/*
  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![5, -1, -7, -1, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {21, 21, w^2 - w - 6}>;

primesArray := [
[3, 3, -w^3 + 2*w^2 + 5*w - 3],
[5, 5, w],
[7, 7, -w^3 + 2*w^2 + 4*w - 3],
[13, 13, -w^2 + w + 4],
[13, 13, -w^3 + 2*w^2 + 5*w - 2],
[16, 2, 2],
[17, 17, -w + 2],
[19, 19, -w^3 + 2*w^2 + 3*w - 2],
[27, 3, w^3 - 3*w^2 - 4*w + 7],
[31, 31, w^3 - 3*w^2 - 3*w + 7],
[31, 31, -w^3 + w^2 + 6*w + 1],
[41, 41, w^2 - w - 1],
[43, 43, 2*w^3 - 5*w^2 - 6*w + 4],
[47, 47, -w^3 + 2*w^2 + 5*w - 1],
[53, 53, -w - 3],
[53, 53, -w^3 + 3*w^2 + 3*w - 6],
[59, 59, 2*w^2 - 3*w - 6],
[59, 59, w^3 - w^2 - 7*w - 3],
[79, 79, 2*w^3 - 4*w^2 - 8*w + 3],
[79, 79, w^2 - 2*w - 1],
[101, 101, 2*w^3 - 4*w^2 - 9*w + 4],
[103, 103, -w^3 + 3*w^2 + 4*w - 2],
[103, 103, w^2 - 3*w - 2],
[107, 107, -w^3 + w^2 + 5*w - 1],
[109, 109, -w^3 + 2*w^2 + 4*w - 6],
[121, 11, -w^3 + 2*w^2 + 6*w - 3],
[121, 11, w^2 - 3*w - 3],
[125, 5, -w^3 + w^2 + 7*w + 1],
[127, 127, 2*w^3 - 5*w^2 - 5*w + 7],
[127, 127, 2*w^3 - 5*w^2 - 7*w + 6],
[167, 167, -2*w^3 + 5*w^2 + 7*w - 11],
[169, 13, -w^2 + w + 8],
[181, 181, -2*w^3 + 5*w^2 + 8*w - 7],
[193, 193, -w^3 + 3*w^2 + 3*w - 1],
[197, 197, 2*w^3 - 4*w^2 - 7*w + 8],
[197, 197, 3*w^3 - 7*w^2 - 10*w + 9],
[199, 199, w^3 - 2*w^2 - 3*w - 3],
[211, 211, -w^3 + w^2 + 7*w - 2],
[211, 211, w^3 - w^2 - 6*w + 1],
[227, 227, 2*w^3 - 3*w^2 - 9*w + 3],
[229, 229, 3*w^3 - 6*w^2 - 13*w + 8],
[239, 239, 2*w^3 - 4*w^2 - 9*w + 3],
[239, 239, 2*w^3 - 4*w^2 - 6*w + 1],
[241, 241, 3*w^3 - 7*w^2 - 9*w + 6],
[241, 241, -2*w^3 + 4*w^2 + 6*w - 3],
[251, 251, -4*w^3 + 10*w^2 + 15*w - 16],
[251, 251, -w^3 + 3*w^2 - 3],
[271, 271, -w^3 + 4*w^2 + 4*w - 11],
[271, 271, -3*w^3 + 9*w^2 + 6*w - 13],
[277, 277, -w^3 + 3*w^2 + 2*w - 9],
[281, 281, -w^3 + 4*w^2 + w - 8],
[293, 293, 3*w^3 - 7*w^2 - 11*w + 13],
[293, 293, w^2 - 6],
[293, 293, -4*w^3 + 11*w^2 + 9*w - 14],
[293, 293, 3*w^3 - 5*w^2 - 15*w + 6],
[311, 311, -2*w^3 + 4*w^2 + 7*w - 4],
[313, 313, -w^3 + 4*w^2 + 3*w - 13],
[313, 313, -w^3 + w^2 + 6*w - 2],
[317, 317, w^3 - 4*w^2 - w + 9],
[337, 337, 3*w^3 - 7*w^2 - 8*w + 7],
[343, 7, -2*w^3 + 3*w^2 + 9*w + 1],
[359, 359, -w^3 + 2*w^2 + 4*w - 7],
[359, 359, 2*w^3 - 3*w^2 - 10*w + 4],
[367, 367, 2*w^3 - 4*w^2 - 5*w + 2],
[367, 367, 2*w^3 - 3*w^2 - 11*w - 2],
[367, 367, 2*w - 7],
[367, 367, w^3 - 7*w - 4],
[373, 373, -w^3 + 4*w^2 + w - 14],
[373, 373, -2*w^3 + 4*w^2 + 10*w - 11],
[379, 379, w^3 - 2*w^2 - 2*w - 1],
[383, 383, w^3 - 8*w - 4],
[397, 397, 4*w^3 - 10*w^2 - 12*w + 7],
[397, 397, -2*w^3 + 3*w^2 + 9*w - 2],
[401, 401, -w^3 + 6*w + 8],
[409, 409, 2*w^3 - 3*w^2 - 11*w + 4],
[419, 419, 3*w^3 - 6*w^2 - 15*w + 7],
[419, 419, -w^2 + 4*w + 8],
[431, 431, 5*w^3 - 15*w^2 - 10*w + 18],
[431, 431, 3*w^3 - 4*w^2 - 16*w - 2],
[439, 439, w^3 - w^2 - 4*w - 4],
[443, 443, -4*w^3 + 9*w^2 + 15*w - 16],
[461, 461, 2*w^3 - 2*w^2 - 13*w - 1],
[467, 467, 2*w^3 - 6*w^2 - 2*w + 7],
[467, 467, 3*w^3 - 3*w^2 - 19*w - 6],
[479, 479, w^2 - 8],
[479, 479, -3*w^3 + 7*w^2 + 14*w - 11],
[491, 491, 3*w^3 - 5*w^2 - 16*w + 2],
[499, 499, -w^2 + w - 2],
[509, 509, -w^3 + 5*w^2 - w - 11],
[509, 509, w^3 - 5*w - 1],
[521, 521, -w^3 + 4*w^2 + 3*w - 7],
[521, 521, -w^3 + 2*w^2 + 7*w - 4],
[541, 541, -2*w^3 + 4*w^2 + 11*w - 6],
[557, 557, -w^3 + w^2 + 8*w + 3],
[557, 557, w^3 - 2*w^2 - 2*w - 2],
[563, 563, 2*w^3 - 2*w^2 - 10*w - 3],
