/*
  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, 3, 3, -4, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([131,131,-w^4 + 2*w^3 + 3*w^2 - 3*w - 1])

primes_array = [
[11, 11, w^4 + w^3 - 4*w^2 - 3*w + 2],\
[23, 23, -w^4 + 3*w^2 + 1],\
[23, 23, -w^4 + 3*w^2 + w - 2],\
[23, 23, w^4 - w^3 - 3*w^2 + 3*w + 2],\
[23, 23, -w^4 + w^3 + 4*w^2 - 3*w - 1],\
[23, 23, -w^2 + w + 3],\
[32, 2, 2],\
[43, 43, -2*w^4 + w^3 + 6*w^2 - 2*w - 1],\
[43, 43, -w^4 + 2*w^2 + w + 1],\
[43, 43, w^3 + w^2 - 4*w - 2],\
[43, 43, 2*w^4 - w^3 - 7*w^2 + 3*w + 3],\
[43, 43, w^4 - w^3 - 4*w^2 + 4*w + 2],\
[67, 67, 2*w^4 - 7*w^2 + 2],\
[67, 67, w^4 - 2*w^3 - 3*w^2 + 6*w + 2],\
[67, 67, 2*w^4 - 7*w^2 - w + 4],\
[67, 67, w^4 - 2*w^3 - 4*w^2 + 6*w + 2],\
[67, 67, -w^4 + w^3 + 5*w^2 - 3*w - 3],\
[89, 89, w^3 + w^2 - 4*w - 1],\
[89, 89, -2*w^4 + w^3 + 7*w^2 - 3*w - 2],\
[89, 89, -w^4 + w^3 + 4*w^2 - 4*w - 3],\
[89, 89, -w^4 + 2*w^2 + w + 2],\
[89, 89, 2*w^4 - w^3 - 6*w^2 + 2*w + 2],\
[109, 109, -w^3 + 2*w^2 + 3*w - 3],\
[109, 109, w^4 - 4*w^2 - 2*w + 3],\
[109, 109, -2*w^4 + 2*w^3 + 7*w^2 - 4*w - 3],\
[109, 109, 2*w^3 - 5*w - 1],\
[109, 109, -w^4 - w^3 + 5*w^2 + 2*w - 4],\
[131, 131, w^4 - 3*w^3 - 2*w^2 + 7*w],\
[131, 131, -w^4 + 2*w^3 + 5*w^2 - 7*w - 5],\
[131, 131, 2*w^4 - 2*w^3 - 6*w^2 + 3*w + 2],\
[131, 131, w^4 - 2*w^3 - 3*w^2 + 7*w],\
[131, 131, 2*w^4 + w^3 - 8*w^2 - 3*w + 4],\
[197, 197, 3*w^4 - w^3 - 10*w^2 + w + 5],\
[197, 197, 2*w^4 - 7*w^2 + w + 1],\
[197, 197, -3*w^4 + 2*w^3 + 10*w^2 - 5*w - 5],\
[197, 197, -2*w^4 - w^3 + 9*w^2 + 2*w - 5],\
[197, 197, -3*w^4 + 3*w^3 + 10*w^2 - 6*w - 5],\
[199, 199, w^4 + 2*w^3 - 5*w^2 - 5*w + 3],\
[199, 199, -2*w^4 + w^3 + 7*w^2 - 4*w - 2],\
[199, 199, -w^4 + 2*w^3 + 4*w^2 - 7*w - 3],\
[199, 199, 2*w^4 - 8*w^2 + w + 4],\
[199, 199, 3*w^4 - w^3 - 10*w^2 + 2*w + 4],\
[241, 241, w^4 - 2*w^3 - w^2 + 3*w - 3],\
[241, 241, -w^4 + 3*w^3 + 2*w^2 - 9*w],\
[241, 241, 3*w^4 - 11*w^2 - 2*w + 6],\
[241, 241, -w^4 + 2*w^3 + 5*w^2 - 6*w - 4],\
[241, 241, -2*w^4 + 2*w^3 + 9*w^2 - 5*w - 6],\
[243, 3, -3],\
[263, 263, -w^4 + 4*w^2 + w + 1],\
