/*
  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([9, -1, -7, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

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

primes_array = [
[2, 2, -w^2 + w + 4],\
[3, 3, -w^2 + w + 3],\
[5, 5, w^2 - 4],\
[8, 2, w^3 - w^2 - 4*w + 5],\
[17, 17, -w^2 + w + 5],\
[27, 3, -w^3 + 4*w - 2],\
[29, 29, -w^2 + w + 1],\
[29, 29, -w^3 + 4*w + 2],\
[37, 37, -2*w^3 + 3*w^2 + 9*w - 13],\
[41, 41, w^3 - w^2 - 5*w + 2],\
[43, 43, -w^3 + w^2 + 3*w - 4],\
[61, 61, w^2 - 2*w - 2],\
[61, 61, 2*w^2 - w - 8],\
[67, 67, -4*w^3 + 5*w^2 + 18*w - 22],\
[73, 73, -w^2 - 2*w + 2],\
[79, 79, w^2 - 2*w - 4],\
[89, 89, w^2 + w - 5],\
[89, 89, 2*w^3 - 2*w^2 - 9*w + 8],\
[89, 89, w^3 - 5*w - 5],\
[89, 89, -w^3 + 2*w^2 + 4*w - 4],\
[97, 97, w^3 + w^2 - 5*w - 4],\
[101, 101, -2*w^3 + 2*w^2 + 8*w - 11],\
[103, 103, w^3 - 5*w + 1],\
[109, 109, 2*w - 1],\
[109, 109, -w^3 + 2*w^2 + 3*w - 7],\
[113, 113, 2*w^2 - 7],\
[125, 5, -w^3 + 3*w^2 + 3*w - 8],\
[127, 127, 2*w^3 - 4*w^2 - 11*w + 16],\
[131, 131, 3*w^2 + 2*w - 8],\
[131, 131, -2*w^3 + 4*w^2 + 8*w - 13],\
[137, 137, w^3 - 3*w^2 - 7*w + 10],\
[149, 149, -w^3 + 4*w - 4],\
[149, 149, w^2 - 2*w - 8],\
[157, 157, -w - 4],\
[163, 163, -w^3 + 2*w^2 + 6*w - 10],\
[167, 167, -w^3 + 2*w^2 + 5*w - 11],\
[167, 167, -3*w^2 - 2*w + 10],\
[167, 167, -w^2 - w + 7],\
[167, 167, 2*w^2 - 2*w - 5],\
[173, 173, -3*w^3 + 2*w^2 + 13*w - 11],\
[179, 179, w^3 - 3*w^2 - 5*w + 10],\
[191, 191, -2*w^3 - 3*w^2 + 10*w + 14],\
[191, 191, 3*w^2 + w - 7],\
[193, 193, w^2 - w + 1],\
[193, 193, -w^2 - w - 1],\
[227, 227, 4*w^3 - 4*w^2 - 17*w + 20],\
[227, 227, -3*w^3 + 4*w^2 + 13*w - 17],\
[229, 229, -w^3 + 6*w - 2],\
[233, 233, -3*w^3 + 3*w^2 + 13*w - 16],\
[241, 241, -w^2 + 2*w - 2],\
[263, 263, 2*w^3 - 5*w^2 - 12*w + 16],\
[263, 263, -3*w^3 + 4*w^2 + 13*w - 19],\
[269, 269, w^3 + 2*w^2 - 5*w - 7],\
[269, 269, -w^3 - 2*w^2 + w + 5],\
[281, 281, 2*w^3 - 2*w^2 - 8*w + 1],\
[281, 281, w^2 - 8],\
[289, 17, 2*w^3 - 10*w - 7],\
[307, 307, w^3 + 2*w^2 - 6*w - 8],\
[307, 307, -2*w^3 + 2*w^2 + 8*w - 7],\
[313, 313, 5*w^3 - 6*w^2 - 24*w + 28],\
[313, 313, 2*w^3 - 2*w^2 - 10*w + 5],\
[337, 337, w^3 - 2*w - 2],\
[347, 347, -w^3 + 4*w^2 + w - 13],\
