/*
  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([2, 0, -5, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([26, 26, -w^3 + w^2 + 3*w])

primes_array = [
[2, 2, w],\
[2, 2, w + 1],\
[13, 13, -w^2 + w + 3],\
[13, 13, w^2 + w - 3],\
[19, 19, -w^3 + 3*w + 1],\
[19, 19, -w^3 + 3*w - 1],\
[43, 43, -w^2 + w - 1],\
[43, 43, w^2 + w + 1],\
[49, 7, w^3 + w^2 - 6*w - 3],\
[49, 7, w^3 - w^2 - 6*w + 3],\
[53, 53, 2*w^3 - w^2 - 9*w + 3],\
[53, 53, 2*w^3 + w^2 - 9*w - 3],\
[59, 59, w^3 - w^2 - 4*w + 1],\
[59, 59, -w^3 - w^2 + 4*w + 1],\
[67, 67, 3*w^3 - 13*w + 1],\
[67, 67, -w^3 + w^2 + 6*w - 5],\
[81, 3, -3],\
[83, 83, -2*w^3 - w^2 + 9*w + 7],\
[83, 83, 4*w^3 - 18*w - 1],\
[89, 89, -2*w^3 + 10*w + 1],\
[89, 89, -w^2 + w + 5],\
[89, 89, w^2 + w - 5],\
[89, 89, 2*w^3 - 10*w + 1],\
[101, 101, -2*w^3 + 8*w + 1],\
[101, 101, 2*w^3 - 8*w + 1],\
[103, 103, w^3 + 2*w^2 - 5*w - 7],\
[103, 103, w^3 + w^2 - 6*w - 7],\
[103, 103, -w^2 - 3*w + 1],\
[103, 103, -w^3 + 2*w^2 + 5*w - 7],\
[127, 127, -w^3 + 2*w^2 + 5*w - 5],\
[127, 127, w^3 + 3*w^2 - 4*w - 13],\
[127, 127, -w^3 + 3*w^2 + 4*w - 13],\
[127, 127, w^3 + 2*w^2 - 5*w - 5],\
[149, 149, -2*w^3 - w^2 + 7*w - 1],\
[149, 149, 2*w^3 - w^2 - 7*w - 1],\
[151, 151, -w^3 + w^2 + 2*w - 3],\
[151, 151, 2*w^3 - 10*w + 3],\
[151, 151, -2*w^3 + 10*w + 3],\
[151, 151, w^3 + w^2 - 2*w - 3],\
[157, 157, w^3 + 2*w^2 - 3*w - 1],\
[157, 157, -w^3 + 2*w^2 + 3*w - 1],\
[169, 13, 2*w^2 - 3],\
[179, 179, 2*w^3 + w^2 - 7*w - 3],\
[179, 179, -2*w^3 + w^2 + 7*w - 3],\
[229, 229, -w^3 + 2*w^2 + 3*w - 7],\
[229, 229, w^3 + 2*w^2 - 3*w - 7],\
[251, 251, -2*w^3 + 2*w^2 + 8*w - 9],\
[251, 251, -2*w^3 - 2*w^2 + 8*w + 9],\
[263, 263, 2*w^3 - w^2 - 3*w + 1],\
[263, 263, -2*w^3 + 2*w^2 + 10*w - 5],\
[263, 263, -2*w^3 - 2*w^2 + 10*w + 5],\
[263, 263, -2*w^3 - w^2 + 3*w + 1],\
[289, 17, 2*w^2 - 5],\
[293, 293, 4*w^3 - w^2 - 19*w + 7],\
[293, 293, -4*w^3 - w^2 + 19*w + 7],\
[307, 307, -w^3 + 3*w - 5],\
[307, 307, w^3 - 3*w - 5],\
[331, 331, 4*w^3 - 2*w^2 - 18*w + 7],\
[331, 331, 5*w^3 - 3*w^2 - 22*w + 11],\
