + 25941289867/269448987*e^9 + 42759113645/269448987*e^8 - 118847559652/269448987*e^7 - 255627485891/269448987*e^6 + 214380279793/269448987*e^5 + 536658619198/269448987*e^4 - 152601854894/269448987*e^3 - 411603900881/269448987*e^2 + 48117553720/269448987*e + 30402673498/89816329, -245657056/269448987*e^12 - 2117879699/269448987*e^11 - 382491142/89816329*e^10 + 31683069595/269448987*e^9 + 61973078105/269448987*e^8 - 129794877931/269448987*e^7 - 349538773676/269448987*e^6 + 178829832304/269448987*e^5 + 694232884099/269448987*e^4 - 50805305975/269448987*e^3 - 485071514828/269448987*e^2 + 8505500641/269448987*e + 31339846550/89816329, 139962821/269448987*e^12 + 1189364620/269448987*e^11 + 175913333/89816329*e^10 - 18028459403/269448987*e^9 - 33630647920/269448987*e^8 + 75721231367/269448987*e^7 + 193682998621/269448987*e^6 - 106695748496/269448987*e^5 - 386349423389/269448987*e^4 + 29106313075/269448987*e^3 + 262543759444/269448987*e^2 - 3164999468/269448987*e - 16201228168/89816329, 136696910/269448987*e^12 + 1176818656/269448987*e^11 + 223393375/89816329*e^10 - 17262076793/269448987*e^9 - 34113027280/269448987*e^8 + 67533789554/269448987*e^7 + 184627872370/269448987*e^6 - 85051893560/269448987*e^5 - 346622718179/269448987*e^4 + 14572420012/269448987*e^3 + 219941456674/269448987*e^2 - 181229966/269448987*e - 12338082706/89816329, -78692120/89816329*e^12 - 658283507/89816329*e^11 - 232124550/89816329*e^10 + 9980806046/89816329*e^9 + 17464021009/89816329*e^8 - 42650867416/89816329*e^7 - 98906544243/89816329*e^6 + 68255054555/89816329*e^5 + 196024103602/89816329*e^4 - 39585545805/89816329*e^3 - 139347701368/89816329*e^2 + 12875193394/89816329*e + 28895708664/89816329, -27607010/269448987*e^12 - 222694051/269448987*e^11 - 9752028/89816329*e^10 + 3430383092/269448987*e^9 + 5354087158/269448987*e^8 - 14789175509/269448987*e^7 - 30990426307/269448987*e^6 + 21194412422/269448987*e^5 + 56321444084/269448987*e^4 - 6481624951/269448987*e^3 - 26020399234/269448987*e^2 + 3545413235/269448987*e + 334380940/89816329, 60292301/269448987*e^12 + 538457350/269448987*e^11 + 147557736/89816329*e^10 - 7665951416/269448987*e^9 - 17402923447/269448987*e^8 + 27425263418/269448987*e^7 + 92953025815/269448987*e^6 - 24468801710/269448987*e^5 - 177040925372/269448987*e^4 - 13237603235/269448987*e^3 + 117579461350/269448987*e^2 + 5134590916/269448987*e - 7033631560/89816329, -174643562/269448987*e^12 - 1496955229/269448987*e^11 - 252598122/89816329*e^10 + 22457634485/269448987*e^9 + 43094050984/269448987*e^8 - 92689321970/269448987*e^7 - 243597466015/269448987*e^6 + 130388433053/269448987*e^5 + 483594394751/269448987*e^4 - 40915047808/269448987*e^3 - 337498924444/269448987*e^2 + 5737547108/269448987*e + 21959583358/89816329, 37469744/89816329*e^12 + 319975231/89816329*e^11 + 165568402/89816329*e^10 - 4743498604/89816329*e^9 - 9251412039/89816329*e^8 + 18753115510/89816329*e^7 + 51770793717/89816329*e^6 - 21874287604/89816329*e^5 - 100054018176/89816329*e^4 - 2419121423/89816329*e^3 + 64859652408/89816329*e^2 + 3001765225/89816329*e - 11179026012/89816329, 73243397/269448987*e^12 + 596223736/269448987*e^11 + 20225299/89816329*e^10 - 9519878018/269448987*e^9 - 14595838747/269448987*e^8 + 44704404239/269448987*e^7 + 90550566397/269448987*e^6 - 77678568278/269448987*e^5 - 186524901341/269448987*e^4 + 43636333417/269448987*e^3 + 126186777946/269448987*e^2 - 12029178581/269448987*e - 7713231862/89816329, -178947521/269448987*e^12 - 1516559953/269448987*e^11 - 206348032/89816329*e^10 + 23195165549/269448987*e^9 + 42266909929/269448987*e^8 - 99870689444/269448987*e^7 - 245526729034/269448987*e^6 + 151449070799/269448987*e^5 + 493595611454/269448987*e^4 - 61642703692/269448987*e^3 - 339810877894/269448987*e^2 + 11465047871/269448987*e + 21360219752/89816329, -116098810/269448987*e^12 - 960864293/269448987*e^11 - 77631845/89816329*e^10 + 14953416958/269448987*e^9 + 24635225234/269448987*e^8 - 67588321219/269448987*e^7 - 145979829344/269448987*e^6 + 118131288424/269448987*e^5 + 300918271855/269448987*e^4 - 78512042525/269448987*e^3 - 220094456144/269448987*e^2 + 23805255631/269448987*e + 14525515510/89816329, -5532302/269448987*e^12 - 49136557/269448987*e^11 - 25119703/89816329*e^10 + 360298076/269448987*e^9 + 1188045418/269448987*e^8 + 1945737823/269448987*e^7 + 2545388492/269448987*e^6 - 11179023823/269448987*e^5 - 29193432712/269448987*e^4 + 14775406307/269448987*e^3 + 45608852534/269448987*e^2 - 8093788732/269448987*e - 5021841950/89816329, -19771866/89816329*e^12 - 164680211/89816329*e^11 - 32761591/89816329*e^10 + 2673492964/89816329*e^9 + 4415427571/89816329*e^8 - 12867883007/89816329*e^7 - 28600328008/89816329*e^6 + 22418465073/89816329*e^5 + 62572257298/89816329*e^4 - 12219158973/89816329*e^3 - 46807067252/89816329*e^2 + 4490229900/89816329*e + 10295322426/89816329, 57502694/269448987*e^12 + 432514444/269448987*e^11 - 81114888/89816329*e^10 - 7545337877/269448987*e^9 - 7025141305/269448987*e^8 + 42817165805/269448987*e^7 + 53549189311/269448987*e^6 - 106543118975/269448987*e^5 - 135163116137/269448987*e^4 + 114880757455/269448987*e^3 + 130884035488/269448987*e^2 - 39607830815/269448987*e - 11777708872/89816329, -324187160/269448987*e^12 - 2740183219/269448987*e^11 - 352048927/89816329*e^10 + 42067381511/269448987*e^9 + 75453891868/269448987*e^8 - 184008281873/269448987*e^7 - 440815551478/269448987*e^6 + 299100741410/269448987*e^5 + 906312462929/269448987*e^4 - 170308346203/269448987*e^3 - 667799727862/269448987*e^2 + 55835749130/269448987*e + 46873080946/89816329, 474548905/269448987*e^12 + 4025179844/269448987*e^11 + 581391653/89816329*e^10 - 60903142264/269448987*e^9 - 112090536314/269448987*e^8 + 257685101848/269448987*e^7 + 639722962934/269448987*e^6 - 392984370682/269448987*e^5 - 1286622571891/269448987*e^4 + 187021532717/269448987*e^3 + 925557633014/269448987*e^2 - 50049701542/269448987*e - 62754109270/89816329, -60801511/269448987*e^12 - 497543435/269448987*e^11 - 15151847/89816329*e^10 + 8072085133/269448987*e^9 + 12200030528/269448987*e^8 - 39738720100/269448987*e^7 - 77738630219/269448987*e^6 + 79218342691/269448987*e^5 + 170645971558/269448987*e^4 - 64835903414/269448987*e^3 - 131382766478/269448987*e^2 + 20770342840/269448987*e + 8465261484/89816329, -14720151/89816329*e^12 - 117530410/89816329*e^11 + 14873798/89816329*e^10 + 1980457550/89816329*e^9 + 2649273344/89816329*e^8 - 10311904679/89816329*e^7 - 18205212953/89816329*e^6 + 20955873973/89816329*e^5 + 41104558789/89816329*e^4 - 15311420416/89816329*e^3 - 31847379552/89816329*e^2 + 3542643384/89816329*e + 