/*
  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 | {7, 7, -w^3 + 2*w^2 + 4*w - 3}>;

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^11 - 28*x^9 - 12*x^8 + 277*x^7 + 232*x^6 - 1078*x^5 - 1280*x^4 + 1127*x^3 + 1586*x^2 - 288*x - 512;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [e, 29621/386912*e^10 - 2431/24182*e^9 - 196851/96728*e^8 + 159745/96728*e^7 + 7555097/386912*e^6 - 277325/48364*e^5 - 15047831/193456*e^4 - 112248/12091*e^3 + 39239891/386912*e^2 + 2294389/193456*e - 485598/12091, -1, 13145/386912*e^10 + 49/12091*e^9 - 75647/96728*e^8 - 20371/96728*e^7 + 2305613/386912*e^6 + 78757/48364*e^5 - 3424291/193456*e^4 + 10006/12091*e^3 + 9533327/386912*e^2 - 1245455/193456*e - 115743/12091, 13099/386912*e^10 - 412/12091*e^9 - 93109/96728*e^8 + 53087/96728*e^7 + 3866503/386912*e^6 - 83561/48364*e^5 - 8523049/193456*e^4 - 56002/12091*e^3 + 26950477/386912*e^2 + 1489363/193456*e - 370889/12091, 2431/48364*e^10 - 656/12091*e^9 - 15538/12091*e^8 + 10155/12091*e^7 + 568167/48364*e^6 - 28684/12091*e^5 - 1084683/24182*e^4 - 91516/12091*e^3 + 2915385/48364*e^2 + 243191/24182*e - 345787/12091, 739/3616*e^10 - 20/113*e^9 - 4917/904*e^8 + 2215/904*e^7 + 186911/3616*e^6 - 877/452*e^5 - 363057/1808*e^4 - 6351/113*e^3 + 900565/3616*e^2 + 99259/1808*e - 10215/113, -7183/96728*e^10 + 1188/12091*e^9 + 46841/24182*e^8 - 41057/24182*e^7 - 1742475/96728*e^6 + 85270/12091*e^5 + 3304213/48364*e^4 + 27424/12091*e^3 - 7801897/96728*e^2 - 277603/48364*e + 324158/12091, 11857/193456*e^10 - 1536/12091*e^9 - 80943/48364*e^8 + 101893/48364*e^7 + 3256757/193456*e^6 - 161751/24182*e^5 - 6707739/96728*e^4 - 242592/12091*e^3 + 14927719/193456*e^2 + 2396537/96728*e - 300646/12091, 2235/96728*e^10 - 1351/12091*e^9 - 17921/24182*e^8 + 51891/24182*e^7 + 870615/96728*e^6 - 128744/12091*e^5 - 2132113/48364*e^4 + 36759/12091*e^3 + 5397469/96728*e^2 + 141339/48364*e - 223644/12091, -6105/96728*e^10 + 769/12091*e^9 + 41811/24182*e^8 - 28785/24182*e^7 - 1640653/96728*e^6 + 73658/12091*e^5 + 3346035/48364*e^4 - 57644/12091*e^3 - 9555815/96728*e^2 - 152693/48364*e + 467262/12091, 26125/386912*e^10 + 43/24182*e^9 - 169771/96728*e^8 - 61127/96728*e^7 + 6240017/386912*e^6 + 493151/48364*e^5 - 11772319/193456*e^4 - 546367/12091*e^3 + 31192187/386912*e^2 + 7398669/193456*e - 410184/12091, 2993/48364*e^10 + 769/12091*e^9 - 21413/12091*e^8 - 20438/12091*e^7 + 854277/48364*e^6 + 182477/12091*e^5 - 1730599/24182*e^4 - 589648/12091*e^3 + 5082303/48364*e^2 + 800251/24182*e - 596746/12091, -6105/96728*e^10 + 769/12091*e^9 + 41811/24182*e^8 - 