/*
  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, -3, -6, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([17, 17, w^4 - w^3 - 4*w^2 + w - 1])

primes_array = [
[3, 3, w^4 - w^3 - 4*w^2 + 1],\
[7, 7, w^4 - w^3 - 5*w^2 + w + 3],\
[11, 11, -w^4 + 5*w^2 + 3*w + 1],\
[17, 17, w^4 - w^3 - 4*w^2 + w - 1],\
[19, 19, w^4 - 6*w^2 - 2*w + 3],\
[19, 19, -w^2 + w + 2],\
[27, 3, -w^3 + w^2 + 3*w - 1],\
[29, 29, w^4 - w^3 - 5*w^2 + 2*w + 4],\
[29, 29, w^3 - w^2 - 5*w + 1],\
[32, 2, 2],\
[37, 37, w^4 - w^3 - 6*w^2 + 2*w + 6],\
[41, 41, w^4 - w^3 - 4*w^2 - 1],\
[47, 47, w^4 - 2*w^3 - 4*w^2 + 5*w + 2],\
[67, 67, w^3 - 2*w^2 - 3*w],\
[83, 83, -w^3 + 2*w^2 + 3*w - 5],\
[97, 97, -w^4 + 2*w^3 + 3*w^2 - 6*w + 1],\
[107, 107, w^3 - 2*w^2 - 4*w + 1],\
[109, 109, -w^4 + 6*w^2 + 3*w - 1],\
[121, 11, -w^4 + 2*w^3 + 5*w^2 - 6*w - 4],\
[121, 11, -2*w^4 + w^3 + 11*w^2 - 5],\
[127, 127, -2*w^4 + w^3 + 10*w^2 + w - 5],\
[127, 127, 3*w^4 - 2*w^3 - 15*w^2 - w + 7],\
[131, 131, 2*w^4 - 2*w^3 - 8*w^2 + w],\
[131, 131, 2*w^4 - w^3 - 10*w^2 - w + 2],\
[137, 137, -w^4 + 6*w^2 + 4*w - 4],\
[149, 149, w^4 - 3*w^3 - w^2 + 7*w - 3],\
[151, 151, -2*w^4 + w^3 + 10*w^2 + 3*w - 1],\
[157, 157, w^4 - w^3 - 5*w^2 + 3*w + 3],\
[157, 157, -w^4 + w^3 + 6*w^2 - 2*w - 5],\
[163, 163, -w^4 + 2*w^3 + 3*w^2 - 4*w + 2],\
[163, 163, w^4 - w^3 - 5*w^2 + 3*w + 4],\
[167, 167, 3*w^4 - 2*w^3 - 15*w^2 + w + 6],\
[167, 167, -2*w^4 + 2*w^3 + 9*w^2 - 3*w - 4],\
[169, 13, w^4 + w^3 - 6*w^2 - 8*w + 2],\
[173, 173, 2*w^4 - 2*w^3 - 9*w^2 + 4*w + 4],\
[179, 179, w^4 - 6*w^2 - w + 2],\
[191, 191, w^2 - 5],\
[193, 193, -w^4 + 5*w^2 + 5*w - 2],\
[193, 193, w^3 - 6*w],\
[193, 193, 2*w^4 - 2*w^3 - 8*w^2 + w + 3],\
[199, 199, -2*w^4 + w^3 + 10*w^2 + 3*w - 8],\
[199, 199, w^4 - w^3 - 4*w^2 - 3],\
[199, 199, 2*w^4 - w^3 - 10*w^2 - 4*w],\
[211, 211, 2*w^3 - 2*w^2 - 9*w + 1],\
[211, 211, -2*w^4 + w^3 + 11*w^2 + 2*w - 4],\
[223, 223, -w^4 + w^3 + 5*w^2 - w - 6],\
[223, 223, 2*w^4 - 2*w^3 - 10*w^2 + w + 2],\
[223, 223, -2*w^4 + 2*w^3 + 9*w^2 - 2*w - 5],\
[233, 233, -2*w^4 + w^3 + 10*w^2 + 3*w - 2],\
[233, 233, -w^4 + 2*w^3 + 4*w^2 - 4*w - 3],\
[239, 239, -w^4 - w^3 + 7*w^2 + 5*w - 6],\
[239, 239, -2*w^4 + w^3 + 9*w^2 + 3*w - 1],\
[241, 241, -2*w^4 + 2*w^3 + 10*w^2 - 2*w - 7],\
[241, 241, w^4 + w^3 - 6*w^2 - 7*w + 3],\