6658279908/89816329, -147246019/269448987*e^12 - 1198999460/269448987*e^11 - 46358897/89816329*e^10 + 19024318504/269448987*e^9 + 29300265029/269448987*e^8 - 88698556816/269448987*e^7 - 179939406713/269448987*e^6 + 156299988406/269448987*e^5 + 374049232486/269448987*e^4 - 95081171555/269448987*e^3 - 268434358316/269448987*e^2 + 25710163546/269448987*e + 18591349164/89816329, 388513208/269448987*e^12 + 3259336699/269448987*e^11 + 343949396/89816329*e^10 - 50714076725/269448987*e^9 - 87378501538/269448987*e^8 + 229160350934/269448987*e^7 + 520656523300/269448987*e^6 - 399683394995/269448987*e^5 - 1094029933319/269448987*e^4 + 266769348676/269448987*e^3 + 834061119634/269448987*e^2 - 86760084929/269448987*e - 60721072102/89816329, -30160429/89816329*e^12 - 269135762/89816329*e^11 - 231213745/89816329*e^10 + 3733429064/89816329*e^9 + 8599702729/89816329*e^8 - 12389583403/89816329*e^7 - 43552969277/89816329*e^6 + 7972073708/89816329*e^5 + 76729818733/89816329*e^4 + 11530358742/89816329*e^3 - 45142148322/89816329*e^2 - 5299096090/89816329*e + 6364534700/89816329, -82670126/269448987*e^12 - 674772580/269448987*e^11 - 53273617/89816329*e^10 + 10128747632/269448987*e^9 + 16366705705/269448987*e^8 - 42830133266/269448987*e^7 - 89634568597/269448987*e^6 + 71779080293/269448987*e^5 + 174104168858/269448987*e^4 - 48278801857/269448987*e^3 - 130565149306/269448987*e^2 + 7732878518/269448987*e + 10410542162/89816329, -392300114/269448987*e^12 - 3261302611/269448987*e^11 - 316249365/89816329*e^10 + 50192853809/269448987*e^9 + 85150958059/269448987*e^8 - 221052551078/269448987*e^7 - 496222188631/269448987*e^6 + 366805777610/269448987*e^5 + 1007723075606/269448987*e^4 - 218670243826/269448987*e^3 - 730901462410/269448987*e^2 + 68394610430/269448987*e + 50693247612/89816329, -258434929/269448987*e^12 - 2181613682/269448987*e^11 - 263799698/89816329*e^10 + 33731950408/269448987*e^9 + 59617437404/269448987*e^8 - 150570505579/269448987*e^7 - 352325653811/269448987*e^6 + 258742441786/269448987*e^5 + 740706274333/269448987*e^4 - 169395273845/269448987*e^3 - 571370763080/269448987*e^2 + 53543323756/269448987*e + 41580178224/89816329, -39928345/89816329*e^12 - 346738225/89816329*e^11 - 190314065/89816329*e^10 + 5267703877/89816329*e^9 + 10331322301/89816329*e^8 - 22471748799/89816329*e^7 - 59888132939/89816329*e^6 + 34485962280/89816329*e^5 + 123669513000/89816329*e^4 - 16983145479/89816329*e^3 - 91369393044/89816329*e^2 + 5485521882/89816329*e + 18357381608/89816329, -337220180/269448987*e^12 - 2850462775/269448987*e^11 - 381927761/89816329*e^10 + 43460876882/269448987*e^9 + 78975879952/269448987*e^8 - 186055743458/269448987*e^7 - 457682584390/269448987*e^6 + 281529541823/269448987*e^5 + 926301546377/269448987*e^4 - 119148606925/269448987*e^3 - 659314090060/269448987*e^2 + 30175895633/269448987*e + 43320313780/89816329, 125409340/89816329*e^12 + 1054265873/89816329*e^11 + 375160914/89816329*e^10 - 16194778213/89816329*e^9 - 28568406597/89816329*e^8 + 71028712043/89816329*e^7 + 167122627400/89816329*e^6 - 116761646384/89816329*e^5 - 345482209664/89816329*e^4 + 67418792944/89816329*e^3 + 258979857992/89816329*e^2 - 19760111894/89816329*e - 54748637292/89816329, -46724666/269448987*e^12 - 402557620/269448987*e^11 - 90141255/89816329*e^10 + 5625549452/269448987*e^9 + 11928923347/269448987*e^8 - 18416774120/269448987*e^7 - 60035839282/269448987*e^6 + 5307609953/269448987*e^5 + 95211549443/269448987*e^4 + 39379972265/269448987*e^3 - 33415724293/269448987*e^2 - 24132485086/269448987*e - 282047510/89816329, -42695374/269448987*e^12 - 367823816/269448987*e^11 - 75033995/89816329*e^10 + 5310509329/269448987*e^9 + 10919751371/269448987*e^8 - 19219099999/269448987*e^7 - 58362032435/269448987*e^6 + 13737093595/269448987*e^5 + 102871736623/269448987*e^4 + 21130549915/269448987*e^3 - 53639664230/269448987*e^2 - 8420358608/269448987*e + 1917389462/89816329, -80237202/89816329*e^12 - 674592085/89816329*e^11 - 249220655/89816329*e^10 + 10281514511/89816329*e^9 + 18188524862/89816329*e^8 - 44486077497/89816329*e^7 - 104476589890/89816329*e^6 + 72784156819/89816329*e^5 + 212517662530/89816329*e^4 - 43294461579/89816329*e^3 - 157375450158/89816329*e^2 + 12339262694/89816329*e + 32379338920/89816329, 31984574/89816329*e^12 + 261266336/89816329*e^11 + 54260913/89816329*e^10 - 3977656838/89816329*e^9 - 6306800957/89816329*e^8 + 17302316101/89816329*e^7 + 35159789284/89816329*e^6 - 29667990372/89816329*e^5 - 67953525098/89816329*e^4 + 19747418026/89816329*e^3 + 48377088356/89816329*e^2 - 4391117165/89816329*e - 11007480818/89816329, 51474947/89816329*e^12 + 430608921/89816329*e^11 + 127752900/89816329*e^10 - 6728280076/89816329*e^9 - 11554513052/89816329*e^8 + 30368510500/89816329*e^7 + 69694904803/89816329*e^6 - 50345610006/89816329*e^5 - 145965248570/89816329*e^4 + 26032740320/89816329*e^3 + 107518293928/89816329*e^2 - 4228212131/89816329*e - 22213787338/89816329, -249321343/269448987*e^12 - 2166301802/269448987*e^11 - 447410899/89816329*e^10 + 31801213735/269448987*e^9 + 64728350687/269448987*e^8 - 124829663842/269448987*e^7 - 355392096287/269448987*e^6 + 159975463261/269448987*e^5 + 693949896811/269448987*e^4 - 36616159130/269448987*e^3 - 484111429262/269448987*e^2 + 10515002872/269448987*e + 31955660960/89816329, -135153803/269448987*e^12 - 1122038212/269448987*e^11 - 98141260/89816329*e^10 + 17443380029/269448987*e^9 + 29235694588/269448987*e^8 - 77871524693/269448987*e^7 - 173309762599/269448987*e^6 + 126629927357/269448987*e^5 + 351585227294/269448987*e^4 - 62267478646/269448987*e^3 - 248520786724/269448987*e^2 + 12500039984/269448987*e + 18175837924/89816329, 86333294/269448987*e^12 + 667636426/269448987*e^11 - 78061573/89816329*e^10 - 11380657271/269448987*e^9 - 12468070564/269448987*e^8 + 62147625905/269448987*e^7 + 87187259167/269448987*e^6 - 148275922739/269448987*e^5 - 204382927835/269448987*e^4 + 156285715150/269448987*e^3 + 177979621726/269448987*e^2 - 58728567938/269448987*e - 14529037774/89816329, -140930701/269448987*e^12 - 1216147226/269448987*e^11 - 242239904/89816329*e^10 + 17738151976/269448987*e^9 + 35703558461/269448987*e^8 - 68704877101/269448987*e^7 - 194217792875/269448987*e^6 + 87069373585/269448987*e^5 + 380510231014/269448987*e^4 - 18551369762/269448987*e^3 - 276078276926/269448987*e^2 + 194076700/269448987*e + 18749402618/89816329, 54162886/89816329*e^12 + 472948350/89816329*e^11 + 295659320/89816329*e^10 - 7008137926/89816329*e^9 - 14303609745/89816329*e^8 + 28005413902/89816329*e^7 + 79480462676/89816329*e^6 - 36152232956/89816329*e^5 - 154285298740/89816329*e^4 + 