/*
  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, 4, 5, -4, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([7, 7, w^4 - 2*w^3 - 3*w^2 + 4*w + 2])

primes_array = [
[3, 3, w - 1],\
[5, 5, w^2 - w - 2],\
[7, 7, w^4 - 2*w^3 - 3*w^2 + 4*w + 2],\
[13, 13, w^3 - 2*w^2 - 2*w + 2],\
[29, 29, -w^4 + 3*w^3 + 2*w^2 - 7*w - 1],\
[29, 29, -w^2 + 2*w + 3],\
[31, 31, w^4 - 2*w^3 - 3*w^2 + 5*w],\
[31, 31, w^3 - 2*w^2 - 3*w + 2],\
[32, 2, 2],\
[43, 43, -w^2 - w + 4],\
[53, 53, -w^4 + w^3 + 6*w^2 - 2*w - 5],\
[53, 53, -w^4 + 2*w^3 + 4*w^2 - 5*w - 2],\
[73, 73, w^4 - w^3 - 6*w^2 + 2*w + 6],\
[73, 73, w^3 - w^2 - 4*w + 2],\
[81, 3, 2*w^4 - 5*w^3 - 4*w^2 + 9*w + 2],\
[83, 83, w^3 - w^2 - 5*w],\
[89, 89, -w^4 + 2*w^3 + 4*w^2 - 4*w - 2],\
[97, 97, w^4 - 3*w^3 - 2*w^2 + 6*w + 2],\
[101, 101, -w^4 + 3*w^3 + 3*w^2 - 7*w - 3],\
[103, 103, -w^4 + w^3 + 6*w^2 - w - 7],\
[103, 103, 2*w^4 - 4*w^3 - 6*w^2 + 8*w + 1],\
[103, 103, w^4 - w^3 - 6*w^2 + 3*w + 4],\
[107, 107, -w^4 + 2*w^3 + 3*w^2 - 5*w + 2],\
[109, 109, w^3 - 4*w - 1],\
[109, 109, -w^2 + 2*w + 4],\
[131, 131, w^4 - w^3 - 6*w^2 + w + 6],\
[137, 137, w^3 - w^2 - 5*w + 3],\
[149, 149, w^4 - 3*w^3 - 3*w^2 + 9*w + 6],\
[149, 149, -w^4 + 6*w^2 + 3*w],\
[163, 163, 2*w^2 - w - 5],\
[167, 167, -2*w^4 + 3*w^3 + 8*w^2 - 4*w - 3],\
[169, 13, w^4 - 3*w^3 + 6*w - 3],\
[169, 13, w^3 - 4*w - 4],\
[173, 173, w^4 - w^3 - 4*w^2 + 2*w + 1],\
[173, 173, -w^4 + 3*w^3 + 3*w^2 - 7*w - 5],\
[173, 173, w^4 - w^3 - 4*w^2 + w - 1],\
[179, 179, w^2 - 3*w - 2],\
[191, 191, -w^4 + 3*w^3 + w^2 - 6*w - 1],\
[193, 193, -w^3 + 2*w^2 + w - 4],\
[193, 193, -w^4 + 3*w^3 + 3*w^2 - 8*w - 1],\
[199, 199, w^4 - 3*w^3 - w^2 + 7*w],\
[199, 199, -2*w^4 + 5*w^3 + 5*w^2 - 10*w - 2],\
[199, 199, w^4 - 3*w^3 + 5*w - 4],\
[211, 211, 2*w^3 - 2*w^2 - 7*w - 1],\
[211, 211, -2*w^3 + 3*w^2 + 5*w - 2],\
[223, 223, -2*w^4 + 3*w^3 + 10*w^2 - 7*w - 9],\
[227, 227, w^3 - w^2 - 4*w + 3],\
[229, 229, w^4 - 4*w^3 + 10*w - 5],\
[229, 229, -2*w^4 + 4*w^3 + 7*w^2 - 9*w - 8],\
[239, 239, -2*w^4 + 3*w^3 + 7*w^2 - 3*w - 3],\
[241, 241, w^3 - w^2 - 2*w - 2],\
[257, 257, -w^4 + w^3 + 6*w^2 - 4*w - 4],\
[263, 263, 2*w^3 - 4*w^2 - 5*w + 6],\
[269, 269, w^3 - 2*w^2 - 4*w + 4],\
[269, 269, -2*w^4 + 2*w^3 + 11*w^2 - 3*w - 10],\
[271, 271, w^3 - 5*w],\
[281, 281, w^4 - w^3 - 5*w^2 + 3*w + 3],\
[281, 281, -2*w^4 + 4*w^3 + 6*w^2 - 6*w - 3],\
[281, 281, w^3 - 5*w - 1],\
[283, 283, -2*w^4 + 4*w^3 + 7*w^2 - 8*w - 3],\
[289, 17, -2*w^4 + 3*w^3 + 8*w^2 - 5*w - 2],\
[293, 293, 2*w^4 - 5*w^3 - 7*w^2 + 14*w + 9],\
[311, 311, -w^4 + 2*w^3 + 2*w^2 - 4*w + 3],\
[313, 313, w^3 - 6*w],\
[331, 331, w^4 - 2*w^3 - 2*w^2 + w - 2],\
[359, 359, w^4 - w^3 - 5*w^2 + 2*w - 1],\
[373, 373, -w^4 + 3*w^3 + 2*w^2 - 8*w - 3],\
[373, 373, 2*w^3 - 4*w^2 - 3*w + 3],\
[379, 379, -w^4 + 4*w^3 - w^2 - 9*w + 3],\
[379, 379, -w^4 + 3*w^3 + w^2 - 6*w - 2],\
