/*
  This code can be loaded, or copied and paste using cpaste, into Sage.
  It will load the data associated to the HMF, including
  the field, level, and Hecke and Atkin-Lehner eigenvalue data.
*/

P.<x> = PolynomialRing(QQ)
g = P([-1, 0, 8, 4, -6, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([59, 59, -w^5 + w^4 + 5*w^3 - 3*w^2 - 4*w - 2])

primes_array = [
[5, 5, w - 1],\
[11, 11, w^3 - 3*w],\
[19, 19, -w^5 + w^4 + 5*w^3 - 4*w^2 - 5*w],\
[25, 5, w^5 - 2*w^4 - 6*w^3 + 8*w^2 + 8*w],\
[29, 29, -w^4 + 4*w^2 + 1],\
[31, 31, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 3*w - 4],\
[31, 31, -w^2 + 2],\
[59, 59, -w^5 + w^4 + 5*w^3 - 3*w^2 - 4*w - 2],\
[59, 59, w^4 - w^3 - 5*w^2 + 3*w + 4],\
[59, 59, -w^4 - w^3 + 4*w^2 + 5*w],\
[61, 61, w^5 - w^4 - 4*w^3 + 5*w^2 - 4],\
[64, 2, 2],\
[71, 71, w^5 - w^4 - 6*w^3 + 4*w^2 + 6*w],\
[71, 71, -w^5 + 2*w^4 + 4*w^3 - 9*w^2 + w + 4],\
[71, 71, 2*w^5 - 3*w^4 - 9*w^3 + 13*w^2 + 4*w - 4],\
[71, 71, w^3 - 5*w],\
[79, 79, w^5 - w^4 - 4*w^3 + 4*w^2 + w - 2],\
[89, 89, w^3 - w^2 - 4*w + 1],\
[101, 101, -2*w^5 + 3*w^4 + 11*w^3 - 13*w^2 - 12*w + 2],\
[101, 101, 2*w^5 - 2*w^4 - 13*w^3 + 7*w^2 + 20*w + 4],\
[101, 101, w^5 - w^4 - 5*w^3 + 5*w^2 + 2*w - 3],\
[101, 101, w^5 - 2*w^4 - 6*w^3 + 9*w^2 + 8*w - 1],\
[109, 109, -w^5 + w^4 + 7*w^3 - 4*w^2 - 11*w - 1],\
[121, 11, -w^5 + w^4 + 4*w^3 - 5*w^2 + w + 4],\
[131, 131, w^4 - 4*w^2 + w - 1],\
[131, 131, -2*w^5 + 2*w^4 + 10*w^3 - 9*w^2 - 7*w + 2],\
[139, 139, w^4 + w^3 - 3*w^2 - 4*w - 4],\
[149, 149, -w^5 + 3*w^4 + 6*w^3 - 13*w^2 - 8*w + 2],\
[149, 149, 2*w^5 - 11*w^3 - 2*w^2 + 11*w + 6],\
[151, 151, 3*w^5 - 5*w^4 - 16*w^3 + 21*w^2 + 16*w - 6],\
[169, 13, w^5 - 3*w^4 - 5*w^3 + 13*w^2 + 6*w - 3],\
[179, 179, w^5 - 2*w^4 - 7*w^3 + 9*w^2 + 12*w - 1],\
[179, 179, 2*w^5 - 4*w^4 - 9*w^3 + 18*w^2 + 4*w - 7],\
[179, 179, -3*w^5 + 3*w^4 + 15*w^3 - 13*w^2 - 12*w + 3],\
[179, 179, -w^5 + 3*w^4 + 5*w^3 - 14*w^2 - 5*w + 6],\
