/*
  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([11, 7, -6, -2, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([49,7,-2*w^2 + w + 9])

primes_array = [
[5, 5, -w^2 + 2*w + 3],\
[9, 3, w^3 - 3*w^2 - 2*w + 9],\
[9, 3, -w^3 + 5*w + 5],\
[11, 11, w],\
[11, 11, w - 1],\
[16, 2, 2],\
[19, 19, -w^3 + 2*w^2 + 3*w - 2],\
[19, 19, w^3 - w^2 - 4*w + 2],\
[29, 29, w^3 - 4*w^2 - w + 10],\
[29, 29, -w^3 + 3*w^2 + w - 7],\
[41, 41, 3*w^2 - 2*w - 10],\
[49, 7, -2*w^2 + 3*w + 8],\
[49, 7, w^3 - 2*w^2 - 2*w + 5],\
[71, 71, -w - 3],\
[71, 71, w - 4],\
[79, 79, -w^3 + w^2 + 3*w + 3],\
[79, 79, -w^3 + 2*w^2 + 2*w - 6],\
[89, 89, w^3 - 3*w^2 - 3*w + 7],\
[89, 89, w^3 - 6*w - 2],\
[101, 101, 2*w^3 - 5*w^2 - 3*w + 9],\
[101, 101, -w^3 + 3*w^2 + 3*w - 12],\
[109, 109, -w^3 + 4*w^2 + w - 9],\
[109, 109, -w^3 + 2*w^2 + 4*w - 2],\
[121, 11, -3*w^2 + 3*w + 10],\
[131, 131, -2*w^3 + 5*w^2 + 4*w - 9],\
[131, 131, -w^3 + w^2 + 3*w + 5],\
[131, 131, -w^3 + 2*w^2 + 2*w - 8],\
[131, 131, -w^3 + 6*w^2 - 18],\
[149, 149, -w^3 - 2*w^2 + 7*w + 8],\
[149, 149, -2*w^3 + 6*w^2 + 5*w - 16],\
[151, 151, w^2 + w - 5],\
[151, 151, w^2 - 3*w - 3],\
[169, 13, w^3 - 4*w^2 - w + 6],\
[169, 13, 2*w^3 - 5*w^2 - 4*w + 6],\
[179, 179, w^3 - 4*w - 6],\
[179, 179, -w^3 + 3*w^2 + w - 9],\
[181, 181, w^3 + 3*w^2 - 7*w - 15],\
[181, 181, w^3 - 6*w^2 + 2*w + 18],\
[191, 191, 5*w^2 - 7*w - 15],\
[191, 191, -4*w^2 + 5*w + 12],\
[199, 199, -w^3 + 3*w^2 + 3*w - 6],\
[199, 199, w^3 - 6*w - 1],\
[211, 211, w^3 - 7*w - 4],\
[211, 211, -w^3 + 3*w^2 + 4*w - 10],\
[229, 229, -w^3 - w^2 + 5*w + 9],\
[229, 229, -w^3 + 4*w^2 - 12],\
[239, 239, 4*w^2 - 5*w - 17],\
[239, 239, 4*w^2 - 3*w - 18],\
[241, 241, -w^3 + 3*w^2 + w - 2],\
[241, 241, -w^3 + 3*w^2 + 4*w - 9],\
[241, 241, w^3 - 7*w - 3],\
[241, 241, -w^3 + 4*w - 1],\
[271, 271, -w - 4],\
[271, 271, w^3 - 3*w^2 - 2*w + 2],\
[271, 271, -2*w^3 + 6*w^2 + 2*w - 7],\
[271, 271, w - 5],\
[281, 281, w^3 - 2*w^2 - 3*w - 1],\
[281, 281, -w^3 + w^2 + 4*w - 5],\
[289, 17, -2*w^3 + w^2 + 9*w + 1],\
[289, 17, -2*w^3 + 5*w^2 + 5*w - 9],\
[311, 311, w^3 - w^2 - 6*w + 1],\