7810892247/89816329*e^3 + 102335218126/89816329*e^2 - 2857865674/89816329*e - 18620295972/89816329, -21103453/89816329*e^12 - 179547399/89816329*e^11 - 85862614/89816329*e^10 + 2635613215/89816329*e^9 + 4721659304/89816329*e^8 - 11061291683/89816329*e^7 - 24140728422/89816329*e^6 + 22294327865/89816329*e^5 + 46369825309/89816329*e^4 - 26298342965/89816329*e^3 - 38153709700/89816329*e^2 + 12026527003/89816329*e + 9363521056/89816329, 325943128/269448987*e^12 + 2795748695/269448987*e^11 + 492081023/89816329*e^10 - 41469461311/269448987*e^9 - 79967080313/269448987*e^8 + 168088234108/269448987*e^7 + 440963047580/269448987*e^6 - 240039866461/269448987*e^5 - 862994308435/269448987*e^4 + 98965667066/269448987*e^3 + 611058863210/269448987*e^2 - 23510709784/269448987*e - 41440649750/89816329, 44781880/89816329*e^12 + 389035125/89816329*e^11 + 238399581/89816329*e^10 - 5708786635/89816329*e^9 - 11475552797/89816329*e^8 + 22671345494/89816329*e^7 + 62376717598/89816329*e^6 - 32182436264/89816329*e^5 - 122451487198/89816329*e^4 + 15811630392/89816329*e^3 + 90473219832/89816329*e^2 - 6671922324/89816329*e - 19988270262/89816329, -154775816/269448987*e^12 - 1314046840/269448987*e^11 - 172690680/89816329*e^10 + 20238533624/269448987*e^9 + 36104155594/269448987*e^8 - 90013255832/269448987*e^7 - 209713748296/269448987*e^6 + 157071240368/269448987*e^5 + 431265839489/269448987*e^4 - 112613018800/269448987*e^3 - 322207780615/269448987*e^2 + 44206631750/269448987*e + 22755827758/89816329, 89678499/89816329*e^12 + 763689353/89816329*e^11 + 361150994/89816329*e^10 - 11428789979/89816329*e^9 - 21365019900/89816329*e^8 + 47514570579/89816329*e^7 + 119253908058/89816329*e^6 - 73180152415/89816329*e^5 - 237304465931/89816329*e^4 + 40820715561/89816329*e^3 + 172685490202/89816329*e^2 - 14125445589/89816329*e - 35442817800/89816329, 41812526/269448987*e^12 + 325372252/269448987*e^11 - 18353518/89816329*e^10 - 5242822076/269448987*e^9 - 6693327856/269448987*e^8 + 25165969244/269448987*e^7 + 42482984434/269448987*e^6 - 45860073227/269448987*e^5 - 88690024928/269448987*e^4 + 24206170522/269448987*e^3 + 62227099918/269448987*e^2 + 1829003341/269448987*e - 3222675766/89816329, -363238484/269448987*e^12 - 3076852270/269448987*e^11 - 413071711/89816329*e^10 + 47026753955/269448987*e^9 + 84731220253/269448987*e^8 - 204886069769/269448987*e^7 - 489641553823/269448987*e^6 + 339997996535/269448987*e^5 + 1006108877126/269448987*e^4 - 213863359393/269448987*e^3 - 759377498092/269448987*e^2 + 72884450234/269448987*e + 55023336946/89816329, -515552059/269448987*e^12 - 4349317793/269448987*e^11 - 529543246/89816329*e^10 + 67079903089/269448987*e^9 + 118989744989/269448987*e^8 - 296213371864/269448987*e^7 - 699852948140/269448987*e^6 + 487403042011/269448987*e^5 + 1444791408013/269448987*e^4 - 278210022992/269448987*e^3 - 1065972775484/269448987*e^2 + 85332427744/269448987*e + 74147226620/89816329, -60893527/89816329*e^12 - 518004659/89816329*e^11 - 240590942/89816329*e^10 + 7745223657/89816329*e^9 + 14336121486/89816329*e^8 - 32233486381/89816329*e^7 - 79229461366/89816329*e^6 + 50344839423/89816329*e^5 + 155583962241/89816329*e^4 - 28638344351/89816329*e^3 - 112501421324/89816329*e^2 + 8065497854/89816329*e + 24374199674/89816329, 564763771/269448987*e^12 + 4742070101/269448987*e^11 + 536777117/89816329*e^10 - 73104552106/269448987*e^9 - 127333191533/269448987*e^8 + 324409430650/269448987*e^7 + 746479644770/269448987*e^6 - 554209083661/269448987*e^5 - 1552245296002/269448987*e^4 + 362191657505/269448987*e^3 + 1188300095516/269448987*e^2 - 116000394472/269448987*e - 87347534920/89816329, 659260879/269448987*e^12 + 5583581753/269448987*e^11 + 765032509/89816329*e^10 - 85060094170/269448987*e^9 - 154516486130/269448987*e^8 + 366149356735/269448987*e^7 + 891036060002/269448987*e^6 - 581150818996/269448987*e^5 - 1816150015744/269448987*e^4 + 311520409070/269448987*e^3 + 1336050231119/269448987*e^2 - 92046525256/269448987*e - 92866993714/89816329, -153336993/89816329*e^12 - 1287328270/89816329*e^11 - 458675729/89816329*e^10 + 19674404542/89816329*e^9 + 34573896337/89816329*e^8 - 85524517214/89816329*e^7 - 199375117501/89816329*e^6 + 140068411161/89816329*e^5 + 404958488252/89816329*e^4 - 82142452978/89816329*e^3 - 297188888214/89816329*e^2 + 22828172381/89816329*e + 61943229812/89816329, -397934351/269448987*e^12 - 3409452262/269448987*e^11 - 588029981/89816329*e^10 + 50836617593/269448987*e^9 + 98205052657/269448987*e^8 - 206941013720/269448987*e^7 - 550691994079/269448987*e^6 + 285189400859/269448987*e^5 + 1088406004331/269448987*e^4 - 89804303032/269448987*e^3 - 760647108934/269448987*e^2 + 21030208349/269448987*e + 49713511900/89816329, -177934744/89816329*e^12 - 1494013531/89816329*e^11 - 531051772/89816329*e^10 + 22866857454/89816329*e^9 + 40251809616/89816329*e^8 - 99540319568/89816329*e^7 - 233245803319/89816329*e^6 + 161989728467/89816329*e^5 + 475704285867/89816329*e^4 - 92873434113/89816329*e^3 - 350750696644/89816329*e^2 + 28267639657/89816329*e + 73971559298/89816329, 489024004/269448987*e^12 + 4090749074/269448987*e^11 + 433745209/89816329*e^10 - 63147713857/269448987*e^9 - 108897810449/269448987*e^8 + 279981711565/269448987*e^7 + 639263312717/269448987*e^6 - 469946175355/269448987*e^5 - 1313295536119/269448987*e^4 + 289747841915/269448987*e^3 + 966839430758/269448987*e^2 - 95219500654/269448987*e - 68480095966/89816329, -294302062/269448987*e^12 - 2453489138/269448987*e^11 - 239215682/89816329*e^10 + 37945706515/269448987*e^9 + 64076405285/269448987*e^8 - 170229566350/269448987*e^7 - 375156698309/269448987*e^6 + 301710193237/269448987*e^5 + 775855247332/269448987*e^4 - 218632661831/269448987*e^3 - 589861832144/269448987*e^2 + 74835317125/269448987*e + 43532353170/89816329, 283783862/269448987*e^12 + 2386807627/269448987*e^11 + 259920151/89816329*e^10 - 37214938535/269448987*e^9 - 64754550520/269448987*e^8 + 167549877866/269448987*e^7 + 387201701827/269448987*e^6 - 279295024880/269448987*e^5 - 800707281902/269448987*e^4 + 155108142172/269448987*e^3 + 572714464432/269448987*e^2 - 42230481842/269448987*e - 37302889844/89816329, -572442298/269448987*e^12 - 4888409570/269448987*e^11 - 751514946/89816329*e^10 + 74204394943/269448987*e^9 + 138612686810/269448987*e^8 - 316076522032/269448987*e^7 - 795609273899/269448987*e^6 + 484938330472/269448987*e^5 + 1607992706815/269448987*e^4 - 229404112466/269448987*e^3 - 1152060123392/269448987*e^2 + 59654707546/269448987*e + 76225716698/89816329, -747694229/269448987*e^12 - 6375706993/269448987*e^11 - 986111442/89816329*e^10 + 96260017727/269448987*e^9 + 179720815372/269448987*e^8 - 406636006898/269448987*e^7 - 1021719775294/269448987*e^6 + 628653116735/269448987*e^5 + 2062316025020/269448987*e^4 - 327061145623/269448987*e^3 - 1507480032106/269448987*e^2 + 100421087471/269448987*e + 104552318596/89816329, 31186627/269448987*e^12 + 237576731/269448987*e^11 - 42664057/89816329*e^10 - 4225527814/269448987*e^9 - 4161239801/269448987*e^8 + 24030615610/269448987*e^7 + 32114836661/269448987*e^6 - 54533906197/269448987*e^5 - 74278885441/269448987*e^4 + 48558628817/269448987*e^3 + 61661294396/269448987*e^2 - 16653504592/269448987*e - 7159905972/89816329, -228550927/269448987*e^12 - 1955837360/269448987*e^11 - 343990211/89816329*e^10 + 28847761381/269448987*e^9 + 55706546192/269448987*e^8 - 114737336617/269448987*e^7 - 303689119103/269448987*e^6 + 152862484564/269448987*e^5 + 577995426121/269448987*e^4 - 42286665494/269448987*e^3 - 382618677110/269448987*e^2 + 4578112321/269448987*e + 22624725062/89816329, -284267008/269448987*e^12 - 2386060313/269448987*e^11 - 285021204/89816329*e^10 + 36478015255/269448987*e^9 + 64517460293/269448987*e^8 - 157927730803/269448987*e^7 - 374625382121/269448987*e^6 + 251035804339/269448987*e^5 + 765956697241/269448987*e^4 - 131572981325/269448987*e^3 - 566181909896/269448987*e^2 + 39277682860/269448987*e + 39363221042/89816329, -119790440/89816329*e^12 - 1038160311/89816329*e^11 - 603522215/89816329*e^10 + 15411406794/89816329*e^9 + 30602619761/89816329*e^8 - 62644656115/89816329*e^7 - 170156187023/89816329*e^6 + 90474636360/89816329*e^5 + 339459411288/89816329*e^4 - 41395809130/89816329*e^3 - 248081357502/89816329*e^2 + 13991252245/89816329*e + 51272978038/89816329, -145865428/269448987*e^12 - 1278466268/269448987*e^11 - 263179513/89816329*e^10 + 19318653847/269448987*e^9 + 39792646703/269448987*e^8 - 80056098544/269448987*e^7 - 233003659961/269448987*e^6 + 105078713443/269448987*e^5 + 484316050930/269448987*e^4 - 12929344193/269448987*e^3 - 354493854236/269448987*e^2 - 1122938696/269448987*e + 24560064388/89816329, 58401941/89816329*e^12 + 515743229/89816329*e^11 + 391739129/89816329*e^10 - 7330001022/89816329*e^9 - 15970675612/89816329*e^8 + 26468051020/89816329*e^7 + 83310705491/89816329*e^6 - 27317577514/89816329*e^5 - 154456211336/89816329*e^4 - 4218763451/89816329*e^3 + 102016487016/89816329*e^2 + 5326956242/89816329*e - 18805758512/89816329, -144543923/269448987*e^12 - 1202636890/269448987*e^11 - 95935675/89816329*e^10 + 19054043192/269448987*e^9 + 31706572297/269448987*e^8 - 88722564005/269448987*e^7 - 195883497646/269448987*e^6 + 157229157980/269448987*e^5 + 419681631428/269448987*e^4 - 102425401663/269448987*e^3 - 317189007955/269448987*e^2 + 32448200060/269448987*e + 22353517642/89816329, 220283470/269448987*e^12 + 1846646852/269448987*e^11 + 164155500/89816329*e^10 - 29387170462/269448987*e^9 - 49550853635/269448987*e^8 + 138156488902/269448987*e^7 + 307236363107/269448987*e^6 - 248367821752/269448987*e^5 - 661145547235/269448987*e^4 + 164479122533/269448987*e^3 + 503787912818/269448987*e^2 - 54451437538/269448987*e - 36684198074/89816329, -172275678/89816329*e^12 - 1453608784/89816329*e^11 - 564246014/89816329*e^10 + 22166373022/89816329*e^9 + 39666361158/89816329*e^8 - 95987938235/89816329*e^7 - 228584585976/89816329*e^6 + 156941987326/89816329*e^5 + 467884500733/89816329*e^4 - 93572324927/89816329*e^3 - 350718967068/89816329*e^2 + 28701805298/89816329*e + 75079760064/89816329, -40890491/269448987*e^12 - 358517989/269448987*e^11 - 84399708/89816329*e^10 + 5204720405/269448987*e^9 + 11432324590/269448987*e^8 - 18570868784/269448987*e^7 - 63498758962/269448987*e^6 + 7487234768/269448987*e^5 + 115880174924/269448987*e^4 + 39107930147/269448987*e^3 - 56038321858/269448987*e^2 - 16928134321/269448987*e + 368406448/89816329, 760115023/269448987*e^12 + 6410334977/269448987*e^11 + 839685698/89816329*e^10 - 97437446488/269448987*e^9 - 175166965562/269448987*e^8 + 417339876547/269448987*e^7 + 1004417934011/269448987*e^6 - 657838155484/269448987*e^5 - 2027293311220/269448987*e^4 + 350420332079/269448987*e^3 + 1468752119186/269448987*e^2 - 103367817469/269448987*e - 100904611562/89816329, -118331264/269448987*e^12 - 892338028/269448987*e^11 + 157882035/89816329*e^10 + 15554658479/269448987*e^9 + 15524268742/269448987*e^8 - 85989502346/269448987*e^7 - 118343240503/269448987*e^6 + 192172920662/269448987*e^5 + 277869382235/269448987*e^4 - 168460157743/269448987*e^3 - 217983603448/269448987*e^2 + 49903979198/269448987*e + 14792338120/89816329, 279093381/89816329*e^12 + 2345582121/89816329*e^11 + 887317069/89816329*e^10 - 35575580900/89816329*e^9 - 63363705489/89816329*e^8 + 151610341097/89816329*e^7 + 360919587716/89816329*e^6 - 236600394785/89816329*e^5 - 720014909785/89816329*e^4 + 120852876779/89816329*e^3 + 511484853944/89816329*e^2 - 31979887715/89816329*e - 102421267590/89816329, 209896023/89816329*e^12 + 1771113219/89816329*e^11 + 678451804/89816329*e^10 - 27089595714/89816329*e^9 - 48420589101/89816329*e^8 + 117864396182/89816329*e^7 + 280743994743/89816329*e^6 - 192557545363/89816329*e^5 - 575909267448/89816329*e^4 + 113501716491/89816329*e^3 + 428908837592/89816329*e^2 - 36092302748/89816329*e - 90503980986/89816329, 119639368/269448987*e^12 + 1080093347/269448987*e^11 + 333060155/89816329*e^10 - 15000721204/269448987*e^9 - 35980199477/269448987*e^8 + 49602618856/269448987*e^7 + 187265477825/269448987*e^6 - 28282643077/269448987*e^5 - 348540832696/269448987*e^4 - 57511335781/269448987*e^3 + 227340761678/269448987*e^2 + 29310524456/269448987*e - 14236312730/89816329, -361324727/269448987*e^12 - 3062499265/269448987*e^11 - 446654271/89816329*e^10 + 46188504116/269448987*e^9 + 85453554994/269448987*e^8 - 193057834622/269448987*e^7 - 486178545433/269448987*e^6 + 279756734105/269448987*e^5 + 968468217434/269448987*e^4 - 100037183320/269448987*e^3 - 678969668260/269448987*e^2 + 19552838318/269448987*e + 44893511260/89816329, 226168318/89816329*e^12 + 1915096571/89816329*e^11 + 790708227/89816329*e^10 - 29138657950/89816329*e^9 - 53038924800/89816329*e^8 + 124856222939/89816329*e^7 + 305311375435/89816329*e^6 - 194872805144/89816329*e^5 - 618512606301/89816329*e^4 + 98785123912/89816329*e^3 + 448511804515/89816329*e^2 - 28782641884/89816329*e - 93178430724/89816329, 3436480/269448987*e^12 + 4114106/269448987*e^11 - 93137179/89816329*e^10 - 1189134787/269448987*e^9 + 2073070093/269448987*e^8 + 16578284731/269448987*e^7 + 7770029921/269448987*e^6 - 63126720274/269448987*e^5 - 63578577247/269448987*e^4 + 83280607472/269448987*e^3 + 104302514774/269448987*e^2 - 