[349, 349, -3*w^3 + 13*w + 3],\
[349, 349, -3*w^3 + 13*w - 3],\
[361, 19, 2*w^2 - 11],\
[373, 373, w^3 + 2*w^2 + w - 3],\
[373, 373, -w^3 + 2*w^2 - w - 3],\
[383, 383, -w^3 + 5*w + 5],\
[383, 383, -3*w^3 + 2*w^2 + 11*w - 5],\
[383, 383, 3*w^3 + 2*w^2 - 11*w - 5],\
[383, 383, w^3 - 5*w + 5],\
[389, 389, w^3 - 4*w^2 + w + 7],\
[389, 389, -2*w^3 - w^2 + 7*w + 7],\
[421, 421, -w^3 - w^2 - 2*w + 1],\
[421, 421, w^3 - w^2 + 2*w + 1],\
[433, 433, 4*w^3 - 2*w^2 - 16*w + 5],\
[433, 433, -4*w + 1],\
[433, 433, 4*w + 1],\
[433, 433, -5*w^3 + 3*w^2 + 24*w - 13],\
[443, 443, -w^3 + w^2 + 3],\
[443, 443, -4*w^2 + 6*w + 7],\
[457, 457, 3*w^3 + w^2 - 12*w - 3],\
[457, 457, -2*w^3 + 6*w - 1],\
[457, 457, 2*w^3 - 6*w - 1],\
[457, 457, 3*w^3 - w^2 - 12*w + 3],\
[461, 461, w^3 - 3*w^2 - 2*w + 7],\
[461, 461, w^3 + 3*w^2 - 2*w - 7],\
[463, 463, -2*w^3 + 3*w^2 + 9*w - 11],\
[463, 463, 2*w^3 - w^2 - 5*w + 1],\
[463, 463, -2*w^3 - w^2 + 5*w + 1],\
[463, 463, -2*w^3 - 3*w^2 + 9*w + 11],\
[467, 467, w^3 - 7*w + 1],\
[467, 467, -w^3 + 7*w + 1],\
[491, 491, 2*w^2 - 2*w - 7],\
[491, 491, 2*w^2 + 2*w - 7],\
[509, 509, w^3 + 3*w^2 - 4*w - 11],\
[509, 509, -w^3 + 3*w^2 + 4*w - 11],\
[523, 523, 2*w^3 - w^2 - 11*w + 3],\
[523, 523, 2*w^3 + w^2 - 11*w - 3],\
[529, 23, 3*w^2 - w - 15],\
[529, 23, -3*w^2 - w + 15],\
[557, 557, 3*w^2 + w - 13],\
[557, 557, -3*w^2 + w + 13],\
[563, 563, -3*w^3 + 3*w^2 + 12*w - 7],\
[563, 563, 2*w^3 - 2*w^2 - 8*w + 3],\
[569, 569, w^3 + 3*w^2 - 6*w - 9],\
[569, 569, 4*w^3 - w^2 - 17*w + 1],\
[569, 569, -4*w^3 - w^2 + 17*w + 1],\
[569, 569, -w^3 + 3*w^2 + 6*w - 9],\
[587, 587, -w^3 + w^2 + 2*w - 5],\
[587, 587, w^3 + w^2 - 2*w - 5],\
[593, 593, 3*w^3 - 2*w^2 - 15*w + 5],\
[593, 593, -w^3 - 2*w^2 + 5*w + 1],\
[593, 593, w^3 - 2*w^2 - 5*w + 1],\
[593, 593, -3*w^3 - 2*w^2 + 15*w + 5],\
[599, 599, w^3 + w^2 - 3],\
[599, 599, -w^2 - w - 3],\
[599, 599, -w^2 + w - 3],\
[599, 599, -w^3 + w^2 - 3],\
[613, 613, -w^3 + w^2 + 6*w - 9],\
[613, 613, w^3 + w^2 - 6*w - 9],\
[625, 5, -5],\
