/*
  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, -1, -6, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([16, 4, 3*w^3 - 5*w^2 - 15*w + 6])

primes_array = [
[2, 2, w^3 - w^2 - 6*w - 2],\
[3, 3, -w^3 + 2*w^2 + 4*w - 2],\
[4, 2, w^3 - w^2 - 5*w - 2],\
[17, 17, -w^3 + w^2 + 6*w - 1],\
[17, 17, -w + 2],\
[29, 29, -w^3 + 2*w^2 + 4*w - 4],\
[29, 29, w^3 - 2*w^2 - 4*w],\
[31, 31, -w^2 + 2],\
[31, 31, -w^3 + 7*w + 5],\
[41, 41, -2*w^3 + 2*w^2 + 13*w - 2],\
[41, 41, 3*w^3 - 4*w^2 - 17*w + 5],\
[67, 67, 3*w^3 - 4*w^2 - 17*w + 1],\
[67, 67, -w^2 + 4*w + 2],\
[83, 83, 2*w^2 - 5*w - 2],\
[83, 83, -w^3 + 8*w + 6],\
[83, 83, w^3 - 2*w^2 - 2*w - 2],\
[83, 83, w^3 - 2*w^2 - 6*w],\
[97, 97, -3*w^3 + 2*w^2 + 17*w + 7],\
[97, 97, w^3 - 4*w^2 + 3*w + 1],\
[97, 97, -5*w^3 + 8*w^2 + 24*w - 8],\
[97, 97, 2*w^3 - 2*w^2 - 13*w - 4],\
[101, 101, -w^3 + 6*w + 6],\
[101, 101, -w^3 + 6*w + 2],\
[103, 103, -4*w^3 + 3*w^2 + 26*w + 12],\
[103, 103, -w^3 + 2*w^2 + 9*w + 3],\
[107, 107, 2*w^3 - 2*w^2 - 11*w],\
[107, 107, -w^3 + 2*w^2 + 3*w - 3],\
[107, 107, w^3 - w^2 - 4*w - 3],\
[107, 107, 2*w^3 - 3*w^2 - 10*w],\
[121, 11, -2*w^3 + 3*w^2 + 8*w + 2],\
[149, 149, -3*w^3 + 5*w^2 + 14*w - 3],\
[149, 149, -2*w^3 + 4*w^2 + 7*w - 4],\
[157, 157, 2*w^3 - 2*w^2 - 10*w - 1],\
[157, 157, 2*w^3 - 3*w^2 - 8*w + 2],\
[157, 157, 2*w^3 - 2*w^2 - 10*w - 3],\
[157, 157, -3*w^3 + 4*w^2 + 15*w + 1],\
[163, 163, -2*w^2 + 4*w + 5],\
[163, 163, 2*w^3 - 4*w^2 - 10*w + 5],\
[169, 13, 2*w^3 - 3*w^2 - 12*w + 2],\
[169, 13, -w^3 + 9*w + 3],\
[173, 173, 3*w^3 - 2*w^2 - 17*w - 9],\
[173, 173, -2*w^3 + 14*w + 7],\
[197, 197, 2*w^3 - 2*w^2 - 12*w + 1],\
[197, 197, 3*w^3 - 3*w^2 - 18*w - 1],\
[199, 199, 3*w^3 - 4*w^2 - 18*w + 8],\
[199, 199, 4*w^3 - 5*w^2 - 24*w + 6],\
[223, 223, w^3 - 2*w^2 - 3*w - 3],\
[223, 223, 2*w^3 - 3*w^2 - 10*w + 6],\
[227, 227, -w^3 + 2*w^2 + 6*w - 8],\
[227, 227, 3*w + 4],\
[227, 227, 3*w^3 - 3*w^2 - 18*w - 7],\
[227, 227, -2*w^3 + 3*w^2 + 12*w - 6],\
[229, 229, -w - 4],\
[229, 229, w^2 - 2*w + 2],\
[229, 229, -w^3 + w^2 + 6*w + 5],\
[229, 229, -w^3 + 2*w^2 + 5*w - 7],\
[233, 233, -2*w^3 + 3*w^2 + 8*w - 4],\
[233, 233, -3*w^3 + 4*w^2 + 15*w + 3],\
[281, 281, -2*w^3 + 3*w^2 + 10*w + 2],\