[257, 257, w^4 - w^3 - 4*w^2 + 2*w - 2],\
[277, 277, -2*w^3 + 2*w^2 + 8*w - 3],\
[283, 283, -w^4 + 2*w^3 + 5*w^2 - 7*w - 4],\
[283, 283, -2*w^3 + w^2 + 9*w],\
[293, 293, -2*w^4 + w^3 + 11*w^2 + w - 4],\
[307, 307, -2*w^4 + 11*w^2 + 5*w - 4],\
[307, 307, 2*w^4 - w^3 - 9*w^2 - 3*w + 4],\
[313, 313, -w^4 + 4*w^2 + 7*w + 1],\
[313, 313, -3*w^4 + 2*w^3 + 15*w^2 - 7],\
[317, 317, w^2 - 2*w - 6],\
[317, 317, -2*w^4 + 3*w^3 + 8*w^2 - 8*w - 3],\
[331, 331, 2*w^4 - w^3 - 11*w^2 - 3*w + 5],\
[331, 331, -w^2 + 3*w + 2],\
[337, 337, -w^4 - w^3 + 7*w^2 + 8*w - 5],\
[347, 347, 2*w^4 - 2*w^3 - 11*w^2 + 2*w + 7],\
[353, 353, -w^4 - 2*w^3 + 7*w^2 + 12*w - 3],\
[353, 353, -2*w^4 + 12*w^2 + 4*w - 7],\
[353, 353, -4*w^4 + 3*w^3 + 20*w^2 - w - 11],\
[361, 19, -2*w^3 + 7*w],\
[373, 373, 3*w^4 - w^3 - 16*w^2 - 4*w + 8],\
[389, 389, w^4 - w^3 - 3*w^2 - 2],\
[397, 397, 3*w^4 - 18*w^2 - 7*w + 11],\
[409, 409, w^4 + w^3 - 7*w^2 - 5*w + 3],\
[419, 419, 2*w^3 - 2*w^2 - 10*w - 1],\
[431, 431, 2*w^4 - 2*w^3 - 11*w^2 + 3*w + 7],\
[433, 433, -w^4 + 3*w^3 + 2*w^2 - 8*w - 3],\
[433, 433, -w^4 + 2*w^3 + 3*w^2 - 5*w - 4],\
[443, 443, 2*w^4 - 2*w^3 - 11*w^2 + 3*w + 9],\
[443, 443, -w^4 - w^3 + 6*w^2 + 6*w - 5],\
[449, 449, w^4 - w^3 - 4*w^2 - w - 2],\
[457, 457, -3*w^4 + w^3 + 15*w^2 + 3*w - 5],\
[463, 463, -w^3 + w^2 + 2*w - 4],\
[479, 479, -w^4 + w^3 + 3*w^2 + 3*w + 2],\
[479, 479, w^4 - 8*w^2 - w + 10],\
[491, 491, w^4 - 5*w^2 - 6*w],\
[491, 491, -3*w^4 + 2*w^3 + 14*w^2 - w - 4],\
[521, 521, -w^4 - w^3 + 5*w^2 + 6*w - 2],\
[523, 523, -2*w^4 + w^3 + 9*w^2 + w - 4],\
[523, 523, w^2 + w - 4],\
[529, 23, -2*w^4 + 2*w^3 + 9*w^2 - 2],\
[541, 541, -2*w^4 - w^3 + 13*w^2 + 10*w - 6],\
[541, 541, 2*w^4 - 2*w^3 - 10*w^2 + 5*w + 4],\
[547, 547, -w^4 - 2*w^3 + 8*w^2 + 11*w - 6],\
[557, 557, w^4 - 5*w^2 - 2*w - 2],\
[569, 569, w^3 - 7*w + 2],\
[571, 571, -2*w^4 + w^3 + 9*w^2 + 2*w - 2],\
[571, 571, -2*w^4 + 2*w^3 + 8*w^2 - w + 3],\
[577, 577, -w^4 + w^3 + 5*w^2 - 4*w - 6],\
[587, 587, -w^4 - w^3 + 9*w^2 + 6*w - 8],\
[587, 587, -w^4 - w^3 + 5*w^2 + 8*w],\
[587, 587, 2*w^4 - w^3 - 11*w^2 - 3*w + 2],\
[593, 593, -w^4 + 2*w^3 + 4*w^2 - 6*w - 7],\
[593, 593, w^2 - 3*w - 3],\
[599, 599, -w^4 + 7*w^2 + 2*w - 3],\
[599, 599, -2*w^4 + w^3 + 10*w^2 + 4*w - 2],\
