/*
  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, -1, -5, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([59, 59, -3*w^4 + 2*w^3 + 14*w^2 - 6*w - 8])

primes_array = [
[5, 5, -2*w^4 + w^3 + 9*w^2 - 2*w - 3],\
[17, 17, -2*w^4 + w^3 + 9*w^2 - 3*w - 5],\
[17, 17, w^2 - 2],\
[23, 23, w^3 - 3*w],\
[29, 29, 2*w^4 - w^3 - 10*w^2 + 2*w + 4],\
[32, 2, 2],\
[37, 37, -w^4 + w^3 + 4*w^2 - 2*w],\
[41, 41, -3*w^4 + 2*w^3 + 14*w^2 - 5*w - 7],\
[43, 43, -3*w^4 + w^3 + 14*w^2 - 3*w - 6],\
[47, 47, -3*w^4 + 2*w^3 + 14*w^2 - 7*w - 6],\
[53, 53, 2*w^4 - w^3 - 8*w^2 + 2*w + 1],\
[53, 53, -2*w^4 + w^3 + 10*w^2 - 4*w - 6],\
[59, 59, -w^4 + 4*w^2 + 1],\
[59, 59, -3*w^4 + 2*w^3 + 14*w^2 - 6*w - 8],\
[61, 61, 4*w^4 - 2*w^3 - 18*w^2 + 5*w + 7],\
[61, 61, 3*w^4 - w^3 - 15*w^2 + 2*w + 7],\
[73, 73, -4*w^4 + 2*w^3 + 18*w^2 - 7*w - 6],\
[83, 83, -2*w^4 + 9*w^2 + 2*w - 4],\
[83, 83, -2*w^4 + 2*w^3 + 10*w^2 - 7*w - 6],\
[97, 97, -2*w^4 + w^3 + 8*w^2 - 3*w + 1],\
[97, 97, -w^3 + w^2 + 4*w - 1],\
[101, 101, 2*w^4 - 9*w^2 - w + 5],\
[103, 103, 2*w^4 - 2*w^3 - 9*w^2 + 8*w + 2],\
[107, 107, -3*w^4 + w^3 + 15*w^2 - 4*w - 8],\
[109, 109, -3*w^4 + w^3 + 13*w^2 - 2*w - 4],\
[113, 113, 4*w^4 - 3*w^3 - 18*w^2 + 8*w + 8],\
[121, 11, -w^4 - w^3 + 5*w^2 + 4*w - 2],\
[131, 131, -4*w^4 + w^3 + 18*w^2 - 5],\
[139, 139, 2*w^3 - w^2 - 8*w + 1],\
[139, 139, -2*w^4 + w^3 + 9*w^2 - 3],\
[149, 149, 5*w^4 - 2*w^3 - 23*w^2 + 4*w + 11],\
[149, 149, w^4 - 4*w^2 - 3],\
[149, 149, 4*w^4 - 3*w^3 - 19*w^2 + 10*w + 8],\
[151, 151, 2*w^4 - w^3 - 9*w^2 + 5*w + 4],\
[157, 157, -2*w^4 - w^3 + 10*w^2 + 5*w - 4],\
[157, 157, 5*w^4 - 3*w^3 - 24*w^2 + 8*w + 13],\
[163, 163, -2*w^4 + 11*w^2 + w - 7],\
[167, 167, w^4 - 3*w^2 - 2*w - 3],\
[167, 167, -3*w^4 + 3*w^3 + 14*w^2 - 10*w - 9],\
[169, 13, 3*w^4 - 2*w^3 - 14*w^2 + 6*w + 3],\
[191, 191, -3*w^4 + w^3 + 15*w^2 - w - 6],\
[193, 193, 3*w^4 - 2*w^3 - 14*w^2 + 4*w + 5],\
[199, 199, -5*w^4 + 2*w^3 + 23*w^2 - 3*w - 10],\
[223, 223, -4*w^4 + w^3 + 20*w^2 - w - 9],\
[223, 223, -w^4 + 3*w^2 + 2],\
[233, 233, w^3 - 4*w - 4],\
[241, 241, -3*w^4 + 2*w^3 + 15*w^2 - 7*w - 7],\