[659, 659, -2*w^3 + 4*w^2 + 4*w - 1],\
[659, 659, 2*w^3 + 4*w^2 - 4*w - 1],\
[661, 661, w^3 + 3*w^2 - 6*w - 7],\
[661, 661, -2*w^3 + 6*w^2 - 7],\
[701, 701, -w^3 - 2*w^2 + 3*w + 9],\
[701, 701, -w^3 + 2*w^2 + 3*w - 9],\
[733, 733, w^3 + 2*w^2 - 7*w - 1],\
[733, 733, -4*w^3 + w^2 + 19*w - 11],\
[739, 739, -w^3 - w^2 + 2*w + 9],\
[739, 739, -w^3 + w^2 + 2*w - 9],\
[757, 757, 3*w^3 - w^2 - 10*w + 5],\
[757, 757, -3*w^3 - w^2 + 10*w + 5],\
[773, 773, -4*w^3 + 5*w^2 + 19*w - 23],\
[773, 773, -7*w^3 + 6*w^2 + 33*w - 29],\
[797, 797, 3*w^3 - 13*w + 5],\
[797, 797, 3*w^3 - 13*w - 5],\
[829, 829, -2*w^3 - w^2 + 9*w - 1],\
[829, 829, 2*w^3 - w^2 - 9*w - 1],\
[859, 859, 3*w^3 - w^2 - 14*w + 1],\
[859, 859, -3*w^3 - w^2 + 14*w + 1],\
[863, 863, -5*w^3 + 21*w + 3],\
[863, 863, -3*w^3 - w^2 + 12*w - 1],\
[863, 863, 3*w^3 - w^2 - 12*w - 1],\
[863, 863, -5*w^3 + 21*w - 3],\
[883, 883, -2*w^3 + 4*w^2 + 8*w - 17],\
[883, 883, 2*w^3 + 4*w^2 - 8*w - 17],\
[953, 953, -w^3 - w^2 + 8*w + 3],\
[953, 953, 4*w^3 - 2*w^2 - 16*w + 7],\
[953, 953, -3*w^3 + w^2 + 16*w - 7],\
[953, 953, w^3 - w^2 - 8*w + 3],\
[961, 31, -4*w^3 + 2*w^2 + 12*w + 3],\
[961, 31, 3*w^3 - w^2 - 10*w - 1],\
[971, 971, 3*w^3 - 4*w^2 - 13*w + 15],\
[971, 971, -4*w^3 + 3*w^2 + 19*w - 17],\
[977, 977, -2*w^3 + w^2 + 9*w + 3],\
[977, 977, -4*w^3 + w^2 + 19*w - 9],\
[977, 977, 3*w^3 - 15*w + 5],\
[977, 977, 2*w^3 + w^2 - 9*w + 3]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^6 + x^5 - 9*x^4 - 5*x^3 + 20*x^2 + 2*x - 6
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [1, e, 1, 1/2*e^5 - 9/2*e^3 + e^2 + 8*e - 3, -1/2*e^5 - e^4 + 7/2*e^3 + 5*e^2 - 4*e - 1, 1/2*e^5 + e^4 - 5/2*e^3 - 4*e^2 + 1, e^5 + e^4 - 8*e^3 - 5*e^2 + 13*e + 6, -e^5 - e^4 + 7*e^3 + 5*e^2 - 8*e - 2, -1/2*e^5 - e^4 + 9/2*e^3 + 7*e^2 - 7*e - 7, e^5 + 2*e^4 - 9*e^3 - 12*e^2 + 18*e + 6, -e^5 + 8*e^3 - 2*e^2 - 11*e + 4, 3/2*e^5 + 2*e^4 - 21/2*e^3 - 8*e^2 + 14*e + 1, e^3 - 2*e^2 - 7*e + 8, 2*e^5 + 3*e^4 - 16*e^3 - 15*e^2 + 28*e + 6, -1/2*e^5 - 2*e^4 + 3/2*e^3 + 10*e^2 - 3, -e^3 + 2*e^2 + 7*e - 8, -e^5 - 2*e^4 + 9*e^3 + 12*e^2 - 18*e - 2, 1/2*e^5 + e^4 - 5/2*e^3 - 8*e^2 - 2*e + 11, -3/2*e^5 - 3*e^4 + 21/2*e^3 + 19*e^2 - 12*e - 15, -1/2*e^5 - 2*e^4 + 1/2*e^3 + 11*e^2 + 10*e - 9, -2*e^2 + 2*e + 6, -e^5 - e^4 + 9*e^3 + 5*e^2 - 20*e - 6, e^5 + 2*e^4 - 7*e^3 - 10*e^2 + 8*e + 4, 1/2*e^5 + 2*e^4 - 7/2*e^3 - 16*e^2 + 2*e + 19, -1/2*e^5 - 2*e^4 + 3/2*e^3 + 10*e^2 + 2*e - 7, -3/2*e^5 - 3*e^4 + 25/2*e^3 + 18*e^2 - 27*e - 11, -e^5 + e^4 + 11*e^3 - 7*e^2 - 24*e + 8, -1/2*e^5 - 2*e^4 + 3/2*e^3 + 11*e^2 + 3*e - 1, e^5 - e^4 - 9*e^3 + 9*e^2 + 16*e - 8, 1/2*e^5 + e^4 - 7/2*e^3 - 7*e^2 + 2*e + 13, 1/2*e^5 + 3*e^4 - 3/2*e^3 - 19*e^2 - 2*e + 13, -2*e^5 - 2*e^4 + 14*e^3 + 10*e^2 - 14*e - 2, 2*e^5 + 4*e^4 - 14*e^3 - 22*e^2 + 24*e + 14, -1/2*e^5 - 2*e^4 + 7/2*e^3 + 12*e^2 - 8*e - 1, -e^5 + e^4 + 10*e^3 - 7*e^2 - 21*e + 8, 2*e^2 + 4*e - 6, e^5 + 3*e^4 - 5*e^3 - 19*e^2 + 4*e + 24, -2*e^4 - 6*e^3 + 10*e^2 + 26*e - 12, -2*e^5 - 5*e^4 + 14*e^3 + 25*e^2 - 22*e - 6, -e^5 - 4*e^4 + 5*e^3 + 26*e^2 - 2*e - 22, -2*e^5 - 3*e^4 + 15*e^3 + 13*e^2 - 29*e + 4, -3/2*e^5 - e^4 + 23/2*e^3 + 3*e^2 - 17*e + 9, e^4 - 2*e^3 - 9*e^2 + 8*e + 18, e^4 + e^3 - 5*e^2 - 5*e + 4, 1/2*e^5 + 3*e^4 - 1/2*e^3 - 16*e^2 + 7, e^4 - 7*e^2 - 4*e, 3/2*e^5 + e^4 - 27/2*e^3 - 2*e^2 + 28*e - 7, -2*e^5 - 3*e^4 + 14*e^3 + 15*e^2 - 20*e - 16, e^5 + e^4 - 5*e^3 + 3*e^2 - 16, e^5 + 2*e^4 - 9*e^3 - 14*e^2 + 26*e + 22, -3/2*e^5 - 2*e^4 + 17/2*e^3 + 5*e^2 - 7*e + 9, 2*e^5 + e^4 - 15*e^3 - e^2 + 27*e - 2, e^5 - 2*e^4 - 11*e^3 + 10*e^2 + 22*e - 2, 3/2*e^5 - 27/2*e^3 - 3*e^2 + 22*e + 15, -5/2*e^5 - 4*e^4 + 29/2*e^3 + 15*e^2 - 8*e + 3, 4*e^4 + e^3 - 28*e^2 - 3*e + 26, -3/2*e^5 - e^4 + 29/2*e^3 + 3*e^2 - 38*e + 1, -5/2*e^5 - e^4 + 45/2*e^3 + 4*e^2 - 40*e + 1, 1/2*e^5 - 4*e^4 - 15/2*e^3 + 24*e^2 + 18*e - 13, -1/2*e^5 + e^4 + 13/2*e^3 - 8*e^2 - 14*e + 25, 3/2*e^5 + 3*e^4 - 19/2*e^3 - 22*e^2 - 4*e + 33, 1/2*e^5 - 13/2*e^3 - 3*e^2 + 22*e + 9, -9/2*e^5 - 6*e^4 + 67/2*e^3 + 30*e^2 - 54*e - 19, 1/2*e^5 + 2*e^4 + 1/2*e^3 - 18*e^2 - 16*e + 31, 2*e^5 + 2*e^4 - 14*e^3 - 10*e^2 + 20*e + 16, -5/2*e^5 - 2*e^4 + 31/2*e^3 + 5*e^2 - 11*e + 3, 1/2*e^5 - 7/2*e^3 - 2*e^2 - 4*e + 3, e^5 + 2*e^4 - 9*e^3 - 8*e^2 + 24*e - 2, -5*e^5 - 6*e^4 + 37*e^3 + 26*e^2 - 54*e - 4, -2*e^5 - 5*e^4 + 15*e^3 + 35*e^2 - 27*e - 30, 5/2*e^5 + 6*e^4 - 31/2*e^3 - 32*e^2 + 16*e + 19, 4*e^4 + e^3 - 20*e^2 + e - 8, e^5 + 3*e^4 - 8*e^3 - 25*e^2 + 23*e + 32, -5/2*e^5 - 5*e^4 + 33/2*e^3 + 24*e^2 - 16*e - 15, -5/2*e^5 + 45/2*e^3 - 3*e^2 - 44*e + 1, -1/2*e^5 + 9/2*e^3 - 9*e - 19, -2*e^5 + 24*e^3 + 2*e^2 - 62*e + 2, 5*e^5 + 8*e^4 - 35*e^3 - 38*e^2 + 46*e + 18, e^5 + 3*e^4 - 3*e^3 - 19*e^2 - 8*e + 24, 5*e^5 + 6*e^4 - 41*e^3 - 32*e^2 + 70*e + 6, 2*e^5 - 18*e^3 + 2*e^2 + 30*e - 2, -2*e^5 - e^4 + 22*e^3 + 9*e^2 - 50*e - 12, 3/2*e^5 + 2*e^4 - 23/2*e^3 - 9*e^2 + 8*e - 1, e^5 - e^4 - 7*e^3 + 15*e^2 + 8*e - 22, 3*e^4 + e^3 - 21*e^2 + e + 28, 1/2*e^5 + 3*e^4 + 1/2*e^3 - 18*e^2 - 25*e + 19, 3*e^5 + 6*e^4 - 19*e^3 - 40*e^2 + 16*e + 42, -e^5 - 2*e^4 + 5*e^3 + 16*e^2 + 4*e - 30, 4*e^5 + 6*e^4 - 28*e^3 - 36*e^2 + 30*e + 32, 5*e^5 + 7*e^4 - 36*e^3 - 35*e^2 + 49*e + 18, -e^5 - 2*e^4 + 6*e^3 + 4*e^2 + e + 24, -3*e^4 + 21*e^2 - 6*e - 12, -e^5 - 2*e^4 + 11*e^3 + 16*e^2 - 28*e - 18, 3/2*e^5 + 2*e^4 - 9/2*e^3 - 4*e^2 - 14*e - 9, -e^4 + 2*e^3 + 5*e^2 - 24*e + 2, -9/2*e^5 - 5*e^4 + 61/2*e^3 + 20*e^2 - 38*e - 3, -2*e^5 - 4*e^4 + 16*e^3 + 26*e^2 - 32*e - 30, -e^4 - 2*e^3 + e^2 + 4*e + 4, e^5 - 5*e^3 + 4*e^2 - 6*e - 16, 5/2*e^5 + 8*e^4 - 31/2*e^3 - 44*e^2 + 20*e + 25, 3/2*e^5 + 3*e^4 - 23/2*e^3 - 14*e^2 + 20*e - 3, -e^5 - 2*e^4 + 9*e^3 + 14*e^2 - 30*e - 14, 3*e^5 + 2*e^4 - 21*e^3 - 12*e^2 + 18*e + 12, 5/2*e^5 + 2*e^4 - 45/2*e^3 - 9*e^2 + 54*e - 9, 5*e^5 + 8*e^4 - 37*e^3 - 42*e^2 + 52*e + 24, -2*e^5 + 15*e^3 - 4*e^2 - 27*e, e^5 + 4*e^4 - 7*e^3 - 22*e^2 + 18*e + 2, e^5 + 2*e^4 - 12*e^3 - 14*e^2 + 25*e + 14, e^4 + 2*e^3 - 5*e^2 - 4*e + 4, -e^5 + 4*e^4 + 9*e^3 - 26*e^2 - 16*e + 8, -2*e^5 + 14*e^3 - 2*e^2 - 6*e + 2, -7/2*e^5 - 11*e^4 + 47/2*e^3 + 62*e^2 - 40*e - 33, e^5 + 8*e^4 - e^3 - 52*e^2 - 14*e + 54, -3*e^5 - 8*e^4 + 21*e^3 + 48*e^2 - 28*e - 26, -2*e^5 - 