/*
  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([15, 15, w^3 - 5*w - 3])

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 + 2*x^5 - 10*x^4 - 21*x^3 + 20*x^2 + 55*x + 21
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 1, 1, -e^5 + 11*e^3 + 2*e^2 - 28*e - 13, e^3 + e^2 - 5*e - 3, -e^4 - e^3 + 6*e^2 + 5*e - 1, -e^4 - e^3 + 7*e^2 + 5*e - 8, e^5 + e^4 - 8*e^3 - 5*e^2 + 11*e + 2, -e^4 - e^3 + 8*e^2 + 5*e - 9, -e^5 - e^4 + 8*e^3 + 7*e^2 - 13*e - 10, -2*e^5 - e^4 + 22*e^3 + 10*e^2 - 58*e - 35, 3*e^5 + e^4 - 31*e^3 - 12*e^2 + 74*e + 43, 2*e^5 + e^4 - 23*e^3 - 12*e^2 + 61*e + 41, 2*e^5 + e^4 - 23*e^3 - 12*e^2 + 63*e + 41, -3*e^5 - 2*e^4 + 28*e^3 + 16*e^2 - 57*e - 36, 2*e^5 + e^4 - 21*e^3 - 13*e^2 + 51*e + 44, 3*e^5 + e^4 - 30*e^3 - 8*e^2 + 67*e + 29, -e^4 - e^3 + 7*e^2 + e - 4, -e^5 - 2*e^4 + 8*e^3 + 14*e^2 - 11*e - 18, 3*e^5 + 3*e^4 - 29*e^3 - 23*e^2 + 66*e + 46, -3*e^5 + 32*e^3 + 3*e^2 - 79*e - 31, -2*e^5 - e^4 + 17*e^3 + 3*e^2 - 31*e + 4, -e^4 + 8*e^2 - 4*e - 11, -3*e^5 - 3*e^4 + 28*e^3 + 24*e^2 - 61*e - 47, 2*e^3 + 3*e^2 - 10*e - 9, 2*e^5 + e^4 - 24*e^3 - 14*e^2 + 66*e + 55, -e^5 + 7*e^3 - 6*e - 6, -4*e^5 - e^4 + 39*e^3 + 8*e^2 - 85*e - 29, -2*e^5 - e^4 + 23*e^3 + 11*e^2 - 61*e - 42, -3*e^5 - e^4 + 31*e^3 + 9*e^2 - 72*e - 32, e^5 + 2*e^4 - 8*e^3 - 11*e^2 + 13*e + 9, 5*e^5 + 3*e^4 - 51*e^3 - 29*e^2 + 126*e + 88, -4*e^5 - 3*e^4 + 39*e^3 + 23*e^2 - 87*e - 42, -3*e^5 + e^4 + 34*e^3 - 4*e^2 - 87*e - 19, -4*e^5 - e^4 + 42*e^3 + 7*e^2 - 98*e - 26, e^5 + e^4 - 12*e^3 - 13*e^2 + 35*e + 44, 2*e^5 - 24*e^3 - 6*e^2 + 68*e + 44, -2*e^5 + e^4 + 23*e^3 - 6*e^2 - 63*e - 9, -2*e^5 - e^4 + 21*e^3 + 11*e^2 - 55*e - 38, 4*e^5 - 44*e^3 - 8*e^2 + 112*e + 58, -4*e^5 - 4*e^4 + 39*e^3 + 29*e^2 - 87*e - 53, 4*e^5 + e^4 - 41*e^3 - 9*e^2 + 97*e + 36, -e^4 - 2*e^3 + 10*e^2 + 14*e - 9, -2*e^5 - 2*e^4 + 20*e^3 + 14*e^2 - 46*e - 26, -e^5 - e^4 + 6*e^3 - e + 19, 7*e^5 + 3*e^4 - 75*e^3 - 31*e^2 + 184*e + 104, 3*e^5 + e^4 - 34*e^3 - 16*e^2 + 91*e + 71, -e^5 + e^4 + 13*e^3 - 3*e^2 - 40*e - 16, -e^4 + 3*e^3 + 9*e^2 - 15*e - 6, -e^4 - 3*e^3 + 2*e^2 + 11*e + 13, -3*e^5 - e^4 + 35*e^3 + 11*e^2 - 92*e - 34, 3*e^5 + 4*e^4 - 28*e^3 - 28*e^2 + 59*e + 42, 5*e^5 + 3*e^4 - 51*e^3 - 27*e^2 + 120*e + 72, -2*e^5 + 23*e^3 - e^2 - 61*e - 13, e^5 + 4*e^4 - 8*e^3 - 30*e^2 + 11*e + 32, e^4 + 7*e^3 + 3*e^2 - 37*e - 40, e^5 + 2*e^4 - e^3 - 6*e^2 - 26*e - 24, 3*e^5 + 2*e^4 - 33*e^3 - 13*e^2 + 86*e + 31, -5*e^5 - 2*e^4 + 57*e^3 + 27*e^2 - 156*e - 105, -3*e^5 + 37*e^3 + 9*e^2 - 106*e - 59, 3*e^5 + 5*e^4 - 30*e^3 - 40*e^2 + 71*e + 69, 5*e^5 + 2*e^4 - 49*e^3 - 23*e^2 + 112*e + 87, 6*e^5 + 2*e^4 - 67*e^3 - 22*e^2 + 171*e + 86, 2*e^5 - e^4 - 28*e^3 + 86*e + 35, e^4 + 9*e^3 + 3*e^2 - 53*e - 42, 7*e^5 + 7*e^4 - 68*e^3 - 54*e^2 + 149*e + 103, 7*e^5 - e^4 - 79*e^3 - 5*e^2 + 208*e + 90, 6*e^5 + 6*e^4 - 61*e^3 - 52*e^2 + 143*e + 110, -9*e^5 - 6*e^4 + 91*e^3 + 51*e^2 - 210*e - 129, 2*e^5 - 18*e^3 - 2*e^2 + 32*e + 18, -e^5 + 12*e^3 + 5*e^2 - 43*e - 37, -4*e^5 + e^4 + 43*e^3 - 3*e^2 - 107*e - 24, 2*e^5 - 23*e^3 - 5*e^2 + 61*e + 31, 7*e^5 + 2*e^4 - 70*e^3 - 24*e^2 + 159*e + 82, 3*e^5 + e^4 - 36*e^3 - 10*e^2 + 105*e + 49, 6*e^5 + e^4 - 68*e^3 - 27*e^2 + 178*e + 124, -2*e^5 + e^4 + 21*e^3 - 4*e^2 - 45*e - 9, 6*e^5 - 60*e^3 - 2*e^2 + 136*e + 38, -e^5 + 11*e^3 + 5*e^2 - 30*e - 15, -3*e^4 - 5*e^3 + 17*e^2 + 29*e + 4, 8*e^5 + 5*e^4 - 85*e^3 - 49*e^2 + 201*e + 136, 5*e^5 + 3*e^4 - 54*e^3 - 34*e^2 + 141*e + 99, e^5 + e^4 - 10*e^3 - 3*e^2 + 21*e - 8, -3*e^5 - 4*e^4 + 31*e^3 + 37*e^2 - 76*e - 69, -3*e^5 + 5*e^4 + 37*e^3 - 29*e^2 - 106*e - 4, 5*e^5 + 5*e^4 - 50*e^3 - 40*e^2 + 123*e + 87, 2*e^5 - 2*e^4 - 25*e^3 + 5*e^2 + 75*e + 45, e^5 + e^4 - 10*e^3 - 12*e^2 + 19*e + 29, 5*e^5 + 5*e^4 - 53*e^3 - 49*e^2 + 130*e + 102, -3*e^5 + 32*e^3 + 4*e^2 - 75*e - 46, 3*e^5 - 35*e^3 - 12*e^2 + 102*e + 60, -2*e^5 + 29*e^3 + 9*e^2 - 91*e - 55, -6*e^5 - 5*e^4 + 61*e^3 + 48*e^2 - 147*e - 111, 3*e^5 + 4*e^4 - 27*e^3 - 27*e^2 + 52*e + 39, e^5 - e^4 - 21*e^3 + e^2 + 80*e + 24, 8*e^5 + 6*e^4 - 76*e^3 - 47*e^2 + 162*e + 107, -2*e^5 + 2*e^4 + 25*e^3 - 67*e - 70, -6*e^5 + 74*e^3 + 15*e^2 - 208*e - 103, -3*e^5 + 3*e^4 + 36*e^3 - 14*e^2 - 105*e - 29, 3*e^5 + 5*e^4 - 19*e^3 - 35*e^2 + 12*e + 44, -e^5 - e^4 + 7*e^3 + 6*e^2 - 2*e - 3, -8*e^5 - 3*e^4 + 75*e^3 + 21*e^2 - 157*e - 52, -3*e^5 - e^4 + 40*e^3 + 18*e^2 - 121*e - 83, -5*e^5 - 6*e^4 + 48*e^3 + 52*e^2 - 109*e - 90, -6*e^5 - 4*e^4 + 63*e^3 + 45*e^2 - 157*e - 127, -2*e^5 - 2*e^4 + 21*e^3 + 17*e^2 - 55*e - 45, e^5 - e^4 - 14*e^3 + 5*e^2 + 53*e + 16, 7*e^5 + 5*e^4 - 75*e^3 - 51*e^2 + 192*e + 146, 6*e^5 + 5*e^4 - 55*e^3 - 29*e^2 + 109*e + 36, 2*e^5 - 3*e^4 - 32*e^3 + 18*e^2 + 106*e + 9, -4*e^4 - 8*e^3 + 16*e^2 + 38*e + 30, 10*e^5 - 