/*
  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([29, 3, -12, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([16, 2, 2])

primes_array = [
[4, 2, 1/2*w^3 - 2*w^2 - 2*w + 15/2],\
[4, 2, -w^2 + w + 8],\
[5, 5, -1/4*w^3 + 1/2*w^2 + 1/2*w - 9/4],\
[5, 5, 1/2*w^3 - w^2 - 4*w + 9/2],\
[19, 19, 1/4*w^3 - 3/2*w^2 - 1/2*w + 21/4],\
[19, 19, 1/4*w^3 - 3/2*w^2 - 1/2*w + 41/4],\
[29, 29, w],\
[29, 29, 1/4*w^3 - 1/2*w^2 - 1/2*w + 1/4],\
[29, 29, 1/4*w^3 - 1/2*w^2 - 5/2*w + 9/4],\
[29, 29, -1/2*w^3 + w^2 + 4*w - 5/2],\
[41, 41, 3/4*w^3 - 5/2*w^2 - 7/2*w + 47/4],\
[41, 41, 1/4*w^3 + 1/2*w^2 - 5/2*w - 15/4],\
[61, 61, -3/2*w^3 + 3*w^2 + 11*w - 21/2],\
[61, 61, w^3 - 2*w^2 - 4*w + 6],\
[79, 79, 3/4*w^3 - 5/2*w^2 - 7/2*w + 27/4],\
[79, 79, 1/4*w^3 + 1/2*w^2 - 5/2*w - 35/4],\
[81, 3, -3],\
[89, 89, 7/4*w^3 - 11/2*w^2 - 21/2*w + 119/4],\
[89, 89, 1/4*w^3 + 3/2*w^2 - 3/2*w - 23/4],\
[109, 109, -1/2*w^3 + 3*w^2 + 2*w - 41/2],\
[109, 109, -5/4*w^3 + 7/2*w^2 + 9/2*w - 45/4],\
[121, 11, -3/4*w^3 + 3/2*w^2 + 9/2*w - 23/4],\
[121, 11, -1/4*w^3 + 1/2*w^2 + 3/2*w - 21/4],\
[131, 131, -1/2*w^3 + w^2 + 5*w - 3/2],\
[131, 131, 3/4*w^3 - 1/2*w^2 - 7/2*w - 1/4],\
[139, 139, -5/4*w^3 + 11/2*w^2 + 9/2*w - 73/4],\
[139, 139, -1/4*w^3 + 7/2*w^2 - 3/2*w - 113/4],\
[149, 149, -1/4*w^3 + 3/2*w^2 + 1/2*w - 49/4],\
[149, 149, 1/4*w^3 - 3/2*w^2 - 1/2*w + 13/4],\
[151, 151, 1/2*w^3 - 3*w^2 - w + 23/2],\
[151, 151, -1/4*w^3 + 3/2*w^2 + 3/2*w - 45/4],\
[151, 151, 3/4*w^3 - 3/2*w^2 - 7/2*w + 11/4],\
[151, 151, -2*w^3 + 6*w^2 + 7*w - 20],\
[169, 13, -1/4*w^3 + 1/2*w^2 + 1/2*w - 25/4],\
[169, 13, 1/2*w^3 - w^2 - 4*w + 17/2],\
[179, 179, -1/4*w^3 + 1/2*w^2 + 7/2*w - 21/4],\
[179, 179, 1/4*w^3 - 1/2*w^2 - 7/2*w - 3/4],\
[181, 181, 1/2*w^3 - 3*w - 7/2],\
[181, 181, -5/4*w^3 + 7/2*w^2 + 15/2*w - 57/4],\
[191, 191, -3/4*w^3 + 5/2*w^2 + 9/2*w - 39/4],\
[191, 191, w^2 - 8],\
