/*
  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, 7, 11, -2, -7, 0, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([25, 5, w^3 + w^2 - 4*w - 3])

primes_array = [
[5, 5, -2*w^5 + w^4 + 13*w^3 - 2*w^2 - 19*w - 5],\
[9, 3, 2*w^5 - w^4 - 14*w^3 + 2*w^2 + 23*w + 6],\
[11, 11, w - 1],\
[25, 5, w^3 + w^2 - 4*w - 3],\
[29, 29, w^5 - w^4 - 7*w^3 + 4*w^2 + 11*w],\
[41, 41, w^4 - w^3 - 5*w^2 + 3*w + 3],\
[49, 7, w^5 - w^4 - 7*w^3 + 4*w^2 + 11*w + 1],\
[59, 59, 2*w^5 - w^4 - 14*w^3 + 2*w^2 + 24*w + 7],\
[59, 59, -w^5 + 8*w^3 + 2*w^2 - 15*w - 8],\
[61, 61, w^5 - 7*w^3 - 2*w^2 + 12*w + 4],\
[61, 61, -w^5 + 7*w^3 - 11*w - 1],\
[64, 2, 2],\
[71, 71, w^3 + w^2 - 5*w - 3],\
[71, 71, -3*w^5 + w^4 + 21*w^3 - w^2 - 33*w - 9],\
[79, 79, -2*w^5 + w^4 + 13*w^3 - 3*w^2 - 19*w - 5],\
[81, 3, 2*w^5 - w^4 - 13*w^3 + w^2 + 19*w + 8],\
[89, 89, 2*w^5 - w^4 - 13*w^3 + 2*w^2 + 20*w + 7],\
[89, 89, -w^5 + 8*w^3 + w^2 - 16*w - 5],\
[89, 89, -3*w^5 + w^4 + 20*w^3 - 30*w - 11],\
[89, 89, -w^5 + 7*w^3 + 2*w^2 - 11*w - 4],\
[89, 89, -2*w^5 + 14*w^3 + 3*w^2 - 22*w - 8],\
[89, 89, 2*w^5 - w^4 - 14*w^3 + 3*w^2 + 22*w + 6],\
[101, 101, 3*w^5 - 2*w^4 - 18*w^3 + 6*w^2 + 22*w + 6],\
[101, 101, w^2 - w - 4],\
[101, 101, -3*w^5 + w^4 + 20*w^3 - 2*w^2 - 29*w - 7],\
[109, 109, w^4 - w^3 - 5*w^2 + 4*w + 5],\
[121, 11, w^5 - 7*w^3 - 2*w^2 + 10*w + 6],\
[131, 131, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 4*w - 3],\
[131, 131, -2*w^5 + w^4 + 13*w^3 - 3*w^2 - 20*w - 6],\
[131, 131, 3*w^5 - w^4 - 21*w^3 + w^2 + 35*w + 11],\
[131, 131, -w^5 + w^4 + 6*w^3 - 4*w^2 - 7*w + 2],\
[139, 139, -w^5 + 6*w^3 + w^2 - 8*w - 1],\
[151, 151, -w^3 + w^2 + 4*w - 2],\
[179, 179, w^4 - 6*w^2 + 6],\
[181, 181, w^3 + w^2 - 3*w],\
[191, 191, 3*w^5 - w^4 - 20*w^3 + 2*w^2 + 28*w + 5],\
[199, 199, -2*w^5 + w^4 + 12*w^3 - 3*w^2 - 15*w - 2],\
[199, 199, 5*w^5 - w^4 - 34*w^3 - w^2 + 52*w + 15],\
[211, 211, 3*w^5 - w^4 - 19*w^3 + w^2 + 26*w + 9],\