[311, 311, -w^3 + 2*w^2 + 5*w - 5],\
[331, 331, -3*w^3 + 5*w^2 + 10*w - 5],\
[331, 331, 3*w^3 - 2*w^2 - 12*w - 6],\
[349, 349, -2*w^3 + 2*w^2 + 10*w + 3],\
[349, 349, -2*w^3 - w^2 + 12*w + 10],\
[349, 349, 2*w^3 + w^2 - 10*w - 12],\
[349, 349, -2*w^3 + 4*w^2 + 8*w - 13],\
[361, 19, -4*w^2 + 4*w + 13],\
[379, 379, w^3 + w^2 - 5*w - 10],\
[379, 379, -3*w^3 + 4*w^2 + 12*w - 7],\
[379, 379, w^3 + 4*w^2 - 8*w - 21],\
[379, 379, w^3 - 3*w - 6],\
[389, 389, 2*w^3 - 6*w^2 - 4*w + 13],\
[389, 389, -5*w^2 + 7*w + 13],\
[389, 389, 2*w^3 - 7*w^2 - 5*w + 20],\
[389, 389, 2*w^3 - 10*w - 5],\
[419, 419, -w^3 + 5*w^2 + w - 13],\
[419, 419, 4*w^2 - 7*w - 14],\
[419, 419, 2*w^3 - 3*w^2 - 5*w - 1],\
[419, 419, -w^3 - 2*w^2 + 8*w + 8],\
[421, 421, -2*w^2 + 5*w + 7],\
[421, 421, w^3 - 6*w^2 + 5*w + 13],\
[439, 439, 2*w^3 - 2*w^2 - 9*w + 3],\
[439, 439, w^3 + w^2 - 7*w - 4],\
[449, 449, 3*w^3 - 6*w^2 - 9*w + 8],\
[449, 449, 5*w^2 - 8*w - 17],\
[449, 449, 2*w^3 - w^2 - 8*w - 7],\
[449, 449, -3*w^3 + 3*w^2 + 12*w - 4],\
[479, 479, -2*w^3 + 3*w^2 + 5*w + 3],\
[479, 479, 3*w^3 - 7*w^2 - 9*w + 15],\
[499, 499, -w^3 + 4*w^2 + 4*w - 9],\
[499, 499, w^3 + w^2 - 9*w - 2],\
[509, 509, 2*w^3 + 2*w^2 - 11*w - 16],\
[509, 509, -2*w^3 + 8*w^2 + w - 23],\
[521, 521, -3*w^3 + w^2 + 13*w + 6],\
[521, 521, w^3 + 4*w^2 - 10*w - 16],\
[541, 541, 3*w^3 - 2*w^2 - 13*w - 3],\
[541, 541, -w^3 + 7*w^2 - w - 25],\
[541, 541, w^3 + 4*w^2 - 10*w - 20],\
[541, 541, -3*w^3 + 7*w^2 + 8*w - 15],\
[571, 571, w^3 + 4*w^2 - 9*w - 15],\
[571, 571, w^3 - 7*w^2 + 2*w + 19],\
[601, 601, -3*w^3 + 2*w^2 + 13*w + 5],\
[601, 601, 3*w^3 - 7*w^2 - 8*w + 17],\
[619, 619, w^3 - 3*w - 7],\
[619, 619, w^3 - 5*w^2 + 3*w + 13],\
[619, 619, 3*w^3 - 4*w^2 - 9*w - 2],\
[619, 619, -w^3 + 3*w^2 - 9],\
[641, 641, 6*w^2 - 4*w - 23],\
[641, 641, -3*w^3 + w^2 + 12*w + 5],\
[659, 659, -2*w^3 + 6*w^2 + 3*w - 17],\
[659, 659, -2*w^3 + 9*w + 10],\
[661, 661, 3*w^3 - 6*w^2 - 9*w + 14],\
[661, 661, 5*w^2 - 6*w - 18],\
[661, 661, -5*w^2 + 4*w + 19],\
[661, 661, 3*w^3 - 3*w^2 - 12*w - 2],\
[691, 691, -3*w^3 + 5*w^2 + 10*w - 6],\
[691, 691, -3*w^3 + 4*w^2 + 11*w - 6],\