[199, 199, -3/4*w^3 + 7/2*w^2 + 5/2*w - 43/4],\
[199, 199, -1/4*w^3 + 5/2*w^2 - 1/2*w - 81/4],\
[199, 199, -3/4*w^3 + 7/2*w^2 + 5/2*w - 75/4],\
[199, 199, -1/4*w^3 + 5/2*w^2 - 1/2*w - 49/4],\
[229, 229, -1/2*w^3 + 2*w^2 + w - 21/2],\
[229, 229, -3/4*w^3 + 5/2*w^2 + 7/2*w - 55/4],\
[239, 239, 3/2*w^3 - 4*w^2 - 9*w + 35/2],\
[239, 239, 3/2*w^3 - 5*w^2 - 7*w + 45/2],\
[241, 241, -5/4*w^3 + 9/2*w^2 + 13/2*w - 93/4],\
[241, 241, -1/4*w^3 - 1/2*w^2 - 1/2*w + 3/4],\
[251, 251, -w^3 + 3*w^2 + 8*w - 13],\
[251, 251, -7/4*w^3 + 13/2*w^2 + 13/2*w - 99/4],\
[269, 269, -9/4*w^3 + 13/2*w^2 + 15/2*w - 85/4],\
[269, 269, -3/4*w^3 + 5/2*w^2 + 3/2*w - 47/4],\
[271, 271, 5/4*w^3 - 5/2*w^2 - 21/2*w + 53/4],\
[271, 271, 5/4*w^3 - 1/2*w^2 - 23/2*w - 23/4],\
[271, 271, 7/4*w^3 - 11/2*w^2 - 13/2*w + 83/4],\
[271, 271, -1/2*w^3 + w^2 - 13/2],\
[281, 281, 3/4*w^3 - 1/2*w^2 - 13/2*w - 1/4],\
[281, 281, -w^3 + 3*w^2 + 4*w - 13],\
[311, 311, -1/4*w^3 + 1/2*w^2 - 1/2*w - 5/4],\
[311, 311, 7/4*w^3 - 13/2*w^2 - 19/2*w + 155/4],\
[311, 311, -1/4*w^3 + 7/2*w^2 + 1/2*w - 49/4],\
[311, 311, -3/4*w^3 + 3/2*w^2 + 13/2*w - 23/4],\
[331, 331, -3/4*w^3 + 1/2*w^2 + 15/2*w + 5/4],\
[331, 331, -3/4*w^3 + 5/2*w^2 + 3/2*w - 39/4],\
[349, 349, -1/4*w^3 + 1/2*w^2 + 7/2*w - 17/4],\
[349, 349, 1/4*w^3 - 1/2*w^2 - 7/2*w + 1/4],\
[359, 359, -5/4*w^3 - 1/2*w^2 + 25/2*w + 55/4],\
[359, 359, w^2 - 2*w - 2],\
[359, 359, -9/4*w^3 + 15/2*w^2 + 17/2*w - 113/4],\
[359, 359, -1/4*w^3 + 3/2*w^2 - 1/2*w - 45/4],\
[361, 19, -w^3 + 2*w^2 + 6*w - 8],\
[379, 379, -5/4*w^3 + 5/2*w^2 + 17/2*w - 37/4],\
[379, 379, -5/4*w^3 + 7/2*w^2 + 9/2*w - 41/4],\
[379, 379, 5/4*w^3 - 3/2*w^2 - 21/2*w - 3/4],\
[379, 379, -w^3 + 2*w^2 + 5*w - 7],\
[389, 389, 9/4*w^3 - 17/2*w^2 - 15/2*w + 117/4],\
[389, 389, -3/4*w^3 - 5/2*w^2 + 21/2*w + 113/4],\
[401, 401, -3/4*w^3 - 7/2*w^2 + 23/2*w + 149/4],\