[349, 349, -2*w^3 + w^2 + 9*w - 7],\
[353, 353, 2*w^3 + w^2 - 7*w + 1],\
[359, 359, -3*w^2 - 3*w + 5],\
[359, 359, 3*w^3 - 5*w^2 - 13*w + 16],\
[367, 367, 3*w^3 - 6*w^2 - 15*w + 23],\
[367, 367, -w^3 + 2*w^2 + 6*w - 4],\
[367, 367, -2*w^3 + 2*w^2 + 8*w - 5],\
[367, 367, 2*w^3 - 3*w^2 - 12*w + 16],\
[373, 373, -2*w^3 + 4*w^2 + 12*w - 17],\
[373, 373, 3*w^2 + 4*w - 8],\
[383, 383, -w^3 + 2*w^2 + 3*w - 13],\
[383, 383, 2*w^2 - 2*w - 11],\
[389, 389, 5*w^3 - 6*w^2 - 24*w + 26],\
[389, 389, -w^3 + 3*w - 5],\
[401, 401, w^3 + 2*w^2 - 4*w - 10],\
[401, 401, 2*w^3 - w^2 - 7*w + 5],\
[409, 409, -2*w^2 + 3*w + 10],\
[419, 419, w^2 - 3*w - 1],\
[419, 419, -w^3 + 5*w^2 + 9*w - 14],\
[421, 421, 2*w^3 - 8*w - 7],\
[431, 431, -3*w^2 + 16],\
[431, 431, -3*w^3 + 11*w - 7],\
[433, 433, 4*w^3 - 7*w^2 - 18*w + 26],\
[439, 439, 3*w - 2],\
[439, 439, -w^3 + w^2 + 5*w - 8],\
[443, 443, 2*w^3 - w^2 - 6*w + 4],\
[443, 443, w^2 + 3*w - 1],\
[449, 449, -2*w^3 + 5*w^2 + 7*w - 17],\
[457, 457, 4*w^3 - 6*w^2 - 19*w + 22],\
[479, 479, 3*w^2 - 3*w - 13],\
[479, 479, -4*w^3 + 8*w^2 + 22*w - 31],\
[479, 479, 3*w^3 - 7*w^2 - 17*w + 26],\
[479, 479, -6*w^3 + 7*w^2 + 28*w - 32],\
[487, 487, -2*w^3 + 4*w^2 + 7*w - 8],\
[491, 491, 3*w^2 - w - 11],\
[491, 491, 4*w^3 - 5*w^2 - 18*w + 20],\
[521, 521, -3*w^3 + 11*w - 5],\
[521, 521, 3*w^3 - 3*w^2 - 15*w + 14],\
[523, 523, -2*w^3 + 5*w^2 + 8*w - 14],\
[529, 23, -2*w^3 + 3*w^2 + 8*w - 14],\
[529, 23, 3*w^3 - 2*w^2 - 14*w + 4],\
[541, 541, -w^3 + 2*w^2 + 7*w - 11],\
[541, 541, -w^3 - w^2 + 5*w - 2],\
[547, 547, -3*w - 2],\
[547, 547, w^3 - 2*w^2 - 7*w + 7],\
[547, 547, w^3 - 4*w^2 - 8*w + 10],\
[547, 547, 2*w^3 - 3*w^2 - 7*w + 11],\
[563, 563, 2*w^3 - 4*w^2 - 12*w + 13],\
[563, 563, -w^3 + 4*w^2 + w - 7],\
[571, 571, -w^3 + 2*w^2 + 2*w - 8],\
[571, 571, 3*w^2 - 10],\
[577, 577, 2*w^3 + w^2 - 7*w - 5],\
[599, 599, 2*w^3 - 7*w + 2],\
[599, 599, -4*w^3 + 7*w^2 + 21*w - 29],\
[617, 617, -2*w^3 + w^2 + 11*w + 1],\
[631, 631, 3*w^2 + w - 13],\
[631, 631, 3*w^2 - 4*w - 10],\
[647, 647, 3*w^3 - 4*w^2 - 13*w + 11],\
[677, 677, -2*w^3 + 4*w^2 + 8*w - 17],\
[691, 691, -w^3 + 3*w^2 + 3*w - 14],\
[733, 733, -w^3 + 4*w^2 + 3*w - 11],\
[733, 733, 3*w^3 - w^2 - 15*w - 2],\