[229, 229, -w^5 + w^4 + 7*w^3 - 3*w^2 - 11*w],\
[229, 229, -w^4 + 2*w^3 + 6*w^2 - 7*w - 6],\
[239, 239, -w^5 + w^4 + 7*w^3 - 3*w^2 - 13*w - 6],\
[239, 239, 3*w^5 - w^4 - 21*w^3 + w^2 + 35*w + 10],\
[239, 239, w^3 - w^2 - 4*w + 1],\
[239, 239, 5*w^5 - 2*w^4 - 34*w^3 + 2*w^2 + 53*w + 17],\
[241, 241, -w^5 + 7*w^3 + w^2 - 13*w - 4],\
[241, 241, -3*w^5 + w^4 + 21*w^3 - 35*w - 10],\
[241, 241, -w^5 + 7*w^3 - 11*w],\
[251, 251, 3*w^5 - w^4 - 21*w^3 + 35*w + 11],\
[251, 251, w^5 - 2*w^4 - 6*w^3 + 9*w^2 + 8*w - 3],\
[269, 269, -w^5 + 8*w^3 + 3*w^2 - 16*w - 8],\
[269, 269, -2*w^5 + w^4 + 13*w^3 - w^2 - 21*w - 9],\
[269, 269, 3*w^5 - 21*w^3 - 3*w^2 + 32*w + 12],\
[271, 271, -5*w^5 + 3*w^4 + 34*w^3 - 8*w^2 - 53*w - 14],\
[281, 281, -w^5 + 8*w^3 + 3*w^2 - 16*w - 11],\
[281, 281, 4*w^5 - w^4 - 29*w^3 + 49*w + 13],\
[281, 281, w^5 - w^4 - 7*w^3 + 3*w^2 + 11*w + 5],\
[281, 281, -5*w^5 + 3*w^4 + 33*w^3 - 8*w^2 - 50*w - 12],\
[311, 311, 2*w^5 - w^4 - 14*w^3 + w^2 + 21*w + 9],\
[311, 311, -3*w^5 + 20*w^3 + 3*w^2 - 30*w - 10],\
[311, 311, 5*w^5 - 2*w^4 - 35*w^3 + 2*w^2 + 57*w + 19],\
[331, 331, -w^5 - w^4 + 7*w^3 + 6*w^2 - 11*w - 7],\
[349, 349, -6*w^5 + 3*w^4 + 41*w^3 - 7*w^2 - 64*w - 17],\
[349, 349, 4*w^5 - w^4 - 29*w^3 - w^2 + 50*w + 17],\
[349, 349, 5*w^5 - w^4 - 34*w^3 - w^2 + 52*w + 17],\
[359, 359, w^5 - 6*w^3 - w^2 + 5*w + 3],\
[379, 379, -w^5 + w^4 + 8*w^3 - 3*w^2 - 17*w - 3],\
[379, 379, 2*w^5 - 14*w^3 - 4*w^2 + 22*w + 11],\
[379, 379, -5*w^5 + 3*w^4 + 34*w^3 - 8*w^2 - 53*w - 13],\
[379, 379, 4*w^5 - 2*w^4 - 27*w^3 + 3*w^2 + 43*w + 14],\
[389, 389, 4*w^5 - 2*w^4 - 28*w^3 + 4*w^2 + 44*w + 13],\
[401, 401, -2*w^5 + 2*w^4 + 13*w^3 - 6*w^2 - 20*w - 6],\
[409, 409, -w^5 + 2*w^4 + 6*w^3 - 8*w^2 - 9*w],\
[419, 419, -5*w^5 + w^4 + 34*w^3 + 2*w^2 - 53*w - 19],\
[419, 419, 2*w^5 - w^4 - 14*w^3 + 4*w^2 + 23*w + 3],\
[421, 421, -w^5 - w^4 + 8*w^3 + 6*w^2 - 13*w - 7],\
[421, 421, 2*w^5 - 2*w^4 - 13*w^3 + 8*w^2 + 18*w + 2],\
