/*
  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^10 - 2*x^9 - 31*x^8 + 50*x^7 + 332*x^6 - 374*x^5 - 1471*x^4 + 822*x^3 + 2372*x^2 + 168*x - 544
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 101/17751*e^9 - 241/35502*e^8 - 3337/17751*e^7 + 1875/11834*e^6 + 75713/35502*e^5 - 13405/11834*e^4 - 168194/17751*e^3 + 52888/17751*e^2 + 224654/17751*e - 1882/17751, -1823/142008*e^9 + 634/17751*e^8 + 52573/142008*e^7 - 11329/11834*e^6 - 61730/17751*e^5 + 192109/23668*e^4 + 1657265/142008*e^3 - 416540/17751*e^2 - 298709/35502*e + 222530/17751, -1, 135/5917*e^9 - 1863/23668*e^8 - 4008/5917*e^7 + 51779/23668*e^6 + 80189/11834*e^5 - 227473/11834*e^4 - 314689/11834*e^3 + 1327349/23668*e^2 + 384837/11834*e - 112648/5917, -4381/142008*e^9 + 2497/35502*e^8 + 126935/142008*e^7 - 10678/5917*e^6 - 297089/35502*e^5 + 336221/23668*e^4 + 3965635/142008*e^3 - 643267/17751*e^2 - 764653/35502*e + 231898/17751, -4969/284016*e^9 + 3397/71004*e^8 + 146927/284016*e^7 - 14367/11834*e^6 - 369467/71004*e^5 + 444177/47336*e^4 + 5800675/284016*e^3 - 1637525/71004*e^2 - 1414675/71004*e + 87953/17751, 10021/284016*e^9 - 8671/71004*e^8 - 268643/284016*e^7 + 18583/5917*e^6 + 585863/71004*e^5 - 1180077/47336*e^4 - 8160871/284016*e^3 + 4677371/71004*e^2 + 2603023/71004*e - 452981/17751, -319/5917*e^9 + 795/5917*e^8 + 9197/5917*e^7 - 20318/5917*e^6 - 173225/11834*e^5 + 320111/11834*e^4 + 300478/5917*e^3 - 834037/11834*e^2 - 279277/5917*e + 157510/5917, -1057/94672*e^9 + 1507/23668*e^8 + 26335/94672*e^7 - 9935/5917*e^6 - 54843/23668*e^5 + 656715/47336*e^4 + 859139/94672*e^3 - 912889/23668*e^2 - 382203/23668*e + 93317/5917, -561/47336*e^9 + 245/11834*e^8 + 16843/47336*e^7 - 5951/11834*e^6 - 41557/11834*e^5 + 1401/388*e^4 + 608987/47336*e^3 - 81371/11834*e^2 - 158459/11834*e - 39544/5917, -665/17751*e^9 + 125/1164*e^8 + 19312/17751*e^7 - 67773/23668*e^6 - 370985/35502*e^5 + 140447/5917*e^4 + 678335/17751*e^3 - 4571773/71004*e^2 - 1442473/35502*e + 442135/17751, 653/35502*e^9 - 736/17751*e^8 - 9161/17751*e^7 + 6447/5917*e^6 + 165043/35502*e^5 - 111561/11834*e^4 - 266860/17751*e^3 + 551540/17751*e^2 + 193945/17751*e - 348176/17751, -41/776*e^9 + 947/5917*e^8 + 70387/47336*e^7 - 24170/5917*e^6 - 163195/11834*e^5 + 753209/23668*e^4 + 2326275/47336*e^3 - 950297/11834*e^2 - 602719/11834*e + 168424/5917, 113/11834*e^9 - 241/5917*e^8 - 1630/5917*e^7 + 6401/5917*e^6 + 34153/11834*e^5 - 104777/11834*e^4 - 83800/5917*e^3 + 142054/5917*e^2 + 155010/5917*e - 70500/5917, 8147/142008*e^9 - 3223/17751*e^8 - 225685/142008*e^7 + 27208/5917*e^6 + 256499/17751*e^5 - 838291/23668*e^4 - 7221845/142008*e^3 + 1563806/17751*e^2 + 2042153/35502*e - 485990/17751, -2941/71004*e^9 + 2419/17751*e^8 + 81467/71004*e^7 - 42063/11834*e^6 - 184124/17751*e^5 + 171960/5917*e^4 + 2488213/71004*e^3 - 2914345/35502*e^2 - 544768/17751*e + 785042/17751, 8173/284016*e^9 - 5011/71004*e^8 - 231419/284016*e^7 + 10167/5917*e^6 + 543881/71004*e^5 - 583321/47336*e^4 - 8069599/284016*e^3 + 1910069/71004*e^2 + 2344675/71004*e - 38453/17751, 2741/284016*e^9 - 743/71004*e^8 - 92515/284016*e^7 + 1534/5917*e^6 + 260059/71004*e^5 - 81637/47336*e^4 - 4278839/284016*e^3 + 82783/71004*e^2 + 1112387/71004*e + 135371/17751, -163/47336*e^9 + 100/5917*e^8 + 6221/47336*e^7 - 5533/11834*e^6 - 21807/11834*e^5 + 91985/23668*e^4 + 509281/47336*e^3 - 50154/5917*e^2 - 246267/11834*e - 19556/5917, 1251/47336*e^9 - 414/5917*e^8 - 36617/47336*e^7 + 10655/5917*e^6 + 88599/11834*e^5 - 341271/23668*e^4 - 1301265/47336*e^3 + 240862/5917*e^2 + 339329/11834*e - 149192/5917, 263/47336*e^9 - 34/5917*e^8 - 6905/47336*e^7 + 1565/11834*e^6 + 13861/11834*e^5 - 31013/23668*e^4 - 159205/47336*e^3 + 45000/5917*e^2 + 41561/11834*e - 41882/5917, 4781/71004*e^9 - 5587/35502*e^8 - 138595/71004*e^7 + 23890/5917*e^6 + 657971/35502*e^5 - 379085/11834*e^4 - 4639385/71004*e^3 + 48941/582*e^2 + 1142906/17751*e - 536842/17751, -260/17751*e^9 + 509/17751*e^8 + 7288/17751*e^7 - 7997/11834*e^6 - 1069/291*e^5 + 53421/11834*e^4 + 412603/35502*e^3 - 294863/35502*e^2 - 108479/17751*e + 15436/17751, -1579/94672*e^9 + 1625/23668*e^8 + 34965/94672*e^7 - 20459/11834*e^6 - 47699/23668*e^5 + 632809/47336*e^4 + 43817/94672*e^3 - 814663/23668*e^2 + 217895/23668*e + 81889/5917, -3343/142008*e^9 + 2191/35502*e^8 + 103865/142008*e^7 - 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4151971/47336*e^4 - 33259165/284016*e^3 + 15460013/71004*e^2 + 9910381/71004*e - 1117721/17751, 17375/142008*e^9 - 19993/71004*e^8 - 504517/142008*e^7 + 170647/23668*e^6 + 603356/17751*e^5 - 1342179/23668*e^4 - 17453489/142008*e^3 + 10256087/71004*e^2 + 2228503/17751*e - 755390/17751, -3805/94672*e^9 + 4949/23668*e^8 + 110843/94672*e^7 - 70843/11834*e^6 - 276347/23668*e^5 + 2574519/47336*e^4 + 4502815/94672*e^3 - 3860377/23668*e^2 - 1461623/23668*e + 358777/5917, -6391/47336*e^9 + 2570/5917*e^8 + 176845/47336*e^7 - 66574/5917*e^6 - 396345/11834*e^5 + 2124667/23668*e^4 + 5311925/47336*e^3 - 1410169/5917*e^2 - 1298671/11834*e + 631884/5917, -5305/142008*e^9 + 3745/35502*e^8 + 135071/142008*e^7 - 14244/5917*e^6 - 133432/17751*e^5 + 371535/23668*e^4 + 3269803/142008*e^3 - 594643/17751*e^2 - 1099273/35502*e + 290824/17751, 1129/35502*e^9 - 1213/35502*e^8 - 17932/17751*e^7 + 11791/11834*e^6 + 375437/35502*e^5 - 117493/11834*e^4 - 714956/17751*e^3 + 1297295/35502*e^2 + 649673/17751*e - 304858/17751, -15235/284016*e^9 + 16711/71004*e^8 + 388301/284016*e^7 - 72365/11834*e^6 - 