/*
  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([19, 19, -w^3 + w^2 + 4*w - 3])

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^12 - 36*x^10 + 490*x^8 - 3132*x^6 + 9413*x^4 - 11088*x^2 + 2304
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, -1/2*e^3 + 9/2*e, 11/1344*e^11 - 27/112*e^9 + 1627/672*e^7 - 1049/112*e^5 + 15055/1344*e^3 - 45/14*e, -1, -1/56*e^10 + 4/7*e^8 - 181/28*e^6 + 214/7*e^4 - 3013/56*e^2 + 114/7, 1/112*e^11 - 2/7*e^9 + 181/56*e^7 - 107/7*e^5 + 3069/112*e^3 - 163/14*e, 3/224*e^11 - 3/7*e^9 + 557/112*e^7 - 178/7*e^5 + 12371/224*e^3 - 493/14*e, 11/1344*e^11 - 27/112*e^9 + 1627/672*e^7 - 1021/112*e^5 + 9679/1344*e^3 + 267/28*e, 1/112*e^11 - 2/7*e^9 + 181/56*e^7 - 435/28*e^5 + 3461/112*e^3 - 529/28*e, -1/56*e^10 + 4/7*e^8 - 181/28*e^6 + 421/14*e^4 - 2649/56*e^2 + 16/7, -1/84*e^11 + 19/56*e^9 - 521/168*e^7 + 481/56*e^5 + 1079/168*e^3 - 197/7*e, -1/192*e^11 + 3/16*e^9 - 245/96*e^7 + 253/16*e^5 - 7877/192*e^3 + 121/4*e, 3/112*e^10 - 6/7*e^8 + 543/56*e^6 - 635/14*e^4 + 8535/112*e^2 - 150/7, 13/1344*e^11 - 37/112*e^9 + 2717/672*e^7 - 2347/112*e^5 + 54569/1344*e^3 - 345/28*e, -1/224*e^11 + 1/7*e^9 - 167/112*e^7 + 36/7*e^5 - 17/224*e^3 - 66/7*e, -11/672*e^11 + 27/56*e^9 - 1627/336*e^7 + 1035/56*e^5 - 12031/672*e^3 - 331/28*e, -1/4*e^6 + 9/2*e^4 - 81/4*e^2 + 16, -23/1344*e^11 + 59/112*e^9 - 3799/672*e^7 + 2789/112*e^5 - 57259/1344*e^3 + 829/28*e, 11/1344*e^11 - 27/112*e^9 + 1627/672*e^7 - 1077/112*e^5 + 19087/1344*e^3 - 251/28*e, 1/56*e^10 - 4/7*e^8 + 181/28*e^6 - 207/7*e^4 + 2397/56*e^2 + 12/7, 1/112*e^10 - 2/7*e^8 + 195/56*e^6 - 277/14*e^4 + 5393/112*e^2 - 183/7, -1/112*e^11 + 2/7*e^9 - 181/56*e^7 + 207/14*e^5 - 2285/112*e^3 - 62/7*e, 1/84*e^11 - 19/56*e^9 + 521/168*e^7 - 467/56*e^5 - 1667/168*e^3 + 1103/28*e, -1/14*e^10 + 121/56*e^8 - 1287/56*e^6 + 5623/56*e^4 - 8629/56*e^2 + 204/7, 11/672*e^11 - 27/56*e^9 + 1627/336*e^7 - 1049/56*e^5 + 15055/672*e^3 - 31/7*e, 5/112*e^10 - 73/56*e^8 + 365/28*e^6 - 2831/56*e^4 + 6455/112*e^2 + 72/7, -3/112*e^10 + 6/7*e^8 - 543/56*e^6 + 635/14*e^4 - 8535/112*e^2 + 178/7, 1/56*e^10 - 4/7*e^8 + 181/28*e^6 - 421/14*e^4 + 2649/56*e^2 + 12/7, 3/112*e^10 - 6/7*e^8 + 529/56*e^6 - 286/7*e^4 + 6267/112*e^2 - 38/7, -3/112*e^11 + 6/7*e^9 - 543/56*e^7 + 1277/28*e^5 - 8815/112*e^3 + 663/28*e, -5/168*e^11 + 51/56*e^9 - 1649/168*e^7 + 2473/56*e^5 - 6521/84*e^3 + 583/14*e, 1/112*e^11 - 2/7*e^9 + 181/56*e^7 - 407/28*e^5 + 1781/112*e^3 + 647/28*e, -1/14*e^10 + 121/56*e^8 - 1259/56*e^6 + 5175/56*e^4 - 7201/56*e^2 + 288/7, 1/112*e^10 - 2/7*e^8 + 181/56*e^6 - 207/14*e^4 + 2173/112*e^2 + 111/7, 1/16*e^10 - 2*e^8 + 179/8*e^6 - 102*e^4 + 2633/16*e^2 - 39, -5/112*e^10 + 73/56*e^8 - 365/28*e^6 + 2887/56*e^4 - 7799/112*e^2 + 117/7, -17/1344*e^11 + 43/112*e^9 - 2629/672*e^7 + 1653/112*e^5 - 18517/1344*e^3 - 251/28*e, -1/672*e^11 + 5/56*e^9 - 545/336*e^7 + 663/56*e^5 - 23117/672*e^3 + 216/7*e, -1/14*e^10 + 121/56*e^8 - 1273/56*e^6 + 5427/56*e^4 - 8335/56*e^2 + 372/7, -1/2*e^4 + 13/2*e^2 - 14, -1/16*e^10 + 2*e^8 - 179/8*e^6 + 102*e^4 - 2665/16*e^2 + 53, -3/112*e^10 + 6/7*e^8 - 557/56*e^6 + 349/7*e^4 - 10915/112*e^2 + 325/7, 23/672*e^11 - 59/56*e^9 + 3799/336*e^7 - 2761/56*e^5 + 51211/672*e^3 - 159/7*e, 1/2*e^4 - 13/2*e^2 + 10, 3/224*e^11 - 3/7*e^9 + 529/112*e^7 - 565/28*e^5 + 5371/224*e^3 + 197/28*e, -9/112*e^10 + 137/56*e^8 - 727/28*e^6 + 6255/56*e^4 - 18955/112*e^2 + 310/7, 1/112*e^11 - 2/7*e^9 + 181/56*e^7 - 421/28*e^5 + 2565/112*e^3 + 241/28*e, -1/56*e^10 + 4/7*e^8 - 181/28*e^6 + 435/14*e^4 - 3489/56*e^2 + 254/7, 1/28*e^10 - 57/56*e^8 + 549/56*e^6 - 2003/56*e^4 + 2197/56*e^2 - 18/7, 3/448*e^11 - 17/112*e^9 + 179/224*e^7 + 305/112*e^5 - 11961/448*e^3 + 1117/28*e, -1/112*e^10 + 9/56*e^8 - 3/28*e^6 - 509/56*e^4 + 3637/112*e^2 - 48/7, -3/112*e^11 + 6/7*e^9 - 557/56*e^7 + 356/7*e^5 - 12483/112*e^3 + 556/7*e, -3/56*e^10 + 89/56*e^8 - 925/56*e^6 + 3911/56*e^4 - 702/7*e^2 + 132/7, -13/672*e^11 + 15/28*e^9 - 1583/336*e^7 + 337/28*e^5 + 8683/672*e^3 - 300/7*e, -17/1344*e^11 + 43/112*e^9 - 2629/672*e^7 + 1541/112*e^5 + 1643/1344*e^3 - 1427/28*e, -11/112*e^10 + 169/56*e^8 - 227/7*e^6 + 7967/56*e^4 - 24645/112*e^2 + 305/7, 1/28*e^10 - 8/7*e^8 + 87/7*e^6 - 365/7*e^4 + 1879/28*e^2 + 24/7, -5/112*e^10 + 73/56*e^8 - 351/28*e^6 + 2355/56*e^4 - 2647/112*e^2 - 114/7, 1/14*e^10 - 121/56*e^8 + 1287/56*e^6 - 5679/56*e^4 + 9357/56*e^2 - 414/7, -3/112*e^10 + 6/7*e^8 - 543/56*e^6 + 635/14*e^4 - 8759/112*e^2 + 276/7, 1/112*e^10 - 9/56*e^8 + 3/28*e^6 + 509/56*e^4 - 3525/112*e^2 + 41/7, -3/112*e^10 + 17/28*e^8 - 207/56*e^6 + 3/28*e^4 + 3841/112*e^2 - 137/7, -1/112*e^11 + 9/56*e^9 + 1/7*e^7 - 859/56*e^5 + 8705/112*e^3 - 2579/28*e, 1/96*e^11 - 3/8*e^9 + 233/48*e^7 - 223/8*e^5 + 6989/96*e^3 - 291/4*e, 1/112*e^10 - 9/56*e^8 + 5/14*e^6 + 341/56*e^4 - 3441/112*e^2 + 195/7, -13/336*e^11 + 67/56*e^9 - 274/21*e^7 + 3315/56*e^5 - 33947/336*e^3 + 1163/28*e, -3/56*e^10 + 89/56*e^8 - 897/56*e^6 + 3463/56*e^4 - 1047/14*e^2 + 202/7, -1/224*e^11 + 1/7*e^9 - 195/112*e^7 + 277/28*e^5 - 5449/224*e^3 + 625/28*e, 1/56*e^10 - 25/56*e^8 + 201/56*e^6 - 599/56*e^4 + 411/28*e^2 - 86/7, 1/224*e^11 - 1/7*e^9 + 167/112*e^7 - 65/14*e^5 - 1439/224*e^3 + 206/7*e, 25/672*e^11 - 31/28*e^9 + 3839/336*e^7 - 335/7*e^5 + 49817/672*e^3 - 943/28*e, -1/32*e^11 + e^9 - 183/16*e^7 + 113/2*e^5 - 3777/32*e^3 + 86*e, -5/112*e^10 + 73/56*e^8 - 365/28*e^6 + 2775/56*e^4 - 5335/112*e^2 - 93/7, 1/56*e^10 - 4/7*e^8 + 181/28*e^6 - 421/14*e^4 + 2761/56*e^2 - 30/7, 5/336*e^11 - 29/56*e^9 + 277/42*e^7 - 2087/56*e^5 + 30115/336*e^3 - 1065/14*e, 5/672*e^11 - 11/56*e^9 + 541/336*e^7 - 179/56*e^5 - 5711/672*e^3 + 461/28*e, 31/1344*e^11 - 85/112*e^9 + 6059/672*e^7 - 5251/112*e^5 + 139547/1344*e^3 - 2269/28*e, -9/224*e^11 + 9/7*e^9 - 1671/112*e^7 + 534/7*e^5 - 37225/224*e^3 + 785/7*e, 1/28*e^10 - 8/7*e^8 + 181/14*e^6 - 435/7*e^4 + 3377/28*e^2 - 312/7, 1/112*e^10 - 2/7*e^8 + 181/56*e^6 - 221/14*e^4 + 3853/112*e^2 - 99/7, -1/224*e^11 + 1/7*e^9 - 167/112*e^7 + 65/14*e^5 + 1439/224*e^3 - 206/7*e, 5/112*e^10 - 10/7*e^8 + 919/56*e^6 - 556/7*e^4 + 15597/112*e^2 - 334/7, -5/168*e^11 + 51/56*e^9 - 1649/168*e^7 + 2473/56*e^5 - 6395/84*e^3 + 211/7*e, 1/672*e^11 + 1/28*e^9 - 589/336*e^7 + 519/28*e^5 - 45511/672*e^3 + 505/7*e, -5/112*e^10 + 73/56*e^8 - 365/28*e^6 + 2887/56*e^4 - 7575/112*e^2 + 75/7, -1/32*e^11 + e^9 - 187/16*e^7 + 243/4*e^5 - 4265/32*e^3 + 301/4*e, 29/672*e^11 - 75/56*e^9 + 4885/336*e^7 - 3589/56*e^5 + 64249/672*e^3 - 20/7*e, 1/4*e^7 - 21/4*e^5 + 127/4*e^3 - 203/4*e, -15/112*e^10 + 113/28*e^8 - 2351/56*e^6 + 4845/28*e^4 - 25931/112*e^2 + 162/7, -1/56*e^10 + 4/7*e^8 - 167/28*e^6 + 295/14*e^4 - 381/56*e^2 - 96/7, 23/672*e^11 - 59/56*e^9 + 3799/336*e^7 - 2761/56*e^5 + 51883/672*e^3 - 194/7*e, 3/28*e^10 - 185/56*e^8 + 1983/56*e^6 - 8599/56*e^4 + 13339/56*e^2 - 558/7, -31/1344*e^11 + 71/112*e^9 - 3791/672*e^7 + 1793/112*e^5 + 6445/1344*e^3 - 895/28*e, -5/672*e^11 + 11/56*e^9 - 625/336*e^7 + 473/56*e^5 - 14281/672*e^3 + 100/7*e, -1/21*e^11 + 83/56*e^9 - 2693/168*e^7 + 3947/56*e^5 - 19603/168*e^3 + 1881/28*e, -1/28*e^10 + 8/7*e^8 - 355/28*e^6 + 779/14*e^4 - 1125/14*e^2 + 144/7, 1/56*e^11 - 4/7*e^9 + 47/7*e^7 - 989/28*e^5 + 4511/56*e^3 - 1751/28*e, 1/28*e^10 - 8/7*e^8 + 181/14*e^6 - 421/7*e^4 + 2593/28*e^2 + 108/7, 1/168*e^11 - 3/28*e^9 - 11/42*e^7 + 375/28*e^5 - 11701/168*e^3 + 669/7*e, 1/112*e^10 - 9/56*e^8 + 17/28*e^6 + 61/56*e^4 - 557/112*e^2 + 76/7, 1/28*e^10 - 8/7*e^8 + 87/7*e^6 - 358/7*e^4 + 1571/28*e^2 + 122/7, 1/112*e^10 - 2/7*e^8 + 195/56*e^6 - 149/7*e^4 + 7017/112*e^2 - 260/7, -9/224*e^11 + 9/7*e^9 - 1671/112*e^7 + 1075/14*e^5 - 38569/224*e^3 + 1759/14*e, -1/2*e^6 + 8*e^4 - 55/2*e^2 + 16, 5/224*e^11 - 5/7*e^9 + 919/112*e^7 - 285/7*e^5 + 18285/224*e^3 - 279/7*e, 11/672*e^11 - 27/56*e^9 + 1627/336*e^7 - 1021/56*e^5 + 8335/672*e^3 + 491/14*e, -1/192*e^11 + 3/16*e^9 - 245/96*e^7 + 261/16*e^5 - 9797/192*e^3 + 295/4*e, 3/112*e^10 - 6/7*e^8 + 515/56*e^6 - 509/14*e^4 + 3551/112*e^2 + 172/7, 1/48*e^11 - 5/8*e^9 + 19/3*e^7 - 187/8*e^5 + 527/48*e^3 + 66*e, 41/1344*e^11 - 107/112*e^9 + 6973/672*e^7 - 5077/112*e^5 + 92173/1344*e^3 - 345/28*e, -85/1344*e^11 + 215/112*e^9 - 13649/672*e^7 + 9833/112*e^5 - 189017/1344*e^3 + 1783/28*e, 5/336*e^11 - 29/56*e^9 + 277/42*e^7 - 2031/56*e^5 + 25411/336*e^3 - 519/14*e, -5/168*e^11 + 51/56*e^9 - 1649/168*e^7 + 2445/56*e^5 - 5597/84*e^3 - 76/7*e, -1/112*e^10 + 2/7*e^8 - 195/56*e^6 + 135/7*e^4 - 3993/112*e^2 - 153/7, 1/28*e^10 - 8/7*e^8 + 87/7*e^6 - 358/7*e^4 + 1515/28*e^2 + 192/7, -25/672*e^11 + 31/28*e^9 - 3755/336*e^7 + 1207/28*e^5 - 33857/672*e^3 + 59/7*e, 1/8*e^10 - 31/8*e^8 + 335/8*e^6 - 1473/8*e^4 + 288*e^2 - 68, 13/112*e^10 - 97/28*e^8 + 1989/56*e^6 - 4031/28*e^4 + 21865/112*e^2 - 286/7, -3/56*e^10 + 89/56*e^8 - 925/56*e^6 + 3967/56*e^4 - 793/7*e^2 + 328/7, -1/48*e^11 + 5/8*e^9 - 79/12*e^7 + 237/8*e^5 - 2867/48*e^3 + 203/4*e, -19/1344*e^11 + 39/112*e^9 - 1619/672*e^7 + 25/112*e^5 + 58057/1344*e^3 - 