/*
  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([31, 31, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 3*w - 4])

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^7 - 6*x^6 - 6*x^5 + 88*x^4 - 103*x^3 - 138*x^2 + 144*x + 112
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -e + 2, -1/4*e^6 + 5/4*e^5 + 5/2*e^4 - 71/4*e^3 + 41/4*e^2 + 39/2*e, 1/8*e^6 - 1/8*e^5 - 25/8*e^4 + 23/8*e^3 + 85/4*e^2 - 18*e - 22, -1/4*e^6 + e^5 + 13/4*e^4 - 29/2*e^3 - e^2 + 21*e + 12, -1, -1/4*e^6 + 3/4*e^5 + 17/4*e^4 - 45/4*e^3 - 29/2*e^2 + 22*e + 24, 1/2*e^6 - 9/4*e^5 - 21/4*e^4 + 125/4*e^3 - 67/4*e^2 - 55/2*e + 2, -1/2*e^5 + 3/2*e^4 + 13/2*e^3 - 41/2*e^2 - e + 16, 1/4*e^6 - 1/2*e^5 - 9/2*e^4 + 7*e^3 + 65/4*e^2 - 19/2*e - 12, 1/4*e^6 - 2*e^5 + e^4 + 51/2*e^3 - 237/4*e^2 + 11/2*e + 54, 1/4*e^6 - 5/4*e^5 - 9/4*e^4 + 71/4*e^3 - 27/2*e^2 - 17*e - 1, 3/4*e^5 - 5/2*e^4 - 39/4*e^3 + 35*e^2 - e - 36, -1/8*e^6 + 5/8*e^5 + 5/8*e^4 - 59/8*e^3 + 61/4*e^2 - 10*e - 14, -1/4*e^6 + e^5 + 3*e^4 - 29/2*e^3 + 13/4*e^2 + 37/2*e + 8, 1/8*e^6 + 5/8*e^5 - 49/8*e^4 - 47/8*e^3 + 251/4*e^2 - 32*e - 64, 1/2*e^6 - 2*e^5 - 27/4*e^4 + 30*e^3 + 13/4*e^2 - 103/2*e - 12, -5/8*e^6 + 19/8*e^5 + 65/8*e^4 - 273/8*e^3 - 1/4*e^2 + 47*e + 14, e^5 - 4*e^4 - 12*e^3 + 56*e^2 - 14*e - 54, 5/8*e^6 - 27/8*e^5 - 25/8*e^4 + 353/8*e^3 - 279/4*e^2 - 7*e + 58, -2*e^2 + 2*e + 18, 5/8*e^6 - 25/8*e^5 - 37/8*e^4 + 335/8*e^3 - 199/4*e^2 - 17*e + 44, -1/4*e^6 + 7*e^4 - 5/2*e^3 - 207/4*e^2 + 65/2*e + 54, -3/8*e^6 + 11/8*e^5 + 35/8*e^4 - 157/8*e^3 + 33/4*e^2 + 21*e - 8, 1/8*e^6 - 5/8*e^5 - 7/8*e^4 + 59/8*e^3 - 10*e^2 + 15/2*e + 8, -3/8*e^6 + 19/8*e^5 + 5/8*e^4 - 237/8*e^3 + 60*e^2 - 25/2*e - 56, 3/4*e^6 - 17/4*e^5 - 17/4*e^4 + 231/4*e^3 - 76*e^2 - 30*e + 50, 1/8*e^6 + 7/8*e^5 - 61/8*e^4 - 65/8*e^3 + 339/4*e^2 - 44*e - 92, -5/8*e^6 + 17/8*e^5 + 73/8*e^4 - 255/8*e^3 - 51/4*e^2 + 57*e + 18, e^6 - 5*e^5 - 7*e^4 + 66*e^3 - 85*e^2 - 16*e + 76, 1/4*e^6 + 1/4*e^5 - 29/4*e^4 - 11/4*e^3 + 111/2*e^2 - 11*e - 52, 