[733, 733, -w^3 + w^2 + 7*w - 2],\
[733, 733, 3*w^3 - 4*w^2 - 16*w + 16],\
[739, 739, -3*w^3 + w^2 + 11*w - 8],\
[743, 743, -3*w^3 + 2*w^2 + 12*w - 14],\
[751, 751, -2*w^3 + w^2 + 8*w - 2],\
[761, 761, -2*w^3 + 2*w^2 + 7*w - 10],\
[761, 761, 2*w^3 - 4*w^2 - 3*w + 8],\
[769, 769, -w^3 + w^2 + 7*w - 4],\
[769, 769, 2*w^3 + 2*w^2 - 8*w - 11],\
[787, 787, -2*w^3 + 3*w^2 + 6*w - 10],\
[787, 787, -2*w^2 - 3*w + 8],\
[797, 797, -2*w^3 + w^2 + 7*w - 1],\
[797, 797, -2*w^3 - 2*w^2 + 11*w + 10],\
[809, 809, -2*w^3 + 5*w^2 + 7*w - 19],\
[811, 811, 2*w^3 - 2*w^2 - 7*w - 2],\
[811, 811, 3*w^3 - 2*w^2 - 11*w - 1],\
[827, 827, 3*w^3 - 2*w^2 - 14*w + 10],\
[829, 829, 2*w^3 - 2*w^2 - 9*w + 2],\
[829, 829, 4*w^2 + 2*w - 11],\
[841, 29, 2*w^3 + w^2 - 6*w - 2],\
[863, 863, 2*w^3 - 8*w - 1],\
[883, 883, 3*w^3 - 4*w^2 - 15*w + 13],\
[887, 887, 3*w^3 - 2*w^2 - 12*w + 10],\
[907, 907, 2*w^3 - 3*w^2 - 9*w + 7],\
[911, 911, 2*w^3 + w^2 - 11*w - 5],\
[919, 919, -2*w^3 + 5*w - 8],\
[929, 929, -w^3 + 4*w^2 + 3*w - 13],\
[937, 937, w^3 - 5*w - 7],\
[937, 937, -2*w^3 + 3*w^2 + 10*w - 8],\
[971, 971, -2*w^3 + 4*w^2 + 11*w - 20],\
[971, 971, -4*w^3 + 4*w^2 + 19*w - 20],\
[977, 977, -4*w^3 + 6*w^2 + 19*w - 28],\
[983, 983, -4*w^2 - 4*w + 7],\
[991, 991, -5*w^3 + 8*w^2 + 26*w - 32],\
[991, 991, -6*w^3 + 6*w^2 + 26*w - 31],\
[997, 997, -3*w^3 + 8*w^2 + 18*w - 26]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^6 - 3*x^5 - 4*x^4 + 16*x^3 - 3*x^2 - 13*x + 4
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, e^5 - e^4 - 7*e^3 + 4*e^2 + 10*e - 1, -1, 3*e^5 - 5*e^4 - 18*e^3 + 23*e^2 + 17*e - 11, 3*e^5 - 4*e^4 - 19*e^3 + 18*e^2 + 20*e - 8, e^4 - 6*e^2 - 2*e + 7, 2*e^5 - 4*e^4 - 11*e^3 + 18*e^2 + 9*e - 4, -3*e^5 + 4*e^4 + 20*e^3 - 18*e^2 - 25*e + 10, 7*e^5 - 10*e^4 - 44*e^3 + 46*e^2 + 47*e - 22, -2*e^5 + 2*e^4 + 12*e^3 - 4*e^2 - 12*e - 6, 2*e^4 - e^3 - 12*e^2 + 3*e + 8, 3*e^5 - 5*e^4 - 18*e^3 + 22*e^2 + 13*e - 3, -6*e^5 + 11*e^4 + 33*e^3 - 48*e^2 - 27*e + 17, -e^4 + 6*e^2 - 2*e - 1, -5*e^5 + 9*e^4 + 27*e^3 - 40*e^2 - 18*e + 15, -7*e^5 + 10*e^4 + 46*e^3 - 46*e^2 - 55*e + 28, 8*e^5 - 11*e^4 - 48*e^3 + 44*e^2 + 48*e - 3, -9*e^5 + 14*e^4 + 52*e^3 - 60*e^2 - 47*e + 26, -3*e^5 + 4*e^4 + 20*e^3 - 16*e^2 - 25*e + 2, -4*e^5 + 