/*
  This code can be loaded, or copied and pasted, into Magma.
  It will load the data associated to the HMF, including
  the field, level, and Hecke and Atkin-Lehner eigenvalue data.
  At the *bottom* of the file, there is code to recreate the
  Hilbert modular form in Magma, by creating the HMF space
  and cutting out the corresponding Hecke irreducible subspace.
  From there, you can ask for more eigenvalues or modify as desired.
  It is commented out, as this computation may be lengthy.
*/

P<x> := PolynomialRing(Rationals());
g := P![4, 6, -7, -1, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {12, 6, -w - 2}>;

primesArray := [
[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 := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x^6 - 2*x^5 - 13*x^4 + 22*x^3 + 29*x^2 - 24*x + 3;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [1, 1, e, 1/2*e^5 - e^4 - 13/2*e^3 + 21/2*e^2 + 15*e - 13/2, 1/2*e^3 + 1/2*e^2 - 11/2*e - 3/2, -1/2*e^5 + 1/2*e^4 + 7*e^3 - 5*e^2 - 37/2*e + 5/2, e^5 - 3/2*e^4 - 27/2*e^3 + 31/2*e^2 + 71/2*e - 13, 1/2*e^5 - e^4 - 7*e^3 + 11*e^2 + 35/2*e - 9, -1/2*e^3 + 1/2*e^2 + 7/2*e + 1/2, e^5 - 3/2*e^4 - 13*e^3 + 16*e^2 + 29*e - 27/2, 1/2*e^5 - e^4 - 7*e^3 + 11*e^2 + 39/2*e - 9, -1/2*e^4 + 4*e^2 + e - 1/2, -e^5 + 2*e^4 + 25/2*e^3 - 41/2*e^2 - 51/2*e + 29/2, -e^5 + 2*e^4 + 13*e^3 - 22*e^2 - 30*e + 20, 1/2*e^5 - 1/2*e^4 - 6*e^3 + 4*e^2 + 23/2*e + 5/2, -1/2*e^5 + e^4 + 8*e^3 - 12*e^2 - 57/2*e + 16, e^5 - 2*e^4 - 27/2*e^3 + 41/2*e^2 + 67/2*e - 31/2, -1/2*e^3 - 1/2*e^2 + 11/2*e + 7/2, -1/2*e^5 + 13/2*e^3 - 1/2*e^2 - 17*e + 19/2, 2*e^5 - 5/2*e^4 - 27*e^3 + 27*e^2 + 66*e - 39/2, 1/2*e^5 - 1/2*e^4 - 8*e^3 + 5*e^2 + 55/2*e + 3/2, 1/2*e^4 + e^3 - 7*e^2 - 10*e + 27/2, -5/2*e^5 + 4*e^4 + 63/2*e^3 - 83/2*e^2 - 66*e + 61/2, -1/2*e^5 + 3/2*e^4 + 6*e^3 - 16*e^2 - 19/2*e + 33/2, -e^5 + e^4 + 13*e^3 - 11*e^2 - 28*e + 10, -e^5 + 2*e^4 + 25/2*e^3 - 43/2*e^2 - 49/2*e + 25/2, 1/2*e^5 - e^4 - 7*e^3 + 9*e^2 + 43/2*e + 1, 1/2*e^4 + e^3 - 5*e^2 - 8*e - 9/2, -e^5 + 5/2*e^4 + 25/2*e^3 - 49/2*e^2 - 57/2*e + 9, e^4 - e^3 - 11*e^2 + 9*e + 10, 1/2*e^5 - 1/2*e^4 - 7*e^3 + 7*e^2 + 41/2*e - 29/2, 3/2*e^5 - 5/2*e^4 - 41/2*e^3 + 51/2*e^2 + 52*e - 16, 1/2*e^5 - 1/2*e^4 - 7*e^3 + 4*e^2 + 29/2*e + 9/2, -2*e^5 + 9/2*e^4 + 55/2*e^3 - 91/2*e^2 - 149/2*e + 26, -5/2*e^5 + 9/2*e^4 + 33*e^3 - 47*e^2 - 145/2*e + 65/2, -5/2*e^3 - 1/2*e^2 + 47/2*e + 11/2, -1/2*e^5 + 1/2*e^4 + 15/2*e^3 - 13/2*e^2 - 22*e + 9, 3/2*e^5 - 5/2*e^4 - 20*e^3 + 25*e^2 + 93/2*e - 21/2, 5/2*e^5 - 9/2*e^4 - 35*e^3 + 47*e^2 + 193/2*e - 81/2, 3/2*e^5 - 7/2*e^4 - 19*e^3 + 37*e^2 + 79/2*e - 59/2, 3/2*e^5 - 5/2*e^4 - 21*e^3 + 27*e^2 + 115/2*e - 33/2, -1/2*e^5 + 1/2*e^4 + 13/2*e^3 - 5/2*e^2 - 12*e - 10, -3/2*e^5 + 3/2*e^4 + 22*e^3 - 17*e^2 - 125/2*e + 35/2, -5/2*e^5 + 4*e^4 + 71/2*e^3 - 87/2*e^2 - 106*e + 65/2, -e^5 + 2*e^4 + 14*e^3 - 20*e^2 - 37*e + 14, 1/2*e^5 - 1/2*e^4 - 13/2*e^3 + 9/2*e^2 + 12*e + 4, 7/2*e^5 - 6*e^4 - 93/2*e^3 + 125/2*e^2 + 112*e - 71/2, -e^4 + 1/2*e^3 + 25/2*e^2 - 15/2*e - 45/2, 2*e^5 - 3*e^4 - 27*e^3 + 29*e^2 + 69*e - 12, -e^5 + 3*e^4 + 14*e^3 - 31*e^2 - 39*e + 18, -3/2*e^5 + 2*e^4 + 21*e^3 - 23*e^2 - 109/2*e + 30, -3/2*e^5 + 5/2*e^4 + 41/2*e^3 - 59/2*e^2 - 54*e + 36, 5/2*e^5 - 9/2*e^4 - 67/2*e^3 + 93/2*e^2 + 84*e - 45, -2*e^5 + 4*e^4 + 53/2*e^3 - 81/2*e^2 - 131/2*e + 63/2, 1/2*e^5 - e^4 - 7*e^3 + 11*e^2 + 27/2*e - 5, -9/2*e^5 + 15/2*e^4 + 59*e^3 - 77*e^2 - 285/2*e + 103/2, 2*e^5 - 7/2*e^4 - 27*e^3 + 38*e^2 + 68*e - 63/2, 4*e^5 - 6*e^4 - 54*e^3 + 64*e^2 + 132*e - 42, -2*e^5 + 4*e^4 + 27*e^3 - 41*e^2 - 67*e + 35, -e^5 + 3/2*e^4 + 11*e^3 - 16*e^2 - 13*e + 51/2, 1/2*e^5 + 1/2*e^4 - 8*e^3 - 8*e^2 + 43/2*e + 47/2, -e^5 + e^4 + 14*e^3 - 8*e^2 - 43*e + 1, 3/2*e^4 + 1/2*e^3 - 37/2*e^2 + 1/2*e + 24, 1/2*e^5 - 3/2*e^4 - 13/2*e^3 + 39/2*e^2 + 9*e - 33, -5/2*e^5 + 7/2*e^4 + 65/2*e^3 - 73/2*e^2 - 76*e + 31, -1/2*e^4 + e^3 + e^2 - 6*e + 53/2, -e^5 + 5/2*e^4 + 13*e^3 - 27*e^2 - 29*e + 39/2, -9/2*e^5 + 17/2*e^4 + 62*e^3 - 91*e^2 - 323/2*e + 125/2, e^5 - e^4 - 14*e^3 + 11*e^2 + 43*e, 1/2*e^5 - 1/2*e^4 - 17/2*e^3 + 15/2*e^2 + 25*e - 22, -3/2*e^5 + 3/2*e^4 + 43/2*e^3 - 29/2*e^2 - 61*e + 4, -3*e^5 + 5*e^4 + 38*e^3 - 52*e^2 - 79*e + 35, -3/2*e^4 + e^3 + 18*e^2 - 10*e - 51/2, 1/2*e^5 + 1/2*e^4 - 10*e^3 - 8*e^2 + 