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

NN = ZF.ideal([11, 11, 1/2*w^5 + 1/2*w^4 - 4*w^3 - 5/2*w^2 + 6*w + 1/2])

primes_array = [
[4, 2, w + 1],\
[9, 3, -1/2*w^5 + 1/2*w^4 + 3*w^3 - 3/2*w^2 - 5*w + 1/2],\
[11, 11, 1/2*w^5 + 1/2*w^4 - 4*w^3 - 5/2*w^2 + 6*w + 1/2],\
[16, 2, -1/2*w^5 + 1/2*w^4 + 3*w^3 - 5/2*w^2 - 3*w + 5/2],\
[29, 29, -1/2*w^5 - 1/2*w^4 + 4*w^3 + 5/2*w^2 - 6*w + 1/2],\
[41, 41, 1/2*w^5 - 1/2*w^4 - 3*w^3 + 3/2*w^2 + 3*w + 3/2],\
[41, 41, 1/2*w^5 - 1/2*w^4 - 2*w^3 + 1/2*w^2 + 5/2],\
[59, 59, -3/2*w^5 + 1/2*w^4 + 9*w^3 + 1/2*w^2 - 11*w - 5/2],\
[59, 59, -1/2*w^5 - 1/2*w^4 + 3*w^3 + 5/2*w^2 - 4*w - 1/2],\
[59, 59, -1/2*w^5 + 1/2*w^4 + 2*w^3 - 1/2*w^2 - 3/2],\
[59, 59, 3/2*w^5 - 1/2*w^4 - 9*w^3 + 1/2*w^2 + 11*w - 1/2],\
[61, 61, 1/2*w^5 - 1/2*w^4 - 3*w^3 + 1/2*w^2 + 4*w + 5/2],\
[71, 71, -1/2*w^5 - 1/2*w^4 + 5*w^3 + 5/2*w^2 - 11*w - 3/2],\
[71, 71, -1/2*w^5 + 1/2*w^4 + 4*w^3 - 5/2*w^2 - 7*w + 3/2],\
[79, 79, -w^5 + 6*w^3 + 2*w^2 - 8*w - 2],\
[79, 79, -3/2*w^5 + 3/2*w^4 + 9*w^3 - 11/2*w^2 - 12*w + 3/2],\
[81, 3, 1/2*w^5 + 1/2*w^4 - 4*w^3 - 5/2*w^2 + 8*w + 3/2],\
[89, 89, 3/2*w^5 - 1/2*w^4 - 10*w^3 - 1/2*w^2 + 14*w + 7/2],\
[89, 89, 3/2*w^5 - 1/2*w^4 - 9*w^3 + 1/2*w^2 + 10*w - 1/2],\
[89, 89, 3/2*w^5 - 1/2*w^4 - 10*w^3 - 1/2*w^2 + 15*w + 9/2],\
[101, 101, -1/2*w^5 + 1/2*w^4 + 3*w^3 - 5/2*w^2 - 5*w + 7/2],\
[101, 101, -w^5 + 5*w^3 + w^2 - 4*w],\
[109, 109, 1/2*w^5 + 1/2*w^4 - 3*w^3 - 5/2*w^2 + 2*w + 3/2],\
[109, 109, -w^5 + 7*w^3 + w^2 - 11*w + 1],\
[121, 11, w^4 - 2*w^3 - 4*w^2 + 6*w],\
[125, 5, -1/2*w^5 + 1/2*w^4 + 3*w^3 - 3/2*w^2 - 4*w + 5/2],\
[131, 131, 3/2*w^5 - 5/2*w^4 - 6*w^3 + 17/2*w^2 + 2*w - 5/2],\
[139, 139, -3/2*w^5 - 1/2*w^4 + 11*w^3 + 7/2*w^2 - 17*w - 1/2],\
[139, 139, -1/2*w^5 - 1/2*w^4 + 3*w^3 + 7/2*w^2 - 4*w - 7/2],\
[139, 139, 3/2*w^5 + 1/2*w^4 - 9*w^3 - 9/2*w^2 + 10*w + 5/2],\
[139, 139, -1/2*w^5 - 1/2*w^4 + 4*w^3 + 7/2*w^2 - 6*w - 11/2],\
[149, 149, -w^5 + 6*w^3 + 2*w^2 - 7*w - 1],\
[179, 179, -w^5 + 7*w^3 + w^2 - 10*w - 4],\
[179, 179, -1/2*w^5 - 3/2*w^4 + 6*w^3 + 13/2*w^2 - 14*w + 1/2],\
[181, 181, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 5*w - 7],\
[191, 191, -1/2*w^5 + 1/2*w^4 + 4*w^3 - 7/2*w^2 - 7*w + 7/2],\
[191, 191, -2*w^5 + w^4 + 13*w^3 - 3*w^2 - 20*w + 4],\
[191, 191, 3/2*w^5 - 1/2*w^4 - 8*w^3 - 1/2*w^2 + 8*w + 3/2],\
[191, 191, 1/2*w^5 + 1/2*w^4 - 5*w^3 - 5/2*w^2 + 10*w + 3/2],\
[199, 199, -3/2*w^5 + 1/2*w^4 + 10*w^3 - 1/2*w^2 - 16*w - 5/2],\
[211, 211, 3/2*w^5 - 3/2*w^4 - 8*w^3 + 9/2*w^2 + 9*w - 1/2],\
[211, 211, -1/2*w^5 + 1/2*w^4 + 3*w^3 - 1/2*w^2 - 4*w - 7/2],\