[421, 421, 4*w^5 - w^4 - 26*w^3 + 37*w + 11],\
[431, 431, 2*w^5 - w^4 - 13*w^3 + 2*w^2 + 20*w + 9],\
[431, 431, w^5 - 8*w^3 - w^2 + 14*w + 2],\
[449, 449, 4*w^5 - 2*w^4 - 26*w^3 + 4*w^2 + 38*w + 9],\
[449, 449, -3*w^5 + w^4 + 20*w^3 - 31*w - 14],\
[461, 461, 3*w^5 - 2*w^4 - 18*w^3 + 6*w^2 + 23*w + 4],\
[461, 461, -4*w^5 + 2*w^4 + 26*w^3 - 5*w^2 - 36*w - 9],\
[461, 461, -4*w^5 + 2*w^4 + 27*w^3 - 3*w^2 - 42*w - 15],\
[491, 491, -3*w^5 + w^4 + 20*w^3 - 29*w - 10],\
[491, 491, -5*w^5 + w^4 + 35*w^3 + 2*w^2 - 56*w - 18],\
[491, 491, 2*w^5 - 14*w^3 - 4*w^2 + 24*w + 13],\
[491, 491, -3*w^5 + w^4 + 21*w^3 - 2*w^2 - 33*w - 10],\
[499, 499, 6*w^5 - 3*w^4 - 40*w^3 + 6*w^2 + 61*w + 18],\
[499, 499, -4*w^5 + w^4 + 29*w^3 + w^2 - 49*w - 17],\
[499, 499, -w^5 - w^4 + 8*w^3 + 5*w^2 - 14*w - 4],\
[499, 499, -3*w^5 + w^4 + 19*w^3 - 2*w^2 - 26*w - 8],\
[509, 509, -4*w^5 + 2*w^4 + 27*w^3 - 5*w^2 - 43*w - 11],\
[509, 509, -2*w^5 + 16*w^3 + 2*w^2 - 30*w - 9],\
[521, 521, 3*w^5 - 21*w^3 - 3*w^2 + 34*w + 10],\
[521, 521, -3*w^5 + w^4 + 19*w^3 - 26*w - 9],\
[521, 521, 4*w^5 - w^4 - 27*w^3 + 40*w + 15],\
[521, 521, -3*w^5 + 22*w^3 + 3*w^2 - 37*w - 11],\
[541, 541, -4*w^5 + w^4 + 29*w^3 + w^2 - 49*w - 18],\
[569, 569, -6*w^5 + 2*w^4 + 40*w^3 - 2*w^2 - 60*w - 19],\
[569, 569, -w^5 + w^4 + 7*w^3 - 2*w^2 - 12*w - 6],\
[571, 571, 4*w^5 - w^4 - 28*w^3 + 43*w + 14],\
[571, 571, -4*w^5 + 2*w^4 + 28*w^3 - 4*w^2 - 45*w - 14],\
[599, 599, -w^5 + w^4 + 7*w^3 - 2*w^2 - 13*w - 7],\
[601, 601, 4*w^5 - w^4 - 26*w^3 + 38*w + 13],\
[601, 601, 4*w^5 - 2*w^4 - 28*w^3 + 5*w^2 + 44*w + 11],\
[601, 601, 3*w^5 - w^4 - 21*w^3 + 2*w^2 + 35*w + 9],\
[619, 619, 4*w^5 - 2*w^4 - 27*w^3 + 4*w^2 + 40*w + 13],\
[619, 619, -4*w^5 + w^4 + 26*w^3 - 36*w - 12],\
[619, 619, w^4 - w^3 - 6*w^2 + 4*w + 4],\
[631, 631, -3*w^5 + w^4 + 20*w^3 - 30*w - 9],\
[631, 631, -5*w^5 + 2*w^4 + 35*w^3 - 3*w^2 - 57*w - 15],\
[641, 641, 5*w^5 - w^4 - 34*w^3 - w^2 + 52*w + 16],\
