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

NN = ZF.ideal([27, 3, -w^4 + w^3 + 4*w^2 - 2*w - 1])

primes_array = [
[3, 3, w^4 - w^3 - 5*w^2 + 3*w + 3],\
[9, 3, -w^4 + 5*w^2 - 3],\
[9, 3, -w^4 + w^3 + 5*w^2 - 3*w - 2],\
[13, 13, -w^4 + w^3 + 4*w^2 - 3*w - 1],\
[17, 17, w^4 - w^3 - 5*w^2 + 3*w + 1],\
[19, 19, -w^3 + w^2 + 4*w - 2],\
[23, 23, -w^2 + 3],\
[31, 31, w^3 - 4*w + 2],\
[32, 2, 2],\
[37, 37, w^3 - 3*w - 1],\
[53, 53, -2*w^4 + w^3 + 9*w^2 - 3*w - 2],\
[59, 59, -w^4 + 5*w^2 + w - 4],\
[61, 61, -w^4 + w^3 + 5*w^2 - 4*w],\
[67, 67, -w^4 + 6*w^2 + 2*w - 4],\
[71, 71, 2*w^4 - w^3 - 9*w^2 + 4*w + 5],\
[79, 79, 2*w^4 - w^3 - 10*w^2 + 2*w + 7],\
[83, 83, -w^4 + 2*w^3 + 5*w^2 - 7*w - 2],\
[83, 83, -w^4 + w^3 + 4*w^2 - 3*w + 3],\
[83, 83, w^4 - w^3 - 5*w^2 + 4*w - 1],\
[83, 83, -w^4 + w^3 + 4*w^2 - 4*w - 2],\
[83, 83, -2*w^4 + w^3 + 9*w^2 - 3*w - 5],\
[97, 97, -w^4 - w^3 + 6*w^2 + 4*w - 4],\
[101, 101, -w^4 + 4*w^2 + 2*w - 2],\
[107, 107, -2*w^4 + w^3 + 11*w^2 - 3*w - 7],\
[127, 127, w^3 - w^2 - 4*w],\
[131, 131, w^4 - w^3 - 4*w^2 + 2*w - 1],\
[137, 137, w^4 - w^3 - 6*w^2 + 3*w + 3],\
[139, 139, -2*w^4 + w^3 + 9*w^2 - 3*w + 1],\
[157, 157, 2*w^4 - w^3 - 9*w^2 + 4*w + 2],\
[163, 163, -w^2 - 2*w + 3],\
[167, 167, w^4 - 5*w^2 + 2*w + 1],\
[169, 13, -2*w^4 + 2*w^3 + 9*w^2 - 7*w - 5],\
[169, 13, w^4 - 2*w^3 - 5*w^2 + 8*w + 2],\
[191, 191, 2*w^4 - w^3 - 9*w^2 + 3*w + 4],\
[193, 193, 2*w^4 - 2*w^3 - 8*w^2 + 7*w],\
[199, 199, -w^4 + 2*w^3 + 5*w^2 - 9*w - 3],\
[211, 211, -3*w^4 + w^3 + 13*w^2 - 2*w - 1],\
[227, 227, 2*w^3 - w^2 - 9*w + 1],\
[233, 233, -w^3 + w^2 + 4*w + 1],\
[251, 251, -3*w^4 + 14*w^2 + w - 2],\
[257, 257, -2*w^4 + 2*w^3 + 10*w^2 - 6*w - 5],\
[257, 257, -w^4 + w^3 + 5*w^2 - 6*w - 1],\
[257, 257, 2*w^4 - 2*w^3 - 11*w^2 + 9*w + 9],\
[257, 257, -2*w^4 + 2*w^3 + 9*w^2 - 6*w - 3],\
[257, 257, 2*w^4 - w^3 - 10*w^2 + 5*w + 5],\
[269, 269, -w^4 + 2*w^3 + 4*w^2 - 6*w - 2],\
[271, 271, -w^4 + 4*w^2 + w - 3],\
[277, 277, -2*w^4 + 9*w^2 + w - 4],\
[281, 281, w^4 - w^3 - 3*w^2 + 3*w - 4],\
[283, 283, 2*w^4 - 3*w^3 - 8*w^2 + 13*w],\
[289, 17, -w^4 + w^3 + 7*w^2 - 5*w - 5],\
[289, 17, 4*w^4 - 3*w^3 - 19*w^2 + 11*w + 6],\
[293, 293, -2*w^4 + 11*w^2 - 7],\
[317, 317, w^3 - 6*w],\
[337, 337, -w^4 + 2*w^3 + 5*w^2 - 9*w - 1],\
[337, 337, w^4 - 2*w^3 - 5*w^2 + 6*w + 3],\
[337, 337, -w^4 + w^3 + 5*w^2 - 4*w - 6],\
[337, 337, -2*w^3 + 8*w + 1],\
[337, 337, w^2 + w - 5],\
[347, 347, -2*w^4 + w^3 + 9*w^2 - 5*w - 3],\
[349, 349, 3*w^4 - 2*w^3 - 13*w^2 + 8*w + 2],\