[263, 263, 2*w^4 - w^3 - 8*w^2 + w + 2],\
[263, 263, 3*w^4 - 3*w^3 - 9*w^2 + 7*w + 2],\
[263, 263, -2*w^3 + w^2 + 4*w - 4],\
[263, 263, -3*w^2 + w + 5],\
[307, 307, 2*w^4 - w^3 - 6*w^2 + 3*w - 2],\
[307, 307, w^4 - 2*w^2 - 2*w - 4],\
[307, 307, -3*w^4 + 2*w^3 + 11*w^2 - 3*w - 6],\
[307, 307, -2*w^4 + 2*w^3 + 7*w^2 - 6*w - 6],\
[307, 307, -w^4 + 3*w^3 + 4*w^2 - 7*w - 3],\
[331, 331, -w^4 - 2*w^3 + 3*w^2 + 7*w - 1],\
[331, 331, -w^4 + 3*w^3 + 4*w^2 - 8*w - 4],\
[331, 331, w^4 - w^2 - 4],\
[331, 331, 3*w^4 - 2*w^3 - 9*w^2 + 5*w + 2],\
[331, 331, -3*w^4 + 2*w^3 + 11*w^2 - 6*w - 5],\
[353, 353, -2*w^4 + w^3 + 9*w^2 - 3*w - 5],\
[353, 353, -2*w^4 - w^3 + 7*w^2 + 4*w - 4],\
[353, 353, -w^4 + 3*w^3 + 3*w^2 - 9*w - 3],\
[353, 353, -3*w^4 + 11*w^2 + w - 7],\
[353, 353, w^4 - w^3 - 6*w^2 + 3*w + 4],\
[373, 373, w^3 + 2*w^2 - 5*w - 3],\
[373, 373, 2*w^4 - 3*w^3 - 6*w^2 + 6*w],\
[373, 373, -w^4 + w^3 + 3*w^2 - 3*w + 3],\
[373, 373, -2*w^4 + 2*w^3 + 8*w^2 - 7*w - 5],\
[373, 373, -w^4 + w^3 + 4*w^2 - 3*w - 6],\
[397, 397, -w^4 - w^3 + 6*w^2 + 3*w - 5],\
[397, 397, 2*w^4 - 2*w^3 - 7*w^2 + 3*w + 3],\
[397, 397, -w^4 + 5*w^2 + 2*w - 5],\
[397, 397, w^4 + 2*w^3 - 5*w^2 - 5*w + 4],\
[397, 397, -w^4 + 3*w^3 + 3*w^2 - 7*w - 2],\
[419, 419, 3*w^3 - w^2 - 8*w],\
[419, 419, 2*w^4 - 3*w^3 - 6*w^2 + 6*w + 1],\
[419, 419, w^4 - 2*w^3 - 5*w^2 + 7*w + 4],\
[419, 419, -2*w^4 - w^3 + 9*w^2 + 3*w - 7],\
[419, 419, -w^4 + 3*w^3 + w^2 - 8*w + 1],\
[439, 439, -w^4 + w^3 + 5*w^2 - 5*w - 5],\
[439, 439, 2*w^4 - 9*w^2 - 2*w + 8],\
[439, 439, -3*w^4 + 2*w^3 + 11*w^2 - 5*w - 3],\
[439, 439, 2*w^4 - 2*w^3 - 8*w^2 + 3*w + 4],\
[439, 439, -w^4 + 3*w^3 + 3*w^2 - 6*w - 3],\
[461, 461, -w^4 + 5*w^2 + 2*w - 6],\
[461, 461, -w^4 + 3*w^2 - w + 3],\
[461, 461, -w^4 - 2*w^3 + 5*w^2 + 5*w - 5],\
[461, 461, -2*w^4 + 7*w^2 + w - 6],\
[461, 461, -w^4 + 3*w^3 + 3*w^2 - 7*w - 3],\
[463, 463, 2*w^4 - 2*w^3 - 8*w^2 + 5*w + 3],\
[463, 463, w^4 + w^3 - 3*w^2 - 2*w - 2],\
[463, 463, 2*w^4 - 7*w^2 - 2*w + 5],\
[463, 463, w^4 - 2*w^3 - 2*w^2 + 6*w + 1],\
[463, 463, -w^3 + 2*w^2 + w - 5],\
