/*
  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, 9, 2, -6, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([27, 3, w^4 - 2*w^3 - 3*w^2 + 5*w])

primes_array = [
[5, 5, w^5 - 2*w^4 - 4*w^3 + 5*w^2 + 5*w],\
[11, 11, w^5 - 2*w^4 - 3*w^3 + 4*w^2 + w + 1],\
[11, 11, w^2 - w - 2],\
[17, 17, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 3*w - 3],\
[27, 3, w^5 - w^4 - 5*w^3 + w^2 + 6*w + 1],\
[27, 3, w^4 - 2*w^3 - 3*w^2 + 5*w],\
[37, 37, -w^2 + 2*w + 2],\
[47, 47, -w^5 + 2*w^4 + 3*w^3 - 3*w^2 - 2*w - 1],\
[53, 53, -w^5 + 3*w^4 + 2*w^3 - 8*w^2 + 3],\
[59, 59, w^4 - 2*w^3 - 2*w^2 + 3*w - 2],\
[64, 2, -2],\
[67, 67, w^5 - 2*w^4 - 3*w^3 + 4*w^2 + w - 2],\
[67, 67, -w^5 + 3*w^4 + w^3 - 7*w^2 + 3*w + 2],\
[71, 71, w^4 - w^3 - 4*w^2 + 2*w + 1],\
[71, 71, w^4 - w^3 - 5*w^2 + 2*w + 4],\
[73, 73, 2*w^5 - 4*w^4 - 7*w^3 + 10*w^2 + 5*w - 3],\
[83, 83, w^4 - 2*w^3 - 4*w^2 + 5*w + 2],\
[83, 83, w^5 - 3*w^4 - 2*w^3 + 9*w^2 - 3],\
[89, 89, -w^5 + w^4 + 6*w^3 - 2*w^2 - 8*w + 1],\
[97, 97, 2*w^5 - 4*w^4 - 7*w^3 + 8*w^2 + 7*w],\
[103, 103, -w^5 + w^4 + 6*w^3 - 2*w^2 - 9*w + 1],\
[107, 107, w^5 - 2*w^4 - 3*w^3 + 3*w^2 + 2*w + 2],\
[113, 113, w^5 - w^4 - 5*w^3 + w^2 + 4*w + 2],\
[127, 127, 2*w^5 - 3*w^4 - 10*w^3 + 8*w^2 + 12*w],\
[127, 127, -2*w^5 + 3*w^4 + 9*w^3 - 6*w^2 - 9*w - 1],\
[131, 131, w^4 - 3*w^3 - 2*w^2 + 7*w + 1],\
[137, 137, -w^5 + 2*w^4 + 3*w^3 - 4*w^2 - 2*w - 2],\
[137, 137, w^2 - 2*w - 3],\
[149, 149, -w^4 + 3*w^3 + w^2 - 7*w + 1],\
[151, 151, -w^5 + w^4 + 6*w^3 - 3*w^2 - 8*w + 4],\
[163, 163, -w^5 + w^4 + 7*w^3 - 5*w^2 - 11*w + 5],\
[173, 173, -2*w^5 + 3*w^4 + 9*w^3 - 7*w^2 - 10*w + 1],\
[179, 179, w^5 - 2*w^4 - 3*w^3 + 5*w^2 + w - 3],\
[191, 191, -w^5 + w^4 + 6*w^3 - 2*w^2 - 7*w - 1],\
[193, 193, 2*w^5 - 4*w^4 - 8*w^3 + 10*w^2 + 9*w],\
[193, 193, -w^5 + 2*w^4 + 5*w^3 - 6*w^2 - 7*w],\
[211, 211, -w^5 + w^4 + 6*w^3 - 2*w^2 - 8*w - 4],\
[211, 211, -3*w^5 + 5*w^4 + 13*w^3 - 13*w^2 - 12*w + 3],\
[223, 223, 3*w^5 - 4*w^4 - 15*w^3 + 9*w^2 + 17*w - 1],\
[227, 227, w^5 - 2*w^4 - 5*w^3 + 8*w^2 + 5*w - 3],\
[229, 229, 2*w^5 - 4*w^4 - 9*w^3 + 12*w^2 + 11*w - 5],\
[229, 229, -w^5 + w^4 + 6*w^3 - 2*w^2 - 10*w],\
[233, 233, -w^5 + w^4 + 7*w^3 - 3*w^2 - 12*w + 1],\
[239, 239, 2*w^5 - 4*w^4 - 8*w^3 + 11*w^2 + 9*w - 2],\
[239, 239, w^5 - 2*w^4 - 4*w^3 + 7*w^2 + 2*w - 6],\
[241, 241, -2*w^5 + 3*w^4 + 10*w^3 - 6*w^2 - 14*w - 3],\
[251, 251, -2*w^5 + 3*w^4 + 11*w^3 - 8*w^2 - 17*w],\
[251, 251, -2*w^5 + 5*w^4 + 5*w^3 - 12*w^2 - 2*w],\
[251, 251, -3*w^5 + 6*w^4 + 11*w^3 - 15*w^2 - 10*w + 2],\
[257, 257, 2*w^5 - 3*w^4 - 9*w^3 + 8*w^2 + 9*w - 1],\
[257, 257, -w^5 + 9*w^3 - 16*w - 3],\
[263, 263, -2*w^5 + 3*w^4 + 9*w^3 - 8*w^2 - 11*w + 2],\
[269, 269, 2*w^5 - 4*w^4 - 8*w^3 + 10*w^2 + 9*w - 1],\
[271, 271, 2*w^5 - 3*w^4 - 10*w^3 + 8*w^2 + 11*w - 2],\
[271, 271, 3*w^5 - 6*w^4 - 11*w^3 + 14*w^2 + 11*w],\
[277, 277, -w^5 + 3*w^4 + w^3 - 7*w^2 + 4*w + 3],\
[293, 293, w^5 - w^4 - 7*w^3 + 3*w^2 + 12*w - 2],\
[293, 293, -w^5 + w^4 + 6*w^3 - 2*w^2 - 10*w - 1],\
[307, 307, w^5 - 7*w^3 - 2*w^2 + 9*w + 5],\
[313, 313, -3*w^5 + 4*w^4 + 15*w^3 - 9*w^2 - 17*w - 1],\
[313, 313, -w^3 + 6*w + 1],\
[317, 317, w^5 - 2*w^4 - 5*w^3 + 7*w^2 + 8*w - 1],\
[317, 317, -3*w^5 + 4*w^4 + 15*w^3 - 9*w^2 - 19*w],\
[317, 317, 2*w^4 - 3*w^3 - 8*w^2 + 5*w + 5],\
[337, 337, w^5 - 2*w^4 - 5*w^3 + 6*w^2 + 5*w - 3],\
