/*
  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([4, 6, -7, -1, 1])
F.<w> = NumberField(g)
ZF = F.ring_of_integers()

NN = ZF.ideal([12, 6, 1/2*w^3 + 1/2*w^2 - 5/2*w])

primes_array = [
[3, 3, -w + 1],\
[4, 2, w],\
[4, 2, -1/2*w^3 + 1/2*w^2 + 7/2*w - 3],\
[7, 7, -1/2*w^3 + 1/2*w^2 + 5/2*w - 2],\
[13, 13, 1/2*w^3 + 1/2*w^2 - 7/2*w - 1],\
[17, 17, 1/2*w^3 - 1/2*w^2 - 5/2*w],\
[27, 3, -w^3 + 7*w + 1],\
[31, 31, w + 3],\
[31, 31, -w^2 + 5],\
[37, 37, w^2 - 3],\
[41, 41, 1/2*w^3 + 1/2*w^2 - 3/2*w - 2],\
[47, 47, w^3 - 5*w - 3],\
[53, 53, 1/2*w^3 - 1/2*w^2 - 7/2*w],\
[61, 61, w^3 - w^2 - 5*w + 3],\
[83, 83, w^3 + w^2 - 6*w - 7],\
[83, 83, -w^3 + 5*w + 1],\
[83, 83, 2*w - 1],\
[83, 83, -3/2*w^3 - 1/2*w^2 + 19/2*w + 2],\
[89, 89, 1/2*w^3 - 1/2*w^2 - 7/2*w - 2],\
[89, 89, w^3 - 5*w + 5],\
[97, 97, -1/2*w^3 + 1/2*w^2 + 7/2*w - 6],\
[97, 97, -1/2*w^3 + 1/2*w^2 + 9/2*w - 1],\
[103, 103, 3/2*w^3 + 3/2*w^2 - 19/2*w - 9],\
[109, 109, 1/2*w^3 - 1/2*w^2 - 9/2*w + 4],\
[127, 127, 1/2*w^3 + 1/2*w^2 - 3/2*w - 3],\
[127, 127, 1/2*w^3 - 1/2*w^2 - 5/2*w + 6],\
[139, 139, 1/2*w^3 + 3/2*w^2 - 9/2*w - 3],\
[139, 139, 3/2*w^3 - 1/2*w^2 - 21/2*w + 1],\
[149, 149, -1/2*w^3 + 1/2*w^2 + 9/2*w - 2],\
[151, 151, -1/2*w^3 - 1/2*w^2 + 9/2*w - 3],\
[157, 157, 3/2*w^3 - 1/2*w^2 - 21/2*w + 4],\
[163, 163, 1/2*w^3 + 3/2*w^2 - 5/2*w - 3],\
[167, 167, -1/2*w^3 + 3/2*w^2 + 9/2*w - 9],\
[179, 179, w^3 - w^2 - 5*w + 1],\
[179, 179, -1/2*w^3 + 1/2*w^2 + 3/2*w - 4],\
[181, 181, 5/2*w^3 + 3/2*w^2 - 31/2*w - 10],\
[191, 191, -1/2*w^3 + 5/2*w^2 + 7/2*w - 14],\
[191, 191, 2*w^3 - 2*w^2 - 12*w + 11],\
[193, 193, w^2 + 1],\
[193, 193, 1/2*w^3 + 3/2*w^2 - 9/2*w - 6],\
[197, 197, 1/2*w^3 + 1/2*w^2 - 11/2*w + 1],\
[197, 197, -3/2*w^3 + 3/2*w^2 + 17/2*w - 8],\
[199, 199, 3/2*w^3 - 3/2*w^2 - 19/2*w + 7],\
[227, 227, 1/2*w^3 + 1/2*w^2 - 7/2*w - 6],\
[227, 227, -2*w^3 - w^2 + 14*w + 9],\
[229, 229, w^3 - w^2 - 4*w + 3],\
[229, 229, 3/2*w^3 - 1/2*w^2 - 17/2*w + 1],\
[233, 233, -w^3 - w^2 + 7*w + 9],\
[233, 233, 1/2*w^3 + 3/2*w^2 - 5/2*w - 9],\
[251, 251, -5/2*w^3 - 1/2*w^2 + 31/2*w + 2],\
[257, 257, -3/2*w^3 - 1/2*w^2 + 19/2*w + 1],\
[257, 257, 1/2*w^3 + 1/2*w^2 - 11/2*w - 1],\