30077010460/269448987*e - 12753320856/89816329, -601616828/269448987*e^12 - 5076975085/269448987*e^11 - 629840936/89816329*e^10 + 78195595391/269448987*e^9 + 139562396332/269448987*e^8 - 344176553657/269448987*e^7 - 822715892830/269448987*e^6 + 562887707789/269448987*e^5 + 1712757499526/269448987*e^4 - 316225642957/269448987*e^3 - 1285658306704/269448987*e^2 + 93786754187/269448987*e + 89724018348/89816329, 79085005/89816329*e^12 + 681108367/89816329*e^11 + 367726451/89816329*e^10 - 10159595977/89816329*e^9 - 19777625784/89816329*e^8 + 41546165884/89816329*e^7 + 110532026690/89816329*e^6 - 58801165851/89816329*e^5 - 218269018025/89816329*e^4 + 21498576838/89816329*e^3 + 153651831070/89816329*e^2 - 4376379884/89816329*e - 32347682584/89816329, -566562244/269448987*e^12 - 4722073298/269448987*e^11 - 423524866/89816329*e^10 + 73922725591/269448987*e^9 + 123976898930/269448987*e^8 - 338571851500/269448987*e^7 - 745978900040/269448987*e^6 + 605370379246/269448987*e^5 + 1580523770938/269448987*e^4 - 421697283695/269448987*e^3 - 1217737442996/269448987*e^2 + 136337822608/269448987*e + 88994994282/89816329, 561942583/269448987*e^12 + 4731782009/269448987*e^11 + 596520940/89816329*e^10 - 72126941329/269448987*e^9 - 128538833300/269448987*e^8 + 310775128222/269448987*e^7 + 739289600279/269448987*e^6 - 493525440478/269448987*e^5 - 1493075971504/269448987*e^4 + 262258221182/269448987*e^3 + 1084397400686/269448987*e^2 - 72689139310/269448987*e - 76371288770/89816329, -224810955/89816329*e^12 - 1892810987/89816329*e^11 - 706699102/89816329*e^10 + 28933853777/89816329*e^9 + 51478056570/89816329*e^8 - 125642731457/89816329*e^7 - 298427107869/89816329*e^6 + 203937479604/89816329*e^5 + 612420478164/89816329*e^4 - 116807778202/89816329*e^3 - 458730509138/89816329*e^2 + 35737443174/89816329*e + 98368281390/89816329, 123134039/89816329*e^12 + 1035934299/89816329*e^11 + 373601880/89816329*e^10 - 15898169700/89816329*e^9 - 28107014226/89816329*e^8 + 69431833413/89816329*e^7 + 163656148310/89816329*e^6 - 112168592423/89816329*e^5 - 333359616664/89816329*e^4 + 62319103512/89816329*e^3 + 241892783676/89816329*e^2 - 20884178560/89816329*e - 50493433002/89816329, -338457922/269448987*e^12 - 2892275054/269448987*e^11 - 465535606/89816329*e^10 + 43562741389/269448987*e^9 + 82579489997/269448987*e^8 - 181724872288/269448987*e^7 - 470482315802/269448987*e^6 + 263448010276/269448987*e^5 + 948551630644/269448987*e^4 - 96346862507/269448987*e^3 - 687798380330/269448987*e^2 + 20325112789/269448987*e + 47902206242/89816329, -227139023/269448987*e^12 - 1845920839/269448987*e^11 - 27764938/89816329*e^10 + 30109678823/269448987*e^9 + 44448965854/269448987*e^8 - 149512134806/269448987*e^7 - 288043467784/269448987*e^6 + 300012059432/269448987*e^5 + 646518679772/269448987*e^4 - 245694723154/269448987*e^3 - 530500511800/269448987*e^2 + 83185381502/269448987*e + 40843997674/89816329, 22109126/269448987*e^12 + 178306027/269448987*e^11 - 34090890/89816329*e^10 - 3717760241/269448987*e^9 - 4312990021/269448987*e^8 + 25751084813/269448987*e^7 + 43839695677/269448987*e^6 - 69374990231/269448987*e^5 - 131750990642/269448987*e^4 + 77322250036/269448987*e^3 + 136356183490/269448987*e^2 - 33298287560/269448987*e - 12256238974/89816329, 135959809/269448987*e^12 + 1146137714/269448987*e^11 + 146890886/89816329*e^10 - 17443526434/269448987*e^9 - 31141175717/269448987*e^8 + 74604162853/269448987*e^7 + 177402689174/269448987*e^6 - 113914218631/269448987*e^5 - 347356231045/269448987*e^4 + 47295266498/269448987*e^3 + 229870313672/269448987*e^2 - 2981985010/269448987*e - 13290327646/89816329, 239758653/89816329*e^12 + 2021513682/89816329*e^11 + 732296863/89816329*e^10 - 31169858935/89816329*e^9 - 55064537922/89816329*e^8 + 138225507200/89816329*e^7 + 323523501896/89816329*e^6 - 234632664020/89816329*e^5 - 673600085634/89816329*e^4 + 151036215303/89816329*e^3 + 511573489516/89816329*e^2 - 49473696060/89816329*e - 110485198404/89816329, 534784858/269448987*e^12 + 4479235514/269448987*e^11 + 482350797/89816329*e^10 - 69263189566/269448987*e^9 - 120223685942/269448987*e^8 + 306844047274/269448987*e^7 + 710204647613/269448987*e^6 - 502127648464/269448987*e^5 - 1461865551334/269448987*e^4 + 271142548289/269448987*e^3 + 1064719546238/269448987*e^2 - 71982806578/269448987*e - 72139850144/89816329, 750298205/269448987*e^12 + 6344722417/269448987*e^11 + 858754234/89816329*e^10 - 96457926491/269448987*e^9 - 174510640804/269448987*e^8 + 413731159241/269448987*e^7 + 1001171737561/269448987*e^6 - 656004107585/269448987*e^5 - 2030561831612/269448987*e^4 + 354477268144/269448987*e^3 + 1491268142572/269448987*e^2 - 106147676018/269448987*e - 104191129520/89816329, 243781370/269448987*e^12 + 2088823804/269448987*e^11 + 391174907/89816329*e^10 - 30436178900/269448987*e^9 - 60196512847/269448987*e^8 + 116520085490/269448987*e^7 + 324133690354/269448987*e^6 - 134765807396/269448987*e^5 - 606452364587/269448987*e^4 - 6194332796/269448987*e^3 + 388024665442/269448987*e^2 + 23548756870/269448987*e - 24094655468/89816329, -1057324054/269448987*e^12 - 9011934755/269448987*e^11 - 1370675032/89816329*e^10 + 136518410860/269448987*e^9 + 254428562180/269448987*e^8 - 579445495129/269448987*e^7 - 1457690007956/269448987*e^6 + 889368434203/269448987*e^5 + 2956836415336/269448987*e^4 - 430769639168/269448987*e^3 - 2157206084636/269448987*e^2 + 121252677151/269448987*e + 147603254612/89816329, -38882897/89816329*e^12 - 322385207/89816329*e^11 - 78623942/89816329*e^10 + 5052658873/89816329*e^9 + 8405803599/89816329*e^8 - 23144325682/89816329*e^7 - 51284091518/89816329*e^6 + 40864779205/89816329*e^5 + 112047736268/89816329*e^4 - 25591243743/89816329*e^3 - 92976228278/89816329*e^2 + 5342111558/89816329*e + 21719956352/89816329, 433629490/269448987*e^12 + 3611784611/269448987*e^11 + 381574466/89816329*e^10 - 55135938343/269448987*e^9 - 94706329874/269448987*e^8 + 239147466955/269448987*e^7 + 543719048456/269448987*e^6 - 392142644437/269448987*e^5 - 1094505546019/269448987*e^4 + 236803734074/269448987*e^3 + 796381767539/269448987*e^2 - 75297040678/269448987*e - 56130014130/89816329, 745452002/269448987*e^12 + 6284799508/269448987*e^11 + 781959780/89816329*e^10 - 96331323122/269448987*e^9 - 171041555857/269448987*e^8 + 421534640297/269448987*e^7 + 993361650013/269448987*e^6 - 698560718303/269448987*e^5 - 2039942221862/269448987*e^4 + 426349476013/269448987*e^3 + 1521713566096/269448987*e^2 - 137636496329/269448987*e - 108639546476/89816329, 45409097/89816329*e^12 + 368856773/89816329*e^11 + 40687462/89816329*e^10 - 5840597178/89816329*e^9 - 