[337, 337, 3*w^5 - 5*w^4 - 14*w^3 + 14*w^2 + 17*w - 4],\
[347, 347, 2*w^5 - 5*w^4 - 5*w^3 + 13*w^2 + 2*w - 3],\
[347, 347, w^5 - 7*w^3 - w^2 + 9*w],\
[353, 353, 3*w^5 - 5*w^4 - 13*w^3 + 12*w^2 + 14*w - 2],\
[361, 19, -w^5 + w^4 + 7*w^3 - 3*w^2 - 10*w - 1],\
[367, 367, 2*w^5 - 4*w^4 - 7*w^3 + 11*w^2 + 3*w - 3],\
[389, 389, -2*w^5 + 3*w^4 + 9*w^3 - 5*w^2 - 10*w - 2],\
[389, 389, 2*w^5 - 4*w^4 - 9*w^3 + 13*w^2 + 10*w - 6],\
[397, 397, 2*w^5 - 4*w^4 - 8*w^3 + 9*w^2 + 9*w + 1],\
[401, 401, -3*w^5 + 4*w^4 + 15*w^3 - 9*w^2 - 18*w],\
[401, 401, -2*w^4 + 4*w^3 + 6*w^2 - 8*w - 1],\
[401, 401, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 6*w - 3],\
[401, 401, -2*w^3 + 3*w^2 + 6*w - 4],\
[419, 419, w^5 - 2*w^4 - 3*w^3 + 6*w^2 - 3],\
[433, 433, w^5 - 3*w^4 - 2*w^3 + 8*w^2 + w + 1],\
[443, 443, 2*w^5 - 3*w^4 - 11*w^3 + 8*w^2 + 16*w + 1],\
[443, 443, w^3 - w^2 - 4*w + 3],\
[461, 461, -w^5 + 3*w^4 - 6*w^2 + 6*w + 2],\
[479, 479, 3*w^5 - 5*w^4 - 13*w^3 + 12*w^2 + 12*w],\
[479, 479, 2*w^5 - 4*w^4 - 9*w^3 + 11*w^2 + 12*w],\
[487, 487, 2*w^5 - 2*w^4 - 12*w^3 + 6*w^2 + 15*w - 2],\
[491, 491, -2*w^4 + 4*w^3 + 7*w^2 - 8*w - 4],\
[491, 491, -2*w^5 + 4*w^4 + 8*w^3 - 10*w^2 - 10*w - 1],\
[499, 499, w^4 - w^3 - 4*w^2 + 2*w - 1],\
[499, 499, w^5 - 8*w^3 + 10*w],\
[499, 499, -2*w^5 + 3*w^4 + 8*w^3 - 4*w^2 - 8*w - 4],\
[503, 503, -2*w^4 + 4*w^3 + 5*w^2 - 7*w - 2],\
[509, 509, 2*w^5 - 4*w^4 - 9*w^3 + 11*w^2 + 13*w - 2],\
[509, 509, w^5 - 9*w^3 + 15*w + 2],\
[509, 509, -w^5 + 9*w^3 - 16*w - 1],\
[521, 521, w^5 - w^4 - 5*w^3 + 5*w + 6],\
[523, 523, -2*w^4 + 5*w^3 + 4*w^2 - 10*w + 1],\
[523, 523, -w^5 + 7*w^3 + 2*w^2 - 11*w - 3],\
[563, 563, -w^5 + w^4 + 5*w^3 - w^2 - 7*w],\
[571, 571, -3*w^5 + 4*w^4 + 15*w^3 - 8*w^2 - 18*w - 2],\
[577, 577, w^5 - 3*w^4 - w^3 + 7*w^2 - 4*w - 2],\
[587, 587, w^5 - w^4 - 5*w^3 - w^2 + 7*w + 5],\
[593, 593, -w^5 + 2*w^4 + 3*w^3 - 3*w^2 - w - 2],\
[593, 593, -w^5 + 9*w^3 - w^2 - 16*w + 1],\
[607, 607, w^5 - 2*w^4 - 3*w^3 + 5*w^2 + 2*w - 4],\
[607, 607, -2*w^5 + 3*w^4 + 9*w^3 - 5*w^2 - 11*w - 1],\
[613, 613, w^5 - 2*w^4 - 6*w^3 + 8*w^2 + 9*w - 4],\
[619, 619, -w^5 + 4*w^4 - 11*w^2 + 4*w + 3],\
[619, 619, w^2 - 5],\
[631, 631, -w^3 + 2*w^2 + w - 5],\
[631, 631, -2*w^3 + 3*w^2 + 6*w - 5],\
[641, 641, w^5 - 8*w^3 + 13*w + 2],\
[643, 643, -w^5 + w^4 + 4*w^3 - 2*w - 4],\
[647, 647, -w^5 + w^4 + 6*w^3 - 3*w^2 - 10*w + 1],\
[647, 647, -w^4 + 6*w^2 + w - 5],\
[653, 653, 2*w^4 - 3*w^3 - 8*w^2 + 6*w + 7],\
[659, 659, w^5 - 7*w^3 + 7*w - 4],\
[659, 659, -2*w^5 + 4*w^4 + 8*w^3 - 11*w^2 - 8*w + 6],\
[673, 673, w^5 - 3*w^4 - 2*w^3 + 10*w^2 - 5],\
[673, 673, w^5 - 2*w^4 - 2*w^3 + 3*w^2 - 2*w + 3],\
[677, 677, -3*w^5 + 5*w^4 + 13*w^3 - 12*w^2 - 13*w + 3],\
[691, 691, -2*w^5 + 3*w^4 + 10*w^3 - 9*w^2 - 12*w + 2],\
[691, 691, -w^5 + 2*w^4 + 5*w^3 - 5*w^2 - 11*w - 3],\
[709, 709, w^4 - 3*w^3 - 2*w^2 + 9*w + 2],\
[719, 719, -2*w^5 + 3*w^4 + 9*w^3 - 7*w^2 - 7*w + 1],\
[719, 719, -2*w^5 + 3*w^4 + 11*w^3 - 9*w^2 - 14*w + 2],\
[719, 719, 2*w^5 - 2*w^4 - 12*w^3 + 5*w^2 + 15*w - 1],\
[727, 727, w^5 - 2*w^4 - 4*w^3 + 6*w^2 + 2*w - 4],\
[727, 727, 2*w^5 - 5*w^4 - 6*w^3 + 14*w^2 + 5*w - 4],\
[733, 733, w^5 - w^4 - 5*w^3 + 2*w^2 + 5*w - 4],\
[733, 733, 2*w^5 - 4*w^4 - 6*w^3 + 8*w^2 + 3*w + 1],\
[739, 739, w^5 - 3*w^4 - 3*w^3 + 10*w^2 + w - 5],\
[739, 739, -2*w^5 + 4*w^4 + 6*w^3 - 7*w^2 - 4*w - 3],\
[751, 751, -2*w^5 + 5*w^4 + 5*w^3 - 11*w^2 - 3*w - 1],\