83/2*e + 35/2, -1/2*e^5 + 3/2*e^4 + 6*e^3 - 14*e^2 - 19/2*e + 1/2, -2*e^5 + 3*e^4 + 55/2*e^3 - 59/2*e^2 - 157/2*e + 39/2, 2*e^5 - 5/2*e^4 - 25*e^3 + 26*e^2 + 48*e - 13/2, -1/2*e^5 + 6*e^3 + 4*e^2 - 25/2*e - 11, 3*e^5 - 5*e^4 - 43*e^3 + 52*e^2 + 132*e - 33, e^5 - 29/2*e^3 + 1/2*e^2 + 95/2*e - 17/2, 1/2*e^5 - 1/2*e^4 - 5*e^3 + 3*e^2 - 7/2*e + 31/2, -3/2*e^5 + 5/2*e^4 + 21*e^3 - 25*e^2 - 103/2*e + 21/2, -7/2*e^5 + 11/2*e^4 + 97/2*e^3 - 117/2*e^2 - 131*e + 41, 5/2*e^5 - 4*e^4 - 63/2*e^3 + 87/2*e^2 + 60*e - 73/2, 2*e^5 - 4*e^4 - 26*e^3 + 42*e^2 + 64*e - 30, e^4 + 3*e^3 - 14*e^2 - 23*e + 25, -1/2*e^5 + 8*e^3 - 65/2*e + 7, -3*e^5 + 9/2*e^4 + 41*e^3 - 48*e^2 - 109*e + 65/2, 2*e^5 - 4*e^4 - 28*e^3 + 40*e^2 + 80*e - 30, 5/2*e^5 - 7/2*e^4 - 63/2*e^3 + 75/2*e^2 + 61*e - 10, 9/2*e^5 - 13/2*e^4 - 59*e^3 + 69*e^2 + 281/2*e - 137/2, -e^4 + 1/2*e^3 + 21/2*e^2 - 7/2*e - 21/2, -2*e^5 + 7/2*e^4 + 29*e^3 - 38*e^2 - 84*e + 55/2, 2*e^5 - 4*e^4 - 26*e^3 + 43*e^2 + 54*e - 41, 4*e^5 - 8*e^4 - 54*e^3 + 82*e^2 + 142*e - 56, -e^5 + 2*e^4 + 12*e^3 - 20*e^2 - 19*e + 8, 5*e^5 - 8*e^4 - 133/2*e^3 + 165/2*e^2 + 337/2*e - 123/2, 2*e^5 - 7/2*e^4 - 55/2*e^3 + 75/2*e^2 + 121/2*e - 27, -2*e^5 + 3*e^4 + 27*e^3 - 34*e^2 - 65*e + 51, 1/2*e^3 + 3/2*e^2 - 21/2*e + 9/2, -2*e^5 + 5*e^4 + 61/2*e^3 - 107/2*e^2 - 203/2*e + 115/2, e^5 - 3*e^4 - 27/2*e^3 + 71/2*e^2 + 65/2*e - 97/2, 4*e^5 - 7*e^4 - 58*e^3 + 74*e^2 + 174*e - 49, 2*e^5 - 7/2*e^4 - 55/2*e^3 + 79/2*e^2 + 157/2*e - 25, -7/2*e^5 + 13/2*e^4 + 48*e^3 - 70*e^2 - 269/2*e + 135/2, 3/2*e^5 - 3/2*e^4 - 24*e^3 + 16*e^2 + 161/2*e - 9/2, -13/2*e^5 + 23/2*e^4 + 86*e^3 - 121*e^2 - 399/2*e + 147/2, -2*e^5 + 4*e^4 + 59/2*e^3 - 83/2*e^2 - 175/2*e + 51/2, e^5 - 2*e^4 - 12*e^3 + 22*e^2 + 21*e - 38, -9/2*e^5 + 8*e^4 + 60*e^3 - 86*e^2 - 289/2*e + 57, e^5 - e^4 - 33/2*e^3 + 21/2*e^2 + 121/2*e - 9/2, e^5 - 1/2*e^4 - 16*e^3 + 8*e^2 + 52*e - 29/2, -3/2*e^5 + 5/2*e^4 + 24*e^3 - 26*e^2 - 161/2*e + 23/2, 3*e^5 - 6*e^4 - 41*e^3 + 61*e^2 + 110*e - 33, -5/2*e^5 + 11/2*e^4 + 73/2*e^3 - 117/2*e^2 - 111*e + 52, 9/2*e^5 - 17/2*e^4 - 60*e^3 + 90*e^2 + 295/2*e - 115/2, 3/2*e^5 - 7/2*e^4 - 47/2*e^3 + 79/2*e^2 + 82*e - 42, -7/2*e^5 + 13/2*e^4 + 47*e^3 - 66*e^2 - 219/2*e + 39/2, 1/2*e^5 - 3/2*e^4 - 17/2*e^3 + 41/2*e^2 + 30*e - 27, 1/2*e^5 - 1/2*e^4 - 17/2*e^3 + 7/2*e^2 + 35*e - 22, 9/2*e^5 - 17/2*e^4 - 60*e^3 + 90*e^2 + 279/2*e - 115/2, -3/2*e^5 + 3/2*e^4 + 39/2*e^3 - 43/2*e^2 - 39*e + 49, -9/2*e^5 + 19/2*e^4 + 119/2*e^3 - 195/2*e^2 - 145*e + 62, 5/2*e^5 - 9/2*e^4 - 33*e^3 + 50*e^2 + 169/2*e - 107/2, -6*e^5 + 17/2*e^4 + 79*e^3 - 87*e^2 - 190*e + 123/2, e^5 - 2*e^4 - 15*e^3 + 20*e^2 + 58*e - 6, -9/2*e^5 + 13/2*e^4 + 65*e^3 - 71*e^2 - 373/2*e + 125/2, -1/2*e^5 + 3/2*e^4 + 13/2*e^3 - 31/2*e^2 - 21*e + 15, 4*e^5 - 6*e^4 - 54*e^3 + 62*e^2 + 142*e - 70, -3*e^5 + 4*e^4 + 40*e^3 - 40*e^2 - 97*e + 30, -4*e^5 + 7*e^4 + 111/2*e^3 - 141/2*e^2 - 321/2*e + 77/2, -e^5 + 11*e^3 + 3*e^2 - 10*e - 31, -2*e^5 + 3*e^4 + 30*e^3 - 34*e^2 - 100*e + 31, 1/2*e^5 - 5/2*e^4 - 9/2*e^3 + 57/2*e^2 - 6*e - 16, -2*e^5 + 7/2*e^4 + 28*e^3 - 42*e^2 - 75*e + 103/2, 5/2*e^5 - 9/2*e^4 - 69/2*e^3 + 91/2*e^2 + 99*e - 32, -e^5 + 2*e^4 + 13*e^3 - 17*e^2 - 34*e - 25, 1/2*e^5 - 2*e^4 - 13/2*e^3 + 41/2*e^2 + 15*e + 21/2, 11/2*e^5 - 9*e^4 - 72*e^3 + 94*e^2 + 347/2*e - 64, -1/2*e^5 + 3/2*e^4 + 9/2*e^3 - 25/2*e^2 + e + 6, e^4 + 1/2*e^3 - 29/2*e^2 - 27/2*e + 57/2, 1/2*e^5 + 1/2*e^4 - 4*e^3 - 5*e^2 - 5/2*e - 47/2, -7/2*e^5 + 4*e^4 + 49*e^3 - 39*e^2 - 265/2*e + 24, 11/2*e^5 - 9*e^4 - 77*e^3 + 93*e^2 + 445/2*e - 73, -1/2*e^5 + 3/2*e^4 + 15/2*e^3 - 31/2*e^2 - 29*e + 36, -3*e^5 + 7*e^4 + 41*e^3 - 74*e^2 - 114*e + 63, -13/2*e^5 + 21/2*e^4 + 181/2*e^3 - 223/2*e^2 - 245*e + 92, -4*e^5 + 6*e^4 + 55*e^3 - 63*e^2 - 141*e + 37, -1/2*e^5 + 2*e^4 + 10*e^3 - 24*e^2 - 77/2*e + 37, -5/2*e^5 + 11/2*e^4 + 67/2*e^3 - 117/2*e^2 - 70*e + 38, 4*e^5 - 7*e^4 - 51*e^3 + 71*e^2 + 119*e - 30, 1/2*e^5 + 1/2*e^4 - 8*e^3 - 7*e^2 + 63/2*e + 1/2, -2*e^5 + 4*e^4 + 29*e^3 - 41*e^2 - 87*e + 43, 3/2*e^5 - 5/2*e^4 - 35/2*e^3 + 49/2*e^2 + 17*e - 9, -2*e^5 + 3*e^4 + 24*e^3 - 30*e^2 - 34*e + 19, 5/2*e^5 - 5*e^4 - 38*e^3 + 56*e^2 + 237/2*e - 42, -2*e^5 + 3*e^4 + 59/2*e^3 - 61/2*e^2 - 193/2*e - 3/2, -6*e^5 + 9*e^4 + 165/2*e^3 - 197/2*e^2 - 449/2*e + 159/2, -6*e^5 + 10*e^4 + 