[641, 641, -5*w^5 + 2*w^4 + 34*w^3 - 2*w^2 - 52*w - 18],\
[659, 659, 3*w^5 - w^4 - 20*w^3 + w^2 + 32*w + 9],\
[659, 659, -4*w^5 + w^4 + 27*w^3 - w^2 - 40*w - 11],\
[661, 661, 4*w^5 - w^4 - 26*w^3 + 38*w + 12],\
[661, 661, -w^5 + 6*w^3 - 8*w + 1],\
[691, 691, 3*w^5 - 20*w^3 - 3*w^2 + 29*w + 9],\
[691, 691, w^5 + w^4 - 8*w^3 - 7*w^2 + 14*w + 9],\
[691, 691, -w^5 + w^4 + 6*w^3 - 3*w^2 - 7*w + 2],\
[701, 701, -2*w^5 + w^4 + 13*w^3 - 2*w^2 - 19*w - 9],\
[701, 701, 5*w^5 - 2*w^4 - 33*w^3 + 3*w^2 + 48*w + 14],\
[701, 701, w^4 + 3*w^3 - 3*w^2 - 10*w - 1],\
[701, 701, -2*w^5 + w^4 + 14*w^3 - 3*w^2 - 24*w - 3],\
[709, 709, -2*w^5 + 2*w^4 + 14*w^3 - 7*w^2 - 22*w - 5],\
[709, 709, -3*w^5 + 21*w^3 + 4*w^2 - 34*w - 11],\
[719, 719, 5*w^5 - 2*w^4 - 35*w^3 + 3*w^2 + 58*w + 17],\
[719, 719, 4*w^5 - 2*w^4 - 26*w^3 + 4*w^2 + 37*w + 11],\
[719, 719, 4*w^5 - 2*w^4 - 27*w^3 + 4*w^2 + 40*w + 12],\
[719, 719, 2*w^5 - 16*w^3 - 3*w^2 + 30*w + 10],\
[739, 739, -5*w^5 + w^4 + 34*w^3 + w^2 - 51*w - 17],\
[751, 751, -w^5 - w^4 + 9*w^3 + 7*w^2 - 18*w - 10],\
[761, 761, 4*w^5 - 2*w^4 - 28*w^3 + 3*w^2 + 46*w + 16],\
[761, 761, -4*w^5 + 2*w^4 + 27*w^3 - 5*w^2 - 43*w - 12],\
[769, 769, -4*w^5 + w^4 + 28*w^3 - 44*w - 12],\
[769, 769, -w^4 + w^3 + 3*w^2 - 3*w + 1],\
[809, 809, 2*w^5 - 2*w^4 - 13*w^3 + 7*w^2 + 20*w + 1],\
[811, 811, -2*w^5 + 15*w^3 + 2*w^2 - 24*w - 8],\
[811, 811, -w^5 + 9*w^3 + w^2 - 18*w - 6],\
[821, 821, -w^5 + 8*w^3 + 3*w^2 - 17*w - 9],\
[821, 821, w^5 + w^4 - 7*w^3 - 6*w^2 + 11*w + 8],\
[821, 821, 4*w^5 - 2*w^4 - 28*w^3 + 4*w^2 + 46*w + 11],\
[821, 821, 5*w^5 - 2*w^4 - 34*w^3 + 4*w^2 + 51*w + 13],\
[829, 829, -2*w^5 + w^4 + 15*w^3 - w^2 - 28*w - 10],\
[829, 829, -6*w^5 + 3*w^4 + 42*w^3 - 7*w^2 - 68*w - 21],\
[829, 829, 4*w^5 - 2*w^4 - 26*w^3 + 5*w^2 + 38*w + 12],\
[829, 829, w^5 - 7*w^3 - 3*w^2 + 11*w + 6],\
[839, 839, 3*w^5 - 2*w^4 - 20*w^3 + 5*w^2 + 32*w + 11],\
[839, 839, -w^4 + w^3 + 6*w^2 - 3*w - 4],\