[751, 751, w^5 - 3*w^4 - 3*w^3 + 11*w^2 + 3*w - 7],\
[757, 757, -w^5 + 2*w^4 + 4*w^3 - 5*w^2 - 7*w],\
[761, 761, 3*w^5 - 4*w^4 - 15*w^3 + 10*w^2 + 17*w - 2],\
[769, 769, -w^5 + 2*w^4 + 4*w^3 - 3*w^2 - 6*w - 4],\
[773, 773, 2*w^4 - 4*w^3 - 5*w^2 + 9*w],\
[787, 787, -2*w^5 + 2*w^4 + 11*w^3 - 5*w^2 - 12*w + 2],\
[787, 787, 2*w^5 - 4*w^4 - 7*w^3 + 10*w^2 + 7*w - 1],\
[787, 787, 3*w^5 - 5*w^4 - 12*w^3 + 11*w^2 + 10*w - 1],\
[797, 797, -w^4 + 2*w^3 + 4*w^2 - 6*w],\
[809, 809, -3*w^5 + 5*w^4 + 13*w^3 - 13*w^2 - 12*w + 2],\
[809, 809, 3*w^5 - 4*w^4 - 14*w^3 + 8*w^2 + 14*w],\
[809, 809, -3*w^5 + 6*w^4 + 11*w^3 - 14*w^2 - 10*w + 2],\
[821, 821, -w^5 + 3*w^4 + 2*w^3 - 10*w^2 + w + 4],\
[823, 823, -w^4 + 2*w^3 + 4*w^2 - 3*w - 5],\
[823, 823, -2*w^5 + 4*w^4 + 7*w^3 - 9*w^2 - 6*w - 3],\
[827, 827, -w^3 + 3*w^2 + 3*w - 4],\
[839, 839, -w^5 + 2*w^4 + 5*w^3 - 7*w^2 - 7*w],\
[839, 839, -2*w^5 + 4*w^4 + 9*w^3 - 11*w^2 - 13*w + 1],\
[839, 839, -2*w^5 + 3*w^4 + 10*w^3 - 7*w^2 - 11*w - 1],\
[841, 29, -w^3 + 3*w^2 + w - 2],\
[857, 857, -2*w^5 + 4*w^4 + 8*w^3 - 9*w^2 - 10*w - 3],\
[859, 859, 3*w^5 - 4*w^4 - 15*w^3 + 9*w^2 + 17*w + 2],\
[859, 859, -2*w^5 + 2*w^4 + 11*w^3 - 3*w^2 - 15*w],\
[863, 863, 2*w^5 - 4*w^4 - 7*w^3 + 8*w^2 + 6*w + 4],\
[863, 863, 3*w^5 - 5*w^4 - 14*w^3 + 12*w^2 + 18*w - 1],\
[881, 881, w^5 - 3*w^4 - w^3 + 6*w^2 - 3*w - 1],\
[887, 887, 2*w^5 - 5*w^4 - 5*w^3 + 11*w^2 + 2*w + 1],\
[907, 907, w^5 - 2*w^4 - 6*w^3 + 7*w^2 + 8*w - 2],\
[919, 919, w^5 - w^4 - 7*w^3 + 3*w^2 + 10*w + 2],\
[929, 929, 2*w^5 - 4*w^4 - 7*w^3 + 10*w^2 + 4*w - 4],\
[937, 937, 3*w^5 - 5*w^4 - 12*w^3 + 10*w^2 + 11*w],\
[953, 953, -3*w^5 + 5*w^4 + 14*w^3 - 12*w^2 - 17*w - 1],\
[953, 953, -2*w^5 + 2*w^4 + 11*w^3 - 4*w^2 - 13*w - 2],\
[967, 967, -w^5 + 3*w^4 - 6*w^2 + 6*w],\
[967, 967, 3*w^5 - 6*w^4 - 11*w^3 + 14*w^2 + 9*w - 1],\
[977, 977, -w^5 + 3*w^4 - 6*w^2 + 5*w + 2],\
[991, 991, -w^3 + 3*w^2 + 2*w - 3],\
[997, 997, w^5 - 2*w^4 - 6*w^3 + 7*w^2 + 10*w - 1],\
[1009, 1009, w^5 - 2*w^4 - 2*w^3 + 3*w^2 - w + 2],\
[1013, 1013, 3*w^5 - 5*w^4 - 14*w^3 + 14*w^2 + 14*w - 4],\
[1019, 1019, -3*w^5 + 5*w^4 + 14*w^3 - 13*w^2 - 18*w + 2],\
[1031, 1031, -2*w^5 + 2*w^4 + 11*w^3 - 3*w^2 - 15*w - 1],\
[1039, 1039, -2*w^4 + 4*w^3 + 7*w^2 - 8*w - 3],\
[1049, 1049, w^5 - 2*w^4 - 4*w^3 + 5*w^2 + 5*w - 4],\
[1063, 1063, -w^4 + 2*w^3 + 3*w^2 - 2*w - 4],\
[1069, 1069, 2*w^5 - 3*w^4 - 8*w^3 + 4*w^2 + 7*w + 4],\
[1069, 1069, w^5 - w^4 - 5*w^3 + 2*w^2 + 3*w + 2],\
[1091, 1091, -2*w^5 + 2*w^4 + 11*w^3 - 4*w^2 - 15*w],\
[1117, 1117, -w^4 + w^3 + 6*w^2 - 3*w - 5],\
[1117, 1117, -3*w^5 + 4*w^4 + 16*w^3 - 11*w^2 - 20*w + 1],\
[1123, 1123, 2*w^5 - 2*w^4 - 14*w^3 + 7*w^2 + 21*w - 3],\
[1129, 1129, w^5 - w^4 - 5*w^3 + 3*w^2 + 3*w - 3],\
[1129, 1129, w^4 - 3*w^3 - w^2 + 6*w - 4],\
[1151, 1151, 2*w^5 - 3*w^4 - 8*w^3 + 5*w^2 + 7*w + 4],\
[1151, 1151, -2*w^5 + 3*w^4 + 10*w^3 - 9*w^2 - 10*w + 5],\
[1151, 1151, -2*w^5 + 4*w^4 + 8*w^3 - 11*w^2 - 10*w + 2],\
[1153, 1153, -w^3 + 2*w^2 - 3],\
[1171, 1171, 2*w^5 - 3*w^4 - 10*w^3 + 8*w^2 + 13*w + 1],\
[1187, 1187, -w^5 + 3*w^4 + 4*w^3 - 10*w^2 - 4*w + 5],\
[1193, 1193, -2*w^5 + 5*w^4 + 5*w^3 - 12*w^2 - 3*w],\
[1193, 1193, -w^3 + 3*w^2 - 6],\
[1201, 1201, -w^4 + 3*w^3 + w^2 - 5*w + 3],\
[1201, 1201, 2*w^4 - 5*w^3 - 4*w^2 + 9*w],\
[1213, 1213, -2*w^5 + 3*w^4 + 11*w^3 - 8*w^2 - 16*w - 2],\