[601, 601, w^4 - 3*w^3 - 2*w^2 + 11*w - 3],\
[601, 601, -2*w^4 + w^3 + 9*w^2 + 4*w + 2],\
[607, 607, -2*w^4 + w^3 + 12*w^2 - w - 5],\
[607, 607, -w^3 + w^2 + 6*w - 2],\
[613, 613, -2*w^4 + w^3 + 9*w^2 + 2*w - 3],\
[619, 619, -2*w^4 + 2*w^3 + 9*w^2 - 3*w - 5],\
[619, 619, -4*w^4 + 4*w^3 + 18*w^2 - 4*w - 7],\
[631, 631, w^4 - 8*w^2 - 2*w + 5],\
[641, 641, -w^4 + 7*w^2 + 3*w - 10],\
[643, 643, -3*w^3 + 3*w^2 + 13*w - 2],\
[653, 653, -w^3 + 3*w^2 + 6*w - 4],\
[653, 653, 2*w^4 - 3*w^3 - 10*w^2 + 7*w + 5],\
[673, 673, w^4 - 6*w^2 - 4*w + 8],\
[673, 673, w^4 - 8*w^2 - 2*w + 11],\
[673, 673, 2*w^4 - 2*w^3 - 11*w^2 + 3*w + 6],\
[701, 701, -w^4 + 2*w^3 + 5*w^2 - 5*w - 5],\
[701, 701, -w^4 + 6*w^2 + 5*w - 3],\
[733, 733, w^4 - 3*w^3 - 2*w^2 + 6*w - 1],\
[733, 733, -3*w^4 + 2*w^3 + 14*w^2 - 3],\
[743, 743, -w^4 + 2*w^3 + 5*w^2 - 4*w - 4],\
[743, 743, -3*w^4 + 2*w^3 + 14*w^2 + 2*w - 7],\
[751, 751, 3*w^4 - 2*w^3 - 16*w^2 + 2*w + 11],\
[751, 751, w^4 - w^3 - 5*w^2 + 2*w + 7],\
[757, 757, -2*w^4 + 12*w^2 + 8*w - 5],\
[761, 761, 2*w^4 - 4*w^3 - 7*w^2 + 9*w - 1],\
[773, 773, -3*w^4 + 2*w^3 + 14*w^2 - 2*w - 4],\
[787, 787, -2*w^4 + 4*w^3 + 7*w^2 - 9*w - 1],\
[811, 811, 2*w^3 - 3*w^2 - 8*w + 4],\
[821, 821, -2*w^4 + 2*w^3 + 11*w^2 - 2*w - 10],\
[823, 823, -2*w^4 - w^3 + 14*w^2 + 8*w - 8],\
[823, 823, 2*w^3 - 2*w^2 - 7*w + 3],\
[827, 827, -2*w^3 + w^2 + 11*w + 1],\
[827, 827, w^3 - 4*w - 7],\
[829, 829, w^4 - 4*w^2 - 6*w - 5],\
[839, 839, -4*w^4 + 4*w^3 + 18*w^2 - 5*w - 6],\
[839, 839, -w^4 - w^3 + 8*w^2 + 3*w - 5],\
[857, 857, w^3 - 7*w - 4],\
[859, 859, -w^4 - w^3 + 6*w^2 + 7*w - 4],\
[863, 863, 3*w^4 - w^3 - 15*w^2 - 6*w + 5],\
[881, 881, -w^4 + 2*w^3 + 3*w^2 - 4*w + 4],\
[907, 907, 3*w^4 - 4*w^3 - 12*w^2 + 6*w],\
[911, 911, 2*w^4 - w^3 - 11*w^2 - w + 1],\
[911, 911, w^4 - 2*w^3 - 2*w^2 + 5*w - 6],\
[919, 919, -w^4 + 8*w^2 + w - 7],\
[919, 919, 3*w^4 - 2*w^3 - 17*w^2 + w + 11],\
[929, 929, 3*w^4 - 2*w^3 - 14*w^2 - w + 3],\
[929, 929, 3*w^4 - 3*w^3 - 16*w^2 + 4*w + 10],\
[941, 941, -3*w^4 + 3*w^3 + 14*w^2 - 2*w - 5],\
[941, 941, -3*w^4 + 3*w^3 + 15*w^2 - 2*w - 8],\
[941, 941, w^4 - 8*w^2 - 2*w + 10],\
[947, 947, -2*w^4 + 2*w^3 + 8*w^2 - 3*w + 3],\
[967, 967, w^4 - 3*w^3 - 3*w^2 + 8*w - 2],\
[967, 967, -3*w^4 + 4*w^3 + 12*w^2 - 7*w - 4],\
[967, 967, 4*w^4 - 2*w^3 - 21*w^2 - 3*w + 11],\