5*e^4 + 26*e^3 - 18*e^2 - 32*e - 5, -3*e^5 + 6*e^4 + 14*e^3 - 30*e^2 + 3*e + 18, 6*e^5 - 9*e^4 - 35*e^3 + 42*e^2 + 31*e - 31, 6*e^5 - 10*e^4 - 36*e^3 + 46*e^2 + 42*e - 28, 4*e^5 - 5*e^4 - 28*e^3 + 20*e^2 + 38*e - 3, 9*e^5 - 14*e^4 - 54*e^3 + 60*e^2 + 51*e - 16, -3*e^5 + 6*e^4 + 18*e^3 - 32*e^2 - 19*e + 22, -e^5 + e^4 + 8*e^3 - 10*e^2 - 13*e + 11, 2*e^4 - 4*e^3 - 10*e^2 + 18*e + 10, -3*e^5 + e^4 + 23*e^3 - 32*e - 3, -4*e^5 + 5*e^4 + 23*e^3 - 22*e^2 - 17*e + 13, 3*e^5 - e^4 - 26*e^3 + 2*e^2 + 45*e + 5, -2*e^5 + 7*e^4 + 10*e^3 - 36*e^2 - 10*e + 25, -e^5 + 2*e^4 + 4*e^3 - 10*e^2 + e + 6, 12*e^5 - 19*e^4 - 72*e^3 + 82*e^2 + 68*e - 25, -e^5 + 2*e^4 + 6*e^3 - 8*e^2 - 9*e + 6, -8*e^5 + 12*e^4 + 50*e^3 - 56*e^2 - 50*e + 36, 4*e^5 - 7*e^4 - 26*e^3 + 36*e^2 + 36*e - 23, 8*e^5 - 14*e^4 - 46*e^3 + 64*e^2 + 44*e - 28, e^5 - 4*e^4 - e^3 + 20*e^2 - 12*e - 4, -e^5 + 4*e^4 + 6*e^3 - 20*e^2 - 3*e, -15*e^5 + 25*e^4 + 92*e^3 - 118*e^2 - 93*e + 63, -7*e^5 + 10*e^4 + 46*e^3 - 50*e^2 - 55*e + 32, -5*e^5 + 6*e^4 + 34*e^3 - 32*e^2 - 41*e + 22, -10*e^5 + 13*e^4 + 63*e^3 - 52*e^2 - 67*e + 13, -2*e^5 - e^4 + 18*e^3 + 10*e^2 - 40*e - 5, 14*e^5 - 18*e^4 - 91*e^3 + 72*e^2 + 113*e - 26, -3*e^5 + 4*e^4 + 18*e^3 - 20*e^2 - 19*e + 14, 10*e^5 - 17*e^4 - 60*e^3 + 76*e^2 + 60*e - 31, -18*e^5 + 28*e^4 + 113*e^3 - 130*e^2 - 121*e + 66, 15*e^5 - 23*e^4 - 90*e^3 + 98*e^2 + 87*e - 39, -12*e^5 + 22*e^4 + 68*e^3 - 102*e^2 - 64*e + 56, -11*e^5 + 13*e^4 + 72*e^3 - 54*e^2 - 95*e + 29, 8*e^5 - 15*e^4 - 48*e^3 + 76*e^2 + 56*e - 49, -12*e^5 + 15*e^4 + 78*e^3 - 60*e^2 - 94*e + 19, -8*e^5 + 14*e^4 + 46*e^3 - 66*e^2 - 42*e + 34, -7*e^5 + 12*e^4 + 40*e^3 - 54*e^2 - 33*e + 42, 4*e^5 - 4*e^4 - 22*e^3 + 12*e^2 + 12*e + 8, -14*e^5 + 19*e^4 + 91*e^3 - 84*e^2 - 103*e + 37, -9*e^5 + 19*e^4 + 47*e^3 - 90*e^2 - 34*e + 49, 5*e^5 - 5*e^4 - 35*e^3 + 20*e^2 + 52*e - 5, -18*e^5 + 27*e^4 + 112*e^3 - 114*e^2 - 126*e + 49, 2*e^5 - 4*e^4 - 13*e^3 + 18*e^2 + 19*e, 19*e^5 - 30*e^4 - 117*e^3 + 140*e^2 + 116*e - 76, 10*e^5 - 12*e^4 - 65*e^3 + 52*e^2 + 79*e - 30, 3*e^4 - 18*e^2 + 4*e + 5, 12*e^5 - 20*e^4 - 68*e^3 + 94*e^2 + 48*e - 54, 6*e^5 - 10*e^4 - 35*e^3 + 44*e^2 + 21*e - 22, e^5 - 2*e^4 - 2*e^3 + 2*e^2 - 7*e + 16, -19*e^5 + 26*e^4 + 122*e^3 - 112*e^2 - 151*e + 60, -e^5 + e^4 + 8*e^3 - 2*e^2 - 19*e - 13, -7*e^5 + 7*e^4 + 50*e^3 - 26*e^2 - 79*e + 9, -6*e^5 + 10*e^4 + 36*e^3 - 46*e^2 - 32*e + 16, 15*e^5 - 20*e^4 - 96*e^3 + 82*e^2 + 115*e - 32, 5*e^4 - 3*e^3 - 28*e^2 - e + 29, -12*e^5 + 18*e^4 + 72*e^3 - 76*e^2 - 66*e + 16, 9*e^5 - 19*e^4 - 54*e^3 + 92*e^2 + 65*e - 61, 11*e^5 - 14*e^4 - 67*e^3 + 52*e^2 + 72*e, -11*e^5 + 21*e^4 + 59*e^3 - 98*e^2 - 42*e + 47, 9*e^5 - 14*e^4 - 58*e^3 + 68*e^2 + 71*e - 48, 3*e^5 - 6*e^4 - 18*e^3 + 28*e^2 + 27*e - 32, -8*e^5 + 8*e^4 + 48*e^3 - 32*e^2 - 36*e + 4, -14*e^5 + 25*e^4 + 81*e^3 - 116*e^2 - 73*e + 71, -16*e^5 + 17*e^4 + 107*e^3 - 74*e^2 - 131*e + 37, -e^5 - 4*e^4 + 14*e^3 + 28*e^2 - 33*e - 22, -2*e^5 + 6*e^4 + 11*e^3 - 30*e^2 - 9*e + 28, -3*e^5 + 4*e^4 + 16*e^3 - 18*e^2 - 7*e + 16, -8*e^5 + 12*e^4 + 49*e^3 - 54*e^2 - 49*e + 26, -12*e^5 + 18*e^4 + 76*e^3 - 82*e^2 - 92*e + 52, 2*e^5 - 4*e^4 - 5*e^3 + 10*e^2 - 23*e + 4, 12*e^5 - 16*e^4 - 78*e^3 + 76*e^2 + 88*e - 54, 4*e^5 - 5*e^4 - 20*e^3 + 14*e^2 + 8*e + 1, 7*e^5 - 8*e^4 - 48*e^3 + 40*e^2 + 67*e - 34, 13*e^5 - 18*e^4 - 80*e^3 + 72*e^2 + 85*e - 20, 3*e^5 - 13*e^4 - 14*e^3 + 72*e^2 + e - 43, 5*e^5 - 7*e^4 - 26*e^3 + 26*e^2 + 5*e - 1, -22*e^5 + 37*e^4 + 125*e^3 - 166*e^2 - 101*e + 69, -5*e^5 + 6*e^4 + 33*e^3 - 24*e^2 - 48*e - 6, -12*e^5 + 18*e^4 + 72*e^3 - 84*e^2 - 74*e + 52, -16*e^5 + 25*e^4 + 92*e^3 - 110*e^2 - 72*e + 47, -7*e^5 + 4*e^4 + 50*e^3 - 4*e^2 - 77*e - 10, 6*e^5 - 6*e^4 - 42*e^3 + 28*e^2 + 46*e - 10, -8*e^5 + 6*e^4 + 56*e^3 - 18*e^2 - 72*e - 12, -2*e^3 + 4*e^2 - 2*e + 2, -21*e^5 + 32*e^4 + 126*e^3 - 146*e^2 - 121*e + 86, -10*e^5 + 11*e^4 + 64*e^3 - 42*e^2 - 74*e + 11, -13*e^5 + 20*e^4 + 82*e^3 - 104*e^2 - 93*e + 82, -17*e^5 + 25*e^4 + 102*e^3 - 112*e^2 - 93*e + 37, -25*e^5 + 38*e^4 + 154*e^3 - 168*e^2 - 157*e + 68, 12*e^5 - 20*e^4 - 73*e^3 + 92*e^2 + 75*e - 46, 11*e^5 - 15*e^4 - 68*e^3 + 62*e^2 + 81*e - 17, 14*e^5 - 22*e^4 - 86*e^3 + 98*e^2 + 94*e - 50, -13*e^5 + 18*e^4 + 82*e^3 - 80*e^2 - 93*e + 56, -8*e^5 + 15*e^4 + 46*e^3 - 72*e^2 - 48*e + 47, 18*e^5 - 24*e^4 - 111*e^3 + 94*e^2 + 105*e - 6, 6*e^5 - 12*e^4 - 35*e^3 + 60*e^2 + 39*e - 60, -12*e^5 + 24*e^4 + 65*e^3 - 106*e^2 - 51*e + 44, -15*e^5 + 23*e^4 + 98*e^3 - 114*e^2 - 