28785/24182*e^7 - 1640653/96728*e^6 + 73658/12091*e^5 + 3346035/48364*e^4 - 57644/12091*e^3 - 9459087/96728*e^2 - 104329/48364*e + 418898/12091, 26601/386912*e^10 - 3033/24182*e^9 - 165711/96728*e^8 + 217517/96728*e^7 + 5968413/386912*e^6 - 531389/48364*e^5 - 11311667/193456*e^4 + 100925/12091*e^3 + 28370111/386912*e^2 + 1607433/193456*e - 280700/12091, -62665/386912*e^10 + 5645/24182*e^9 + 404335/96728*e^8 - 373061/96728*e^7 - 14932285/386912*e^6 + 664853/48364*e^5 + 27903939/193456*e^4 + 236831/12091*e^3 - 59949599/386912*e^2 - 5258633/193456*e + 521560/12091, -1101/24182*e^10 - 2012/12091*e^9 + 16780/12091*e^8 + 48914/12091*e^7 - 337021/24182*e^6 - 399098/12091*e^5 + 625005/12091*e^4 + 1190582/12091*e^3 - 1338323/24182*e^2 - 788789/12091*e + 239892/12091, 1778/12091*e^10 - 1760/12091*e^9 - 51714/12091*e^8 + 24591/12091*e^7 + 541662/12091*e^6 + 4436/12091*e^5 - 2318242/12091*e^4 - 834156/12091*e^3 + 3103054/12091*e^2 + 842606/12091*e - 1191364/12091, -15493/193456*e^10 + 2781/12091*e^9 + 101139/48364*e^8 - 216953/48364*e^7 - 3934345/193456*e^6 + 619055/24182*e^5 + 8209079/96728*e^4 - 462311/12091*e^3 - 22225059/193456*e^2 + 1736803/96728*e + 541736/12091, 1849/48364*e^10 - 1056/12091*e^9 - 14101/12091*e^8 + 19591/12091*e^7 + 649493/48364*e^6 - 89230/12091*e^5 - 1604227/24182*e^4 - 21690/12091*e^3 + 5457151/48364*e^2 + 138157/24182*e - 709982/12091, 8509/386912*e^10 - 3981/24182*e^9 - 35531/96728*e^8 + 330185/96728*e^7 + 847681/386912*e^6 - 1103241/48364*e^5 - 1772239/193456*e^4 + 644215/12091*e^3 + 9779019/386912*e^2 - 5221955/193456*e - 170292/12091, -15727/96728*e^10 + 2490/12091*e^9 + 104833/24182*e^8 - 78787/24182*e^7 - 4026795/96728*e^6 + 106665/12091*e^5 + 7921661/48364*e^4 + 452208/12091*e^3 - 18795881/96728*e^2 - 2069343/48364*e + 699818/12091, 52089/193456*e^10 - 3141/12091*e^9 - 352295/48364*e^8 + 183213/48364*e^7 + 13687117/193456*e^6 - 137997/24182*e^5 - 27268003/96728*e^4 - 858056/12091*e^3 + 68789807/193456*e^2 + 6474521/96728*e - 1613108/12091, -1431/96728*e^10 - 1115/12091*e^9 + 7709/24182*e^8 + 56233/24182*e^7 - 126371/96728*e^6 - 232552/12091*e^5 - 444403/48364*e^4 + 669514/12091*e^3 + 5404975/96728*e^2 - 1564331/48364*e - 438604/12091, -96127/386912*e^10 + 3635/24182*e^9 + 642393/96728*e^8 - 154379/96728*e^7 - 24476971/386912*e^6 - 302737/48364*e^5 + 47838533/193456*e^4 + 979639/12091*e^3 - 124795865/386912*e^2 - 12793839/193456*e + 1647632/12091, 7891/96728*e^10 - 1194/12091*e^9 - 49337/24182*e^8 + 42791/24182*e^7 + 1774175/96728*e^6 - 109272/12091*e^5 - 3446513/48364*e^4 + 115209/12091*e^3 + 