[353, 353, w^4 - 3*w^3 - 4*w^2 + 12*w + 2],\
[359, 359, 2*w^3 - w^2 - 7*w + 3],\
[361, 19, w^4 - 2*w^3 - 4*w^2 + 7*w + 3],\
[361, 19, w^4 - w^3 - 3*w^2 + 3*w - 3],\
[367, 367, -2*w^4 + w^3 + 9*w^2 - w - 2],\
[379, 379, -2*w^3 + w^2 + 7*w + 2],\
[379, 379, -2*w^4 + w^3 + 10*w^2 - 4*w],\
[379, 379, 2*w^3 - w^2 - 6*w - 2],\
[379, 379, -2*w^3 + 2*w^2 + 6*w - 3],\
[379, 379, -3*w^4 + 2*w^3 + 14*w^2 - 7*w - 6],\
[383, 383, 2*w^4 + w^3 - 10*w^2 - 7*w + 4],\
[383, 383, -2*w^3 + w^2 + 10*w],\
[383, 383, w^3 + w^2 - 5*w - 1],\
[383, 383, 3*w^4 + 3*w^3 - 15*w^2 - 15*w + 4],\
[383, 383, -2*w^4 + 3*w^3 + 10*w^2 - 10*w - 2],\
[389, 389, 3*w^4 - w^3 - 14*w^2 + 3*w + 3],\
[397, 397, w^4 - 6*w^2 - 2*w + 5],\
[397, 397, w^4 - 2*w^3 - 2*w^2 + 6*w - 5],\
[397, 397, 2*w^4 - 2*w^3 - 11*w^2 + 10*w + 6],\
[397, 397, w^4 - w^3 - 3*w^2 + 4*w - 6],\
[397, 397, w^3 + w^2 - 3*w - 4],\
[401, 401, w^3 - w^2 - 6*w + 3],\
[401, 401, -w^4 + 4*w^2 + 2*w - 3],\
[401, 401, -w^4 + 6*w^2 - w - 7],\
[421, 421, -w^4 - w^3 + 5*w^2 + 5*w - 4],\
[421, 421, -w^4 + w^3 + 6*w^2 - 3*w - 2],\
[421, 421, -w^4 - w^3 + 6*w^2 + 6*w - 5],\
[421, 421, 3*w^4 - w^3 - 15*w^2 + w + 10],\
[421, 421, 2*w^4 - 9*w^2 + 2*w + 4],\
[431, 431, 2*w^4 - 11*w^2 - 2*w + 11],\
[439, 439, 2*w^4 - 3*w^3 - 9*w^2 + 10*w + 6],\
[443, 443, -3*w^4 + 2*w^3 + 14*w^2 - 7*w - 2],\
[449, 449, -w^4 + 2*w^3 + 5*w^2 - 6*w - 4],\
[461, 461, 3*w^4 - 4*w^3 - 14*w^2 + 14*w + 5],\
[463, 463, w^3 - 6*w - 1],\
[467, 467, 3*w^4 - 3*w^3 - 13*w^2 + 10*w],\
[487, 487, 3*w^4 - w^3 - 14*w^2 + w + 3],\
[487, 487, 2*w^2 - w - 4],\
[487, 487, -2*w^4 + 2*w^3 + 9*w^2 - 8*w - 5],\
[487, 487, 2*w^4 - 10*w^2 - 3*w + 4],\
[487, 487, -2*w^4 + w^3 + 8*w^2 - 3*w - 1],\
[499, 499, -w^4 + 2*w^3 + 4*w^2 - 8*w - 2],\
[499, 499, -2*w^4 + w^3 + 10*w^2 - w - 9],\
[499, 499, -w^3 - 2*w^2 + 2*w + 5],\
[499, 499, -w^4 + 4*w^2 + 4*w],\
[499, 499, -2*w^4 + w^3 + 12*w^2 - 4*w - 9],\
[509, 509, 3*w^4 - 2*w^3 - 16*w^2 + 6*w + 9],\
[521, 521, -2*w^4 + w^3 + 10*w^2 - 5*w - 4],\
[523, 523, w - 4],\
[529, 23, -w^3 + 2*w^2 + 4*w - 4],\
[529, 23, w^4 + 2*w^3 - 6*w^2 - 11*w + 4],\
[569, 569, -2*w^4 + 11*w^2 - 10],\
[571, 571, -2*w^4 + w^3 + 10*w^2 - 3*w - 2],\
[593, 593, -2*w^4 + 3*w^3 + 10*w^2 - 11*w - 8],\
[613, 613, -2*w^3 + 2*w^2 + 9*w - 5],\
[617, 617, -2*w^4 + 10*w^2 - w - 7],\
[631, 631, -2*w^4 + 2*w^3 + 7*w^2 - 8*w + 3],\
[641, 641, -2*w^4 + 2*w^3 + 8*w^2 - 9*w + 3],\
[643, 643, -3*w^4 + w^3 + 13*w^2 - w + 1],\
[643, 643, w^4 + w^3 - 3*w^2 - 6*w - 2],\