[971, 971, w^4 - w^3 - 4*w^2 - w - 3],\
[991, 991, 2*w^4 + w^3 - 13*w^2 - 8*w + 5],\
[997, 997, w^4 + 2*w^3 - 8*w^2 - 11*w + 2]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^8 + 3*x^7 - 12*x^6 - 26*x^5 + 62*x^4 + 53*x^3 - 125*x^2 + 12*x + 28
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 1/2*e^7 + 2*e^6 - 3*e^5 - 14*e^4 + 9*e^3 + 55/2*e^2 - 16*e - 7, 1/2*e^7 + 2*e^6 - 4*e^5 - 17*e^4 + 13*e^3 + 77/2*e^2 - 19*e - 14, -1, -3/2*e^7 - 6*e^6 + 9*e^5 + 43*e^4 - 23*e^3 - 167/2*e^2 + 36*e + 19, 3/2*e^7 + 7*e^6 - 7*e^5 - 52*e^4 + 12*e^3 + 211/2*e^2 - 26*e - 28, -e^6 - e^5 + 10*e^4 + 2*e^3 - 24*e^2 + 4*e + 2, -5/2*e^7 - 11*e^6 + 13*e^5 + 81*e^4 - 26*e^3 - 325/2*e^2 + 44*e + 42, -1/2*e^7 - 2*e^6 + 2*e^5 + 12*e^4 - e^3 - 41/2*e^2 - 3*e + 8, -e^7 - 5*e^6 + 5*e^5 + 40*e^4 - 11*e^3 - 87*e^2 + 25*e + 23, -3/2*e^7 - 7*e^6 + 8*e^5 + 54*e^4 - 21*e^3 - 233/2*e^2 + 45*e + 36, 2*e^7 + 10*e^6 - 9*e^5 - 77*e^4 + 16*e^3 + 159*e^2 - 40*e - 35, -2*e^7 - 9*e^6 + 9*e^5 + 63*e^4 - 17*e^3 - 121*e^2 + 40*e + 21, -2*e^7 - 7*e^6 + 15*e^5 + 52*e^4 - 45*e^3 - 105*e^2 + 59*e + 30, 3/2*e^7 + 7*e^6 - 6*e^5 - 49*e^4 + 9*e^3 + 195/2*e^2 - 23*e - 30, -3/2*e^7 - 6*e^6 + 8*e^5 + 41*e^4 - 18*e^3 - 165/2*e^2 + 30*e + 34, 4*e^7 + 18*e^6 - 19*e^5 - 131*e^4 + 32*e^3 + 265*e^2 - 57*e - 78, 3*e^7 + 13*e^6 - 15*e^5 - 95*e^4 + 23*e^3 + 191*e^2 - 37*e - 57, 3*e^7 + 11*e^6 - 19*e^5 - 76*e^4 + 46*e^3 + 140*e^2 - 55*e - 36, -3/2*e^7 - 8*e^6 + e^5 + 50*e^4 + 20*e^3 - 175/2*e^2 - 17*e + 22, 6*e^7 + 25*e^6 - 32*e^5 - 178*e^4 + 65*e^3 + 352*e^2 - 95*e - 105, 1/2*e^7 + 4*e^6 - e^5 - 35*e^4 + 4*e^3 + 161/2*e^2 - 30*e - 17, 7*e^7 + 32*e^6 - 36*e^5 - 238*e^4 + 87*e^3 + 488*e^2 - 176*e - 130, -3*e^7 - 15*e^6 + 14*e^5 + 114*e^4 - 37*e^3 - 239*e^2 + 96*e + 60, e^7 + 5*e^6 - 3*e^5 - 35*e^4 + e^3 + 71*e^2 - 10*e - 14, -3/2*e^7 - 7*e^6 + 7*e^5 + 53*e^4 - 9*e^3 - 225/2*e^2 + 7*e + 36, 1/2*e^7 + 3*e^6 + e^5 - 19*e^4 - 17*e^3 + 69/2*e^2 + 24*e - 20, -2*e^7 - 9*e^6 + 9*e^5 + 64*e^4 - 10*e^3 - 118*e^2 + 16*e + 25, 5*e^7 + 24*e^6 - 21*e^5 - 174*e^4 + 32*e^3 + 343*e^2 - 76*e - 84, 1/2*e^7 + e^6 - 5*e^5 - 7*e^4 + 18*e^3 + 43/2*e^2 - 23*e - 19, -11/2*e^7 - 26*e^6 + 26*e^5 + 196*e^4 - 50*e^3 - 829/2*e^2 + 109*e + 128, 1/2*e^7 + 2*e^6 - 3*e^5 - 14*e^4 + 9*e^3 + 49/2*e^2 - 22*e - 2, 1/2*e^7 + 2*e^6 - 4*e^5 - 19*e^4 + 8*e^3 + 97/2*e^2 - 6*e - 18, 3/2*e^7 + 6*e^6 - 3*e^5 - 27*e^4 - 11*e^3 + 41/2*e^2 + 18*e + 8, 7/2*e^7 + 16*e^6 - 16*e^5 - 115*e^4 + 29*e^3 + 463/2*e^2 - 62*e - 69, 2*e^7 + 9*e^6 - 9*e^5 - 65*e^4 + 9*e^3 + 128*e^2 - 9*e - 44, e^6 - e^5 - 14*e^4 + 13*e^3 + 39*e^2 - 39*e - 14, 1/2*e^7 - e^6 - 9*e^5 + 10*e^4 + 33*e^3 - 55/2*e^2 - 20*e - 3, -3*e^7 - 14*e^6 + 17*e^5 + 112*e^4 - 42*e^3 - 240*e^2 + 86*e + 48, e^7 + 6*e^6 - 5*e^5 - 50*e^4 + 23*e^3 + 111*e^2 - 69*e - 24, 5/2*e^7 + 13*e^6 - 10*e^5 - 100*e^4 + 19*e^3 + 443/2*e^2 - 63*e - 78, e^6 + e^5 - 12*e^4 - 5*e^3 + 36*e^2 - 5*e - 20, -e^7 - 3*e^6 + 9*e^5 + 26*e^4 - 26*e^3 - 69*e^2 + 28*e + 32, 5*e^7 + 20*e^6 - 30*e^5 - 148*e^4 + 65*e^3 + 295*e^2 - 97*e - 65, e^7 + 7*e^6 - 51*e^4 - 6*e^3 + 104*e^2 - 21*e - 34, -5/2*e^7 - 12*e^6 + 11*e^5 + 88*e^4 - 24*e^3 - 365/2*e^2 + 63*e + 47, -13/2*e^7 - 30*e^6 + 33*e^5 + 228*e^4 - 68*e^3 - 955/2*e^2 + 135*e + 136, 1/2*e^7 + 3*e^6 + e^5 - 17*e^4 - 14*e^3 + 35/2*e^2 + 8*e + 14, -3/2*e^7 - 7*e^6 + 5*e^5 + 45*e^4 - 9*e^3 - 173/2*e^2 + 41*e + 28, 3*e^7 + 11*e^6 - 25*e^5 - 94*e^4 + 77*e^3 + 214*e^2 - 107*e - 67, 5/2*e^7 + 13*e^6 - 9*e^5 - 96*e^4 + 12*e^3 + 397/2*e^2 - 39*e - 63, -15/2*e^7 - 31*e^6 + 42*e^5 + 225*e^4 - 91*e^3 - 897/2*e^2 + 142*e + 114, -1/2*e^7 + 4*e^5 - 8*e^4 - 3*e^3 + 65/2*e^2 - 19*e - 4, e^6 + 3*e^5 - 6*e^4 - 15*e^3 + 9*e^2 + 7*e + 3, 11/2*e^7 + 24*e^6 - 29*e^5 - 178*e^4 + 62*e^3 + 745/2*e^2 - 115*e - 115, 3*e^7 + 17*e^6 - 8*e^5 - 124*e^4 + 7*e^3 + 243*e^2 - 59*e - 53, -4*e^7 - 19*e^6 + 16*e^5 + 135*e^4 - 21*e^3 - 269*e^2 + 48*e + 88, 2*e^7 + 8*e^6 - 7*e^5 - 44*e^4 + 2*e^3 + 54*e^2 - 3*e + 14, -7/2*e^7 - 14*e^6 + 26*e^5 + 114*e^4 - 80*e^3 - 495/2*e^2 + 119*e + 74, -1/2*e^7 - 4*e^6 - e^5 + 29*e^4 + 7*e^3 - 109/2*e^2 + 12*e - 5, -5*e^7 - 22*e^6 + 31*e^5 + 173*e^4 - 89*e^3 - 368*e^2 + 165*e + 97, -4*e^7 - 17*e^6 + 17*e^5 + 114*e^4 - 12*e^3 - 211*e^2 + 7*e + 62, -9*e^7 - 40*e^6 + 46*e^5 + 295*e^4 - 93*e^3 - 602*e^2 + 165*e + 174, -1/2*e^7 - 4*e^6 + 32*e^4 + e^3 - 145/2*e^2 + 20*e + 31, -e^7 - 6*e^6 + 4*e^5 + 53*e^4 - 5*e^3 - 133*e^2 + 18*e + 52, -5*e^7 - 19*e^6 + 35*e^5 + 147*e^4 - 93*e^3 - 313*e^2 + 120*e + 104, e^7 + e^6 - 11*e^5 - 2*e^4 + 36*e^3 - 3*e^2 - 24*e - 24, e^7 + 2*e^6 - 14*e^5 - 22*e^4 + 59*e^3 + 61*e^2 - 67*e - 34, e^7 + 4*e^6 - 5*e^5 - 26*e^4 + 7*e^3 + 42*e^2 + 5*e - 12, -5/2*e^7 - 11*e^6 + 16*e^5 + 91*e^4 - 41*e^3 - 417/2*e^2 + 73*e + 80, e^6 - 17*e^4 - 7*e^3 + 53*e^2 + 13*e - 18, -3*e^7 - 12*e^6 + 13*e^5 + 76*e^4 - 9*e^3 - 125*e^2 + 11*e + 9, -5/2*e^7 - 14*e^6 + 2*e^5 + 94*e^4 + 33*e^3 - 349/2*e^2 - 24*e + 44, 11/2*e^7 + 27*e^6 - 22*e^5 - 193*e^4 + 44*e^3 + 765/2*e^2 - 121*e - 105, -e^7 - 4*e^6 + 7*e^5 + 32*e^4 - 16*e^3 - 67*e^2 + 7*e + 22, -15/2*e^7 - 35*e^6 + 34*e^5 + 253*e^4 - 65*e^3 - 1005/2*e^2 + 139*e + 131, 5*e^7 + 24*e^6 - 25*e^5 - 187*e^4 + 53*e^3 + 402*e^2 - 114*e - 109, 15/2*e^7 + 31*e^6 - 39*e^5 - 214*e^4 + 78*e^3 + 793/2*e^2 - 120*e - 78, -21/2*e^7 - 46*e^6 + 52*e^5 + 329*e^4 - 99*e^3 - 1281/2*e^2 + 173*e + 147, -15/2*e^7 - 33*e^6 + 44*e^5 + 257*e^4 - 109*e^3 - 1107/2*e^2 + 193*e + 170, -3/2*e^7 - 5*e^6 + 10*e^5 + 32*e^4 - 27*e^3 - 103/2*e^2 + 41*e + 9, -3/2*e^7 - 6*e^6 + 15*e^5 + 57*e^4 - 60*e^3 - 267/2*e^2 + 95*e + 41, 5*e^7 + 23*e^6 - 25*e^5 - 166*e^4 + 72*e^3 + 334*e^2 - 165*e - 78, -e^7 - 7*e^6 + 6*e^5 + 64*e^4 - 37*e^3 - 150*e^2 + 115*e + 30, -2*e^7 - 12*e^6 - e^5 + 73*e^4 + 23*e^3 - 121*e^2 + 8*e + 26, 4*e^7 + 17*e^6 - 30*e^5 - 145*e^4 + 95*e^3 + 327*e^2 - 154*e - 104, 12*e^7 + 54*e^6 - 58*e^5 - 392*e^4 + 112*e^3 + 784*e^2 - 216*e - 200, 2*e^7 + 9*e^6 - 6*e^5 - 60*e^4 - 16*e^3 + 108*e^2 + 31*e - 41, 3*e^7 + 13*e^6 - 19*e^5 - 102*e^4 + 56*e^3 + 216*e^2 - 99*e - 40, -15/2*e^7 - 37*e^6 + 34*e^5 + 280*e^4 - 73*e^3 - 1169/2*e^2 + 178*e + 150, -7/2*e^7 - 12*e^6 + 28*e^5 + 93*e^4 - 88*e^3 - 403/2*e^2 + 116*e + 67, 5/2*e^7 + 13*e^6 - 11*e^5 - 102*e^4 + 28*e^3 + 453/2*e^2 - 92*e - 71, 2*e^7 + 9*e^6 - 15*e^5 - 83*e^4 + 43*e^3 + 208*e^2 - 74*e - 89, 6*e^7 + 26*e^6 - 33*e^5 - 191*e^4 + 81*e^3 + 383*e^2 - 136*e - 92, 9/2*e^7 + 23*e^6 - 25*e^5 - 192*e^4 + 71*e^3 + 867/2*e^2 - 170*e - 120, 13/2*e^7 + 27*e^6 - 36*e^5 - 194*e^4 + 85*e^3 + 779/2*e^2 - 152*e - 100, -e^7 - e^6 + 15*e^5 + 16*e^4 - 53*e^3 - 57*e^2 + 55*e + 30, -1/2*e^7 + 10*e^5 + 5*e^4 - 45*e^3 - 33/2*e^2 + 49*e - 4, -7/2*e^7 - 16*e^6 + 13*e^5 + 106*e^4 - 16*e^3 - 389/2*e^2 + 56*e + 36, -5/2*e^7 - 10*e^6 + 14*e^5 + 70*e^4 - 27*e^3 - 247/2*e^2 + 38*e + 2, 1/2*e^7 + 3*e^6 - 6*e^5 - 41*e^4 + 15*e^3 + 235/2*e^2 - 26*e - 31, 11/2*e^7 + 26*e^6 - 28*e^5 - 202*e^4 + 64*e^3 + 