10794741/96728*e^2 + 531023/48364*e - 653962/12091, 59927/386912*e^10 - 2663/12091*e^9 - 404929/96728*e^8 + 333771/96728*e^7 + 15922339/386912*e^6 - 393809/48364*e^5 - 32400429/193456*e^4 - 617822/12091*e^3 + 81088769/386912*e^2 + 12303471/193456*e - 927309/12091, 48267/386912*e^10 - 4047/24182*e^9 - 356445/96728*e^8 + 247423/96728*e^7 + 15207911/386912*e^6 - 156183/48364*e^5 - 32639593/193456*e^4 - 753729/12091*e^3 + 79273069/386912*e^2 + 11791371/193456*e - 847660/12091, 23215/193456*e^10 - 457/12091*e^9 - 174677/48364*e^8 + 10235/48364*e^7 + 7565563/193456*e^6 + 160421/24182*e^5 - 17005877/96728*e^4 - 660858/12091*e^3 + 52606537/193456*e^2 + 4310207/96728*e - 1478136/12091, -40129/193456*e^10 + 1041/12091*e^9 + 249471/48364*e^8 - 33421/48364*e^7 - 8617973/193456*e^6 - 122915/24182*e^5 + 15003387/96728*e^4 + 481046/12091*e^3 - 37103975/193456*e^2 - 3481105/96728*e + 949480/12091, 2431/24182*e^10 - 1312/12091*e^9 - 31076/12091*e^8 + 20310/12091*e^7 + 568167/24182*e^6 - 57368/12091*e^5 - 1084683/12091*e^4 - 183032/12091*e^3 + 2963749/24182*e^2 + 243191/12091*e - 812484/12091, -54119/386912*e^10 + 3457/24182*e^9 + 397569/96728*e^8 - 196587/96728*e^7 - 16921395/386912*e^6 - 1873/48364*e^5 + 36944957/193456*e^4 + 824269/12091*e^3 - 101340401/386912*e^2 - 13298551/193456*e + 1333998/12091, -52953/386912*e^10 + 1060/12091*e^9 + 373375/96728*e^8 - 52533/96728*e^7 - 15070157/386912*e^6 - 598749/48364*e^5 + 30700899/193456*e^4 + 1192126/12091*e^3 - 75235727/386912*e^2 - 14940081/193456*e + 998367/12091, 29573/386912*e^10 - 908/12091*e^9 - 265539/96728*e^8 + 118641/96728*e^7 + 13389417/386912*e^6 - 48223/48364*e^5 - 34288695/193456*e^4 - 509160/12091*e^3 + 119488451/386912*e^2 + 10072829/193456*e - 1864735/12091, -66427/386912*e^10 + 6993/24182*e^9 + 486045/96728*e^8 - 450927/96728*e^7 - 20510935/386912*e^6 + 511427/48364*e^5 + 43052857/193456*e^4 + 952365/12091*e^3 - 95028989/386912*e^2 - 13509771/193456*e + 925752/12091, -131391/386912*e^10 + 4044/12091*e^9 + 865081/96728*e^8 - 527651/96728*e^7 - 32661803/386912*e^6 + 953549/48364*e^5 + 64426309/193456*e^4 + 254810/12091*e^3 - 179898201/386912*e^2 - 6958599/193456*e + 2364697/12091, 25197/193456*e^10 - 158/12091*e^9 - 143547/48364*e^8 - 17495/48364*e^7 + 4252977/193456*e^6 + 142481/24182*e^5 - 5684847/96728*e^4 - 165512/12091*e^3 + 11801627/193456*e^2 + 1404909/96728*e - 382352/12091, -24993/193456*e^10 + 567/12091*e^9 + 145287/48364*e^8 - 1269/48364*e^7 - 4479925/193456*e^6 - 191203/24182*e^5 + 6158635/96728*e^4 + 468150/12091*e^3 - 6958679/193456*e^2 - 2035217/96728*e - 