[243, 3, -3],\
[251, 251, -3*w^4 + 3*w^3 + 13*w^2 - 8*w - 6],\
[257, 257, -4*w^4 + w^3 + 20*w^2 - 2*w - 9],\
[257, 257, -3*w^4 + 2*w^3 + 15*w^2 - 5*w - 11],\
[269, 269, 2*w^4 - 11*w^2 - w + 6],\
[271, 271, w^4 + w^3 - 5*w^2 - 6*w + 2],\
[271, 271, 3*w^4 - w^3 - 15*w^2 + 8],\
[277, 277, -w^4 - w^3 + 6*w^2 + 3*w - 5],\
[283, 283, -5*w^4 + 3*w^3 + 23*w^2 - 10*w - 10],\
[293, 293, -w^4 + w^3 + 6*w^2 - 3*w - 8],\
[307, 307, -w^4 - w^3 + 6*w^2 + 4*w - 2],\
[311, 311, -w^3 + 2*w^2 + 3*w - 2],\
[311, 311, 2*w^4 - w^3 - 10*w^2 + 5*w + 7],\
[313, 313, -5*w^4 + 4*w^3 + 23*w^2 - 12*w - 11],\
[313, 313, -w^4 - w^3 + 5*w^2 + 3*w - 3],\
[347, 347, -w^4 + 2*w^3 + 3*w^2 - 7*w + 1],\
[353, 353, -3*w^4 + 14*w^2 + 3*w - 7],\
[353, 353, -3*w^4 + 3*w^3 + 13*w^2 - 9*w - 7],\
[367, 367, -w^4 + w^3 + 5*w^2 - 6*w - 4],\
[367, 367, -3*w^4 + w^3 + 15*w^2 - 3*w - 5],\
[379, 379, 5*w^4 - 2*w^3 - 23*w^2 + 6*w + 9],\
[383, 383, 4*w^4 - 2*w^3 - 19*w^2 + 7*w + 11],\
[397, 397, w^4 - 3*w^2 - w - 3],\
[397, 397, -2*w^3 + w^2 + 8*w],\
[401, 401, 2*w^4 - 2*w^3 - 8*w^2 + 5*w],\
[421, 421, -4*w^4 + 2*w^3 + 17*w^2 - 5*w - 6],\
[421, 421, -w^4 + 2*w^3 + 6*w^2 - 8*w - 5],\
[431, 431, 5*w^4 - 2*w^3 - 22*w^2 + 5*w + 7],\
[431, 431, -w^4 - w^3 + 6*w^2 + 5*w - 4],\
[439, 439, 4*w^4 - 2*w^3 - 19*w^2 + 7*w + 10],\
[443, 443, 4*w^4 - w^3 - 19*w^2 + 3*w + 8],\
[457, 457, -3*w^4 + 3*w^3 + 15*w^2 - 10*w - 9],\
[461, 461, -w^3 + 6*w],\
[461, 461, 3*w^4 - 3*w^3 - 14*w^2 + 9*w + 8],\
[463, 463, 5*w^4 - 3*w^3 - 23*w^2 + 7*w + 8],\
[499, 499, 6*w^4 - 3*w^3 - 27*w^2 + 7*w + 11],\
[509, 509, 2*w^4 - w^3 - 8*w^2 + w - 1],\
[509, 509, 3*w^4 - 2*w^3 - 13*w^2 + 6*w + 7],\
[521, 521, w^3 - 6*w + 1],\
[523, 523, 4*w^4 - 2*w^3 - 18*w^2 + 3*w + 7],\
[541, 541, w^2 + w - 5],\
[547, 547, 5*w^4 - 2*w^3 - 25*w^2 + 4*w + 12],\
[547, 547, -6*w^4 + 3*w^3 + 27*w^2 - 10*w - 9],\
[557, 557, -4*w^4 + 3*w^3 + 18*w^2 - 10*w - 9],\
[557, 557, -4*w^4 + w^3 + 19*w^2 - 3*w - 6],\
[557, 557, 3*w^4 - 2*w^3 - 14*w^2 + 8*w + 7],\
[563, 563, -w^4 + 3*w^3 + 4*w^2 - 11*w + 1],\
[569, 569, w^2 + 3*w - 2],\