[269, 269, 2*w^3 - 2*w^2 - 13*w + 15],\
[269, 269, 1/2*w^3 + 3/2*w^2 - 9/2*w - 4],\
[271, 271, 1/2*w^3 + 3/2*w^2 - 5/2*w - 6],\
[277, 277, -1/2*w^3 + 5/2*w^2 + 5/2*w - 16],\
[281, 281, -2*w^3 + 12*w + 1],\
[281, 281, -3/2*w^3 - 1/2*w^2 + 15/2*w - 3],\
[283, 283, 5/2*w^3 + 3/2*w^2 - 29/2*w - 8],\
[283, 283, 3/2*w^3 + 1/2*w^2 - 15/2*w],\
[293, 293, -w^3 - w^2 + 6*w + 1],\
[307, 307, -3/2*w^3 + 1/2*w^2 + 13/2*w + 4],\
[307, 307, -3/2*w^3 - 1/2*w^2 + 13/2*w - 2],\
[311, 311, 2*w^2 + w - 11],\
[311, 311, 1/2*w^3 + 3/2*w^2 - 5/2*w - 5],\
[313, 313, 3/2*w^3 - 1/2*w^2 - 17/2*w + 2],\
[317, 317, w^3 + 2*w^2 - 7*w - 3],\
[331, 331, 2*w^2 + 2*w - 9],\
[343, 7, -w^3 + 2*w^2 + 5*w - 11],\
[349, 349, 5/2*w^3 + 1/2*w^2 - 35/2*w - 6],\
[353, 353, 1/2*w^3 + 3/2*w^2 - 7/2*w - 4],\
[359, 359, w - 5],\
[361, 19, -5/2*w^3 + 1/2*w^2 + 33/2*w],\
[361, 19, w^3 - w^2 - 8*w + 3],\
[367, 367, -3/2*w^3 + 3/2*w^2 + 15/2*w - 8],\
[383, 383, -1/2*w^3 + 1/2*w^2 + 1/2*w - 3],\
[397, 397, -3/2*w^3 + 5/2*w^2 + 17/2*w - 16],\
[397, 397, 1/2*w^3 - 1/2*w^2 - 5/2*w - 3],\
[401, 401, -w^3 + 3*w - 3],\
[401, 401, 3/2*w^3 + 3/2*w^2 - 21/2*w - 4],\
[409, 409, 3/2*w^3 - 1/2*w^2 - 19/2*w - 3],\
[419, 419, -5/2*w^3 - 1/2*w^2 + 29/2*w + 1],\
[421, 421, -1/2*w^3 + 3/2*w^2 + 9/2*w - 11],\
[421, 421, -3*w + 1],\
[431, 431, 1/2*w^3 - 1/2*w^2 + 1/2*w + 2],\
[431, 431, w^3 - 7*w - 5],\
[433, 433, 1/2*w^3 + 1/2*w^2 - 3/2*w - 6],\
[433, 433, w^3 + w^2 - 6*w + 3],\
[467, 467, 1/2*w^3 + 3/2*w^2 - 11/2*w - 6],\
[487, 487, -2*w^3 + w^2 + 12*w - 9],\
[503, 503, 3/2*w^3 - 3/2*w^2 - 19/2*w + 6],\
[503, 503, w^2 + 2*w - 7],\
[523, 523, w^3 - w^2 - 6*w + 1],\
[523, 523, -w^3 + 3*w^2 + 7*w - 19],\
[541, 541, -3/2*w^3 + 3/2*w^2 + 15/2*w - 7],\
[541, 541, w^3 - w^2 - 8*w + 7],\
[547, 547, -1/2*w^3 + 3/2*w^2 + 3/2*w - 8],\
[557, 557, 2*w^2 - w - 9],\
[563, 563, -3*w^3 - w^2 + 19*w + 5],\
[563, 563, 7/2*w^3 + 5/2*w^2 - 45/2*w - 16],\
[563, 563, -w^3 + 3*w + 3],\
[563, 563, -w^2 + 2*w - 3],\
[569, 569, w^3 - w^2 - 6*w - 1],\
[571, 571, -5/2*w^3 + 3/2*w^2 + 31/2*w - 11],\
[577, 577, 2*w^2 - 2*w - 5],\
[587, 587, 3/2*w^3 + 1/2*w^2 - 23/2*w - 3],\
[587, 587, -2*w^3 + 14*w + 1],\