4120/12091, 44489/193456*e^10 - 2494/12091*e^9 - 297631/48364*e^8 + 123613/48364*e^7 + 11316093/193456*e^6 + 89185/24182*e^5 - 21518339/96728*e^4 - 1175277/12091*e^3 + 47341567/193456*e^2 + 8293305/96728*e - 951930/12091, 241/904*e^10 - 3/113*e^9 - 1587/226*e^8 - 263/226*e^7 + 58677/904*e^6 + 2802/113*e^5 - 109683/452*e^4 - 13038/113*e^3 + 277943/904*e^2 + 36197/452*e - 13934/113, 157307/386912*e^10 - 10657/24182*e^9 - 1019565/96728*e^8 + 634159/96728*e^7 + 37818071/386912*e^6 - 678499/48364*e^5 - 71885561/193456*e^4 - 1090569/12091*e^3 + 172384893/386912*e^2 + 19810027/193456*e - 1939642/12091, 43749/193456*e^10 - 2081/12091*e^9 - 292563/48364*e^8 + 102537/48364*e^7 + 11175849/193456*e^6 + 64405/24182*e^5 - 21886583/96728*e^4 - 911303/12091*e^3 + 55480899/193456*e^2 + 6712493/96728*e - 1110472/12091, -13945/48364*e^10 + 4335/12091*e^9 + 91583/12091*e^8 - 76267/12091*e^7 - 3471565/48364*e^6 + 341499/12091*e^5 + 6959359/24182*e^4 - 43068/12091*e^3 - 20155463/48364*e^2 - 889657/24182*e + 2194524/12091, -71657/386912*e^10 - 55/24182*e^9 + 498335/96728*e^8 + 116427/96728*e^7 - 19510045/386912*e^6 - 1024435/48364*e^5 + 38432051/193456*e^4 + 1233095/12091*e^3 - 99263231/386912*e^2 - 13784681/193456*e + 1241116/12091, 190583/386912*e^10 - 5399/12091*e^9 - 1281969/96728*e^8 + 594747/96728*e^7 + 49367683/386912*e^6 - 162217/48364*e^5 - 96951981/193456*e^4 - 1860036/12091*e^3 + 238181089/386912*e^2 + 28432015/193456*e - 2767907/12091, 18189/48364*e^10 - 4202/12091*e^9 - 112283/12091*e^8 + 63094/12091*e^7 + 3890017/48364*e^6 - 188306/12091*e^5 - 6837151/24182*e^4 - 347776/12091*e^3 + 16071691/48364*e^2 + 1180245/24182*e - 1284038/12091, -51977/193456*e^10 + 1706/12091*e^9 + 319111/48364*e^8 - 55061/48364*e^7 - 10792285/193456*e^6 - 235361/24182*e^5 + 17737731/96728*e^4 + 969208/12091*e^3 - 34335871/193456*e^2 - 6568321/96728*e + 617146/12091, -68541/96728*e^10 + 10725/12091*e^9 + 459479/24182*e^8 - 342777/24182*e^7 - 17791185/96728*e^6 + 500438/12091*e^5 + 35550423/48364*e^4 + 1693124/12091*e^3 - 90063195/96728*e^2 - 7712993/48364*e + 4223522/12091, -67481/193456*e^10 + 6895/12091*e^9 + 428691/48364*e^8 - 466829/48364*e^7 - 15598221/193456*e^6 + 928401/24182*e^5 + 28739651/96728*e^4 + 240342/12091*e^3 - 59595887/193456*e^2 - 3449977/96728*e + 946436/12091, -91451/386912*e^10 + 578/12091*e^9 + 659517/96728*e^8 + 45201/96728*e^7 - 27236119/386912*e^6 - 1000367/48364*e^5 + 58190201/193456*e^4 + 1498378/12091*e^3 - 172182845/386912*e^2 - 19926195/193456*e + 2321473/12091, -59577/386912*e^10 + 2353/24182*e^9 + 373775/96728*e^8 - 