[841, 29, -3*w^5 + w^4 + 22*w^3 - 38*w - 11],\
[911, 911, 3*w^5 - w^4 - 21*w^3 + 36*w + 12],\
[919, 919, -w^5 - w^4 + 7*w^3 + 6*w^2 - 12*w - 5],\
[941, 941, -w^5 + w^4 + 7*w^3 - 5*w^2 - 11*w],\
[941, 941, 4*w^5 - w^4 - 29*w^3 + 48*w + 15],\
[971, 971, -4*w^5 + w^4 + 27*w^3 + w^2 - 41*w - 13],\
[991, 991, w^5 - w^4 - 8*w^3 + 3*w^2 + 16*w + 2],\
[991, 991, -4*w^5 + 3*w^4 + 27*w^3 - 9*w^2 - 42*w - 10]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^8 + 6*x^7 - 7*x^6 - 86*x^5 - 78*x^4 + 140*x^3 + 69*x^2 - 88*x + 16
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -5/24*e^7 - 4/3*e^6 + 7/8*e^5 + 109/6*e^4 + 293/12*e^3 - 37/2*e^2 - 197/8*e + 59/6, -1/12*e^7 - 7/12*e^6 + 43/6*e^4 + 167/12*e^3 + 5/2*e^2 - 29/4*e - 11/3, 1, 1/6*e^7 + 7/6*e^6 - 1/4*e^5 - 95/6*e^4 - 313/12*e^3 + 59/4*e^2 + 121/4*e - 29/3, -7/24*e^7 - 23/12*e^6 + 11/8*e^5 + 82/3*e^4 + 191/6*e^3 - 83/2*e^2 - 267/8*e + 109/6, 25/24*e^7 + 83/12*e^6 - 27/8*e^5 - 280/3*e^4 - 1597/12*e^3 + 325/4*e^2 + 863/8*e - 253/6, 1/4*e^7 + 2*e^6 + e^5 - 101/4*e^4 - 56*e^3 - 3/4*e^2 + 177/4*e - 3, 5/8*e^7 + 4*e^6 - 21/8*e^5 - 54*e^4 - 287/4*e^3 + 93/2*e^2 + 443/8*e - 27/2, 9/8*e^7 + 29/4*e^6 - 37/8*e^5 - 393/4*e^4 - 131*e^3 + 363/4*e^2 + 859/8*e - 83/2, -1/6*e^7 - 7/6*e^6 + 1/4*e^5 + 46/3*e^4 + 295/12*e^3 - 27/4*e^2 - 55/4*e - 13/3, 1/12*e^7 + 5/6*e^6 + 5/4*e^5 - 113/12*e^4 - 359/12*e^3 - 29/2*e^2 + 14*e + 17/3, -5/24*e^7 - 4/3*e^6 + 7/8*e^5 + 221/12*e^4 + 74/3*e^3 - 43/2*e^2 - 211/8*e + 53/6, -11/24*e^7 - 37/12*e^6 + 9/8*e^5 + 122/3*e^4 + 755/12*e^3 - 95/4*e^2 - 381/8*e + 47/6, 1/3*e^7 + 25/12*e^6 - 7/4*e^5 - 175/6*e^4 - 419/12*e^3 + 79/2*e^2 + 43*e - 64/3, -3/8*e^7 - 5/2*e^6 + 5/8*e^5 + 127/4*e^4 + 223/4*e^3 - 19/4*e^2 - 341/8*e + 5/2, -2/3*e^7 - 25/6*e^6 + 15/4*e^5 + 703/12*e^4 + 389/6*e^3 - 319/4*e^2 - 64*e + 98/3, 5/12*e^7 + 29/12*e^6 - 11/4*e^5 - 97/3*e^4 - 100/3*e^3 + 105/4*e^2 + 11*e - 32/3, 11/24*e^7 + 37/12*e^6 - 5/8*e^5 - 235/6*e^4 - 839/12*e^3 + 21/4*e^2 + 