[379, 379, w^4 + w^3 - 7*w^2 - 6*w + 3],\
[383, 383, -w^4 + 2*w^3 + 3*w^2 - 6*w - 2],\
[383, 383, w^4 - 5*w^2 - 3*w + 3],\
[383, 383, 2*w^4 - 5*w^3 - 3*w^2 + 8*w],\
[389, 389, 3*w^4 - 7*w^3 - 8*w^2 + 16*w + 1],\
[397, 397, -2*w^4 + 3*w^3 + 8*w^2 - 3*w - 7],\
[397, 397, -w^4 + 2*w^3 + 3*w^2 - 4*w - 5],\
[397, 397, -2*w^4 + 3*w^3 + 7*w^2 - 4*w - 3],\
[409, 409, -w^4 + w^3 + 7*w^2 - 5*w - 9],\
[419, 419, w^4 - 2*w^3 - w^2 + 2*w - 2],\
[419, 419, 2*w^4 - 3*w^3 - 7*w^2 + 5*w + 2],\
[419, 419, -w^4 + 4*w^3 - 9*w - 2],\
[433, 433, -w^4 + 3*w^3 - 8*w + 4],\
[433, 433, w^4 - 7*w^2 - w + 6],\
[439, 439, 3*w^4 - 6*w^3 - 10*w^2 + 11*w + 7],\
[449, 449, -2*w^4 + 5*w^3 + 5*w^2 - 11*w - 4],\
[457, 457, -2*w^4 + 5*w^3 + 4*w^2 - 10*w - 2],\
[463, 463, 2*w^4 - 5*w^3 - 4*w^2 + 8*w + 1],\
[467, 467, 2*w^4 - 4*w^3 - 6*w^2 + 6*w + 1],\
[479, 479, 3*w^4 - 4*w^3 - 12*w^2 + 4*w + 7],\
[479, 479, 2*w^4 - 6*w^3 - 4*w^2 + 14*w + 1],\
[491, 491, w^4 - 6*w^2 - w + 4],\
[503, 503, 2*w^4 - w^3 - 11*w^2 - 3*w + 8],\
[503, 503, 2*w^3 - 5*w^2 - 2*w + 6],\
[509, 509, w^4 - 5*w^2 - 6*w],\
[509, 509, w^4 - 3*w^3 - 3*w^2 + 9*w + 1],\
[523, 523, 3*w^4 - 7*w^3 - 7*w^2 + 12*w + 3],\
[523, 523, 3*w^4 - 8*w^3 - 7*w^2 + 17*w + 3],\
[523, 523, w^4 - 7*w^2 - 2*w + 4],\
[529, 23, -w^4 + w^3 + 7*w^2 - 2*w - 9],\
[541, 541, w^4 - 3*w^3 - 3*w^2 + 5*w + 2],\
[547, 547, -w^3 + 3*w^2 + 3*w - 4],\
[557, 557, 2*w^3 - 4*w^2 - 6*w + 9],\
[577, 577, 2*w^4 - 2*w^3 - 11*w^2 + 5*w + 10],\
[577, 577, w^4 - 4*w^3 - w^2 + 9*w],\
[577, 577, 2*w^4 - 3*w^3 - 9*w^2 + 4*w + 8],\
[577, 577, w^4 - 7*w^2 - 3*w + 7],\
[577, 577, -3*w^4 + 3*w^3 + 13*w^2 - w - 4],\
[593, 593, 3*w - 2],\
[601, 601, 2*w^4 - 4*w^3 - 7*w^2 + 5*w + 6],\
[601, 601, -w^4 + 3*w^3 + w^2 - 7*w - 1],\
[607, 607, w^3 - w^2 - 2*w - 3],\
[625, 5, 2*w^4 - 5*w^3 - 8*w^2 + 14*w + 11],\
[631, 631, -w^2 + w - 2],\
[631, 631, w^4 - 7*w^2 - w + 8],\
[643, 643, -2*w^4 + 4*w^3 + 9*w^2 - 10*w - 8],\
[647, 647, 3*w^4 - 6*w^3 - 10*w^2 + 12*w + 8],\
[653, 653, -3*w^4 + 6*w^3 + 11*w^2 - 12*w - 9],\
[653, 653, w^4 - w^3 - 2*w^2 - 3*w - 3],\
[653, 653, -2*w^4 + 4*w^3 + 7*w^2 - 6*w - 8],\
[701, 701, w^4 - w^3 - 2*w^2 - w - 5],\
[719, 719, 2*w^4 - 5*w^3 - 6*w^2 + 14*w + 2],\
[727, 727, 2*w^4 - 5*w^3 - 5*w^2 + 9*w + 3],\
[733, 733, 2*w^4 - 5*w^3 - 5*w^2 + 13*w + 3],\
[739, 739, -2*w^3 + 4*w^2 + 4*w - 5],\
[743, 743, w^4 - 2*w^3 - 3*w^2 + 6*w - 3],\
[743, 743, 2*w^4 - 2*w^3 - 11*w^2 + 2*w + 10],\
[757, 757, -w^4 + 2*w^3 + 5*w^2 - 6*w - 10],\
[757, 757, 2*w^4 - 6*w^3 - 2*w^2 + 11*w - 4],\
[761, 761, 3*w^3 - 4*w^2 - 9*w + 3],\
[769, 769, 3*w^3 - 5*w^2 - 9*w + 7],\
[769, 769, -2*w^4 + 4*w^3 + 7*w^2 - 11*w - 2],\
[773, 773, 2*w^4 - 5*w^3 - 6*w^2 + 12*w + 1],\
[773, 773, 3*w^4 - 4*w^3 - 12*w^2 + 3*w + 5],\
[773, 773, 2*w^3 - w^2 - 10*w - 4],\
[797, 797, -w^4 + 4*w^3 + 2*w^2 - 12*w - 3],\
[811, 811, w^4 - 2*w^3 - 6*w^2 + 8*w + 4],\
