/*
  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, -12, 12, 7, -7, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([29, 29, 2*w^5 - 13*w^3 + 19*w - 2])

primes_array = [
[4, 2, -w^5 + 6*w^3 + w^2 - 8*w - 2],\
[11, 11, w + 1],\
[16, 2, -w^5 + 6*w^3 + w^2 - 7*w - 2],\
[19, 19, -w^3 + w^2 + 4*w - 3],\
[29, 29, 2*w^5 - 13*w^3 + 19*w - 2],\
[31, 31, -2*w^5 + 12*w^3 + w^2 - 16*w - 2],\
[41, 41, -w^5 + 7*w^3 + w^2 - 12*w - 2],\
[41, 41, 2*w^5 + w^4 - 13*w^3 - 5*w^2 + 19*w + 4],\
[59, 59, -w^5 + 7*w^3 + w^2 - 11*w],\
[61, 61, w^5 - 7*w^3 + 10*w],\
[61, 61, -2*w^5 + 12*w^3 + w^2 - 16*w - 3],\
[71, 71, -2*w^5 - w^4 + 12*w^3 + 5*w^2 - 16*w - 4],\
[71, 71, -3*w^5 - w^4 + 20*w^3 + 6*w^2 - 31*w - 5],\
[71, 71, -w^5 + 7*w^3 - w^2 - 12*w + 2],\
[79, 79, w^5 + w^4 - 7*w^3 - 5*w^2 + 10*w + 4],\
[79, 79, -w^5 - w^4 + 8*w^3 + 4*w^2 - 15*w + 1],\
[79, 79, 2*w^5 + w^4 - 13*w^3 - 5*w^2 + 20*w + 3],\
[89, 89, 2*w^5 + w^4 - 14*w^3 - 5*w^2 + 23*w + 1],\
[89, 89, -2*w^5 - w^4 + 12*w^3 + 5*w^2 - 15*w - 4],\
[89, 89, 2*w^5 + w^4 - 11*w^3 - 5*w^2 + 13*w + 3],\
[101, 101, w^5 + w^4 - 7*w^3 - 3*w^2 + 11*w - 2],\
[109, 109, w^5 + w^4 - 8*w^3 - 4*w^2 + 14*w],\
[121, 11, -w^5 - w^4 + 8*w^3 + 4*w^2 - 13*w - 2],\
[125, 5, -w^5 + 6*w^3 - 8*w - 2],\
[131, 131, -w^4 + 5*w^2 - w - 3],\
[131, 131, -w^5 - w^4 + 6*w^3 + 5*w^2 - 9*w - 3],\
[139, 139, 2*w^5 - w^4 - 11*w^3 + 4*w^2 + 12*w - 2],\
[149, 149, w^5 + w^4 - 7*w^3 - 5*w^2 + 9*w + 4],\
[151, 151, w^5 - 8*w^3 + 2*w^2 + 15*w - 6],\
[151, 151, -w^5 + 7*w^3 - 12*w + 3],\
[151, 151, w^5 - 5*w^3 + 4*w - 3],\
[151, 151, -w^4 + w^3 + 5*w^2 - 4*w - 5],\
[179, 179, -3*w^5 - w^4 + 20*w^3 + 4*w^2 - 29*w - 1],\
[179, 179, -3*w^5 - 2*w^4 + 20*w^3 + 10*w^2 - 31*w - 6],\
[179, 179, -w^4 + 3*w^2 - 2*w + 2],\
[179, 179, 3*w^5 + w^4 - 18*w^3 - 4*w^2 + 23*w + 1],\
[181, 181, -2*w^5 - w^4 + 13*w^3 + 4*w^2 - 20*w + 1],\
[181, 181, w^5 - 8*w^3 + 14*w - 3],\
[191, 191, w^5 + w^4 - 7*w^3 - 6*w^2 + 11*w + 5],\
[199, 199, -2*w^5 - 2*w^4 + 14*w^3 + 10*w^2 - 23*w - 5],\
[199, 199, w^5 + w^4 - 8*w^3 - 6*w^2 + 14*w + 4],\
[199, 199, -w^5 + 6*w^3 + 2*w^2 - 8*w - 2],\
[199, 199, w^5 - w^4 - 6*w^3 + 4*w^2 + 8*w - 2],\
[211, 211, -3*w^5 - 2*w^4 + 20*w^3 + 9*w^2 - 30*w - 5],\
[229, 229, 2*w^5 + w^4 - 14*w^3 - 4*w^2 + 22*w - 1],\
[229, 229, 4*w^5 + w^4 - 25*w^3 - 5*w^2 + 35*w + 1],\
[239, 239, 2*w^4 - w^3 - 8*w^2 + 5*w + 2],\
[241, 241, w^4 - 3*w^2 + w - 2],\
[251, 251, -3*w^5 - 2*w^4 + 21*w^3 + 9*w^2 - 33*w - 3],\
[251, 251, -3*w^5 - w^4 + 21*w^3 + 4*w^2 - 34*w + 1],\
[251, 251, -2*w^5 - 2*w^4 + 15*w^3 + 9*w^2 - 26*w - 4],\
[251, 251, 2*w^5 - 11*w^3 + w^2 + 12*w - 3],\
[269, 269, -2*w^5 + 11*w^3 - w^2 - 12*w + 1],\
[271, 271, -w^5 + 5*w^3 - w^2 - 5*w + 3],\
[281, 281, w^4 - w^3 - 5*w^2 + 5*w + 5],\
[289, 17, -2*w^5 - w^4 + 11*w^3 + 4*w^2 - 12*w - 2],\
[311, 311, -3*w^5 + 19*w^3 - w^2 - 26*w + 4],\
[311, 311, -w^4 + 3*w^2 - w + 3],\
[311, 311, 3*w^5 - 19*w^3 + w^2 + 27*w - 4],\
[311, 311, w^5 + 2*w^4 - 7*w^3 - 10*w^2 + 12*w + 8],\
[331, 331, -3*w^5 - w^4 + 19*w^3 + 4*w^2 - 27*w - 1],\
[349, 349, -2*w^5 - 2*w^4 + 14*w^3 + 8*w^2 - 22*w - 3],\
[349, 349, -2*w^5 - w^4 + 14*w^3 + 4*w^2 - 22*w + 2],\
[349, 349, 3*w^5 + w^4 - 19*w^3 - 6*w^2 + 25*w + 4],\
[359, 359, -4*w^5 - w^4 + 25*w^3 + 4*w^2 - 35*w + 2],\
[359, 359, 4*w^5 + w^4 - 25*w^3 - 6*w^2 + 34*w + 4],\
[361, 19, 2*w^5 - w^4 - 12*w^3 + 5*w^2 + 15*w - 6],\
[379, 379, 2*w^5 + 2*w^4 - 14*w^3 - 8*w^2 + 23*w + 1],\
[379, 379, -2*w^5 - 2*w^4 + 14*w^3 + 10*w^2 - 23*w - 7],\
[389, 389, w^5 - w^4 - 4*w^3 + 5*w^2 + w - 3],\
[401, 401, -w^5 + w^4 + 7*w^3 - 4*w^2 - 12*w + 1],\
[401, 401, -3*w^5 - 2*w^4 + 20*w^3 + 8*w^2 - 31*w - 2],\
[401, 401, 2*w^5 + w^4 - 11*w^3 - 6*w^2 + 12*w + 5],\