[563, 563, 3*w^3 - 5*w^2 - 15*w + 1],
[569, 569, 2*w^2 - 3*w - 4],
[569, 569, 3*w^3 - 8*w^2 - 9*w + 7],
[571, 571, -w^3 + 4*w^2 - 11],
[571, 571, 3*w^3 - 8*w^2 - 11*w + 11],
[577, 577, 3*w^3 - 8*w^2 - 5*w + 11],
[577, 577, -4*w^3 + 11*w^2 + 9*w - 9],
[593, 593, 2*w^3 - 7*w^2 - 2*w + 9],
[601, 601, -w^3 + 3*w^2 + 5*w - 9],
[613, 613, 3*w^3 - 5*w^2 - 14*w + 8],
[613, 613, -w^3 + 2*w^2 + 7*w - 3],
[617, 617, -2*w^3 + 6*w^2 + 5*w - 4],
[617, 617, -w^3 + 3*w^2 - w - 6],
[641, 641, 4*w^3 - 9*w^2 - 17*w + 14],
[641, 641, -5*w^3 + 12*w^2 + 18*w - 17],
[643, 643, -3*w^3 + 8*w^2 + 10*w - 13],
[647, 647, 3*w - 4],
[647, 647, -w^3 + 4*w^2 + 2*w - 9],
[653, 653, -w^3 + 2*w^2 + 5*w - 8],
[661, 661, 2*w^3 - 7*w^2 - 5*w + 21],
[661, 661, -w^3 + 2*w^2 + 3*w - 8],
[673, 673, 2*w^3 - 7*w^2 - 5*w + 9],
[673, 673, w^3 - 2*w^2 - 3*w - 4],
[677, 677, -w^3 + 4*w^2 + 3*w - 8],
[683, 683, -3*w^3 + 4*w^2 + 17*w - 1],
[683, 683, -3*w^3 + 7*w^2 + 8*w - 2],
[691, 691, w^2 - 4*w - 2],
[701, 701, 3*w^3 - 6*w^2 - 11*w + 3],
[709, 709, -w^3 + 4*w^2 + 3*w - 17],
[709, 709, w^3 + w^2 - 10*w - 8],
[709, 709, -3*w^3 + 10*w^2 + 2*w - 16],
[709, 709, w^3 - w^2 - 8*w + 1],
[727, 727, -w^3 + 5*w^2 - w - 13],
[727, 727, 2*w^3 - 4*w^2 - 11*w + 2],
[733, 733, -2*w^3 + 3*w^2 + 10*w - 6],
[733, 733, 2*w^3 - 5*w^2 - 5*w + 9],
[739, 739, -3*w^3 + 6*w^2 + 12*w - 8],
[743, 743, 3*w^3 - 4*w^2 - 17*w - 4],
[743, 743, 2*w^3 - 3*w^2 - 8*w + 1],
[743, 743, -3*w^3 + 7*w^2 + 11*w - 7],
[743, 743, -3*w^3 + 6*w^2 + 11*w - 9],
[757, 757, 2*w^3 - 5*w^2 - 6*w + 11],
[757, 757, -w^3 + w^2 + 8*w + 2],
[761, 761, -5*w^3 + 14*w^2 + 13*w - 12],
[769, 769, -3*w^2 + 4*w + 13],
[773, 773, 3*w^3 - 4*w^2 - 18*w + 3],
[797, 797, 4*w^3 - 7*w^2 - 21*w + 8],
[797, 797, -3*w^3 + 7*w^2 + 11*w - 16],
[809, 809, -2*w^2 + 5*w + 11],
[827, 827, w - 6],
[829, 829, -w^3 - w^2 + 11*w + 8],
[841, 29, -3*w^3 + 6*w^2 + 14*w - 6],
[841, 29, -2*w^3 + 5*w^2 + 8*w - 4],
[853, 853, 3*w^3 - 6*w^2 - 9*w + 8],
[857, 857, 2*w^2 - 3*w - 3],
[859, 859, -w^3 + w^2 + 4*w + 7],
[863, 863, 2*w^3 - 3*w^2 - 7*w - 2],
[863, 863, -3*w^3 + 6*w^2 + 10*w - 11],
[881, 881, -3*w^2 + 4*w + 12],
[881, 881, w^2 - 2*w + 3],
[883, 883, 4*w^3 - 13*w^2 - 6*w + 17],
[883, 883, -2*w^3 + 4*w^2 + 12*w - 3],
[887, 887, -3*w^3 + 5*w^2 + 16*w - 8],
[887, 887, 3*w^3 - 5*w^2 - 14*w + 3],
[911, 911, -w^3 + 10*w + 1],
[919, 919, 5*w^3 - 13*w^2 - 14*w + 11],
[929, 929, 2*w^3 - 3*w^2 - 12*w - 4],
[937, 937, -3*w - 7],
[941, 941, -w^3 + 3*w^2 + 3*w - 12],
[947, 947, 2*w^3 - 6*w^2 - 9*w + 8],
[947, 947, -4*w^3 + 7*w^2 + 19*w - 6],
[953, 953, 3*w^2 - w - 9],
[961, 31, 4*w^3 - 12*w^2 - 5*w + 17],
[971, 971, 3*w^3 - 6*w^2 - 16*w + 12],
[983, 983, w^3 + w^2 - 7*w - 12],
[991, 991, -2*w^3 + 7*w^2 + 3*w - 12],
[991, 991, -2*w^3 + 4*w^2 + 12*w - 9],
[997, 997, 3*w^3 - 5*w^2 - 14*w + 9],
[997, 997, -2*w^3 + 3*w^2 + 11*w - 7],
[1013, 1013, -2*w^3 + 6*w^2 + 3*w - 11],
[1019, 1019, -w^3 + 5*w^2 + 2*w - 8],
[1021, 1021, -w^3 + 5*w^2 - w - 17],
[1021, 1021, 3*w^3 - 6*w^2 - 8*w + 3],
[1033, 1033, -2*w^3 + 5*w^2 + 6*w - 13],
[1033, 1033, 3*w^3 - 6*w^2 - 11*w + 4],
[1051, 1051, 3*w^3 - 7*w^2 - 10*w + 13],
[1061, 1061, 2*w^2 - 5*w - 13],
[1063, 1063, -w^3 + w^2 + 5*w + 8],
[1069, 1069, -5*w^3 + 12*w^2 + 19*w - 18],
[1069, 1069, w^3 - 5*w^2 - w + 9],
[1097, 1097, -3*w^3 + 9*w^2 + 8*w - 12],
[1097, 1097, -2*w^3 + 6*w^2 + 7*w - 12],