[701, 701, -w^3 - 4*w^2 + 9*w + 20],\
[701, 701, -w^3 + 4*w^2 + 3*w - 19],\
[701, 701, -w^3 + 4*w^2 + 4*w - 15],\
[701, 701, w^3 - 7*w^2 + 2*w + 24],\
[709, 709, 3*w^2 - 5*w - 13],\
[709, 709, 3*w^2 - w - 15],\
[719, 719, -w^3 + 3*w^2 + 4*w - 4],\
[719, 719, -w^3 + 7*w - 2],\
[739, 739, -w^3 + 4*w^2 + 3*w - 9],\
[739, 739, -2*w^3 - w^2 + 11*w + 8],\
[739, 739, 2*w^3 - 7*w^2 - 3*w + 16],\
[739, 739, -w^3 - w^2 + 8*w + 3],\
[751, 751, 3*w^3 - 5*w^2 - 10*w + 10],\
[751, 751, 2*w^2 - 5*w - 5],\
[761, 761, 3*w^3 - 3*w^2 - 11*w + 3],\
[761, 761, w^3 - 2*w^2 - 3*w - 2],\
[761, 761, -w^3 + w^2 + 4*w - 6],\
[761, 761, -3*w^3 + 6*w^2 + 8*w - 8],\
[769, 769, -w^3 - w^2 + 7*w + 1],\
[769, 769, -2*w^3 + 6*w^2 + 6*w - 15],\
[769, 769, -2*w^3 + 5*w^2 + 5*w - 7],\
[769, 769, 2*w^3 + w^2 - 12*w - 9],\
[809, 809, -2*w^3 + 8*w^2 + 4*w - 23],\
[809, 809, -3*w^3 + 11*w^2 + 2*w - 28],\
[829, 829, -3*w^3 + 7*w^2 + 7*w - 9],\
[829, 829, w^3 + 2*w^2 - 6*w - 15],\
[829, 829, -w^3 + 5*w^2 - w - 18],\
[829, 829, -3*w^3 + 2*w^2 + 12*w - 2],\
[839, 839, 2*w^3 - 9*w^2 + 20],\
[839, 839, -3*w^3 + 10*w^2 + 5*w - 30],\
[841, 29, 5*w^2 - 5*w - 16],\
[881, 881, -w^3 - 4*w^2 + 8*w + 18],\
[881, 881, 2*w^3 - 7*w^2 - w + 9],\
[881, 881, 2*w^3 - 6*w^2 - 3*w + 6],\
[881, 881, -w^3 + 7*w^2 - 3*w - 21],\
[911, 911, -w^3 - 4*w^2 + 8*w + 16],\
[911, 911, -w^3 - w^2 + 9*w + 5],\
[911, 911, -w^3 + 4*w^2 + 4*w - 12],\
[911, 911, w^3 - 7*w^2 + 3*w + 19],\
[919, 919, -4*w^3 + 7*w^2 + 14*w - 9],\
[919, 919, 4*w^3 - 5*w^2 - 16*w + 8],\
[929, 929, 3*w^2 - w - 16],\
[929, 929, 3*w^2 - 5*w - 14],\
[941, 941, -w^3 - w^2 + 9*w + 7],\
[941, 941, -3*w^3 + 7*w^2 + 7*w - 15],\
[941, 941, 3*w^3 - 2*w^2 - 12*w - 4],\
[941, 941, w^3 + 4*w^2 - 13*w - 16],\
[961, 31, -2*w^2 + 2*w + 13],\
[961, 31, 5*w^2 - 5*w - 18],\
[971, 971, w^3 + 4*w^2 - 9*w - 19],\
[971, 971, w^3 - 7*w^2 + 2*w + 23],\
[991, 991, 3*w^3 - 7*w^2 - 7*w + 14],\
[991, 991, -3*w^3 + 2*w^2 + 12*w + 3]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^7 + 3*x^6 - 8*x^5 - 21*x^4 + 19*x^3 + 31*x^2 - 5