[401, 401, -4*w^5 - w^4 + 26*w^3 + 4*w^2 - 38*w + 1],\
[409, 409, -w^5 + w^4 + 7*w^3 - 4*w^2 - 11*w + 3],\
[409, 409, 3*w^5 - 17*w^3 - w^2 + 20*w + 2],\
[419, 419, -3*w^5 - w^4 + 21*w^3 + 4*w^2 - 33*w + 1],\
[419, 419, -2*w^5 + w^4 + 12*w^3 - 5*w^2 - 16*w + 4],\
[419, 419, -2*w^5 - 2*w^4 + 15*w^3 + 9*w^2 - 26*w - 3],\
[419, 419, w^2 + 2*w - 2],\
[421, 421, 3*w^5 + w^4 - 21*w^3 - 5*w^2 + 34*w],\
[421, 421, w^4 - 4*w^2 - 2*w + 2],\
[421, 421, -3*w^5 + 18*w^3 + w^2 - 24*w - 3],\
[421, 421, -2*w^5 + 14*w^3 + w^2 - 22*w + 1],\
[431, 431, 2*w^5 + w^4 - 13*w^3 - 3*w^2 + 18*w - 1],\
[431, 431, 3*w^5 + 2*w^4 - 20*w^3 - 8*w^2 + 30*w + 1],\
[431, 431, 2*w^5 + w^4 - 11*w^3 - 6*w^2 + 12*w + 7],\
[439, 439, -3*w^5 + 19*w^3 + 2*w^2 - 27*w - 3],\
[461, 461, -3*w^5 + 20*w^3 - w^2 - 30*w + 5],\
[461, 461, w^5 - 5*w^3 + 5*w - 3],\
[491, 491, -w^5 - w^4 + 9*w^3 + 4*w^2 - 18*w + 1],\
[491, 491, 2*w^5 - w^4 - 12*w^3 + 3*w^2 + 15*w],\
[499, 499, -3*w^5 - w^4 + 20*w^3 + 5*w^2 - 29*w - 3],\
[499, 499, -2*w^5 - w^4 + 12*w^3 + 4*w^2 - 16*w - 3],\
[509, 509, -w^5 + w^4 + 6*w^3 - 4*w^2 - 9*w],\
[509, 509, 2*w^5 - 14*w^3 + 24*w - 3],\
[509, 509, -2*w^5 - w^4 + 14*w^3 + 5*w^2 - 24*w],\
[509, 509, -2*w^5 - 2*w^4 + 14*w^3 + 9*w^2 - 22*w - 5],\
[569, 569, -2*w^5 + w^4 + 12*w^3 - 3*w^2 - 17*w + 3],\
[571, 571, -w^5 + w^4 + 5*w^3 - 4*w^2 - 5*w - 1],\
[571, 571, -w^5 - w^4 + 8*w^3 + 3*w^2 - 16*w + 2],\
[571, 571, -2*w^5 + 13*w^3 - 21*w + 2],\
[571, 571, 2*w^5 + w^4 - 12*w^3 - 7*w^2 + 15*w + 8],\
[571, 571, 2*w^5 + 2*w^4 - 13*w^3 - 10*w^2 + 19*w + 8],\
[571, 571, 2*w^5 - 12*w^3 + 15*w - 4],\
[601, 601, 3*w^5 + 2*w^4 - 21*w^3 - 9*w^2 + 33*w + 2],\
[601, 601, 3*w^5 + w^4 - 19*w^3 - 3*w^2 + 25*w - 4],\
[601, 601, -2*w^5 - 2*w^4 + 14*w^3 + 10*w^2 - 22*w - 5],\
[601, 601, -3*w^5 - w^4 + 18*w^3 + 6*w^2 - 23*w - 6],\
[619, 619, w^5 + w^4 - 7*w^3 - 5*w^2 + 13*w + 4],\
[631, 631, 2*w^5 + w^4 - 15*w^3 - 4*w^2 + 26*w - 1],\
[631, 631, -2*w^5 + 12*w^3 + w^2 - 14*w - 4],\
[641, 641, -w^5 + w^4 + 6*w^3 - 6*w^2 - 9*w + 7],\
[641, 641, -2*w^5 - w^4 + 13*w^3 + 7*w^2 - 19*w - 8],\
[659, 659, 2*w^5 - w^4 - 12*w^3 + 4*w^2 + 16*w - 4],\
[659, 659, 2*w^5 - 13*w^3 + 20*w - 4],\
[661, 661, -2*w^5 - w^4 + 13*w^3 + 3*w^2 - 19*w],\
[661, 661, -w^5 - w^4 + 6*w^3 + 7*w^2 - 8*w - 8],\
[661, 661, -3*w^5 - 2*w^4 + 21*w^3 + 10*w^2 - 34*w - 5],\
[691, 691, 3*w^5 + w^4 - 20*w^3 - 3*w^2 + 31*w - 3],\
[691, 691, 5*w^5 + 2*w^4 - 34*w^3 - 9*w^2 + 54*w + 3],\
[691, 691, -2*w^5 - w^4 + 13*w^3 + 5*w^2 - 22*w - 1],\
[691, 691, 3*w^5 + w^4 - 19*w^3 - 5*w^2 + 28*w],\
[691, 691, w^5 + w^4 - 8*w^3 - 3*w^2 + 14*w - 4],\
[691, 691, -w^5 - 2*w^4 + 8*w^3 + 9*w^2 - 15*w - 5],\
[701, 701, -3*w^5 - w^4 + 19*w^3 + 7*w^2 - 26*w - 11],\
[709, 709, -w^5 + 7*w^3 - w^2 - 13*w + 4],\
[709, 709, -w^5 + 4*w^3 - 2*w - 4],\
[709, 709, 2*w^5 + 2*w^4 - 15*w^3 - 8*w^2 + 27*w + 1],\
[709, 709, -w^5 - w^4 + 6*w^3 + 6*w^2 - 7*w - 4],\
[719, 719, -w^4 + w^3 + 4*w^2 - 3*w + 2],\
[719, 719, -3*w^5 - w^4 + 20*w^3 + 6*w^2 - 32*w - 2],\
[729, 3, -3],\
[739, 739, w^5 + 2*w^4 - 7*w^3 - 9*w^2 + 11*w + 7],\
[739, 739, -3*w^5 - 2*w^4 + 21*w^3 + 10*w^2 - 34*w - 6],\
[739, 739, w^5 + w^4 - 6*w^3 - 3*w^2 + 9*w - 3],\
[739, 739, w^4 + w^3 - 4*w^2 - 2*w + 1],\
[739, 739, -3*w^5 + 18*w^3 + w^2 - 23*w + 1],\
[739, 739, 3*w^5 - 18*w^3 - 2*w^2 + 24*w + 5],\
[751, 751, -w^5 + w^4 + 5*w^3 - 5*w^2 - 5*w + 2],\
[761, 761, -w^5 - 2*w^4 + 8*w^3 + 8*w^2 - 15*w - 4],\
[761, 761, -w^5 + 6*w^3 - 6*w + 2],\
[769, 769, w^3 - 2*w^2 - 3*w + 3],\
[811, 811, -3*w^5 + 19*w^3 + w^2 - 25*w - 1],\
[829, 829, -2*w^5 + w^4 + 13*w^3 - 4*w^2 - 19*w + 2],\
[829, 829, 3*w^5 + w^4 - 20*w^3 - 4*w^2 + 29*w - 1],\
[839, 839, -2*w^5 - w^4 + 15*w^3 + 5*w^2 - 25*w - 1],\