163/2*e^3 - 219/2*e^2 - 419/2*e + 187/2, 5/2*e^5 - 13/2*e^4 - 33*e^3 + 69*e^2 + 165/2*e - 149/2, -3/2*e^5 + 5/2*e^4 + 21*e^3 - 23*e^2 - 119/2*e - 3/2, -e^5 - 3/2*e^4 + 15*e^3 + 18*e^2 - 49*e - 39/2, 5/2*e^5 - 13/2*e^4 - 33*e^3 + 67*e^2 + 157/2*e - 81/2, 5/2*e^5 - 9/2*e^4 - 35*e^3 + 47*e^2 + 185/2*e - 69/2, e^5 - 2*e^4 - 27/2*e^3 + 47/2*e^2 + 85/2*e - 79/2, 3/2*e^5 - 5/2*e^4 - 39/2*e^3 + 43/2*e^2 + 44*e + 15, -6*e^5 + 17/2*e^4 + 155/2*e^3 - 171/2*e^2 - 357/2*e + 54, 2*e^5 - 11/2*e^4 - 53/2*e^3 + 117/2*e^2 + 119/2*e - 50, 3/2*e^5 - 3/2*e^4 - 49/2*e^3 + 39/2*e^2 + 88*e - 13, -5/2*e^5 + 5*e^4 + 35*e^3 - 57*e^2 - 175/2*e + 71, 5*e^5 - 6*e^4 - 137/2*e^3 + 125/2*e^2 + 351/2*e - 97/2, 1/2*e^5 - 3/2*e^4 - 9/2*e^3 + 31/2*e^2 - 5*e + 9, 11/2*e^5 - 19/2*e^4 - 72*e^3 + 102*e^2 + 349/2*e - 173/2, -2*e^5 + 3*e^4 + 26*e^3 - 32*e^2 - 56*e - 3, 3*e^5 - 13/2*e^4 - 38*e^3 + 72*e^2 + 74*e - 141/2, 13/2*e^5 - 19/2*e^4 - 88*e^3 + 98*e^2 + 451/2*e - 165/2, -e^5 + e^4 + 12*e^3 - 8*e^2 - 17*e - 5, -2*e^5 + 7*e^4 + 53/2*e^3 - 145/2*e^2 - 127/2*e + 97/2, -2*e^5 + e^4 + 23*e^3 - 8*e^2 - 37*e - 5, -6*e^5 + 10*e^4 + 79*e^3 - 105*e^2 - 183*e + 47, -6*e^5 + 11*e^4 + 80*e^3 - 112*e^2 - 200*e + 69, 3/2*e^5 - 7/2*e^4 - 21*e^3 + 41*e^2 + 127/2*e - 75/2, e^5 + e^4 - 15*e^3 - 7*e^2 + 46*e - 4, 6*e^5 - 9*e^4 - 163/2*e^3 + 197/2*e^2 + 413/2*e - 181/2, -7*e^5 + 11*e^4 + 92*e^3 - 114*e^2 - 219*e + 85, -2*e^5 + 5*e^4 + 27*e^3 - 56*e^2 - 63*e + 57, e^5 - 2*e^4 - 15*e^3 + 18*e^2 + 50*e + 8, 7/2*e^5 - 11/2*e^4 - 46*e^3 + 62*e^2 + 205/2*e - 125/2, 4*e^5 - 6*e^4 - 53*e^3 + 57*e^2 + 129*e - 19, e^5 - 5/2*e^4 - 18*e^3 + 34*e^2 + 72*e - 117/2, -15/2*e^5 + 29/2*e^4 + 100*e^3 - 147*e^2 - 493/2*e + 157/2, 5*e^5 - 8*e^4 - 63*e^3 + 79*e^2 + 130*e - 47, -5/2*e^5 + 6*e^4 + 32*e^3 - 66*e^2 - 141/2*e + 71, 2*e^5 - 7*e^4 - 25*e^3 + 80*e^2 + 43*e - 69, -11/2*e^5 + 17/2*e^4 + 149/2*e^3 - 189/2*e^2 - 183*e + 80, -11/2*e^5 + 15/2*e^4 + 75*e^3 - 83*e^2 - 399/2*e + 175/2, 3/2*e^5 - 3*e^4 - 41/2*e^3 + 77/2*e^2 + 52*e - 105/2, 9/2*e^5 - 13/2*e^4 - 127/2*e^3 + 147/2*e^2 + 183*e - 67, 1/2*e^4 - 3/2*e^3 - 25/2*e^2 + 33/2*e + 39, -1/2*e^5 + 3/2*e^4 + 2*e^3 - 