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 1/2*e^6 + 3/2*e^5 - 7/2*e^4 - 9*e^3 + 7*e^2 + 17/2*e, e^6 + 5/2*e^5 - 19/2*e^4 - 31/2*e^3 + 29*e^2 + 10*e - 15/2, 1/2*e^5 + 5/2*e^4 - 3/2*e^3 - 13*e^2 + 3*e + 11/2, -1/2*e^5 - 3/2*e^4 + 7/2*e^3 + 8*e^2 - 8*e - 9/2, -3/2*e^6 - 4*e^5 + 13*e^4 + 47/2*e^3 - 39*e^2 - 31/2*e + 21/2, -5/2*e^6 - 6*e^5 + 23*e^4 + 75/2*e^3 - 66*e^2 - 67/2*e + 25/2, 1/2*e^6 + e^5 - 6*e^4 - 17/2*e^3 + 20*e^2 + 21/2*e - 15/2, e^6 + 3/2*e^5 - 25/2*e^4 - 23/2*e^3 + 43*e^2 + 11*e - 35/2, -1/2*e^6 - 1/2*e^5 + 13/2*e^4 + 5*e^3 - 19*e^2 - 13/2*e, -5/2*e^6 - 6*e^5 + 23*e^4 + 73/2*e^3 - 67*e^2 - 55/2*e + 31/2, 3/2*e^6 + 3*e^5 - 15*e^4 - 35/2*e^3 + 48*e^2 + 25/2*e - 45/2, 1, 1/2*e^6 + e^5 - 7*e^4 - 19/2*e^3 + 26*e^2 + 23/2*e - 21/2, 3*e^6 + 13/2*e^5 - 57/2*e^4 - 75/2*e^3 + 87*e^2 + 22*e - 61/2, -3/2*e^6 - 7/2*e^5 + 31/2*e^4 + 24*e^3 - 47*e^2 - 45/2*e, -1/2*e^6 - 1/2*e^5 + 9/2*e^4 + e^3 - 10*e^2 + 11/2*e, 2*e^6 + 6*e^5 - 16*e^4 - 35*e^3 + 47*e^2 + 21*e - 15, 1/2*e^6 + 1/2*e^5 - 15/2*e^4 - 7*e^3 + 25*e^2 + 27/2*e - 5, -1/2*e^5 - 7/2*e^4 + 1/2*e^3 + 20*e^2 - 19/2, 2*e^6 + 6*e^5 - 16*e^4 - 37*e^3 + 44*e^2 + 30*e - 7, 2*e^4 + 3*e^3 - 10*e^2 - 5*e - 5, -7/2*e^6 - 8*e^5 + 31*e^4 + 89/2*e^3 - 88*e^2 - 47/2*e + 55/2, -e^6 - 5/2*e^5 + 21/2*e^4 + 41/2*e^3 - 30*e^2 - 30*e - 1/2, 4*e^6 + 19/2*e^5 - 71/2*e^4 - 117/2*e^3 + 94*e^2 + 48*e - 29/2, 1/2*e^6 + e^5 - 3*e^4 - 7/2*e^3 + 2*e^2 - 9/2*e - 1/2, -2*e^6 - 4*e^5 + 19*e^4 + 23*e^3 - 57*e^2 - 19*e + 22, -5/2*e^6 - 6*e^5 + 26*e^4 + 89/2*e^3 - 77*e^2 - 107/2*e + 21/2, -7/2*e^6 - 17/2*e^5 + 67/2*e^4 + 59*e^3 - 97*e^2 - 137/2*e + 20, -4*e^6 - 12*e^5 + 30*e^4 + 71*e^3 - 79*e^2 - 61*e + 20, 1/2*e^6 + 3/2*e^5 - 9/2*e^4 - 9*e^3 + 14*e^2 + 3/2*e - 2, 2*e^6 + 6*e^5 - 16*e^4 - 40*e^3 + 40*e^2 + 47*e - 2, 3*e^6 + 8*e^5 - 27*e^4 - 52*e^3 + 77*e^2 + 46*e - 15, -11/2*e^6 - 14*e^5 + 47*e^4 + 161/2*e^3 - 137*e^2 - 107/2*e + 85/2, -11/2*e^6 - 13*e^5 + 53*e^4 + 165/2*e^3 - 161*e^2 - 137/2*e + 65/2, 5/2*e^6 + 13/2*e^5 - 37/2*e^4 - 34*e^3 + 46*e^2 + 45/2*e - 20, -1/2*e^6 + 7*e^4 - 11/2*e^3 - 30*e^2 + 63/2*e + 29/2, -3*e^6 - 11/2*e^5 + 63/2*e^4 + 59/2*e^3 - 104*e^2 - e + 79/2, 9/2*e^6 + 21/2*e^5 - 87/2*e^4 - 