[1213, 1213, 2*w^5 - w^4 - 13*w^3 + w^2 + 17*w - 2],\
[1213, 1213, 3*w^5 - 5*w^4 - 12*w^3 + 13*w^2 + 10*w - 2],\
[1213, 1213, -2*w^5 + 4*w^4 + 7*w^3 - 11*w^2 - 5*w + 5],\
[1217, 1217, -w^5 + 4*w^4 + w^3 - 13*w^2 + 3*w + 9],\
[1229, 1229, -w^5 + 2*w^4 + 3*w^3 - 6*w^2 + w + 4],\
[1229, 1229, -w^5 + w^4 + 4*w^3 + w^2 - 3*w - 6],\
[1231, 1231, 2*w^5 - 4*w^4 - 9*w^3 + 13*w^2 + 9*w - 5],\
[1277, 1277, -w^5 + 2*w^4 + 5*w^3 - 5*w^2 - 9*w],\
[1277, 1277, w^5 - 9*w^3 + 15*w],\
[1301, 1301, 2*w^4 - 4*w^3 - 5*w^2 + 8*w + 1],\
[1301, 1301, 2*w^5 - 4*w^4 - 8*w^3 + 9*w^2 + 9*w + 3],\
[1307, 1307, 2*w^5 - 4*w^4 - 9*w^3 + 13*w^2 + 9*w - 8],\
[1307, 1307, 3*w^5 - 6*w^4 - 12*w^3 + 14*w^2 + 13*w - 1],\
[1319, 1319, w^3 - 2*w - 3],\
[1319, 1319, w^5 - 2*w^4 - 6*w^3 + 9*w^2 + 7*w - 8],\
[1321, 1321, 3*w^5 - 5*w^4 - 14*w^3 + 12*w^2 + 18*w],\
[1327, 1327, w^5 - 2*w^4 - 5*w^3 + 8*w^2 + 4*w - 5],\
[1327, 1327, -w^5 + 7*w^3 + 3*w^2 - 10*w - 3],\
[1327, 1327, -w^4 + 4*w^3 + w^2 - 10*w - 2],\
[1361, 1361, -2*w^5 + 3*w^4 + 11*w^3 - 9*w^2 - 16*w],\
[1361, 1361, 2*w^5 - 5*w^4 - 6*w^3 + 14*w^2 + 3*w - 6],\
[1367, 1367, w^5 - 2*w^4 - 2*w^3 + 2*w^2 + 4],\
[1367, 1367, -w^5 + 3*w^4 + 2*w^3 - 7*w^2 - w - 3],\
[1369, 37, -w^5 + 7*w^3 + w^2 - 10*w + 1],\
[1399, 1399, -w^4 + w^3 + 4*w^2 - 4*w - 4],\
[1427, 1427, -w^5 + 3*w^4 + 2*w^3 - 7*w^2 + w + 3],\
[1429, 1429, -3*w^5 + 6*w^4 + 12*w^3 - 15*w^2 - 14*w],\
[1429, 1429, -2*w^5 + 5*w^4 + 7*w^3 - 15*w^2 - 7*w + 5],\
[1433, 1433, -w^5 + 4*w^4 - w^3 - 8*w^2 + 4*w - 2],\
[1439, 1439, -w^5 + w^4 + 8*w^3 - 6*w^2 - 12*w + 2],\
[1439, 1439, -w^4 - w^3 + 5*w^2 + 7*w - 1],\
[1447, 1447, 2*w^5 - 2*w^4 - 11*w^3 + 6*w^2 + 11*w - 3],\
[1471, 1471, -w^5 + 2*w^4 + 2*w^3 - 4*w^2 + 3],\
[1483, 1483, 2*w^5 - 4*w^4 - 9*w^3 + 12*w^2 + 10*w - 2],\
[1483, 1483, -w^4 + 2*w^3 + 2*w^2 - w - 4],\
[1487, 1487, -3*w^5 + 4*w^4 + 14*w^3 - 7*w^2 - 16*w - 3],\
[1489, 1489, -2*w^3 + 3*w^2 + 5*w - 5],\
[1493, 1493, -3*w^5 + 3*w^4 + 18*w^3 - 6*w^2 - 25*w - 1],\
[1499, 1499, 3*w^5 - 5*w^4 - 16*w^3 + 15*w^2 + 23*w - 3],\
[1511, 1511, 2*w^5 - 4*w^4 - 8*w^3 + 10*w^2 + 11*w],\
[1511, 1511, -2*w^5 + 2*w^4 + 11*w^3 - 2*w^2 - 15*w - 3],\
[1511, 1511, -2*w^5 + 2*w^4 + 11*w^3 - 3*w^2 - 14*w],\
[1571, 1571, -2*w^5 + 4*w^4 + 6*w^3 - 9*w^2 - 2*w + 4],\
[1571, 1571, 2*w^5 - w^4 - 12*w^3 + w^2 + 14*w - 1],\
[1571, 1571, -3*w^5 + 5*w^4 + 13*w^3 - 13*w^2 - 13*w],\
[1579, 1579, -2*w^5 + 3*w^4 + 10*w^3 - 9*w^2 - 10*w - 1],\
[1583, 1583, -2*w^5 + 4*w^4 + 6*w^3 - 6*w^2 - 6*w - 5],\
[1607, 1607, -w^4 + 4*w^3 + w^2 - 11*w],\
[1607, 1607, 2*w^5 - 3*w^4 - 10*w^3 + 8*w^2 + 10*w],\
[1613, 1613, 2*w^5 - 5*w^4 - 5*w^3 + 10*w^2 + 2*w + 2],\
[1619, 1619, -w^5 + w^4 + 8*w^3 - 4*w^2 - 17*w],\
[1637, 1637, 2*w^4 - 5*w^3 - 5*w^2 + 11*w],\
[1663, 1663, w^5 - 4*w^4 + 2*w^3 + 9*w^2 - 8*w - 2],\
[1669, 1669, -w^5 + 2*w^4 + 7*w^3 - 10*w^2 - 13*w + 7],\
[1697, 1697, -2*w^5 + 5*w^4 + 3*w^3 - 9*w^2 + 4*w - 2],\
[1709, 1709, 2*w^4 - 4*w^3 - 4*w^2 + 10*w - 1],\
[1733, 1733, 2*w^5 - 2*w^4 - 14*w^3 + 8*w^2 + 23*w - 4],\
[1753, 1753, -w^5 + w^4 + 5*w^3 - 4*w - 4],\
[1777, 1777, -4*w^5 + 9*w^4 + 12*w^3 - 22*w^2 - 7*w + 6],\
[1783, 1783, w^5 - 2*w^4 - 6*w^3 + 6*w^2 + 11*w - 1],\
[1801, 1801, -2*w^5 + 4*w^4 + 7*w^3 - 11*w^2 - 5*w + 8],\
[1811, 1811, 2*w^5 - 15*w^3 - 3*w^2 + 22*w + 5],\
[1811, 1811, w^2 + w - 5],\
[1811, 1811, w^2 - 3*w - 4],\
[1823, 1823, -4*w^5 + 7*w^4 + 18*w^3 - 20*w^2 - 20*w + 5],\