[401, 401, 11/4*w^3 - 21/2*w^2 - 19/2*w + 143/4],\
[409, 409, -3/4*w^3 + 5/2*w^2 + 9/2*w - 31/4],\
[409, 409, w^2 - 10],\
[421, 421, 5/4*w^3 - 5/2*w^2 - 19/2*w + 49/4],\
[421, 421, -1/4*w^3 + 5/2*w^2 - 1/2*w - 41/4],\
[421, 421, 5/4*w^3 - 5/2*w^2 - 7/2*w + 41/4],\
[421, 421, 9/4*w^3 - 9/2*w^2 - 35/2*w + 77/4],\
[431, 431, 7/4*w^3 - 9/2*w^2 - 11/2*w + 59/4],\
[431, 431, 5/4*w^3 - 9/2*w^2 - 13/2*w + 85/4],\
[431, 431, 5/4*w^3 - 5/2*w^2 - 11/2*w + 33/4],\
[431, 431, -2*w^2 + w + 12],\
[439, 439, -1/2*w^3 + w^2 + 5*w - 7/2],\
[439, 439, 2*w - 1],\
[461, 461, -7/4*w^3 + 13/2*w^2 + 21/2*w - 163/4],\
[461, 461, 3/2*w^3 - 5*w^2 - 4*w + 31/2],\
[491, 491, 5/4*w^3 - 3/2*w^2 - 17/2*w + 21/4],\
[491, 491, -7/4*w^3 + 9/2*w^2 + 19/2*w - 83/4],\
[509, 509, -3/2*w^3 + 4*w^2 + 7*w - 27/2],\
[509, 509, -3/2*w^3 + 3*w^2 + 10*w - 27/2],\
[521, 521, -5/4*w^3 + 3/2*w^2 + 11/2*w - 17/4],\
[521, 521, -5/2*w^3 + 6*w^2 + 17*w - 53/2],\
[521, 521, -1/2*w^3 + 3*w^2 + w - 31/2],\
[541, 541, 9/4*w^3 - 7/2*w^2 - 35/2*w + 37/4],\
[541, 541, w^3 - 2*w^2 - 8*w + 12],\
[541, 541, -1/4*w^3 - 3/2*w^2 + 7/2*w + 35/4],\
[541, 541, -3/4*w^3 + 9/2*w^2 + 5/2*w - 119/4],\
[569, 569, -w^3 + 3*w^2 + 6*w - 7],\
[569, 569, -7/4*w^3 + 9/2*w^2 + 23/2*w - 75/4],\
[599, 599, 1/4*w^3 + 5/2*w^2 - 9/2*w - 95/4],\
[599, 599, -7/4*w^3 + 13/2*w^2 + 15/2*w - 91/4],\
[619, 619, 9/4*w^3 - 13/2*w^2 - 19/2*w + 97/4],\
[619, 619, -7/4*w^3 + 3/2*w^2 + 29/2*w + 9/4],\
[619, 619, -1/4*w^3 + 3/2*w^2 - 3/2*w - 45/4],\
[619, 619, -1/4*w^3 - 1/2*w^2 + 9/2*w - 1/4],\
[631, 631, -9/4*w^3 + 13/2*w^2 + 15/2*w - 93/4],\
[631, 631, -13/4*w^3 + 21/2*w^2 + 39/2*w - 233/4],\
[631, 631, 7/4*w^3 - 9/2*w^2 - 15/2*w + 67/4],\
[631, 631, 1/4*w^3 + 7/2*w^2 - 3/2*w - 51/4],\
[641, 641, -1/4*w^3 + 5/2*w^2 + 1/2*w - 57/4],\
[641, 641, -w^3 + 4*w^2 + 5*w - 19],\
[661, 661, -2*w^3 + 20*w + 19],\
[661, 661, 5/4*w^3 - 11/2*w^2 - 13/2*w + 149/4],\