[229, 229, -3/2*w^5 + 1/2*w^4 + 10*w^3 - 3/2*w^2 - 13*w + 1/2],\
[229, 229, -w^5 - w^4 + 8*w^3 + 5*w^2 - 14*w],\
[239, 239, -1/2*w^5 + 1/2*w^4 + 4*w^3 - 7/2*w^2 - 8*w + 7/2],\
[239, 239, -1/2*w^5 + 1/2*w^4 + 2*w^3 - 1/2*w^2 - w - 7/2],\
[241, 241, -1/2*w^5 + 1/2*w^4 + w^3 - 1/2*w^2 + 5*w - 1/2],\
[241, 241, -w^5 + 2*w^4 + 3*w^3 - 6*w^2 + 3*w - 2],\
[241, 241, 2*w^5 - 13*w^3 - 3*w^2 + 17*w + 2],\
[241, 241, 1/2*w^5 + 1/2*w^4 - 5*w^3 - 7/2*w^2 + 11*w + 7/2],\
[251, 251, -1/2*w^5 - 1/2*w^4 + 4*w^3 + 7/2*w^2 - 7*w - 3/2],\
[251, 251, -w^5 + 2*w^4 + 4*w^3 - 8*w^2 - w + 5],\
[269, 269, 1/2*w^5 + 1/2*w^4 - 5*w^3 - 3/2*w^2 + 11*w - 9/2],\
[271, 271, -1/2*w^5 + 1/2*w^4 + 3*w^3 - 7/2*w^2 - 3*w + 13/2],\
[271, 271, -1/2*w^5 + 3/2*w^4 + w^3 - 13/2*w^2 + 3*w + 9/2],\
[271, 271, 1/2*w^5 - 1/2*w^4 - 4*w^3 + 7/2*w^2 + 7*w - 5/2],\
[281, 281, -2*w^5 + w^4 + 13*w^3 - 3*w^2 - 19*w + 1],\
[289, 17, -w^4 + 3*w^3 + 3*w^2 - 10*w + 2],\
[331, 331, w^5 + w^4 - 7*w^3 - 5*w^2 + 10*w + 1],\
[331, 331, -3/2*w^5 + 1/2*w^4 + 10*w^3 - 1/2*w^2 - 13*w - 3/2],\
[349, 349, 1/2*w^5 - 3/2*w^4 - 3*w^3 + 13/2*w^2 + 4*w - 5/2],\
[349, 349, 1/2*w^5 - 3/2*w^4 + 11/2*w^2 - 6*w - 5/2],\
[349, 349, -2*w^5 + 2*w^4 + 12*w^3 - 8*w^2 - 16*w + 7],\
[349, 349, w^4 - 2*w^3 - 3*w^2 + 8*w - 1],\
[349, 349, -3/2*w^5 + 3/2*w^4 + 9*w^3 - 11/2*w^2 - 11*w + 1/2],\
[349, 349, 3/2*w^5 + 1/2*w^4 - 11*w^3 - 7/2*w^2 + 17*w - 1/2],\
[359, 359, -w^5 + w^4 + 7*w^3 - 3*w^2 - 11*w],\
[389, 389, 2*w^5 - w^4 - 13*w^3 + 2*w^2 + 19*w],\
[389, 389, 1/2*w^5 - 1/2*w^4 - 2*w^3 + 3/2*w^2 + w - 7/2],\
[401, 401, -3/2*w^5 + 1/2*w^4 + 10*w^3 - 3/2*w^2 - 13*w + 5/2],\
[409, 409, 3/2*w^5 - 1/2*w^4 - 10*w^3 + 1/2*w^2 + 13*w + 5/2],\
[419, 419, 2*w^3 - 2*w^2 - 7*w + 4],\
[421, 421, -w^5 - w^4 + 9*w^3 + 5*w^2 - 17*w - 2],\
[421, 421, -1/2*w^5 + 3/2*w^4 + w^3 - 11/2*w^2 + w - 1/2],\
[421, 421, -3/2*w^5 + 1/2*w^4 + 8*w^3 - 1/2*w^2 - 7*w - 1/2],\
[421, 421, -2*w^5 + w^4 + 12*w^3 - w^2 - 15*w - 2],\
[431, 431, 2*w^5 - 12*w^3 - 3*w^2 + 14*w + 4],\
[431, 431, -3/2*w^5 + 1/2*w^4 + 10*w^3 - 3/2*w^2 - 16*w + 3/2],\
[431, 431, -w^5 + 8*w^3 + w^2 - 14*w - 3],\
[431, 431, -3/2*w^5 - 1/2*w^4 + 10*w^3 + 7/2*w^2 - 14*w - 1/2],\
[439, 439, 3/2*w^5 + 1/2*w^4 - 10*w^3 - 9/2*w^2 + 12*w + 7/2],\
[439, 439, 1/2*w^5 + 3/2*w^4 - 5*w^3 - 15/2*w^2 + 9*w + 5/2],\
[439, 439, -1/2*w^5 - 1/2*w^4 + 5*w^3 + 5/2*w^2 - 12*w + 1/2],\
[449, 449, 1/2*w^5 + 3/2*w^4 - 4*w^3 - 15/2*w^2 + 5*w + 9/2],\
[449, 449, w^5 - 2*w^4 - 4*w^3 + 8*w^2 + 2*w - 2],\
[461, 461, 3/2*w^5 + 1/2*w^4 - 11*w^3 - 7/2*w^2 + 16*w + 1/2],\