899/2*e^2 - 129*e - 163, 3*e^7 + 14*e^6 - 18*e^5 - 117*e^4 + 38*e^3 + 264*e^2 - 55*e - 91, -9/2*e^7 - 23*e^6 + 16*e^5 + 168*e^4 - 18*e^3 - 669/2*e^2 + 78*e + 66, -7/2*e^7 - 21*e^6 + 12*e^5 + 171*e^4 - 20*e^3 - 745/2*e^2 + 108*e + 70, 5/2*e^7 + 12*e^6 - 9*e^5 - 81*e^4 + 9*e^3 + 281/2*e^2 - 28*e - 32, -e^7 - e^6 + 16*e^5 + 17*e^4 - 58*e^3 - 47*e^2 + 50*e + 12, -2*e^7 - 6*e^6 + 21*e^5 + 55*e^4 - 72*e^3 - 118*e^2 + 91*e + 18, 21/2*e^7 + 48*e^6 - 52*e^5 - 351*e^4 + 119*e^3 + 1411/2*e^2 - 238*e - 193, 6*e^7 + 31*e^6 - 19*e^5 - 229*e^4 - 4*e^3 + 472*e^2 - 41*e - 136, -17/2*e^7 - 39*e^6 + 40*e^5 + 281*e^4 - 91*e^3 - 1131/2*e^2 + 213*e + 138, -11/2*e^7 - 28*e^6 + 16*e^5 + 197*e^4 + 5*e^3 - 773/2*e^2 + 30*e + 116, 9*e^7 + 37*e^6 - 53*e^5 - 273*e^4 + 126*e^3 + 551*e^2 - 199*e - 154, e^7 + 6*e^6 - 3*e^5 - 47*e^4 + 12*e^3 + 109*e^2 - 63*e - 23, -10*e^7 - 46*e^6 + 48*e^5 + 338*e^4 - 99*e^3 - 686*e^2 + 217*e + 170, 3*e^5 + 10*e^4 - 18*e^3 - 55*e^2 + 34*e + 54, -6*e^7 - 24*e^6 + 39*e^5 + 183*e^4 - 98*e^3 - 368*e^2 + 143*e + 77, -7*e^7 - 35*e^6 + 27*e^5 + 259*e^4 - 35*e^3 - 538*e^2 + 112*e + 160, -2*e^6 - 4*e^5 + 16*e^4 + 17*e^3 - 39*e^2 - 9*e + 17, e^7 + 3*e^6 - 9*e^5 - 28*e^4 + 10*e^3 + 57*e^2 + 38*e - 16, -19/2*e^7 - 42*e^6 + 49*e^5 + 310*e^4 - 98*e^3 - 1247/2*e^2 + 178*e + 148, 9/2*e^7 + 21*e^6 - 20*e^5 - 150*e^4 + 37*e^3 + 575/2*e^2 - 83*e - 62, 17/2*e^7 + 40*e^6 - 40*e^5 - 300*e^4 + 66*e^3 + 1225/2*e^2 - 124*e - 184, -10*e^7 - 45*e^6 + 53*e^5 + 340*e^4 - 119*e^3 - 715*e^2 + 226*e + 206, -14*e^7 - 70*e^6 + 61*e^5 + 529*e^4 - 126*e^3 - 1113*e^2 + 328*e + 312, -8*e^7 - 35*e^6 + 43*e^5 + 254*e^4 - 112*e^3 - 509*e^2 + 222*e + 128, -19/2*e^7 - 43*e^6 + 48*e^5 + 318*e^4 - 104*e^3 - 1299/2*e^2 + 195*e + 177, e^7 + e^6 - 17*e^5 - 21*e^4 + 61*e^3 + 66*e^2 - 61*e - 40, 17/2*e^7 + 37*e^6 - 38*e^5 - 253*e^4 + 56*e^3 + 951/2*e^2 - 99*e - 128, -2*e^7 - 3*e^6 + 25*e^5 + 25*e^4 - 88*e^3 - 47*e^2 + 77*e - 8, -2*e^7 - 7*e^6 + 18*e^5 + 62*e^4 - 54*e^3 - 142*e^2 + 45*e + 58, e^6 + 3*e^5 - 7*e^4 - 13*e^3 + 32*e^2 + e - 44, 19/2*e^7 + 42*e^6 - 52*e^5 - 313*e^4 + 129*e^3 + 1269/2*e^2 - 239*e - 162, 9/2*e^7 + 24*e^6 - 13*e^5 - 170*e^4 + 8*e^3 + 627/2*e^2 - 74*e - 30, -e^7 - 11*e^6 - 10*e^5 + 76*e^4 + 50*e^3 - 139*e^2 - 12*e + 27, 3/2*e^7 + 10*e^6 - 5*e^5 - 84*e^4 + 23*e^3 + 