[571, 571, w^4 - w^3 - 3*w^2 + 2*w - 3],\
[571, 571, 3*w^4 - 2*w^3 - 10*w^2 + 6*w + 2],\
[571, 571, -2*w^4 + 2*w^3 + 8*w^2 - 7*w - 6],\
[571, 571, 2*w^4 - 5*w^2 - 2*w - 2],\
[571, 571, 3*w^4 - w^3 - 9*w^2 + 2*w + 3],\
[593, 593, 3*w^4 - w^3 - 9*w^2 + w + 3],\
[593, 593, -w^4 + 2*w^3 + 5*w^2 - 7*w - 3],\
[593, 593, -2*w^4 + 2*w^3 + 7*w^2 - 7*w - 4],\
[593, 593, w^4 - w^2 - 2*w - 4],\
[593, 593, 3*w^4 - w^3 - 10*w^2 + 3*w + 2],\
[617, 617, -w^4 - w^3 + 6*w^2 + 4*w - 5],\
[617, 617, 3*w^3 - w^2 - 7*w],\
[617, 617, 2*w^4 - w^3 - 8*w^2 + 6],\
[617, 617, 2*w^4 - 3*w^3 - 7*w^2 + 6*w + 3],\
[617, 617, -w^4 - 2*w^3 + 6*w^2 + 5*w - 6],\
[659, 659, -w^4 + w^3 + 4*w^2 - 5*w - 4],\
[659, 659, 2*w^3 + w^2 - 7*w],\
[659, 659, -3*w^4 + 2*w^3 + 9*w^2 - 4*w - 4],\
[659, 659, 3*w^4 - w^3 - 11*w^2 + 3*w + 3],\
[659, 659, w^4 - w^2 - w - 5],\
[661, 661, -5*w^4 + 2*w^3 + 18*w^2 - 4*w - 9],\
[661, 661, -w^4 + 3*w^3 + 6*w^2 - 9*w - 8],\
[661, 661, w^4 + 2*w^3 - 2*w^2 - 7*w - 2],\
[661, 661, -w^4 + w^3 + 5*w^2 - 2*w - 9],\
[661, 661, -3*w^4 + 2*w^3 + 12*w^2 - 2*w - 8],\
[683, 683, -w^4 + w^3 + 4*w^2 - 5*w - 3],\
[683, 683, 2*w^3 + w^2 - 7*w - 1],\
[683, 683, w^4 - w^2 - w - 4],\
[683, 683, 3*w^4 - 2*w^3 - 9*w^2 + 4*w + 3],\
[683, 683, 3*w^4 - w^3 - 11*w^2 + 3*w + 4],\
[727, 727, -5*w^4 + 3*w^3 + 19*w^2 - 7*w - 9],\
[727, 727, -2*w^4 - 2*w^3 + 7*w^2 + 9*w - 4],\
[727, 727, 3*w^4 + 2*w^3 - 13*w^2 - 6*w + 6],\
[727, 727, w^4 - 2*w^2 + 3*w - 4],\
[727, 727, -2*w^4 + 5*w^3 + 6*w^2 - 14*w - 4],\
[769, 769, -2*w^4 - w^3 + 9*w^2 + 2*w - 7],\
[769, 769, -w^4 + 4*w^2 + 3*w - 4],\
[769, 769, -w^3 + 3*w^2 + 3*w - 4],\
[769, 769, 3*w^4 - 3*w^3 - 10*w^2 + 6*w + 3],\
[769, 769, 3*w^3 - 8*w - 2],\
[857, 857, w^4 - 5*w^3 - 2*w^2 + 14*w - 1],\
[857, 857, 4*w^4 - w^3 - 13*w^2 + 4],\
[857, 857, -2*w^4 + 4*w^3 + 6*w^2 - 10*w - 5],\
[857, 857, 4*w^4 + w^3 - 14*w^2 - 5*w + 6],\
[857, 857, 4*w^4 + w^3 - 16*w^2 - 4*w + 8],\
[859, 859, 3*w^4 - w^3 - 11*w^2 + 5*w + 5],\
[859, 859, -2*w^4 + 5*w^3 + 6*w^2 - 13*w - 1],\
[859, 859, -2*w^4 - 2*w^3 + 5*w^2 + 7*w + 1],\
[859, 859, -w^3 + w^2 + 6*w + 1],\