[461, 461, -1/2*w^5 + 1/2*w^4 + 4*w^3 - 7/2*w^2 - 6*w + 9/2],\
[461, 461, -w^5 + 2*w^4 + 5*w^3 - 7*w^2 - 5*w + 1],\
[499, 499, 2*w^5 - w^4 - 12*w^3 + w^2 + 14*w + 3],\
[499, 499, 1/2*w^5 - 1/2*w^4 - 3*w^3 + 5/2*w^2 + 6*w - 5/2],\
[509, 509, 3/2*w^5 - 1/2*w^4 - 9*w^3 - 1/2*w^2 + 12*w + 1/2],\
[521, 521, 1/2*w^5 + 1/2*w^4 - 4*w^3 - 5/2*w^2 + 7*w - 5/2],\
[521, 521, -3/2*w^5 + 1/2*w^4 + 8*w^3 + 1/2*w^2 - 7*w - 7/2],\
[521, 521, 1/2*w^5 - 3/2*w^4 - w^3 + 9/2*w^2 - 3*w + 5/2],\
[521, 521, -w^5 + w^4 + 5*w^3 - 4*w^2 - 3*w + 5],\
[521, 521, 3/2*w^5 - 1/2*w^4 - 8*w^3 - 1/2*w^2 + 8*w + 7/2],\
[521, 521, 1/2*w^5 + 1/2*w^4 - 5*w^3 - 3/2*w^2 + 11*w + 3/2],\
[529, 23, 1/2*w^5 + 3/2*w^4 - 5*w^3 - 15/2*w^2 + 8*w + 9/2],\
[541, 541, w^3 - 2*w^2 - 3*w + 3],\
[541, 541, 1/2*w^5 - 1/2*w^4 - w^3 + 3/2*w^2 - 3*w - 5/2],\
[569, 569, -3/2*w^5 + 3/2*w^4 + 9*w^3 - 9/2*w^2 - 11*w - 1/2],\
[569, 569, -3/2*w^5 + 1/2*w^4 + 9*w^3 - 1/2*w^2 - 9*w - 3/2],\
[569, 569, 1/2*w^5 + 3/2*w^4 - 6*w^3 - 11/2*w^2 + 13*w - 1/2],\
[569, 569, -3/2*w^5 + 1/2*w^4 + 10*w^3 - 3/2*w^2 - 13*w + 3/2],\
[571, 571, w^5 + w^4 - 8*w^3 - 4*w^2 + 13*w - 2],\
[599, 599, w^5 - w^4 - 6*w^3 + 5*w^2 + 7*w - 3],\
[599, 599, 1/2*w^5 - 3/2*w^4 + 11/2*w^2 - 6*w - 1/2],\
[599, 599, -1/2*w^5 + 3/2*w^4 - 9/2*w^2 + 7*w - 1/2],\
[599, 599, -3/2*w^5 + 3/2*w^4 + 9*w^3 - 9/2*w^2 - 13*w + 1/2],\
[601, 601, -1/2*w^5 - 3/2*w^4 + 5*w^3 + 13/2*w^2 - 10*w - 5/2],\
[619, 619, 1/2*w^5 - 1/2*w^4 - 2*w^3 + 3/2*w^2 + 2*w - 5/2],\
[631, 631, -1/2*w^5 - 3/2*w^4 + 6*w^3 + 13/2*w^2 - 14*w - 5/2],\
[631, 631, -2*w^4 + 3*w^3 + 8*w^2 - 9*w - 1],\
[631, 631, -1/2*w^5 + 3/2*w^4 - 11/2*w^2 + 7*w + 3/2],\
[641, 641, -1/2*w^5 + 3/2*w^4 + 3*w^3 - 13/2*w^2 - 5*w + 7/2],\
[661, 661, -1/2*w^5 - 3/2*w^4 + 3*w^3 + 19/2*w^2 - 2*w - 19/2],\
[691, 691, 3/2*w^5 - 1/2*w^4 - 8*w^3 - 1/2*w^2 + 7*w + 9/2],\
[691, 691, w^5 + w^4 - 8*w^3 - 4*w^2 + 13*w],\
[691, 691, 3/2*w^5 - 3/2*w^4 - 7*w^3 + 9/2*w^2 + 5*w - 5/2],\
[701, 701, -3/2*w^5 + 3/2*w^4 + 8*w^3 - 9/2*w^2 - 9*w - 3/2],\
[701, 701, 3/2*w^5 - 3/2*w^4 - 9*w^3 + 9/2*w^2 + 11*w - 1/2],\
[701, 701, -3/2*w^5 + 3/2*w^4 + 8*w^3 - 7/2*w^2 - 8*w - 7/2],\
[709, 709, -1/2*w^5 - 1/2*w^4 + 3*w^3 + 9/2*w^2 - 4*w - 7/2],\
[719, 719, -2*w^5 + w^4 + 11*w^3 - w^2 - 12*w - 2],\
[719, 719, 1/2*w^5 - 3/2*w^4 - 2*w^3 + 13/2*w^2 + 3*w - 7/2],\
[739, 739, 1/2*w^5 + 1/2*w^4 - 3*w^3 - 7/2*w^2 + 5*w + 9/2],\
[739, 739, -w^5 - w^4 + 7*w^3 + 5*w^2 - 10*w + 1],\
[739, 739, 3/2*w^5 + 1/2*w^4 - 10*w^3 - 7/2*w^2 + 12*w + 5/2],\
[751, 751, w^5 - w^4 - 7*w^3 + 4*w^2 + 10*w - 2],\
[751, 751, 1/2*w^5 - 3/2*w^4 - w^3 + 9/2*w^2 - 3*w + 7/2],\