[577, 577, -5*w^4 + 2*w^3 + 23*w^2 - 6*w - 8],\
[587, 587, -2*w^4 + 10*w^2 + 3*w - 6],\
[593, 593, 4*w^4 - 3*w^3 - 19*w^2 + 8*w + 11],\
[601, 601, -4*w^4 + w^3 + 18*w^2 - 3*w - 6],\
[601, 601, -5*w^4 + 3*w^3 + 24*w^2 - 10*w - 13],\
[601, 601, -w^4 + 5*w^2 + 3*w - 3],\
[607, 607, -3*w^4 + 2*w^3 + 15*w^2 - 8*w - 9],\
[613, 613, 3*w^4 - 14*w^2 - 2*w + 8],\
[617, 617, -4*w^4 + w^3 + 19*w^2 - 3*w - 7],\
[619, 619, w^3 + w^2 - 3*w - 5],\
[625, 5, 4*w^4 - 2*w^3 - 19*w^2 + 3*w + 8],\
[631, 631, 3*w^4 - w^3 - 12*w^2 - 1],\
[641, 641, -w^4 + 2*w^3 + 3*w^2 - 7*w],\
[647, 647, 2*w^2 - w - 5],\
[647, 647, -2*w^3 + w^2 + 8*w - 5],\
[647, 647, 5*w^4 - 3*w^3 - 23*w^2 + 9*w + 12],\
[661, 661, -8*w^4 + 3*w^3 + 39*w^2 - 7*w - 19],\
[677, 677, -7*w^4 + 4*w^3 + 34*w^2 - 11*w - 17],\
[691, 691, w^2 + 2*w - 4],\
[691, 691, -5*w^4 + 2*w^3 + 23*w^2 - 3*w - 8],\
[691, 691, -7*w^4 + 5*w^3 + 32*w^2 - 14*w - 15],\
[701, 701, w - 4],\
[709, 709, -3*w^4 + 3*w^3 + 14*w^2 - 8*w - 7],\
[709, 709, 5*w^4 - 2*w^3 - 24*w^2 + 5*w + 9],\
[709, 709, -w^4 + w^3 + 5*w^2 - 3*w - 7],\
[719, 719, -3*w^4 + 13*w^2 + w - 7],\
[719, 719, -3*w^4 + 14*w^2 - 4],\
[727, 727, -7*w^4 + 4*w^3 + 32*w^2 - 10*w - 16],\
[727, 727, -3*w^4 + w^3 + 14*w^2 - 5*w - 8],\
[733, 733, -3*w^4 + 2*w^3 + 15*w^2 - 8*w - 10],\
[733, 733, -3*w^4 + 3*w^3 + 13*w^2 - 10*w - 7],\
[733, 733, 8*w^4 - 4*w^3 - 38*w^2 + 9*w + 15],\
[739, 739, 4*w^4 - 3*w^3 - 20*w^2 + 9*w + 11],\
[739, 739, -w^4 + w^3 + 5*w^2 - 3*w + 1],\
[743, 743, -5*w^4 + 4*w^3 + 24*w^2 - 13*w - 16],\
[743, 743, w^4 - 7*w^2 - 2*w + 5],\
[751, 751, -w^4 + 2*w^3 + 3*w^2 - 7*w - 1],\
[757, 757, 5*w^4 - 2*w^3 - 22*w^2 + 5*w + 8],\
[757, 757, w^4 + w^3 - 6*w^2 - 5*w + 2],\
[761, 761, 8*w^4 - 3*w^3 - 38*w^2 + 8*w + 18],\
[761, 761, 3*w^4 - w^3 - 14*w^2 + 2*w + 10],\
[761, 761, -4*w^4 + 3*w^3 + 19*w^2 - 7*w - 10],\
[769, 769, -w^4 + 2*w^3 + 5*w^2 - 8*w - 1],\
[773, 773, 9*w^4 - 4*w^3 - 41*w^2 + 9*w + 15],\
[773, 773, 4*w^4 - 2*w^3 - 18*w^2 + 3*w + 6],\
[773, 773, 2*w^2 - 5],\
[787, 787, -w^4 + 6*w^2 - w - 7],\
[787, 787, w^4 - w^3 - 6*w^2 + w + 6],\