[599, 599, -3/2*w^3 - 1/2*w^2 + 13/2*w + 4],\
[607, 607, -3/2*w^3 - 3/2*w^2 + 21/2*w + 13],\
[613, 613, -1/2*w^3 + 3/2*w^2 + 11/2*w - 6],\
[613, 613, w^3 + w^2 - 8*w - 7],\
[617, 617, 2*w^2 - w - 5],\
[625, 5, -5],\
[653, 653, -1/2*w^3 + 3/2*w^2 + 9/2*w - 3],\
[653, 653, -2*w^3 - w^2 + 14*w + 3],\
[659, 659, -7/2*w^3 - 1/2*w^2 + 43/2*w + 6],\
[661, 661, 5/2*w^3 + 1/2*w^2 - 25/2*w - 5],\
[661, 661, w^3 + w^2 - 5*w - 7],\
[677, 677, -11/2*w^3 - 3/2*w^2 + 73/2*w + 13],\
[683, 683, -7/2*w^3 + 5/2*w^2 + 45/2*w - 16],\
[683, 683, -w^3 + 3*w^2 + 5*w - 11],\
[691, 691, 2*w^2 - 15],\
[691, 691, w^3 + w^2 - 4*w - 5],\
[701, 701, -7/2*w^3 - 1/2*w^2 + 47/2*w + 5],\
[701, 701, -w^3 + w^2 + 3*w - 5],\
[719, 719, 5/2*w^3 + 1/2*w^2 - 27/2*w - 5],\
[727, 727, -1/2*w^3 - 1/2*w^2 + 3/2*w - 4],\
[733, 733, 3/2*w^3 - 1/2*w^2 - 15/2*w + 1],\
[733, 733, -w^3 - 2*w^2 + 5*w + 5],\
[733, 733, 1/2*w^3 - 1/2*w^2 + 3/2*w + 2],\
[733, 733, 1/2*w^3 + 5/2*w^2 - 5/2*w - 13],\
[739, 739, 2*w^2 - 7],\
[743, 743, 3/2*w^3 - 1/2*w^2 - 9/2*w + 4],\
[743, 743, 2*w^3 - 12*w + 3],\
[751, 751, 1/2*w^3 + 1/2*w^2 - 11/2*w - 5],\
[751, 751, -1/2*w^3 + 1/2*w^2 + 11/2*w - 2],\
[761, 761, -3/2*w^3 + 3/2*w^2 + 23/2*w - 5],\
[769, 769, w^3 - 2*w^2 - 5*w + 13],\
[787, 787, -3/2*w^3 + 1/2*w^2 + 15/2*w - 3],\
[787, 787, 2*w^3 - 10*w - 3],\
[797, 797, 3/2*w^3 - 1/2*w^2 - 21/2*w + 7],\
[797, 797, -2*w^3 + 2*w^2 + 14*w - 13],\
[809, 809, -4*w^3 - 2*w^2 + 25*w + 15],\
[821, 821, 2*w^3 + 2*w^2 - 13*w - 11],\
[839, 839, -1/2*w^3 + 3/2*w^2 + 3/2*w - 9],\
[839, 839, -7/2*w^3 - 5/2*w^2 + 47/2*w + 18],\
[841, 29, 3/2*w^3 - 1/2*w^2 - 17/2*w + 10],\
[841, 29, 2*w^3 - 15*w + 5],\
[853, 853, 2*w^3 - 9*w - 3],\
[853, 853, -1/2*w^3 - 3/2*w^2 - 3/2*w + 7],\
[857, 857, 3/2*w^3 + 3/2*w^2 - 9/2*w - 4],\
[857, 857, w^3 - 3*w^2 - 5*w + 9],\
[857, 857, -w^3 + 3*w^2 + 6*w - 13],\
[857, 857, 1/2*w^3 + 5/2*w^2 - 7/2*w - 14],\
[859, 859, -5/2*w^3 - 1/2*w^2 + 35/2*w + 3],\
[863, 863, 2*w^3 - 2*w^2 - 13*w + 9],\
[881, 881, 2*w^2 + w - 13],\
[881, 881, 5/2*w^3 - 1/2*w^2 - 33/2*w - 1],\
[907, 907, -w^3 + 3*w^2 + 6*w - 15],\
[919, 919, 3/2*w^3 + 5/2*w^2 - 19/2*w - 4],\
[929, 929, 3/2*w^3 + 1/2*w^2 - 19/2*w + 1],\