[1831, 1831, 3*w^5 - 5*w^4 - 14*w^3 + 11*w^2 + 19*w + 4],\
[1831, 1831, -w^5 + 2*w^4 + 3*w^3 - 4*w^2 + w - 2],\
[1847, 1847, w^5 - 2*w^4 - w^3 + 3*w^2 - 7*w - 2],\
[1849, 43, w^3 - 3*w - 4],\
[1861, 1861, -w^5 + 3*w^4 + 4*w^3 - 12*w^2 - 6*w + 10],\
[1861, 1861, w^4 - 4*w^3 - 3*w^2 + 10*w + 3],\
[1861, 1861, -w^5 + 4*w^4 - 2*w^3 - 10*w^2 + 9*w + 3],\
[1861, 1861, w^5 - 2*w^4 - 2*w^3 + 5*w^2 - 4*w - 2],\
[1867, 1867, -w^5 + 7*w^3 - w^2 - 7*w + 3],\
[1873, 1873, -3*w^5 + 5*w^4 + 12*w^3 - 11*w^2 - 11*w],\
[1877, 1877, 4*w^5 - 8*w^4 - 13*w^3 + 17*w^2 + 8*w + 1],\
[1889, 1889, -w^4 + 5*w^2 + 3*w - 4],\
[1901, 1901, -2*w^5 + 3*w^4 + 10*w^3 - 6*w^2 - 15*w - 1],\
[1949, 1949, -w^5 + 2*w^4 + 2*w^3 - 2*w^2 + w - 5],\
[1951, 1951, -2*w^5 + 4*w^4 + 6*w^3 - 7*w^2 - 3*w - 2],\
[1973, 1973, w^5 - 9*w^3 + w^2 + 16*w],\
[1987, 1987, -3*w^5 + 6*w^4 + 12*w^3 - 16*w^2 - 14*w + 3],\
[1999, 1999, -2*w^5 + 5*w^4 + 6*w^3 - 15*w^2 - 4*w + 6]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^10 + 4*x^9 - 13*x^8 - 57*x^7 + 35*x^6 + 189*x^5 - 43*x^4 - 130*x^3 + 53*x^2 - x - 1
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [e, 5794/5043*e^9 + 8386/1681*e^8 - 66622/5043*e^7 - 353363/5043*e^6 + 79987/5043*e^5 + 1128893/5043*e^4 + 48392/1681*e^3 - 736264/5043*e^2 + 20577/1681*e + 27731/5043, 1711/1681*e^9 + 7485/1681*e^8 - 19487/1681*e^7 - 105024/1681*e^6 + 21008/1681*e^5 + 333621/1681*e^4 + 52254/1681*e^3 - 208336/1681*e^2 + 4570/1681*e + 5721/1681, -1759/1681*e^9 - 7694/1681*e^8 + 20072/1681*e^7 + 107652/1681*e^6 - 23018/1681*e^5 - 338572/1681*e^4 - 41052/1681*e^3 + 201103/1681*e^2 - 30373/1681*e - 3780/1681, -551/5043*e^9 - 718/1681*e^8 + 7871/5043*e^7 + 33109/5043*e^6 - 26225/5043*e^5 - 133564/5043*e^4 + 5531/1681*e^3 + 153677/5043*e^2 + 11058/1681*e - 24892/5043, 1, 18613/5043*e^9 + 26396/1681*e^8 - 221908/5043*e^7 - 1116980/5043*e^6 + 370306/5043*e^5 + 3605231/5043*e^4 + 30153/1681*e^3 - 2368426/5043*e^2 + 144784/1681*e + 56213/5043, -1079/5043*e^9 - 2605/1681*e^8 - 823/5043*e^7 + 102361/5043*e^6 + 168514/5043*e^5 - 260308/5043*e^4 - 195459/1681*e^3 + 69071/5043*e^2 + 89590/1681*e - 28756/5043, -2941/5043*e^9 - 3930/1681*e^8 + 38470/5043*e^7 + 168164/5043*e^6 - 107395/5043*e^5 - 555677/5043*e^4 + 50109/1681*e^3 + 360241/5043*e^2 - 62299/1681*e + 3463/5043, -4154/1681*e^9 - 17737/1681*e^8 + 49156/1681*e^7 + 250125/1681*e^6 - 76871/1681*e^5 - 807043/1681*e^4 - 42102/1681*e^3 + 530362/1681*e^2 - 85347/1681*e - 9158/1681, 13327/5043*e^9 + 18794/1681*e^8 - 159376/5043*e^7 - 794792/5043*e^6 + 268726/5043*e^5 + 2560535/5043*e^4 + 26573/1681*e^3 - 1660255/5043*e^2 + 90420/1681*e + 18446/5043, -12299/5043*e^9 - 17909/1681*e^8 + 139703/5043*e^7 + 751957/5043*e^6 - 147512/5043*e^5 - 2373673/5043*e^4 - 120271/1681*e^3 + 1460891/5043*e^2 - 52042/1681*e - 35221/5043, 2299/5043*e^9 + 2648/1681*e^8 - 36319/5043*e^7 - 120407/5043*e^6 + 167503/5043*e^5 + 465293/5043*e^4 - 114895/1681*e^3 - 446266/5043*e^2 + 72285/1681*e - 826/5043, -893/5043*e^9 - 584/1681*e^8 + 20234/5043*e^7 + 34183/5043*e^6 - 147710/5043*e^5 - 200989/5043*e^4 + 121649/1681*e^3 + 320882/5043*e^2 - 55057/1681*e - 40690/5043, 7783/5043*e^9 + 11588/1681*e^8 - 84244/5043*e^7 - 481172/5043*e^6 + 36571/5043*e^5 + 1466744/5043*e^4 + 131736/1681*e^3 - 793654/5043*e^2 - 1139/1681*e + 28304/5043, -36775/5043*e^9 - 52546/1681*e^8 + 