[859, 859, 4*w^4 - w^3 - 13*w^2 + 3*w + 4],\
[881, 881, 2*w^4 + w^3 - 11*w^2 - 3*w + 11],\
[881, 881, w^4 - 6*w^2 - 3*w + 5],\
[881, 881, -2*w^4 + 5*w^3 + 6*w^2 - 12*w - 1],\
[881, 881, -2*w^4 - 3*w^3 + 9*w^2 + 8*w - 4],\
[881, 881, 3*w^4 + w^3 - 12*w^2 - 3*w + 7],\
[947, 947, 2*w^4 + 3*w^3 - 7*w^2 - 8*w],\
[947, 947, 2*w^4 - 3*w^3 - 6*w^2 + 4*w],\
[947, 947, 2*w^4 + 2*w^3 - 7*w^2 - 8*w + 4],\
[947, 947, -w^4 + 2*w^3 - 7*w + 3],\
[947, 947, -4*w^4 + 5*w^3 + 14*w^2 - 12*w - 5],\
[967, 967, 2*w^4 - w^3 - 9*w^2 + 3*w + 4],\
[967, 967, -2*w^4 - w^3 + 7*w^2 + 4*w - 5],\
[967, 967, w^4 - 2*w^2 + w - 4],\
[967, 967, w^4 - w^3 - 2*w^2 - 3],\
[967, 967, -2*w^4 + 3*w^3 + 6*w^2 - 8*w - 4],\
[991, 991, -w^4 + 4*w^3 + 2*w^2 - 12*w - 1],\
[991, 991, w^4 + 3*w^3 - 3*w^2 - 11*w - 1],\
[991, 991, 2*w^3 - 2*w^2 - 5*w + 8],\
[991, 991, -2*w^4 + 3*w^3 + 4*w^2 - 5*w + 3],\
[991, 991, 4*w^4 - 4*w^3 - 11*w^2 + 9*w]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^5 - 6*x^4 - 13*x^3 + 146*x^2 - 295*x + 164
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 3/2*e^4 - 19/4*e^3 - 133/4*e^2 + 499/4*e - 81, -e^4 + 3*e^3 + 22*e^2 - 81*e + 55, 3/2*e^4 - 5*e^3 - 33*e^2 + 263/2*e - 91, -e^4 + 3*e^3 + 22*e^2 - 81*e + 55, 1/2*e^3 - 1/2*e^2 - 23/2*e + 20, -1/4*e^4 + 3/4*e^3 + 25/4*e^2 - 39/2*e + 5, -e^4 + 7/2*e^3 + 43/2*e^2 - 185/2*e + 71, -1/4*e^4 + e^3 + 6*e^2 - 101/4*e + 14, 1/2*e^3 - 1/2*e^2 - 19/2*e + 16, -e^4 + 3*e^3 + 22*e^2 - 79*e + 51, -e^4 + 3*e^3 + 22*e^2 - 79*e + 51, -5/4*e^4 + 4*e^3 + 28*e^2 - 425/4*e + 69, -e^4 + 4*e^3 + 21*e^2 - 104*e + 91, 7/2*e^4 - 23/2*e^3 - 151/2*e^2 + 303*e - 225, 1/2*e^4 - 7/4*e^3 - 45/4*e^2 + 183/4*e - 30, 1/2*e^4 - 2*e^3 - 11*e^2 + 105/2*e - 40, -1/2*e^4 + 5/4*e^3 + 43/4*e^2 - 141/4*e + 23, 1/2*e^4 - 3/2*e^3 - 23/2*e^2 + 41*e - 22, -3*e^4 + 19/2*e^3 + 131/2*e^2 - 509/2*e + 179, 2*e^4 - 13/2*e^3 - 89/2*e^2 + 339/2*e - 101, -2*e^4 + 13/2*e^3 + 87/2*e^2 - 343/2*e + 124, -5/4*e^4 + 9/2*e^3 + 55/2*e^2 - 463/4*e + 83, 5/2*e^4 - 17/2*e^3 - 107/2*e^2 + 224*e - 176, 7/4*e^4 - 6*e^3 - 38*e^2 + 627/4*e - 119, e^4 - 13/4*e^3 - 83/4*e^2 + 351/4*e - 75, -2*e^4 + 7*e^3 + 43*e^2 - 183*e + 140, 11/2*e^4 - 37/2*e^3 - 239/2*e^2 + 485*e - 360, e^4 - 3*e^3 - 23*e^2 + 77*e - 32, 11/2*e^4 - 37/2*e^3 - 239/2*e^2 + 485*e - 360, 1, -5/2*e^4 + 15/2*e^3 + 113/2*e^2 - 199*e + 114, 3/4*e^3 + 1/4*e^2 - 57/4*e + 12, -e^4 + 5/2*e^3 + 43/2*e^2 - 137/2*e + 40, -5*e^4 + 16*e^3 + 109*e^2 - 424*e + 297, -2*e^4 + 11/2*e^3 + 91/2*e^2 - 293/2*e + 72, -1/2*e^4 + 3/2*e^3 + 23/2*e^2 - 44*e + 21, -2*e^4 + 6*e^3 + 45*e^2 - 160*e + 94, 1/2*e^4 - 2*e^3 - 10*e^2 + 105/2*e - 52, -13/4*e^4 + 23/2*e^3 + 141/2*e^2 - 1203/4*e + 227, 1/2*e^4 - 9/4*e^3 - 47/4*e^2 + 209/4*e - 15, 1/4*e^4 - 3/2*e^3 - 7/2*e^2 + 147/4*e - 54, -1/2*e^4 + e^3 + 12*e^2 - 53/2*e - 3, 4*e^4 - 12*e^3 - 88*e^2 + 325*e - 219, 9/2*e^4 - 29/2*e^3 - 197/2*e^2 + 385*e - 275, 3/4*e^4 - e^3 - 18*e^2 + 127/4*e + 4, -e^4 + 4*e^3 + 20*e^2 - 105*e + 96, 1/2*e^4 - 3/2*e^3 - 21/2*e^2 + 42*e - 24, -4*e^4 + 14*e^3 + 86*e^2 - 363*e + 288, 2*e^2 - 24, 7/2*e^4 - 47/4*e^3 - 313/4*e^2 + 1215/4*e - 185, -3/2*e^4 + 9/2*e^3 + 67/2*e^2 - 121*e + 70, -3/4*e^4 + 5/2*e^3 + 35/2*e^2 - 269/4*e + 33, 13/2*e^4 - 43/2*e^3 - 285/2*e^2 + 567*e - 408, -5/2*e^4 + 7*e^3 + 56*e^2 - 373/2*e + 101, -3/4*e^4 + 3*e^3 + 17*e^2 - 307/4*e + 49, -6*e^4 + 41/2*e^3 + 259/2*e^2 - 1077/2*e + 414, e^4 - 3*e^3 - 22*e^2 + 82*e - 60, -5/4*e^4 + 11/2*e^3 + 51/2*e^2 - 559/4*e + 128, 2*e^4 - 13/2*e^3 - 91/2*e^2 + 347/2*e - 88, -5/2*e^4 + 8*e^3 + 55*e^2 - 425/2*e + 153, -9/4*e^4 + 8*e^3 + 48*e^2 - 837/4*e + 163, 9/2*e^4 - 15*e^3 - 99*e^2 + 777/2*e - 266, -13/2*e^4 + 21*e^3 + 143*e^2 - 1103/2*e + 376, 1/2*e^4 - 5/2*e^3 - 21/2*e^2 + 63*e - 63, -1/2*e^4 + 12*e^2 - 13/2*e - 28, 3/2*e^4 - 15/4*e^3 - 129/4*e^2 + 415/4*e - 71, -3/2*e^4 + 5*e^3 + 33*e^2 - 253/2*e + 84, -9/2*e^4 + 29/2*e^3 + 197/2*e^2 - 387*e + 265, -5/2*e^4 + 17/2*e^3 + 105/2*e^2 - 228*e + 202, 9/4*e^4 - 13/2*e^3 - 99/2*e^2 + 699/4*e - 119, 6*e^4 - 79/4*e^3 - 529/4*e^2 + 2057/4*e - 341, -11/2*e^4 + 19*e^3 + 120*e^2 - 989/2*e + 369, 3/2*e^4 - 7/2*e^3 - 69/2*e^2 + 96*e - 42, -3*e^4 + 10*e^3 + 67*e^2 - 264*e + 171, 1/2*e^4 - 2*e^3 - 11*e^2 + 101/2*e - 11, -11/2*e^4 + 