[839, 839, -w^5 + 6*w^3 + 2*w^2 - 6*w - 6],\
[841, 29, 4*w^5 + 2*w^4 - 27*w^3 - 10*w^2 + 41*w + 5],\
[859, 859, -2*w^5 + 13*w^3 - 17*w + 2],\
[881, 881, -2*w^5 - 2*w^4 + 14*w^3 + 8*w^2 - 23*w - 3],\
[881, 881, w^5 - 7*w^3 + w^2 + 11*w],\
[911, 911, 4*w^5 - 25*w^3 + 35*w - 3],\
[911, 911, 6*w^5 + 2*w^4 - 39*w^3 - 11*w^2 + 58*w + 5],\
[919, 919, w^4 + w^3 - 6*w^2 - 3*w + 6],\
[919, 919, -3*w^5 + 17*w^3 - 20*w + 1],\
[929, 929, -w^3 + 2*w^2 + 3*w - 8],\
[941, 941, 2*w^5 + 2*w^4 - 15*w^3 - 8*w^2 + 27*w],\
[941, 941, 2*w^5 + w^4 - 15*w^3 - 3*w^2 + 25*w - 3],\
[961, 31, -3*w^5 - w^4 + 18*w^3 + 6*w^2 - 21*w - 6],\
[971, 971, -w^5 + 4*w^3 + 2*w^2 - 5],\
[991, 991, -2*w^5 - 3*w^4 + 14*w^3 + 13*w^2 - 22*w - 6],\
[1009, 1009, -3*w^5 + 17*w^3 - 20*w],\
[1009, 1009, 4*w^5 - 25*w^3 + 35*w - 1],\
[1019, 1019, -3*w^5 + 17*w^3 + 2*w^2 - 20*w - 4],\
[1019, 1019, -w^5 + 5*w^3 - w^2 - 3*w + 1],\
[1019, 1019, -w^3 + 2*w^2 + 5*w - 5],\
[1021, 1021, 2*w^5 + w^4 - 13*w^3 - 4*w^2 + 18*w + 3],\
[1031, 1031, 2*w^5 - 11*w^3 - 2*w^2 + 12*w + 6],\
[1031, 1031, 2*w^5 - 14*w^3 + w^2 + 23*w - 2],\
[1039, 1039, w^4 - 2*w^3 - 5*w^2 + 7*w + 5],\
[1039, 1039, 2*w^5 - w^4 - 11*w^3 + 5*w^2 + 13*w - 5],\
[1039, 1039, -w^5 - w^4 + 7*w^3 + 6*w^2 - 13*w - 6],\
[1039, 1039, 4*w^5 + w^4 - 23*w^3 - 5*w^2 + 28*w + 3],\
[1049, 1049, -w^5 + w^4 + 6*w^3 - 6*w^2 - 9*w + 6],\
[1049, 1049, -3*w^5 + 19*w^3 + w^2 - 25*w + 2],\
[1051, 1051, w^5 + w^4 - 7*w^3 - 2*w^2 + 12*w - 5],\
[1069, 1069, w^5 + 2*w^4 - 7*w^3 - 9*w^2 + 12*w + 6],\
[1091, 1091, -4*w^5 + w^4 + 24*w^3 - 4*w^2 - 30*w + 2],\
[1109, 1109, w^5 + w^4 - 5*w^3 - 5*w^2 + 6*w + 3],\
[1129, 1129, -3*w^5 + 19*w^3 + 2*w^2 - 26*w - 3],\
[1129, 1129, -2*w^5 - w^4 + 14*w^3 + 2*w^2 - 22*w + 2],\
[1129, 1129, 2*w^5 - 11*w^3 - 2*w^2 + 11*w + 3],\
[1129, 1129, -4*w^5 - 2*w^4 + 25*w^3 + 11*w^2 - 35*w - 11],\
[1151, 1151, 2*w^5 + w^4 - 14*w^3 - 5*w^2 + 21*w + 4],\
[1181, 1181, w^5 - 7*w^3 + w^2 + 12*w],\
[1201, 1201, w^5 + 2*w^4 - 6*w^3 - 9*w^2 + 8*w + 5],\
[1229, 1229, w^5 + 2*w^4 - 8*w^3 - 10*w^2 + 14*w + 6],\
[1229, 1229, 2*w^5 + w^4 - 13*w^3 - 5*w^2 + 17*w + 4],\
[1231, 1231, -2*w^5 - 2*w^4 + 15*w^3 + 9*w^2 - 25*w - 3],\
[1249, 1249, -2*w^5 - 2*w^4 + 14*w^3 + 10*w^2 - 21*w - 7],\
[1249, 1249, -w^5 - w^4 + 7*w^3 + 7*w^2 - 11*w - 8],\
[1259, 1259, w^3 + w^2 - 3*w - 5],\
[1259, 1259, -w^5 - w^4 + 9*w^3 + 3*w^2 - 19*w + 2],\
[1259, 1259, -w^4 + w^3 + 3*w^2 - 3*w + 4],\
[1279, 1279, -5*w^5 - 2*w^4 + 35*w^3 + 9*w^2 - 57*w - 2],\
[1279, 1279, 3*w^5 + 2*w^4 - 20*w^3 - 9*w^2 + 31*w + 5],\
[1289, 1289, -w^5 + w^4 + 5*w^3 - 5*w^2 - 6*w + 4],\
[1291, 1291, w^5 + w^4 - 7*w^3 - 3*w^2 + 10*w - 4],\
[1291, 1291, -w^5 - w^4 + 9*w^3 + 3*w^2 - 18*w + 4],\
[1291, 1291, 2*w^5 - 13*w^3 + 17*w],\
[1291, 1291, -5*w^5 - 3*w^4 + 32*w^3 + 15*w^2 - 46*w - 8],\
[1321, 1321, w^4 - w^3 - 4*w^2 + 2*w - 1],\
[1321, 1321, 2*w^5 - 2*w^4 - 12*w^3 + 8*w^2 + 14*w - 3],\
[1321, 1321, 3*w^5 - 19*w^3 - 2*w^2 + 26*w + 4],\
[1321, 1321, -2*w^5 - w^4 + 12*w^3 + 3*w^2 - 15*w + 1],\
[1331, 11, -3*w^5 + 18*w^3 - 24*w + 1],\
[1361, 1361, -4*w^5 - w^4 + 25*w^3 + 6*w^2 - 35*w - 6],\
[1381, 1381, -2*w^5 - 3*w^4 + 14*w^3 + 14*w^2 - 24*w - 6],\
[1381, 1381, -3*w^5 - w^4 + 19*w^3 + 4*w^2 - 28*w + 3],\
[1381, 1381, 2*w^5 + w^4 - 12*w^3 - 3*w^2 + 15*w - 3],\
[1399, 1399, 4*w^5 + 2*w^4 - 27*w^3 - 10*w^2 + 44*w + 4],\
[1409, 1409, 2*w^5 - 14*w^3 + 21*w - 1],\
[1429, 1429, -3*w^5 - w^4 + 20*w^3 + 6*w^2 - 29*w - 5],\
[1429, 1429, -3*w^5 + 18*w^3 - w^2 - 23*w + 3],\
[1429, 1429, w^4 - 2*w^2 - 2*w - 5],\
[1439, 1439, 3*w^5 + 3*w^4 - 19*w^3 - 14*w^2 + 27*w + 5],\
[1451, 1451, w^5 + 2*w^4 - 10*w^3 - 6*w^2 + 22*w - 4],\
[1459, 1459, -w^5 + w^4 + 7*w^3 - 5*w^2 - 10*w + 4],\