[181, 181, w^3 + w^2 - 4*w - 6],\
[191, 191, -w^5 + w^4 + 4*w^3 - 5*w^2 + w + 3],\
[191, 191, -w^5 + w^4 + 6*w^3 - 4*w^2 - 7*w + 3],\
[191, 191, -w^5 + 2*w^4 + 4*w^3 - 9*w^2 - w + 3],\
[191, 191, -w^5 + w^4 + 7*w^3 - 4*w^2 - 12*w - 2],\
[199, 199, w^5 - w^4 - 6*w^3 + 4*w^2 + 9*w - 1],\
[199, 199, w^4 + w^3 - 5*w^2 - 3*w + 3],\
[199, 199, -w^5 + w^4 + 3*w^3 - 4*w^2 + 3*w + 2],\
[199, 199, w^2 + w - 3],\
[211, 211, 3*w^5 - 4*w^4 - 16*w^3 + 17*w^2 + 16*w - 3],\
[239, 239, -3*w^5 + 3*w^4 + 16*w^3 - 12*w^2 - 16*w + 3],\
[239, 239, 4*w^5 - 6*w^4 - 21*w^3 + 25*w^2 + 19*w - 5],\
[239, 239, -w^5 + w^4 + 7*w^3 - 5*w^2 - 10*w + 2],\
[241, 241, w^5 - 2*w^4 - 5*w^3 + 8*w^2 + 4*w + 2],\
[251, 251, 3*w^5 - 4*w^4 - 16*w^3 + 18*w^2 + 15*w - 5],\
[251, 251, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 6*w - 2],\
[251, 251, -3*w^5 + 4*w^4 + 16*w^3 - 17*w^2 - 15*w + 2],\
[251, 251, -w^5 + 2*w^4 + 4*w^3 - 9*w^2 - w + 4],\
[269, 269, w^5 - w^4 - 6*w^3 + 6*w^2 + 7*w - 5],\
[271, 271, 3*w^5 - 3*w^4 - 15*w^3 + 12*w^2 + 11*w - 1],\
[271, 271, -w^5 + 2*w^4 + 5*w^3 - 8*w^2 - 2*w],\
[281, 281, w^2 - w - 4],\
[281, 281, -3*w^5 + 4*w^4 + 16*w^3 - 18*w^2 - 14*w + 4],\
[281, 281, w^5 - w^4 - 6*w^3 + 4*w^2 + 9*w],\
[281, 281, -3*w^5 + 3*w^4 + 14*w^3 - 13*w^2 - 8*w + 4],\
[289, 17, 2*w^5 - 2*w^4 - 11*w^3 + 8*w^2 + 10*w - 1],\
[311, 311, -w^5 - w^4 + 6*w^3 + 6*w^2 - 8*w - 5],\
[311, 311, -2*w^5 + 3*w^4 + 10*w^3 - 13*w^2 - 8*w + 7],\
[331, 331, 2*w^5 - 3*w^4 - 11*w^3 + 12*w^2 + 12*w - 4],\
[331, 331, -3*w^5 + 4*w^4 + 15*w^3 - 16*w^2 - 12*w + 3],\
[331, 331, -w^5 + w^4 + 4*w^3 - 3*w^2 + w - 1],\
[331, 331, -2*w^5 + 5*w^4 + 10*w^3 - 21*w^2 - 8*w + 5],\
[359, 359, 2*w^4 - 2*w^3 - 9*w^2 + 7*w + 3],\
[361, 19, -w^4 + 2*w^3 + 4*w^2 - 6*w - 2],\
[379, 379, 3*w^5 - 2*w^4 - 15*w^3 + 8*w^2 + 11*w - 1],\
[379, 379, 2*w^5 - 2*w^4 - 11*w^3 + 8*w^2 + 13*w - 3],\
[389, 389, w^5 + w^4 - 5*w^3 - 5*w^2 + 3*w + 4],\