[1103, 1103, -3*w^3 + 4*w^2 + 15*w - 3],
[1103, 1103, -w^3 + 3*w^2 + 5*w - 11],
[1109, 1109, 5*w^3 - 11*w^2 - 16*w + 6],
[1129, 1129, -w^2 + 3*w - 4],
[1129, 1129, 2*w^3 - 2*w^2 - 10*w - 9],
[1151, 1151, 4*w^3 - 10*w^2 - 14*w + 13],
[1153, 1153, -2*w^3 + 5*w^2 + 11*w - 12],
[1153, 1153, -2*w^3 + 8*w^2 - 13],
[1153, 1153, -w^3 + 3*w^2 + 5*w - 12],
[1153, 1153, 2*w^3 - w^2 - 11*w - 4],
[1163, 1163, -w^3 + w^2 + 9*w - 4],
[1163, 1163, 2*w^3 - 4*w^2 - 10*w - 1],
[1171, 1171, 3*w^3 - 4*w^2 - 18*w - 1],
[1193, 1193, w^3 - 4*w^2 + 2*w + 6],
[1193, 1193, w^3 - 2*w^2 - 5*w - 4],
[1201, 1201, 2*w^3 - 4*w^2 - 9*w - 3],
[1201, 1201, 4*w^3 - 10*w^2 - 13*w + 11],
[1213, 1213, -4*w^3 + 7*w^2 + 19*w - 11],
[1217, 1217, -2*w^3 + 8*w^2 + 2*w - 13],
[1229, 1229, -4*w^3 + 13*w^2 + 6*w - 19],
[1229, 1229, -4*w^3 + 8*w^2 + 16*w - 13],
[1229, 1229, -3*w^3 + 9*w^2 + 6*w - 16],
[1229, 1229, 2*w^3 - 3*w^2 - 6*w - 1],
[1231, 1231, -3*w^3 + 6*w^2 + 16*w - 8],
[1231, 1231, -3*w^2 + w + 12],
[1237, 1237, -2*w^3 + 5*w^2 + 4*w - 9],
[1237, 1237, -w^2 - 3],
[1237, 1237, -w^3 + 6*w - 3],
[1237, 1237, -4*w - 1],
[1249, 1249, -2*w^3 + 4*w^2 + 5*w - 8],
[1283, 1283, 3*w - 8],
[1289, 1289, 2*w^3 - w^2 - 14*w - 6],
[1289, 1289, 4*w^3 - 9*w^2 - 13*w + 8],
[1291, 1291, w^3 - w^2 - 3*w - 4],
[1297, 1297, 4*w^3 - 9*w^2 - 15*w + 9],
[1303, 1303, -w^3 + 4*w^2 - 13],
[1321, 1321, 3*w^3 - 6*w^2 - 13*w + 3],
[1321, 1321, -3*w^3 + 6*w^2 + 11*w - 7],
[1367, 1367, -2*w^3 + 6*w^2 + 4*w - 13],
[1369, 37, 2*w^2 - w - 11],
[1369, 37, w^3 - 2*w^2 - w - 2],
[1373, 1373, -w^3 + 3*w^2 + 8*w - 6],
[1381, 1381, -w^3 + 3*w^2 - 9],
[1381, 1381, 3*w^3 - 8*w^2 - 8*w + 14],
[1427, 1427, 3*w^3 - 7*w^2 - 9*w + 12],
[1429, 1429, 4*w^3 - 9*w^2 - 11*w + 8],
[1433, 1433, -w^3 + 8*w + 12],
[1447, 1447, -4*w^3 + 10*w^2 + 15*w - 14],
[1447, 1447, 6*w^3 - 14*w^2 - 21*w + 19],
[1451, 1451, w^3 - w^2 - 9*w - 4],
[1459, 1459, 3*w^3 - 7*w^2 - 13*w + 9],
[1481, 1481, -3*w^2 + 3*w + 19],
[1481, 1481, -w^3 + 5*w^2 - 3*w - 14],
[1487, 1487, -2*w^3 + 6*w^2 + w - 6],
[1489, 1489, -3*w^3 + 3*w^2 + 19*w + 3],
[1499, 1499, 3*w^2 - 4*w - 7],
[1511, 1511, 4*w^3 - 6*w^2 - 20*w + 3],
[1523, 1523, 8*w^3 - 23*w^2 - 17*w + 27],
[1531, 1531, -w^3 + 2*w^2 + 3*w - 9],
[1531, 1531, 3*w^3 - 9*w^2 - 8*w + 19],
[1549, 1549, -5*w^3 + 11*w^2 + 17*w - 18],
[1553, 1553, 2*w^2 - 9],
[1567, 1567, 2*w^3 - 7*w^2 - 4*w + 22],
[1579, 1579, -2*w^3 + 4*w^2 + 8*w + 3],
[1579, 1579, -3*w^3 + 5*w^2 + 13*w - 1],
[1607, 1607, w^3 - w^2 - 6*w - 8],
[1609, 1609, -4*w^3 + 7*w^2 + 19*w - 2],
[1619, 1619, -5*w^3 + 11*w^2 + 13*w - 9],
[1627, 1627, 4*w^3 - 9*w^2 - 16*w + 11],
[1657, 1657, 2*w^3 - 8*w^2 - w + 12],
[1657, 1657, -4*w^3 + 11*w^2 + 15*w - 17],
[1667, 1667, -w^3 + 5*w^2 - 6],
[1667, 1667, -3*w^3 + 6*w^2 + 10*w - 6],
[1697, 1697, w^3 + w^2 - 9*w - 7],
[1697, 1697, 3*w^3 - 6*w^2 - 13*w + 2],
[1697, 1697, w^3 - 6*w + 1],
[1697, 1697, -5*w^3 + 11*w^2 + 22*w - 17],
[1709, 1709, w^3 - w^2 - 8*w - 9],
[1709, 1709, -w^3 + 3*w^2 - 13],
[1723, 1723, 2*w^3 - 3*w^2 - 7*w - 3],
[1733, 1733, -w^3 + 4*w^2 + 3*w - 19],
[1741, 1741, -w^3 + 5*w^2 - 14],
[1747, 1747, -4*w^3 + 6*w^2 + 22*w + 1],
[1747, 1747, 2*w^3 - 5*w^2 - 9*w + 2],
[1753, 1753, -2*w^3 + 5*w^2 + 3*w - 1],
[1759, 1759, -w^3 + 2*w^2 + 4*w - 9],
[1783, 1783, -3*w^3 + 8*w^2 + 5*w - 12],
[1783, 1783, -2*w^3 + 6*w^2 + 3*w - 12],
[1783, 1783, 2*w^3 - 7*w^2 - 4*w + 17],
[1783, 1783, 2*w^3 - 6*w^2 - w + 7],