[1471, 1471, -w^5 - 2*w^4 + 9*w^3 + 9*w^2 - 17*w - 6],\
[1481, 1481, 2*w^5 + w^4 - 14*w^3 - 5*w^2 + 21*w + 5],\
[1489, 1489, 3*w^5 - w^4 - 17*w^3 + 3*w^2 + 22*w - 2],\
[1499, 1499, -2*w^4 + w^3 + 8*w^2 - 3*w - 4],\
[1511, 1511, 3*w^5 - 18*w^3 - 2*w^2 + 23*w + 4],\
[1511, 1511, w^5 + 2*w^4 - 8*w^3 - 10*w^2 + 14*w + 8],\
[1511, 1511, w^5 + 2*w^4 - 10*w^3 - 7*w^2 + 22*w - 3],\
[1511, 1511, 5*w^5 + w^4 - 29*w^3 - 5*w^2 + 34*w + 4],\
[1531, 1531, 2*w^4 - 3*w^3 - 8*w^2 + 8*w + 2],\
[1549, 1549, -4*w^5 + 27*w^3 - 41*w + 6],\
[1549, 1549, w^5 + w^4 - 7*w^3 - 4*w^2 + 13*w + 5],\
[1559, 1559, 2*w^5 - 11*w^3 + w^2 + 12*w - 4],\
[1559, 1559, -w^5 + 6*w^3 + w^2 - 10*w - 3],\
[1571, 1571, w^3 + 2*w^2 - 4*w - 6],\
[1579, 1579, 2*w^5 + 2*w^4 - 15*w^3 - 11*w^2 + 26*w + 8],\
[1601, 1601, -w^5 + 8*w^3 - 2*w^2 - 16*w + 3],\
[1601, 1601, 3*w^5 + 2*w^4 - 19*w^3 - 7*w^2 + 27*w - 2],\
[1609, 1609, -5*w^5 - 2*w^4 + 32*w^3 + 10*w^2 - 47*w - 2],\
[1619, 1619, 4*w^5 + 3*w^4 - 25*w^3 - 14*w^2 + 35*w + 8],\
[1619, 1619, -2*w^5 + 13*w^3 - 17*w + 1],\
[1621, 1621, -5*w^5 - 3*w^4 + 34*w^3 + 15*w^2 - 53*w - 7],\
[1621, 1621, 4*w^5 + 2*w^4 - 26*w^3 - 7*w^2 + 38*w - 5],\
[1669, 1669, w^5 + w^4 - 9*w^3 - 4*w^2 + 17*w - 1],\
[1681, 41, 4*w^5 - 24*w^3 - 2*w^2 + 33*w + 5],\
[1681, 41, 2*w^4 - 2*w^3 - 9*w^2 + 6*w + 4],\
[1699, 1699, -3*w^5 - 2*w^4 + 18*w^3 + 10*w^2 - 24*w - 3],\
[1699, 1699, -2*w^5 + w^4 + 13*w^3 - 3*w^2 - 19*w + 4],\
[1699, 1699, 4*w^5 - w^4 - 23*w^3 + 3*w^2 + 28*w - 1],\
[1699, 1699, 2*w^4 - w^3 - 8*w^2 + 3*w + 2],\
[1709, 1709, -4*w^5 - 2*w^4 + 26*w^3 + 11*w^2 - 38*w - 7],\
[1709, 1709, 3*w^5 - 17*w^3 + w^2 + 20*w - 4],\
[1721, 1721, 2*w^5 + 2*w^4 - 14*w^3 - 9*w^2 + 22*w - 1],\
[1721, 1721, -2*w^5 + w^4 + 12*w^3 - 5*w^2 - 17*w + 5],\
[1721, 1721, w^5 - w^4 - 7*w^3 + 7*w^2 + 10*w - 12],\
[1721, 1721, -2*w^5 - w^4 + 16*w^3 + 4*w^2 - 30*w + 4],\
[1741, 1741, -2*w^5 + w^4 + 12*w^3 - 3*w^2 - 15*w + 1],\
[1741, 1741, 3*w^5 + 2*w^4 - 19*w^3 - 10*w^2 + 26*w + 8],\
[1759, 1759, 3*w^5 + w^4 - 19*w^3 - 6*w^2 + 25*w + 5],\
[1789, 1789, w^4 + w^3 - 4*w^2 - 5*w + 2],\
[1789, 1789, w^5 - 3*w^3 - 3*w + 3],\
[1789, 1789, -3*w^5 - w^4 + 19*w^3 + 7*w^2 - 26*w - 8],\
[1789, 1789, 2*w^5 - 13*w^3 + w^2 + 20*w - 1],\
[1801, 1801, 6*w^5 + 2*w^4 - 39*w^3 - 9*w^2 + 56*w + 3],\
[1811, 1811, 2*w^5 + w^4 - 15*w^3 - 4*w^2 + 26*w - 3],\
[1811, 1811, -4*w^5 - w^4 + 26*w^3 + 5*w^2 - 37*w - 5],\
[1811, 1811, -4*w^5 + w^4 + 23*w^3 - 3*w^2 - 27*w],\
[1831, 1831, 5*w^5 + w^4 - 30*w^3 - 4*w^2 + 39*w],\
[1831, 1831, 2*w^5 - 12*w^3 - w^2 + 16*w + 6],\
[1831, 1831, 2*w^5 + 2*w^4 - 14*w^3 - 12*w^2 + 22*w + 13],\
[1831, 1831, w^5 - 7*w^3 + 11*w + 3],\
[1871, 1871, 3*w^5 + w^4 - 21*w^3 - 3*w^2 + 32*w - 1],\
[1871, 1871, 3*w^5 + w^4 - 17*w^3 - 7*w^2 + 22*w + 8],\
[1871, 1871, w - 4],\
[1879, 1879, -3*w^5 - 2*w^4 + 21*w^3 + 9*w^2 - 32*w - 6],\
[1901, 1901, 3*w^5 + 2*w^4 - 20*w^3 - 7*w^2 + 31*w - 5],\
[1931, 1931, -4*w^5 - 3*w^4 + 27*w^3 + 15*w^2 - 41*w - 10],\
[1931, 1931, -3*w^5 - w^4 + 19*w^3 + 7*w^2 - 26*w - 7],\
[1949, 1949, -2*w^5 - 3*w^4 + 13*w^3 + 13*w^2 - 19*w - 8],\
[1949, 1949, -5*w^5 - 2*w^4 + 33*w^3 + 8*w^2 - 50*w - 2],\
[1949, 1949, -4*w^5 - 2*w^4 + 28*w^3 + 11*w^2 - 45*w - 6],\
[1951, 1951, 5*w^5 + w^4 - 31*w^3 - 3*w^2 + 42*w - 5],\
[1951, 1951, 3*w^5 + 2*w^4 - 21*w^3 - 11*w^2 + 35*w + 8],\
[1979, 1979, 5*w^5 + w^4 - 31*w^3 - 3*w^2 + 43*w - 6],\
[1979, 1979, -5*w^5 - w^4 + 31*w^3 + 7*w^2 - 42*w - 9],\
[1999, 1999, -3*w^5 - w^4 + 21*w^3 + 4*w^2 - 33*w + 2],\
[1999, 1999, 3*w^5 + 2*w^4 - 17*w^3 - 10*w^2 + 20*w + 7],\
[1999, 1999, w^5 + w^4 - 9*w^3 - 5*w^2 + 19*w + 6]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^10 - 23*x^8 + 176*x^6 - 528*x^4 + 559*x^2 - 121