[389, 389, 3*w^5 - 5*w^4 - 16*w^3 + 21*w^2 + 16*w - 5],\
[389, 389, -w^5 + 4*w^4 + 5*w^3 - 17*w^2 - 4*w + 4],\
[389, 389, 3*w^5 - 4*w^4 - 15*w^3 + 18*w^2 + 10*w - 6],\
[401, 401, w^5 - 2*w^4 - 6*w^3 + 7*w^2 + 8*w + 3],\
[401, 401, -2*w^5 + 4*w^4 + 11*w^3 - 17*w^2 - 13*w + 3],\
[409, 409, w^3 + w^2 - 3*w - 5],\
[419, 419, -w^5 + w^4 + 4*w^3 - 6*w^2 + 4],\
[419, 419, -w^4 + 2*w^3 + 5*w^2 - 8*w - 6],\
[421, 421, w^5 - w^4 - 5*w^3 + 5*w^2 + 3*w - 6],\
[431, 431, 2*w^3 + w^2 - 9*w - 3],\
[439, 439, -w^5 + 6*w^3 + w^2 - 6*w - 4],\
[439, 439, w^5 - 2*w^4 - 4*w^3 + 9*w^2 - 7],\
[439, 439, 3*w^5 - 5*w^4 - 16*w^3 + 21*w^2 + 14*w - 4],\
[439, 439, -2*w^5 + 3*w^4 + 11*w^3 - 11*w^2 - 13*w - 1],\
[439, 439, w^4 - w^3 - 3*w^2 + 3*w - 3],\
[439, 439, -3*w^5 + 4*w^4 + 16*w^3 - 16*w^2 - 17*w + 2],\
[449, 449, -w^3 - 2*w^2 + 5*w + 6],\
[461, 461, w^5 - w^4 - 6*w^3 + 3*w^2 + 10*w + 1],\
[479, 479, 3*w^5 - 5*w^4 - 16*w^3 + 21*w^2 + 15*w - 2],\
[491, 491, w^5 - w^4 - 6*w^3 + 3*w^2 + 10*w + 2],\
[499, 499, w^5 - 5*w^3 - 2*w^2 + 4*w + 4],\
[509, 509, -w^5 + 2*w^4 + 5*w^3 - 10*w^2 - 4*w + 4],\
[509, 509, -w^5 + w^4 + 6*w^3 - 6*w^2 - 7*w + 4],\
[521, 521, -3*w^5 + 5*w^4 + 16*w^3 - 22*w^2 - 14*w + 5],\
[541, 541, -w^4 + w^3 + 5*w^2 - 2*w - 5],\
[541, 541, 2*w^5 - 3*w^4 - 9*w^3 + 14*w^2 + 4*w - 5],\
[541, 541, -2*w^5 + 3*w^4 + 9*w^3 - 13*w^2 - 2*w + 4],\
[569, 569, 2*w^5 - w^4 - 11*w^3 + 5*w^2 + 11*w - 3],\
[571, 571, w^5 - w^4 - 6*w^3 + 2*w^2 + 8*w + 4],\
[571, 571, 3*w^5 - 5*w^4 - 15*w^3 + 22*w^2 + 10*w - 7],\
[599, 599, -w^4 + w^3 + 3*w^2 - 4*w],\
[599, 599, -w^4 + 6*w^2 + w - 4],\
[601, 601, -2*w^5 + 3*w^4 + 10*w^3 - 12*w^2 - 7*w + 4],\
[619, 619, -3*w^5 + 4*w^4 + 15*w^3 - 16*w^2 - 11*w + 2],\
[631, 631, w^4 + 2*w^3 - 5*w^2 - 8*w + 2],\
[631, 631, -w^5 + 4*w^4 + 5*w^3 - 18*w^2 - 4*w + 6],\
[631, 631, w^4 + 2*w^3 - 4*w^2 - 8*w + 1],\
[641, 641, -w^5 - w^4 + 5*w^3 + 5*w^2 - 5*w - 2],\