[691, 691, -5/4*w^3 + 3/2*w^2 + 13/2*w - 9/4],\
[691, 691, -7/4*w^3 + 11/2*w^2 + 23/2*w - 135/4],\
[739, 739, -2*w^3 + 7*w^2 + 10*w - 34],\
[739, 739, 1/4*w^3 + 5/2*w^2 - 7/2*w - 59/4],\
[751, 751, -1/2*w^3 + 3*w^2 + 2*w - 33/2],\
[751, 751, -3/4*w^3 + 7/2*w^2 + 7/2*w - 67/4],\
[761, 761, -w^3 + 4*w^2 + 5*w - 27],\
[761, 761, 7/4*w^3 - 9/2*w^2 - 15/2*w + 63/4],\
[769, 769, -5/4*w^3 + 1/2*w^2 + 25/2*w + 19/4],\
[769, 769, 3/2*w^3 - 5*w^2 - 4*w + 39/2],\
[769, 769, -3*w^3 + 10*w^2 + 11*w - 37],\
[769, 769, -7/4*w^3 + 5/2*w^2 + 27/2*w - 31/4],\
[811, 811, -w^3 + 3*w^2 + 6*w - 9],\
[811, 811, -3/4*w^3 + 7/2*w^2 + 5/2*w - 39/4],\
[811, 811, -1/4*w^3 + 5/2*w^2 - 1/2*w - 85/4],\
[811, 811, -5/4*w^3 + 7/2*w^2 + 17/2*w - 57/4],\
[821, 821, -3/4*w^3 + 3/2*w^2 + 3/2*w - 35/4],\
[821, 821, -5/4*w^3 + 11/2*w^2 + 9/2*w - 121/4],\
[829, 829, 7/4*w^3 - 13/2*w^2 - 19/2*w + 115/4],\
[829, 829, 1/4*w^3 - 7/2*w^2 - 1/2*w + 89/4],\
[839, 839, -3/4*w^3 + 5/2*w^2 + 3/2*w - 51/4],\
[839, 839, -3/4*w^3 + 1/2*w^2 + 15/2*w - 7/4],\
[911, 911, -3/4*w^3 + 1/2*w^2 + 11/2*w - 15/4],\
[911, 911, -3/4*w^3 + 7/2*w^2 + 3/2*w - 75/4],\
[929, 929, 9/4*w^3 - 9/2*w^2 - 35/2*w + 73/4],\
[929, 929, -3/4*w^3 + 7/2*w^2 + 9/2*w - 51/4],\
[929, 929, -3/4*w^3 + 7/2*w^2 + 9/2*w - 91/4],\
[929, 929, 5/2*w^3 - 4*w^2 - 19*w + 25/2],\
[961, 31, -5/4*w^3 + 5/2*w^2 + 15/2*w - 37/4],\
[961, 31, -1/2*w^3 + w^2 + 3*w - 19/2]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^5 - 3*x^4 - 14*x^3 + 40*x^2 - 4
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [-1, -1, e, e, -1/4*e^4 + 1/4*e^3 + 7/2*e^2 - 7/2*e, -1/4*e^4 + 1/4*e^3 + 7/2*e^2 - 7/2*e, 1/2*e^3 - 1/2*e^2 - 7*e + 7, -1/2*e^4 + 3/2*e^3 + 7*e^2 - 18*e, 1/2*e^3 - 1/2*e^2 - 7*e + 7, -1/2*e^4 + 3/2*e^3 + 7*e^2 - 18*e, -3/4*e^4 + 7/4*e^3 + 21/2*e^2 - 49/2*e, -3/4*e^4 + 7/4*e^3 + 21/2*e^2 - 49/2*e, 1/2*e^4 - 3/2*e^3 - 6*e^2 + 20*e - 6, 1/2*e^4 - 3/2*e^3 - 6*e^2 + 20*e - 6, 1/2*e^3 - 1/2*e^2 - 7*e + 7, 1/2*e^3 - 1/2*e^2 - 7*e + 7, -1/2*e^4 + 3/2*e^3 + 7*e^2 - 21*e + 10, 3/4*e^4 - 11/4*e^3 - 23/2*e^2 + 75/2*e + 6, 3/4*e^4 - 11/4*e^3 - 23/2*e^2 + 75/2*e + 6, -3/2*e^4 + 9/2*e^3 + 21*e^2 - 59*e, -3/2*e^4 + 9/2*e^3 + 21*e^2 - 59*e, e^4 - 7/2*e^3 - 27/2*e^2 + 48*e + 5, 1/2*e^4 - e^3 - 15/2*e^2 + 11*e + 19, -1/4*e^4 + 3/4*e^3 + 4*e^2 - 21/2*e - 7, -1/4*e^4 + 3/4*e^3 + 4*e^2 - 21/2*e - 7, 5/4*e^4 - 17/4*e^3 - 35/2*e^2 + 111/2*e, 5/4*e^4 - 17/4*e^3 - 35/2*e^2 + 111/2*e, 3/2*e^3 - 3/2*e^2 - 18*e + 13, 3/2*e^3 - 3/2*e^2 - 18*e + 13, e^4 - 3*e^3 - 15*e^2 + 38*e + 6, e^4 - 2*e^3 - 15*e^2 + 24*e + 14, e^4 - 2*e^3 - 15*e^2 + 24*e + 14, e^4 - 3*e^3 - 15*e^2 + 38*e + 6, -3/4*e^4 + 9/4*e^3 + 10*e^2 - 61/2*e - 1, -3/4*e^4 + 9/4*e^3 + 10*e^2 - 61/2*e - 1, -5/4*e^4 + 15/4*e^3 + 18*e^2 - 97/2*e - 7, -5/4*e^4 + 15/4*e^3 + 18*e^2 - 97/2*e - 7, e^4 - 7/2*e^3 - 27/2*e^2 + 45*e + 3, e^4 - 7/2*e^3 - 27/2*e^2 + 45*e + 3, 1/2*e^4 - 1/2*e^3 - 6*e^2 + 7*e - 14, 1/2*e^4 - 1/2*e^3 - 6*e^2 + 7*e - 14, -2*e^4 + 11/2*e^3 + 59/2*e^2 - 73*e - 5, -2*e^4 + 11/2*e^3 + 59/2*e^2 - 73*e - 5, -1/2*e^3 + 1/2*e^2 + 7*e - 7, -1/2*e^3 + 1/2*e^2 + 7*e - 7, 1/2*e^4 - 3/2*e^3 - 5*e^2 + 18*e - 12, 1/2*e^4 - 3/2*e^3 - 5*e^2 + 18*e - 12, 2*e^4 - 5*e^3 - 28*e^2 + 66*e, 2*e^4 - 5*e^3 - 28*e^2 + 66*e, 1/4*e^4 - 9/4*e^3 - 7/2*e^2 + 61/2*e - 8, 1/4*e^4 - 9/4*e^3 - 7/2*e^2 + 61/2*e - 8, -5/4*e^4 + 19/4*e^3 + 16*e^2 - 125/2*e + 5, -5/4*e^4 + 19/4*e^3 + 16*e^2 - 125/2*e + 5, 1/2*e^4 - e^3 - 15/2*e^2 + 11*e + 7, 1/2*e^4 - e^3 - 15/2*e^2 + 11*e + 7, 3/2*e^4 - 3*e^3 - 47/2*e^2 + 38*e + 19, 1/2*e^4 - 17/2*e^2 + 5, 1/2*e^4 - 17/2*e^2 + 5, 3/2*e^4 - 3*e^3 - 47/2*e^2 + 38*e + 19, 5/4*e^4 - 15/4*e^3 - 18*e^2 + 97/2*e + 9, 5/4*e^4 - 15/4*e^3 - 18*e^2 + 97/2*e + 9, 3/2*e^4 - 3*e^3 - 39/2*e^2 + 38*e - 5, 1/2*e^3 - 5/2*e^2 - 7*e + 11, 1/2*e^3 - 5/2*e^2 - 7*e + 11, 3/2*e^4 - 3*e^3 - 39/2*e^2 + 38*e - 5, -3/4*e^4 + 3/4*e^3 + 23/2*e^2 - 21/2*e - 14, -3/4*e^4 + 3/4*e^3 + 23/2*e^2 - 21/2*e - 14, 2*e^4 - 9/2*e^3 - 57/2*e^2 + 64*e + 7, 2*e^4 - 9/2*e^3 - 57/2*e^2 + 64*e + 7, 1/2*e^4 - 1/2*e^3 - 9*e^2 + 7*e + 12, e^4 - 5/2*e^3 - 31/2*e^2 + 39*e + 13, 1/2*e^4 - 1/2*e^3 - 9*e^2 + 7*e + 12, e^4 - 5/2*e^3 - 31/2*e^2 + 39*e + 13, 1/2*e^4 - 2*e^3 - 17/2*e^2 + 27*e + 25, -3/4*e^4 + 5/4*e^3 + 11*e^2 - 19/2*e - 7, 5/4*e^4 - 21/4*e^3 - 33/2*e^2 + 139/2*e - 14, 5/4*e^4 - 21/4*e^3 - 33/2*e^2 + 139/2*e - 14, -3/4*e^4 + 5/4*e^3 + 11*e^2 - 19/2*e - 7, -1/2*e^4 + 3/2*e^3 + 7*e^2 - 21*e + 18, -1/2*e^4 + 3/2*e^3 + 7*e^2 - 21*e + 18, 3/4*e^4 - 7/4*e^3 - 21/2*e^2 + 43/2*e - 8, 3/4*e^4 - 7/4*e^3 - 21/2*e^2 + 43/2*e - 8, -1/4*e^4 + 5/4*e^3 + 9/2*e^2 - 45/2*e + 2, -1/4*e^4 + 5/4*e^3 + 9/2*e^2 - 45/2*e + 2, -2*e^4 + 5*e^3 + 28*e^2 - 66*e - 8, -2*e^4 + 5*e^3 + 28*e^2 - 66*e - 8, -e^3 + 11*e - 8, -e^3 + 11*e - 8, 2*e^4 - 9/2*e^3 - 53/2*e^2 + 59*e - 13, 1/2*e^4 - 1/2*e^3 - 9*e^2 + 7*e + 4, 2*e^4 - 9/2*e^3 - 53/2*e^2 + 59*e - 13, 1/2*e^4 - 1/2*e^3 - 9*e^2 + 7*e + 4, -e^4 + 5/2*e^3 + 31/2*e^2 - 39*e - 13, -e^4 + 5/2*e^3 + 31/2*e^2 - 39*e - 13, -5/2*e^3 + 3/2*e^2 + 32*e - 29, -5/2*e^3 + 3/2*e^2 + 32*e - 29, -1/4*e^4 + 7/4*e^3 + e^2 - 49/2*e + 19, -1/4*e^4 + 7/4*e^3 + e^2 - 49/2*e + 19, 2*e^4 - 5*e^3 - 29*e^2 + 58*e + 14, 2*e^4 - 5*e^3 - 29*e^2 + 58*e + 14, 1/4*e^4 + 3/4*e^3 - 7/2*e^2 - 21/2*e, 1/4*e^4 + 3/4*e^3 - 7/2*e^2 - 21/2*e, -2*e^4 + 5*e^3 + 29*e^2 - 62*e + 12, -1/2*e^4 + 5/2*e^3 + 10*e^2 - 36*e - 34, -1/2*e^4 + 2*e^3 + 9/2*e^2 - 23*e + 19, -1/2*e^4 + 2*e^3 + 9/2*e^2 - 23*e + 19, -1/2*e^4 + 5/2*e^3 + 10*e^2 - 36*e - 34, -7/4*e^4 + 17/4*e^3 + 25*e^2 - 111/2*e - 17, -7/4*e^4 + 17/4*e^3 + 25*e^2 - 111/2*e - 17, 2*e^4 - 7*e^3 - 27*e^2 + 86*e - 14, 2*e^4 - 7*e^3 - 27*e^2 + 86*e - 14, -1/2*e^4 + 5/2*e^3 + 8*e^2 - 39*e + 14, -1/2*e^4 + 5/2*e^3 + 8*e^2 - 39*e + 14, -7/4*e^4 + 17/4*e^3 + 25*e^2 - 111/2*e - 7, -7/4*e^4 + 17/4*e^3 + 25*e^2 - 111/2*e - 7, 3/2*e^4 - 4*e^3 - 37/2*e^2 + 52*e - 19, -5/2*e^4 + 15/2*e^3 + 34*e^2 - 101*e + 14, 3/2*e^4 - 4*e^3 - 37/2*e^2 + 52*e - 19, -5/2*e^4 + 15/2*e^3 + 34*e^2 - 101*e + 14, 3/2*e^4 - 5*e^3 - 37/2*e^2 + 61*e - 7, 3/2*e^4 - 5*e^3 - 37/2*e^2 + 61*e - 7, -2*e^4 + 5*e^3 + 28*e^2 - 74*e, -2*e^4 + 5*e^3 + 28*e^2 - 74*e, 1/2*e^4 - 3/2*e^3 - 6*e^2 + 21*e - 2, 1/2*e^4 - 3/2*e^3 - 6*e^2 + 21*e - 2, 1/4*e^4 - 3/4*e^3 - 5*e^2 + 21/2*e + 5, 1/4*e^4 - 3/4*e^3 - 5*e^2 + 21/2*e + 5, -e^4 + 2*e^3 + 14*e^2 - 20*e - 8, -e^4 + 2*e^3 + 14*e^2 - 20*e - 8, -1/4*e^4 + 9/4*e^3 + 1/2*e^2 - 47/2*e + 18, -1/4*e^4 + 9/4*e^3 + 1/2*e^2 - 47/2*e + 18, 5/4*e^4 - 15/4*e^3 - 20*e^2 + 87/2*e + 19, 5/4*e^4 - 15/4*e^3 - 20*e^2 + 87/2*e + 19, 9/4*e^4 - 15/4*e^3 - 36*e^2 + 97/2*e + 29, 9/4*e^4 - 15/4*e^3 - 36*e^2 + 97/2*e + 29, 9/4*e^4 - 19/4*e^3 - 34*e^2 + 125/2*e + 11, -3/4*e^4 + 5/4*e^3 + 7*e^2 - 35/2*e + 17, -3/4*e^4 + 5/4*e^3 + 7*e^2 - 35/2*e + 17, 9/4*e^4 - 19/4*e^3 - 34*e^2 + 125/2*e + 11, 4*e^4 - 23/2*e^3 - 111/2*e^2 + 157*e + 3, 4*e^4 - 23/2*e^3 - 111/2*e^2 + 157*e + 3, -e^3 - 6*e^2 + 18*e + 44, -e^3 - 6*e^2 + 18*e + 44, -e^4 + 9/2*e^3 + 31/2*e^2 - 67*e + 3, -e^4 + 9/2*e^3 + 31/2*e^2 - 67*e + 3, 1/2*e^4 - 4*e^3 - 15/2*e^2 + 60*e - 17, 1/2*e^4 - 4*e^3 - 15/2*e^2 + 60*e - 17, -e^4 + 2*e^3 + 15*e^2 - 28*e + 22, -13/4*e^4 + 27/4*e^3 + 48*e^2 - 195/2*e - 19, -13/4*e^4 + 27/4*e^3 + 48*e^2 - 195/2*e - 19, -e^4 + 2*e^3 + 15*e^2 - 28*e + 22, 1/2*e^4 - e^3 - 15/2*e^2 + 11*e + 59, -9/4*e^4 + 21/4*e^3 + 65/2*e^2 - 145/2*e + 34]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([4, 2, 1/2*w^3 - 2*w^2 - 2*w + 15/2])] = 1
AL_eigenvalues[ZF.ideal([4, 2, -w^2 + w + 8])] = 1

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