778247/71004*e^5 + 2292687/47336*e^4 + 9436057/284016*e^3 - 8432255/71004*e^2 - 2678389/71004*e + 377561/17751, -9139/142008*e^9 + 2351/17751*e^8 + 262517/142008*e^7 - 18683/5917*e^6 - 300922/17751*e^5 + 520727/23668*e^4 + 7681021/142008*e^3 - 829162/17751*e^2 - 1522939/35502*e + 259540/17751, 3833/142008*e^9 - 646/17751*e^8 - 114511/142008*e^7 + 10429/11834*e^6 + 270343/35502*e^5 - 153477/23668*e^4 - 3157979/142008*e^3 + 305495/17751*e^2 - 284131/35502*e - 93284/17751, -6191/94672*e^9 + 4143/23668*e^8 + 188281/94672*e^7 - 28384/5917*e^6 - 478779/23668*e^5 + 1992277/47336*e^4 + 7304893/94672*e^3 - 3002071/23668*e^2 - 1827781/23668*e + 298251/5917, -2721/47336*e^9 + 2955/23668*e^8 + 75539/47336*e^7 - 70161/23668*e^6 - 82101/5917*e^5 + 483581/23668*e^4 + 1832131/47336*e^3 - 978611/23668*e^2 - 73884/5917*e - 1264/5917, -2267/47336*e^9 + 841/11834*e^8 + 75041/47336*e^7 - 22903/11834*e^6 - 103159/5917*e^5 + 400617/23668*e^4 + 3314745/47336*e^3 - 313154/5917*e^2 - 858115/11834*e + 238676/5917, -512/17751*e^9 + 3008/17751*e^8 + 13819/17751*e^7 - 55021/11834*e^6 - 250157/35502*e^5 + 231785/5917*e^4 + 969073/35502*e^3 - 1777171/17751*e^2 - 814280/17751*e + 104320/17751, 13507/94672*e^9 - 8353/23668*e^8 - 388525/94672*e^7 + 53174/5917*e^6 + 918945/23668*e^5 - 3355849/47336*e^4 - 12991865/94672*e^3 + 4452771/23668*e^2 + 2931925/23668*e - 394065/5917, -13721/142008*e^9 + 4852/17751*e^8 + 412291/142008*e^7 - 44254/5917*e^6 - 1025569/35502*e^5 + 1528651/23668*e^4 + 15041843/142008*e^3 - 3352097/17751*e^2 - 3241697/35502*e + 1617080/17751, -8263/94672*e^9 + 7453/23668*e^8 + 230793/94672*e^7 - 98385/11834*e^6 - 543151/23668*e^5 + 3274093/47336*e^4 + 8399309/94672*e^3 - 4670103/23668*e^2 - 2826849/23668*e + 496363/5917, -10993/142008*e^9 + 4922/17751*e^8 + 298199/142008*e^7 - 42211/5917*e^6 - 646655/35502*e^5 + 1332915/23668*e^4 + 8237887/142008*e^3 - 5234651/35502*e^2 - 31471/582*e + 1090222/17751, 13241/284016*e^9 - 6671/71004*e^8 - 378511/284016*e^7 + 13762/5917*e^6 + 847555/71004*e^5 - 832785/47336*e^4 - 9771731/284016*e^3 + 3162907/71004*e^2 + 786179/71004*e - 561625/17751, 29005/142008*e^9 - 19021/35502*e^8 - 851243/142008*e^7 + 165581/11834*e^6 + 2072669/35502*e^5 - 2683083/23668*e^4 - 30813115/142008*e^3 + 87805/291*e^2 + 8359339/35502*e - 1655944/17751, -6835/47336*e^9 + 2114/5917*e^8 + 202417/47336*e^7 - 54824/5917*e^6 - 495693/11834*e^5 + 1752823/23668*e^4 + 7239065/47336*e^3 - 1152747/5917*e^2 - 1751183/11834*e + 440450/5917, 1841/17751*e^9 - 5687/17751*e^8 - 50566/17751*e^7 + 94171/11834*e^6 + 454747/17751*e^5 - 699603/11834*e^4 - 3159391/35502*e^3 + 4812923/35502*e^2 + 1603409/17751*e - 506854/17751, -1195/35502*e^9 + 1601/71004*e^8 + 19345/17751*e^7 - 241/388*e^6 - 405629/35502*e^5 + 30998/5917*e^4 + 731510/17751*e^3 - 688135/71004*e^2 - 1008379/35502*e - 301628/17751, 1166/17751*e^9 - 9359/71004*e^8 - 60761/35502*e^7 + 65701/23668*e^6 + 238609/17751*e^5 - 85874/5917*e^4 - 558815/17751*e^3 + 794185/71004*e^2 - 110675/35502*e + 383858/17751, -1481/142008*e^9 + 1174/17751*e^8 + 47347/142008*e^7 - 23015/11834*e^6 - 142045/35502*e^5 + 429753/23668*e^4 + 3240647/142008*e^3 - 1947955/35502*e^2 - 1862573/35502*e + 37892/17751, 16601/284016*e^9 - 3749/71004*e^8 - 499735/284016*e^7 + 14363/11834*e^6 + 1210759/71004*e^5 - 407841/47336*e^4 - 16140107/284016*e^3 + 1437451/71004*e^2 + 2270699/71004*e + 4415/291, -7441/71004*e^9 + 4627/17751*e^8 + 223409/71004*e^7 - 41100/5917*e^6 - 561329/17751*e^5 + 692183/11834*e^4 + 8617993/71004*e^3 - 5890681/35502*e^2 - 2231530/17751*e + 1147466/17751, -2093/71004*e^9 + 3511/35502*e^8 + 51859/71004*e^7 - 13539/5917*e^6 - 192779/35502*e^5 + 175491/11834*e^4 + 981293/71004*e^3 - 830093/35502*e^2 - 227375/17751*e - 233294/17751, -1147/23668*e^9 + 2757/11834*e^8 + 32693/23668*e^7 - 39234/5917*e^6 - 76423/5917*e^5 + 356472/5917*e^4 + 1055959/23668*e^3 - 1098155/5917*e^2 - 271804/5917*e + 537090/5917, -7021/142008*e^9 + 2387/17751*e^8 + 213203/142008*e^7 - 21116/5917*e^6 - 270550/17751*e^5 + 699905/23668*e^4 + 8404819/142008*e^3 - 1430428/17751*e^2 - 2695477/35502*e + 244282/17751, 937/35502*e^9 - 7445/71004*e^8 - 22643/35502*e^7 + 61331/23668*e^6 + 76357/17751*e^5 - 115312/5917*e^4 - 103370/17751*e^3 + 3765985/71004*e^2 - 636191/35502*e - 777088/17751, -17647/142008*e^9 + 13597/35502*e^8 + 491261/142008*e^7 - 57469/5917*e^6 - 1118165/35502*e^5 + 1772503/23668*e^4 + 15725065/142008*e^3 - 3311578/17751*e^2 - 4607875/35502*e + 1022908/17751, -1847/142008*e^9 - 1243/35502*e^8 + 72013/142008*e^7 + 5333/5917*e^6 - 226441/35502*e^5 - 145277/23668*e^4 + 4022489/142008*e^3 + 106006/17751*e^2 - 1009043/35502*e + 273848/17751, -9625/71004*e^9 + 7762/17751*e^8 + 268565/71004*e^7 - 137687/11834*e^6 - 1220539/35502*e^5 + 1153053/11834*e^4 + 8403379/71004*e^3 - 9831571/35502*e^2 - 2216380/17751*e + 2252624/17751, -6691/71004*e^9 + 4162/17751*e^8 + 3149/1164*e^7 - 71291/11834*e^6 - 457382/17751*e^5 + 285779/5917*e^4 + 6727243/71004*e^3 - 4693897/35502*e^2 - 1724296/17751*e + 1039532/17751, -2405/142008*e^9 - 187/35502*e^8 + 93895/142008*e^7 - 2599/11834*e^6 - 293695/35502*e^5 + 151563/23668*e^4 + 5145191/142008*e^3 - 1215745/35502*e^2 - 1278215/35502*e + 501308/17751, 2079/11834*e^9 - 10145/23668*e^8 - 60113/11834*e^7 + 260289/23668*e^6 + 570517/11834*e^5 - 1028281/11834*e^4 - 1016539/5917*e^3 + 5319963/23668*e^2 + 2046915/11834*e - 414710/5917, 3607/47336*e^9 - 2603/11834*e^8 - 100425/47336*e^7 + 33492/5917*e^6 + 227125/11834*e^5 - 1081505/23668*e^4 - 3060429/47336*e^3 + 1489085/11834*e^2 + 669763/11834*e - 213428/5917, -7355/35502*e^9 + 36733/71004*e^8 + 211561/35502*e^7 - 313077/23668*e^6 - 2003677/35502*e^5 + 616918/5917*e^4 + 7167929/35502*e^3 - 19246205/71004*e^2 - 7194821/35502*e + 1656374/17751, -11039/284016*e^9 + 6947/71004*e^8 + 301897/284016*e^7 - 27975/11834*e^6 - 673873/71004*e^5 + 815511/47336*e^4 + 9226853/284016*e^3 - 2861503/71004*e^2 - 2280989/71004*e + 393331/17751, -6959/47336*e^9 + 1908/5917*e^8 + 203529/47336*e^7 - 48996/5917*e^6 - 485289/11834*e^5 + 1562975/23668*e^4 + 6735705/47336*e^3 - 2142979/11834*e^2 - 1498853/11834*e + 561354/5917, 8311/142008*e^9 - 14465/71004*e^8 - 243677/142008*e^7 + 138163/23668*e^6 + 591779/35502*e^5 - 1277241/23668*e^4 - 8696857/142008*e^3 + 12195733/71004*e^2 + 1035176/17751*e - 1635652/17751, 2433/47336*e^9 - 503/5917*e^8 - 66523/47336*e^7 + 10779/5917*e^6 + 146459/11834*e^5 - 254605/23668*e^4 - 1955803/47336*e^3 + 133017/5917*e^2 + 483061/11834*e - 213240/5917, 5431/71004*e^9 - 11719/71004*e^8 - 157979/71004*e^7 + 97869/23668*e^6 + 373706/17751*e^5 - 382779/11834*e^4 - 5083189/71004*e^3 + 6689381/71004*e^2 + 1901903/35502*e - 1038716/17751, 589/4656*e^9 - 21661/71004*e^8 - 997031/284016*e^7 + 42908/5917*e^6 + 2260883/71004*e^5 - 2394461/47336*e^4 - 31200787/284016*e^3 + 7863161/71004*e^2 + 7964299/71004*e - 717119/17751, -10999/284016*e^9 + 1141/71004*e^8 + 361841/284016*e^7 - 5451/11834*e^6 - 978023/71004*e^5 + 210911/47336*e^4 + 15218389/284016*e^3 - 976493/71004*e^2 - 64453/1164*e - 408847/17751, 1346/17751*e^9 - 18827/71004*e^8 - 75329/35502*e^7 + 168297/23668*e^6 + 349072/17751*e^5 - 354167/5917*e^4 - 1267511/17751*e^3 + 12058861/71004*e^2 + 2885641/35502*e - 1430536/17751, -6455/35502*e^9 + 7849/17751*e^8 + 92663/17751*e^7 - 65387/5917*e^6 - 1743235/35502*e^5 + 987695/11834*e^4 + 3070072/17751*e^3 - 3582035/17751*e^2 - 3208846/17751*e + 1167908/17751, 23597/284016*e^9 - 17771/71004*e^8 - 724795/284016*e^7 + 82851/11834*e^6 + 1899103/71004*e^5 - 2923041/47336*e^4 - 31851767/284016*e^3 + 12455965/71004*e^2 + 10802675/71004*e - 726949/17751, -31003/284016*e^9 + 16663/71004*e^8 + 926741/284016*e^7 - 35420/5917*e^6 - 2282861/71004*e^5 + 2216303/47336*e^4 + 33615193/284016*e^3 - 8542367/71004*e^2 - 9140269/71004*e + 992777/17751, -13615/142008*e^9 + 12331/35502*e^8 + 401897/142008*e^7 - 113137/11834*e^6 - 1007891/35502*e^5 + 1959581/23668*e^4 + 16075969/142008*e^3 - 4156072/17751*e^2 - 4880329/35502*e + 1031380/17751, -1829/142008*e^9 + 2539/17751*e^8 + 21931/142008*e^7 - 22885/5917*e^6 + 20809/17751*e^5 + 773425/23668*e^4 - 2153677/142008*e^3 - 1626104/17751*e^2 + 1023667/35502*e + 723512/17751, -1875/47336*e^9 + 848/5917*e^8 + 52401/47336*e^7 - 45395/11834*e^6 - 60215/5917*e^5 + 749439/23668*e^4 + 1755765/47336*e^3 - 492589/5917*e^2 - 567939/11834*e + 165036/5917, -19313/142008*e^9 + 34525/71004*e^8 + 538399/142008*e^7 - 302951/23668*e^6 - 1249807/35502*e^5 + 2456355/23668*e^4 + 18907715/142008*e^3 - 19092563/71004*e^2 - 3186196/17751*e + 1270694/17751, 308/17751*e^9 - 2455/35502*e^8 - 22205/35502*e^7 + 12096/5917*e^6 + 274517/35502*e^5 - 110293/5917*e^4 - 642317/17751*e^3 + 879427/17751*e^2 + 833966/17751*e + 169172/17751, 685/23668*e^9 + 237/11834*e^8 - 24745/23668*e^7 - 3280/5917*e^6 + 147763/11834*e^5 + 50455/11834*e^4 - 1273895/23668*e^3 - 24302/5917*e^2 + 341659/5917*e - 145066/5917, -336/5917*e^9 + 1523/11834*e^8 + 10454/5917*e^7 - 43469/11834*e^6 - 222023/11834*e^5 + 397541/11834*e^4 + 476807/5917*e^3 - 592274/5917*e^2 - 721266/5917*e + 225794/5917, 19297/142008*e^9 - 16657/35502*e^8 - 525827/142008*e^7 + 72456/5917*e^6 + 581992/17751*e^5 - 2325483/23668*e^4 - 16053991/142008*e^3 + 8988557/35502*e^2 + 4724263/35502*e - 1243078/17751, -9673/284016*e^9 + 13507/71004*e^8 + 288239/284016*e^7 - 31106/5917*e^6 - 778547/71004*e^5 + 2149785/47336*e^4 + 15596851/284016*e^3 - 9169547/71004*e^2 - 7682239/71004*e + 770741/17751, -159/5917*e^9 + 1457/23668*e^8 + 9163/11834*e^7 - 37799/23668*e^6 - 85939/11834*e^5 + 76126/5917*e^4 + 310761/11834*e^3 - 743767/23668*e^2 - 414931/11834*e - 78208/5917, 26177/142008*e^9 - 38101/71004*e^8 - 738019/142008*e^7 + 335303/23668*e^6 + 849056/17751*e^5 - 2800417/23668*e^4 - 23204159/142008*e^3 + 24310139/71004*e^2 + 2635762/17751*e - 2821796/17751, -3913/71004*e^9 + 391/17751*e^8 + 124409/71004*e^7 - 2879/11834*e^6 - 654247/35502*e^5 - 9291/11834*e^4 + 5019523/71004*e^3 + 279059/35502*e^2 - 1222192/17751*e - 450430/17751, 20045/142008*e^9 - 8314/17751*e^8 - 545827/142008*e^7 + 71472/5917*e^6 + 597992/17751*e^5 - 2277653/23668*e^4 - 15588419/142008*e^3 + 4599467/17751*e^2 + 3658763/35502*e - 1882286/17751, -25/388*e^9 + 31/194*e^8 + 753/388*e^7 - 829/194*e^6 - 3787/194*e^5 + 3485/97*e^4 + 28881/388*e^3 - 19775/194*e^2 - 7266/97*e + 5402/97, -5857/47336*e^9 + 4677/11834*e^8 + 2611/776*e^7 - 117481/11834*e^6 - 175102/5917*e^5 + 1815699/23668*e^4 + 4639279/47336*e^3 - 2423289/11834*e^2 - 1129315/11834*e + 695526/5917, -21553/142008*e^9 + 7439/17751*e^8 + 640943/142008*e^7 - 67764/5917*e^6 - 1583705/35502*e^5 + 2342615/23668*e^4 + 23715511/142008*e^3 - 10165403/35502*e^2 - 6004363/35502*e + 2165242/17751, -4293/94672*e^9 + 2683/23668*e^8 + 118123/94672*e^7 - 31029/11834*e^6 - 267625/23668*e^5 + 854071/47336*e^4 + 3811687/94672*e^3 - 1048709/23668*e^2 - 1125579/23668*e + 262911/5917]
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]