1/2*e^6 - 3*e^5 - 3*e^4 + 42*e^3 - 99/2*e^2 - 39*e + 36, -3/8*e^6 + 15/8*e^5 + 17/8*e^4 - 193/8*e^3 + 79/2*e^2 - 9/2*e - 34, 3/2*e^6 - 25/4*e^5 - 17*e^4 + 353/4*e^3 - 35*e^2 - 93*e, -7/8*e^6 + 33/8*e^5 + 67/8*e^4 - 451/8*e^3 + 169/4*e^2 + 38*e - 18, -7/4*e^5 + 27/4*e^4 + 83/4*e^3 - 381/4*e^2 + 63/2*e + 96, 1/4*e^6 - 9/4*e^5 + 3/4*e^4 + 123/4*e^3 - 109/2*e^2 - 19*e + 38, -1/2*e^6 + 13/4*e^5 - 165/4*e^3 + 92*e^2 - 17*e - 84, -1/4*e^6 + 1/2*e^5 + 11/2*e^4 - 9*e^3 - 129/4*e^2 + 77/2*e + 42, 3/4*e^6 - 3*e^5 - 9*e^4 + 85/2*e^3 - 47/4*e^2 - 97/2*e + 6, -5/8*e^6 + 23/8*e^5 + 49/8*e^4 - 325/8*e^3 + 111/4*e^2 + 40*e - 14, -e^3 + 10*e + 4, -1/8*e^6 + 21/8*e^5 - 61/8*e^4 - 243/8*e^3 + 261/2*e^2 - 99/2*e - 130, -3/8*e^6 + 15/8*e^5 + 23/8*e^4 - 209/8*e^3 + 111/4*e^2 + 21*e - 4, -1/4*e^6 - 1/4*e^5 + 29/4*e^4 + 11/4*e^3 - 109/2*e^2 + 10*e + 52, 1/4*e^5 - 1/2*e^4 - 13/4*e^3 + 5*e^2 + e + 4, -1/2*e^6 + 2*e^5 + 6*e^4 - 28*e^3 + 13/2*e^2 + 32*e + 6, -3/4*e^6 + 4*e^5 + 9/2*e^4 - 105/2*e^3 + 297/4*e^2 + 17/2*e - 56, -1/4*e^6 + 3/2*e^5 + 3/4*e^4 - 20*e^3 + 71/2*e^2 + 7*e - 50, 3/4*e^6 - 13/4*e^5 - 33/4*e^4 + 187/4*e^3 - 22*e^2 - 56*e + 14, -1/4*e^6 - 1/4*e^5 + 35/4*e^4 - 5/4*e^3 - 76*e^2 + 59*e + 84, 3/4*e^6 - 15/4*e^5 - 25/4*e^4 + 205/4*e^3 - 49*e^2 - 34*e + 26, -e^6 + 9/2*e^5 + 21/2*e^4 - 127/2*e^3 + 73/2*e^2 + 66*e - 22, -7/4*e^6 + 33/4*e^5 + 31/2*e^4 - 451/4*e^3 + 411/4*e^2 + 147/2*e - 68, 3/8*e^6 - 21/8*e^5 - 3/8*e^4 + 279/8*e^3 - 251/4*e^2 - 6*e + 44, -1/4*e^5 + 1/4*e^4 + 13/4*e^3 - 23/4*e^2 + 3/2*e + 20, 1/2*e^5 - 2*e^4 - 9/2*e^3 + 28*e^2 - 25*e - 20, 1/4*e^5 - 7/4*e^4 - 5/4*e^3 + 101/4*e^2 - 57/2*e - 30, -5/4*e^6 + 13/2*e^5 + 35/4*e^4 - 88*e^3 + 211/2*e^2 + 44*e - 80, -5/2*e^5 + 39/4*e^4 + 61/2*e^3 - 535/4*e^2 + 59/2*e + 120, 1/2*e^6 - 13/4*e^5 + 165/4*e^3 - 93*e^2 + 11*e + 94, -5/4*e^6 + 13/2*e^5 + 37/4*e^4 - 88*e^3 + 99*e^2 + 45*e - 70, -5/4*e^5 + 17/4*e^4 + 61/4*e^3 - 231/4*e^2 + 23/2*e + 48, 1/2*e^6 - 15/4*e^5 + 1/4*e^4 + 199/4*e^3 - 381/4*e^2 - 17/2*e + 86, -13/8*e^6 + 61/8*e^5 + 119/8*e^4 - 835/8*e^3 + 179/2*e^2 + 141/2*e - 66, 3/4*e^6 - 4*e^5 - 6*e^4 + 111/2*e^3 - 203/4*e^2 - 89/2*e + 14, 3/4*e^6 - 15/4*e^5 - 25/4*e^4 + 201/4*e^3 - 49*e^2 - 25*e + 28, 1/8*e^6 + 3/8*e^5 - 49/8*e^4 - 5/8*e^3 + 253/4*e^2 - 53*e - 74, 1/8*e^6 - 21/8*e^5 + 47/8*e^4 + 275/8*e^3 - 423/4*e^2 + 4*e + 94, -1/4*e^6 + 3*e^5 - 17/4*e^4 - 77/2*e^3 + 207/2*e^2 - 6*e - 94, -3/4*e^6 + 3*e^5 + 19/2*e^4 - 85/2*e^3 + 21/4*e^2 + 87/2*e + 6, -3/4*e^6 + 15/4*e^5 + 27/4*e^4 - 205/4*e^3 + 83/2*e^2 + 34*e - 2, 1/2*e^6 - 2*e^5 - 11/2*e^4 + 27*e^3 - 15*e^2 - 20*e + 26, 1/4*e^6 - 3/2*e^5 - e^4 + 20*e^3 - 121/4*e^2 - 19/2*e + 24, -3/4*e^6 + 13/4*e^5 + 29/4*e^4 - 179/4*e^3 + 34*e^2 + 37*e - 10, 1/4*e^6 - 3*e^5 + 21/4*e^4 + 75/2*e^3 - 237/2*e^2 + 19*e + 114, e^5 - 5*e^4 - 10*e^3 + 69*e^2 - 41*e - 76, 1/4*e^6 + 3/2*e^5 - 57/4*e^4 - 13*e^3 + 153*e^2 - 88*e - 158, -e^6 + 9/2*e^5 + 9*e^4 - 123/2*e^3 + 55*e^2 + 41*e - 26, e^5 - 5/2*e^4 - 14*e^3 + 61/2*e^2 + 14*e - 2, 1/2*e^6 - 11/4*e^5 - 9/4*e^4 + 143/4*e^3 - 235/4*e^2 - 5/2*e + 34, -1/4*e^6 + e^5 + 13/4*e^4 - 31/2*e^3 + e^2 + 38*e - 8, -3/4*e^6 + 13/4*e^5 + 31/4*e^4 - 179/4*e^3 + 53/2*e^2 + 37*e - 2, -3/2*e^6 + 13/2*e^5 + 31/2*e^4 - 179/2*e^3 + 57*e^2 + 66*e - 28, 1/2*e^6 - 1/4*e^5 - 51/4*e^4 + 29/4*e^3 + 343/4*e^2 - 117/2*e - 74, -11/8*e^6 + 59/8*e^5 + 63/8*e^4 - 789/8*e^3 + 555/4*e^2 + 40*e - 102, e^6 - 6*e^5 - 13/2*e^4 + 84*e^3 - 181/2*e^2 - 77*e + 56, 5/4*e^5 - 11/2*e^4 - 57/4*e^3 + 80*e^2 - 24*e - 98, 1/2*e^6 - 9/2*e^5 + 4*e^4 + 117/2*e^3 - 289/2*e^2 + 4*e + 112, -1/4*e^6 + 6*e^4 + 3/2*e^3 - 159/4*e^2 - 25/2*e + 52, 1/2*e^6 - 9/2*e^5 + 5/2*e^4 + 121/2*e^3 - 122*e^2 - 21*e + 82, 3/4*e^6 - 17/4*e^5 - 21/4*e^4 + 235/4*e^3 - 58*e^2 - 42*e + 10, 3/8*e^6 + 21/8*e^5 - 167/8*e^4 - 219/8*e^3 + 893/4*e^2 - 98*e - 218, -7/8*e^6 + 31/8*e^5 + 65/8*e^4 - 433/8*e^3 + 47*e^2 + 101/2*e - 48, 1/2*e^6 - 7/4*e^5 - 31/4*e^4 + 107/4*e^3 + 67/4*e^2 - 99/2*e - 26, e^6 - 4*e^5 - 21/2*e^4 + 54*e^3 - 69/2*e^2 - 