[941, 941, 3/2*w^3 - 1/2*w^2 - 13/2*w],\
[947, 947, -1/2*w^3 + 5/2*w^2 + 13/2*w - 11],\
[947, 947, -7/2*w^3 - 1/2*w^2 + 43/2*w + 4],\
[947, 947, 1/2*w^3 + 1/2*w^2 - 13/2*w - 1],\
[947, 947, -4*w - 3],\
[953, 953, 3/2*w^3 - 7/2*w^2 - 21/2*w + 22],\
[953, 953, 1/2*w^3 + 5/2*w^2 - 3/2*w - 10],\
[961, 31, 3/2*w^3 + 3/2*w^2 - 17/2*w - 10],\
[967, 967, w^3 - 2*w^2 - 7*w + 7],\
[967, 967, 1/2*w^3 - 1/2*w^2 - 5/2*w - 4],\
[977, 977, -2*w^3 + 11*w + 1],\
[977, 977, 3/2*w^3 + 1/2*w^2 - 25/2*w + 4],\
[991, 991, -1/2*w^3 + 1/2*w^2 + 5/2*w - 8],\
[997, 997, 1/2*w^3 + 3/2*w^2 - 1/2*w - 7],\
[1013, 1013, 2*w^3 - w^2 - 14*w + 5],\
[1013, 1013, 3/2*w^3 + 3/2*w^2 - 23/2*w - 3],\
[1019, 1019, -1/2*w^3 + 3/2*w^2 + 3/2*w - 12],\
[1019, 1019, -3/2*w^3 + 7/2*w^2 + 17/2*w - 22],\
[1049, 1049, -5/2*w^3 - 5/2*w^2 + 33/2*w + 15],\
[1049, 1049, -3*w^3 - w^2 + 18*w + 3],\
[1051, 1051, 3*w^3 - 3*w^2 - 18*w + 17],\
[1061, 1061, 3/2*w^3 + 1/2*w^2 - 15/2*w - 7],\
[1061, 1061, -3*w - 5],\
[1087, 1087, w^2 - 2*w - 7],\
[1087, 1087, -w^3 - w^2 + 7*w - 1],\
[1091, 1091, 3/2*w^3 - 3/2*w^2 - 23/2*w + 3],\
[1093, 1093, 2*w^2 + w + 1],\
[1103, 1103, -2*w^3 + w^2 + 12*w - 1],\
[1103, 1103, 11/2*w^3 + 3/2*w^2 - 69/2*w - 11],\
[1103, 1103, -3/2*w^3 - 3/2*w^2 + 23/2*w + 9],\
[1103, 1103, 3/2*w^3 - 3/2*w^2 - 15/2*w + 1],\
[1109, 1109, -9/2*w^3 - 1/2*w^2 + 57/2*w + 3],\
[1151, 1151, 5/2*w^3 + 5/2*w^2 - 31/2*w - 14],\
[1151, 1151, -1/2*w^3 - 1/2*w^2 + 7/2*w - 5],\
[1153, 1153, -1/2*w^3 + 5/2*w^2 + 9/2*w - 15],\
[1163, 1163, -1/2*w^3 + 3/2*w^2 + 5/2*w - 13],\
[1163, 1163, -5/2*w^3 - 1/2*w^2 + 33/2*w + 1],\
[1181, 1181, -5/2*w^3 + 1/2*w^2 + 33/2*w - 5],\
[1181, 1181, -w^3 + w^2 + 4*w - 9],\
[1181, 1181, -5/2*w^3 + 1/2*w^2 + 35/2*w],\
[1181, 1181, -3/2*w^3 - 3/2*w^2 + 13/2*w + 6],\
[1187, 1187, 7/2*w^3 - 5/2*w^2 - 43/2*w + 15],\
[1193, 1193, -3/2*w^3 + 1/2*w^2 + 13/2*w - 2],\
[1201, 1201, -2*w^3 - 2*w^2 + 13*w + 5],\
[1201, 1201, 3/2*w^3 + 1/2*w^2 - 25/2*w + 2],\
[1213, 1213, 3*w^3 - w^2 - 18*w + 3],\
[1213, 1213, 3/2*w^3 + 5/2*w^2 - 21/2*w - 6],\
[1217, 1217, -1/2*w^3 - 1/2*w^2 + 11/2*w - 7],\
[1223, 1223, -1/2*w^3 - 1/2*w^2 - 5/2*w],\