123*e + 81, 7*e^5 - 8*e^4 - 45*e^3 + 28*e^2 + 62*e + 14, 2*e^5 - 6*e^4 - 6*e^3 + 28*e^2 - 14*e - 20, 5*e^5 - 18*e^4 - 17*e^3 + 88*e^2 - 14*e - 52, -4*e^5 + 12*e^4 + 24*e^3 - 62*e^2 - 34*e + 52, 14*e^5 - 13*e^4 - 102*e^3 + 46*e^2 + 148*e - 7, -13*e^5 + 9*e^4 + 92*e^3 - 30*e^2 - 121*e - 3, 23*e^5 - 37*e^4 - 143*e^3 + 170*e^2 + 154*e - 87, 15*e^5 - 18*e^4 - 96*e^3 + 66*e^2 + 107*e - 18, e^5 - 8*e^4 + 8*e^3 + 44*e^2 - 47*e - 22, 5*e^5 - 8*e^4 - 26*e^3 + 30*e^2 + 17*e + 18, -14*e^5 + 24*e^4 + 81*e^3 - 106*e^2 - 69*e + 32, -15*e^5 + 21*e^4 + 90*e^3 - 82*e^2 - 85*e + 13, -12*e^5 + 8*e^4 + 84*e^3 - 32*e^2 - 110*e + 22, 8*e^5 - 12*e^4 - 62*e^3 + 66*e^2 + 98*e - 48, 5*e^5 - 16*e^4 - 18*e^3 + 78*e^2 - 3*e - 34, 12*e^5 - 18*e^4 - 70*e^3 + 70*e^2 + 60*e - 4, 2*e^5 - 12*e^4 - 8*e^3 + 60*e^2 + 6*e - 30, e^5 + 3*e^4 - 12*e^3 - 24*e^2 + 35*e + 23, 11*e^5 - 19*e^4 - 68*e^3 + 88*e^2 + 67*e - 41, 3*e^4 + 3*e^3 - 30*e^2 - 13*e + 37, -6*e^5 + 13*e^4 + 28*e^3 - 50*e^2 - 4*e + 9, e^5 - 6*e^4 - 4*e^3 + 42*e^2 - 3*e - 34, -8*e^5 + 16*e^4 + 40*e^3 - 74*e^2 - 18*e + 52, -5*e^5 + 6*e^4 + 34*e^3 - 24*e^2 - 49*e - 8, 7*e^5 + e^4 - 58*e^3 - 14*e^2 + 95*e + 7, e^5 - 6*e^4 - 2*e^3 + 24*e^2 + 7*e + 16, 19*e^5 - 24*e^4 - 124*e^3 + 112*e^2 + 143*e - 58, -20*e^5 + 34*e^4 + 118*e^3 - 146*e^2 - 118*e + 54, 19*e^5 - 33*e^4 - 112*e^3 + 164*e^2 + 103*e - 99, -3*e^5 + 6*e^4 + 25*e^3 - 26*e^2 - 52*e - 2, -10*e^5 + 10*e^4 + 70*e^3 - 34*e^2 - 96*e - 8, -4*e^5 + 10*e^4 + 14*e^3 - 38*e^2 + 18*e + 4, -26*e^5 + 34*e^4 + 174*e^3 - 144*e^2 - 214*e + 44, -13*e^5 + 13*e^4 + 84*e^3 - 50*e^2 - 91*e + 11, 6*e^5 - 15*e^4 - 26*e^3 + 74*e^2 + 2*e - 51, -5*e^5 + 6*e^4 + 42*e^3 - 32*e^2 - 87*e + 20, 28*e^5 - 33*e^4 - 182*e^3 + 132*e^2 + 218*e - 33, 11*e^5 - 19*e^4 - 70*e^3 + 98*e^2 + 87*e - 77, -3*e^5 - 5*e^4 + 32*e^3 + 24*e^2 - 65*e - 13, 13*e^5 - 19*e^4 - 88*e^3 + 82*e^2 + 127*e - 47, 24*e^5 - 40*e^4 - 138*e^3 + 176*e^2 + 116*e - 82, -10*e^5 + 14*e^4 + 72*e^3 - 66*e^2 - 110*e + 28, 8*e^5 - 16*e^4 - 53*e^3 + 86*e^2 + 83*e - 60, -23*e^5 + 30*e^4 + 140*e^3 - 112*e^2 - 149*e + 6]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

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

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