[1787, 1787, -5*w^3 + 8*w^2 + 25*w - 3],
[1823, 1823, w^3 - 8*w - 1],
[1823, 1823, -3*w^3 + 5*w^2 + 14*w + 6],
[1831, 1831, -3*w^3 + 8*w^2 + 14*w - 18],
[1847, 1847, w^3 - 3*w^2 - w + 14],
[1847, 1847, -2*w^3 + 2*w^2 + 11*w + 11],
[1861, 1861, 2*w^2 - w - 12],
[1871, 1871, 4*w^3 - 8*w^2 - 19*w + 9],
[1871, 1871, -w^3 + 5*w^2 - w - 7],
[1873, 1873, -3*w^3 + 5*w^2 + 13*w - 4],
[1877, 1877, -4*w^3 + 8*w^2 + 16*w - 7],
[1877, 1877, 3*w^3 - 5*w^2 - 15*w - 2],
[1879, 1879, -w^3 + 4*w^2 - w - 12],
[1907, 1907, w^3 - w^2 - 10*w - 6],
[1931, 1931, -w^3 + 5*w^2 - w - 19],
[1931, 1931, -6*w^3 + 17*w^2 + 12*w - 22],
[1951, 1951, 4*w^3 - 10*w^2 - 14*w + 21],
[1951, 1951, -2*w^3 + 4*w^2 + 13*w - 13],
[1993, 1993, 2*w^3 - 2*w^2 - 11*w + 1],
[1993, 1993, -w^3 + 6*w + 14]];
primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x^6 - 3*x^5 - 11*x^4 + 33*x^3 - 8*x^2 - 8*x - 1;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [-1, e, 1, 15*e^5 - 48*e^4 - 155*e^3 + 526*e^2 - 230*e - 75, -12*e^5 + 38*e^4 + 125*e^3 - 416*e^2 + 173*e + 58, -e^5 + 3*e^4 + 11*e^3 - 33*e^2 + 7*e + 6, 10*e^5 - 32*e^4 - 104*e^3 + 351*e^2 - 146*e - 52, -3*e^5 + 10*e^4 + 30*e^3 - 110*e^2 + 57*e + 15, 41*e^5 - 132*e^4 - 423*e^3 + 1447*e^2 - 634*e - 199, 34*e^5 - 109*e^4 - 351*e^3 + 1194*e^2 - 523*e - 165, -4*e^5 + 12*e^4 + 43*e^3 - 131*e^2 + 45*e + 20, -14*e^5 + 45*e^4 + 145*e^3 - 493*e^2 + 209*e + 70, -11*e^5 + 36*e^4 + 112*e^3 - 395*e^2 + 186*e + 52, -47*e^5 + 152*e^4 + 483*e^3 - 1667*e^2 + 746*e + 229, -20*e^5 + 65*e^4 + 205*e^3 - 714*e^2 + 322*e + 99, -9*e^5 + 29*e^4 + 92*e^3 - 317*e^2 + 148*e + 36, -3*e^5 + 9*e^4 + 33*e^3 - 99*e^2 + 25*e + 17, 7*e^5 - 22*e^4 - 73*e^3 + 240*e^2 - 103*e - 28, e^3 - e^2 - 11*e + 6, -18*e^5 + 57*e^4 + 188*e^3 - 625*e^2 + 256*e + 91, -3*e^5 + 10*e^4 + 30*e^3 - 110*e^2 + 58*e + 7, 4*e^5 - 12*e^4 - 42*e^3 + 129*e^2 - 55*e - 7, -7*e^5 + 22*e^4 + 73*e^3 - 240*e^2 + 97*e + 32, 33*e^5 - 105*e^4 - 343*e^3 + 1149*e^2 - 481*e - 159, -5*e^5 + 16*e^4 + 51*e^3 - 174*e^2 + 86*e + 16, -64*e^5 + 205*e^4 + 662*e^3 - 2244*e^2 + 971*e + 300, -31*e^5 + 99*e^4 + 321*e^3 - 1084*e^2 + 465*e + 147, 64*e^5 - 205*e^4 - 663*e^3 + 2246*e^2 - 962*e - 305, -29*e^5 + 93*e^4 + 300*e^3 - 1018*e^2 + 442*e + 129, 2*e^5 - 6*e^4 - 21*e^3 + 65*e^2 - 29*e - 12, -108*e^5 + 346*e^4 + 1116*e^3 - 3789*e^2 + 1653*e + 519, 22*e^5 - 71*e^4 - 227*e^3 + 779*e^2 - 343*e - 100, -79*e^5 + 252*e^4 + 819*e^3 - 2760*e^2 + 1184*e + 377, -26*e^5 + 85*e^4 + 266*e^3 - 933*e^2 + 425*e + 124, 55*e^5 - 175*e^4 - 571*e^3 + 1916*e^2 - 817*e - 268, 43*e^5 - 136*e^4 - 448*e^3 + 1488*e^2 - 624*e - 204, -65*e^5 + 209*e^4 + 670*e^3 - 2291*e^2 + 1013*e + 310, -16*e^5 + 52*e^4 + 164*e^3 - 569*e^2 + 257*e + 71, 28*e^5 - 89*e^4 - 291*e^3 + 975*e^2 - 410*e - 140, -51*e^5 + 165*e^4 + 523*e^3 - 1810*e^2 + 822*e + 246, -5*e^5 + 16*e^4 + 51*e^3 - 175*e^2 + 87*e + 17, -91*e^5 + 293*e^4 + 938*e^3 - 3211*e^2 + 1419*e + 436, 6*e^5 - 17*e^4 - 67*e^3 + 183*e^2 - 46*e - 20, 48*e^5 - 155*e^4 - 494*e^3 + 1701*e^2 - 757*e - 239, -2*e^5 + 6*e^4 + 21*e^3 - 63*e^2 + 24*e - 17, -71*e^5 + 228*e^4 + 733*e^3 - 2498*e^2 + 1099*e + 340, -16*e^5 + 53*e^4 + 163*e^3 - 583*e^2 + 262*e + 92, -59*e^5 + 190*e^4 + 609*e^3 - 2083*e^2 + 908*e + 279, 118*e^5 - 381*e^4 - 1214*e^3 + 4179*e^2 - 1860*e - 577, 95*e^5 - 305*e^4 - 981*e^3 + 3343*e^2 - 1456*e - 468, -50*e^5 + 161*e^4 + 514*e^3 - 1765*e^2 + 795*e + 243, 