[1237, 1237, -w^3 - 2*w^2 + 7*w + 9],\
[1259, 1259, -1/2*w^3 + 3/2*w^2 + 11/2*w - 12],\
[1279, 1279, 1/2*w^3 + 5/2*w^2 - 3/2*w - 13],\
[1279, 1279, 3/2*w^3 - 1/2*w^2 - 11/2*w + 1],\
[1297, 1297, -4*w^3 + 25*w - 1],\
[1301, 1301, 5/2*w^3 - 1/2*w^2 - 29/2*w + 4],\
[1303, 1303, -3/2*w^3 - 1/2*w^2 + 25/2*w + 4],\
[1303, 1303, w^3 + w^2 - 7*w + 3],\
[1319, 1319, 9/2*w^3 - 9/2*w^2 - 57/2*w + 29],\
[1321, 1321, 1/2*w^3 + 5/2*w^2 - 3/2*w - 8],\
[1321, 1321, w^2 - 2*w - 9],\
[1381, 1381, 1/2*w^3 + 1/2*w^2 - 1/2*w - 7],\
[1399, 1399, -1/2*w^3 + 1/2*w^2 + 1/2*w - 7],\
[1399, 1399, -w^2 - 3],\
[1409, 1409, -5/2*w^3 - 3/2*w^2 + 25/2*w],\
[1423, 1423, 5/2*w^3 - 3/2*w^2 - 31/2*w + 5],\
[1423, 1423, -w^3 + 9*w - 3],\
[1439, 1439, w^3 + 2*w^2 - 7*w - 7],\
[1439, 1439, -5/2*w^3 - 5/2*w^2 + 33/2*w + 7],\
[1447, 1447, 3/2*w^3 - 5/2*w^2 - 17/2*w + 9],\
[1451, 1451, 1/2*w^3 + 5/2*w^2 - 7/2*w - 5],\
[1459, 1459, -1/2*w^3 + 1/2*w^2 + 13/2*w],\
[1459, 1459, 1/2*w^3 + 3/2*w^2 - 17/2*w - 3],\
[1481, 1481, 3/2*w^3 - 3/2*w^2 - 21/2*w + 4],\
[1487, 1487, 7/2*w^3 - 1/2*w^2 - 43/2*w + 1],\
[1499, 1499, -3/2*w^3 - 5/2*w^2 + 11/2*w + 8],\
[1523, 1523, -5/2*w^3 + 1/2*w^2 + 29/2*w - 1],\
[1523, 1523, -3/2*w^3 + 1/2*w^2 + 11/2*w + 5],\
[1543, 1543, -2*w^3 + 10*w - 3],\
[1567, 1567, -1/2*w^3 - 5/2*w^2 + 9/2*w + 5],\
[1567, 1567, 2*w^3 - 15*w - 3],\
[1579, 1579, 1/2*w^3 + 3/2*w^2 - 3/2*w - 10],\
[1579, 1579, -3/2*w^3 + 3/2*w^2 + 13/2*w - 10],\
[1597, 1597, -1/2*w^3 - 3/2*w^2 + 11/2*w + 8],\
[1601, 1601, 2*w^3 - w^2 - 10*w + 1],\
[1601, 1601, 3/2*w^3 + 1/2*w^2 - 21/2*w + 2],\
[1613, 1613, -1/2*w^3 - 1/2*w^2 + 5/2*w - 5],\
[1619, 1619, 5/2*w^3 - 1/2*w^2 - 29/2*w + 3],\
[1619, 1619, 3*w^3 - 3*w^2 - 17*w + 19],\
[1621, 1621, w^3 + w^2 - w - 5],\
[1621, 1621, 3/2*w^3 + 5/2*w^2 - 23/2*w - 7],\
[1637, 1637, -7/2*w^3 + 1/2*w^2 + 45/2*w - 4],\
[1657, 1657, -7/2*w^3 - 5/2*w^2 + 45/2*w + 14],\
[1669, 1669, -w^3 - w^2 + 2*w + 5],\
[1693, 1693, 11/2*w^3 + 1/2*w^2 - 71/2*w - 4],\
[1699, 1699, 7/2*w^3 - 9/2*w^2 - 47/2*w + 27],\
[1699, 1699, -1/2*w^3 + 5/2*w^2 + 11/2*w - 14],\
[1733, 1733, w^3 - 9*w + 1],\
[1741, 1741, 5/2*w^3 - 1/2*w^2 - 31/2*w - 4],\
[1747, 1747, 7/2*w^3 - 5/2*w^2 - 45/2*w + 12],\