3*e^4 + 18*e^3 + 11*e^2 - 34*e + 14, 5/2*e^5 + 3*e^4 - 35/2*e^3 - 12*e^2 + 27*e + 9, -e^5 - 2*e^4 + 4*e^3 + 14*e^2 + 9*e - 10, 4*e^5 + 6*e^4 - 23*e^3 - 28*e^2 + 11*e + 28, 7/2*e^5 + 4*e^4 - 59/2*e^3 - 22*e^2 + 63*e + 1, 2*e^5 + 2*e^4 - 22*e^3 - 8*e^2 + 62*e + 12, 2*e^5 + 6*e^4 - 13*e^3 - 36*e^2 + 19*e + 18, 2*e^5 + 5*e^4 - 18*e^3 - 35*e^2 + 44*e + 24, 5/2*e^5 + 6*e^4 - 29/2*e^3 - 33*e^2 + 20*e + 21, -3*e^5 - 5*e^4 + 22*e^3 + 35*e^2 - 27*e - 48, -2*e^5 - 4*e^4 + 11*e^3 + 28*e^2 + 3*e - 38, e^5 + 4*e^4 - 5*e^3 - 28*e^2 - 2*e + 48, 3/2*e^5 + 2*e^4 - 9/2*e^3 - 2*e^2 - 20*e - 9, 3*e^5 + 4*e^4 - 29*e^3 - 26*e^2 + 66*e + 26, -1/2*e^5 - e^4 + 17/2*e^3 + 8*e^2 - 26*e - 1, 2*e^5 + e^4 - 27*e^3 - 11*e^2 + 81*e + 8, 4*e^5 + 8*e^4 - 31*e^3 - 44*e^2 + 49*e + 32, -5/2*e^5 - 3*e^4 + 45/2*e^3 + 20*e^2 - 48*e - 27, 1/2*e^5 + 2*e^4 - 1/2*e^3 - 11*e^2 - 18*e + 1, 3*e^5 - 28*e^3 + 4*e^2 + 43*e - 12, e^5 - 10*e^3 - 12*e^2 + 17*e + 50, -5/2*e^5 - 3*e^4 + 37/2*e^3 + 14*e^2 - 30*e - 23, -2*e^5 + e^4 + 18*e^3 - 13*e^2 - 32*e + 34, -11/2*e^5 - 7*e^4 + 91/2*e^3 + 34*e^2 - 70*e - 17, e^5 - 11*e^3 - 2*e^2 + 18*e + 14, -2*e^4 - 8*e^3 + 18*e^2 + 42*e - 38, -5*e^5 - 4*e^4 + 35*e^3 + 16*e^2 - 38*e - 12, -e^5 + e^4 + 9*e^3 - 13*e^2 - 32*e + 36, -1/2*e^5 - 8*e^4 + 3/2*e^3 + 62*e^2 + 6*e - 71, e^5 + 2*e^4 - 9*e^3 - 24*e^2 + 16*e + 26, -9/2*e^5 - 9*e^4 + 85/2*e^3 + 50*e^2 - 100*e - 15, -3*e^5 - 6*e^4 + 17*e^3 + 36*e^2 - 2*e - 48, -e^5 + 13*e^3 - 8*e^2 - 42*e + 20, -e^4 + 3*e^2 - 4*e - 36, -8*e^5 - 8*e^4 + 62*e^3 + 34*e^2 - 104*e - 10, -13/2*e^5 - 13*e^4 + 93/2*e^3 + 75*e^2 - 69*e - 49, 4*e^3 + 6*e^2 - 38*e - 14, -9*e^5 - 9*e^4 + 72*e^3 + 43*e^2 - 117*e - 12, 7/2*e^5 + 10*e^4 - 29/2*e^3 - 54*e^2 - 8*e + 53, -2*e^5 - 4*e^4 + 12*e^3 + 10*e^2 - 8*e + 22, -e^4 + 2*e^3 + 13*e^2 - 12*e - 36, e^5 + 5*e^4 + e^3 - 25*e^2 - 18*e + 6, 9/2*e^5 + 8*e^4 - 73/2*e^3 - 46*e^2 + 45*e + 21]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([2,2,w])] = -1
AL_eigenvalues[ZF.ideal([13,13,-w^2+w+3])] = -1

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