29*e + 10, 1/2*e^6 - 3/2*e^5 - 13/2*e^4 + 39/2*e^3 - 4*e + 10, -1/2*e^6 + e^5 + 23/2*e^4 - 18*e^3 - 69*e^2 + 66*e + 94, 1/2*e^6 - 3*e^5 - 5/2*e^4 + 40*e^3 - 56*e^2 - 20*e + 46, 2*e^6 - 35/4*e^5 - 41/2*e^4 + 479/4*e^3 - 81*e^2 - 87*e + 62, -1/4*e^6 + 19/4*e^5 - 11*e^4 - 241/4*e^3 + 787/4*e^2 - 49/2*e - 166, -e^6 + 11/2*e^5 + 6*e^4 - 147/2*e^3 + 98*e^2 + 30*e - 76, 7/4*e^6 - 7*e^5 - 83/4*e^4 + 193/2*e^3 - 29*e^2 - 86*e, 1/2*e^6 - 5/4*e^5 - 39/4*e^4 + 77/4*e^3 + 191/4*e^2 - 93/2*e - 74, -3/4*e^6 + 25/4*e^5 - 9/4*e^4 - 331/4*e^3 + 329/2*e^2 + 16*e - 122, 1/2*e^6 - 3/4*e^5 - 19/2*e^4 + 51/4*e^3 + 81/2*e^2 - 42*e - 28, 13/8*e^6 - 33/8*e^5 - 223/8*e^4 + 495/8*e^3 + 187/2*e^2 - 229/2*e - 114, 1/2*e^6 - 3*e^5 - 2*e^4 + 39*e^3 - 127/2*e^2 - 5*e + 44, 3/8*e^6 - 21/8*e^5 + 13/8*e^4 + 255/8*e^3 - 375/4*e^2 + 34*e + 104, -3/4*e^6 + 5/4*e^5 + 67/4*e^4 - 95/4*e^3 - 197/2*e^2 + 102*e + 110, 5/4*e^6 - 4*e^5 - 37/2*e^4 + 115/2*e^3 + 141/4*e^2 - 159/2*e - 74, 3/8*e^6 - 31/8*e^5 + 51/8*e^4 + 369/8*e^3 - 161*e^2 + 109/2*e + 170, -3/2*e^6 + 9/2*e^5 + 49/2*e^4 - 137/2*e^3 - 70*e^2 + 135*e + 102, -e^5 + 5*e^4 + 11*e^3 - 71*e^2 + 30*e + 86, -1/4*e^6 + 4*e^5 - 37/4*e^4 - 99/2*e^3 + 343/2*e^2 - 38*e - 156, -5/4*e^5 + 21/4*e^4 + 57/4*e^3 - 299/4*e^2 + 75/2*e + 78, -3/2*e^6 + 17/4*e^5 + 95/4*e^4 - 249/4*e^3 - 227/4*e^2 + 207/2*e + 46, -1/8*e^6 - 19/8*e^5 + 101/8*e^4 + 205/8*e^3 - 615/4*e^2 + 71*e + 148, 5/4*e^6 - 27/4*e^5 - 37/4*e^4 + 365/4*e^3 - 189/2*e^2 - 53*e + 42, e^6 - 21/4*e^5 - 27/4*e^4 + 285/4*e^3 - 355/4*e^2 - 71/2*e + 66, 1/2*e^6 - 2*e^5 - 9/2*e^4 + 28*e^3 - 30*e^2 - 25*e + 26, 3/8*e^6 + 5/8*e^5 - 115/8*e^4 - 11/8*e^3 + 531/4*e^2 - 87*e - 144, 1/4*e^5 + 3/4*e^4 - 17/4*e^3 - 53/4*e^2 + 29/2*e + 22, -2*e^6 + 35/4*e^5 + 41/2*e^4 - 483/4*e^3 + 79*e^2 + 99*e - 38, -3/4*e^6 + 4*e^5 + 4*e^4 - 103/2*e^3 + 331/4*e^2 + 1/2*e - 68, -1/4*e^6 + 1/2*e^5 + 29/4*e^4 - 12*e^3 - 57*e^2 + 71*e + 76, -5/4*e^6 + 6*e^5 + 11*e^4 - 163/2*e^3 + 285/4*e^2 + 107/2*e - 26, -5/8*e^6 + 19/8*e^5 + 61/8*e^4 - 257/8*e^3 + 29/4*e^2 + 23*e + 8, 1/2*e^6 - 9/2*e^5 + 9/2*e^4 + 115/2*e^3 - 156*e^2 + 16*e + 152, -e^6 + 3*e^5 + 16*e^4 - 43*e^3 - 43*e^2 + 68*e + 76, 5/4*e^6 - 8*e^5 - 5*e^4 + 217/2*e^3 - 629/4*e^2 - 105/2*e + 116, -2*e^6 + 7*e^5 + 57/2*e^4 - 103*e^3 - 73/2*e^2 + 165*e + 78, 1/2*e^6 + e^5 - 17*e^4 - 8*e^3 + 297/2*e^2 - 77*e - 162, 1/2*e^6 - 9/2*e^5 + 5*e^4 + 113/2*e^3 - 329/2*e^2 + 29*e + 170, 3/2*e^6 - 21/4*e^5 - 41/2*e^4 + 309/4*e^3 + 25/2*e^2 - 122*e - 34, -3/8*e^6 + 19/8*e^5 + 15/8*e^4 - 269/8*e^3 + 167/4*e^2 + 34*e - 28, 15/8*e^6 - 63/8*e^5 - 159/8*e^4 + 873/8*e^3 - 241/4*e^2 - 98*e + 16, -1/4*e^6 + 13/4*e^5 - 21/4*e^4 - 171/4*e^3 + 116*e^2 + 7*e - 102, -5/2*e^5 + 10*e^4 + 61/2*e^3 - 141*e^2 + 38*e + 146, -7/4*e^6 + 25/4*e^5 + 89/4*e^4 - 339/4*e^3 + 8*e^2 + 59*e + 18, -7/4*e^6 + 35/4*e^5 + 65/4*e^4 - 489/4*e^3 + 90*e^2 + 104*e - 22, e^5 - 4*e^4 - 14*e^3 + 53*e^2 + 14*e - 46, e^6 - 27/4*e^5 - 3*e^4 + 367/4*e^3 - 275/2*e^2 - 38*e + 84, 11/4*e^6 - 13*e^5 - 105/4*e^4 + 361/2*e^3 - 263/2*e^2 - 157*e + 64, -e^6 + 3*e^5 + 15*e^4 - 42*e^3 - 26*e^2 + 45*e + 28, -13/4*e^6 + 59/4*e^5 + 129/4*e^4 - 817/4*e^3 + 275/2*e^2 + 170*e - 38, 3/2*e^6 - 11/4*e^5 - 32*e^4 + 195/4*e^3 + 175*e^2 - 178*e - 202, e^6 - 2*e^5 - 39/2*e^4 + 31*e^3 + 191/2*e^2 - 75*e - 124, -3/8*e^6 - 1/8*e^5 + 99/8*e^4 - 25/8*e^3 - 423/4*e^2 + 69*e + 140, -9/8*e^6 + 21/8*e^5 + 167/8*e^4 - 331/8*e^3 - 86*e^2 + 207/2*e + 80, 1/2*e^6 - 5/2*e^5 - 7/2*e^4 + 65/2*e^3 - 46*e^2 - 3*e + 52, e^6 - 17/2*e^5 + 15/2*e^4 + 213/2*e^3 - 579/2*e^2 + 61*e + 274, -13/4*e^5 + 14*e^4 + 149/4*e^3 - 393/2*e^2 + 69*e + 192, -1/2*e^6 + 2*e^5 + 25/4*e^4 - 28*e^3 + 21/4*e^2 + 51/2*e + 16, 3/8*e^6 + 9/8*e^5 - 107/8*e^4 - 95/8*e^3 + 463/4*e^2 - 46*e - 88, 1/4*e^6 + 1/4*e^5 - 37/4*e^4 + 1/4*e^3 + 173/2*e^2 - 55*e - 106]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([31, 31, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 3*w - 4])] = 1

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