[821, 821, 2*w^4 - w^3 - 9*w^2 + 4*w + 8],\
[823, 823, 6*w^4 - w^3 - 27*w^2 - w + 8],\
[827, 827, -3*w^4 + 2*w^3 + 16*w^2 - 6*w - 9],\
[827, 827, -8*w^4 + 5*w^3 + 37*w^2 - 16*w - 17],\
[839, 839, 2*w^4 - 10*w^2 + w + 8],\
[853, 853, 2*w^4 - 2*w^3 - 11*w^2 + 7*w + 7],\
[857, 857, 5*w^4 - 2*w^3 - 24*w^2 + 7*w + 14],\
[877, 877, -w^4 + 2*w^3 + 5*w^2 - 10*w - 6],\
[883, 883, 3*w^4 - 3*w^3 - 15*w^2 + 12*w + 10],\
[887, 887, -4*w^4 + w^3 + 17*w^2 - w - 7],\
[907, 907, 2*w^4 - 11*w^2 - w + 2],\
[907, 907, -2*w^4 - w^3 + 10*w^2 + 4*w - 5],\
[911, 911, -9*w^4 + 4*w^3 + 43*w^2 - 9*w - 19],\
[919, 919, 4*w^4 - w^3 - 20*w^2 + w + 8],\
[937, 937, w^4 - 7*w^2 - 2*w + 4],\
[947, 947, 2*w^4 + 2*w^3 - 10*w^2 - 9*w + 3],\
[953, 953, -2*w^3 + 5*w + 4],\
[961, 31, -4*w^4 + w^3 + 19*w^2 - w - 4],\
[967, 967, 8*w^4 - 5*w^3 - 37*w^2 + 13*w + 18],\
[967, 967, 3*w^4 - w^3 - 13*w^2 - 2*w + 3],\
[971, 971, -4*w^4 + 3*w^3 + 21*w^2 - 10*w - 15],\
[971, 971, -3*w^4 + 12*w^2 + 3*w - 4],\
[971, 971, w^4 - 6*w^2 + 3*w + 6],\
[983, 983, -7*w^4 + 2*w^3 + 34*w^2 - 5*w - 16],\
[983, 983, w^4 - 7*w^2 - w + 8],\
[991, 991, -4*w^4 + 4*w^3 + 19*w^2 - 15*w - 12],\
[991, 991, -8*w^4 + 3*w^3 + 37*w^2 - 5*w - 15],\
[991, 991, -w^4 + w^3 + 7*w^2 - 3*w - 7],\
[997, 997, -8*w^4 + 5*w^3 + 37*w^2 - 16*w - 16]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^4 - 11*x^2 + 4*x + 4
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -e^3 + 10*e, -2*e + 1, -e^2 - e + 8, 1/2*e^3 - 7/2*e + 1, 5/4*e^3 + 1/2*e^2 - 55/4*e + 3/2, -e^3 - e^2 + 9*e + 4, 1/2*e^3 + e^2 - 13/2*e - 5, -1/4*e^3 + 3/2*e^2 + 15/4*e - 15/2, -1/2*e^3 + 13/2*e + 1, -5/4*e^3 - 1/2*e^2 + 55/4*e - 3/2, 3/4*e^3 + 1/2*e^2 - 29/4*e + 9/2, 3/2*e^3 - 31/2*e + 3, 1, -e^2 + e + 5, -1/2*e^3 + 9/2*e - 2, 5/4*e^3 + 1/2*e^2 - 47/4*e + 3/2, e^3 - e^2 - 8*e + 10, -e^3 + e^2 + 11*e - 5, 2*e^3 + 2*e^2 - 19*e - 2, -1/2*e^3 - e^2 + 3/2*e + 1, 5/2*e^3 + 2*e^2 - 55/2*e + 3, -3/2*e^3 - 3*e^2 + 31/2*e + 8, 3/2*e^3 - 35/2*e + 5, -e^2 + 4*e + 6, 3/2*e^3 + e^2 - 23/2*e - 3, -e^3 - 2*e^2 + 9*e + 8, 1/2*e^3 - 9/2*e - 7, -1/2*e^3 + 5/2*e + 1, 1/2*e^3 - 2*e^2 - 19/2*e + 