432541/5043*e^7 + 2219774/5043*e^6 - 645451/5043*e^5 - 7133300/5043*e^4 - 160879/1681*e^3 + 4650055/5043*e^2 - 204657/1681*e - 162077/5043, -18962/5043*e^9 - 26564/1681*e^8 + 228788/5043*e^7 + 1123060/5043*e^6 - 414548/5043*e^5 - 3616189/5043*e^4 + 8273/1681*e^3 + 2347670/5043*e^2 - 176327/1681*e - 26446/5043, -2992/5043*e^9 - 3969/1681*e^8 + 38146/5043*e^7 + 167174/5043*e^6 - 95032/5043*e^5 - 533306/5043*e^4 + 34955/1681*e^3 + 330808/5043*e^2 - 46958/1681*e - 1724/5043, 15304/5043*e^9 + 20998/1681*e^8 - 190720/5043*e^7 - 891686/5043*e^6 + 418963/5043*e^5 + 2905133/5043*e^4 - 91710/1681*e^3 - 1932520/5043*e^2 + 179601/1681*e + 5636/5043, -24362/5043*e^9 - 35242/1681*e^8 + 281993/5043*e^7 + 1489312/5043*e^6 - 363308/5043*e^5 - 4795987/5043*e^4 - 175131/1681*e^3 + 3200669/5043*e^2 - 94155/1681*e - 163615/5043, 4382/5043*e^9 + 5823/1681*e^8 - 57398/5043*e^7 - 249160/5043*e^6 + 159542/5043*e^5 + 825097/5043*e^4 - 70102/1681*e^3 - 544334/5043*e^2 + 86534/1681*e - 10568/5043, -7373/5043*e^9 - 9989/1681*e^8 + 94166/5043*e^7 + 429307/5043*e^6 - 227426/5043*e^5 - 1449319/5043*e^4 + 50837/1681*e^3 + 1089305/5043*e^2 - 47897/1681*e - 81235/5043, -23879/5043*e^9 - 32895/1681*e^8 + 297224/5043*e^7 + 1401091/5043*e^6 - 645032/5043*e^5 - 4607380/5043*e^4 + 122445/1681*e^3 + 3184253/5043*e^2 - 243893/1681*e - 85123/5043, 41659/5043*e^9 + 58654/1681*e^8 - 500890/5043*e^7 - 2482130/5043*e^6 + 887791/5043*e^5 + 8013188/5043*e^4 + 5358/1681*e^3 - 5256796/5043*e^2 + 360761/1681*e + 112088/5043, -11473/5043*e^9 - 15893/1681*e^8 + 141193/5043*e^7 + 675635/5043*e^6 - 285646/5043*e^5 - 2208557/5043*e^4 + 30501/1681*e^3 + 1491433/5043*e^2 - 105543/1681*e - 51182/5043, 4992/1681*e^9 + 21736/1681*e^8 - 57478/1681*e^7 - 305251/1681*e^6 + 71198/1681*e^5 + 972136/1681*e^4 + 109190/1681*e^3 - 612740/1681*e^2 + 76281/1681*e + 14985/1681, 15490/5043*e^9 + 23019/1681*e^8 - 169663/5043*e^7 - 959864/5043*e^6 + 102739/5043*e^5 + 2959409/5043*e^4 + 225398/1681*e^3 - 1625236/5043*e^2 + 36635/1681*e - 31513/5043, -38381/5043*e^9 - 55554/1681*e^8 + 441818/5043*e^7 + 2338801/5043*e^6 - 542501/5043*e^5 - 7439806/5043*e^4 - 295520/1681*e^3 + 4707479/5043*e^2 - 156022/1681*e - 163744/5043, -23636/5043*e^9 - 33698/1681*e^8 + 280079/5043*e^7 + 1426870/5043*e^6 - 442592/5043*e^5 - 4616671/5043*e^4 - 80738/1681*e^3 + 3086285/5043*e^2 - 125651/1681*e - 143173/5043, 12887/1681*e^9 + 54186/1681*e^8 - 156535/1681*e^7 - 767340/1681*e^6 + 294007/1681*e^5 + 2505345/1681*e^4 - 31083/1681*e^3 - 1703864/1681*e^2 + 311257/1681*e + 45484/1681, 28570/5043*e^9 + 41723/1681*e^8 - 326554/5043*e^7 - 1761725/5043*e^6 + 368056/5043*e^5 + 5655878/5043*e^4 + 268594/1681*e^3 - 3721423/5043*e^2 + 69873/1681*e + 173321/5043, -44995/5043*e^9 - 63776/1681*e^8 + 533983/5043*e^7 + 2689991/5043*e^6 - 861067/5043*e^5 - 8593463/5043*e^4 - 108941/1681*e^3 + 5392042/5043*e^2 - 317229/1681*e - 50312/5043, 49855/5043*e^9 + 71250/1681*e^8 - 589432/5043*e^7 - 3016592/5043*e^6 + 920854/5043*e^5 + 9749081/5043*e^4 + 163731/1681*e^3 - 6428533/5043*e^2 + 318583/1681*e + 139976/5043, -28276/5043*e^9 - 39125/1681*e^8 + 350077/5043*e^7 + 1662419/5043*e^6 - 747838/5043*e^5 - 5425304/5043*e^4 + 158623/1681*e^3 + 3642802/5043*e^2 - 348559/1681*e - 49679/5043, -13168/1681*e^9 - 56215/1681*e^8 + 155442/1681*e^7 + 791550/1681*e^6 - 237063/1681*e^5 - 2542769/1681*e^4 - 169567/1681*e^3 + 