[643, 643, -w^4 - w^3 + 6*w^2 + 3*w - 4],\
[643, 643, 2*w^4 - w^3 - 10*w^2 + 4*w + 1],\
[643, 643, 2*w^4 - 2*w^3 - 8*w^2 + 6*w + 5],\
[647, 647, -2*w^3 + w^2 + 6*w - 4],\
[659, 659, 4*w^4 - 3*w^3 - 19*w^2 + 11*w + 10],\
[661, 661, 2*w^4 + 3*w^3 - 11*w^2 - 14*w + 6],\
[673, 673, w^4 - 3*w^3 - 3*w^2 + 10*w - 1],\
[683, 683, w^4 - 2*w^3 - 4*w^2 + 6*w - 4],\
[701, 701, w^3 - w^2 - 2*w + 4],\
[727, 727, -w^4 + 6*w^2 + 2*w - 7],\
[743, 743, w^4 - w^3 - 7*w^2 + 5*w + 9],\
[769, 769, w^4 + 2*w^3 - 5*w^2 - 9*w + 4],\
[787, 787, w^4 + w^3 - 7*w^2 - 3*w + 5],\
[797, 797, -2*w^4 - w^3 + 10*w^2 + 4*w - 4],\
[797, 797, w^4 - 3*w^3 - 5*w^2 + 12*w + 5],\
[797, 797, -3*w^4 + 2*w^3 + 13*w^2 - 8*w],\
[797, 797, -w^4 + w^3 + 3*w^2 - 5*w - 1],\
[797, 797, 2*w^4 - 11*w^2 + 2*w + 7],\
[809, 809, -4*w^4 + 2*w^3 + 18*w^2 - 6*w + 1],\
[809, 809, 3*w^4 - 3*w^3 - 14*w^2 + 11*w + 8],\
[809, 809, w^4 - 2*w^3 - 2*w^2 + 8*w - 4],\
[809, 809, 2*w^4 - 8*w^2 - 2*w + 3],\
[809, 809, 2*w^4 - 3*w^3 - 9*w^2 + 13*w + 4],\
[821, 821, -2*w^4 + 2*w^3 + 8*w^2 - 6*w + 3],\
[823, 823, -2*w^4 + 3*w^3 + 8*w^2 - 12*w - 1],\
[829, 829, 2*w^4 - 3*w^3 - 10*w^2 + 13*w + 4],\
[839, 839, -2*w^4 + 12*w^2 - w - 10],\
[863, 863, 2*w^4 - w^3 - 9*w^2 + 5],\
[877, 877, -w^4 + w^3 + 5*w^2 - 5*w - 7],\
[881, 881, 2*w^4 - w^3 - 9*w^2 + w - 1],\
[887, 887, 3*w^4 - 3*w^3 - 15*w^2 + 11*w + 6],\
[907, 907, -3*w^4 + w^3 + 13*w^2 - w - 5],\
[919, 919, w^4 + w^3 - 3*w^2 - 5*w - 3],\
[929, 929, 2*w^4 - 3*w^3 - 10*w^2 + 9*w + 4],\
[937, 937, -2*w^4 + 10*w^2 + 3*w - 7],\
[941, 941, -w^4 + 2*w^3 + 3*w^2 - 6*w - 2],\
[961, 31, 2*w^4 + 2*w^3 - 10*w^2 - 12*w + 5],\
[961, 31, -w^4 + 5*w^2 - w - 7],\
[967, 967, -2*w^4 + w^3 + 9*w^2 - 3*w + 2],\
[991, 991, -3*w^4 + w^3 + 15*w^2 - 4*w - 5],\
[997, 997, -3*w^4 + 15*w^2 - 5],\
[997, 997, 2*w^4 - w^3 - 9*w^2 + 6*w + 2],\
[997, 997, 2*w^4 - w^3 - 11*w^2 + w + 7],\
[997, 997, 2*w^3 - 5*w - 1],\
[997, 997, 2*w^4 - 3*w^3 - 6*w^2 + 5*w + 1]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^7 - 6*x^6 - 28*x^5 + 182*x^4 + 40*x^3 - 664*x^2 + 288*x - 32
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [-1, 1, e, 3/32*e^6 - 9/16*e^5 - 11/4*e^4 + 273/16*e^3 + 31/4*e^2 - 62*e + 27/2, 3/32*e^6 - 9/16*e^5 - 11/4*e^4 + 273/16*e^3 + 31/4*e^2 - 62*e + 27/2, 3/16*e^6 - 17/16*e^5 - 11/2*e^4 + 257/8*e^3 + 119/8*e^2 - 461/4*e + 55/2, -9/32*e^6 + 13/8*e^5 + 33/4*e^4 - 787/16*e^3 - 181/8*e^2 + 709/4*e - 39, -21/32*e^6 + 61/16*e^5 + 77/4*e^4 - 1855/16*e^3 - 53*e^2 + 