18*e^2 + 65/2*e + 105/2, 1/2*e^5 - 7/2*e^4 - 13/2*e^3 + 77/2*e^2 + 11*e - 30, -3/2*e^5 + 3*e^4 + 47/2*e^3 - 75/2*e^2 - 75*e + 131/2, -e^5 + 5/2*e^4 + 33/2*e^3 - 45/2*e^2 - 109/2*e - 13, e^5 - 15*e^3 - 2*e^2 + 52*e + 22, -6*e^5 + 9*e^4 + 78*e^3 - 93*e^2 - 184*e + 46, 8*e^5 - 13*e^4 - 215/2*e^3 + 273/2*e^2 + 545/2*e - 197/2, 2*e^5 - 3*e^4 - 30*e^3 + 36*e^2 + 96*e - 23, -e^5 + 13*e^3 - 6*e^2 - 24*e + 40, 7/2*e^5 - 7/2*e^4 - 48*e^3 + 34*e^2 + 249/2*e - 57/2, -2*e^5 + 3/2*e^4 + 27*e^3 - 18*e^2 - 66*e + 75/2, -e^5 + 13*e^3 - 2*e^2 - 34*e + 14, -e^5 + e^4 + 12*e^3 - 8*e^2 - 5*e - 11, -3*e^5 + 9/2*e^4 + 39*e^3 - 49*e^2 - 87*e + 39/2, -3/2*e^5 + 5/2*e^4 + 31/2*e^3 - 57/2*e^2 - 11*e + 35, -4*e^5 + 15/2*e^4 + 48*e^3 - 82*e^2 - 77*e + 147/2, 2*e^5 - e^4 - 27*e^3 + 11*e^2 + 65*e - 12, 1/2*e^5 - 7/2*e^4 - 2*e^3 + 38*e^2 - 57/2*e - 73/2, 5/2*e^5 - 5/2*e^4 - 32*e^3 + 26*e^2 + 131/2*e - 7/2, -3*e^5 + 6*e^4 + 75/2*e^3 - 129/2*e^2 - 131/2*e + 75/2, -2*e^5 + 3*e^4 + 29*e^3 - 37*e^2 - 95*e + 48, -5/2*e^5 + 13/2*e^4 + 31*e^3 - 65*e^2 - 117/2*e + 85/2, -7/2*e^5 + 11/2*e^4 + 50*e^3 - 51*e^2 - 285/2*e + 23/2, 5*e^5 - 10*e^4 - 129/2*e^3 + 211/2*e^2 + 285/2*e - 125/2, 9/2*e^5 - 11/2*e^4 - 63*e^3 + 51*e^2 + 345/2*e - 63/2, -4*e^5 + 7*e^4 + 58*e^3 - 72*e^2 - 160*e + 21, -17/2*e^5 + 25/2*e^4 + 114*e^3 - 133*e^2 - 563/2*e + 193/2, 2*e^5 - 3*e^4 - 26*e^3 + 35*e^2 + 46*e - 38, -9*e^5 + 15*e^4 + 123*e^3 - 162*e^2 - 326*e + 127, 4*e^5 - 15/2*e^4 - 59*e^3 + 85*e^2 + 178*e - 185/2, e^5 - 4*e^4 - 13*e^3 + 46*e^2 + 44*e - 74, 7*e^5 - 11*e^4 - 195/2*e^3 + 237/2*e^2 + 515/2*e - 213/2, e^4 - 5*e^3 - 5*e^2 + 49*e - 4, 4*e^5 - 7*e^4 - 53*e^3 + 68*e^2 + 125*e - 61, -5/2*e^5 + 9/2*e^4 + 61/2*e^3 - 95/2*e^2 - 55*e + 4, -5*e^5 + 7*e^4 + 133/2*e^3 - 141/2*e^2 - 307/2*e + 87/2, 13/2*e^5 - 23/2*e^4 - 181/2*e^3 + 249/2*e^2 + 255*e - 92, -3/2*e^5 + 5/2*e^4 + 17*e^3 - 25*e^2 - 43/2*e - 15/2, e^5 - 2*e^4 - 13*e^3 + 19*e^2 + 34*e - 11, -7*e^5 + 12*e^4 + 92*e^3 - 124*e^2 - 205*e + 96, 9/2*e^5 - 15/2*e^4 - 63*e^3 + 83*e^2 + 357/2*e - 167/2, 3*e^5 - 9/2*e^4 - 44*e^3 + 48*e^2 + 128*e - 109/2, -11/2*e^5 + 9*e^4 + 80*e^3 - 94*e^2 - 495/2*e + 74, 