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 5/88*e^9 - 13/11*e^7 + 15/2*e^5 - 15*e^3 + 375/88*e, -5/176*e^9 + 13/22*e^7 - 7/2*e^5 + 9/2*e^3 + 637/176*e, -1/16*e^8 + 5/4*e^6 - 29/4*e^4 + 45/4*e^2 + 13/16, -1, 3/44*e^9 - 69/44*e^7 + 47/4*e^5 - 127/4*e^3 + 481/22*e, 1/88*e^9 - 3/22*e^7 - 1/2*e^5 + 17/2*e^3 - 1157/88*e, 7/44*e^9 - 75/22*e^7 + 23*e^5 - 109/2*e^3 + 1537/44*e, -9/176*e^9 + 49/44*e^7 - 31/4*e^5 + 79/4*e^3 - 3227/176*e, -1/2*e^4 + 5*e^2 - 5/2, 3/176*e^9 - 9/44*e^7 - 1/4*e^5 + 25/4*e^3 - 1535/176*e, -1/22*e^9 + 23/22*e^7 - 8*e^5 + 47/2*e^3 - 427/22*e, -1/2*e^4 + 5*e^2 - 9/2, -1/88*e^9 + 3/22*e^7 + 1/2*e^5 - 17/2*e^3 + 1685/88*e, 1/22*e^9 - 23/22*e^7 + 8*e^5 - 49/2*e^3 + 625/22*e, -3/88*e^9 + 10/11*e^7 - 8*e^5 + 26*e^3 - 2205/88*e, 1/4*e^6 - 17/4*e^4 + 69/4*e^2 - 5/4, -e^3 + 7*e, 1/16*e^9 - 5/4*e^7 + 29/4*e^5 - 45/4*e^3 - 45/16*e, 1/8*e^8 - 5/2*e^6 + 15*e^4 - 59/2*e^2 + 151/8, -3/16*e^8 + 15/4*e^6 - 91/4*e^4 + 183/4*e^2 - 425/16, -1/88*e^9 + 3/22*e^7 + 1/2*e^5 - 19/2*e^3 + 1949/88*e, 1/44*e^9 - 23/44*e^7 + 17/4*e^5 - 57/4*e^3 + 307/22*e, 1/4*e^8 - 5*e^6 + 29*e^4 - 44*e^2 - 25/4, 3/88*e^9 - 10/11*e^7 + 8*e^5 - 24*e^3 + 973/88*e, -1/4*e^8 + 5*e^6 - 30*e^4 + 56*e^2 - 75/4, 1/8*e^8 - 3*e^6 + 23*e^4 - 60*e^2 + 255/8, 1/4*e^6 - 17/4*e^4 + 65/4*e^2 + 7/4, 3/16*e^8 - 17/4*e^6 + 121/4*e^4 - 285/4*e^2 + 625/16, -9/44*e^9 + 49/11*e^7 - 31*e^5 + 78*e^3 - 2479/44*e, 1/44*e^9 - 17/22*e^7 + 17/2*e^5 - 67/2*e^3 + 1549/44*e, -1/88*e^9 + 3/22*e^7 - 1/2*e^3 - 1087/88*e, 1/2*e^4 - 4*e^2 - 1/2, -1/4*e^6 + 15/4*e^4 - 49/4*e^2 + 35/4, 1/8*e^8 - 11/4*e^6 + 75/4*e^4 - 171/4*e^2 + 245/8, -1/4*e^8 + 5*e^6 - 61/2*e^4 + 62*e^2 - 97/4, -1/11*e^9 + 81/44*e^7 - 43/4*e^5 + 59/4*e^3 + 283/44*e, -19/88*e^9 + 213/44*e^7 - 141/4*e^5 + 375/4*e^3 - 5539/88*e, 1/4*e^8 - 21/4*e^6 + 137/4*e^4 - 297/4*e^2 + 33, -1/4*e^8 + 19/4*e^6 - 99/4*e^4 + 111/4*e^2 + 41/2, 1/4*e^8 - 11/2*e^6 + 38*e^4 - 179/2*e^2 + 163/4, -1/4*e^8 + 11/2*e^6 - 77/2*e^4 + 187/2*e^2 - 177/4, -5/88*e^9 + 13/11*e^7 - 7*e^5 + 7*e^3 + 2045/88*e, 1/4*e^8 - 21/4*e^6 + 129/4*e^4 - 209/4*e^2 + 1, -7/176*e^9 + 43/44*e^7 - 33/4*e^5 + 109/4*e^3 - 4661/176*e, 1/8*e^8 - 5/2*e^6 + 27/2*e^4 - 19/2*e^2 - 157/8, 1/22*e^9 - 23/22*e^7 + 8*e^5 - 47/2*e^3 + 427/22*e, -1/4*e^8 + 5*e^6 - 59/2*e^4 + 51*e^2 - 81/4, -1/8*e^8 + 2*e^6 - 7*e^4 - 4*e^2 + 73/8, -17/88*e^9 + 95/22*e^7 - 63/2*e^5 + 171/2*e^3 - 5499/88*e, 1/8*e^8 - 9/4*e^6 + 43/4*e^4 - 57/4*e^2 + 77/8, -4/11*e^9 + 173/22*e^7 - 54*e^5 + 263/2*e^3 - 971/11*e, 1/2*e^6 - 15/2*e^4 + 49/2*e^2 - 15/2, -1/22*e^9 + 17/11*e^7 - 17*e^5 + 67*e^3 - 1549/22*e, -3/44*e^9 + 29/22*e^7 - 15/2*e^5 + 29/2*e^3 - 467/44*e, -1/4*e^8 + 11/2*e^6 - 38*e^4 + 179/2*e^2 - 203/4, -5/16*e^8 + 27/4*e^6 - 185/4*e^4 + 451/4*e^2 - 1007/16, 3/16*e^8 - 17/4*e^6 + 123/4*e^4 - 301/4*e^2 + 681/16, 1/8*e^8 - 2*e^6 + 7*e^4 - e^2 + 127/8, -1/16*e^8 + 5/4*e^6 - 31/4*e^4 + 53/4*e^2 + 53/16, 1/8*e^8 - 5/2*e^6 + 31/2*e^4 - 71/2*e^2 + 243/8, -7/16*e^8 + 37/4*e^6 - 237/4*e^4 + 457/4*e^2 - 573/16, -3/16*e^9 + 15/4*e^7 - 91/4*e^5 + 187/4*e^3 - 505/16*e, 5/44*e^9 - 26/11*e^7 + 16*e^5 - 45*e^3 + 2663/44*e, 1/8*e^8 - 5/2*e^6 + 29/2*e^4 - 43/2*e^2 + 43/8, -1/4*e^9 + 11/2*e^7 - 39*e^5 + 207/2*e^3 - 375/4*e, -3/8*e^8 + 31/4*e^6 - 195/4*e^4 + 391/4*e^2 - 275/8, 69/176*e^9 - 361/44*e^7 + 213/4*e^5 - 467/4*e^3 + 10279/176*e, -5/16*e^8 + 25/4*e^6 - 149/4*e^4 + 289/4*e^2 - 559/16, 13/88*e^9 - 36/11*e^7 + 23*e^5 - 55*e^3 + 2691/88*e, 1/88*e^9 - 3/22*e^7 - 3/2*e^5 + 43/2*e^3 - 4325/88*e, -1/88*e^9 + 3/22*e^7 + 5/2*e^3 - 2935/88*e, 3/8*e^8 - 15/2*e^6 + 44*e^4 - 143/2*e^2 + 5/8, -3/8*e^8 + 29/4*e^6 - 161/4*e^4 + 257/4*e^2 - 135/8, -3/22*e^9 + 127/44*e^7 - 73/4*e^5 + 129/4*e^3 + 23/44*e, 19/88*e^9 - 101/22*e^7 + 61/2*e^5 - 141/2*e^3 + 4241/88*e, 