859/2*e - 183/2, -29/64*e^6 + 41/16*e^5 + 107/8*e^4 - 2487/32*e^3 - 617/16*e^2 + 2273/8*e - 117/2, 27/32*e^6 - 39/8*e^5 - 99/4*e^4 + 2369/16*e^3 + 543/8*e^2 - 2179/4*e + 117, -3/16*e^6 + 17/16*e^5 + 11/2*e^4 - 257/8*e^3 - 119/8*e^2 + 461/4*e - 51/2, 1/32*e^5 - 5/4*e^3 + 3/16*e^2 + 75/8*e - 7/4, -1/8*e^6 + 3/4*e^5 + 7/2*e^4 - 91/4*e^3 - 5*e^2 + 83*e - 26, 1/32*e^6 - 1/4*e^5 - 3/4*e^4 + 123/16*e^3 - 17/8*e^2 - 115/4*e + 18, -21/32*e^6 + 61/16*e^5 + 77/4*e^4 - 1855/16*e^3 - 53*e^2 + 857/2*e - 187/2, -11/32*e^6 + 63/32*e^5 + 41/4*e^4 - 957/16*e^3 - 517/16*e^2 + 1767/8*e - 161/4, 1/32*e^6 - 1/4*e^5 - 3/4*e^4 + 123/16*e^3 - 17/8*e^2 - 115/4*e + 14, 7/32*e^6 - 5/4*e^5 - 25/4*e^4 + 605/16*e^3 + 105/8*e^2 - 553/4*e + 36, 33/32*e^6 - 191/32*e^5 - 121/4*e^4 + 2903/16*e^3 + 1321/16*e^2 - 5371/8*e + 609/4, 25/32*e^6 - 73/16*e^5 - 91/4*e^4 + 2219/16*e^3 + 58*e^2 - 1021/2*e + 239/2, 55/32*e^6 - 159/16*e^5 - 201/4*e^4 + 4829/16*e^3 + 134*e^2 - 2227/2*e + 489/2, 39/32*e^6 - 7*e^5 - 143/4*e^4 + 3397/16*e^3 + 789/8*e^2 - 3105/4*e + 162, 63/32*e^6 - 91/8*e^5 - 231/4*e^4 + 5525/16*e^3 + 1267/8*e^2 - 5067/4*e + 279, 3/32*e^6 - 17/32*e^5 - 11/4*e^4 + 261/16*e^3 + 111/16*e^2 - 501/8*e + 87/4, -29/16*e^6 + 21/2*e^5 + 53*e^4 - 2551/8*e^3 - 567/4*e^2 + 2351/2*e - 256, 41/32*e^6 - 117/16*e^5 - 151/4*e^4 + 3555/16*e^3 + 215/2*e^2 - 1645/2*e + 351/2, e^6 - 91/16*e^5 - 59/2*e^4 + 345/2*e^3 + 679/8*e^2 - 2529/4*e + 273/2, 17/16*e^6 - 197/32*e^5 - 31*e^4 + 1497/8*e^3 + 1293/16*e^2 - 5547/8*e + 619/4, 5/8*e^6 - 119/32*e^5 - 18*e^4 + 113*e^3 + 659/16*e^2 - 3325/8*e + 417/4, 65/32*e^6 - 187/16*e^5 - 239/4*e^4 + 5683/16*e^3 + 669/4*e^2 - 1310*e + 573/2, 35/32*e^6 - 101/16*e^5 - 129/4*e^4 + 3073/16*e^3 + 369/4*e^2 - 712*e + 295/2, -17/16*e^6 + 197/32*e^5 + 31*e^4 - 1497/8*e^3 - 1293/16*e^2 + 5515/8*e - 595/4, 55/32*e^6 - 159/16*e^5 - 201/4*e^4 + 4829/16*e^3 + 134*e^2 - 2223/2*e + 493/2, 23/16*e^6 - 265/32*e^5 - 42*e^4 + 2015/8*e^3 + 1769/16*e^2 - 7487/8*e + 839/4, -111/32*e^6 + 639/32*e^5 + 407/4*e^4 - 9697/16*e^3 - 4461/16*e^2 + 17799/8*e - 1937/4, -5/32*e^6 + 15/16*e^5 + 17/4*e^4 - 455/16*e^3 - 13/4*e^2 + 106*e - 89/2, -93/32*e^6 + 537/32*e^5 + 341/4*e^4 - 8163/16*e^3 - 3731/16*e^2 + 15105/8*e - 1623/4, 1/16*e^6 - 1/4*e^5 - 2*e^4 + 59/8*e^3 + 33/4*e^2 - 45/2*e + 14, -39/32*e^6 + 7*e^5 + 143/4*e^4 - 3405/16*e^3 - 781/8*e^2 + 3165/4*e - 168, -11/32*e^6 + 2*e^5 + 39/4*e^4 - 969/16*e^3 - 145/8*e^2 + 889/4*e - 70, 3/16*e^6 - 17/16*e^5 - 11/2*e^4 + 257/8*e^3 + 119/8*e^2 - 457/4*e + 55/2, -83/32*e^6 + 477/32*e^5 + 305/4*e^4 - 7245/16*e^3 - 3403/16*e^2 + 13337/8*e - 1411/4, 5/8*e^6 - 115/32*e^5 - 37/2*e^4 + 109*e^3 + 895/16*e^2 - 3201/8*e + 261/4, 1/32*e^6 - 5/32*e^5 - 3/4*e^4 + 79/16*e^3 - 41/16*e^2 - 213/8*e + 91/4, 15/32*e^6 - 21/8*e^5 - 55/4*e^4 + 1269/16*e^3 + 295/8*e^2 - 1143/4*e + 77, 1/2*e^6 - 93/32*e^5 - 29/2*e^4 + 355/4*e^3 + 553/16*e^2 - 2711/8*e + 347/4, -41/16*e^6 + 473/32*e^5 + 75*e^4 - 3593/8*e^3 - 3233/16*e^2 + 13279/8*e - 1407/4, -21/16*e^6 + 121/16*e^5 + 77/2*e^4 - 1835/8*e^3 - 843/8*e^2 + 3361/4*e - 371/2, -1/16*e^6 + 3/8*e^5 + 2*e^4 - 91/8*e^3 - 21/2*e^2 + 36*e + 17, -35/16*e^6 + 203/16*e^5 + 64*e^4 - 3081/8*e^3 - 1369/8*e^2 + 5643/4*e - 645/2, 81/32*e^6 - 117/8*e^5 - 297/4*e^4 + 7107/16*e^3 + 1629/8*e^2 - 6557/4*e + 361, 11/4*e^6 - 507/32*e^5 - 161/2*e^4 + 1923/4*e^3 + 3471/16*e^2 - 14097/8*e + 1533/4, -11/4*e^6 + 509/32*e^5 + 161/2*e^4 - 1931/4*e^3 - 3481/16*e^2 + 14167/8*e - 1515/4, -17/8*e^6 + 99/8*e^5 + 62*e^4 - 1505/4*e^3 - 645/4*e^2 + 2779/2*e - 319, 65/32*e^6 - 93/8*e^5 - 239/4*e^4 + 5651/16*e^3 + 1341/8*e^2 - 5213/4*e + 277, -77/32*e^6 + 111/8*e^5 + 283/4*e^4 - 6743/16*e^3 - 1589/8*e^2 + 6205/4*e - 323, -91/32*e^6 + 263/16*e^5 + 333/4*e^4 - 7993/16*e^3 - 449/2*e^2 + 3689/2*e - 797/2, 33/16*e^6 - 191/16*e^5 - 121/2*e^4 + 2899/8*e^3 + 1329/8*e^2 - 5327/4*e + 593/2, -39/32*e^6 + 223/32*e^5 + 143/4*e^4 - 3385/16*e^3 - 1565/16*e^2 + 6215/8*e - 641/4, 1/16*e^6 - 5/16*e^5 - 2*e^4 + 75/8*e^3 + 71/8*e^2 - 117/4*e + 19/2, 25/32*e^6 - 9/2*e^5 - 91/4*e^4 + 2187/16*e^3 + 459/8*e^2 - 2015/4*e + 130, -43/32*e^6 + 123/16*e^5 + 159/4*e^4 - 3737/16*e^3 - 117*e^2 + 1725/2*e - 349/2, -37/16*e^6 + 215/16*e^5 + 135/2*e^4 - 3267/8*e^3 - 1425/8*e^2 + 6035/4*e - 657/2, -9/32*e^6 + 49/32*e^5 + 35/4*e^4 - 743/16*e^3 - 579/16*e^2 + 1369/8*e - 47/4, -73/32*e^6 + 423/32*e^5 + 267/4*e^4 - 6423/16*e^3 - 2881/16*e^2 + 11819/8*e - 1273/4, 3/8*e^6 - 33/16*e^5 - 11*e^4 + 251/4*e^3 + 225/8*e^2 - 935/4*e + 143/2, -9/32*e^6 + 53/32*e^5 + 33/4*e^4 - 807/16*e^3 - 375/16*e^2 + 1517/8*e - 107/4, 31/32*e^6 - 45/8*e^5 - 113/4*e^4 + 2733/16*e^3 + 583/8*e^2 - 2531/4*e + 157, -11/4*e^6 + 509/32*e^5 + 161/2*e^4 - 1931/4*e^3 - 3481/16*e^2 + 14151/8*e - 1539/4, 99/32*e^6 - 143/8*e^5 - 363/4*e^4 + 8697/16*e^3 + 1991/8*e^2 - 8063/4*e + 441, 31/16*e^6 - 45/4*e^5 - 113/2*e^4 + 2737/8*e^3 + 587/4*e^2 - 2535/2*e + 286, 127/32*e^6 - 367/16*e^5 - 465/4*e^4 + 11141/16*e^3 + 315*e^2 - 5115/2*e + 1105/2, -3/16*e^6 + 19/16*e^5 + 5*e^4 - 289/8*e^3 - 9/8*e^2 + 547/4*e - 117/2, -37/32*e^6 + 213/32*e^5 + 135/4*e^4 - 3227/16*e^3 - 1407/16*e^2 + 5837/8*e - 691/4, 5/32*e^6 - 15/16*e^5 - 19/4*e^4 + 455/16*e^3 + 69/4*e^2 - 100*e + 33/2, -23/8*e^6 + 265/16*e^5 + 169/2*e^4 - 2011/4*e^3 - 1897/8*e^2 + 7383/4*e - 775/2, 69/32*e^6 - 399/32*e^5 - 253/4*e^4 + 6059/16*e^3 + 2769/16*e^2 - 11147/8*e + 1297/4, -35/32*e^6 + 99/16*e^5 + 129/4*e^4 - 3009/16*e^3 - 92*e^2 + 1393/2*e - 277/2, 111/32*e^6 - 639/32*e^5 - 407/4*e^4 + 9713/16*e^3 + 4461/16*e^2 - 17991/8*e + 1969/4, -7/2*e^6 + 325/16*e^5 + 205/2*e^4 - 1235/2*e^3 - 2225/8*e^2 + 9151/4*e - 999/2, 9/8*e^6 - 101/16*e^5 - 67/2*e^4 + 765/4*e^3 + 837/8*e^2 - 2795/4*e + 255/2, -15/8*e^6 + 173/16*e^5 + 55*e^4 - 1315/4*e^3 - 1197/8*e^2 + 4875/4*e - 543/2, -5/2*e^6 + 231/16*e^5 + 73*e^4 - 877/2*e^3 - 1531/8*e^2 + 6453/4*e - 717/2, 1/8*e^6 - 27/32*e^5 - 7/2*e^4 + 26*e^3 + 87/16*e^2 - 809/8*e + 141/4, -47/16*e^6 + 271/16*e^5 + 86*e^4 - 4113/8*e^3 - 1853/8*e^2 + 7567/4*e - 853/2, 3/32*e^6 - 3/8*e^5 - 13/4*e^4 + 177/16*e^3 + 167/8*e^2 - 143/4*e - 9, 11/8*e^6 - 8*e^5 - 40*e^4 + 971/4*e^3 + 201/2*e^2 - 889*e + 218, -23/32*e^6 + 137/32*e^5 + 83/4*e^4 - 2089/16*e^3 - 783/16*e^2 + 3893/8*e - 455/4, 7/16*e^6 - 5/2*e^5 - 13*e^4 + 609/8*e^3 + 157/4*e^2 - 569/2*e + 46, 77/32*e^6 - 221/16*e^5 - 283/4*e^4 + 6711/16*e^3 + 198*e^2 - 3081/2*e + 679/2, -79/32*e^6 + 227/16*e^5 + 289/4*e^4 - 6901/16*e^3 - 387/2*e^2 + 3205/2*e - 717/2, -43/32*e^6 + 251/32*e^5 + 157/4*e^4 - 3813/16*e^3 - 1649/16*e^2 + 7003/8*e - 821/4, -129/32*e^6 + 93/4*e^5 + 473/4*e^4 - 11299/16*e^3 - 2591/8*e^2 + 10399/4*e - 568, -7/16*e^6 + 81/32*e^5 + 25/2*e^4 - 619/8*e^3 - 401/16*e^2 + 2359/8*e - 327/4, -135/32*e^6 + 195/8*e^5 + 495/4*e^4 - 11853/16*e^3 - 2715/8*e^2 + 10947/4*e - 603, e^6 - 183/32*e^5 - 59/2*e^4 + 697/4*e^3 + 1371/16*e^2 - 5237/8*e + 473/4, -3/16*e^6 + 17/16*e^5 + 11/2*e^4 - 261/8*e^3 - 119/8*e^2 + 509/4*e - 71/2, 79/32*e^6 - 457/32*e^5 - 289/4*e^4 + 6937/16*e^3 + 3119/16*e^2 - 12725/8*e + 1407/4, -9/4*e^6 + 13*e^5 + 66*e^4 - 791/2*e^3 - 181*e^2 + 1468*e - 308, 31/32*e^6 - 89/16*e^5 - 113/4*e^4 + 2709/16*e^3 + 293/4*e^2 - 635*e + 295/2, -1/32*e^5 + 1/4*e^3 + 29/16*e^2 + 93/8*e - 81/4, 5/2*e^6 - 115/8*e^5 - 147/2*e^4 + 436*e^3 + 827/4*e^2 - 3185/2*e + 341, -29/16*e^6 + 21/2*e^5 + 53*e^4 - 2551/8*e^3 - 563/4*e^2 + 2339/2*e - 264, -9/8*e^6 + 207/32*e^5 + 33*e^4 - 196*e^3 - 1467/16*e^2 + 5709/8*e - 553/4, -3/32*e^6 + 15/32*e^5 + 11/4*e^4 - 229/16*e^3 - 101/16*e^2 + 423/8*e - 97/4, 29/32*e^6 - 167/32*e^5 - 107/4*e^4 + 2539/16*e^3 + 1241/16*e^2 - 4691/8*e + 433/4, -63/32*e^6 + 183/16*e^5 + 231/4*e^4 - 5557/16*e^3 - 158*e^2 + 2545/2*e - 565/2, -37/16*e^6 + 213/16*e^5 + 68*e^4 - 3235/8*e^3 - 1519/8*e^2 + 5965/4*e - 647/2, -53/32*e^6 + 155/16*e^5 + 193/4*e^4 - 4719/16*e^3 - 499/4*e^2 + 1099*e - 513/2, -87/32*e^6 + 499/32*e^5 + 319/4*e^4 - 7561/16*e^3 - 3505/16*e^2 + 13787/8*e - 1501/4, -97/32*e^6 + 35/2*e^5 + 355/4*e^4 - 8491/16*e^3 - 1907/8*e^2 + 7751/4*e - 442, 5/8*e^6 - 57/16*e^5 - 37/2*e^4 + 431/4*e^3 + 457/8*e^2 - 1543/4*e + 99/2, -21/32*e^6 + 121/32*e^5 + 77/4*e^4 - 1835/16*e^3 - 819/16*e^2 + 3337/8*e - 407/4, 57/16*e^6 - 41/2*e^5 - 209/2*e^4 + 4983/8*e^3 + 1143/4*e^2 - 4611/2*e + 504, 127/32*e^6 - 737/32*e^5 - 465/4*e^4 + 11193/16*e^3 + 5047/16*e^2 - 20557/8*e + 2207/4, 7/32*e^6 - 43/32*e^5 - 25/4*e^4 + 649/16*e^3 + 233/16*e^2 - 1179/8*e + 101/4, 95/32*e^6 - 273/16*e^5 - 349/4*e^4 + 8293/16*e^3 + 969/4*e^2 - 1913*e + 819/2, 91/32*e^6 - 261/16*e^5 - 335/4*e^4 + 7929/16*e^3 + 949/4*e^2 - 1821*e + 795/2, 17/8*e^6 - 49/4*e^5 - 125/2*e^4 + 1489/4*e^3 + 174*e^2 - 1376*e + 312, 25/16*e^6 - 287/32*e^5 - 46*e^4 + 2177/8*e^3 + 2079/16*e^2 - 7953/8*e + 921/4, -19/16*e^6 + 55/8*e^5 + 35*e^4 - 1673/8*e^3 - 101*e^2 + 777*e - 169, -17/16*e^6 + 49/8*e^5 + 31*e^4 - 1491/8*e^3 - 80*e^2 + 695*e - 155, -21/32*e^6 + 59/16*e^5 + 77/4*e^4 - 1791/16*e^3 - 211/4*e^2 + 415*e - 189/2, -107/32*e^6 + 39/2*e^5 + 391/4*e^4 - 9489/16*e^3 - 2081/8*e^2 + 8777/4*e - 482, 41/32*e^6 - 117/16*e^5 - 151/4*e^4 + 3539/16*e^3 + 217/2*e^2 - 1595/2*e + 307/2, 1/8*e^6 - 21/32*e^5 - 7/2*e^4 + 20*e^3 + 89/16*e^2 - 655/8*e + 35/4, 93/32*e^6 - 67/4*e^5 - 341/4*e^4 + 8143/16*e^3 + 1859/8*e^2 - 7519/4*e + 412, -79/32*e^6 + 227/16*e^5 + 291/4*e^4 - 6901/16*e^3 - 415/2*e^2 + 3201/2*e - 657/2, 53/16*e^6 - 153/8*e^5 - 97*e^4 + 4647/8*e^3 + 262*e^2 - 2143*e + 463, -75/32*e^6 + 425/32*e^5 + 277/4*e^4 - 6453/16*e^3 - 3223/16*e^2 + 11901/8*e - 1239/4, 65/32*e^6 - 187/16*e^5 - 237/4*e^4 + 5667/16*e^3 + 617/4*e^2 - 1290*e + 597/2, -25/32*e^6 + 73/16*e^5 + 91/4*e^4 - 2227/16*e^3 - 57*e^2 + 1049/2*e - 247/2, -2*e^6 + 369/32*e^5 + 117/2*e^4 - 1399/4*e^3 - 2477/16*e^2 + 10227/8*e - 1191/4, 27/16*e^6 - 157/16*e^5 - 49*e^4 + 2381/8*e^3 + 971/8*e^2 - 4385/4*e + 555/2, 93/32*e^6 - 67/4*e^5 - 341/4*e^4 + 8135/16*e^3 + 1883/8*e^2 - 7479/4*e + 396, -1/16*e^6 + 1/8*e^5 + 5/2*e^4 - 27/8*e^3 - 24*e^2 + 13*e + 39, 3/32*e^6 - 1/2*e^5 - 9/4*e^4 + 233/16*e^3 - 55/8*e^2 - 181/4*e + 54, 21/32*e^6 - 15/4*e^5 - 77/4*e^4 + 1823/16*e^3 + 411/8*e^2 - 1687/4*e + 112, -3*e^6 + 277/16*e^5 + 88*e^4 - 1051/2*e^3 - 1929/8*e^2 + 7703/4*e - 839/2, -5/32*e^6 + 13/16*e^5 + 21/4*e^4 - 399/16*e^3 - 30*e^2 + 189/2*e - 15/2, -37/16*e^6 + 213/16*e^5 + 68*e^4 - 3243/8*e^3 - 1519/8*e^2 + 6069/4*e - 615/2, 151/32*e^6 - 869/32*e^5 - 553/4*e^4 + 13185/16*e^3 + 6011/16*e^2 - 24153/8*e + 2635/4, 17/4*e^6 - 49/2*e^5 - 249/2*e^4 + 1489/2*e^3 + 337*e^2 - 2752*e + 622, -19/4*e^6 + 439/16*e^5 + 279/2*e^4 - 834*e^3 - 3099/8*e^2 + 12317/4*e - 1309/2, -25/8*e^6 + 287/16*e^5 + 183/2*e^4 - 2179/4*e^3 - 1959/8*e^2 + 8041/4*e - 925/2, -45/16*e^6 + 65/4*e^5 + 165/2*e^4 - 3955/8*e^3 - 905/4*e^2 + 3681/2*e - 402, -163/32*e^6 + 471/16*e^5 + 597/4*e^4 - 14305/16*e^3 - 811/2*e^2 + 6589/2*e - 1453/2, -131/32*e^6 + 763/32*e^5 + 479/4*e^4 - 11597/16*e^3 - 5121/16*e^2 + 21395/8*e - 2365/4, -19/8*e^6 + 55/4*e^5 + 70*e^4 - 1669/4*e^3 - 201*e^2 + 1522*e - 318, 53/16*e^6 - 307/16*e^5 - 97*e^4 + 4659/8*e^3 + 2093/8*e^2 - 8551/4*e + 985/2, 3/2*e^6 - 69/8*e^5 - 44*e^4 + 262*e^3 + 489/4*e^2 - 1943/2*e + 177, -111/32*e^6 + 161/8*e^5 + 405/4*e^4 - 9781/16*e^3 - 2135/8*e^2 + 9019/4*e - 489, -13/2*e^6 + 1203/32*e^5 + 190*e^4 - 4567/4*e^3 - 8087/16*e^2 + 33673/8*e - 3709/4, -75/32*e^6 + 215/16*e^5 + 275/4*e^4 - 6521/16*e^3 - 377/2*e^2 + 2977/2*e - 641/2, 17/32*e^6 - 3*e^5 - 63/4*e^4 + 1475/16*e^3 + 379/8*e^2 - 1447/4*e + 54, -69/32*e^6 + 199/16*e^5 + 253/4*e^4 - 6039/16*e^3 - 697/4*e^2 + 1379*e - 601/2, -37/16*e^6 + 209/16*e^5 + 137/2*e^4 - 3171/8*e^3 - 1627/8*e^2 + 5809/4*e - 571/2, -53/16*e^6 + 305/16*e^5 + 97*e^4 - 4631/8*e^3 - 2083/8*e^2 + 8505/4*e - 955/2, 105/32*e^6 - 605/32*e^5 - 385/4*e^4 + 9191/16*e^3 + 4239/16*e^2 - 16925/8*e + 1747/4, 65/32*e^6 - 191/16*e^5 - 237/4*e^4 + 5803/16*e^3 + 623/4*e^2 - 1335*e + 545/2, -21/32*e^6 + 15/4*e^5 + 77/4*e^4 - 1823/16*e^3 - 419/8*e^2 + 1699/4*e - 88, 57/16*e^6 - 41/2*e^5 - 209/2*e^4 + 4979/8*e^3 + 1143/4*e^2 - 4567/2*e + 482, 29/32*e^6 - 83/16*e^5 - 105/4*e^4 + 2535/16*e^3 + 247/4*e^2 - 607*e + 345/2, 143/32*e^6 - 411/16*e^5 - 525/4*e^4 + 12485/16*e^3 + 725/2*e^2 - 5757/2*e + 1305/2, 101/32*e^6 - 291/16*e^5 - 371/4*e^4 + 8847/16*e^3 + 1027/4*e^2 - 2045*e + 889/2, 151/32*e^6 - 219/8*e^5 - 553/4*e^4 + 13317/16*e^3 + 3003/8*e^2 - 12315/4*e + 667]
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^4 - w^3 - 5*w^2 + 3*w + 3])] = 1
AL_eigenvalues[ZF.ideal([9, 3, -w^4 + 5*w^2 - 3])] = -1

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