[751, 751, 1/2*w^5 + 1/2*w^4 - 6*w^3 - 3/2*w^2 + 15*w - 1/2],\
[751, 751, 3/2*w^5 + 1/2*w^4 - 10*w^3 - 7/2*w^2 + 13*w + 5/2],\
[761, 761, 5/2*w^5 - 1/2*w^4 - 16*w^3 - 1/2*w^2 + 22*w - 3/2],\
[761, 761, -1/2*w^5 - 1/2*w^4 + 4*w^3 + 3/2*w^2 - 8*w + 7/2],\
[769, 769, 1/2*w^5 - 1/2*w^4 - 4*w^3 + 5/2*w^2 + 9*w - 9/2],\
[769, 769, 1/2*w^5 + 1/2*w^4 - 4*w^3 - 1/2*w^2 + 6*w - 7/2],\
[809, 809, w^5 + w^4 - 8*w^3 - 6*w^2 + 13*w + 2],\
[809, 809, 3/2*w^5 - 1/2*w^4 - 9*w^3 - 1/2*w^2 + 10*w + 1/2],\
[811, 811, -1/2*w^5 - 3/2*w^4 + 5*w^3 + 13/2*w^2 - 10*w - 3/2],\
[811, 811, 3/2*w^5 - 3/2*w^4 - 8*w^3 + 11/2*w^2 + 7*w - 9/2],\
[811, 811, 3/2*w^5 - 1/2*w^4 - 8*w^3 - 3/2*w^2 + 7*w + 7/2],\
[821, 821, 2*w^5 - 13*w^3 - 2*w^2 + 16*w + 2],\
[829, 829, 2*w^5 - w^4 - 12*w^3 + 3*w^2 + 13*w],\
[829, 829, -1/2*w^5 - 1/2*w^4 + 4*w^3 + 5/2*w^2 - 9*w + 1/2],\
[839, 839, 3/2*w^5 - 1/2*w^4 - 11*w^3 + 1/2*w^2 + 19*w + 3/2],\
[841, 29, 1/2*w^5 + 3/2*w^4 - 6*w^3 - 13/2*w^2 + 12*w + 5/2],\
[881, 881, -3/2*w^5 + 1/2*w^4 + 9*w^3 - 1/2*w^2 - 9*w - 1/2],\
[881, 881, -2*w^5 + 14*w^3 + w^2 - 21*w - 1],\
[911, 911, -4*w^5 + 2*w^4 + 25*w^3 - 6*w^2 - 33*w + 5],\
[911, 911, 3/2*w^5 - 3/2*w^4 - 7*w^3 + 7/2*w^2 + 3*w + 3/2],\
[911, 911, w^5 - 6*w^3 - 2*w^2 + 9*w + 1],\
[919, 919, 1/2*w^5 - 3/2*w^4 - 3*w^3 + 15/2*w^2 + 4*w - 13/2],\
[929, 929, 3/2*w^5 - 3/2*w^4 - 8*w^3 + 9/2*w^2 + 8*w - 7/2],\
[929, 929, -2*w^5 + 12*w^3 + 2*w^2 - 14*w - 3],\
[941, 941, 3/2*w^5 + 1/2*w^4 - 10*w^3 - 9/2*w^2 + 15*w + 7/2],\
[941, 941, -1/2*w^5 - 1/2*w^4 + 4*w^3 + 7/2*w^2 - 5*w - 11/2],\
[941, 941, -5/2*w^5 + 1/2*w^4 + 15*w^3 + 3/2*w^2 - 18*w - 5/2],\
[971, 971, 1/2*w^5 - 3/2*w^4 - w^3 + 9/2*w^2 - 2*w + 7/2],\
[971, 971, -3/2*w^5 + 1/2*w^4 + 11*w^3 - 3/2*w^2 - 17*w + 3/2],\
[991, 991, 2*w^5 - w^4 - 13*w^3 + 4*w^2 + 17*w - 2],\
[991, 991, -1/2*w^5 + 3/2*w^4 - 5/2*w^2 + 5*w - 11/2],\
[991, 991, 2*w^5 - 13*w^3 - 2*w^2 + 16*w],\
[1009, 1009, -1/2*w^5 + 3/2*w^4 + 2*w^3 - 13/2*w^2 + 11/2],\
[1009, 1009, -5/2*w^5 + 1/2*w^4 + 18*w^3 - 1/2*w^2 - 29*w - 5/2],\
[1009, 1009, -w^5 + w^4 + 7*w^3 - 3*w^2 - 11*w - 2],\
[1019, 1019, 1/2*w^5 + 1/2*w^4 - 6*w^3 - 1/2*w^2 + 14*w - 11/2],\
[1021, 1021, -1/2*w^5 + 3/2*w^4 + 3*w^3 - 15/2*w^2 - 4*w + 7/2],\
[1021, 1021, -1/2*w^5 - 1/2*w^4 + 5*w^3 + 7/2*w^2 - 12*w - 7/2],\
[1031, 1031, -w^5 - w^4 + 9*w^3 + 4*w^2 - 17*w - 1],\
[1039, 1039, 1/2*w^5 - 1/2*w^4 + 1/2*w^2 - 6*w - 1/2],\
[1039, 1039, 1/2*w^5 - 3/2*w^4 - 4*w^3 + 11/2*w^2 + 8*w - 1/2],\
[1039, 1039, 1/2*w^5 + 1/2*w^4 - 4*w^3 - 7/2*w^2 + 7*w + 1/2],\
[1039, 1039, 5/2*w^5 - 3/2*w^4 - 17*w^3 + 11/2*w^2 + 26*w - 7/2],\