[281, 281, -w^3 + 2*w^2 + 3*w - 5],\
[289, 17, -2*w^3 + 2*w^2 + 14*w + 5],\
[293, 293, w^2 - 6],\
[293, 293, w^3 - 7*w - 1],\
[331, 331, -6*w^3 + 10*w^2 + 27*w - 6],\
[331, 331, 2*w^3 - 2*w^2 - 12*w - 7],\
[347, 347, 3*w^3 - 2*w^2 - 18*w - 6],\
[347, 347, -4*w^3 + 2*w^2 + 23*w + 10],\
[347, 347, 2*w^3 - 6*w^2 - w + 4],\
[347, 347, -4*w^3 + 3*w^2 + 24*w + 8],\
[359, 359, -3*w^3 + 4*w^2 + 17*w + 1],\
[359, 359, w^2 - 4*w - 4],\
[359, 359, w^3 - 8*w],\
[359, 359, -w^3 + 2*w^2 + 6*w - 6],\
[367, 367, 2*w^2 - 3*w - 4],\
[367, 367, -w^3 + 3*w^2 + 4*w - 7],\
[379, 379, 3*w^3 - 3*w^2 - 16*w - 3],\
[379, 379, 2*w^3 - 2*w^2 - 9*w - 2],\
[461, 461, -2*w^3 + 5*w^2 + 2*w + 2],\
[461, 461, 4*w^3 - 4*w^2 - 26*w - 11],\
[463, 463, -2*w^3 + 13*w + 8],\
[463, 463, -w^3 - w^2 + 6*w + 7],\
[487, 487, 2*w^3 - 17*w - 8],\
[487, 487, -w^3 + 10*w + 4],\
[491, 491, -5*w^3 + 3*w^2 + 30*w + 13],\
[491, 491, -5*w^3 + 4*w^2 + 28*w + 14],\
[491, 491, 3*w^3 - 8*w^2 - 4*w + 4],\
[491, 491, 7*w^3 - 12*w^2 - 33*w + 15],\
[499, 499, -2*w^3 + 2*w^2 + 12*w - 5],\
[499, 499, 2*w^2 - 7*w],\
[529, 23, -w^3 + 3*w^2 + 4*w - 5],\
[529, 23, 2*w^2 - 3*w - 6],\
[557, 557, -2*w^3 + 3*w^2 + 12*w + 4],\
[557, 557, w^3 - 9*w - 9],\
[569, 569, 4*w^3 - 5*w^2 - 22*w + 4],\
[569, 569, -3*w^3 + 2*w^2 + 20*w + 4],\
[577, 577, 3*w^3 - 3*w^2 - 20*w + 3],\
[577, 577, -4*w^3 + 8*w^2 + 16*w - 9],\
[577, 577, 7*w^3 - 11*w^2 - 34*w + 9],\
[577, 577, -4*w^3 + 6*w^2 + 22*w - 11],\
[593, 593, -6*w^3 + 10*w^2 + 29*w - 14],\
[593, 593, -w^3 + 4*w^2 - w - 7],\
[619, 619, -3*w^3 + 5*w^2 + 12*w - 1],\
[619, 619, -4*w^3 + 8*w^2 + 18*w - 15],\
[625, 5, -5],\
[631, 631, -3*w^3 + 8*w^2 + 6*w - 4],\
[631, 631, -2*w^3 + 8*w^2 - 3*w - 8],\
[643, 643, 3*w^3 - 4*w^2 - 14*w + 2],\
[643, 643, -3*w^3 + 4*w^2 + 14*w + 2],\
[661, 661, w^3 - 8*w - 10],\
[661, 661, -3*w^3 + 2*w^2 + 21*w + 3],\
[661, 661, w^3 - 2*w^2 - 6*w - 4],\
[661, 661, 2*w^3 - 3*w^2 - 14*w + 4],\
[677, 677, -9*w^3 + 12*w^2 + 50*w - 10],\
[677, 677, 3*w^3 - 4*w^2 - 17*w - 7],\
[691, 691, 3*w^3 - 2*w^2 - 21*w - 9],\
[691, 691, 2*w^3 - 3*w^2 - 14*w - 2],\
[701, 701, -9*w^3 + 13*w^2 + 48*w - 15],\
[701, 701, 2*w^3 - 6*w^2 + w - 2],\
[709, 709, 2*w^2 - 2*w - 5],\
[709, 709, 2*w^2 - 2*w - 7],\