9/44*e^9 - 49/11*e^7 + 30*e^5 - 64*e^3 + 675/44*e, 3/16*e^9 - 17/4*e^7 + 125/4*e^5 - 341/4*e^3 + 1281/16*e, 3/8*e^8 - 8*e^6 + 107/2*e^4 - 121*e^2 + 473/8, -1/8*e^8 + 2*e^6 - 7*e^4 - 2*e^2 + 121/8, 1/44*e^9 - 17/22*e^7 + 17/2*e^5 - 65/2*e^3 + 1241/44*e, 3/8*e^8 - 31/4*e^6 + 199/4*e^4 - 435/4*e^2 + 419/8, 35/88*e^9 - 193/22*e^7 + 125/2*e^5 - 325/2*e^3 + 9841/88*e, 23/176*e^9 - 113/44*e^7 + 59/4*e^5 - 103/4*e^3 + 2429/176*e, -1/4*e^8 + 5*e^6 - 29*e^4 + 46*e^2 - 23/4, 15/88*e^9 - 167/44*e^7 + 105/4*e^5 - 225/4*e^3 + 1103/88*e, -1/8*e^9 + 3*e^7 - 47/2*e^5 + 65*e^3 - 323/8*e, 9/88*e^9 - 30/11*e^7 + 24*e^5 - 77*e^3 + 5823/88*e, -1/8*e^8 + 5/2*e^6 - 13*e^4 + 13/2*e^2 + 81/8, -1/8*e^8 + 5/2*e^6 - 29/2*e^4 + 37/2*e^2 + 125/8, 13/44*e^9 - 277/44*e^7 + 169/4*e^5 - 403/4*e^3 + 1659/22*e, 1/16*e^8 - 7/4*e^6 + 63/4*e^4 - 191/4*e^2 + 443/16, -3/88*e^9 + 10/11*e^7 - 15/2*e^5 + 15*e^3 + 1887/88*e, 2/11*e^9 - 81/22*e^7 + 43/2*e^5 - 65/2*e^3 - 41/22*e, -3/44*e^9 + 29/22*e^7 - 7*e^5 + 11/2*e^3 + 1139/44*e, 3/2*e^4 - 20*e^2 + 81/2, -9/88*e^9 + 65/44*e^7 - 7/4*e^5 - 129/4*e^3 + 6343/88*e, -5/8*e^8 + 25/2*e^6 - 147/2*e^4 + 251/2*e^2 - 175/8, 35/176*e^9 - 193/44*e^7 + 123/4*e^5 - 299/4*e^3 + 7201/176*e, 1/2*e^8 - 10*e^6 + 60*e^4 - 114*e^2 + 103/2, 3/8*e^8 - 15/2*e^6 + 89/2*e^4 - 173/2*e^2 + 393/8, 1/2*e^6 - 8*e^4 + 55/2*e^2 - 8, -2/11*e^9 + 151/44*e^7 - 73/4*e^5 + 101/4*e^3 - 259/44*e, 1/8*e^8 - 2*e^6 + 7*e^4 - e^2 + 31/8, -21/88*e^9 + 59/11*e^7 - 77/2*e^5 + 97*e^3 - 5535/88*e, 9/44*e^9 - 49/11*e^7 + 30*e^5 - 65*e^3 + 1335/44*e, 1/88*e^9 + 5/44*e^7 - 23/4*e^5 + 163/4*e^3 - 6371/88*e, e^4 - 16*e^2 + 41, -5/22*e^9 + 52/11*e^7 - 30*e^5 + 61*e^3 - 617/22*e, 7/22*e^9 - 75/11*e^7 + 46*e^5 - 110*e^3 + 1735/22*e, -9/44*e^9 + 49/11*e^7 - 63/2*e^5 + 84*e^3 - 2721/44*e, -3/176*e^9 + 31/44*e^7 - 41/4*e^5 + 229/4*e^3 - 15977/176*e, 9/88*e^9 - 109/44*e^7 + 81/4*e^5 - 267/4*e^3 + 7517/88*e, 3/8*e^8 - 17/2*e^6 + 59*e^4 - 247/2*e^2 + 245/8, -1/8*e^8 + 3*e^6 - 24*e^4 + 70*e^2 - 263/8, -7/88*e^9 + 43/22*e^7 - 33/2*e^5 + 115/2*e^3 - 7037/88*e, -3/8*e^8 + 15/2*e^6 - 91/2*e^4 + 179/2*e^2 - 105/8, 1/16*e^8 - 3/4*e^6 + 3/4*e^4 + 5/4*e^2 + 299/16, 1/8*e^8 - 5/2*e^6 + 31/2*e^4 - 67/2*e^2 + 339/8, 7/88*e^9 - 43/22*e^7 + 16*e^5 - 103/2*e^3 + 5849/88*e, -9/88*e^9 + 49/22*e^7 - 31/2*e^5 + 85/2*e^3 - 4547/88*e, 1/16*e^9 - 5/4*e^7 + 29/4*e^5 - 49/4*e^3 + 131/16*e, 3/44*e^9 - 9/11*e^7 - 2*e^5 + 40*e^3 - 3735/44*e, -1/4*e^8 + 9/2*e^6 - 41/2*e^4 + 27/2*e^2 + 59/4, 1/8*e^8 - 2*e^6 + 7*e^4 + 7*e^2 - 161/8, -3/11*e^9 + 287/44*e^7 - 209/4*e^5 + 633/4*e^3 - 5619/44*e, 5/8*e^8 - 27/2*e^6 + 179/2*e^4 - 377/2*e^2 + 591/8, -1/8*e^8 + 5/2*e^6 - 31/2*e^4 + 69/2*e^2 - 219/8, -95/176*e^9 + 505/44*e^7 - 305/4*e^5 + 687/4*e^3 - 16365/176*e, 9/44*e^9 - 49/11*e^7 + 31*e^5 - 77*e^3 + 2523/44*e, 3/16*e^8 - 13/4*e^6 + 55/4*e^4 - 37/4*e^2 + 265/16, -21/176*e^9 + 85/44*e^7 - 23/4*e^5 - 73/4*e^3 + 9953/176*e, 3/8*e^8 - 8*e^6 + 55*e^4 - 135*e^2 + 493/8, -1/2*e^6 + 11*e^4 - 127/2*e^2 + 65, -1/4*e^8 + 9/2*e^6 - 41/2*e^4 + 25/2*e^2 + 127/4, 1/2*e^8 - 41/4*e^6 + 251/4*e^4 - 473/4*e^2 + 197/4, 1/22*e^9 - 23/22*e^7 + 9*e^5 - 77/2*e^3 + 1351/22*e, -1/16*e^8 + 9/4*e^6 - 97/4*e^4 + 329/4*e^2 - 611/16, -2/11*e^9 + 46/11*e^7 - 63/2*e^5 + 88*e^3 - 1499/22*e, 15/88*e^9 - 39/11*e^7 + 45/2*e^5 - 47*e^3 + 2357/88*e, -1/4*e^8 + 11/2*e^6 - 75/2*e^4 + 163/2*e^2 - 173/4, -1/11*e^9 + 23/11*e^7 - 16*e^5 + 48*e^3 - 592/11*e, -1/44*e^9 + 17/22*e^7 - 17/2*e^5 + 67/2*e^3 - 1285/44*e, 1/16*e^8 - 9/4*e^6 + 99/4*e^4 - 361/4*e^2 + 987/16, -1/88*e^9 + 7/11*e^7 - 8*e^5 + 27*e^3 - 207/88*e, -3/8*e^8 + 8*e^6 - 101/2*e^4 + 85*e^2 - 1/8, -51/88*e^9 + 137/11*e^7 - 84*e^5 + 196*e^3 - 10293/88*e, -15/88*e^9 + 39/11*e^7 - 45/2*e^5 + 46*e^3 - 861/88*e, -1/4*e^8 + 5*e^6 - 30*e^4 + 53*e^2 + 73/4, -1/4*e^8 + 5*e^6 - 63/2*e^4 + 71*e^2 - 65/4, 1/8*e^8 - 9/4*e^6 + 45/4*e^4 - 41/4*e^2 - 359/8, 13/44*e^9 - 133/22*e^7 + 38*e^5 - 161/2*e^3 + 1987/44*e, -1/4*e^8 + 11/2*e^6 - 39*e^4 + 207/2*e^2 - 279/4, 3/8*e^8 - 8*e^6 + 53*e^4 - 122*e^2 + 581/8, 5/44*e^9 - 115/44*e^7 + 79/4*e^5 - 237/4*e^3 + 938/11*e, 1/2*e^8 - 21/2*e^6 + 133/2*e^4 - 257/2*e^2 + 48, 5/8*e^8 - 25/2*e^6 + 147/2*e^4 - 259/2*e^2 + 367/8, -19/88*e^9 + 101/22*e^7 - 31*e^5 + 159/2*e^3 - 7805/88*e, 13/22*e^9 - 565/44*e^7 + 357/4*e^5 - 895/4*e^3 + 6625/44*e, -7/44*e^9 + 32/11*e^7 - 13*e^5 - 2*e^3 + 1587/44*e, 1/4*e^8 - 5*e^6 + 30*e^4 - 60*e^2 + 187/4, 1/8*e^8 - 3*e^6 + 51/2*e^4 - 87*e^2 + 483/8, -3/8*e^8 + 15/2*e^6 - 91/2*e^4 + 193/2*e^2 - 449/8, 3/8*e^8 - 15/2*e^6 + 83/2*e^4 - 85/2*e^2 - 367/8, -19/176*e^9 + 101/44*e^7 - 61/4*e^5 + 143/4*e^3 - 7673/176*e, -9/88*e^9 + 65/44*e^7 - 3/4*e^5 - 177/4*e^3 + 9247/88*e, 1/8*e^8 - 9/4*e^6 + 47/4*e^4 - 109/4*e^2 + 301/8, 43/88*e^9 - 239/22*e^7 + 78*e^5 - 407/2*e^3 + 12773/88*e, -9/44*e^9 + 87/22*e^7 - 20*e^5 + 9/2*e^3 + 3109/44*e, -89/176*e^9 + 487/44*e^7 - 309/4*e^5 + 769/4*e^3 - 23219/176*e, 61/88*e^9 - 337/22*e^7 + 217/2*e^5 - 553/2*e^3 + 16103/88*e, -1/2*e^8 + 10*e^6 - 59*e^4 + 105*e^2 - 47/2, -7/44*e^9 + 117/44*e^7 - 35/4*e^5 - 85/4*e^3 + 1525/22*e, -41/88*e^9 + 477/44*e^7 - 331/4*e^5 + 915/4*e^3 - 12865/88*e, 23/44*e^9 - 124/11*e^7 + 151/2*e^5 - 167*e^3 + 3419/44*e, -1/2*e^8 + 39/4*e^6 - 221/4*e^4 + 327/4*e^2 + 153/4, 3/8*e^8 - 33/4*e^6 + 229/4*e^4 - 561/4*e^2 + 695/8, 7/16*e^8 - 37/4*e^6 + 243/4*e^4 - 525/4*e^2 + 437/16, 5/16*e^8 - 29/4*e^6 + 217/4*e^4 - 553/4*e^2 + 1359/16, 9/22*e^9 - 98/11*e^7 + 62*e^5 - 153*e^3 + 1929/22*e, 1/4*e^9 - 6*e^7 + 48*e^5 - 145*e^3 + 435/4*e, -1/2*e^6 + 13/2*e^4 - 13/2*e^2 - 75/2, -1/2*e^8 + 9*e^6 - 42*e^4 + 29*e^2 + 77/2, -9/16*e^9 + 49/4*e^7 - 339/4*e^5 + 817/4*e^3 - 1843/16*e, -3/22*e^9 + 29/11*e^7 - 14*e^5 + 11*e^3 + 875/22*e, -21/44*e^9 + 107/11*e^7 - 60*e^5 + 118*e^3 - 1751/44*e, -5/176*e^9 - 7/44*e^7 + 45/4*e^5 - 305/4*e^3 + 19601/176*e, 1/2*e^6 - 19/2*e^4 + 87/2*e^2 - 65/2, 17/22*e^9 - 369/22*e^7 + 114*e^5 - 527/2*e^3 + 3277/22*e, 1/2*e^8 - 43/4*e^6 + 289/4*e^4 - 651/4*e^2 + 291/4, 3/8*e^8 - 31/4*e^6 + 195/4*e^4 - 383/4*e^2 + 67/8, -1/8*e^8 + 13/4*e^6 - 119/4*e^4 + 413/4*e^2 - 533/8, 1/2*e^6 - 15/2*e^4 + 61/2*e^2 - 87/2, 3/8*e^8 - 15/2*e^6 + 93/2*e^4 - 195/2*e^2 + 209/8, -1/4*e^8 + 21/4*e^6 - 129/4*e^4 + 213/4*e^2 - 18, -35/88*e^9 + 375/44*e^7 - 233/4*e^5 + 585/4*e^3 - 9291/88*e, -3/8*e^8 + 17/2*e^6 - 60*e^4 + 269/2*e^2 - 565/8, -85/176*e^9 + 431/44*e^7 - 243/4*e^5 + 513/4*e^3 - 14031/176*e, 1/4*e^8 - 11/2*e^6 + 39*e^4 - 191/2*e^2 + 167/4, 41/88*e^9 - 111/11*e^7 + 70*e^5 - 173*e^3 + 7607/88*e, -7/2*e^4 + 41*e^2 - 131/2, -1/8*e^8 + 5/2*e^6 - 15*e^4 + 45/2*e^2 + 305/8, -1/8*e^8 + 11/4*e^6 - 69/4*e^4 + 79/4*e^2 + 199/8, -17/88*e^9 + 42/11*e^7 - 21*e^5 + 24*e^3 + 2377/88*e, 59/88*e^9 - 309/22*e^7 + 185/2*e^5 - 437/2*e^3 + 14105/88*e, 17/88*e^9 - 179/44*e^7 + 109/4*e^5 - 253/4*e^3 + 1253/88*e, 3/16*e^8 - 13/4*e^6 + 55/4*e^4 + 3/4*e^2 - 727/16, 5/88*e^9 - 37/22*e^7 + 35/2*e^5 - 147/2*e^3 + 8735/88*e, -1/2*e^8 + 11*e^6 - 151/2*e^4 + 171*e^2 - 68, -17/88*e^9 + 53/11*e^7 - 40*e^5 + 124*e^3 - 9767/88*e, -3/44*e^9 + 29/22*e^7 - 13/2*e^5 - 7/2*e^3 + 2041/44*e, -1/2*e^8 + 23/2*e^6 - 85*e^4 + 431/2*e^2 - 219/2, 1/8*e^8 - 3*e^6 + 53/2*e^4 - 100*e^2 + 787/8, -6/11*e^9 + 497/44*e^7 - 289/4*e^5 + 639/4*e^3 - 4539/44*e, 1/2*e^8 - 19/2*e^6 + 103/2*e^4 - 145/2*e^2 + 8, 3/44*e^9 - 91/44*e^7 + 81/4*e^5 - 281/4*e^3 + 642/11*e, -1/44*e^9 + 17/22*e^7 - 15/2*e^5 + 45/2*e^3 - 757/44*e, -9/88*e^9 + 109/44*e^7 - 83/4*e^5 + 279/4*e^3 - 5449/88*e, -23/44*e^9 + 135/11*e^7 - 94*e^5 + 258*e^3 - 7269/44*e, e^6 - 17*e^4 + 71*e^2 - 15, -1/16*e^9 + 5/4*e^7 - 25/4*e^5 - 31/4*e^3 + 1229/16*e, 3/4*e^8 - 16*e^6 + 213/2*e^4 - 242*e^2 + 547/4, -13/88*e^9 + 25/11*e^7 - 5*e^5 - 31*e^3 + 5669/88*e, -35/88*e^9 + 91/11*e^7 - 52*e^5 + 100*e^3 - 1173/88*e, -1/8*e^8 + 3/2*e^6 + 3/2*e^4 - 85/2*e^2 + 477/8, -1/11*e^9 + 23/11*e^7 - 18*e^5 + 78*e^3 - 1538/11*e, 109/176*e^9 - 591/44*e^7 + 365/4*e^5 - 841/4*e^3 + 19967/176*e, 15/44*e^9 - 145/22*e^7 + 35*e^5 - 75/2*e^3 - 1295/44*e, 53/176*e^9 - 291/44*e^7 + 187/4*e^5 - 489/4*e^3 + 16383/176*e, -7/88*e^9 + 43/22*e^7 - 33/2*e^5 + 113/2*e^3 - 6773/88*e, 1/2*e^9 - 43/4*e^7 + 287/4*e^5 - 615/4*e^3 + 225/4*e, -27/88*e^9 + 327/44*e^7 - 241/4*e^5 + 733/4*e^3 - 12475/88*e, -1/44*e^9 + 17/22*e^7 - 7*e^5 + 23/2*e^3 + 1641/44*e, -1/16*e^8 + 9/4*e^6 - 101/4*e^4 + 381/4*e^2 - 1187/16, 1/176*e^9 + 63/44*e^7 - 109/4*e^5 + 553/4*e^3 - 30285/176*e, 3/8*e^8 - 7*e^6 + 35*e^4 - 34*e^2 - 131/8, 3/22*e^9 - 29/11*e^7 + 27/2*e^5 - 3*e^3 - 762/11*e, -5/8*e^8 + 12*e^6 - 133/2*e^4 + 104*e^2 - 71/8, -5/8*e^8 + 25/2*e^6 - 151/2*e^4 + 287/2*e^2 - 319/8, -1/8*e^8 + 2*e^6 - 15/2*e^4 - 3*e^2 + 373/8, 1/8*e^8 - 2*e^6 + 15/2*e^4 - 4*e^2 + 131/8, -43/88*e^9 + 239/22*e^7 - 155/2*e^5 + 391/2*e^3 - 10705/88*e, -7/44*e^9 + 75/22*e^7 - 47/2*e^5 + 119/2*e^3 - 1559/44*e, 5/88*e^9 - 41/44*e^7 + 7/4*e^5 + 105/4*e^3 - 7875/88*e, 13/88*e^9 - 61/22*e^7 + 25/2*e^5 + 19/2*e^3 - 7913/88*e, -1/22*e^9 + 35/44*e^7 - 11/4*e^5 - 39/4*e^3 + 1797/44*e, -1/4*e^8 + 5*e^6 - 30*e^4 + 69*e^2 - 287/4, -3/4*e^9 + 67/4*e^7 - 481/4*e^5 + 1223/4*e^3 - 403/2*e, -3/16*e^8 + 13/4*e^6 - 57/4*e^4 + 53/4*e^2 - 289/16, -81/176*e^9 + 441/44*e^7 - 275/4*e^5 + 659/4*e^3 - 20947/176*e, -3/8*e^8 + 7*e^6 - 37*e^4 + 44*e^2 + 387/8, -35/44*e^9 + 182/11*e^7 - 105*e^5 + 215*e^3 - 3813/44*e, 19/88*e^9 - 235/44*e^7 + 177/4*e^5 - 545/4*e^3 + 9939/88*e, -85/88*e^9 + 453/22*e^7 - 273/2*e^5 + 609/2*e^3 - 13679/88*e, 1/8*e^8 - 3*e^6 + 23*e^4 - 52*e^2 + 239/8, 23/88*e^9 - 237/44*e^7 + 137/4*e^5 - 307/4*e^3 + 4431/88*e, -43/88*e^9 + 239/22*e^7 - 155/2*e^5 + 391/2*e^3 - 10177/88*e, -1/2*e^8 + 21/2*e^6 - 131/2*e^4 + 215/2*e^2 + 26, 1/8*e^8 - 4*e^6 + 41*e^4 - 142*e^2 + 855/8, -73/88*e^9 + 203/11*e^7 - 265/2*e^5 + 342*e^3 - 19907/88*e, -e^5 + 15*e^3 - 52*e, -3/8*e^8 + 13/2*e^6 - 29*e^4 + 37/2*e^2 + 275/8, -17/176*e^9 + 51/44*e^7 + 9/4*e^5 - 171/4*e^3 + 8317/176*e, 91/176*e^9 - 493/44*e^7 + 303/4*e^5 - 699/4*e^3 + 21961/176*e, -e^6 + 19*e^4 - 98*e^2 + 92, -3/8*e^8 + 9*e^6 - 70*e^4 + 189*e^2 - 605/8, -15/16*e^8 + 77/4*e^6 - 477/4*e^4 + 957/4*e^2 - 1989/16, -11/16*e^8 + 57/4*e^6 - 353/4*e^4 + 653/4*e^2 - 809/16, 3/8*e^8 - 17/2*e^6 + 123/2*e^4 - 297/2*e^2 + 793/8, -1/8*e^8 + 3/2*e^6 + 4*e^4 - 141/2*e^2 + 809/8, 7/16*e^8 - 35/4*e^6 + 207/4*e^4 - 403/4*e^2 + 1333/16, -1/4*e^8 + 6*e^6 - 50*e^4 + 156*e^2 - 383/4, 5/8*e^9 - 14*e^7 + 203/2*e^5 - 271*e^3 + 1687/8*e, 9/16*e^8 - 45/4*e^6 + 263/4*e^4 - 389/4*e^2 - 669/16, 3/8*e^8 - 29/4*e^6 + 149/4*e^4 - 81/4*e^2 - 561/8, 13/44*e^9 - 72/11*e^7 + 47*e^5 - 119*e^3 + 2339/44*e, 7/4*e^6 - 115/4*e^4 + 487/4*e^2 - 451/4, -1/8*e^8 + 3*e^6 - 23*e^4 + 65*e^2 - 343/8, -1/8*e^8 + 9/4*e^6 - 47/4*e^4 + 41/4*e^2 + 587/8, -3/4*e^8 + 31/2*e^6 - 201/2*e^4 + 459/2*e^2 - 447/4, 3/2*e^6 - 57/2*e^4 + 275/2*e^2 - 221/2, -3/4*e^8 + 31/2*e^6 - 189/2*e^4 + 319/2*e^2 - 111/4, -1/4*e^9 + 5*e^7 - 29*e^5 + 48*e^3 - 111/4*e, 21/44*e^9 - 118/11*e^7 + 77*e^5 - 187*e^3 + 3467/44*e, -1/16*e^8 + 3/4*e^6 + 1/4*e^4 - 53/4*e^2 + 613/16, -23/22*e^9 + 981/44*e^7 - 597/4*e^5 + 1395/4*e^3 - 9313/44*e]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([29, 29, 2*w^5 - 13*w^3 + 19*w - 2])] = 1

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