34*e^5 - 109*e^4 - 352*e^3 + 1193*e^2 - 508*e - 159, -e^5 + 2*e^4 + 14*e^3 - 23*e^2 - 27*e + 21, -93*e^5 + 298*e^4 + 961*e^3 - 3265*e^2 + 1425*e + 450, 16*e^5 - 54*e^4 - 161*e^3 + 595*e^2 - 287*e - 90, -66*e^5 + 211*e^4 + 685*e^3 - 2312*e^2 + 979*e + 315, 34*e^5 - 110*e^4 - 349*e^3 + 1206*e^2 - 553*e - 161, 48*e^5 - 155*e^4 - 494*e^3 + 1700*e^2 - 754*e - 222, -62*e^5 + 199*e^4 + 639*e^3 - 2179*e^2 + 963*e + 292, 14*e^5 - 46*e^4 - 142*e^3 + 504*e^2 - 245*e - 66, -40*e^5 + 128*e^4 + 412*e^3 - 1403*e^2 + 631*e + 187, 21*e^5 - 66*e^4 - 218*e^3 + 720*e^2 - 315*e - 75, -35*e^5 + 111*e^4 + 363*e^3 - 1211*e^2 + 525*e + 141, -38*e^5 + 121*e^4 + 394*e^3 - 1325*e^2 + 576*e + 183, -21*e^5 + 68*e^4 + 214*e^3 - 746*e^2 + 351*e + 105, -37*e^5 + 118*e^4 + 385*e^3 - 1295*e^2 + 542*e + 191, -58*e^5 + 183*e^4 + 606*e^3 - 2001*e^2 + 826*e + 269, -37*e^5 + 117*e^4 + 385*e^3 - 1279*e^2 + 540*e + 158, 81*e^5 - 260*e^4 - 839*e^3 + 2850*e^2 - 1222*e - 393, -74*e^5 + 238*e^4 + 764*e^3 - 2608*e^2 + 1136*e + 368, e^5 - 3*e^4 - 9*e^3 + 34*e^2 - 34*e - 2, 57*e^5 - 183*e^4 - 589*e^3 + 2007*e^2 - 878*e - 296, 10*e^5 - 34*e^4 - 101*e^3 + 378*e^2 - 177*e - 69, 65*e^5 - 208*e^4 - 674*e^3 + 2280*e^2 - 976*e - 327, -22*e^5 + 70*e^4 + 227*e^3 - 767*e^2 + 342*e + 112, 80*e^5 - 258*e^4 - 824*e^3 + 2829*e^2 - 1249*e - 385, 69*e^5 - 223*e^4 - 709*e^3 + 2443*e^2 - 1097*e - 327, e^5 - 5*e^4 - 5*e^3 + 56*e^2 - 68*e + 6, -97*e^5 + 313*e^4 + 998*e^3 - 3432*e^2 + 1528*e + 467, -65*e^5 + 208*e^4 + 671*e^3 - 2279*e^2 + 1004*e + 303, 61*e^5 - 194*e^4 - 634*e^3 + 2124*e^2 - 895*e - 295, -13*e^5 + 43*e^4 + 132*e^3 - 472*e^2 + 229*e + 62, -117*e^5 + 375*e^4 + 1211*e^3 - 4108*e^2 + 1770*e + 552, -7*e^5 + 24*e^4 + 67*e^3 - 263*e^2 + 160*e + 9, -40*e^5 + 129*e^4 + 412*e^3 - 1414*e^2 + 623*e + 190, 4*e^5 - 15*e^4 - 38*e^3 + 168*e^2 - 85*e - 48, 61*e^5 - 196*e^4 - 629*e^3 + 2146*e^2 - 949*e - 304, 6*e^5 - 20*e^4 - 63*e^3 + 224*e^2 - 80*e - 53, -25*e^5 + 81*e^4 + 259*e^3 - 890*e^2 + 373*e + 144, 110*e^5 - 352*e^4 - 1137*e^3 + 3857*e^2 - 1686*e - 535, 66*e^5 - 209*e^4 - 688*e^3 + 2287*e^2 - 939*e - 312, -136*e^5 + 434*e^4 + 1409*e^3 - 4750*e^2 + 2040*e + 643, 126*e^5 - 403*e^4 - 1305*e^3 + 4414*e^2 - 1902*e - 608, -13*e^5 + 42*e^4 + 134*e^3 - 460*e^2 + 208*e + 71, 57*e^5 - 185*e^4 - 583*e^3 + 2029*e^2 - 932*e - 270, 63*e^5 - 201*e^4 - 651*e^3 + 2200*e^2 - 964*e - 294, -7*e^5 + 21*e^4 + 74*e^3 - 226*e^2 + 84*e + 19, 109*e^5 - 348*e^4 - 1131*e^3 + 3813*e^2 - 1611*e - 530, -13*e^5 + 45*e^4 + 127*e^3 - 497*e^2 + 269*e + 57, -78*e^5 + 251*e^4 + 804*e^3 - 2752*e^2 + 1213*e + 384, -111*e^5 + 354*e^4 + 1150*e^3 - 3876*e^2 + 1669*e + 525, -42*e^5 + 135*e^4 + 434*e^3 - 1479*e^2 + 645*e + 176, 11*e^5 - 33*e^4 - 119*e^3 + 361*e^2 - 114*e - 65, -51*e^5 + 163*e^4 + 530*e^3 - 1783*e^2 + 740*e + 232, 17*e^5 - 54*e^4 - 177*e^3 + 589*e^2 - 243*e - 93, 45*e^5 - 144*e^4 - 466*e^3 + 1580*e^2 - 675*e - 231, 109*e^5 - 349*e^4 - 1125*e^3 + 3822*e^2 - 1685*e - 521, 2*e^5 - 10*e^4 - 12*e^3 + 112*e^2 - 117*e - 13, -79*e^5 + 252*e^4 + 821*e^3 - 2761*e^2 + 1157*e + 379, -99*e^5 + 320*e^4 + 1020*e^3 - 3510*e^2 + 1546*e + 505, 138*e^5 - 444*e^4 - 1421*e^3 + 4864*e^2 - 2169*e - 662, 36*e^5 - 115*e^4 - 374*e^3 + 1259*e^2 - 532*e - 167, 84*e^5 - 271*e^4 - 865*e^3 + 2969*e^2 - 1314*e - 404, 170*e^5 - 544*e^4 - 1759*e^3 + 5958*e^2 - 2580*e - 813, -47*e^5 + 148*e^4 + 491*e^3 - 1617*e^2 + 661*e + 220, -47*e^5 + 151*e^4 + 487*e^3 - 1656*e^2 + 705*e + 218, 84*e^5 - 268*e^4 - 868*e^3 + 2931*e^2 - 1284*e - 378, -88*e^5 + 283*e^4 + 907*e^3 - 3100*e^2 + 1372*e + 403, 56*e^5 - 179*e^4 - 578*e^3 + 1958*e^2 - 864*e - 243, 58*e^5 - 184*e^4 - 605*e^3 + 2018*e^2 - 827*e - 292, -64*e^5 + 208*e^4 + 655*e^3 - 2280*e^2 + 1046*e + 293, -2*e^5 + 6*e^4 + 21*e^3 - 64*e^2 + 22*e - 3, 121*e^5 - 388*e^4 - 1251*e^3 + 4253*e^2 - 1854*e - 589, 155*e^5 - 497*e^4 - 1602*e^3 + 5443*e^2 - 2366*e - 743, -3*e^5 + 12*e^4 + 26*e^3 - 135*e^2 + 99*e + 13, 10*e^5 - 35*e^4 - 96*e^3 + 384*e^2 - 226*e - 35, 48*e^5 - 153*e^4 - 498*e^3 + 1676*e^2 - 715*e - 216, -28*e^5 + 90*e^4 + 292*e^3 - 989*e^2 + 386*e + 167, 33*e^5 - 105*e^4 - 342*e^3 + 1154*e^2 - 494*e - 199, 93*e^5 - 300*e^4 - 959*e^3 + 3288*e^2 - 1439*e - 454, 75*e^5 - 241*e^4 - 773*e^3 + 2637*e^2 - 1168*e - 349, -62*e^5 + 196*e^4 + 648*e^3 - 2142*e^2 + 868*e + 290, 23*e^5 - 75*e^4 - 237*e^3 + 828*e^2 - 358*e - 146, 63*e^5 - 205*e^4 - 644*e^3 + 2247*e^2 - 1035*e - 312, -111*e^5 + 355*e^4 + 1148*e^3 - 3886*e^2 + 1686*e + 511, -124*e^5 + 396*e^4 + 1284*e^3 - 4337*e^2 + 1881*e + 591, 15*e^5 - 49*e^4 - 153*e^3 + 534*e^2 - 248*e - 50, 216*e^5 - 692*e^4 - 2235*e^3 + 7579*e^2 - 3274*e - 1028, 65*e^5 - 208*e^4 - 674*e^3 + 2279*e^2 - 973*e - 312, 136*e^5 - 435*e^4 - 1409*e^3 + 4763*e^2 - 2041*e - 646, 104*e^5 - 333*e^4 - 1074*e^3 + 3647*e^2 - 1604*e - 505, -77*e^5 + 246*e^4 + 796*e^3 - 2687*e^2 + 1179*e + 332, 112*e^5 - 358*e^4 - 1159*e^3 + 3917*e^2 - 1693*e - 510, 12*e^5 - 36*e^4 - 128*e^3 + 394*e^2 - 143*e - 86, -107*e^5 + 344*e^4 + 1101*e^3 - 3768*e^2 + 1690*e + 509, 69*e^5 - 218*e^4 - 720*e^3 + 2382*e^2 - 989*e - 329, -112*e^5 + 357*e^4 + 1162*e^3 - 3906*e^2 + 1666*e + 508, 94*e^5 - 304*e^4 - 967*e^3 + 3332*e^2 - 1477*e - 462, -60*e^5 + 192*e^4 + 621*e^3 - 2104*e^2 + 901*e + 292, 164*e^5 - 526*e^4 - 1695*e^3 + 5763*e^2 - 2503*e - 788, 111*e^5 - 352*e^4 - 1154*e^3 + 3847*e^2 - 1634*e - 498, 117*e^5 - 376*e^4 - 1207*e^3 + 4118*e^2 - 1811*e - 550, -16*e^5 + 54*e^4 + 162*e^3 - 598*e^2 + 276*e + 100, 36*e^5 - 118*e^4 - 362*e^3 + 1293*e^2 - 659*e - 155, 86*e^5 - 275*e^4 - 892*e^3 + 3012*e^2 - 1278*e - 393, -216*e^5 + 695*e^4 + 2226*e^3 - 7620*e^2 + 3372*e + 1057, -122*e^5 + 393*e^4 + 1258*e^3 - 4308*e^2 + 1885*e + 590, 22*e^5 - 73*e^4 - 222*e^3 + 802*e^2 - 391*e - 116, 123*e^5 - 390*e^4 - 1281*e^3 + 4269*e^2 - 1788*e - 591, 56*e^5 - 181*e^4 - 572*e^3 + 1980*e^2 - 929*e - 246, -17*e^5 + 56*e^4 + 176*e^3 - 620*e^2 + 255*e + 119, 100*e^5 - 322*e^4 - 1028*e^3 + 3529*e^2 - 1593*e - 469, 177*e^5 - 564*e^4 - 1837*e^3 + 6174*e^2 - 2616*e - 845, 45*e^5 - 145*e^4 - 464*e^3 + 1592*e^2 - 697*e - 237, -30*e^5 + 96*e^4 + 309*e^3 - 1052*e^2 + 475*e + 130, 31*e^5 - 102*e^4 - 319*e^3 + 1126*e^2 - 491*e - 184, 12*e^5 - 38*e^4 - 127*e^3 + 417*e^2 - 157*e - 56, -123*e^5 + 397*e^4 + 1265*e^3 - 4355*e^2 + 1948*e + 599, -124*e^5 + 400*e^4 + 1276*e^3 - 4383*e^2 + 1954*e + 585, 49*e^5 - 152*e^4 - 519*e^3 + 1660*e^2 - 617*e - 250, 5*e^5 - 20*e^4 - 41*e^3 + 218*e^2 - 191*e - 10, 11*e^5 - 35*e^4 - 116*e^3 + 386*e^2 - 140*e - 71, -9*e^5 + 27*e^4 + 94*e^3 - 287*e^2 + 131*e - 10, -185*e^5 + 592*e^4 + 1914*e^3 - 6483*e^2 + 2811*e + 880, 52*e^5 - 172*e^4 - 528*e^3 + 1891*e^2 - 884*e - 280, 129*e^5 - 415*e^4 - 1329*e^3 + 4550*e^2 - 2014*e - 630, 203*e^5 - 652*e^4 - 2097*e^3 + 7144*e^2 - 3111*e - 988, 169*e^5 - 544*e^4 - 1743*e^3 + 5964*e^2 - 2631*e - 814, 79*e^5 - 253*e^4 - 820*e^3 + 2775*e^2 - 1174*e - 382, -82*e^5 + 264*e^4 + 845*e^3 - 2892*e^2 + 1281*e + 390, -198*e^5 + 639*e^4 + 2040*e^3 - 7009*e^2 + 3098*e + 963, 84*e^5 - 270*e^4 - 866*e^3 + 2961*e^2 - 1303*e - 407, -21*e^5 + 63*e^4 + 227*e^3 - 688*e^2 + 224*e + 94, -3*e^5 + 9*e^4 + 31*e^3 - 94*e^2 + 62*e - 20, -99*e^5 + 318*e^4 + 1021*e^3 - 3481*e^2 + 1531*e + 463, -124*e^5 + 399*e^4 + 1280*e^3 - 4372*e^2 + 1904*e + 587, 14*e^5 - 47*e^4 - 142*e^3 + 520*e^2 - 226*e - 111, 132*e^5 - 423*e^4 - 1364*e^3 + 4635*e^2 - 2021*e - 626, 51*e^5 - 162*e^4 - 527*e^3 + 1776*e^2 - 787*e - 250, -135*e^5 + 434*e^4 + 1393*e^3 - 4758*e^2 + 2091*e + 630, 135*e^5 - 431*e^4 - 1401*e^3 + 4719*e^2 - 2010*e - 649, -2*e^5 + 9*e^4 + 17*e^3 - 107*e^2 + 69*e + 31, 45*e^5 - 148*e^4 - 456*e^3 + 1622*e^2 - 769*e - 199, 102*e^5 - 330*e^4 - 1047*e^3 + 3617*e^2 - 1637*e - 480, 54*e^5 - 173*e^4 - 560*e^3 + 1892*e^2 - 800*e - 232, -33*e^5 + 108*e^4 + 337*e^3 - 1188*e^2 + 540*e + 182, 13*e^5 - 39*e^4 - 140*e^3 + 419*e^2 - 136*e - 28, -64*e^5 + 200*e^4 + 672*e^3 - 2184*e^2 + 875*e + 284, 6*e^5 - 21*e^4 - 55*e^3 + 231*e^2 - 172*e - 22, 46*e^5 - 149*e^4 - 470*e^3 + 1638*e^2 - 757*e - 260, -49*e^5 + 161*e^4 + 501*e^3 - 1774*e^2 + 800*e + 290, -104*e^5 + 334*e^4 + 1075*e^3 - 3660*e^2 + 1575*e + 520, 229*e^5 - 735*e^4 - 2363*e^3 + 8054*e^2 - 3539*e - 1095, 44*e^5 - 142*e^4 - 455*e^3 + 1554*e^2 - 661*e - 188, -38*e^5 + 119*e^4 + 399*e^3 - 1299*e^2 + 515*e + 167, -121*e^5 + 386*e^4 + 1253*e^3 - 4223*e^2 + 1837*e + 555, -43*e^5 + 137*e^4 + 448*e^3 - 1501*e^2 + 618*e + 251, 6*e^5 - 24*e^4 - 53*e^3 + 271*e^2 - 183*e - 36, 122*e^5 - 391*e^4 - 1262*e^3 + 4282*e^2 - 1850*e - 561, 18*e^5 - 54*e^4 - 193*e^3 + 586*e^2 - 213*e - 57, -10*e^5 + 34*e^4 + 95*e^3 - 375*e^2 + 248*e + 57, 196*e^5 - 624*e^4 - 2036*e^3 + 6830*e^2 - 2888*e - 940, 71*e^5 - 233*e^4 - 720*e^3 + 2555*e^2 - 1233*e - 336, 68*e^5 - 217*e^4 - 705*e^3 + 2373*e^2 - 1015*e - 333, 54*e^5 - 171*e^4 - 562*e^3 + 1875*e^2 - 787*e - 271, 157*e^5 - 510*e^4 - 1610*e^3 + 5598*e^2 - 2526*e - 780, -149*e^5 + 477*e^4 + 1540*e^3 - 5221*e^2 + 2274*e + 686, 71*e^5 - 225*e^4 - 737*e^3 + 2458*e^2 - 1045*e - 313, 44*e^5 - 145*e^4 - 446*e^3 + 1592*e^2 - 773*e - 198, -128*e^5 + 413*e^4 + 1317*e^3 - 4528*e^2 + 2026*e + 615, -108*e^5 + 351*e^4 + 1106*e^3 - 3852*e^2 + 1754*e + 531, 189*e^5 - 609*e^4 - 1949*e^3 + 6677*e^2 - 2931*e - 901, 96*e^5 - 309*e^4 - 989*e^3 + 3386*e^2 - 1496*e - 452, -8*e^5 + 27*e^4 + 80*e^3 - 298*e^2 + 141*e + 66, 184*e^5 - 589*e^4 - 1904*e^3 + 6451*e^2 - 2787*e - 904, 147*e^5 - 475*e^4 - 1511*e^3 + 5205*e^2 - 2322*e - 691, -205*e^5 + 655*e^4 + 2123*e^3 - 7176*e^2 + 3100*e + 988, -115*e^5 + 370*e^4 + 1184*e^3 - 4058*e^2 + 1812*e + 559, -289*e^5 + 923*e^4 + 2996*e^3 - 10105*e^2 + 4326*e + 1374, -144*e^5 + 458*e^4 + 1497*e^3 - 5014*e^2 + 2120*e + 691, 45*e^5 - 144*e^4 - 466*e^3 + 1581*e^2 - 695*e - 242, 284*e^5 - 907*e^4 - 2944*e^3 + 9932*e^2 - 4249*e - 1346, 115*e^5 - 370*e^4 - 1188*e^3 + 4056*e^2 - 1763*e - 545, 175*e^5 - 564*e^4 - 1803*e^3 + 6180*e^2 - 2740*e - 849, -49*e^5 + 157*e^4 + 510*e^3 - 1729*e^2 + 708*e + 273, -76*e^5 + 245*e^4 + 785*e^3 - 2688*e^2 + 1157*e + 377, -79*e^5 + 251*e^4 + 820*e^3 - 2746*e^2 + 1184*e + 361, 177*e^5 - 569*e^4 - 1827*e^3 + 6238*e^2 - 2740*e - 872, 164*e^5 - 525*e^4 - 1699*e^3 + 5749*e^2 - 2464*e - 746, 42*e^5 - 129*e^4 - 446*e^3 + 1406*e^2 - 523*e - 188, -121*e^5 + 386*e^4 + 1257*e^3 - 4229*e^2 + 1775*e + 604, -43*e^5 + 137*e^4 + 450*e^3 - 1509*e^2 + 591*e + 254, 166*e^5 - 534*e^4 - 1711*e^3 + 5852*e^2 - 2589*e - 779, -236*e^5 + 761*e^4 + 2430*e^3 - 8337*e^2 + 3700*e + 1135, 94*e^5 - 302*e^4 - 974*e^3 + 3310*e^2 - 1404*e - 470, 82*e^5 - 259*e^4 - 856*e^3 + 2833*e^2 - 1158*e - 377, -86*e^5 + 273*e^4 + 897*e^3 - 2989*e^2 + 1220*e + 410, -101*e^5 + 324*e^4 + 1047*e^3 - 3557*e^2 + 1502*e + 511, 5*e^5 - 13*e^4 - 59*e^3 + 139*e^2 - 64, 31*e^5 - 102*e^4 - 312*e^3 + 1121*e^2 - 559*e - 145, 268*e^5 - 855*e^4 - 2778*e^3 + 9362*e^2 - 4015*e - 1266, -193*e^5 + 620*e^4 + 1992*e^3 - 6789*e^2 + 2968*e + 914, 139*e^5 - 448*e^4 - 1433*e^3 + 4911*e^2 - 2164*e - 693, 5*e^5 - 16*e^4 - 54*e^3 + 178*e^2 - 57*e - 27, -96*e^5 + 310*e^4 + 989*e^3 - 3402*e^2 + 1493*e + 500, 54*e^5 - 173*e^4 - 564*e^3 + 1895*e^2 - 750*e - 283, 60*e^5 - 189*e^4 - 631*e^3 + 2065*e^2 - 804*e - 288, 156*e^5 - 503*e^4 - 1608*e^3 + 5516*e^2 - 2426*e - 749, -122*e^5 + 393*e^4 + 1256*e^3 - 4304*e^2 + 1926*e + 546, -111*e^5 + 353*e^4 + 1153*e^3 - 3861*e^2 + 1637*e + 551, -34*e^5 + 111*e^4 + 349*e^3 - 1221*e^2 + 532*e + 180, 116*e^5 - 369*e^4 - 1204*e^3 + 4037*e^2 - 1730*e - 541, 27*e^5 - 88*e^4 - 272*e^3 + 958*e^2 - 492*e - 97, -263*e^5 + 842*e^4 + 2721*e^3 - 9227*e^2 + 3995*e + 1262, -61*e^5 + 193*e^4 + 638*e^3 - 2116*e^2 + 865*e + 297, 136*e^5 - 441*e^4 - 1397*e^3 + 4837*e^2 - 2155*e - 694, -193*e^5 + 616*e^4 + 2003*e^3 - 6747*e^2 + 2865*e + 909, 24*e^5 - 75*e^4 - 249*e^3 + 815*e^2 - 362*e - 70, -175*e^5 + 562*e^4 + 1806*e^3 - 6157*e^2 + 2717*e + 821, 69*e^5 - 223*e^4 - 707*e^3 + 2446*e^2 - 1127*e - 337, -69*e^5 + 219*e^4 + 722*e^3 - 2395*e^2 + 965*e + 308, 204*e^5 - 654*e^4 - 2109*e^3 + 7163*e^2 - 3109*e - 986, 261*e^5 - 838*e^4 - 2695*e^3 + 9180*e^2 - 4028*e - 1241, 58*e^5 - 187*e^4 - 595*e^3 + 2050*e^2 - 929*e - 309, -130*e^5 + 414*e^4 + 1351*e^3 - 4536*e^2 + 1908*e + 623, -13*e^5 + 33*e^4 + 153*e^3 - 359*e^2 + 15*e + 83, -14*e^5 + 44*e^4 + 146*e^3 - 480*e^2 + 214*e + 68, 18*e^5 - 57*e^4 - 187*e^3 + 626*e^2 - 265*e - 121, 56*e^5 - 182*e^4 - 577*e^3 + 1999*e^2 - 863*e - 320, 82*e^5 - 268*e^4 - 839*e^3 + 2946*e^2 - 1346*e - 431, -282*e^5 + 903*e^4 + 2915*e^3 - 9889*e^2 + 4310*e + 1356, 256*e^5 - 824*e^4 - 2643*e^3 + 9035*e^2 - 3947*e - 1254, 40*e^5 - 125*e^4 - 419*e^3 + 1369*e^2 - 564*e - 178, -147*e^5 + 471*e^4 + 1523*e^3 - 5157*e^2 + 2195*e + 685, 2*e^5 - 9*e^4 - 15*e^3 + 105*e^2 - 101*e - 44, 189*e^5 - 612*e^4 - 1943*e^3 + 6713*e^2 - 3010*e - 917, 14*e^5 - 42*e^4 - 155*e^3 + 465*e^2 - 105*e - 74, 60*e^5 - 188*e^4 - 631*e^3 + 2051*e^2 - 808*e - 279, 52*e^5 - 168*e^4 - 535*e^3 + 1844*e^2 - 817*e - 236, 152*e^5 - 490*e^4 - 1564*e^3 + 5372*e^2 - 2387*e - 777, 103*e^5 - 332*e^4 - 1063*e^3 + 3639*e^2 - 1604*e - 471, -171*e^5 + 548*e^4 + 1767*e^3 - 6002*e^2 + 2615*e + 802, -104*e^5 + 335*e^4 + 1069*e^3 - 3672*e^2 + 1665*e + 497, 61*e^5 - 196*e^4 - 630*e^3 + 2149*e^2 - 938*e - 302, 28*e^5 - 88*e^4 - 293*e^3 + 968*e^2 - 394*e - 129, -139*e^5 + 445*e^4 + 1439*e^3 - 4874*e^2 + 2112*e + 664, -108*e^5 + 355*e^4 + 1098*e^3 - 3897*e^2 + 1832*e + 523, -15*e^5 + 48*e^4 + 154*e^3 - 524*e^2 + 242*e + 66];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {3, 3, -w^3 + 2*w^2 + 5*w - 3}>] := 1;
ALEigenvalues[ideal<ZF | {7, 7, -w^3 + 2*w^2 + 4*w - 3}>] := -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;