[823, 823, w^4 - 4*w^3 - w^2 + 10*w + 1],\
[823, 823, 2*w^4 - 4*w^3 - 4*w^2 + 4*w - 3],\
[827, 827, -w^4 + 2*w^3 + 2*w^2 - w + 3],\
[827, 827, 2*w^4 - 4*w^3 - 5*w^2 + 7*w + 2],\
[829, 829, -w^4 + 4*w^3 + 2*w^2 - 10*w - 2],\
[829, 829, 3*w^3 - 3*w^2 - 11*w - 2],\
[829, 829, w^4 - 2*w^3 - 3*w^2 + 2*w - 3],\
[839, 839, -w^4 + 5*w^3 - 3*w^2 - 10*w + 5],\
[839, 839, -w^4 + w^3 + 5*w^2 - 9],\
[853, 853, 2*w^4 - 6*w^3 - 5*w^2 + 15*w + 4],\
[859, 859, -3*w^4 + 8*w^3 + 6*w^2 - 18*w + 5],\
[863, 863, w^4 - w^3 - 6*w^2 + 5*w + 2],\
[877, 877, 3*w^3 - 4*w^2 - 8*w + 1],\
[881, 881, 3*w^4 - 7*w^3 - 9*w^2 + 15*w + 3],\
[881, 881, -w^3 + 7*w + 1],\
[883, 883, -2*w^4 + 6*w^3 + 3*w^2 - 15*w],\
[887, 887, w^4 - w^3 - 5*w^2 + w - 1],\
[907, 907, 3*w^4 - 5*w^3 - 11*w^2 + 9*w + 5],\
[919, 919, w^4 - 2*w^3 - 6*w^2 + 8*w + 7],\
[937, 937, 2*w^4 - 2*w^3 - 9*w^2 + 2*w + 3],\
[937, 937, -3*w^4 + 8*w^3 + 6*w^2 - 16*w + 1],\
[937, 937, 3*w^4 - 5*w^3 - 11*w^2 + 7*w + 4],\
[947, 947, w^3 - w^2 - 7*w + 2],\
[947, 947, -w^4 + 2*w^3 + 4*w^2 - 7*w - 3],\
[967, 967, -w^4 + 4*w^3 - 11*w],\
[971, 971, 3*w^4 - 6*w^3 - 8*w^2 + 10*w],\
[971, 971, w^4 - 8*w^2 + 2*w + 9],\
[971, 971, w^4 - 4*w^3 + 2*w^2 + 7*w - 4],\
[977, 977, -w^4 + 4*w^3 - 12*w + 5],\
[983, 983, -w^4 + w^3 + 4*w^2 + 3*w - 2],\
[983, 983, -2*w^4 + 3*w^3 + 8*w^2 - 6*w - 4],\
[997, 997, 2*w^4 - 4*w^3 - 5*w^2 + 5*w - 3],\
[997, 997, w^4 + w^3 - 5*w^2 - 9*w - 2]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^8 - x^7 - 18*x^6 + 14*x^5 + 95*x^4 - 51*x^3 - 136*x^2 + 36*x + 32
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 5/128*e^7 - 7/128*e^6 - 25/32*e^5 + 55/64*e^4 + 559/128*e^3 - 453/128*e^2 - 307/64*e + 25/8, 1, 17/128*e^7 - 11/128*e^6 - 69/32*e^5 + 59/64*e^4 + 1235/128*e^3 - 273/128*e^2 - 615/64*e + 5/8, 7/128*e^7 + 3/128*e^6 - 35/32*e^5 - 51/64*e^4 + 885/128*e^3 + 761/128*e^2 - 801/64*e - 45/8, -13/128*e^7 + 31/128*e^6 + 49/32*e^5 - 207/64*e^4 - 839/128*e^3 + 1421/128*e^2 + 523/64*e - 65/8, -2*e + 2, 1/64*e^7 + 5/64*e^6 - 5/16*e^5 - 53/32*e^4 + 99/64*e^3 + 607/64*e^2 + 9/32*e - 27/4, 1/32*e^7 + 5/32*e^6 - 5/8*e^5 - 37/16*e^4 + 99/32*e^3 + 255/32*e^2 - 23/16*e - 5/2, -3/32*e^7 + 1/32*e^6 + 15/8*e^5 - 1/16*e^4 - 361/32*e^3 - 77/32*e^2 + 293/16*e + 5/2, -31/128*e^7 + 5/128*e^6 + 139/32*e^5 - 21/64*e^4 - 2749/128*e^3 + 31/128*e^2 + 1449/64*e + 21/8, -15/128*e^7 + 21/128*e^6 + 59/32*e^5 - 101/64*e^4 - 1037/128*e^3 - 49/128*e^2 + 505/64*e + 85/8, 7/128*e^7 + 3/128*e^6 - 35/32*e^5 - 51/64*e^4 + 885/128*e^3 + 505/128*e^2 - 929/64*e + 19/8, 9/128*e^7 + 13/128*e^6 - 45/32*e^5 - 93/64*e^4 + 1083/128*e^3 + 695/128*e^2 - 1039/64*e - 35/8, -27/128*e^7 + 25/128*e^6 + 119/32*e^5 - 105/64*e^4 - 2353/128*e^3 - 101/128*e^2 + 1229/64*e + 41/8, -21/64*e^7 + 23/64*e^6 + 89/16*e^5 - 167/32*e^4 - 1631/64*e^3 + 1205/64*e^2 + 739/32*e - 25/4, -9/128*e^7 + 51/128*e^6 + 29/32*e^5 - 419/64*e^4 - 187/128*e^3 + 3593/128*e^2 - 465/64*e - 157/8, 3/128*e^7 - 17/128*e^6 - 15/32*e^5 + 161/64*e^4 + 489/128*e^3 - 1667/128*e^2 - 581/64*e + 79/8, 27/128*e^7 - 25/128*e^6 - 103/32*e^5 + 169/64*e^4 + 1585/128*e^3 - 1051/128*e^2 - 429/64*e + 23/8, -5/64*e^7 - 25/64*e^6 + 25/16*e^5 + 201/32*e^4 - 623/64*e^3 - 1627/64*e^2 + 563/32*e + 63/4, 21/64*e^7 - 23/64*e^6 - 89/16*e^5 + 167/32*e^4 + 1567/64*e^3 - 1269/64*e^2 - 483/32*e + 57/4, 5/64*e^7 - 7/64*e^6 - 25/16*e^5 + 55/32*e^4 + 559/64*e^3 - 325/64*e^2 - 371/32*e - 7/4, 11/64*e^7 - 9/64*e^6 - 55/16*e^5 + 57/32*e^4 + 1345/64*e^3 - 299/64*e^2 - 1181/32*e + 7/4, -25/128*e^7 + 35/128*e^6 + 93/32*e^5 - 211/64*e^4 - 1387/128*e^3 + 985/128*e^2 + 319/64*e + 51/8, 17/128*e^7 - 11/128*e^6 - 85/32*e^5 + 59/64*e^4 + 2003/128*e^3 - 273/128*e^2 - 1287/64*e + 5/8, 9/32*e^7 - 19/32*e^6 - 37/8*e^5 + 131/16*e^4 + 635/32*e^3 - 873/32*e^2 - 191/16*e + 29/2, -7/128*e^7 - 3/128*e^6 + 35/32*e^5 + 51/64*e^4 - 1013/128*e^3 - 505/128*e^2 + 1121/64*e - 35/8, 1/128*e^7 - 27/128*e^6 + 11/32*e^5 + 203/64*e^4 - 733/128*e^3 - 1729/128*e^2 + 1353/64*e + 117/8, 19/128*e^7 - 1/128*e^6 - 79/32*e^5 + 17/64*e^4 + 1433/128*e^3 - 339/128*e^2 - 725/64*e + 79/8, -9/32*e^7 + 3/32*e^6 + 37/8*e^5 - 3/16*e^4 - 667/32*e^3 - 167/32*e^2 + 271/16*e + 19/2, 1/4*e^7 - 1/4*e^6 - 4*e^5 + 7/2*e^4 + 71/4*e^3 - 51/4*e^2 - 35/2*e + 4, -7/128*e^7 - 3/128*e^6 + 35/32*e^5 + 51/64*e^4 - 629/128*e^3 - 1017/128*e^2 - 95/64*e + 109/8, 21/128*e^7 + 9/128*e^6 - 89/32*e^5 - 89/64*e^4 + 1503/128*e^3 + 875/128*e^2 - 387/64*e - 23/8, -39/128*e^7 + 29/128*e^6 + 163/32*e^5 - 173/64*e^4 - 2901/128*e^3 + 1255/128*e^2 + 1025/64*e - 99/8, -3/128*e^7 - 47/128*e^6 + 15/32*e^5 + 351/64*e^4 - 361/128*e^3 - 2493/128*e^2 + 389/64*e + 65/8, 15/128*e^7 - 21/128*e^6 - 59/32*e^5 + 229/64*e^4 + 909/128*e^3 - 2767/128*e^2 - 121/64*e + 171/8, 1/32*e^7 + 5/32*e^6 - 5/8*e^5 - 53/16*e^4 + 99/32*e^3 + 543/32*e^2 - 55/16*e - 3/2, 1/16*e^7 - 3/16*e^6 - 5/4*e^5 + 27/8*e^4 + 115/16*e^3 - 265/16*e^2 - 111/8*e + 13, -11/128*e^7 - 23/128*e^6 + 55/32*e^5 + 135/64*e^4 - 1281/128*e^3 - 885/128*e^2 + 1149/64*e + 105/8, -3/128*e^7 + 17/128*e^6 + 31/32*e^5 - 97/64*e^4 - 1257/128*e^3 + 259/128*e^2 + 1701/64*e + 33/8, 17/64*e^7 - 11/64*e^6 - 69/16*e^5 + 59/32*e^4 + 1107/64*e^3 - 145/64*e^2 - 231/32*e - 27/4, -7/16*e^7 + 13/16*e^6 + 31/4*e^5 - 93/8*e^4 - 629/16*e^3 + 663/16*e^2 + 361/8*e - 17, -25/64*e^7 + 35/64*e^6 + 109/16*e^5 - 275/32*e^4 - 2155/64*e^3 + 2201/64*e^2 + 1183/32*e - 45/4, 7/16*e^7 - 5/16*e^6 - 31/4*e^5 + 29/8*e^4 + 597/16*e^3 - 111/16*e^2 - 273/8*e - 1, 1/8*e^7 - 3/8*e^6 - 3/2*e^5 + 19/4*e^4 + 19/8*e^3 - 121/8*e^2 + 45/4*e + 8, -31/64*e^7 + 5/64*e^6 + 139/16*e^5 - 21/32*e^4 - 2877/64*e^3 + 31/64*e^2 + 1929/32*e - 3/4, 1/2*e^6 - 8*e^4 - e^3 + 67/2*e^2 + 3*e - 28, -43/128*e^7 + 9/128*e^6 + 183/32*e^5 + 39/64*e^4 - 3297/128*e^3 - 1429/128*e^2 + 1373/64*e + 121/8, -3/16*e^7 + 9/16*e^6 + 11/4*e^5 - 65/8*e^4 - 153/16*e^3 + 475/16*e^2 - 27/8*e - 15, 15/32*e^7 - 5/32*e^6 - 67/8*e^5 + 37/16*e^4 + 1389/32*e^3 - 319/32*e^2 - 937/16*e + 3/2, 3/128*e^7 - 81/128*e^6 + 1/32*e^5 + 609/64*e^4 - 407/128*e^3 - 4675/128*e^2 + 795/64*e + 223/8, 71/128*e^7 - 61/128*e^6 - 307/32*e^5 + 333/64*e^4 + 5941/128*e^3 - 1351/128*e^2 - 3073/64*e - 13/8, -5/64*e^7 + 7/64*e^6 + 25/16*e^5 - 55/32*e^4 - 687/64*e^3 + 453/64*e^2 + 819/32*e - 33/4, -35/128*e^7 + 49/128*e^6 + 127/32*e^5 - 321/64*e^4 - 1865/128*e^3 + 2275/128*e^2 + 581/64*e - 31/8, -1/128*e^7 + 27/128*e^6 + 5/32*e^5 - 267/64*e^4 - 291/128*e^3 + 2881/128*e^2 + 471/64*e - 117/8, -7/32*e^7 - 3/32*e^6 + 27/8*e^5 + 51/16*e^4 - 437/32*e^3 - 761/32*e^2 + 97/16*e + 69/2, 1/128*e^7 - 27/128*e^6 - 5/32*e^5 + 203/64*e^4 + 35/128*e^3 - 1089/128*e^2 + 297/64*e - 43/8, -55/128*e^7 + 13/128*e^6 + 243/32*e^5 - 93/64*e^4 - 4869/128*e^3 + 1079/128*e^2 + 3121/64*e - 115/8, -11/32*e^7 + 9/32*e^6 + 47/8*e^5 - 25/16*e^4 - 897/32*e^3 - 277/32*e^2 + 429/16*e + 33/2, -13/64*e^7 + 31/64*e^6 + 49/16*e^5 - 207/32*e^4 - 711/64*e^3 + 1293/64*e^2 - 53/32*e - 25/4, 11/128*e^7 - 41/128*e^6 - 71/32*e^5 + 313/64*e^4 + 2177/128*e^3 - 2379/128*e^2 - 2141/64*e + 55/8, 3/128*e^7 - 81/128*e^6 - 15/32*e^5 + 673/64*e^4 + 361/128*e^3 - 5315/128*e^2 - 133/64*e + 111/8, -7/16*e^7 + 5/16*e^6 + 27/4*e^5 - 29/8*e^4 - 421/16*e^3 + 175/16*e^2 + 113/8*e - 13, -15/128*e^7 + 21/128*e^6 + 91/32*e^5 - 229/64*e^4 - 2317/128*e^3 + 2511/128*e^2 + 1465/64*e - 155/8, -13/64*e^7 - 1/64*e^6 + 49/16*e^5 - 15/32*e^4 - 583/64*e^3 + 237/64*e^2 - 341/32*e + 15/4, -15/64*e^7 + 21/64*e^6 + 59/16*e^5 - 101/32*e^4 - 909/64*e^3 + 79/64*e^2 + 57/32*e + 69/4, -7/128*e^7 - 3/128*e^6 + 19/32*e^5 - 13/64*e^4 - 117/128*e^3 + 1159/128*e^2 - 255/64*e - 211/8, -33/128*e^7 + 59/128*e^6 + 165/32*e^5 - 491/64*e^4 - 3715/128*e^3 + 3873/128*e^2 + 2231/64*e - 21/8, 3/8*e^7 - 5/8*e^6 - 13/2*e^5 + 41/4*e^4 + 257/8*e^3 - 359/8*e^2 - 141/4*e + 30, -1/2*e^7 + 1/2*e^6 + 9*e^5 - 7*e^4 - 89/2*e^3 + 51/2*e^2 + 37*e - 14, -11/64*e^7 - 23/64*e^6 + 71/16*e^5 + 167/32*e^4 - 1921/64*e^3 - 1397/64*e^2 + 1309/32*e + 73/4, -3/8*e^7 + 1/8*e^6 + 13/2*e^5 - 9/4*e^4 - 249/8*e^3 + 115/8*e^2 + 105/4*e - 22, -13/64*e^7 - 1/64*e^6 + 65/16*e^5 + 49/32*e^4 - 1543/64*e^3 - 851/64*e^2 + 1163/32*e + 79/4, 17/64*e^7 + 21/64*e^6 - 69/16*e^5 - 197/32*e^4 + 1171/64*e^3 + 1935/64*e^2 - 423/32*e - 163/4, 11/128*e^7 + 23/128*e^6 - 55/32*e^5 - 263/64*e^4 + 1153/128*e^3 + 2677/128*e^2 - 189/64*e - 89/8, -37/128*e^7 + 103/128*e^6 + 105/32*e^5 - 727/64*e^4 - 527/128*e^3 + 5605/128*e^2 - 1293/64*e - 265/8, 3/32*e^7 + 15/32*e^6 - 15/8*e^5 - 127/16*e^4 + 329/32*e^3 + 1181/32*e^2 - 165/16*e - 85/2, 83/128*e^7 - 65/128*e^6 - 367/32*e^5 + 465/64*e^4 + 7385/128*e^3 - 3347/128*e^2 - 4373/64*e + 15/8, -47/128*e^7 + 53/128*e^6 + 203/32*e^5 - 389/64*e^4 - 4205/128*e^3 + 2607/128*e^2 + 3385/64*e - 75/8, 25/64*e^7 - 35/64*e^6 - 93/16*e^5 + 211/32*e^4 + 1387/64*e^3 - 1241/64*e^2 - 319/32*e + 29/4, 1/4*e^7 - 1/4*e^6 - 4*e^5 + 7/2*e^4 + 71/4*e^3 - 55/4*e^2 - 43/2*e + 22, 1/8*e^7 + 1/8*e^6 - 5/2*e^5 - 9/4*e^4 + 107/8*e^3 + 91/8*e^2 - 59/4*e - 2, -9/128*e^7 - 13/128*e^6 + 61/32*e^5 + 93/64*e^4 - 1851/128*e^3 - 823/128*e^2 + 1711/64*e + 131/8, -65/128*e^7 + 27/128*e^6 + 309/32*e^5 - 139/64*e^4 - 6627/128*e^3 + 321/128*e^2 + 4151/64*e - 69/8, 17/32*e^7 - 27/32*e^6 - 69/8*e^5 + 155/16*e^4 + 1203/32*e^3 - 545/32*e^2 - 407/16*e - 35/2, 9/32*e^7 - 19/32*e^6 - 37/8*e^5 + 163/16*e^4 + 667/32*e^3 - 1577/32*e^2 - 351/16*e + 69/2, -3/8*e^7 + 5/8*e^6 + 11/2*e^5 - 33/4*e^4 - 153/8*e^3 + 199/8*e^2 + 5/4*e - 6, 1/4*e^7 - 1/4*e^6 - 4*e^5 + 7/2*e^4 + 71/4*e^3 - 55/4*e^2 - 47/2*e - 2, -25/32*e^7 + 3/32*e^6 + 109/8*e^5 - 19/16*e^4 - 2027/32*e^3 + 121/32*e^2 + 799/16*e + 27/2, -17/64*e^7 + 43/64*e^6 + 69/16*e^5 - 347/32*e^4 - 1171/64*e^3 + 2993/64*e^2 + 391/32*e - 117/4, -1/64*e^7 - 5/64*e^6 + 5/16*e^5 - 11/32*e^4 + 29/64*e^3 + 545/64*e^2 - 425/32*e - 69/4, -13/64*e^7 - 33/64*e^6 + 65/16*e^5 + 305/32*e^4 - 1479/64*e^3 - 2867/64*e^2 + 875/32*e + 135/4, 27/64*e^7 - 25/64*e^6 - 103/16*e^5 + 169/32*e^4 + 1649/64*e^3 - 1307/64*e^2 - 557/32*e + 71/4, -21/64*e^7 + 23/64*e^6 + 89/16*e^5 - 167/32*e^4 - 1695/64*e^3 + 1141/64*e^2 + 1059/32*e - 9/4, 19/128*e^7 - 65/128*e^6 - 47/32*e^5 + 401/64*e^4 - 487/128*e^3 - 2067/128*e^2 + 2347/64*e + 47/8, -5/128*e^7 + 7/128*e^6 + 25/32*e^5 - 55/64*e^4 - 431/128*e^3 + 709/128*e^2 - 717/64*e - 105/8, 1/2*e^7 - 8*e^5 - e^4 + 65/2*e^3 + 9*e^2 - 14*e - 20, -31/64*e^7 + 5/64*e^6 + 139/16*e^5 + 43/32*e^4 - 2877/64*e^3 - 1249/64*e^2 + 1833/32*e + 21/4, -7/16*e^7 - 3/16*e^6 + 31/4*e^5 + 27/8*e^4 - 597/16*e^3 - 217/16*e^2 + 297/8*e + 17, -71/128*e^7 + 61/128*e^6 + 307/32*e^5 - 461/64*e^4 - 5301/128*e^3 + 3655/128*e^2 + 1025/64*e - 115/8, 13/32*e^7 - 31/32*e^6 - 49/8*e^5 + 207/16*e^4 + 743/32*e^3 - 1293/32*e^2 - 187/16*e + 33/2, -23/64*e^7 + 13/64*e^6 + 99/16*e^5 - 125/32*e^4 - 1829/64*e^3 + 1015/64*e^2 + 881/32*e + 45/4, -23/128*e^7 - 83/128*e^6 + 115/32*e^5 + 643/64*e^4 - 2469/128*e^3 - 5225/128*e^2 + 1169/64*e + 189/8, 95/128*e^7 - 69/128*e^6 - 443/32*e^5 + 533/64*e^4 + 9085/128*e^3 - 4447/128*e^2 - 4681/64*e + 139/8, 41/128*e^7 - 19/128*e^6 - 189/32*e^5 + 131/64*e^4 + 4123/128*e^3 - 1193/128*e^2 - 3471/64*e + 61/8, -33/128*e^7 + 123/128*e^6 + 133/32*e^5 - 1003/64*e^4 - 2179/128*e^3 + 8545/128*e^2 - 137/64*e - 437/8, -17/128*e^7 + 11/128*e^6 + 85/32*e^5 - 187/64*e^4 - 1747/128*e^3 + 2449/128*e^2 + 903/64*e - 101/8, -51/128*e^7 + 97/128*e^6 + 207/32*e^5 - 625/64*e^4 - 3577/128*e^3 + 3699/128*e^2 + 1141/64*e - 143/8, -13/128*e^7 + 31/128*e^6 + 65/32*e^5 - 143/64*e^4 - 1351/128*e^3 - 1011/128*e^2 + 427/64*e + 399/8, -29/128*e^7 + 79/128*e^6 + 81/32*e^5 - 575/64*e^4 - 375/128*e^3 + 4509/128*e^2 - 1253/64*e - 225/8, -13/128*e^7 - 33/128*e^6 + 81/32*e^5 + 305/64*e^4 - 1991/128*e^3 - 2995/128*e^2 + 651/64*e + 111/8, 13/64*e^7 + 1/64*e^6 - 49/16*e^5 - 49/32*e^4 + 775/64*e^3 + 787/64*e^2 - 363/32*e - 55/4, 1/128*e^7 - 27/128*e^6 + 27/32*e^5 + 139/64*e^4 - 1757/128*e^3 + 191/128*e^2 + 3049/64*e - 139/8, -61/64*e^7 + 79/64*e^6 + 257/16*e^5 - 543/32*e^4 - 4759/64*e^3 + 3805/64*e^2 + 2043/32*e - 145/4, -3/32*e^7 + 1/32*e^6 + 15/8*e^5 - 33/16*e^4 - 297/32*e^3 + 435/32*e^2 + 85/16*e + 21/2, 57/64*e^7 - 3/64*e^6 - 253/16*e^5 - 13/32*e^4 + 4939/64*e^3 + 263/64*e^2 - 2463/32*e - 11/4, 31/64*e^7 - 69/64*e^6 - 123/16*e^5 + 469/32*e^4 + 2237/64*e^3 - 2911/64*e^2 - 1353/32*e + 59/4, 19/128*e^7 + 63/128*e^6 - 111/32*e^5 - 495/64*e^4 + 2841/128*e^3 + 3309/128*e^2 - 2133/64*e + 79/8, -37/128*e^7 + 103/128*e^6 + 137/32*e^5 - 791/64*e^4 - 1807/128*e^3 + 6501/128*e^2 - 845/64*e - 361/8, 125/128*e^7 + 17/128*e^6 - 545/32*e^5 - 225/64*e^4 + 10391/128*e^3 + 2819/128*e^2 - 5275/64*e - 191/8, 129/128*e^7 - 91/128*e^6 - 581/32*e^5 + 651/64*e^4 + 11811/128*e^3 - 4737/128*e^2 - 6807/64*e + 85/8, 15/32*e^7 - 21/32*e^6 - 59/8*e^5 + 133/16*e^4 + 941/32*e^3 - 719/32*e^2 - 201/16*e + 15/2, 39/64*e^7 - 93/64*e^6 - 147/16*e^5 + 653/32*e^4 + 2261/64*e^3 - 4519/64*e^2 - 417/32*e + 163/4, -13/32*e^7 + 15/32*e^6 + 49/8*e^5 - 111/16*e^4 - 679/32*e^3 + 829/32*e^2 + 27/16*e - 45/2, 11/32*e^7 - 25/32*e^6 - 39/8*e^5 + 185/16*e^4 + 545/32*e^3 - 1563/32*e^2 - 45/16*e + 95/2, 15/32*e^7 - 21/32*e^6 - 59/8*e^5 + 133/16*e^4 + 1005/32*e^3 - 847/32*e^2 - 425/16*e + 47/2, 7/32*e^7 + 3/32*e^6 - 35/8*e^5 - 19/16*e^4 + 885/32*e^3 + 57/32*e^2 - 865/16*e + 3/2, 3/16*e^7 - 1/16*e^6 - 11/4*e^5 + 17/8*e^4 + 201/16*e^3 - 307/16*e^2 - 221/8*e + 27, 53/128*e^7 - 23/128*e^6 - 217/32*e^5 + 263/64*e^4 + 3647/128*e^3 - 3445/128*e^2 - 1315/64*e + 249/8, 1/16*e^7 + 5/16*e^6 - 5/4*e^5 - 37/8*e^4 + 131/16*e^3 + 223/16*e^2 - 199/8*e - 1, -83/128*e^7 + 129/128*e^6 + 335/32*e^5 - 849/64*e^4 - 6105/128*e^3 + 5459/128*e^2 + 3413/64*e - 15/8, -75/128*e^7 + 105/128*e^6 + 359/32*e^5 - 761/64*e^4 - 7489/128*e^3 + 5259/128*e^2 + 3165/64*e - 71/8, 57/128*e^7 - 3/128*e^6 - 253/32*e^5 - 141/64*e^4 + 5323/128*e^3 + 2951/128*e^2 - 3487/64*e - 115/8, -15/128*e^7 + 85/128*e^6 + 43/32*e^5 - 677/64*e^4 - 13/128*e^3 + 5519/128*e^2 - 1447/64*e - 347/8, 71/128*e^7 + 3/128*e^6 - 323/32*e^5 - 115/64*e^4 + 6837/128*e^3 + 1145/128*e^2 - 4385/64*e + 131/8, -17/128*e^7 - 117/128*e^6 + 101/32*e^5 + 901/64*e^4 - 2515/128*e^3 - 7535/128*e^2 + 1511/64*e + 363/8, 39/64*e^7 - 61/64*e^6 - 163/16*e^5 + 429/32*e^4 + 3029/64*e^3 - 2951/64*e^2 - 1185/32*e + 75/4, -7/16*e^7 - 3/16*e^6 + 31/4*e^5 + 19/8*e^4 - 565/16*e^3 - 57/16*e^2 + 185/8*e - 1, 3/8*e^7 - 1/8*e^6 - 11/2*e^5 + 9/4*e^4 + 137/8*e^3 - 83/8*e^2 + 11/4*e + 10, 11/32*e^7 - 41/32*e^6 - 39/8*e^5 + 281/16*e^4 + 609/32*e^3 - 1803/32*e^2 - 285/16*e + 31/2, -1/4*e^7 - 3/4*e^6 + 6*e^5 + 25/2*e^4 - 159/4*e^3 - 229/4*e^2 + 121/2*e + 46, 33/128*e^7 - 59/128*e^6 - 101/32*e^5 + 363/64*e^4 + 771/128*e^3 - 2849/128*e^2 + 649/64*e + 293/8, -4*e^3 + 24*e + 2, -27/128*e^7 + 89/128*e^6 + 119/32*e^5 - 617/64*e^4 - 2737/128*e^3 + 4315/128*e^2 + 3213/64*e - 279/8, -1/2*e^6 + 8*e^4 + e^3 - 57/2*e^2 - 3*e - 10, -29/32*e^7 + 31/32*e^6 + 113/8*e^5 - 207/16*e^4 - 1815/32*e^3 + 1389/32*e^2 + 555/16*e - 25/2, -73/128*e^7 + 51/128*e^6 + 317/32*e^5 - 227/64*e^4 - 6139/128*e^3 - 631/128*e^2 + 3055/64*e + 259/8, -9/32*e^7 + 19/32*e^6 + 37/8*e^5 - 131/16*e^4 - 699/32*e^3 + 1001/32*e^2 + 511/16*e - 53/2, 9/64*e^7 - 51/64*e^6 - 29/16*e^5 + 483/32*e^4 + 251/64*e^3 - 5001/64*e^2 + 177/32*e + 237/4, -5/8*e^7 + 7/8*e^6 + 23/2*e^5 - 47/4*e^4 - 495/8*e^3 + 341/8*e^2 + 311/4*e - 34, -27/32*e^7 + 25/32*e^6 + 119/8*e^5 - 137/16*e^4 - 2353/32*e^3 + 507/32*e^2 + 1293/16*e + 13/2, 13/128*e^7 - 31/128*e^6 - 49/32*e^5 + 207/64*e^4 + 583/128*e^3 - 653/128*e^2 + 565/64*e + 81/8, -47/64*e^7 + 21/64*e^6 + 219/16*e^5 - 69/32*e^4 - 4653/64*e^3 - 369/64*e^2 + 2489/32*e + 13/4, -71/64*e^7 + 61/64*e^6 + 323/16*e^5 - 397/32*e^4 - 6453/64*e^3 + 2247/64*e^2 + 3073/32*e + 21/4, 27/64*e^7 - 25/64*e^6 - 135/16*e^5 + 169/32*e^4 + 3377/64*e^3 - 1307/64*e^2 - 2957/32*e + 63/4, -5/32*e^7 + 23/32*e^6 + 17/8*e^5 - 119/16*e^4 - 335/32*e^3 + 341/32*e^2 + 435/16*e + 27/2, 13/128*e^7 + 97/128*e^6 - 97/32*e^5 - 625/64*e^4 + 2887/128*e^3 + 3443/128*e^2 - 2539/64*e + 81/8, -61/128*e^7 + 239/128*e^6 + 241/32*e^5 - 1823/64*e^4 - 4183/128*e^3 + 14589/128*e^2 + 1531/64*e - 561/8, 1/128*e^7 + 37/128*e^6 - 21/32*e^5 - 309/64*e^4 + 931/128*e^3 + 2943/128*e^2 - 1079/64*e - 59/8, -15/32*e^7 + 37/32*e^6 + 51/8*e^5 - 277/16*e^4 - 621/32*e^3 + 2207/32*e^2 + 25/16*e - 67/2, -5/32*e^7 - 9/32*e^6 + 33/8*e^5 + 57/16*e^4 - 911/32*e^3 - 267/32*e^2 + 723/16*e + 23/2, -5/16*e^7 + 15/16*e^6 + 17/4*e^5 - 103/8*e^4 - 255/16*e^3 + 749/16*e^2 + 195/8*e - 31, -9/64*e^7 - 77/64*e^6 + 45/16*e^5 + 669/32*e^4 - 1083/64*e^3 - 6263/64*e^2 + 1103/32*e + 251/4, 11/32*e^7 - 41/32*e^6 - 47/8*e^5 + 313/16*e^4 + 961/32*e^3 - 2315/32*e^2 - 749/16*e + 71/2, -19/64*e^7 + 65/64*e^6 + 79/16*e^5 - 529/32*e^4 - 1305/64*e^3 + 4627/64*e^2 + 277/32*e - 175/4, -153/128*e^7 + 99/128*e^6 + 669/32*e^5 - 659/64*e^4 - 12907/128*e^3 + 4377/128*e^2 + 5759/64*e - 45/8, 21/64*e^7 - 23/64*e^6 - 73/16*e^5 + 39/32*e^4 + 927/64*e^3 + 971/64*e^2 + 125/32*e - 55/4, -19/64*e^7 + 33/64*e^6 + 79/16*e^5 - 273/32*e^4 - 1369/64*e^3 + 2739/64*e^2 + 309/32*e - 127/4, -13/128*e^7 + 31/128*e^6 + 49/32*e^5 - 463/64*e^4 - 327/128*e^3 + 6029/128*e^2 - 1269/64*e - 225/8, -11/32*e^7 - 23/32*e^6 + 47/8*e^5 + 199/16*e^4 - 961/32*e^3 - 1781/32*e^2 + 845/16*e + 89/2]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([7, 7, w^4 - 2*w^3 - 3*w^2 + 4*w + 2])] = -1

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