[1777, 1777, -3/2*w^3 - 1/2*w^2 + 23/2*w - 3],\
[1777, 1777, -1/2*w^3 - 1/2*w^2 - 3/2*w - 3],\
[1787, 1787, -2*w^3 - 2*w^2 + 15*w + 5],\
[1801, 1801, -1/2*w^3 - 5/2*w^2 + 11/2*w + 6],\
[1801, 1801, 1/2*w^3 - 1/2*w^2 - 9/2*w - 5],\
[1823, 1823, w^3 + 3*w^2 - 7*w - 17],\
[1823, 1823, 5/2*w^3 + 5/2*w^2 - 33/2*w - 9],\
[1847, 1847, -w^3 - 3*w^2 + 7*w + 5],\
[1861, 1861, -1/2*w^3 + 1/2*w^2 + 9/2*w - 10],\
[1861, 1861, -3/2*w^3 + 3/2*w^2 + 17/2*w - 2],\
[1871, 1871, -w^3 + w^2 + 10*w - 11],\
[1873, 1873, -5*w^3 - w^2 + 31*w + 7],\
[1879, 1879, -2*w^3 - w^2 + 8*w + 5],\
[1889, 1889, w^3 + w^2 - 7*w - 11],\
[1889, 1889, -3/2*w^3 - 1/2*w^2 + 9/2*w + 4],\
[1901, 1901, 4*w^3 - 4*w^2 - 26*w + 27],\
[1901, 1901, 3/2*w^3 + 3/2*w^2 - 21/2*w - 2],\
[1901, 1901, -1/2*w^3 + 1/2*w^2 + 13/2*w - 1],\
[1901, 1901, w^2 + 4*w - 3],\
[1907, 1907, 1/2*w^3 - 5/2*w^2 - 5/2*w + 19],\
[1913, 1913, -2*w^3 + 2*w^2 + 12*w - 7],\
[1931, 1931, -w^3 - 3*w^2 + 6*w + 5],\
[1973, 1973, 4*w^3 - 4*w^2 - 25*w + 21],\
[1973, 1973, 1/2*w^3 + 3/2*w^2 - 3/2*w - 12],\
[1979, 1979, -w^3 + 2*w^2 + 9*w - 9],\
[1979, 1979, -3/2*w^3 + 3/2*w^2 + 23/2*w - 8],\
[1987, 1987, 1/2*w^3 + 5/2*w^2 - 5/2*w - 7],\
[1993, 1993, -3*w^3 + 17*w - 3],\
[1993, 1993, -1/2*w^3 - 5/2*w^2 + 9/2*w + 11],\
[1999, 1999, -2*w^3 + 12*w - 5]]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x^2 - 5
K.<e> = NumberField(heckePol)

hecke_eigenvalues_array = [1, e, -1, -2, -e - 1, -e + 3, 2*e - 2, -8, 2, e - 7, 2, -2*e - 2, -5*e - 1, e - 3, 14, 4*e - 6, -4*e + 4, -4*e + 4, 5*e - 5, -5*e - 5, 3*e + 3, -2, -4*e + 4, -e - 15, -12, 4*e - 2, 4*e, -4*e, -4*e - 10, -8, 3*e + 13, -8*e + 4, 6*e - 2, -2*e + 10, 6*e - 10, 2, 6*e + 2, -8, 4*e - 6, -8*e - 6, -3*e + 3, 4*e - 2, -8*e, -8*e + 8, -2*e - 2, -10, -e + 15, 5*e - 1, 3*e - 1, 4*e + 2, 5*e + 13, -2, 5*e - 15, 9*e + 5, 2*e + 2, -2*e - 12, -6*e + 12, e - 13, 8*e - 6, 6*e - 6, -6*e + 4, -22, -12, 4*e + 12, 2, 3*e + 19, 3*e - 7, -8, -8*e + 4, 4*e - 10, e - 1, -8*e + 10, 3*e - 3, e - 3, 4*e - 12, -10*e - 6, -4*e - 2, 9*e - 17, -13*e - 3, -18, 9*e + 5, -12*e, 5*e - 23, -4*e + 2, 4*e + 12, 12, 4*e - 6, -26, 8, -14*e - 2, -4*e + 4, 8*e - 6, -4*e - 