73*e^3 + 123*e^2 + 175/2*e - 22, -7*e^6 - 15*e^5 + 71*e^4 + 96*e^3 - 219*e^2 - 77*e + 58, 9/2*e^6 + 11*e^5 - 42*e^4 - 147/2*e^3 + 119*e^2 + 167/2*e - 35/2, 3/2*e^6 + 7/2*e^5 - 21/2*e^4 - 16*e^3 + 22*e^2 + 9/2*e + 5, 4*e^6 + 17/2*e^5 - 77/2*e^4 - 105/2*e^3 + 110*e^2 + 40*e - 49/2, -5/2*e^6 - 6*e^5 + 27*e^4 + 93/2*e^3 - 84*e^2 - 129/2*e + 31/2, 3/2*e^6 + 11/2*e^5 - 21/2*e^4 - 36*e^3 + 25*e^2 + 79/2*e + 5, 3/2*e^6 + 4*e^5 - 13*e^4 - 57/2*e^3 + 36*e^2 + 95/2*e - 35/2, -3/2*e^6 - 5/2*e^5 + 35/2*e^4 + 13*e^3 - 68*e^2 + 3/2*e + 35, 3*e^6 + 9*e^5 - 23*e^4 - 53*e^3 + 62*e^2 + 42*e - 20, 11/2*e^6 + 23/2*e^5 - 113/2*e^4 - 75*e^3 + 176*e^2 + 137/2*e - 48, 3/2*e^6 + 9/2*e^5 - 21/2*e^4 - 26*e^3 + 29*e^2 + 51/2*e - 27, e^6 + 7/2*e^5 - 5/2*e^4 - 27/2*e^3 - 6*e^2 - e + 11/2, 7/2*e^6 + 15/2*e^5 - 71/2*e^4 - 49*e^3 + 107*e^2 + 93/2*e - 28, -1/2*e^6 - 2*e^5 + 2*e^4 + 19/2*e^3 - 6*e^2 - 13/2*e + 31/2, 8*e^6 + 41/2*e^5 - 141/2*e^4 - 251/2*e^3 + 203*e^2 + 107*e - 91/2, -9/2*e^6 - 10*e^5 + 46*e^4 + 139/2*e^3 - 142*e^2 - 153/2*e + 69/2, 2*e^6 + 4*e^5 - 18*e^4 - 22*e^3 + 48*e^2 + 10*e - 12, -2*e^5 - 5*e^4 + 12*e^3 + 19*e^2 - 14*e + 12, 3/2*e^6 + 7/2*e^5 - 37/2*e^4 - 32*e^3 + 58*e^2 + 95/2*e - 8, 7*e^6 + 17*e^5 - 61*e^4 - 102*e^3 + 167*e^2 + 87*e - 25, -5/2*e^6 - 5*e^5 + 25*e^4 + 77/2*e^3 - 64*e^2 - 129/2*e + 5/2, e^6 + 1/2*e^5 - 29/2*e^4 + 1/2*e^3 + 58*e^2 - 18*e - 61/2, 5/2*e^6 + 9/2*e^5 - 49/2*e^4 - 25*e^3 + 68*e^2 - 1/2*e - 13, -5*e^6 - 16*e^5 + 35*e^4 + 92*e^3 - 89*e^2 - 73*e + 13, 3/2*e^6 + 5/2*e^5 - 41/2*e^4 - 18*e^3 + 81*e^2 + 15/2*e - 32, -11/2*e^6 - 16*e^5 + 45*e^4 + 199/2*e^3 - 125*e^2 - 181/2*e + 35/2, -2*e^5 - 3*e^4 + 18*e^3 + 16*e^2 - 39*e - 10, 7/2*e^6 + 11/2*e^5 - 87/2*e^4 - 39*e^3 + 154*e^2 + 49/2*e - 60, 7/2*e^6 + 10*e^5 - 27*e^4 - 121/2*e^3 + 67*e^2 + 119/2*e - 25/2, 2*e^6 + 11/2*e^5 - 41/2*e^4 - 89/2*e^3 + 57*e^2 + 67*e + 11/2, 4*e^4 + 7*e^3 - 15*e^2 - 11*e - 10, -5/2*e^6 - 2*e^5 + 37*e^4 + 35/2*e^3 - 137*e^2 + 9/2*e + 85/2, -7*e^6 - 35/2*e^5 + 125/2*e^4 + 211/2*e^3 - 180*e^2 - 76*e + 75/2, 3*e^6 + 15/2*e^5 - 47/2*e^4 - 69/2*e^3 + 68*e^2 - 8*e - 65/2, -2*e^6 - 9/2*e^5 + 43/2*e^4 + 51/2*e^3 - 77*e^2 - 6*e + 25/2, -3/2*e^6 - 2*e^5 + 19*e^4 + 37/2*e^3 - 63*e^2 - 57/2*e + 55/2, -4*e^6 - 19/2*e^5 + 73/2*e^4 + 129/2*e^3 - 95*e^2 - 80*e + 45/2, -7/2*e^6 - 8*e^5 + 33*e^4 + 95/2*e^3 - 104*e^2 - 65/2*e + 75/2, 4*e^6 + 25/2*e^5 - 63/2*e^4 - 157/2*e^3 + 88*e^2 + 83*e - 25/2, -1/2*e^6 + 9*e^4 - 3/2*e^3 - 40*e^2 + 51/2*e + 35/2, 4*e^6 + 17/2*e^5 - 85/2*e^4 - 111/2*e^3 + 136*e^2 + 37*e - 105/2, 7*e^6 + 29/2*e^5 - 139/2*e^4 - 181/2*e^3 + 208*e^2 + 68*e - 105/2, 5/2*e^6 + 8*e^5 - 14*e^4 - 79/2*e^3 + 29*e^2 + 33/2*e - 21/2, 5/2*e^6 + 17/2*e^5 - 23/2*e^4 - 40*e^3 + 18*e^2 + 35/2*e - 13, -4*e^6 - 23/2*e^5 + 75/2*e^4 + 167/2*e^3 - 113*e^2 - 110*e + 55/2, -9*e^6 - 41/2*e^5 + 173/2*e^4 + 253/2*e^3 - 265*e^2 - 101*e + 155/2, -5/2*e^5 - 19/2*e^4 + 9/2*e^3 + 37*e^2 + 18*e - 15/2, 3/2*e^6 + 5/2*e^5 - 45/2*e^4 - 22*e^3 + 89*e^2 + 23/2*e - 35, -3/2*e^6 - 3*e^5 + 15*e^4 + 47/2*e^3 - 40*e^2 - 93/2*e - 5/2, -7/2*e^6 - 19/2*e^5 + 61/2*e^4 + 60*e^3 - 81*e^2 - 83/2*e, 9*e^6 + 18*e^5 - 95*e^4 - 118*e^3 + 295*e^2 + 96*e - 80, 7/2*e^6 + 8*e^5 - 33*e^4 - 117/2*e^3 + 80*e^2 + 155/2*e + 5/2, -21/2*e^6 - 53/2*e^5 + 183/2*e^4 + 162*e^3 - 255*e^2 - 293/2*e + 50, 1/2*e^6 + 5*e^5 + 6*e^4 - 61/2*e^3 - 37*e^2 + 97/2*e + 25/2, -6*e^6 - 16*e^5 + 48*e^4 + 102*e^3 - 112*e^2 - 116*e + 10, -2*e^6 - 2*e^5 + 27*e^4 + 23*e^3 - 87*e^2 - 49*e + 30, 5/2*e^6 + 6*e^5 - 19*e^4 - 51/2*e^3 + 54*e^2 - 11/2*e - 21/2, 3*e^6 + 6*e^5 - 32*e^4 - 40*e^3 + 102*e^2 + 26*e - 53, -21/2*e^6 - 22*e^5 + 102*e^4 + 261/2*e^3 - 308*e^2 - 161/2*e + 201/2, 12*e^6 + 61/2*e^5 - 221/2*e^4 - 383/2*e^3 + 325*e^2 + 147*e - 151/2, -9*e^6 - 23*e^5 + 78*e^4 + 134*e^3 - 230*e^2 - 85*e + 77, 13/2*e^6 + 16*e^5 - 58*e^4 - 179/2*e^3 + 175*e^2 + 83/2*e - 109/2, 2*e^6 + 1/2*e^5 - 57/2*e^4 - 11/2*e^3 + 98*e^2 - 89/2, -9/2*e^6 - 15*e^5 + 30*e^4 + 175/2*e^3 - 79*e^2 - 155/2*e + 81/2, e^6 - 21*e^4 - 15*e^3 + 79*e^2 + 45*e - 27, 2*e^6 + 11/2*e^5 - 27/2*e^4 - 41/2*e^3 + 33*e^2 - 30*e + 1/2, 13/2*e^6 + 23/2*e^5 - 145/2*e^4 - 74*e^3 + 236*e^2 + 85/2*e - 70, 21/2*e^6 + 23*e^5 - 105*e^4 - 301/2*e^3 + 318*e^2 + 273/2*e - 145/2, -e^6 - 7/2*e^5 + 