1/2*e^4 - 5/2*e^3 - 11/2*e^2 + 15/2*e + 16, -2*e^5 + 4*e^4 + 53/2*e^3 - 81/2*e^2 - 121/2*e + 45/2, -7*e^5 + 12*e^4 + 94*e^3 - 130*e^2 - 217*e + 114, -11/2*e^5 + 10*e^4 + 151/2*e^3 - 203/2*e^2 - 193*e + 89/2, -3*e^5 + 5*e^4 + 38*e^3 - 50*e^2 - 87*e + 31, -3/2*e^5 + 1/2*e^4 + 31/2*e^3 - 11/2*e^2 - 8*e + 11, 3*e^5 - 7/2*e^4 - 39*e^3 + 37*e^2 + 83*e - 97/2, -5/2*e^5 + 7*e^4 + 35*e^3 - 73*e^2 - 203/2*e + 73, -3*e^5 + 5*e^4 + 39*e^3 - 57*e^2 - 84*e + 74, -11/2*e^5 + 17/2*e^4 + 153/2*e^3 - 189/2*e^2 - 192*e + 105, 7*e^5 - 12*e^4 - 91*e^3 + 123*e^2 + 206*e - 71, e^5 - 2*e^4 - 18*e^3 + 18*e^2 + 83*e - 4, 7/2*e^5 - 9/2*e^4 - 50*e^3 + 48*e^2 + 269/2*e - 11/2, -4*e^5 + 11/2*e^4 + 101/2*e^3 - 125/2*e^2 - 187/2*e + 80, -3*e^5 + 8*e^4 + 79/2*e^3 - 169/2*e^2 - 211/2*e + 131/2, 2*e^5 - 3*e^4 - 27*e^3 + 28*e^2 + 63*e - 25, 2*e^5 - 4*e^4 - 30*e^3 + 42*e^2 + 92*e - 56, 5*e^5 - 9/2*e^4 - 67*e^3 + 50*e^2 + 169*e - 97/2, 2*e^5 - 4*e^4 - 27*e^3 + 50*e^2 + 55*e - 90, -3*e^5 + 5/2*e^4 + 39*e^3 - 20*e^2 - 103*e - 59/2, -3/2*e^5 + e^4 + 43/2*e^3 - 23/2*e^2 - 51*e - 13/2, 6*e^5 - 19/2*e^4 - 74*e^3 + 106*e^2 + 137*e - 207/2, -9/2*e^5 + 19/2*e^4 + 59*e^3 - 103*e^2 - 237/2*e + 175/2, -3/2*e^5 + 5/2*e^4 + 20*e^3 - 32*e^2 - 109/2*e + 131/2, 2*e^5 - 5*e^4 - 57/2*e^3 + 129/2*e^2 + 169/2*e - 187/2, -e^5 + 11*e^3 - 3*e^2 - 12*e + 21, -5/2*e^5 + 2*e^4 + 38*e^3 - 20*e^2 - 241/2*e + 9, 1/2*e^5 - 3*e^4 - 4*e^3 + 36*e^2 - 27/2*e - 78, 13/2*e^5 - 17/2*e^4 - 82*e^3 + 90*e^2 + 327/2*e - 115/2, 2*e^5 - 3/2*e^4 - 51/2*e^3 + 23/2*e^2 + 125/2*e + 13, 3/2*e^5 - 3/2*e^4 - 43/2*e^3 + 19/2*e^2 + 50*e + 10, 9*e^5 - 33/2*e^4 - 120*e^3 + 170*e^2 + 300*e - 225/2, 7/2*e^5 - 5/2*e^4 - 50*e^3 + 26*e^2 + 281/2*e + 9/2, -4*e^5 + 5*e^4 + 53*e^3 - 59*e^2 - 125*e + 96, 7/2*e^5 - 11/2*e^4 - 51*e^3 + 51*e^2 + 299/2*e + 5/2, 4*e^5 - 7*e^4 - 117/2*e^3 + 143/2*e^2 + 351/2*e - 79/2, -e^5 + 4*e^4 + 14*e^3 - 40*e^2 - 47*e + 60, -5*e^5 + 6*e^4 + 73*e^3 - 63*e^2 - 220*e + 37, 3*e^5 - 8*e^4 - 67/2*e^3 + 175/2*e^2 + 93/2*e - 171/2, -6*e^5 + 12*e^4 + 161/2*e^3 - 241/2*e^2 - 377/2*e + 69/2, -3*e^5 + 6*e^4 + 40*e^3 - 64*e^2 - 89*e + 36, 6*e^5 - 10*e^4 - 84*e^3 + 100*e^2 + 244*e - 66, 13/2*e^5 - 11*e^4 - 175/2*e^3 + 243/2*e^2 + 230*e - 199/2, 3*e^5 - 11/2*e^4 - 39*e^3 + 52*e^2 + 103*e - 3/2, 13*e^5 - 21*e^4 - 171*e^3 + 218*e^2 + 388*e - 135, 3*e^5 - 6*e^4 - 75/2*e^3 + 113/2*e^2 + 147/2*e + 25/2, -15/2*e^5 + 12*e^4 + 197/2*e^3 - 245/2*e^2 - 248*e + 131/2, -8*e^5 + 11*e^4 + 217/2*e^3 - 235/2*e^2 - 543/2*e + 211/2];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {3, 3, -w + 1}>] := -1;
ALEigenvalues[ideal<ZF | {4, 2, w}>] := -1;

// EXAMPLE:
// pp := Factorization(2*ZF)[1][1];
// heckeEigenvalues[pp];

print "To reconstruct the Hilbert newform f, type
  f, iso := Explode(make_newform());";

function make_newform();
 M := HilbertCuspForms(F, NN);
 S := NewSubspace(M);
 // SetVerbose("ModFrmHil", 1);
 NFD := NewformDecomposition(S);
 newforms := [* Eigenform(U) : U in NFD *];

 if #newforms eq 0 then;
  print "No Hilbert newforms at this level";
  return 0;
 end if;

 print "Testing ", #newforms, " possible newforms";
 newforms := [* f: f in newforms | IsIsomorphic(BaseField(f), K) *];
 print #newforms, " newforms have the correct Hecke field";

 if #newforms eq 0 then;
  print "No Hilbert newform found with the correct Hecke field";
  return 0;
 end if;

 autos := Automorphisms(K);
 xnewforms := [* *];
 for f in newforms do;
  if K eq RationalField() then;
   Append(~xnewforms, [* f, autos[1] *]);
  else;
   flag, iso := IsIsomorphic(K,BaseField(f));
   for a in autos do;
    Append(~xnewforms, [* f, a*iso *]);
   end for;
  end if;
 end for;
 newforms := xnewforms;

 for P in primes do;
  xnewforms := [* *];
  for f_iso in newforms do;
   f, iso := Explode(f_iso);
   if HeckeEigenvalue(f,P) eq iso(heckeEigenvalues[P]) then;
    Append(~xnewforms, f_iso);
   end if;
  end for;
  newforms := xnewforms;
  if #newforms eq 0 then;
   print "No Hilbert newform found which matches the Hecke eigenvalues";
   return 0;
  else if #newforms eq 1 then;
   print "success: unique match";
   return newforms[1];
  end if;
  end if;
 end for;
 print #newforms, "Hilbert newforms found which match the Hecke eigenvalues";
 return newforms[1];

end function;