16, -11/4*e^3 - 1/2*e^2 + 101/4*e + 3/2, 5/4*e^3 + 5/2*e^2 - 35/4*e - 25/2, -1/4*e^3 + 3/2*e^2 + 11/4*e - 23/2, -e^3 - e^2 + 8*e + 8, -1/2*e^3 + 2*e^2 + 11/2*e - 13, -e^3 + 13*e + 6, -e^3 - e^2 + 12*e - 4, -5/2*e^3 - 2*e^2 + 49/2*e - 5, -e^3 - 2*e^2 + 9*e - 4, -1/2*e^3 + e^2 + 9/2*e - 17, 2*e^3 + e^2 - 17*e, -2*e^3 - e^2 + 14*e - 2, -3/2*e^3 + e^2 + 39/2*e - 6, -15/4*e^3 - 1/2*e^2 + 141/4*e - 1/2, -1/2*e^3 - 3*e^2 + 3/2*e + 25, 2*e^2 + e - 18, 2*e^3 - 2*e^2 - 22*e + 14, -2*e^3 + 13*e - 11, -1/4*e^3 + 5/2*e^2 + 19/4*e - 31/2, 1/2*e^3 + e^2 + 1/2*e - 5, 3/2*e^3 - 3*e^2 - 33/2*e + 25, 2*e^3 - 18*e + 4, 2*e^3 + 3*e^2 - 23*e - 14, 2*e^3 + e^2 - 23*e, 7/4*e^3 - 1/2*e^2 - 81/4*e + 21/2, -7/4*e^3 + 3/2*e^2 + 85/4*e - 25/2, e^3 - 2*e^2 - 8*e + 24, 1/2*e^3 - e^2 - 15/2*e - 9, 11/4*e^3 - 1/2*e^2 - 117/4*e - 3/2, -7/4*e^3 - 3/2*e^2 + 57/4*e - 17/2, 5/2*e^3 - 59/2*e + 9, -e^3 + 12*e - 6, 3*e^3 + 2*e^2 - 33*e, 4*e^3 + 3*e^2 - 34*e - 8, -5/4*e^3 + 1/2*e^2 + 43/4*e - 19/2, 1/4*e^3 + 1/2*e^2 + 17/4*e + 19/2, 4*e^3 + 2*e^2 - 48*e + 10, -3/4*e^3 - 3/2*e^2 + 37/4*e - 21/2, 7/2*e^3 + 2*e^2 - 71/2*e + 1, -5/2*e^3 - e^2 + 67/2*e - 10, e^3 + 2*e^2 - 7*e - 22, -3/2*e^3 - 2*e^2 + 37/2*e + 20, 5*e^3 + 3*e^2 - 51*e + 4, 7/2*e^3 - 61/2*e + 23, -3*e + 15, 7/4*e^3 + 1/2*e^2 - 69/4*e - 11/2, -3/2*e^3 + 33/2*e - 2, -7/2*e^3 + 65/2*e - 10, -2*e^3 - e^2 + 14*e + 1, -5/2*e^3 + 63/2*e + 1, -1/2*e^3 + e^2 + 29/2*e - 17, -3*e^2 + 5*e + 20, -1/2*e^3 - 7/2*e - 9, -13/4*e^3 + 3/2*e^2 + 139/4*e - 15/2, -1/4*e^3 - 9/2*e^2 + 23/4*e + 49/2, 3*e^3 - 31*e + 2, -4*e^3 - 2*e^2 + 40*e + 2, 7/2*e^3 + 4*e^2 - 69/2*e - 6, -2*e^3 + e^2 + 15*e - 16, -2*e^3 - 5*e^2 + 19*e + 2, 3*e^3 - 2*e^2 - 34*e + 12, 3*e^3 - 2*e^2 - 35*e + 18, 1/2*e^3 - e^2 - 11/2*e - 3, -3/2*e^3 - 3*e^2 + 33/2*e + 27, -2*e^3 - 2*e^2 + 25*e - 4, -3/2*e^3 - 2*e^2 + 13/2*e + 7, -5/2*e^3 + e^2 + 43/2*e - 23, -11/2*e^3 - 4*e^2 + 97/2*e + 11, 6*e^3 + 5*e^2 - 52*e - 11, 1/2*e^3 - 3*e^2 - 17/2*e + 15, -5/4*e^3 - 5/2*e^2 + 55/4*e - 39/2, -5/2*e^3 - e^2 + 59/2*e + 21, 1/2*e^3 - 4*e^2 - 27/2*e + 35, 1/2*e^3 - e^2 - 29/2*e - 5, 1/2*e^3 + e^2 - 5/2*e - 2, -1/2*e^3 + 3*e^2 + 25/2*e - 29, 5/2*e^3 - 2*e^2 - 65/2*e + 11, -2*e^3 + e^2 + 24*e - 34, -2*e^3 + 4*e^2 + 24*e - 20, 11/2*e^3 + 4*e^2 - 109/2*e + 20, -2*e^3 + e^2 + 21*e - 10, -7/4*e^3 - 3/2*e^2 + 85/4*e + 19/2, -1/2*e^3 + 3*e^2 + 17/2*e - 11, -4*e^3 - 3*e^2 + 50*e + 1, e^3 - e^2 - 8*e - 20, e^2 + 3*e, -1/2*e^3 + e^2 - 1/2*e - 6, 5/2*e^3 + 3*e^2 - 31/2*e - 19, 3/2*e^3 + 2*e^2 - 33/2*e - 22, -3*e^3 - 4*e^2 + 26*e + 12, 3*e^3 + 4*e^2 - 33*e + 10, 2*e^3 - 2*e^2 - 24*e - 18, 5/2*e^3 - 3*e^2 - 37/2*e + 30, -1/2*e^3 + e^2 - 1/2*e - 9, -5*e^3 + 53*e - 12, -1/4*e^3 - 1/2*e^2 - 5/4*e + 61/2, e^3 - 14*e + 22, 5*e^3 + e^2 - 54*e + 6, -13/2*e^3 - 2*e^2 + 141/2*e - 5, 4*e^3 - 42*e + 16, 3/2*e^3 + 4*e^2 - 31/2*e - 37, 3/2*e^3 - 5*e^2 - 33/2*e + 11, 3/4*e^3 + 9/2*e^2 + 19/4*e - 59/2, -3/2*e^3 + e^2 + 51/2*e - 35, 3*e^3 - 42*e + 18, 1/4*e^3 + 5/2*e^2 - 55/4*e - 49/2, -5/2*e^3 + 75/2*e - 25, -9/2*e^3 + 3*e^2 + 87/2*e - 19, -e^3 - 3*e^2 + 19*e + 27, -7/2*e^3 + 73/2*e - 23, e^3 - 6*e + 14, -7/4*e^3 + 3/2*e^2 + 45/4*e - 57/2, e^3 - 2*e^2 - e + 12, 11/2*e^3 + 2*e^2 - 125/2*e - 5, -25/4*e^3 - 1/2*e^2 + 215/4*e - 31/2, -3/4*e^3 - 3/2*e^2 + 29/4*e - 29/2, -e^3 + 17*e + 14, -1/2*e^3 - e^2 + 19/2*e - 1, 3/2*e^3 - 6*e^2 - 37/2*e + 45, 9/2*e^3 + 3*e^2 - 109/2*e - 11, -2*e^3 + 3*e^2 + 24*e - 15, 15/2*e^3 - 151/2*e + 7, -4*e^3 - 3*e^2 + 49*e, 17/4*e^3 + 5/2*e^2 - 207/4*e + 15/2, -13/4*e^3 - 3/2*e^2 + 87/4*e - 7/2, -3/4*e^3 - 3/2*e^2 + 21/4*e + 47/2, 25/4*e^3 + 1/2*e^2 - 327/4*e + 27/2, 1/2*e^3 + 4*e^2 - 15/2*e - 23, -3*e^3 + 4*e^2 + 22*e - 43, 23/4*e^3 + 3/2*e^2 - 245/4*e - 7/2, -5/2*e^3 - e^2 + 47/2*e + 5, -7/2*e^3 - 2*e^2 + 57/2*e + 30, -11/2*e^3 - 2*e^2 + 109/2*e + 16, 15/2*e^3 + 6*e^2 - 155/2*e + 7, -11/2*e^3 + 143/2*e - 9, -1/2*e^3 + e^2 + 11/2*e + 25, 4*e^3 + 3*e^2 - 45*e - 8, -3*e^3 - 6*e^2 + 33*e + 26, e^3 + 3*e^2 - 28, 2*e^2 - 5*e - 7, -e^3 - 4*e^2 + 17*e + 32, 5/2*e^3 + 5*e^2 - 39/2*e - 11]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([59, 59, -3*w^4 + 2*w^3 + 14*w^2 - 6*w - 8])] = -1

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