9/2*e^4 + 35/2*e^3 - 8*e^2 - 17*e - 5/2, -4*e^6 - 9*e^5 + 39*e^4 + 61*e^3 - 119*e^2 - 73*e + 50, 19/2*e^6 + 43/2*e^5 - 195/2*e^4 - 145*e^3 + 305*e^2 + 271/2*e - 77, 3*e^3 + 5*e^2 - 9*e - 37, 11/2*e^6 + 29/2*e^5 - 109/2*e^4 - 106*e^3 + 162*e^2 + 267/2*e - 40, 15/2*e^6 + 33/2*e^5 - 157/2*e^4 - 110*e^3 + 249*e^2 + 191/2*e - 60, -23/2*e^6 - 26*e^5 + 109*e^4 + 329/2*e^3 - 321*e^2 - 327/2*e + 161/2, 5*e^6 + 31/2*e^5 - 77/2*e^4 - 199/2*e^3 + 101*e^2 + 118*e - 29/2, -4*e^6 - 10*e^5 + 31*e^4 + 49*e^3 - 95*e^2 - 17*e + 68, 3/2*e^6 + 3/2*e^5 - 43/2*e^4 - 9*e^3 + 80*e^2 - 27/2*e - 32, -6*e^6 - 11*e^5 + 69*e^4 + 73*e^3 - 234*e^2 - 36*e + 82, -12*e^6 - 57/2*e^5 + 217/2*e^4 + 349/2*e^3 - 313*e^2 - 162*e + 169/2, 25/2*e^6 + 29*e^5 - 114*e^4 - 359/2*e^3 + 321*e^2 + 345/2*e - 119/2, 3*e^5 + 9*e^4 - 13*e^3 - 33*e^2 + 14*e + 2, 7*e^6 + 17*e^5 - 58*e^4 - 93*e^3 + 162*e^2 + 55*e - 73, -17/2*e^6 - 41/2*e^5 + 161/2*e^4 + 126*e^3 - 253*e^2 - 191/2*e + 88, -4*e^6 - 5*e^5 + 53*e^4 + 36*e^3 - 189*e^2 - 16*e + 80, -2*e^6 - 8*e^5 + 5*e^4 + 40*e^3 + 14*e^2 - 29*e - 35, -12*e^6 - 30*e^5 + 114*e^4 + 198*e^3 - 339*e^2 - 196*e + 65, 4*e^4 + 17*e^3 - 7*e^2 - 59*e - 15, 1/2*e^6 + 5*e^5 + 7*e^4 - 57/2*e^3 - 41*e^2 + 89/2*e + 45/2, -2*e^6 - 11/2*e^5 + 37/2*e^4 + 53/2*e^3 - 66*e^2 + 21*e + 45/2, -5/2*e^6 - 7*e^5 + 15*e^4 + 63/2*e^3 - 27*e^2 - 5/2*e + 5/2, -17/2*e^6 - 41/2*e^5 + 163/2*e^4 + 133*e^3 - 253*e^2 - 255/2*e + 70, 5*e^6 + 9*e^5 - 56*e^4 - 60*e^3 + 183*e^2 + 33*e - 62, -11*e^6 - 49/2*e^5 + 229/2*e^4 + 329/2*e^3 - 361*e^2 - 136*e + 181/2, -9*e^6 - 35/2*e^5 + 193/2*e^4 + 227/2*e^3 - 303*e^2 - 84*e + 171/2, -3/2*e^6 - 3/2*e^5 + 43/2*e^4 + 8*e^3 - 86*e^2 + 7/2*e + 33, 21/2*e^6 + 26*e^5 - 94*e^4 - 309/2*e^3 + 278*e^2 + 221/2*e - 179/2, -14*e^6 - 61/2*e^5 + 275/2*e^4 + 397/2*e^3 - 404*e^2 - 186*e + 211/2, -19/2*e^6 - 23*e^5 + 89*e^4 + 287/2*e^3 - 263*e^2 - 209/2*e + 135/2, -8*e^6 - 14*e^5 + 90*e^4 + 90*e^3 - 295*e^2 - 43*e + 105, -15*e^6 - 37*e^5 + 135*e^4 + 232*e^3 - 377*e^2 - 203*e + 75, -7/2*e^6 - 19/2*e^5 + 71/2*e^4 + 66*e^3 - 124*e^2 - 149/2*e + 55, 6*e^6 + 23/2*e^5 - 129/2*e^4 - 157/2*e^3 + 194*e^2 + 