389/8*e - 35/6, -3/4*e^7 - 9/2*e^6 + 17/4*e^5 + 121/2*e^4 + 143/2*e^3 - 52*e^2 - 203/4*e + 17, 9/8*e^7 + 29/4*e^6 - 33/8*e^5 - 387/4*e^4 - 138*e^3 + 293/4*e^2 + 907/8*e - 75/2, -7/24*e^7 - 23/12*e^6 + 7/8*e^5 + 307/12*e^4 + 463/12*e^3 - 19*e^2 - 261/8*e + 31/6, -1/4*e^7 - 7/4*e^6 + 1/4*e^5 + 23*e^4 + 40*e^3 - 49/4*e^2 - 79/2*e + 4, 2/3*e^7 + 25/6*e^6 - 13/4*e^5 - 679/12*e^4 - 211/3*e^3 + 221/4*e^2 + 97/2*e - 92/3, 2/3*e^7 + 47/12*e^6 - 19/4*e^5 - 166/3*e^4 - 625/12*e^3 + 80*e^2 + 60*e - 92/3, -1/4*e^7 - 2*e^6 - 3/4*e^5 + 26*e^4 + 105/2*e^3 - 9*e^2 - 167/4*e + 5, -1/24*e^7 - 2/3*e^6 - 15/8*e^5 + 22/3*e^4 + 197/6*e^3 + 61/4*e^2 - 267/8*e - 59/6, -1/4*e^7 - 5/4*e^6 + 11/4*e^5 + 37/2*e^4 + 7*e^3 - 149/4*e^2 - 14*e + 8, -17/12*e^7 - 55/6*e^6 + 21/4*e^5 + 737/6*e^4 + 1037/6*e^3 - 99*e^2 - 571/4*e + 149/3, 17/24*e^7 + 13/3*e^6 - 29/8*e^5 - 349/6*e^4 - 439/6*e^3 + 193/4*e^2 + 491/8*e - 89/6, -7/8*e^7 - 11/2*e^6 + 31/8*e^5 + 147/2*e^4 + 387/4*e^3 - 58*e^2 - 505/8*e + 53/2, -5/12*e^7 - 19/6*e^6 - 1/2*e^5 + 251/6*e^4 + 943/12*e^3 - 95/4*e^2 - 72*e + 56/3, -7/12*e^7 - 49/12*e^6 + e^5 + 164/3*e^4 + 1031/12*e^3 - 83/2*e^2 - 273/4*e + 67/3, -1/3*e^7 - 11/6*e^6 + 11/4*e^5 + 151/6*e^4 + 233/12*e^3 - 115/4*e^2 - 11/4*e + 25/3, -1/4*e^7 - 3/2*e^6 + 5/4*e^5 + 77/4*e^4 + 99/4*e^3 - 13/2*e^2 - 4*e - 2, -19/12*e^7 - 31/3*e^6 + 25/4*e^5 + 1697/12*e^4 + 2255/12*e^3 - 148*e^2 - 161*e + 214/3, 1/6*e^7 + 2/3*e^6 - 13/4*e^5 - 151/12*e^4 + 85/6*e^3 + 217/4*e^2 + 2*e - 56/3, 23/24*e^7 + 19/3*e^6 - 25/8*e^5 - 1031/12*e^4 - 745/6*e^3 + 82*e^2 + 989/8*e - 251/6, -11/24*e^7 - 37/12*e^6 + 11/8*e^5 + 253/6*e^4 + 367/6*e^3 - 87/2*e^2 - 515/8*e + 77/6, -25/12*e^7 - 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803/4*e^4 - 979/4*e^3 + 198*e^2 + 1539/8*e - 171/2, 5/6*e^7 + 67/12*e^6 - 3/2*e^5 - 427/6*e^4 - 368/3*e^3 + 43/4*e^2 + 385/4*e - 1/3, 1/12*e^7 + 1/3*e^6 - 7/4*e^5 - 83/12*e^4 + 103/12*e^3 + 34*e^2 + 6*e + 8/3, 7/4*e^7 + 45/4*e^6 - 29/4*e^5 - 611/4*e^4 - 817/4*e^3 + 577/4*e^2 + 741/4*e - 57, 3/4*e^6 + 13/4*e^5 - 35/4*e^4 - 85/2*e^3 - 27/2*e^2 + 111/4*e - 3, 7/24*e^7 + 17/12*e^6 - 31/8*e^5 - 70/3*e^4 - 1/3*e^3 + 145/2*e^2 + 203/8*e - 145/6, -29/24*e^7 - 97/12*e^6 + 31/8*e^5 + 1319/12*e^4 + 467/3*e^3 - 419/4*e^2 - 1093/8*e + 287/6, 3/2*e^7 + 19/2*e^6 - 11/2*e^5 - 123*e^4 - 181*e^3 + 89/2*e^2 + 110*e + 2, 13/12*e^7 + 91/12*e^6 - 5/2*e^5 - 1259/12*e^4 - 925/6*e^3 + 121*e^2 + 165*e - 184/3, 31/24*e^7 + 101/12*e^6 - 47/8*e^5 - 355/3*e^4 - 436/3*e^3 + 321/2*e^2 + 1267/8*e - 481/6, -3/4*e^7 - 5*e^6 + 3*e^5 + 283/4*e^4 + 92*e^3 - 411/4*e^2 - 503/4*e + 61, 5/3*e^7 + 67/6*e^6 - 11/2*e^5 - 1837/12*e^4 - 2551/12*e^3 + 162*e^2 + 781/4*e - 239/3, 35/24*e^7 + 28/3*e^6 - 55/8*e^5 - 1547/12*e^4 - 1895/12*e^3 + 599/4*e^2 + 1083/8*e - 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35*e - 2/3, 7/24*e^7 + 5/3*e^6 - 11/8*e^5 - 61/3*e^4 - 94/3*e^3 - 21/4*e^2 + 153/8*e - 31/6, -17/12*e^7 - 26/3*e^6 + 17/2*e^5 + 1459/12*e^4 + 394/3*e^3 - 669/4*e^2 - 543/4*e + 203/3, 11/12*e^7 + 37/6*e^6 - e^5 - 229/3*e^4 - 1693/12*e^3 - 65/4*e^2 + 71*e + 82/3, 1/4*e^7 + 3/2*e^6 - 2*e^5 - 43/2*e^4 - 61/4*e^3 + 115/4*e^2 + 9/2*e + 22, 29/24*e^7 + 85/12*e^6 - 65/8*e^5 - 1181/12*e^4 - 1199/12*e^3 + 259/2*e^2 + 779/8*e - 485/6, 2*e^7 + 13*e^6 - 9*e^5 - 725/4*e^4 - 889/4*e^3 + 229*e^2 + 799/4*e - 107, -11/24*e^7 - 43/12*e^6 - 19/8*e^5 + 125/3*e^4 + 1301/12*e^3 + 177/4*e^2 - 493/8*e - 97/6, 1/2*e^7 + 5/2*e^6 - 25/4*e^5 - 159/4*e^4 - 4*e^3 + 439/4*e^2 + 21*e - 36, -1/3*e^7 - 19/12*e^6 + 15/4*e^5 + 269/12*e^4 + 43/6*e^3 - 38*e^2 - 13/4*e + 67/3, -19/12*e^7 - 31/3*e^6 + 7*e^5 + 434/3*e^4 + 2177/12*e^3 - 769/4*e^2 - 415/2*e + 316/3, -5/6*e^7 - 67/12*e^6 + 3/2*e^5 + 215/3*e^4 + 733/6*e^3 - 59/4*e^2 - 335/4*e - 77/3, -13/8*e^7 - 43/4*e^6 + 35/8*e^5 + 281/2*e^4 + 218*e^3 - 66*e^2 - 1187/8*e + 55/2, 13/12*e^7 + 79/12*e^6 - 7*e^5 - 1127/12*e^4 - 281/3*e^3 + 287/2*e^2 + 193/2*e - 142/3, 11/12*e^7 + 77/12*e^6 + 1/4*e^5 - 473/6*e^4 - 475/3*e^3 - 97/4*e^2 + 205/2*e + 40/3, -5/6*e^7 - 73/12*e^6 - 1/4*e^5 + 481/6*e^4 + 1769/12*e^3 - 44*e^2 - 130*e + 100/3, -85/24*e^7 - 275/12*e^6 + 101/8*e^5 + 3661/12*e^4 + 5257/12*e^3 - 439/2*e^2 - 2763/8*e + 601/6, 7/3*e^7 + 46/3*e^6 - 17/2*e^5 - 2495/12*e^4 - 3413/12*e^3 + 383/2*e^2 + 893/4*e - 253/3, -13/6*e^7 - 41/3*e^6 + 41/4*e^5 + 2239/12*e^4 + 1415/6*e^3 - 761/4*e^2 - 216*e + 224/3, -11/4*e^7 - 71/4*e^6 + 39/4*e^5 + 473/2*e^4 + 683/2*e^3 - 701/4*e^2 - 553/2*e + 88, -1/8*e^7 - e^6 - 3/8*e^5 + 51/4*e^4 + 24*e^3 - e^2 + 75/8*e + 17/2, 7/6*e^7 + 101/12*e^6 - 3/4*e^5 - 671/6*e^4 - 2269/12*e^3 + 74*e^2 + 156*e - 86/3, 59/24*e^7 + 49/3*e^6 - 59/8*e^5 - 653/3*e^4 - 1915/6*e^3 + 617/4*e^2 + 1841/8*e - 311/6, -3/4*e^7 - 17/4*e^6 + 27/4*e^5 + 251/4*e^4 + 151/4*e^3 - 487/4*e^2 - 123/4*e + 41, 5/2*e^7 + 65/4*e^6 - 37/4*e^5 - 877/4*e^4 - 306*e^3 + 192*e^2 + 1061/4*e - 111, -7/4*e^7 - 45/4*e^6 + 15/2*e^5 + 153*e^4 + 805/4*e^3 - 144*e^2 - 737/4*e + 49, 1/6*e^7 + 7/6*e^6 + 1/4*e^5 - 169/12*e^4 - 203/6*e^3 - 35/4*e^2 + 81/2*e + 40/3, 3/2*e^7 + 21/2*e^6 - 3/2*e^5 - 136*e^4 - 234*e^3 + 87/2*e^2 + 153*e - 2, -11/3*e^7 - 145/6*e^6 + 25/2*e^5 + 1955/6*e^4 + 1378/3*e^3 - 283*e^2 - 729/2*e + 422/3, -13/12*e^7 - 79/12*e^6 + 25/4*e^5 + 1109/12*e^4 + 1295/12*e^3 - 525/4*e^2 - 617/4*e + 223/3, -41/24*e^7 - 71/6*e^6 + 29/8*e^5 + 1913/12*e^4 + 2921/12*e^3 - 531/4*e^2 - 1637/8*e + 359/6, 2/3*e^7 + 41/12*e^6 - 33/4*e^5 - 160/3*e^4 - 43/12*e^3 + 137*e^2 + 10*e - 194/3, -25/12*e^7 - 163/12*e^6 + 31/4*e^5 + 1099/6*e^4 + 1513/6*e^3 - 631/4*e^2 - 187*e + 220/3, -41/12*e^7 - 127/6*e^6 + 37/2*e^5 + 3499/12*e^4 + 1021/3*e^3 - 1319/4*e^2 - 1213/4*e + 443/3, 5/24*e^7 + 7/3*e^6 + 29/8*e^5 - 341/12*e^4 - 493/6*e^3 - 15*e^2 + 439/8*e - 101/6]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([25, 5, w^3 + w^2 - 4*w - 3])] = -1

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