[641, 641, -w^4 + 6*w^2 + w - 5],\
[641, 641, w^5 - 2*w^4 - 4*w^3 + 9*w^2 + 2*w - 5],\
[659, 659, -w^4 - 2*w^3 + 5*w^2 + 8*w - 1],\
[661, 661, 2*w^5 - 2*w^4 - 9*w^3 + 8*w^2 + 3*w + 1],\
[661, 661, 2*w^5 - 3*w^4 - 11*w^3 + 12*w^2 + 10*w - 1],\
[661, 661, w^5 - 3*w^4 - 6*w^3 + 12*w^2 + 9*w],\
[661, 661, -2*w^5 + 3*w^4 + 12*w^3 - 13*w^2 - 14*w + 1],\
[691, 691, w^5 - 6*w^3 - w^2 + 9*w + 1],\
[691, 691, 3*w^5 - 5*w^4 - 15*w^3 + 21*w^2 + 13*w - 5],\
[691, 691, w^5 - 2*w^4 - 6*w^3 + 8*w^2 + 6*w + 2],\
[691, 691, 2*w^5 - 3*w^4 - 12*w^3 + 12*w^2 + 16*w - 2],\
[701, 701, -w^5 - w^4 + 6*w^3 + 4*w^2 - 8*w - 2],\
[709, 709, -3*w^5 + 3*w^4 + 14*w^3 - 12*w^2 - 8*w + 3],\
[709, 709, w^5 + w^4 - 6*w^3 - 4*w^2 + 8*w + 1],\
[709, 709, 2*w^5 - 4*w^4 - 10*w^3 + 16*w^2 + 9*w - 2],\
[709, 709, 2*w^5 - 2*w^4 - 12*w^3 + 9*w^2 + 14*w - 3],\
[719, 719, w^4 - w^3 - 6*w^2 + 3*w + 4],\
[729, 3, -3],\
[739, 739, -w^5 + w^4 + 6*w^3 - 3*w^2 - 9*w - 5],\
[751, 751, -2*w^5 + 3*w^4 + 11*w^3 - 13*w^2 - 12*w + 1],\
[751, 751, -w^5 + w^4 + 4*w^3 - 4*w^2 - 2*w - 1],\
[761, 761, -2*w^5 + 2*w^4 + 12*w^3 - 9*w^2 - 15*w],\
[769, 769, -3*w^5 + 5*w^4 + 17*w^3 - 21*w^2 - 19*w + 3],\
[769, 769, -2*w^5 + 2*w^4 + 9*w^3 - 7*w^2 - 5*w - 1],\
[769, 769, -2*w^5 + 4*w^4 + 10*w^3 - 18*w^2 - 9*w + 7],\
[769, 769, 2*w^5 - w^4 - 12*w^3 + 3*w^2 + 14*w + 2],\
[811, 811, -3*w^5 + 2*w^4 + 16*w^3 - 9*w^2 - 15*w + 2],\
[821, 821, 2*w^3 - w^2 - 8*w + 1],\
[829, 829, w^5 - w^4 - 7*w^3 + 3*w^2 + 11*w + 1],\
[829, 829, 2*w^5 - 2*w^4 - 10*w^3 + 9*w^2 + 8*w - 6],\
[839, 839, -w^4 - 2*w^3 + 5*w^2 + 6*w - 1],\
[841, 29, -2*w^5 + 2*w^4 + 12*w^3 - 9*w^2 - 16*w + 2],\
[859, 859, -w^5 + 2*w^4 + 4*w^3 - 10*w^2 - w + 4],\
[859, 859, 2*w^5 - 3*w^4 - 10*w^3 + 11*w^2 + 7*w + 1],\
[881, 881, -2*w^5 + 3*w^4 + 9*w^3 - 14*w^2 - 4*w + 4],\
[881, 881, 2*w^5 - 2*w^4 - 10*w^3 + 10*w^2 + 6*w - 5],\
[911, 911, w^5 - w^4 - 4*w^3 + 5*w^2 - 2*w - 5],\
[911, 911, w^3 - 4*w - 4],\