1645026/1681*e^2 - 198290/1681*e - 39059/1681, -36794/5043*e^9 - 52165/1681*e^8 + 438551/5043*e^7 + 2205265/5043*e^6 - 732608/5043*e^5 - 7095301/5043*e^4 - 55249/1681*e^3 + 4600229/5043*e^2 - 282761/1681*e - 114766/5043, 1724/5043*e^9 + 3296/1681*e^8 - 10505/5043*e^7 - 131371/5043*e^6 - 96748/5043*e^5 + 345223/5043*e^4 + 116076/1681*e^3 - 66749/5043*e^2 - 27701/1681*e - 7097/5043, 1237/123*e^9 + 1778/41*e^8 - 14443/123*e^7 - 75116/123*e^6 + 20173/123*e^5 + 241439/123*e^4 + 7172/41*e^3 - 158284/123*e^2 + 5608/41*e + 6341/123, 3506/1681*e^9 + 14075/1681*e^8 - 45461/1681*e^7 - 201199/1681*e^6 + 118657/1681*e^5 + 672124/1681*e^4 - 114294/1681*e^3 - 470834/1681*e^2 + 104305/1681*e - 780/1681, 24054/1681*e^9 + 102844/1681*e^8 - 284543/1681*e^7 - 1448915/1681*e^6 + 447068/1681*e^5 + 4659856/1681*e^4 + 223250/1681*e^3 - 3025609/1681*e^2 + 451835/1681*e + 75630/1681, 37696/5043*e^9 + 52657/1681*e^8 - 461101/5043*e^7 - 2238680/5043*e^6 + 912844/5043*e^5 + 7325270/5043*e^4 - 107234/1681*e^3 - 5025973/5043*e^2 + 380300/1681*e + 116324/5043, 14258/5043*e^9 + 18616/1681*e^8 - 191630/5043*e^7 - 805000/5043*e^6 + 580664/5043*e^5 + 2756128/5043*e^4 - 272716/1681*e^3 - 2083205/5043*e^2 + 276470/1681*e + 4858/5043, 25816/5043*e^9 + 36255/1681*e^8 - 313792/5043*e^7 - 1542863/5043*e^6 + 591874/5043*e^5 + 5058518/5043*e^4 - 23569/1681*e^3 - 3465067/5043*e^2 + 217482/1681*e + 44513/5043, -4/1681*e^9 - 998/1681*e^8 - 4574/1681*e^7 + 10305/1681*e^6 + 64551/1681*e^5 + 568/1681*e^4 - 204989/1681*e^3 - 53134/1681*e^2 + 134431/1681*e - 22952/1681, -61487/5043*e^9 - 87759/1681*e^8 + 722792/5043*e^7 + 3702193/5043*e^6 - 1075106/5043*e^5 - 11844286/5043*e^4 - 268579/1681*e^3 + 7575461/5043*e^2 - 335262/1681*e - 200803/5043, -8954/1681*e^9 - 38637/1681*e^8 + 104294/1681*e^7 + 543183/1681*e^6 - 143391/1681*e^5 - 1735841/1681*e^4 - 157437/1681*e^3 + 1103113/1681*e^2 - 130699/1681*e - 28545/1681, 898/1681*e^9 + 3840/1681*e^8 - 10314/1681*e^7 - 53368/1681*e^6 + 12809/1681*e^5 + 166659/1681*e^4 + 15263/1681*e^3 - 109058/1681*e^2 + 33694/1681*e + 2140/1681, 13292/5043*e^9 + 18965/1681*e^8 - 156533/5043*e^7 - 800020/5043*e^6 + 236372/5043*e^5 + 2555419/5043*e^4 + 55001/1681*e^3 - 1591460/5043*e^2 + 78370/1681*e - 15965/5043, -19778/5043*e^9 - 28869/1681*e^8 + 223604/5043*e^7 + 1213123/5043*e^6 - 216740/5043*e^5 - 3843241/5043*e^4 - 234191/1681*e^3 + 2441558/5043*e^2 + 1889/1681*e - 144739/5043, -61895/5043*e^9 - 88071/1681*e^8 + 735329/5043*e^7 + 3729574/5043*e^6 - 1188008/5043*e^5 - 12068758/5043*e^4 - 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473125/1681*e^6 + 209865/1681*e^5 + 1606889/1681*e^4 - 62153/1681*e^3 - 1242743/1681*e^2 + 124895/1681*e + 109215/1681, 102229/5043*e^9 + 143833/1681*e^8 - 1225849/5043*e^7 - 6068138/5043*e^6 + 2141977/5043*e^5 + 19402700/5043*e^4 + 25952/1681*e^3 - 12250234/5043*e^2 + 876208/1681*e + 164747/5043, -18508/5043*e^9 - 25228/1681*e^8 + 238594/5043*e^7 + 1097363/5043*e^6 - 606082/5043*e^5 - 3852119/5043*e^4 + 173695/1681*e^3 + 3377404/5043*e^2 - 143935/1681*e - 371549/5043, 34234/1681*e^9 + 148150/1681*e^8 - 397265/1681*e^7 - 2083596/1681*e^6 + 526229/1681*e^5 + 6673794/1681*e^4 + 685861/1681*e^3 - 4350571/1681*e^2 + 384906/1681*e + 206519/1681, 199583/5043*e^9 + 284828/1681*e^8 - 2345321/5043*e^7 - 12004270/5043*e^6 + 3494195/5043*e^5 + 38292373/5043*e^4 + 823862/1681*e^3 - 