[1049, 1049, -1/2*w^5 - 1/2*w^4 + 4*w^3 + 7/2*w^2 - 5*w - 9/2],\
[1051, 1051, 3/2*w^5 + 1/2*w^4 - 10*w^3 - 7/2*w^2 + 15*w + 3/2],\
[1061, 1061, -w^5 - w^4 + 8*w^3 + 4*w^2 - 14*w + 1],\
[1061, 1061, 3/2*w^5 - 1/2*w^4 - 8*w^3 + 1/2*w^2 + 4*w - 3/2],\
[1069, 1069, -1/2*w^5 - 3/2*w^4 + 5*w^3 + 15/2*w^2 - 10*w - 3/2],\
[1069, 1069, -5/2*w^5 + 7/2*w^4 + 12*w^3 - 23/2*w^2 - 9*w + 1/2],\
[1069, 1069, 1/2*w^5 - 1/2*w^4 - 4*w^3 + 7/2*w^2 + 9*w - 11/2],\
[1069, 1069, -2*w^5 + 12*w^3 + w^2 - 15*w + 3],\
[1091, 1091, 1/2*w^5 + 1/2*w^4 - 3*w^3 - 7/2*w^2 + 2*w + 11/2],\
[1091, 1091, 3*w^4 - 5*w^3 - 12*w^2 + 17*w],\
[1091, 1091, -3/2*w^5 - 1/2*w^4 + 10*w^3 + 7/2*w^2 - 14*w + 1/2],\
[1091, 1091, -2*w^5 - w^4 + 15*w^3 + 6*w^2 - 25*w - 4],\
[1091, 1091, -2*w^5 + 13*w^3 + 2*w^2 - 19*w - 1],\
[1091, 1091, -3/2*w^5 + 3/2*w^4 + 7*w^3 - 9/2*w^2 - 3*w + 5/2],\
[1109, 1109, w^5 + w^4 - 8*w^3 - 6*w^2 + 12*w + 3],\
[1109, 1109, -3*w^3 + 3*w^2 + 10*w - 5],\
[1129, 1129, 5/2*w^5 + 1/2*w^4 - 15*w^3 - 11/2*w^2 + 16*w + 3/2],\
[1151, 1151, 1/2*w^5 + 3/2*w^4 - 6*w^3 - 11/2*w^2 + 13*w + 3/2],\
[1151, 1151, 2*w^5 - 2*w^4 - 12*w^3 + 7*w^2 + 16*w - 2],\
[1171, 1171, 3/2*w^5 + 1/2*w^4 - 11*w^3 - 7/2*w^2 + 16*w - 1/2],\
[1171, 1171, -3*w^5 + 2*w^4 + 17*w^3 - 4*w^2 - 20*w - 1],\
[1171, 1171, -3/2*w^5 + 1/2*w^4 + 10*w^3 - 3/2*w^2 - 15*w - 1/2],\
[1171, 1171, -2*w^5 + w^4 + 11*w^3 - w^2 - 12*w + 2],\
[1181, 1181, 3/2*w^5 + 1/2*w^4 - 12*w^3 - 7/2*w^2 + 21*w + 5/2],\
[1201, 1201, -w^5 + 3*w^4 + 3*w^3 - 13*w^2 + 2*w + 7],\
[1229, 1229, 3/2*w^5 + 1/2*w^4 - 10*w^3 - 7/2*w^2 + 14*w - 3/2],\
[1229, 1229, -1/2*w^5 + 1/2*w^4 + w^3 + 1/2*w^2 + 4*w - 5/2],\
[1231, 1231, 3/2*w^5 + 1/2*w^4 - 10*w^3 - 7/2*w^2 + 13*w - 7/2],\
[1249, 1249, 3/2*w^5 - 1/2*w^4 - 9*w^3 + 5/2*w^2 + 10*w - 13/2],\
[1259, 1259, -1/2*w^5 - 1/2*w^4 + 4*w^3 + 5/2*w^2 - 6*w - 9/2],\
[1259, 1259, 1/2*w^5 + 3/2*w^4 - 4*w^3 - 15/2*w^2 + 6*w + 11/2],\
[1279, 1279, 3/2*w^5 + 1/2*w^4 - 11*w^3 - 9/2*w^2 + 18*w + 5/2],\
[1279, 1279, -w^5 + w^4 + 4*w^3 - 3*w^2 - w + 3],\
[1289, 1289, -2*w^4 + 3*w^3 + 8*w^2 - 8*w - 2],\
[1289, 1289, 3/2*w^5 + 1/2*w^4 - 8*w^3 - 9/2*w^2 + 7*w + 3/2],\
[1291, 1291, 1/2*w^5 + 1/2*w^4 - 4*w^3 - 5/2*w^2 + 7*w + 9/2],\
[1291, 1291, 2*w^5 - w^4 - 12*w^3 + 3*w^2 + 16*w - 1],\
[1291, 1291, -w^5 + w^4 + 6*w^3 - 2*w^2 - 11*w - 4],\
[1301, 1301, w^5 + w^4 - 9*w^3 - 5*w^2 + 18*w - 1],\
[1319, 1319, 1/2*w^5 + 1/2*w^4 - 2*w^3 - 9/2*w^2 + 7/2],\
[1319, 1319, w^2 + w - 5],\
[1321, 1321, -1/2*w^5 + 3/2*w^4 + w^3 - 11/2*w^2 + 5*w + 7/2],\
[1331, 11, -3/2*w^5 + 3/2*w^4 + 9*w^3 - 9/2*w^2 - 12*w + 1/2],\