79*e - 65/2, -17/2*e^6 - 43/2*e^5 + 145/2*e^4 + 114*e^3 - 220*e^2 - 63/2*e + 80, -3/2*e^6 - 2*e^5 + 19*e^4 + 33/2*e^3 - 61*e^2 - 27/2*e + 25/2, -5*e^6 - 35/2*e^5 + 59/2*e^4 + 211/2*e^3 - 61*e^2 - 124*e + 35/2, 7/2*e^6 + 10*e^5 - 32*e^4 - 141/2*e^3 + 88*e^2 + 167/2*e - 25/2, 19/2*e^6 + 22*e^5 - 91*e^4 - 275/2*e^3 + 276*e^2 + 237/2*e - 175/2, 1/2*e^6 - 11/2*e^5 - 49/2*e^4 + 28*e^3 + 105*e^2 - 97/2*e - 45, 25/2*e^6 + 28*e^5 - 124*e^4 - 371/2*e^3 + 369*e^2 + 385/2*e - 155/2, 15/2*e^6 + 21*e^5 - 57*e^4 - 237/2*e^3 + 150*e^2 + 167/2*e - 59/2, 17/2*e^6 + 21*e^5 - 74*e^4 - 259/2*e^3 + 193*e^2 + 245/2*e - 19/2, 6*e^6 + 17*e^5 - 46*e^4 - 96*e^3 + 123*e^2 + 65*e - 27, 31/2*e^6 + 83/2*e^5 - 267/2*e^4 - 251*e^3 + 385*e^2 + 393/2*e - 102, -17/2*e^6 - 21*e^5 + 80*e^4 + 271/2*e^3 - 236*e^2 - 247/2*e + 101/2, -17/2*e^6 - 20*e^5 + 75*e^4 + 241/2*e^3 - 201*e^2 - 187/2*e + 79/2, 21/2*e^6 + 20*e^5 - 121*e^4 - 283/2*e^3 + 406*e^2 + 217/2*e - 271/2, 17/2*e^6 + 37/2*e^5 - 171/2*e^4 - 120*e^3 + 255*e^2 + 207/2*e - 48, -8*e^6 - 27/2*e^5 + 175/2*e^4 + 173/2*e^3 - 274*e^2 - 61*e + 189/2, -15/2*e^6 - 19*e^5 + 61*e^4 + 231/2*e^3 - 144*e^2 - 217/2*e + 5/2, -6*e^6 - 27/2*e^5 + 133/2*e^4 + 199/2*e^3 - 218*e^2 - 101*e + 145/2, -3*e^6 - 11/2*e^5 + 67/2*e^4 + 69/2*e^3 - 114*e^2 - 18*e + 95/2, 25/2*e^6 + 31*e^5 - 113*e^4 - 387/2*e^3 + 323*e^2 + 315/2*e - 135/2, -8*e^6 - 37/2*e^5 + 145/2*e^4 + 223/2*e^3 - 203*e^2 - 83*e + 121/2, -9*e^6 - 22*e^5 + 82*e^4 + 146*e^3 - 215*e^2 - 152*e + 22, 8*e^6 + 39/2*e^5 - 153/2*e^4 - 251/2*e^3 + 240*e^2 + 122*e - 151/2, e^6 - 19*e^4 - 6*e^3 + 75*e^2 - 2*e - 17, -12*e^6 - 57/2*e^5 + 217/2*e^4 + 353/2*e^3 - 307*e^2 - 160*e + 169/2, 5*e^6 + 25/2*e^5 - 85/2*e^4 - 155/2*e^3 + 115*e^2 + 85*e - 101/2, -6*e^6 - 16*e^5 + 54*e^4 + 105*e^3 - 158*e^2 - 109*e + 52, -2*e^6 - 15/2*e^5 + 25/2*e^4 + 73/2*e^3 - 38*e^2 + 6*e + 19/2, e^6 - 3/2*e^5 - 43/2*e^4 + 1/2*e^3 + 83*e^2 + 15*e - 109/2, 15*e^6 + 71/2*e^5 - 295/2*e^4 - 449/2*e^3 + 468*e^2 + 170*e - 299/2]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([49,7,-2*w^2 + w + 9])] = -1

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