24240653/5043*e^2 + 1198372/1681*e + 647974/5043, -132211/5043*e^9 - 191481/1681*e^8 + 1516240/5043*e^7 + 8050055/5043*e^6 - 1779931/5043*e^5 - 25493492/5043*e^4 - 1137551/1681*e^3 + 15805534/5043*e^2 - 422892/1681*e - 547829/5043, -44182/5043*e^9 - 67604/1681*e^8 + 462613/5043*e^7 + 2823245/5043*e^6 + 19571/5043*e^5 - 8774468/5043*e^4 - 1009954/1681*e^3 + 5255782/5043*e^2 + 165596/1681*e - 302243/5043, 16767/1681*e^9 + 70800/1681*e^8 - 202982/1681*e^7 - 1003304/1681*e^6 + 375794/1681*e^5 + 3287418/1681*e^4 - 35562/1681*e^3 - 2293375/1681*e^2 + 387364/1681*e + 86104/1681, 9917/1681*e^9 + 39363/1681*e^8 - 130214/1681*e^7 - 563548/1681*e^6 + 360852/1681*e^5 + 1894951/1681*e^4 - 436913/1681*e^3 - 1359865/1681*e^2 + 497607/1681*e - 21638/1681, -131026/5043*e^9 - 186224/1681*e^8 + 1552543/5043*e^7 + 7865405/5043*e^6 - 2474782/5043*e^5 - 25253279/5043*e^4 - 343637/1681*e^3 + 16314100/5043*e^2 - 942105/1681*e - 253769/5043, -49138/5043*e^9 - 71295/1681*e^8 + 564619/5043*e^7 + 3003812/5043*e^6 - 674611/5043*e^5 - 9563444/5043*e^4 - 418496/1681*e^3 + 5970184/5043*e^2 - 118558/1681*e - 201434/5043, -50404/1681*e^9 - 217086/1681*e^8 + 587823/1681*e^7 + 3052113/1681*e^6 - 817138/1681*e^5 - 9766940/1681*e^4 - 845307/1681*e^3 + 6314602/1681*e^2 - 804040/1681*e - 205503/1681, 94919/5043*e^9 + 133200/1681*e^8 - 1152938/5043*e^7 - 5663713/5043*e^6 + 2162405/5043*e^5 + 18529423/5043*e^4 - 61121/1681*e^3 - 12611069/5043*e^2 + 730650/1681*e + 218071/5043, 13865/1681*e^9 + 59495/1681*e^8 - 162781/1681*e^7 - 836855/1681*e^6 + 241245/1681*e^5 + 2684178/1681*e^4 + 173954/1681*e^3 - 1765566/1681*e^2 + 261881/1681*e + 88095/1681, -9197/5043*e^9 - 10395/1681*e^8 + 136568/5043*e^7 + 438397/5043*e^6 - 560999/5043*e^5 - 1392031/5043*e^4 + 389406/1681*e^3 + 743849/5043*e^2 - 320943/1681*e - 12520/5043, -55249/5043*e^9 - 76067/1681*e^8 + 689842/5043*e^7 + 3238790/5043*e^6 - 1538821/5043*e^5 - 10627151/5043*e^4 + 378170/1681*e^3 + 7245244/5043*e^2 - 694459/1681*e - 232631/5043, -35146/5043*e^9 - 49026/1681*e^8 + 426871/5043*e^7 + 2081417/5043*e^6 - 789673/5043*e^5 - 6794759/5043*e^4 - 12548/1681*e^3 + 4672057/5043*e^2 - 227843/1681*e - 73823/5043, -114164/5043*e^9 - 166210/1681*e^8 + 1307744/5043*e^7 + 7013653/5043*e^6 - 1510232/5043*e^5 - 22478608/5043*e^4 - 1026526/1681*e^3 + 14685062/5043*e^2 - 305354/1681*e - 622750/5043, 31552/1681*e^9 + 137943/1681*e^8 - 359325/1681*e^7 - 1932554/1681*e^6 + 395009/1681*e^5 + 6114959/1681*e^4 + 858323/1681*e^3 - 3776583/1681*e^2 + 362978/1681*e + 107579/1681, 8542/1681*e^9 + 40065/1681*e^8 - 86245/1681*e^7 - 555927/1681*e^6 - 47845/1681*e^5 + 1705252/1681*e^4 + 723427/1681*e^3 - 939522/1681*e^2 - 215591/1681*e + 17889/1681, 11573/5043*e^9 + 13003/1681*e^8 - 178133/5043*e^7 - 568483/5043*e^6 + 786569/5043*e^5 + 2007766/5043*e^4 - 554067/1681*e^3 - 1639001/5043*e^2 + 414695/1681*e + 29908/5043, 10796/5043*e^9 + 14782/1681*e^8 - 136199/5043*e^7 - 628063/5043*e^6 + 328529/5043*e^5 + 2047498/5043*e^4 - 124013/1681*e^3 - 1362416/5043*e^2 + 180805/1681*e + 150526/5043, -168323/5043*e^9 - 240158/1681*e^8 + 1978208/5043*e^7 + 10126366/5043*e^6 - 2944154/5043*e^5 - 32352799/5043*e^4 - 703031/1681*e^3 + 20586068/5043*e^2 - 1079132/1681*e - 516400/5043]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([27, 3, w^4 - 2*w^3 - 3*w^2 + 5*w])] = -1

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