[1361, 1361, w^4 - w^3 - 4*w^2 + w - 2],\
[1361, 1361, 1/2*w^5 + 1/2*w^4 - 3*w^3 - 9/2*w^2 + 3*w + 5/2],\
[1361, 1361, 1/2*w^5 - 1/2*w^4 - 5*w^3 + 9/2*w^2 + 11*w - 7/2],\
[1381, 1381, -w^4 + 5*w^2 + 3*w - 4],\
[1381, 1381, -1/2*w^5 - 3/2*w^4 + 5*w^3 + 11/2*w^2 - 9*w - 1/2],\
[1381, 1381, 1/2*w^5 - 5/2*w^4 + w^3 + 15/2*w^2 - 8*w + 5/2],\
[1381, 1381, w^5 + w^4 - 6*w^3 - 5*w^2 + 6*w - 2],\
[1399, 1399, -2*w^5 + 3*w^4 + 9*w^3 - 12*w^2 - 3*w + 4],\
[1409, 1409, -w^5 + w^4 + 7*w^3 - 2*w^2 - 11*w - 5],\
[1429, 1429, -w^5 + 2*w^4 + 4*w^3 - 6*w^2 - 2*w - 2],\
[1429, 1429, 2*w^4 - 3*w^3 - 7*w^2 + 9*w],\
[1451, 1451, -3/2*w^5 + 3/2*w^4 + 8*w^3 - 13/2*w^2 - 10*w + 7/2],\
[1451, 1451, 1/2*w^5 + 3/2*w^4 - 5*w^3 - 15/2*w^2 + 8*w + 5/2],\
[1451, 1451, -3/2*w^5 + 5/2*w^4 + 8*w^3 - 17/2*w^2 - 8*w + 7/2],\
[1451, 1451, 2*w^5 - w^4 - 12*w^3 + 2*w^2 + 14*w - 2],\
[1459, 1459, 3/2*w^5 - 3/2*w^4 - 6*w^3 + 7/2*w^2 + 3/2],\
[1459, 1459, -5/2*w^5 + 1/2*w^4 + 15*w^3 + 3/2*w^2 - 18*w - 7/2],\
[1459, 1459, 1/2*w^5 + 1/2*w^4 - 3*w^3 - 5/2*w^2 + 4*w + 9/2],\
[1459, 1459, -3/2*w^5 - 3/2*w^4 + 12*w^3 + 13/2*w^2 - 19*w - 5/2],\
[1471, 1471, 3/2*w^5 + 1/2*w^4 - 11*w^3 - 7/2*w^2 + 19*w - 3/2],\
[1471, 1471, -5/2*w^5 + 1/2*w^4 + 16*w^3 + 3/2*w^2 - 23*w - 13/2],\
[1481, 1481, -2*w^5 + 2*w^4 + 10*w^3 - 5*w^2 - 6*w - 2],\
[1489, 1489, w^4 - 3*w^3 - 4*w^2 + 10*w + 3],\
[1489, 1489, -1/2*w^5 - 1/2*w^4 + 2*w^3 + 11/2*w^2 + 2*w - 11/2],\
[1489, 1489, -w^4 + 5*w^2 + 2*w - 5],\
[1499, 1499, -w^5 - w^4 + 7*w^3 + 6*w^2 - 11*w - 3],\
[1511, 1511, -2*w^5 + w^4 + 12*w^3 - 2*w^2 - 16*w - 4],\
[1549, 1549, -7/2*w^5 + 5/2*w^4 + 20*w^3 - 15/2*w^2 - 22*w + 3/2],\
[1549, 1549, -3*w^5 + 20*w^3 + 4*w^2 - 27*w - 3],\
[1549, 1549, -3/2*w^5 + 3/2*w^4 + 11*w^3 - 11/2*w^2 - 19*w + 5/2],\
[1549, 1549, 1/2*w^5 - 5/2*w^4 + 21/2*w^2 - 5*w - 3/2],\
[1559, 1559, 2*w^5 - w^4 - 11*w^3 + 2*w^2 + 12*w + 1],\
[1559, 1559, -3/2*w^5 - 1/2*w^4 + 12*w^3 + 7/2*w^2 - 22*w + 3/2],\
[1571, 1571, 3/2*w^5 + 1/2*w^4 - 11*w^3 - 7/2*w^2 + 19*w + 3/2],\
[1579, 1579, 1/2*w^5 + 5/2*w^4 - 8*w^3 - 21/2*w^2 + 20*w + 5/2],\
[1601, 1601, -1/2*w^5 + 1/2*w^4 + 3*w^3 - 5/2*w^2 - 6*w + 7/2],\
[1601, 1601, -w^5 - w^4 + 8*w^3 + 5*w^2 - 12*w],\
[1601, 1601, 1/2*w^5 + 3/2*w^4 - 6*w^3 - 13/2*w^2 + 14*w + 7/2],\
[1609, 1609, -5/2*w^5 - 1/2*w^4 + 17*w^3 + 9/2*w^2 - 23*w + 3/2],\
[1621, 1621, -w^5 - w^4 + 8*w^3 + 4*w^2 - 15*w + 4],\
[1621, 1621, 2*w^4 - 5*w^3 - 6*w^2 + 17*w - 5],\
[1669, 1669, -1/2*w^5 - 1/2*w^4 + 4*w^3 + 5/2*w^2 - 9*w - 3/2],\
[1681, 41, -2*w^5 + 2*w^4 + 11*w^3 - 5*w^2 - 11*w - 4],\