16, -8*e + 4, -7*e + 27, -3*e + 17, 8*e - 12, 16*e - 2, -8*e + 4, -4*e + 4, -8*e + 4, 2*e - 26, 13*e + 5, 32, 3*e - 17, -4*e - 2, 4*e + 8, -8*e - 10, -8*e + 8, -6*e + 24, 16*e - 6, -8*e + 18, 8*e - 14, -3*e + 19, -4*e + 14, -4*e + 30, -8*e + 2, -8*e - 18, 3*e + 43, 2*e - 26, -2*e - 26, -2*e + 2, -8, -2*e - 8, -7*e + 27, 8*e - 30, -2*e - 2, 12*e + 14, 4*e - 6, -7*e + 29, 7*e - 1, -8*e + 10, -6*e + 34, 8*e - 16, -48, -4*e - 28, 9*e - 3, 13*e - 5, -4*e + 18, -12*e + 8, -8*e - 2, -e + 23, 8*e + 30, 16*e + 2, -16*e, -8*e, 15*e - 3, -9*e - 13, 3*e - 31, 14, -5*e - 17, -4*e + 18, 5*e - 27, 16*e - 2, 12*e - 10, -10*e + 14, 16*e + 2, -9*e - 23, 4*e + 28, -2*e - 10, 8*e + 30, 20*e + 2, -8*e - 2, -4*e + 8, -8*e - 12, 4*e - 32, 2*e + 24, 10*e - 36, -10*e + 12, 6*e - 42, -2*e - 22, 9*e + 3, 24*e - 2, 2*e + 42, 8*e - 2, 5*e - 1, 16*e - 6, 10*e + 30, 4*e + 30, 8*e - 30, 12*e + 10, -4*e - 8, 19*e - 3, -11*e + 17, -4*e - 52, -2, 12*e - 8, -23*e - 1, 8*e - 16, 8*e - 16, -4*e + 4, 4*e - 36, -5*e + 5, 18*e - 18, -2*e - 38, -e - 21, 4*e + 4, 18*e - 26, -5*e + 27, -38, 5*e + 17, 2, 8*e - 12, -17*e - 21, 13*e - 3, 2, -4*e - 26, -12*e + 14, 15*e + 3, 12*e + 34, 12*e - 2, -16*e - 10, 40, -6*e + 30, -3*e - 7, 16*e + 22, 12*e + 4, 4, 16*e - 10, e - 43, -8*e - 18, 10*e + 12, -6*e - 10, -8*e - 40, -8*e + 30, -16*e - 6, -4*e + 44, 2*e - 30, 16*e, 8*e - 32, 14*e + 2, -20*e + 10, -10*e - 30, 19*e - 3, -18*e - 22, 8*e - 20, 14, -36, -8*e + 24, 12*e + 8, 14*e - 42, 12*e, 20*e, 4*e - 62, -8*e - 38, -5*e - 3, -e - 51, 10*e - 10, -8*e + 50, 8*e - 18, 5*e + 47, -4*e - 22, -20*e + 18, 23*e - 15, -10*e + 4, -24*e + 20, -10*e + 50, -8*e + 34, 9*e - 13, -24*e - 12, 9*e + 13, -14*e - 32, -28*e + 8, 4*e + 62, 42, 20*e + 4, 16*e + 14, 6*e - 42, -13*e + 37, 14*e - 28, 8*e - 8, -25*e - 11, 70, 9*e - 15, 9*e - 35, 10*e - 28, 19*e - 23, -8*e - 18, 13*e + 47, 6*e - 2, -15*e - 21, -4*e + 32, 4*e + 74, -29*e + 9, -4*e, 8*e - 20, 4*e - 32, 11*e - 31, 16*e - 46, -18*e - 30]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal([3, 3, -w + 1])] = -1
AL_eigenvalues[ZF.ideal([4, 2, -1/2*w^3 + 1/2*w^2 + 7/2*w - 3])] = 1

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