2*e^4 - 111*e^3 - e^2 + 287*e + 101, 3*e^5 + 2*e^4 - 24*e^3 - 6*e^2 + 37*e, -5*e^5 - 3*e^4 + 52*e^3 + 30*e^2 - 127*e - 79, 2*e^5 - e^4 - 22*e^3 + 6*e^2 + 52*e + 13, -e^5 - 5*e^4 + 4*e^3 + 38*e^2 + 9*e - 45, 2*e^5 - 2*e^4 - 23*e^3 + 17*e^2 + 49*e - 15, -11*e^5 - 4*e^4 + 116*e^3 + 37*e^2 - 289*e - 139, -4*e^5 - e^4 + 41*e^3 + 23*e^2 - 95*e - 92, -4*e^5 - e^4 + 46*e^3 + 12*e^2 - 122*e - 47, -4*e^5 + 48*e^3 + 13*e^2 - 130*e - 83, 5*e^5 + 7*e^4 - 46*e^3 - 46*e^2 + 97*e + 57, -e^5 + e^4 + 7*e^3 - 7*e^2 - 2*e - 14, -8*e^5 - e^4 + 93*e^3 + 33*e^2 - 255*e - 168, -4*e^5 - 3*e^4 + 47*e^3 + 39*e^2 - 143*e - 126, -4*e^5 - 5*e^4 + 43*e^3 + 45*e^2 - 103*e - 98, 6*e^5 + e^4 - 66*e^3 - 18*e^2 + 172*e + 79, e^5 + 4*e^4 - 7*e^3 - 37*e^2 + 10*e + 53, -10*e^5 - 3*e^4 + 105*e^3 + 32*e^2 - 247*e - 121, -4*e^5 + 4*e^4 + 43*e^3 - 23*e^2 - 99*e - 5, 2*e^5 - 4*e^4 - 29*e^3 + 24*e^2 + 91*e + 10, -8*e^5 - 2*e^4 + 90*e^3 + 34*e^2 - 242*e - 162, e^5 - 11*e^3 - 4*e^2 + 32*e + 16, -6*e^5 - 4*e^4 + 69*e^3 + 47*e^2 - 199*e - 157, 6*e^5 + 8*e^4 - 57*e^3 - 65*e^2 + 119*e + 109, -6*e^5 - 3*e^4 + 61*e^3 + 15*e^2 - 143*e - 20, 6*e^5 - 65*e^3 - 14*e^2 + 155*e + 76, -e^5 + 9*e^3 + 7*e^2 - 20*e - 21, 6*e^5 + 3*e^4 - 66*e^3 - 31*e^2 + 154*e + 96, -9*e^5 - 5*e^4 + 98*e^3 + 46*e^2 - 249*e - 133, -5*e^4 - 9*e^3 + 35*e^2 + 45*e - 10, -7*e^5 - 3*e^4 + 73*e^3 + 37*e^2 - 186*e - 130, e^5 - 3*e^4 - 22*e^3 + 14*e^2 + 83*e + 29, -6*e^5 + 63*e^3 - 2*e^2 - 151*e - 30, -9*e^5 - 2*e^4 + 92*e^3 + 29*e^2 - 215*e - 133, -2*e^5 + 2*e^4 + 23*e^3 - 13*e^2 - 61*e - 17, -7*e^5 - 5*e^4 + 73*e^3 + 47*e^2 - 166*e - 130, -3*e^5 - e^4 + 33*e^3 + 11*e^2 - 90*e - 42, 2*e^5 - 6*e^4 - 38*e^3 + 26*e^2 + 148*e + 32, 6*e^5 - 4*e^4 - 69*e^3 + 19*e^2 + 179*e + 49, 2*e^5 - e^4 - 34*e^3 - 10*e^2 + 116*e + 87, -2*e^5 - 3*e^4 + 25*e^3 + 27*e^2 - 75*e - 54, e^5 + 8*e^4 - 6*e^3 - 56*e^2 + 9*e + 74, 8*e^5 - 84*e^3 - 5*e^2 + 198*e + 33, 6*e^5 + 5*e^4 - 56*e^3 - 46*e^2 + 122*e + 125, -4*e^5 - e^4 + 38*e^3 + 2*e^2 - 84*e + 9, -2*e^4 - 12*e^3 - 8*e^2 + 76*e + 84, 7*e^5 + e^4 - 65*e^3 - 7*e^2 + 126*e + 30, -9*e^5 - e^4 + 100*e^3 + 22*e^2 - 251*e - 109, 9*e^5 + 3*e^4 - 96*e^3 - 38*e^2 + 227*e + 135, e^5 + 3*e^4 + 2*e^3 - 53*e - 63]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

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

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