[709, 709, 4*w^3 - 5*w^2 - 20*w - 4],\
[709, 709, -3*w^3 + 6*w^2 + 14*w - 10],\
[727, 727, 7*w^3 - 10*w^2 - 36*w + 8],\
[727, 727, 3*w^2 - 6*w - 8],\
[743, 743, 9*w^3 - 12*w^2 - 51*w + 13],\
[743, 743, w^3 - 2*w^2 - w - 5],\
[743, 743, -4*w^3 + 4*w^2 + 27*w - 8],\
[743, 743, -3*w^3 + 4*w^2 + 21*w + 9],\
[751, 751, -w^3 + 10*w + 2],\
[751, 751, 3*w^3 - 4*w^2 - 18*w + 2],\
[761, 761, 4*w^3 - 4*w^2 - 23*w - 2],\
[761, 761, -3*w^3 + 2*w^2 + 19*w + 5],\
[809, 809, -3*w^3 + 5*w^2 + 10*w + 5],\
[809, 809, -w^3 - w^2 + 10*w + 3],\
[821, 821, -w^3 + 3*w^2 + 2*w - 9],\
[821, 821, 2*w^2 - 4*w - 9],\
[823, 823, w^3 - 6*w^2 + 9*w + 1],\
[823, 823, -3*w^3 + 2*w^2 + 15*w + 5],\
[827, 827, 3*w^3 - 3*w^2 - 18*w + 1],\
[827, 827, 2*w^3 - 16*w - 11],\
[827, 827, 3*w^3 - 24*w - 14],\
[827, 827, 3*w - 4],\
[829, 829, w^2 - 6*w - 2],\
[829, 829, 2*w^3 - 2*w^2 - 10*w - 9],\
[829, 829, 5*w^3 - 6*w^2 - 29*w - 1],\
[829, 829, w^3 + 2*w^2 - 14*w - 6],\
[841, 29, -2*w^3 + 2*w^2 + 14*w + 3],\
[857, 857, -3*w^3 + 6*w^2 + 11*w - 7],\
[857, 857, -4*w^3 + 7*w^2 + 18*w - 4],\
[859, 859, -w^3 + w^2 + 6*w - 5],\
[859, 859, w - 6],\
[883, 883, 5*w^3 - 5*w^2 - 26*w - 11],\
[883, 883, -3*w^3 + 3*w^2 + 14*w + 5],\
[887, 887, 5*w^3 - 2*w^2 - 34*w - 16],\
[887, 887, -w^3 + 4*w^2 - 10],\
[887, 887, 4*w^3 - 2*w^2 - 26*w - 11],\
[887, 887, 2*w^3 - 8*w^2 + 4*w + 7],\
[907, 907, 6*w^3 - 8*w^2 - 34*w + 7],\
[907, 907, -w^3 + w^2 + 8*w - 7],\
[941, 941, 2*w^3 - 2*w^2 - 8*w - 5],\
[941, 941, -3*w^3 + 23*w + 11],\
[953, 953, 2*w^3 - 10*w - 3],\
[953, 953, -4*w^3 + 2*w^2 + 24*w + 15],\
[961, 31, -2*w^3 + 2*w^2 + 14*w - 7],\
[991, 991, -3*w^3 + 4*w^2 + 13*w + 3],\
[991, 991, 4*w^3 - 5*w^2 - 20*w + 2]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^8 - 48*x^6 + 720*x^4 - 3456*x^2 + 64
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [1/128*e^7 - 21/64*e^5 + 63/16*e^3 - 109/8*e, 1/64*e^6 - 9/16*e^4 + 37/8*e^2 - 5/2, 0, -1/64*e^7 + 21/32*e^5 - 63/8*e^3 + 105/4*e, e, 1/64*e^7 - 51/64*e^5 + 51/4*e^3 - 511/8*e, 1/128*e^7 - 9/64*e^5 - 45/16*e^3 + 319/8*e, 3/64*e^6 - 55/32*e^4 + 113/8*e^2 - 19/4, -1/64*e^6 + 19/32*e^4 - 39/8*e^2 - 25/4, -1/128*e^7 + 3/64*e^5 + 97/16*e^3 - 525/8*e, 17/64*e^5 - 75/8*e^3 + 589/8*e, 3/32*e^6 - 27/8*e^4 + 105/4*e^2 + 8, -3/32*e^6 + 27/8*e^4 - 105/4*e^2 - 10, -1/128*e^7 + 11/64*e^5 + 25/16*e^3 - 221/8*e, 1/64*e^7 - 53/64*e^5 + 29/2*e^3 - 681/8*e, -1/32*e^7 + 95/64*e^5 - 175/8*e^3 + 811/8*e, 3/128*e^7 - 67/64*e^5 + 233/16*e^3 - 539/8*e, 1/64*e^6 - 17/32*e^4 + 23/8*e^2 + 67/4, -7/64*e^6 + 125/32*e^4 - 245/8*e^2 + 1/4, 3/32*e^6 - 27/8*e^4 + 103/4*e^2 + 14, -5/32*e^6 + 45/8*e^4 - 177/4*e^2 - 10, 5/64*e^7 - 207/64*e^5 + 151/4*e^3 - 971/8*e, 5/128*e^7 - 109/64*e^5 + 351/16*e^3 - 709/8*e, 5/64*e^6 - 45/16*e^4 + 181/8*e^2 - 7/2, 1/64*e^6 - 9/16*e^4 + 41/8*e^2 - 19/2, -1/64*e^7 + 27/32*e^5 - 115/8*e^3 + 311/4*e, 3/128*e^7 - 77/64*e^5 + 317/16*e^3 - 821/8*e, -1/32*e^7 + 17/16*e^5 - 27/4*e^3 - 37/2*e, -1/32*e^7 + 91/64*e^5 - 155/8*e^3 + 615/8*e, 1/32*e^6 - 9/8*e^4 + 37/4*e^2 - 3, 1/64*e^7 - 1/2*e^5 + 13/8*e^3 + 29*e, 1/64*e^7 - 1/2*e^5 + 13/8*e^3 + 29*e, 1/64*e^6 - 13/32*e^4 - 1/8*e^2 + 79/4, -1/32*e^6 + 39/32*e^4 - 12*e^2 + 55/4, -7/64*e^6 + 121/32*e^4 - 221/8*e^2 - 59/4, -3/32*e^6 + 105/32*e^4 - 25*e^2 - 23/4, -9/64*e^6 + 39/8*e^4 - 293/8*e^2 - 8, -5/64*e^6 + 3*e^4 - 225/8*e^2 + 25, -3/64*e^6 + 29/16*e^4 - 139/8*e^2 + 47/2, -7/64*e^6 + 61/16*e^4 - 231/8*e^2 - 1/2, -5/64*e^7 + 107/32*e^5 - 335/8*e^3 + 631/4*e, -1/16*e^7 + 43/16*e^5 - 34*e^3 + 265/2*e, -1/32*e^5 + 3/4*e^3 - 21/4*e, 3/64*e^7 - 57/32*e^5 + 133/8*e^3 - 81/4*e, -9/64*e^6 + 79/16*e^4 - 305/8*e^2 - 23/2, -5/64*e^6 + 47/16*e^4 - 213/8*e^2 + 25/2, 1/16*e^6 - 71/32*e^4 + 71/4*e^2 - 71/4, 1/16*e^6 - 73/32*e^4 + 77/4*e^2 - 89/4, -1/32*e^7 + 43/32*e^5 - 33/2*e^3 + 231/4*e, -5/64*e^7 + 229/64*e^5 - 50*e^3 + 1737/8*e, -3/128*e^7 + 47/64*e^5 - 49/16*e^3 - 185/8*e, -3/64*e^7 + 57/32*e^5 - 133/8*e^3 + 89/4*e, 3/32*e^6 - 103/32*e^4 + 49/2*e^2 - 7/4, 9/64*e^6 - 81/16*e^4 + 329/8*e^2 - 45/2, 5/32*e^6 - 185/32*e^4 + 99/2*e^2 - 73/4, 5/64*e^6 - 45/16*e^4 + 189/8*e^2 - 57/2, 5/64*e^7 - 27/8*e^5 + 341/8*e^3 - 157*e, 1/64*e^7 - 17/32*e^5 + 27/8*e^3 + 19/4*e, 1/64*e^7 - 33/32*e^5 + 171/8*e^3 - 549/4*e, 3/64*e^7 - 27/16*e^5 + 111/8*e^3 - 11/2*e, 5/32*e^6 - 45/8*e^4 + 185/4*e^2 - 7, -3/64*e^7 + 73/32*e^5 - 281/8*e^3 + 725/4*e, -1/8*e^7 + 41/8*e^5 - 59*e^3 + 186*e, -1/8*e^6 + 139/32*e^4 - 125/4*e^2 - 125/4, 1/8*e^6 - 139/32*e^4 + 125/4*e^2 + 61/4, 1/4*e^5 - 19/2*e^3 + 83*e, -1/128*e^7 + 25/64*e^5 - 91/16*e^3 + 185/8*e, -1/64*e^7 + 25/64*e^5 + 2*e^3 - 443/8*e, -1/32*e^7 + 43/32*e^5 - 35/2*e^3 + 291/4*e, 57/64*e^5 - 259/8*e^3 + 2101/8*e, -1/128*e^7 - 13/64*e^5 + 225/16*e^3 - 957/8*e, -5/64*e^7 + 51/16*e^5 - 289/8*e^3 + 215/2*e, -1/64*e^7 + 25/32*e^5 - 99/8*e^3 + 269/4*e, -5/64*e^6 + 3*e^4 - 213/8*e^2 + 8, 3/64*e^6 - 15/8*e^4 + 139/8*e^2 - 7, -3/64*e^6 + 57/32*e^4 - 117/8*e^2 - 3/4, 9/64*e^6 - 165/32*e^4 + 339/8*e^2 + 15/4, -7/128*e^7 + 123/64*e^5 - 237/16*e^3 - 29/8*e, 1/64*e^7 - 3/64*e^5 - 57/4*e^3 + 1249/8*e, -1/8*e^6 + 73/16*e^4 - 36*e^2 - 65/2, 3/16*e^6 - 109/16*e^4 + 109/2*e^2 - 23/2, 1/16*e^6 - 71/32*e^4 + 63/4*e^2 + 9/4, -3/16*e^6 + 215/32*e^4 - 211/4*e^2 - 105/4, 9/128*e^7 - 231/64*e^5 + 959/16*e^3 - 2599/8*e, -3/64*e^5 + 17/8*e^3 - 191/8*e, 1/32*e^7 - 77/64*e^5 + 105/8*e^3 - 393/8*e, 5/128*e^7 - 115/64*e^5 + 411/16*e^3 - 939/8*e, -1/16*e^6 + 21/8*e^4 - 53/2*e^2 + 25, 1/16*e^6 - 21/8*e^4 + 53/2*e^2 - 17, -3/32*e^6 + 101/32*e^4 - 23*e^2 - 51/4, -5/32*e^6 + 187/32*e^4 - 51*e^2 + 51/4, 1/32*e^7 - 105/64*e^5 + 221/8*e^3 - 1165/8*e, -5/128*e^7 + 119/64*e^5 - 435/16*e^3 + 959/8*e, -5/64*e^7 + 201/64*e^5 - 69/2*e^3 + 741/8*e, 3/128*e^7 - 51/64*e^5 + 81/16*e^3 + 157/8*e, 3/64*e^6 - 15/8*e^4 + 159/8*e^2 - 27, -11/64*e^6 + 6*e^4 - 367/8*e^2 - 4, -7/64*e^6 + 33/8*e^4 - 299/8*e^2 + 29, 15/64*e^6 - 33/4*e^4 + 507/8*e^2 + 18, -1/8*e^7 + 39/8*e^5 - 49*e^3 + 102*e, -9/64*e^7 + 191/32*e^5 - 579/8*e^3 + 995/4*e, 19/64*e^6 - 341/32*e^4 + 685/8*e^2 - 89/4, 7/64*e^6 - 127/32*e^4 + 277/8*e^2 - 179/4, 7/32*e^6 - 63/8*e^4 + 259/4*e^2 - 34, 9/32*e^6 - 161/16*e^4 + 313/4*e^2 + 29/2, -5/32*e^6 + 89/16*e^4 - 165/4*e^2 - 73/2, 5/32*e^6 - 187/32*e^4 + 101/2*e^2 - 59/4, 1/32*e^6 - 29/32*e^4 + 5*e^2 + 19/4, -1/8*e^6 + 141/32*e^4 - 125/4*e^2 - 75/4, -17/64*e^6 + 301/32*e^4 - 567/8*e^2 - 175/4, 5/16*e^6 - 357/32*e^4 + 347/4*e^2 + 147/4, 15/64*e^6 - 265/32*e^4 + 493/8*e^2 + 107/4, 9/64*e^7 - 199/32*e^5 + 655/8*e^3 - 1311/4*e, 3/32*e^7 - 115/32*e^5 + 35*e^3 - 279/4*e, 17/64*e^6 - 153/16*e^4 + 621/8*e^2 - 5/2, 9/64*e^6 - 81/16*e^4 + 341/8*e^2 - 29/2, -9/128*e^7 + 203/64*e^5 - 663/16*e^3 + 1195/8*e, -1/32*e^7 + 21/64*e^5 + 167/8*e^3 - 1983/8*e, -27/64*e^6 + 241/16*e^4 - 947/8*e^2 - 59/2, 1/64*e^6 - 7/16*e^4 - 15/8*e^2 + 61/2, -3/64*e^6 + 43/32*e^4 - 69/8*e^2 + 135/4, -27/64*e^6 + 497/32*e^4 - 1041/8*e^2 + 189/4, 7/64*e^6 - 127/32*e^4 + 261/8*e^2 - 155/4, 3/64*e^6 - 53/32*e^4 + 109/8*e^2 - 161/4, 3/64*e^7 - 115/64*e^5 + 17*e^3 - 247/8*e, -7/128*e^7 + 199/64*e^5 - 917/16*e^3 + 2767/8*e, 19/128*e^7 - 395/64*e^5 + 1153/16*e^3 - 1803/8*e, -11/64*e^7 + 437/64*e^5 - 295/4*e^3 + 1609/8*e, -1/64*e^6 + 25/32*e^4 - 75/8*e^2 - 19/4, 3/64*e^6 - 61/32*e^4 + 149/8*e^2 - 121/4, -1/16*e^7 + 111/32*e^5 - 247/4*e^3 + 1387/4*e, -1/64*e^7 - 1/32*e^5 + 129/8*e^3 - 617/4*e, -1/64*e^7 - 21/64*e^5 + 109/4*e^3 - 1985/8*e, -7/128*e^7 + 203/64*e^5 - 933/16*e^3 + 2651/8*e, -7/64*e^7 + 311/64*e^5 - 66*e^3 + 2347/8*e, -19/128*e^7 + 423/64*e^5 - 1433/16*e^3 + 3095/8*e, 3/16*e^6 - 113/16*e^4 + 127/2*e^2 - 95/2, 1/4*e^6 - 139/16*e^4 + 66*e^2 + 7/2, 35/32*e^5 - 157/4*e^3 + 1271/4*e, 13/128*e^7 - 207/64*e^5 + 227/16*e^3 + 961/8*e, 1/16*e^7 - 221/64*e^5 + 483/8*e^3 - 2665/8*e, -5/64*e^7 + 77/32*e^5 - 71/8*e^3 - 411/4*e, -3/16*e^6 + 213/32*e^4 - 203/4*e^2 - 83/4, -1/16*e^6 + 35/16*e^4 - 17*e^2 - 23/2, 1/8*e^6 - 141/32*e^4 + 129/4*e^2 + 91/4, -1/16*e^6 + 37/16*e^4 - 20*e^2 - 5/2, -1/32*e^6 + 9/8*e^4 - 37/4*e^2 + 3, -11/128*e^7 + 281/64*e^5 - 1141/16*e^3 + 2969/8*e, -1/16*e^7 + 127/64*e^5 - 73/8*e^3 - 493/8*e, 11/32*e^6 - 25/2*e^4 + 405/4*e^2 - 3, -3/32*e^6 + 7/2*e^4 - 109/4*e^2 - 27, 3/32*e^6 - 31/8*e^4 + 163/4*e^2 - 53, 7/32*e^6 - 59/8*e^4 + 207/4*e^2 + 31, 9/128*e^7 - 207/64*e^5 + 735/16*e^3 - 1695/8*e, -1/64*e^7 + 61/64*e^5 - 37/2*e^3 + 897/8*e, 3/32*e^7 - 249/64*e^5 + 369/8*e^3 - 1269/8*e, -3/128*e^7 + 47/64*e^5 - 49/16*e^3 - 217/8*e, -11/64*e^6 + 105/16*e^4 - 467/8*e^2 + 87/2, 1/64*e^6 - 15/16*e^4 + 97/8*e^2 + 15/2, 11/64*e^7 - 115/16*e^5 + 679/8*e^3 - 547/2*e, 5/64*e^7 - 97/32*e^5 + 239/8*e^3 - 245/4*e, -1/16*e^7 + 97/32*e^5 - 181/4*e^3 + 825/4*e, -11/16*e^5 + 25*e^3 - 397/2*e, -1/4*e^6 + 9*e^4 - 74*e^2 + 21, 9/32*e^6 - 10*e^4 + 301/4*e^2 + 24, -11/32*e^6 + 49/4*e^4 - 375/4*e^2 - 54]
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, w^3 - w^2 - 5*w - 2])] = -1

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