2859/28*e, -11/672*e^11 + 27/56*e^9 - 1627/336*e^7 + 1049/56*e^5 - 16399/672*e^3 + 157/7*e, 25/1344*e^11 - 69/112*e^9 + 5057/672*e^7 - 4675/112*e^5 + 140117/1344*e^3 - 2771/28*e, -1/16*e^10 + 7/4*e^8 - 129/8*e^6 + 209/4*e^4 - 477/16*e^2 - 28, 3/112*e^10 - 6/7*e^8 + 543/56*e^6 - 635/14*e^4 + 8535/112*e^2 - 178/7, 1/672*e^11 - 5/56*e^9 + 629/336*e^7 - 957/56*e^5 + 41765/672*e^3 - 1389/28*e, -1/28*e^10 + 8/7*e^8 - 181/14*e^6 + 421/7*e^4 - 2649/28*e^2 + 46/7, 1/28*e^10 - 8/7*e^8 + 369/28*e^6 - 905/14*e^4 + 818/7*e^2 - 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8857/56*e^2 + 720/7, 9/56*e^10 - 137/28*e^8 + 727/14*e^6 - 6283/28*e^4 + 19907/56*e^2 - 1068/7, 15/112*e^10 - 219/56*e^8 + 1095/28*e^6 - 8605/56*e^4 + 22949/112*e^2 - 680/7, 1/112*e^10 - 9/56*e^8 - 11/28*e^6 + 1097/56*e^4 - 9909/112*e^2 + 608/7, 5/84*e^11 - 109/56*e^9 + 3823/168*e^7 - 6297/56*e^5 + 34967/168*e^3 - 1821/28*e, 11/672*e^11 - 17/28*e^9 + 2761/336*e^7 - 335/7*e^5 + 69571/672*e^3 - 495/28*e, -31/448*e^11 + 241/112*e^9 - 5191/224*e^7 + 11119/112*e^5 - 61091/448*e^3 - 123/28*e, -17/672*e^11 + 43/56*e^9 - 2629/336*e^7 + 1625/56*e^5 - 13141/672*e^3 - 234/7*e, 31/448*e^11 - 227/112*e^9 + 4547/224*e^7 - 8949/112*e^5 + 49835/448*e^3 - 2047/28*e, 3/28*e^10 - 89/28*e^8 + 897/28*e^6 - 3407/28*e^4 + 865/7*e^2 + 100/7, -79/1344*e^11 + 213/112*e^9 - 14915/672*e^7 + 12547/112*e^5 - 310043/1344*e^3 + 4399/28*e, -1/28*e^10 + 57/56*e^8 - 507/56*e^6 + 1219/56*e^4 + 1793/56*e^2 - 570/7, 9/224*e^11 - 65/56*e^9 + 1237/112*e^7 - 1955/56*e^5 - 1219/224*e^3 + 727/7*e, -17/112*e^10 + 129/28*e^8 - 2741/56*e^6 + 5967/28*e^4 - 37557/112*e^2 + 549/7, 1/21*e^11 - 19/14*e^9 + 271/21*e^7 - 607/14*e^5 + 332/21*e^3 + 459/7*e, 1/28*e^11 - 71/56*e^9 + 941/56*e^7 - 5629/56*e^5 + 14237/56*e^3 - 1355/7*e, 1/96*e^11 - 3/8*e^9 + 233/48*e^7 - 215/8*e^5 + 5213/96*e^3 + 19/4*e, 5/112*e^10 - 33/28*e^8 + 541/56*e^6 - 621/28*e^4 - 2183/112*e^2 + 142/7, 13/224*e^11 - 13/7*e^9 + 2395/112*e^7 - 1489/14*e^5 + 47821/224*e^3 - 857/7*e, 67/672*e^11 - 181/56*e^9 + 12575/336*e^7 - 10303/56*e^5 + 236591/672*e^3 - 1158/7*e, -3/56*e^10 + 41/28*e^8 - 375/28*e^6 + 1301/28*e^4 - 3355/56*e^2 + 356/7, 5/112*e^10 - 73/56*e^8 + 351/28*e^6 - 2439/56*e^4 + 4383/112*e^2 + 2/7, -121/1344*e^11 + 325/112*e^9 - 22097/672*e^7 + 17195/112*e^5 - 346709/1344*e^3 + 1529/28*e, 17/672*e^11 - 9/14*e^9 + 1327/336*e^7 + 311/28*e^5 - 88079/672*e^3 + 4751/28*e, 1/56*e^10 - 39/56*e^8 + 523/56*e^6 - 2769/56*e^4 + 1063/14*e^2 + 320/7, 31/672*e^11 - 39/28*e^9 + 4925/336*e^7 - 1733/28*e^5 + 55463/672*e^3 + 129/7*e, 13/224*e^11 - 111/56*e^9 + 2745/112*e^7 - 7433/56*e^5 + 67841/224*e^3 - 1585/7*e, -1/16*e^10 + 2*e^8 - 187/8*e^6 + 121*e^4 - 4153/16*e^2 + 132, 5/56*e^10 - 20/7*e^8 + 905/28*e^6 - 1070/7*e^4 + 15401/56*e^2 - 934/7, 1/16*e^10 - 13/8*e^8 + 53/4*e^6 - 251/8*e^4 - 245/16*e^2 + 11, 3/56*e^10 - 89/56*e^8 + 925/56*e^6 - 4023/56*e^4 + 898/7*e^2 - 580/7, -19/112*e^10 + 283/56*e^8 - 1443/28*e^6 + 11441/56*e^4 - 28393/112*e^2 + 215/7, -1/56*e^10 + 39/56*e^8 - 523/56*e^6 + 2881/56*e^4 - 1511/14*e^2 + 408/7, -5/28*e^10 + 313/56*e^8 - 3403/56*e^6 + 14971/56*e^4 - 23487/56*e^2 + 804/7, 3/56*e^10 - 12/7*e^8 + 543/28*e^6 - 642/7*e^4 + 9487/56*e^2 - 636/7, -121/1344*e^11 + 311/112*e^9 - 20501/672*e^7 + 16033/112*e^5 - 367373/1344*e^3 + 4819/28*e, 9/112*e^10 - 65/28*e^8 + 1195/56*e^6 - 1717/28*e^4 + 41/112*e^2 + 327/7, -25/112*e^10 + 193/28*e^8 - 4133/56*e^6 + 8887/28*e^4 - 53485/112*e^2 + 963/7, -1/672*e^11 + 5/56*e^9 - 629/336*e^7 + 943/56*e^5 - 44117/672*e^3 + 1671/14*e, 1/7*e^10 - 235/56*e^8 + 2357/56*e^6 - 9181/56*e^4 + 11147/56*e^2 - 114/7, -15/112*e^10 + 113/28*e^8 - 2351/56*e^6 + 4915/28*e^4 - 29123/112*e^2 + 540/7, 1/28*e^10 - 43/56*e^8 + 241/56*e^6 + 139/56*e^4 - 3235/56*e^2 + 360/7, -9/56*e^10 + 137/28*e^8 - 727/14*e^6 + 6283/28*e^4 - 19235/56*e^2 + 508/7, 5/56*e^10 - 73/28*e^8 + 737/28*e^6 - 2985/28*e^4 + 8541/56*e^2 - 304/7, -1/7*e^10 + 121/28*e^8 - 1273/28*e^6 + 5427/28*e^4 - 8055/28*e^2 + 534/7, -11/336*e^11 + 61/56*e^9 - 559/42*e^7 + 4121/56*e^5 - 61885/336*e^3 + 5141/28*e, -41/1344*e^11 + 121/112*e^9 - 9577/672*e^7 + 9711/112*e^5 - 321493/1344*e^3 + 5973/28*e, -9/56*e^10 + 267/56*e^8 - 2747/56*e^6 + 11257/56*e^4 - 1812/7*e^2 + 4/7, 23/224*e^11 - 177/56*e^9 + 3743/112*e^7 - 7667/56*e^5 + 34747/224*e^3 + 692/7*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([19, 19, -w^3 + w^2 + 4*w - 3])] = 1

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