[929, 929, -w^5 + 3*w^4 + 6*w^3 - 12*w^2 - 9*w + 1],\
[941, 941, 2*w^4 - 10*w^2 + w + 6],\
[941, 941, 3*w^5 - 3*w^4 - 15*w^3 + 14*w^2 + 10*w - 5],\
[941, 941, -w^5 + 5*w^3 + w^2 - 2*w - 4],\
[961, 31, -w^4 - w^3 + 6*w^2 + 4*w - 4],\
[961, 31, 2*w^5 - 3*w^4 - 12*w^3 + 12*w^2 + 15*w - 3],\
[971, 971, -2*w^5 + 3*w^4 + 12*w^3 - 13*w^2 - 14*w],\
[991, 991, w^5 - 3*w^4 - 4*w^3 + 14*w^2 + w - 6]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^6 + 12*x^5 + 53*x^4 + 104*x^3 + 84*x^2 + 16*x - 3
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -e - 3, -e^5 - 12*e^4 - 51*e^3 - 88*e^2 - 49*e - 2, -e^5 - 10*e^4 - 33*e^3 - 40*e^2 - 15*e - 4, 2*e^3 + 11*e^2 + 13*e + 2, -e^3 - 4*e^2 + e + 4, 2*e^5 + 20*e^4 + 69*e^3 + 93*e^2 + 34*e - 8, 1, -2*e^2 - 6*e - 2, 2*e^5 + 20*e^4 + 70*e^3 + 100*e^2 + 48*e + 5, -2*e^3 - 14*e^2 - 23*e + 2, 2*e^5 + 21*e^4 + 75*e^3 + 103*e^2 + 43*e + 6, -2*e^5 - 19*e^4 - 62*e^3 - 77*e^2 - 20*e + 5, 4*e^4 + 31*e^3 + 70*e^2 + 37*e - 8, -3*e^5 - 27*e^4 - 78*e^3 - 72*e^2 + 2*e + 6, -2*e^5 - 17*e^4 - 42*e^3 - 19*e^2 + 26*e + 11, 3*e^5 + 31*e^4 + 106*e^3 + 126*e^2 + 21*e - 13, -2*e^5 - 20*e^4 - 70*e^3 - 103*e^2 - 60*e - 6, -2*e^4 - 15*e^3 - 29*e^2 - 2*e + 4, 2*e^5 + 18*e^4 + 50*e^3 + 40*e^2 - 4*e + 2, -e^5 - 8*e^4 - 18*e^3 + 32*e + 8, -e^5 - 13*e^4 - 55*e^3 - 81*e^2 - 15*e + 19, -2*e^5 - 20*e^4 - 66*e^3 - 78*e^2 - 22*e - 5, -3*e^5 - 31*e^4 - 112*e^3 - 166*e^2 - 84*e - 4, -e^5 - 11*e^4 - 38*e^3 - 35*e^2 + 27*e + 17, 2*e^5 + 16*e^4 + 34*e^3 - 3*e^2 - 48*e - 12, 4*e^5 + 39*e^4 + 127*e^3 + 149*e^2 + 31*e - 20, e^5 + 14*e^4 + 61*e^3 + 88*e^2 + 10*e - 18, e^5 + 10*e^4 + 40*e^3 + 86*e^2 + 90*e + 12, -e^5 - 9*e^4 - 27*e^3 - 37*e^2 - 37*e - 17, 2*e^5 + 22*e^4 + 86*e^3 + 138*e^2 + 74*e - 4, 2*e^5 + 16*e^4 + 36*e^3 + 11*e^2 - 23*e - 6, -5*e^4 - 38*e^3 - 84*e^2 - 52*e - 7, 3*e^5 + 33*e^4 + 122*e^3 + 167*e^2 + 61*e + 1, 2*e^4 + 18*e^3 + 55*e^2 + 60*e + 12, e^5 + 9*e^4 + 24*e^3 + 19*e^2 + 17*e + 21, -4*e^4 - 31*e^3 - 70*e^2 - 41*e - 10, e^4 + 6*e^3 + 8*e^2 - 6*e - 12, -2*e^5 - 21*e^4 - 77*e^3 - 113*e^2 - 47*e + 14, -e^5 - 10*e^4 - 39*e^3 - 76*e^2 - 68*e - 1, -7*e^5 - 69*e^4 - 232*e^3 - 302*e^2 - 118*e + 1, -2*e^5 - 18*e^4 - 44*e^3 - 2*e^2 + 60*e + 8, -4*e^5 - 40*e^4 - 138*e^3 - 195*e^2 - 104*e - 3, 2*e^5 + 16*e^4 + 37*e^3 + 19*e^2 - e + 13, 6*e^5 + 58*e^4 + 191*e^3 + 244*e^2 + 92*e - 14, -7*e^5 - 68*e^4 - 221*e^3 - 268*e^2 - 86*e + 6, e^5 + 13*e^4 + 62*e^3 + 134*e^2 + 120*e + 11, e^5 + 15*e^4 + 70*e^3 + 118*e^2 + 51*e - 13, 7*e^4 + 54*e^3 + 120*e^2 + 60*e - 19, -3*e^5 - 27*e^4 - 75*e^3 - 57*e^2 + 15*e + 9, e^5 + 12*e^4 + 49*e^3 + 78*e^2 + 38*e - 12, 4*e^5 + 38*e^4 + 124*e^3 + 158*e^2 + 49*e - 22, 4*e^5 + 43*e^4 + 158*e^3 + 226*e^2 + 96*e - 12, 2*e^5 + 16*e^4 + 32*e^3 - 16*e^2 - 69*e - 6, 4*e^5 + 43*e^4 + 165*e^3 + 258*e^2 + 116*e - 18, 3*e^5 + 30*e^4 + 98*e^3 + 106*e^2 + 14*e + 8, 2*e^5 + 21*e^4 + 75*e^3 + 95*e^2 + 13*e - 8, 2*e^5 + 18*e^4 + 53*e^3 + 59*e^2 + 26*e + 10, -2*e^4 - 12*e^3 - 12*e^2 + 12*e - 2, 5*e^5 + 52*e^4 + 187*e^3 + 266*e^2 + 116*e - 6, -e^5 - 11*e^4 - 48*e^3 - 97*e^2 - 71*e - 1, -6*e^5 - 55*e^4 - 163*e^3 - 160*e^2 - 14*e + 12, -8*e^5 - 83*e^4 - 293*e^3 - 393*e^2 - 137*e + 24, -e^5 - 14*e^4 - 71*e^3 - 152*e^2 - 119*e - 14, 2*e^5 + 18*e^4 + 56*e^3 + 67*e^2 + 8*e - 19, -2*e^4 - 8*e^3 + 2*e^2 + 4*e - 24, 2*e^5 + 19*e^4 + 65*e^3 + 103*e^2 + 65*e - 14, 2*e^5 + 18*e^4 + 55*e^3 + 72*e^2 + 48*e, 4*e^5 + 40*e^4 + 133*e^3 + 161*e^2 + 50*e - 6, -2*e^5 - 21*e^4 - 77*e^3 - 120*e^2 - 80*e - 22, 3*e^5 + 27*e^4 + 72*e^3 + 40*e^2 - 39*e - 19, -4*e^5 - 40*e^4 - 134*e^3 - 172*e^2 - 73*e + 8, -e^5 - 11*e^4 - 46*e^3 - 92*e^2 - 80*e + 4, 4*e^5 + 41*e^4 + 147*e^3 + 202*e^2 + 50*e - 36, 8*e^5 + 78*e^4 + 258*e^3 + 318*e^2 + 76*e - 36, 7*e^5 + 70*e^4 + 241*e^3 + 328*e^2 + 136*e - 23, 3*e^5 + 38*e^4 + 166*e^3 + 292*e^2 + 176*e, -e^5 - 7*e^4 - 16*e^3 - 25*e^2 - 31*e + 5, -8*e^4 - 60*e^3 - 122*e^2 - 36*e + 33, 2*e^5 + 16*e^4 + 40*e^3 + 32*e^2 - 4*e - 24, -4*e^4 - 34*e^3 - 90*e^2 - 68*e - 8, -4*e^5 - 33*e^4 - 82*e^3 - 49*e^2 + 32*e + 15, 2*e^5 + 22*e^4 + 90*e^3 + 162*e^2 + 106*e + 14, -e^5 - 3*e^4 + 20*e^3 + 88*e^2 + 90*e - 10, 8*e^5 + 84*e^4 + 310*e^3 + 468*e^2 + 234*e - 2, -5*e^5 - 56*e^4 - 220*e^3 - 350*e^2 - 185*e + 4, -5*e^5 - 57*e^4 - 230*e^3 - 383*e^2 - 221*e - 9, 11*e^5 + 108*e^4 + 360*e^3 + 456*e^2 + 143*e - 42, 5*e^5 + 58*e^4 + 231*e^3 + 354*e^2 + 148*e - 25, 2*e^5 + 15*e^4 + 23*e^3 - 36*e^2 - 58*e + 24, -4*e^5 - 32*e^4 - 72*e^3 - 26*e^2 + 22*e - 20, -2*e^5 - 28*e^4 - 130*e^3 - 223*e^2 - 78*e + 33, 4*e^5 + 46*e^4 + 179*e^3 + 266*e^2 + 118*e + 18, 6*e^5 + 60*e^4 + 200*e^3 + 241*e^2 + 70*e - 6, 5*e^5 + 52*e^4 + 189*e^3 + 278*e^2 + 135*e - 6, e^5 + 8*e^4 + 12*e^3 - 40*e^2 - 100*e - 22, -7*e^5 - 62*e^4 - 170*e^3 - 128*e^2 + 33*e + 4, 2*e^5 + 27*e^4 + 121*e^3 + 200*e^2 + 72*e - 16, 2*e^4 + 8*e^3 - 12*e^2 - 57*e - 32, -6*e^5 - 52*e^4 - 130*e^3 - 46*e^2 + 118*e + 26, -2*e^5 - 20*e^4 - 67*e^3 - 72*e^2 + 3*e - 16, 2*e^5 + 24*e^4 + 101*e^3 + 167*e^2 + 77*e + 7, 4*e^5 + 45*e^4 + 186*e^3 + 324*e^2 + 182*e + 5, 3*e^5 + 31*e^4 + 99*e^3 + 95*e^2 + 15*e + 27, -10*e^5 - 102*e^4 - 351*e^3 - 446*e^2 - 126*e + 26, 6*e^5 + 60*e^4 + 204*e^3 + 262*e^2 + 90*e, -e^5 - 24*e^4 - 149*e^3 - 327*e^2 - 207*e + 1, e^5 + 11*e^4 + 44*e^3 + 73*e^2 + 39*e + 7, e^5 + 5*e^4 - 6*e^3 - 46*e^2 - 40*e - 15, -11*e^5 - 110*e^4 - 380*e^3 - 514*e^2 - 187*e + 30, 4*e^5 + 32*e^4 + 74*e^3 + 28*e^2 - 48*e - 12, 2*e^5 + 30*e^4 + 142*e^3 + 239*e^2 + 75*e - 44, -6*e^5 - 64*e^4 - 234*e^3 - 335*e^2 - 153*e + 10, 5*e^5 + 43*e^4 + 108*e^3 + 50*e^2 - 71*e - 33, e^5 + 6*e^4 - 11*e^3 - 110*e^2 - 146*e - 15, 2*e^5 + 12*e^4 - 3*e^3 - 110*e^2 - 142*e - 16, -8*e^5 - 80*e^4 - 269*e^3 - 345*e^2 - 147*e - 25, 2*e^5 + 18*e^4 + 47*e^3 + 20*e^2 - 37*e - 14, 3*e^5 + 31*e^4 + 119*e^3 + 211*e^2 + 158*e + 10, 2*e^5 + 22*e^4 + 82*e^3 + 118*e^2 + 54*e - 17, -8*e^4 - 66*e^3 - 165*e^2 - 102*e + 24, -3*e^5 - 39*e^4 - 176*e^3 - 318*e^2 - 181*e - 3, -3*e^4 - 19*e^3 - 34*e^2 - 26*e - 24, -e^5 - 14*e^4 - 66*e^3 - 122*e^2 - 64*e + 34, 14*e^3 + 80*e^2 + 108*e + 16, -6*e^5 - 58*e^4 - 199*e^3 - 289*e^2 - 151*e - 13, 8*e^5 + 81*e^4 + 282*e^3 + 386*e^2 + 166*e + 10, 8*e^5 + 83*e^4 + 292*e^3 + 381*e^2 + 96*e - 49, -6*e^5 - 62*e^4 - 224*e^3 - 333*e^2 - 181*e - 20, 4*e^4 + 43*e^3 + 149*e^2 + 177*e + 21, -2*e^5 - 21*e^4 - 96*e^3 - 222*e^2 - 190*e - 9, -e^5 - 10*e^4 - 37*e^3 - 76*e^2 - 100*e - 31, 5*e^5 + 47*e^4 + 154*e^3 + 214*e^2 + 128*e + 24, 2*e^5 + 6*e^4 - 37*e^3 - 130*e^2 - 51*e + 28, -6*e^4 - 50*e^3 - 117*e^2 - 58*e - 2, 4*e^5 + 38*e^4 + 118*e^3 + 120*e^2 + 14*e + 34, 5*e^5 + 49*e^4 + 159*e^3 + 193*e^2 + 71*e - 17, 2*e^5 + 12*e^4 + 10*e^3 - 33*e^2 - 24*e + 33, -e^5 - 12*e^4 - 60*e^3 - 136*e^2 - 80*e + 40, -e^4 - 19*e^3 - 88*e^2 - 116*e - 10, 4*e^5 + 48*e^4 + 186*e^3 + 245*e^2 + 38*e - 40, -4*e^5 - 45*e^4 - 170*e^3 - 228*e^2 - 30*e + 35, -14*e^5 - 139*e^4 - 465*e^3 - 585*e^2 - 199*e + 4, -2*e^5 - 18*e^4 - 41*e^3 + 12*e^2 + 75*e + 12, -10*e^5 - 85*e^4 - 219*e^3 - 135*e^2 + 91*e + 32, e^5 + 13*e^4 + 62*e^3 + 128*e^2 + 110*e + 18, 8*e^5 + 82*e^4 + 283*e^3 + 364*e^2 + 134*e + 22, 6*e^5 + 56*e^4 + 172*e^3 + 186*e^2 + 44*e + 13, -8*e^5 - 84*e^4 - 293*e^3 - 364*e^2 - 77*e + 46, 4*e^5 + 28*e^4 + 44*e^3 - 33*e^2 - 66*e - 6, 7*e^5 + 69*e^4 + 226*e^3 + 262*e^2 + 51*e - 13, 5*e^5 + 42*e^4 + 100*e^3 + 40*e^2 - 35*e + 14, -2*e^5 - 32*e^4 - 167*e^3 - 323*e^2 - 160*e + 22, -e^5 - 7*e^4 - 4*e^3 + 40*e^2 + 43*e - 3, -2*e^5 - 30*e^4 - 144*e^3 - 252*e^2 - 118*e - 12, 8*e^5 + 79*e^4 + 265*e^3 + 339*e^2 + 111*e - 2]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([59, 59, -w^5 + w^4 + 5*w^3 - 3*w^2 - 4*w - 2])] = -1

# EXAMPLE:
# pp = ZF.ideal(2).factor()[0][0]
# hecke_eigenvalues[pp]