[1681, 41, -1/2*w^5 + 3/2*w^4 + w^3 - 13/2*w^2 + 5*w + 13/2],\
[1709, 1709, 5/2*w^5 - 3/2*w^4 - 17*w^3 + 13/2*w^2 + 25*w - 11/2],\
[1721, 1721, w^5 - 8*w^3 + 13*w + 1],\
[1721, 1721, 2*w^5 - 2*w^4 - 13*w^3 + 7*w^2 + 21*w - 4],\
[1741, 1741, -w^5 + w^4 + 6*w^3 - 4*w^2 - 10*w - 1],\
[1741, 1741, -w^4 + w^3 + 6*w^2 - 3*w - 4],\
[1759, 1759, 1/2*w^5 + 1/2*w^4 - 4*w^3 - 7/2*w^2 + 8*w - 1/2],\
[1789, 1789, -1/2*w^5 + 1/2*w^4 + w^3 + 1/2*w^2 + 4*w - 7/2],\
[1811, 1811, 3/2*w^5 - 1/2*w^4 - 9*w^3 + 3/2*w^2 + 9*w + 1/2],\
[1849, 43, -7/2*w^5 + 5/2*w^4 + 20*w^3 - 13/2*w^2 - 24*w + 1/2],\
[1861, 1861, 2*w^5 - 15*w^3 + 26*w - 8],\
[1861, 1861, 2*w^5 + w^4 - 15*w^3 - 5*w^2 + 24*w - 2],\
[1861, 1861, -1/2*w^5 + 3/2*w^4 + 2*w^3 - 15/2*w^2 - 2*w + 13/2],\
[1861, 1861, 1/2*w^5 + 1/2*w^4 - 3*w^3 - 7/2*w^2 + 3*w - 3/2],\
[1871, 1871, 1/2*w^5 + 3/2*w^4 - 6*w^3 - 13/2*w^2 + 10*w + 3/2],\
[1879, 1879, w^5 - w^4 - 7*w^3 + 3*w^2 + 13*w],\
[1879, 1879, -1/2*w^5 + 3/2*w^4 - 9/2*w^2 + 7*w + 1/2],\
[1889, 1889, -2*w^5 + w^4 + 11*w^3 - 2*w^2 - 12*w + 1],\
[1901, 1901, 3*w^5 - w^4 - 19*w^3 + w^2 + 26*w + 3],\
[1931, 1931, -3*w^5 + w^4 + 19*w^3 - 24*w - 4],\
[1949, 1949, 1/2*w^5 - 3/2*w^4 - 3*w^3 + 15/2*w^2 + 4*w - 11/2],\
[1949, 1949, 1/2*w^5 - 3/2*w^4 + w^3 + 9/2*w^2 - 10*w - 5/2],\
[1949, 1949, -2*w^5 + w^4 + 12*w^3 - w^2 - 13*w - 2],\
[1951, 1951, 2*w^5 - 14*w^3 + 20*w - 1],\
[1951, 1951, w^5 + 2*w^4 - 8*w^3 - 9*w^2 + 12*w - 1],\
[1951, 1951, 3*w^5 - w^4 - 17*w^3 + 18*w],\
[1979, 1979, -3/2*w^5 + 1/2*w^4 + 11*w^3 - 1/2*w^2 - 20*w - 3/2],\
[1979, 1979, 5/2*w^5 - 3/2*w^4 - 15*w^3 + 3/2*w^2 + 20*w + 11/2],\
[1979, 1979, -2*w^5 + 3*w^4 + 10*w^3 - 11*w^2 - 11*w + 6],\
[1979, 1979, 1/2*w^5 - 3/2*w^4 - 3*w^3 + 15/2*w^2 + 4*w - 9/2],\
[1999, 1999, -1/2*w^5 - 3/2*w^4 + 6*w^3 + 11/2*w^2 - 11*w + 3/2],\
[1999, 1999, 3/2*w^5 - 1/2*w^4 - 9*w^3 - 1/2*w^2 + 11*w - 1/2]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^2 + 2*x - 1
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 2*e + 3, 1, -e - 2, -3*e, -e - 10, 3*e - 2, -6*e - 6, 2*e - 6, -10, -2, e + 4, 2*e + 4, -4*e + 4, 2*e + 4, 2*e - 12, 2*e - 5, -6*e + 1, -6*e - 11, 2*e - 3, -e - 8, -10*e - 6, -6*e - 13, 3*e, -5*e - 12, -8*e - 2, 6*e - 2, -16, -6*e - 14, -6*e - 8, -4*e - 14, 5*e + 8, 6*e + 6, 8*e + 10, -13*e - 14, -6*e - 16, 14*e + 18, -2*e + 10, 12*e + 18, -12*e - 14, 14*e + 14, -8*e - 16, -12*e - 21, -10*e + 5, 20, 10*e + 16, 4*e - 11, 3*e + 4, -9*e - 10, -10*e - 6, -4*e - 16, -6*e - 10, 2*e - 9, 14, 2*e - 24, -14*e - 18, 9*e + 24, e - 20, 12*e + 24, 4*e - 8, 7*e + 10, 10*e + 6, e + 16, -18*e - 19, 22*e + 19, -6*e - 10, 14*e + 22, 2*e + 19, -7*e - 10, -2*e + 1, 20*e + 11, 10*e + 20, 18*e + 6, 2*e + 3, -e + 24, 8*e + 11, 8*e - 12, -12*e + 6, -8*e + 18, -8*e - 28, -2*e + 4, -36, 14*e + 14, 2*e + 2, 12*e + 31, 18*e + 30, 10*e + 6, -8*e + 10, -14*e - 2, 2*e + 16, e + 4, -4*e + 9, -4*e - 6, 7*e + 26, 19*e + 30, 2*e + 7, 4*e - 11, -18*e - 9, 4*e + 10, -22*e - 21, -4*e + 7, -8*e - 42, -2*e + 33, 16*e + 39, -10*e - 24, -14*e - 2, -18*e - 14, 16*e + 20, 18*e + 18, 24*e + 33, 18*e + 30, 8*e - 22, 6*e + 6, 6*e + 8, 18*e + 26, -6*e - 2, 10*e + 14, -8*e + 22, -16*e - 16, -2*e + 2, 24*e + 19, e + 20, 12*e - 2, -12*e + 8, 22*e + 34, -4*e - 34, -10*e + 8, 14*e + 12, -18*e, -6*e - 20, -30*e - 18, 8*e + 26, -29*e - 36, -22*e - 6, 4*e + 19, 20*e + 42, 5*e + 20, -8*e - 15, -8*e - 46, 22*e + 30, -18*e - 36, -13, -5*e - 36, 24*e + 15, 6*e + 6, 5*e + 2, 2*e - 25, -19*e - 18, 10*e + 2, -12*e - 4, -6*e - 8, 8*e + 22, -2*e - 14, -31*e - 30, -16*e - 17, 3*e - 28, -2*e + 46, 8*e - 10, 20*e + 18, -12*e - 6, 8*e - 6, -10*e - 16, 30*e + 26, 13*e + 26, 12*e - 9, -6*e - 40, e - 24, 18*e + 38, 14*e + 4, -26*e - 2, 10*e + 16, -20*e, -2*e - 14, -27*e - 36, 24*e + 6, -29, 19*e + 8, -e + 10, -16*e - 22, -7*e + 20, -6*e - 39, -14*e + 10, 20*e, 12*e + 32, 8*e - 22, -6*e + 34, 16*e + 26, -42*e - 38, 22*e - 6, 6*e - 42, -62, 34*e + 32, 28*e + 34, 20*e + 34, 36*e + 22, 26*e - 2, 21*e + 10, 10*e + 1, 32*e + 18, -3*e - 10, 12*e + 10, 30*e + 57, -10*e - 56, -6*e - 2, -16*e - 60, 8*e + 24, 11*e - 14, -18*e + 21, -4*e + 8, 30*e + 42, 4*e + 30, -7*e + 6, 12*e + 6, 16*e - 2, 31*e + 6, -12*e + 2, -16*e + 2, -16*e - 23, -18*e - 35, -19*e + 16, -20*e - 41, -3*e - 12, 10*e + 14, -16*e + 2, -17*e - 34, 34*e + 14, -8*e + 38, -20*e - 40, -66, 10*e + 52, -14*e - 20, 32*e + 16, -42*e - 36, -26*e - 6, -6*e - 48, 26*e + 64, 20*e + 4, -18*e - 26, 6*e - 18, -14*e + 34, 32*e + 26, 18*e - 28, -6*e - 50, 38*e + 50, 4*e - 6, -32*e - 47, -22*e - 54, 14*e + 62, -20*e - 8, -38, 22*e + 70, 21*e - 10, -6*e - 14, 22*e + 33, 17*e - 6, -23*e - 22, 8*e - 49, -2*e + 57, -27*e - 24, 11*e - 46, -16*e - 26, 6*e - 63, -6*e + 2, -10*e + 42, -6*e + 31, -14*e + 12, -11*e - 38, 22*e + 68, 6*e - 18, -30*e - 19, -16*e - 22, 10*e + 13, -6*e - 29, -38*e - 26, 24*e + 4, -4*e + 50, 49*e + 58, -6*e + 6, 8*e - 16, -15*e - 4, -2*e - 62, 38*e + 19, -16*e - 32, 2*e - 10, -8*e, -14*e - 34, -14*e - 40, 22*e - 10, 20*e + 30, -28*e - 42, -2*e - 82]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([11, 11, 1/2*w^5 + 1/2*w^4 - 4*w^3 - 5/2*w^2 + 6*w + 1/2])] = -1

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