19*e^3 + 120*e^2 - 983/2*e + 357, 6*e^4 - 20*e^3 - 130*e^2 + 529*e - 386, 11/2*e^4 - 37/2*e^3 - 235/2*e^2 + 487*e - 384, 1/4*e^4 - 6*e^2 - 3/4*e + 9, -5/4*e^4 + 9/2*e^3 + 51/2*e^2 - 487/4*e + 103, 9*e^4 - 30*e^3 - 196*e^2 + 791*e - 582, 3*e^4 - 17/2*e^3 - 131/2*e^2 + 465/2*e - 158, 5/2*e^4 - 31/4*e^3 - 217/4*e^2 + 819/4*e - 153, -9/2*e^4 + 29/2*e^3 + 197/2*e^2 - 382*e + 271, 7/2*e^4 - 23/2*e^3 - 151/2*e^2 + 308*e - 238, -4*e^4 + 15*e^3 + 86*e^2 - 385*e + 300, -2*e^4 + 25/4*e^3 + 175/4*e^2 - 647/4*e + 103, -9/4*e^4 + 15/2*e^3 + 95/2*e^2 - 811/4*e + 176, -7/2*e^4 + 11*e^3 + 78*e^2 - 589/2*e + 182, 9/2*e^4 - 14*e^3 - 100*e^2 + 749/2*e - 252, -15/2*e^4 + 47/2*e^3 + 329/2*e^2 - 628*e + 422, -7/2*e^4 + 25/2*e^3 + 151/2*e^2 - 325*e + 266, -11/4*e^4 + 21/2*e^3 + 119/2*e^2 - 1077/4*e + 207, -5/2*e^4 + 17/2*e^3 + 107/2*e^2 - 230*e + 172, e^4 - 13/4*e^3 - 91/4*e^2 + 343/4*e - 59, 3*e^4 - 21/2*e^3 - 129/2*e^2 + 547/2*e - 219, 3/2*e^4 - 7/2*e^3 - 69/2*e^2 + 100*e - 24, 15/2*e^4 - 25*e^3 - 166*e^2 + 1303/2*e - 437, 13/2*e^4 - 22*e^3 - 142*e^2 + 1147/2*e - 405, 5*e^4 - 35/2*e^3 - 217/2*e^2 + 915/2*e - 334, -11/2*e^4 + 37/2*e^3 + 239/2*e^2 - 481*e + 366, -10*e^4 + 65/2*e^3 + 437/2*e^2 - 1715/2*e + 598, 9*e^4 - 61/2*e^3 - 393/2*e^2 + 1607/2*e - 597, 13/4*e^4 - 19/2*e^3 - 145/2*e^2 + 1035/4*e - 147, -3/2*e^3 + 3/2*e^2 + 71/2*e - 56, 13/2*e^4 - 43/2*e^3 - 285/2*e^2 + 562*e - 387, 7/2*e^4 - 13*e^3 - 77*e^2 + 679/2*e - 254, 7*e^4 - 47/2*e^3 - 303/2*e^2 + 1235/2*e - 470, -5*e^4 + 16*e^3 + 107*e^2 - 422*e + 331, -21/4*e^4 + 17*e^3 + 113*e^2 - 1805/4*e + 349, e^4 - 4*e^3 - 21*e^2 + 108*e - 103, -2*e^3 + 2*e^2 + 52*e - 88, -2*e^4 + 15/2*e^3 + 87/2*e^2 - 375/2*e + 133, 4*e^4 - 13*e^3 - 88*e^2 + 341*e - 215, -13/2*e^4 + 39/2*e^3 + 291/2*e^2 - 524*e + 309, -1/2*e^4 + 3/2*e^3 + 19/2*e^2 - 37*e + 37, 1/4*e^3 - 9/4*e^2 - 47/4*e + 43, -5/2*e^4 + 19/2*e^3 + 111/2*e^2 - 246*e + 171, 2*e^4 - 31/4*e^3 - 165/4*e^2 + 805/4*e - 168, 7/2*e^4 - 23/2*e^3 - 157/2*e^2 + 304*e - 186, 3*e^4 - 21/2*e^3 - 131/2*e^2 + 549/2*e - 214, -11/2*e^4 + 61/4*e^3 + 491/4*e^2 - 1649/4*e + 229, 1/2*e^4 - 