415/2*e^2 - 86*e - 76, -2*e^7 - 10*e^6 + 4*e^5 + 59*e^4 - 5*e^3 - 88*e^2 + 66*e - 15, -8*e^7 - 41*e^6 + 30*e^5 + 306*e^4 - 39*e^3 - 642*e^2 + 133*e + 205, 8*e^7 + 41*e^6 - 34*e^5 - 314*e^4 + 69*e^3 + 671*e^2 - 193*e - 214, -19/2*e^7 - 39*e^6 + 63*e^5 + 300*e^4 - 189*e^3 - 1255/2*e^2 + 304*e + 162, 11*e^7 + 49*e^6 - 61*e^5 - 369*e^4 + 155*e^3 + 759*e^2 - 286*e - 217, -5*e^7 - 25*e^6 + 22*e^5 + 191*e^4 - 41*e^3 - 402*e^2 + 113*e + 105, -13*e^7 - 63*e^6 + 53*e^5 + 458*e^4 - 80*e^3 - 929*e^2 + 206*e + 270, -25/2*e^7 - 54*e^6 + 64*e^5 + 390*e^4 - 129*e^3 - 1589/2*e^2 + 212*e + 256, -11/2*e^7 - 28*e^6 + 26*e^5 + 222*e^4 - 52*e^3 - 939/2*e^2 + 126*e + 101, 3*e^7 + 13*e^6 - 13*e^5 - 83*e^4 + 35*e^3 + 158*e^2 - 92*e - 53, 21/2*e^7 + 48*e^6 - 50*e^5 - 347*e^4 + 106*e^3 + 1395/2*e^2 - 209*e - 205, -5/2*e^7 - 18*e^6 - 6*e^5 + 120*e^4 + 47*e^3 - 473/2*e^2 + 9*e + 92, 21/2*e^7 + 50*e^6 - 45*e^5 - 365*e^4 + 67*e^3 + 1455/2*e^2 - 160*e - 164, 9/2*e^7 + 22*e^6 - 19*e^5 - 167*e^4 + 17*e^3 + 689/2*e^2 - 26*e - 106, -6*e^7 - 28*e^6 + 30*e^5 + 211*e^4 - 60*e^3 - 420*e^2 + 110*e + 85, -31/2*e^7 - 72*e^6 + 77*e^5 + 542*e^4 - 166*e^3 - 2287/2*e^2 + 336*e + 359, -12*e^7 - 60*e^6 + 53*e^5 + 453*e^4 - 114*e^3 - 934*e^2 + 300*e + 216, 10*e^7 + 43*e^6 - 54*e^5 - 319*e^4 + 111*e^3 + 662*e^2 - 179*e - 221, -9/2*e^7 - 17*e^6 + 27*e^5 + 124*e^4 - 46*e^3 - 493/2*e^2 + 48*e + 80, 6*e^7 + 24*e^6 - 33*e^5 - 171*e^4 + 63*e^3 + 349*e^2 - 88*e - 130, 6*e^7 + 27*e^6 - 26*e^5 - 191*e^4 + 30*e^3 + 368*e^2 - 56*e - 94, -15/2*e^7 - 36*e^6 + 30*e^5 + 261*e^4 - 31*e^3 - 1037/2*e^2 + 91*e + 130, 9*e^7 + 42*e^6 - 40*e^5 - 305*e^4 + 61*e^3 + 603*e^2 - 124*e - 150, -5*e^7 - 17*e^6 + 29*e^5 + 105*e^4 - 49*e^3 - 158*e^2 + 42*e + 11, -11/2*e^7 - 25*e^6 + 28*e^5 + 183*e^4 - 70*e^3 - 745/2*e^2 + 138*e + 98, 9*e^7 + 40*e^6 - 45*e^5 - 296*e^4 + 78*e^3 + 605*e^2 - 128*e - 175, 1/2*e^7 + 11*e^6 + 21*e^5 - 75*e^4 - 111*e^3 + 311/2*e^2 + 96*e - 42, 2*e^7 + 14*e^6 + 6*e^5 - 92*e^4 - 58*e^3 + 180*e^2 + 40*e - 55, -11*e^7 - 50*e^6 + 53*e^5 + 363*e^4 - 107*e^3 - 724*e^2 + 210*e + 181, -7/2*e^7 - 12*e^6 + 30*e^5 + 100*e^4 - 91*e^3 - 455/2*e^2 + 100*e + 103]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([17, 17, w^4 - w^3 - 4*w^2 + w - 1])] = 1

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