8955046465/89816329*e^8 + 27371343553/89816329*e^7 + 55276793988/89816329*e^6 - 50984072969/89816329*e^5 - 119950235128/89816329*e^4 + 39405835147/89816329*e^3 + 97998839191/89816329*e^2 - 15535867516/89816329*e - 22730872922/89816329, 266239906/269448987*e^12 + 2255713172/269448987*e^11 + 299312192/89816329*e^10 - 34538984845/269448987*e^9 - 61781993702/269448987*e^8 + 152320355251/269448987*e^7 + 357365912714/269448987*e^6 - 268064382427/269448987*e^5 - 746126870719/269448987*e^4 + 200773855757/269448987*e^3 + 588704795084/269448987*e^2 - 68093402572/269448987*e - 45008854594/89816329, 715053256/269448987*e^12 + 6124241165/269448987*e^11 + 1048881319/89816329*e^10 - 91367159929/269448987*e^9 - 176095884818/269448987*e^8 + 372278997544/269448987*e^7 + 987351038489/269448987*e^6 - 511946187793/269448987*e^5 - 1947985765462/269448987*e^4 + 151779406658/269448987*e^3 + 1355940213692/269448987*e^2 - 26984445868/269448987*e - 87779415552/89816329, -449428874/269448987*e^12 - 3796577770/269448987*e^11 - 514465167/89816329*e^10 + 57617800643/269448987*e^9 + 104815456405/269448987*e^8 - 243725611244/269448987*e^7 - 600345644095/269448987*e^6 + 356965366205/269448987*e^5 + 1188434630141/269448987*e^4 - 126526240648/269448987*e^3 - 805059923773/269448987*e^2 + 21136247576/269448987*e + 49553945028/89816329, -38023940/269448987*e^12 - 316567114/269448987*e^11 - 70113621/89816329*e^10 + 3909919835/269448987*e^9 + 7738388023/269448987*e^8 - 8941821410/269448987*e^7 - 24382425613/269448987*e^6 - 468104293/269448987*e^5 + 5410133078/269448987*e^4 + 10099186433/269448987*e^3 + 32831192246/269448987*e^2 - 10039469524/269448987*e - 4883963254/89816329, -660992758/269448987*e^12 - 5640841964/269448987*e^11 - 883140581/89816329*e^10 + 85238189938/269448987*e^9 + 160471362731/269448987*e^8 - 358429916245/269448987*e^7 - 918880568717/269448987*e^6 + 529827034099/269448987*e^5 + 1859520913264/269448987*e^4 - 213325282385/269448987*e^3 - 1344650688758/269448987*e^2 + 50191204126/269448987*e + 90810922856/89816329, 618766583/269448987*e^12 + 5206832185/269448987*e^11 + 556922631/89816329*e^10 - 81562113215/269448987*e^9 - 141414735145/269448987*e^8 + 372841559099/269448987*e^7 + 855883476433/269448987*e^6 - 654388504277/269448987*e^5 - 1827732888182/269448987*e^4 + 433211604586/269448987*e^3 + 1413677850400/269448987*e^2 - 146597749676/269448987*e - 102843077074/89816329, 246410738/269448987*e^12 + 2068826734/269448987*e^11 + 238397195/89816329*e^10 - 31682172167/269448987*e^9 - 54774852610/269448987*e^8 + 139859797307/269448987*e^7 + 313573007905/269448987*e^6 - 247124365181/269448987*e^5 - 638849182601/269448987*e^4 + 185792511871/269448987*e^3 + 481967640058/269448987*e^2 - 69222459422/269448987*e - 34892041462/89816329, -1127079940/269448987*e^12 - 9604480244/269448987*e^11 - 1515798589/89816329*e^10 + 144080558674/269448987*e^9 + 270594698174/269448987*e^8 - 597688183813/269448987*e^7 - 1520402629637/269448987*e^6 + 876905284747/269448987*e^5 + 3005101910668/269448987*e^4 - 371036458730/269448987*e^3 - 2108248537958/269448987*e^2 + 93896511280/269448987*e + 139307349872/89816329, 909974428/269448987*e^12 + 7658358107/269448987*e^11 + 920862986/89816329*e^10 - 117699272122/269448987*e^9 - 208446551117/269448987*e^8 + 514931129875/269448987*e^7 + 1218923056208/269448987*e^6 - 828062184403/269448987*e^5 - 2491156169677/269448987*e^4 + 440332120874/269448987*e^3 + 1804444389710/269448987*e^2 - 129283244485/269448987*e - 123614696578/89816329, -2255537/89816329*e^12 - 39237108/89816329*e^11 - 149715211/89816329*e^10 + 380729881/89816329*e^9 + 2676201163/89816329*e^8 + 363178339/89816329*e^7 - 12338840129/89816329*e^6 - 6002161414/89816329*e^5 + 23224578043/89816329*e^4 + 10034655475/89816329*e^3 - 17675790710/89816329*e^2 - 4465401436/89816329*e + 1825047484/89816329, 9540399/89816329*e^12 + 63344581/89816329*e^11 - 103872976/89816329*e^10 - 1239662747/89816329*e^9 - 148320322/89816329*e^8 + 8704498221/89816329*e^7 + 4772854079/89816329*e^6 - 29619699052/89816329*e^5 - 22292273558/89816329*e^4 + 44972056117/89816329*e^3 + 37117753280/89816329*e^2 - 19449056750/89816329*e - 12660514658/89816329, 523802611/269448987*e^12 + 4356007466/269448987*e^11 + 400229609/89816329*e^10 - 67536295105/269448987*e^9 - 113246699219/269448987*e^8 + 303836077513/269448987*e^7 + 667722780497/269448987*e^6 - 534912706426/269448987*e^5 - 1388287344367/269448987*e^4 + 373210969493/269448987*e^3 + 1055777170724/269448987*e^2 - 124486028092/269448987*e - 76676380726/89816329, 769091851/269448987*e^12 + 6498265283/269448987*e^11 + 843751767/89816329*e^10 - 99233861398/269448987*e^9 - 177004348091/269448987*e^8 + 432690124408/269448987*e^7 + 1017705499094/269448987*e^6 - 728318405602/269448987*e^5 - 2081246503936/269448987*e^4 + 477662955185/269448987*e^3 + 1565064431603/269448987*e^2 - 152197551616/269448987*e - 112795248018/89816329, 401455555/269448987*e^12 + 3387661919/269448987*e^11 + 401131678/89816329*e^10 - 52679570506/269448987*e^9 - 93743717717/269448987*e^8 + 235009150699/269448987*e^7 + 564105839891/269448987*e^6 - 379276710280/269448987*e^5 - 1187271591103/269448987*e^4 + 186584330345/269448987*e^3 + 884879787776/269448987*e^2 - 48355462822/269448987*e - 62411835728/89816329, 69130598/89816329*e^12 + 584970979/89816329*e^11 + 255035416/89816329*e^10 - 8834484566/89816329*e^9 - 16608270428/89816329*e^8 + 36189836466/89816329*e^7 + 96147915634/89816329*e^6 - 43443731799/89816329*e^5 - 190360535882/89816329*e^4 - 6906032811/89816329*e^3 + 126340716674/89816329*e^2 + 8145353511/89816329*e - 23444194302/89816329, 160900996/89816329*e^12 + 1351088250/89816329*e^11 + 473468797/89816329*e^10 - 20752517708/89816329*e^9 - 36581891263/89816329*e^8 + 90507442160/89816329*e^7 + 213806597500/89816329*e^6 - 143335965494/89816329*e^5 - 435326169895/89816329*e^4 + 70559143655/89816329*e^3 + 312120097288/89816329*e^2 - 18698228262/89816329*e - 62705947584/89816329, 41997668/269448987*e^12 + 341943940/269448987*e^11 - 16090792/89816329*e^10 - 6017836706/269448987*e^9 - 7717889488/269448987*e^8 + 34940943431/269448987*e^7 + 55588754068/269448987*e^6 - 91093857137/269448987*e^5 - 136472962337/269448987*e^4 + 110519180719/269448987*e^3 + 120074284090/269448987*e^2 - 51045871934/269448987*e - 10737132388/89816329, -233485756/269448987*e^12 - 1935812309/269448987*e^11 - 195721725/89816329*e^10 + 29379317539/269448987*e^9 + 49982499512/269448987*e^8 - 125766320578/269448987*e^7 - 282978339896/269448987*e^6 + 202168545424/269448987*e^5 + 558727072063/269448987*e^4 - 121140784361/269448987*e^3 - 399559382708/269448987*e^2 + 46541072749/269448987*e + 29103364816/89816329, -606630925/269448987*e^12 - 5119180160/269448987*e^11 - 656157413/89816329*e^10 + 78366096295/269448987*e^9 + 140879550542/269448987*e^8 - 339472853107/269448987*e^7 - 821532351512/269448987*e^6 + 532530020317/269448987*e^5 + 1682108161768/269448987*e^4 - 256259386526/269448987*e^3 - 1227503837846/269448987*e^2 + 60113119375/269448987*e + 83727366766/89816329, -81934817/89816329*e^12 - 687313344/89816329*e^11 - 220866815/89816329*e^10 + 10653273586/89816329*e^9 + 18320675898/89816329*e^8 - 47921705782/89816329*e^7 - 107930529748/89816329*e^6 + 84263849129/89816329*e^5 + 224616337517/89816329*e^4 - 57886758291/89816329*e^3 - 170246015350/89816329*e^2 + 17666686713/89816329*e + 36073255242/89816329, 441924449/269448987*e^12 + 3814330066/269448987*e^11 + 726978582/89816329*e^10 - 56310100721/269448987*e^9 - 111463746805/269448987*e^8 + 224768083160/269448987*e^7 + 613342070815/269448987*e^6 - 304530243299/269448987*e^5 - 1196111996801/269448987*e^4 + 101275501114/269448987*e^3 + 832919414584/269448987*e^2 - 31276108364/269448987*e - 53669742424/89816329, -186712124/89816329*e^12 - 1575778220/89816329*e^11 - 614573499/89816329*e^10 + 23978705300/89816329*e^9 + 42686741879/89816329*e^8 - 104145386582/89816329*e^7 - 243828974572/89816329*e^6 + 177605659217/89816329*e^5 + 500131873154/89816329*e^4 - 124167933779/89816329*e^3 - 385111827193/89816329*e^2 + 42690225200/89816329*e + 83993660514/89816329, -152414145/89816329*e^12 - 1287332458/89816329*e^11 - 541440620/89816329*e^10 + 19329741482/89816329*e^9 + 35014561048/89816329*e^8 - 81048757392/89816329*e^7 - 195000264322/89816329*e^6 + 127201779430/89816329*e^5 + 383594605261/89816329*e^4 - 72730755277/89816329*e^3 - 274226137916/89816329*e^2 + 21652376018/89816329*e + 56787083286/89816329, -586435808/269448987*e^12 - 5037087718/269448987*e^11 - 899036398/89816329*e^10 + 74781215864/269448987*e^9 + 145075084240/269448987*e^8 - 303467417336/269448987*e^7 - 804376459936/269448987*e^6 + 432819184445/269448987*e^5 + 1588013331329/269448987*e^4 - 179762840632/269448987*e^3 - 1137536546272/269448987*e^2 + 48592513448/269448987*e + 78168704468/89816329, -133758076/89816329*e^12 - 1147585393/89816329*e^11 - 657565764/89816329*e^10 + 16663538051/89816329*e^9 + 33028949365/89816329*e^8 - 63605865642/89816329*e^7 - 176168166337/89816329*e^6 + 76457856294/89816329*e^5 + 328210989369/89816329*e^4 - 10034134616/89816329*e^3 - 212396244044/89816329*e^2 + 875057207/89816329*e + 36832627310/89816329, 94867631/89816329*e^12 + 811152696/89816329*e^11 + 420280732/89816329*e^10 - 11990819000/89816329*e^9 - 22923599778/89816329*e^8 + 48679072382/89816329*e^7 + 125647799882/89816329*e^6 - 73991155018/89816329*e^5 - 249688040965/89816329*e^4 + 43703478149/89816329*e^3 + 188701664592/89816329*e^2 - 15514435522/89816329*e - 41963400060/89816329, 331404101/269448987*e^12 + 2795407411/269448987*e^11 + 360616677/89816329*e^10 - 42595089854/269448987*e^9 - 76188760795/269448987*e^8 + 183469813160/269448987*e^7 + 437185847923/269448987*e^6 - 291299314982/269448987*e^5 - 878950344650/269448987*e^4 + 151841831317/269448987*e^3 + 627692563318/269448987*e^2 - 38664145979/269448987*e - 43222969006/89816329, -58486655/269448987*e^12 - 460928536/269448987*e^11 + 20558774/89816329*e^10 + 7457942660/269448987*e^9 + 9366835615/269448987*e^8 - 36732066572/269448987*e^7 - 56351420422/269448987*e^6 + 75043419449/269448987*e^5 + 105103546583/269448987*e^4 - 65809087789/269448987*e^3 - 56041286389/269448987*e^2 + 27878885084/269448987*e + 3457133444/89816329, 219141898/269448987*e^12 + 1853112866/269448987*e^11 + 196784075/89816329*e^10 - 29441270377/269448987*e^9 - 51227856860/269448987*e^8 + 138025786159/269448987*e^7 + 318754515611/269448987*e^6 - 247330192822/269448987*e^5 - 699746392321/269448987*e^4 + 163453987424/269448987*e^3 + 559794491228/269448987*e^2 - 56009266447/269448987*e - 43203623004/89816329, -817083455/269448987*e^12 - 6957560836/269448987*e^11 - 1100839628/89816329*e^10 + 104073815240/269448987*e^9 + 195403200094/269448987*e^8 - 429177656321/269448987*e^7 - 1091119342075/269448987*e^6 + 625657791533/269448987*e^5 + 2142187523234/269448987*e^4 - 265242757390/269448987*e^3 - 1494943303540/269448987*e^2 + 70734445526/269448987*e + 97827892270/89816329, -92421492/89816329*e^12 - 778024580/89816329*e^11 - 317358672/89816329*e^10 + 11657662815/89816329*e^9 + 21038194946/89816329*e^8 - 48163540797/89816329*e^7 - 116314147663/89816329*e^6 + 69715304058/89816329*e^5 + 219390743461/89816329*e^4 - 27283044835/89816329*e^3 - 136395494998/89816329*e^2 + 7059821205/89816329*e + 21898590916/89816329, -319072241/269448987*e^12 - 2691066958/269448987*e^11 - 348679663/89816329*e^10 + 41080250063/269448987*e^9 + 74209271734/269448987*e^8 - 176075132402/269448987*e^7 - 431115304552/269448987*e^6 + 264917328791/269448987*e^5 + 869794202033/269448987*e^4 - 104601915331/269448987*e^3 - 603907615870/269448987*e^2 + 19078647860/269448987*e + 38174312334/89816329, -945684991/269448987*e^12 - 7956841415/269448987*e^11 - 971697656/89816329*e^10 + 121817551372/269448987*e^9 + 215755393877/269448987*e^8 - 531552446527/269448987*e^7 - 1253652813122/269448987*e^6 + 876550967728/269448987*e^5 + 2584325469661/269448987*e^4 - 529543998491/269448987*e^3 - 1949774823314/269448987*e^2 + 170016011824/269448987*e + 140653021220/89816329, 119148462/89816329*e^12 + 1010757238/89816329*e^11 + 457183580/89816329*e^10 - 15154174469/89816329*e^9 - 28227654861/89816329*e^8 + 62363801777/89816329*e^7 + 158432575596/89816329*e^6 - 86750874329/89816329*e^5 - 308163899731/89816329*e^4 + 25609182204/89816329*e^3 + 206322044768/89816329*e^2 - 3856778186/89816329*e - 37594315782/89816329, -406351622/269448987*e^12 - 3414490933/269448987*e^11 - 387653893/89816329*e^10 + 52777115420/269448987*e^9 + 92382826027/269448987*e^8 - 234309100676/269448987*e^7 - 545476430878/269448987*e^6 + 391039240259/269448987*e^5 + 1130468725910/269448987*e^4 - 235011392464/269448987*e^3 - 838644149803/269448987*e^2 + 76603634252/269448987*e + 59071426534/89816329, -84942793/269448987*e^12 - 748460381/269448987*e^11 - 191409423/89816329*e^10 + 10388305258/269448987*e^9 + 22054226075/269448987*e^8 - 36581381770/269448987*e^7 - 104998491257/269448987*e^6 + 47527192327/269448987*e^5 + 175549818667/269448987*e^4 - 27403087211/269448987*e^3 - 106114639094/269448987*e^2 + 2325014191/269448987*e + 4955822132/89816329, 255897101/269448987*e^12 + 2157262765/269448987*e^11 + 253341925/89816329*e^10 - 33371706170/269448987*e^9 - 58541122861/269448987*e^8 + 148982580620/269448987*e^7 + 344825950780/269448987*e^6 - 254649901394/269448987*e^5 - 716300964812/269448987*e^4 + 161871451081/269448987*e^3 + 534181172158/269448987*e^2 - 52547356514/269448987*e - 36785686700/89816329, -52817872/89816329*e^12 - 458913937/89816329*e^11 - 281101771/89816329*e^10 + 6764297051/89816329*e^9 + 13700228700/89816329*e^8 - 27052849296/89816329*e^7 - 76061871931/89816329*e^6 + 38164967719/89816329*e^5 + 154165311960/89816329*e^4 - 17289488075/89816329*e^3 - 118264496120/89816329*e^2 + 7672543466/89816329*e + 26085749932/89816329, 324798107/269448987*e^12 + 2656977946/269448987*e^11 + 102652659/89816329*e^10 - 42637577777/269448987*e^9 - 65472008935/269448987*e^8 + 205529030837/269448987*e^7 + 411809640085/269448987*e^6 - 398135161346/269448987*e^5 - 908911538660/269448987*e^4 + 311398932121/269448987*e^3 + 746194795648/269448987*e^2 - 102848955971/269448987*e - 58880024526/89816329, 107556880/89816329*e^12 + 942653422/89816329*e^11 + 666042041/89816329*e^10 - 13524363132/89816329*e^9 - 28718062825/89816329*e^8 + 50346467644/89816329*e^7 + 152338942168/89816329*e^6 - 59352683199/89816329*e^5 - 290966790207/89816329*e^4 + 11506437394/89816329*e^3 + 204240610758/89816329*e^2 - 4285110126/89816329*e - 42024143282/89816329, 89462812/269448987*e^12 + 820045103/269448987*e^11 + 285235762/89816329*e^10 - 11088352234/269448987*e^9 - 28108373972/269448987*e^8 + 33463164349/269448987*e^7 + 140296464428/269448987*e^6 - 6805662154/269448987*e^5 - 242799555847/269448987*e^4 - 57263874769/269448987*e^3 + 129619492514/269448987*e^2 + 17553507272/269448987*e - 2771258702/89816329, -843909779/269448987*e^12 - 7066768729/269448987*e^11 - 749047397/89816329*e^10 + 109292568698/269448987*e^9 + 187957955425/269448987*e^8 - 488226072713/269448987*e^7 - 1105048773961/269448987*e^6 + 841897127618/269448987*e^5 + 2289556753892/269448987*e^4 - 556111928686/269448987*e^3 - 1726004143600/269448987*e^2 + 175700737190/269448987*e + 124142972224/89816329, -287106374/89816329*e^12 - 2424800749/89816329*e^11 - 944847366/89816329*e^10 + 37065561258/89816329*e^9 + 66578340089/89816329*e^8 - 160748933984/89816329*e^7 - 386110130539/89816329*e^6 + 258483778173/89816329*e^5 + 790606313613/89816329*e^4 - 142612639206/89816329*e^3 - 584314087846/89816329*e^2 + 43416309896/89816329*e + 121845551738/89816329, 464027662/269448987*e^12 + 4034964389/269448987*e^11 + 815025245/89816329*e^10 - 59805665416/269448987*e^9 - 121168709108/269448987*e^8 + 239290626799/269448987*e^7 + 677174066771/269448987*e^6 - 311066022589/269448987*e^5 - 1339788077467/269448987*e^4 + 66325227551/269448987*e^3 + 941144126615/269448987*e^2 - 17009384902/269448987*e - 62643371498/89816329, -243640270/269448987*e^12 - 1931414624/269448987*e^11 + 78000805/89816329*e^10 + 31842198490/269448987*e^9 + 41780842442/269448987*e^8 - 162419638882/269448987*e^7 - 275145852575/269448987*e^6 + 347100025606/269448987*e^5 + 622626769951/269448987*e^4 - 316078602821/269448987*e^3 - 525426961316/269448987*e^2 + 103035975601/269448987*e + 43309531426/89816329, -15979343/269448987*e^12 - 108732730/269448987*e^11 + 15039438/89816329*e^10 + 1185949616/269448987*e^9 + 115515034/269448987*e^8 - 2435061794/269448987*e^7 + 11963950967/269448987*e^6 + 12757060337/269448987*e^5 - 43368596545/269448987*e^4 - 44599007227/269448987*e^3 + 29337499598/269448987*e^2 + 31332664124/269448987*e - 2910308864/89816329, -1221096980/269448987*e^12 - 10291826350/269448987*e^11 - 1272732307/89816329*e^10 + 157722871988/269448987*e^9 + 279310812673/269448987*e^8 - 690791023580/269448987*e^7 - 1619480236030/269448987*e^6 + 1152981041651/269448987*e^5 + 3325136780933/269448987*e^4 - 718004936416/269448987*e^3 - 2491497684886/269448987*e^2 + 222631655699/269448987*e + 177970572220/89816329, -104089993/89816329*e^12 - 889493413/89816329*e^11 - 427163502/89816329*e^10 + 13416418950/89816329*e^9 + 25330004137/89816329*e^8 - 56629395515/89816329*e^7 - 144799467176/89816329*e^6 + 88134463283/89816329*e^5 + 298092681034/89816329*e^4 - 47350958264/89816329*e^3 - 227811926016/89816329*e^2 + 13351736154/89816329*e + 48879503652/89816329, 104050650/89816329*e^12 + 837429692/89816329*e^11 + 909006/89816329*e^10 - 13613213182/89816329*e^9 - 19637943247/89816329*e^8 + 66585260211/89816329*e^7 + 126658376179/89816329*e^6 - 126470866119/89816329*e^5 - 275723846293/89816329*e^4 + 88935777480/89816329*e^3 + 210973765522/89816329*e^2 - 25898851468/89816329*e - 47548109860/89816329, 537626108/269448987*e^12 + 4629575977/269448987*e^11 + 831626049/89816329*e^10 - 69247703984/269448987*e^9 - 135545943343/269448987*e^8 + 283774109573/269448987*e^7 + 767830286020/269448987*e^6 - 393961260293/269448987*e^5 - 1543510450544/269448987*e^4 + 123527414962/269448987*e^3 + 1109619112492/269448987*e^2 - 22468402991/269448987*e - 74120558508/89816329];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {41, 41, w^4 - w^3 - 5*w^2 + 3*w + 3}>] := -1;

// EXAMPLE:
// pp := Factorization(2*ZF)[1][1];
// heckeEigenvalues[pp];

print "To reconstruct the Hilbert newform f, type
  f, iso := Explode(make_newform());";

function make_newform();
 M := HilbertCuspForms(F, NN);
 S := NewSubspace(M);
 // SetVerbose("ModFrmHil", 1);
 NFD := NewformDecomposition(S);
 newforms := [* Eigenform(U) : U in NFD *];

 if #newforms eq 0 then;
  print "No Hilbert newforms at this level";
  return 0;
 end if;

 print "Testing ", #newforms, " possible newforms";
 newforms := [* f: f in newforms | IsIsomorphic(BaseField(f), K) *];
 print #newforms, " newforms have the correct Hecke field";

 if #newforms eq 0 then;
  print "No Hilbert newform found with the correct Hecke field";
  return 0;
 end if;

 autos := Automorphisms(K);
 xnewforms := [* *];
 for f in newforms do;
  if K eq RationalField() then;
   Append(~xnewforms, [* f, autos[1] *]);
  else;
   flag, iso := IsIsomorphic(K,BaseField(f));
   for a in autos do;
    Append(~xnewforms, [* f, a*iso *]);
   end for;
  end if;
 end for;
 newforms := xnewforms;

 for P in primes do;
  xnewforms := [* *];
  for f_iso in newforms do;
   f, iso := Explode(f_iso);
   if HeckeEigenvalue(f,P) eq iso(heckeEigenvalues[P]) then;
    Append(~xnewforms, f_iso);
   end if;
  end for;
  newforms := xnewforms;
  if #newforms eq 0 then;
   print "No Hilbert newform found which matches the Hecke eigenvalues";
   return 0;
  else if #newforms eq 1 then;
   print "success: unique match";
   return newforms[1];
  end if;
  end if;
 end for;
 print #newforms, "Hilbert newforms found which match the Hecke eigenvalues";
 return newforms[1];

end function;