14*e^2 + 17/2*e + 30, -1/2*e^4 + 14*e^2 - 1/2*e - 58, 19/2*e^4 - 115/4*e^3 - 841/4*e^2 + 3087/4*e - 488, -9/2*e^4 + 27/2*e^3 + 195/2*e^2 - 368*e + 269, -7/2*e^4 + 11*e^3 + 75*e^2 - 597/2*e + 234, e^4 - 4*e^3 - 22*e^2 + 101*e - 90, -3/2*e^3 + 1/2*e^2 + 59/2*e - 31, 1/2*e^4 + 1/2*e^3 - 23/2*e^2 - 8*e + 23, -4*e^4 + 49/4*e^3 + 359/4*e^2 - 1303/4*e + 189, -7*e^4 + 45/2*e^3 + 307/2*e^2 - 1193/2*e + 404, 1/2*e^4 + 1/2*e^3 - 23/2*e^2 - 4*e + 17, -4*e^4 + 25/2*e^3 + 175/2*e^2 - 673/2*e + 252, e^4 - 4*e^3 - 22*e^2 + 105*e - 96, 11/2*e^4 - 37/2*e^3 - 239/2*e^2 + 485*e - 372, 9/2*e^4 - 14*e^3 - 98*e^2 + 751/2*e - 244, -6*e^4 + 39/2*e^3 + 261/2*e^2 - 1037/2*e + 358, -6*e^4 + 18*e^3 + 132*e^2 - 479*e + 310, 3*e^4 - 9*e^3 - 66*e^2 + 240*e - 174, 1/2*e^4 - e^3 - 11*e^2 + 55/2*e - 28, -4*e^4 + 15*e^3 + 85*e^2 - 395*e + 332, -11/2*e^4 + 33/2*e^3 + 245/2*e^2 - 440*e + 261, 3*e^4 - 19/2*e^3 - 131/2*e^2 + 503/2*e - 168, 5/2*e^4 - 7*e^3 - 55*e^2 + 387/2*e - 136, -e^4 + 5/2*e^3 + 43/2*e^2 - 137/2*e + 52, -e^4 + 9/2*e^3 + 39/2*e^2 - 245/2*e + 132, -5*e^4 + 31/2*e^3 + 219/2*e^2 - 813/2*e + 263, 6*e^4 - 39/2*e^3 - 267/2*e^2 + 1011/2*e - 305, e^4 - 5*e^3 - 22*e^2 + 123*e - 97, 8*e^4 - 27*e^3 - 173*e^2 + 707*e - 522, 27/4*e^4 - 23*e^3 - 148*e^2 + 2415/4*e - 450, 9*e^4 - 55/2*e^3 - 397/2*e^2 + 1481/2*e - 483, 37/4*e^4 - 61/2*e^3 - 397/2*e^2 + 3219/4*e - 604, 11/2*e^4 - 17*e^3 - 121*e^2 + 915/2*e - 290, -3/2*e^4 + 7/2*e^3 + 65/2*e^2 - 97*e + 63, 1/2*e^3 - 5/2*e^2 - 43/2*e + 52, 7/4*e^4 - 4*e^3 - 41*e^2 + 415/4*e - 24, 4*e^4 - 27/2*e^3 - 179/2*e^2 + 699/2*e - 229, -17/2*e^4 + 55/2*e^3 + 381/2*e^2 - 723*e + 448, -2*e^4 + 19/4*e^3 + 181/4*e^2 - 525/4*e + 41, -2*e^4 + 25/4*e^3 + 175/4*e^2 - 687/4*e + 101, -5/2*e^4 + 23/2*e^3 + 105/2*e^2 - 289*e + 268, 4*e^4 - 27/2*e^3 - 173/2*e^2 + 691/2*e - 264, e^4 - 7/2*e^3 - 41/2*e^2 + 173/2*e - 82, 3/2*e^4 - 11/2*e^3 - 65/2*e^2 + 146*e - 130, 4*e^4 - 23/2*e^3 - 185/2*e^2 + 619/2*e - 149]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([131,131,-w^4 + 2*w^3 + 3*w^2 - 3*w - 1])] = -1

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