114661/96728*e^7 - 13163309/386912*e^6 - 8179/48364*e^5 + 23874307/193456*e^4 + 332039/12091*e^3 - 64296175/386912*e^2 - 5620089/193456*e + 880982/12091, -29485/96728*e^10 + 1377/12091*e^9 + 198011/24182*e^8 - 11041/24182*e^7 - 7577425/96728*e^6 - 210584/12091*e^5 + 14944535/48364*e^4 + 1416756/12091*e^3 - 40267291/96728*e^2 - 4246121/48364*e + 2080010/12091, -99793/386912*e^10 + 7922/12091*e^9 + 668023/96728*e^8 - 1214045/96728*e^7 - 26247781/386912*e^6 + 3220755/48364*e^5 + 53298635/193456*e^4 - 811846/12091*e^3 - 124594903/386912*e^2 + 7215927/193456*e + 1315799/12091, 3577/386912*e^10 + 889/12091*e^9 - 32079/96728*e^8 - 120859/96728*e^7 + 1190829/386912*e^6 + 219777/48364*e^5 - 1505603/193456*e^4 + 112446/12091*e^3 + 1518319/386912*e^2 - 5226527/193456*e + 159381/12091, 22625/96728*e^10 - 909/12091*e^9 - 148415/24182*e^8 - 3301/24182*e^7 + 5540101/96728*e^6 + 220726/12091*e^5 - 10664459/48364*e^4 - 1273318/12091*e^3 + 28284215/96728*e^2 + 4260237/48364*e - 1311122/12091, -37157/96728*e^10 + 4516/12091*e^9 + 246371/24182*e^8 - 132297/24182*e^7 - 9322121/96728*e^6 + 118431/12091*e^5 + 17949463/48364*e^4 + 1060862/12091*e^3 - 43100547/96728*e^2 - 4011413/48364*e + 1777594/12091, 1263/3616*e^10 - 115/226*e^9 - 8105/904*e^8 + 8275/904*e^7 + 300507/3616*e^6 - 20107/452*e^5 - 587509/1808*e^4 + 3677/113*e^3 + 1590953/3616*e^2 + 20879/1808*e - 18280/113, 104343/386912*e^10 - 6129/24182*e^9 - 686113/96728*e^8 + 386811/96728*e^7 + 25745443/386912*e^6 - 611631/48364*e^5 - 49612269/193456*e^4 - 291677/12091*e^3 + 127001729/386912*e^2 + 2285639/193456*e - 1482774/12091, 13051/386912*e^10 - 209/24182*e^9 - 65069/96728*e^8 + 11983/96728*e^7 + 1188759/386912*e^6 - 47915/48364*e^5 + 1834855/193456*e^4 + 91181/12091*e^3 - 27446339/386912*e^2 - 4080661/193456*e + 668174/12091, 151679/386912*e^10 - 14117/24182*e^9 - 1044809/96728*e^8 + 941299/96728*e^7 + 41894251/386912*e^6 - 1583271/48364*e^5 - 87027653/193456*e^4 - 933059/12091*e^3 + 228511321/386912*e^2 + 21597455/193456*e - 2811996/12091, 6491/193456*e^10 - 796/12091*e^9 - 69813/48364*e^8 + 36903/48364*e^7 + 3699607/193456*e^6 + 156579/24182*e^5 - 8226681/96728*e^4 - 963020/12091*e^3 + 8819037/193456*e^2 + 5185731/96728*e + 200818/12091, -25581/193456*e^10 + 5078/12091*e^9 + 174411/48364*e^8 - 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456343/24182*e + 13952/12091, -38749/48364*e^10 + 5985/12091*e^9 + 253418/12091*e^8 - 84963/12091*e^7 - 9402145/48364*e^6 + 171089/12091*e^5 + 18086091/24182*e^4 + 1032160/12091*e^3 - 50345555/48364*e^2 - 2702295/24182*e + 5182510/12091, -42839/48364*e^10 + 16096/12091*e^9 + 288945/12091*e^8 - 282493/12091*e^7 - 11353699/48364*e^6 + 1209860/12091*e^5 + 23407353/24182*e^4 + 293236/12091*e^3 - 64179021/48364*e^2 - 2626127/24182*e + 6302744/12091, -34697/386912*e^10 - 1028/12091*e^9 + 187695/96728*e^8 + 233179/96728*e^7 - 5185469/386912*e^6 - 928557/48364*e^5 + 6923155/193456*e^4 + 517759/12091*e^3 - 24199455/386912*e^2 - 8465681/193456*e + 244705/12091, 29763/386912*e^10 + 4676/12091*e^9 - 332197/96728*e^8 - 992241/96728*e^7 + 17540287/386912*e^6 + 4771011/48364*e^5 - 39950769/193456*e^4 - 4475728/12091*e^3 + 75674869/386912*e^2 + 47552987/193456*e - 531201/12091, 7666/12091*e^10 - 11791/12091*e^9 - 203602/12091*e^8 + 198470/12091*e^7 + 1966164/12091*e^6 - 746551/12091*e^5 - 7918232/12091*e^4 - 820148/12091*e^3 + 10264761/12091*e^2 + 1342193/12091*e - 4233774/12091, 284603/193456*e^10 - 21443/12091*e^9 - 1868365/48364*e^8 + 1403335/48364*e^7 + 70699831/193456*e^6 - 2497903/24182*e^5 - 139358761/96728*e^4 - 1616078/12091*e^3 + 368572653/193456*e^2 + 19600427/96728*e - 8973128/12091, 84955/193456*e^10 - 2563/12091*e^9 - 669405/48364*e^8 + 66767/48364*e^7 + 29964055/193456*e^6 + 915513/24182*e^5 - 67424105/96728*e^4 - 4002622/12091*e^3 + 188505341/193456*e^2 + 27204427/96728*e - 5083224/12091, 77421/48364*e^10 - 17092/12091*e^9 - 496113/12091*e^8 + 232959/12091*e^7 + 18023193/48364*e^6 - 236882/12091*e^5 - 33211147/24182*e^4 - 4473822/12091*e^3 + 77124939/48364*e^2 + 7965869/24182*e - 6592344/12091, -447471/386912*e^10 + 15780/12091*e^9 + 2982745/96728*e^8 - 1906739/96728*e^7 - 113730075/386912*e^6 + 1963429/48364*e^5 + 219207029/193456*e^4 + 3637876/12091*e^3 - 498617449/386912*e^2 - 54963223/193456*e + 5114855/12091, 52269/48364*e^10 - 9698/12091*e^9 - 336535/12091*e^8 + 119715/12091*e^7 + 12266389/48364*e^6 + 73302/12091*e^5 - 22727635/24182*e^4 - 3470772/12091*e^3 + 54511135/48364*e^2 + 6202861/24182*e - 4664256/12091, -125059/193456*e^10 + 14619/12091*e^9 + 833741/48364*e^8 - 1037999/48364*e^7 - 32415455/193456*e^6 + 2278611/24182*e^5 + 65264177/96728*e^4 + 133264/12091*e^3 - 160182453/193456*e^2 - 8851987/96728*e + 3651068/12091, 451/386912*e^10 - 1000/12091*e^9 + 89195/96728*e^8 + 152447/96728*e^7 - 7598913/386912*e^6 - 593369/48364*e^5 + 24781839/193456*e^4 + 597750/12091*e^3 - 101910283/386912*e^2 - 5087157/193456*e + 1598395/12091, -76163/386912*e^10 - 7311/24182*e^9 + 482661/96728*e^8 + 755641/96728*e^7 - 16295167/386912*e^6 - 2983093/48364*e^5 + 25508881/193456*e^4 + 1769447/12091*e^3 - 51612853/386912*e^2 - 9950451/193456*e + 490882/12091, 72251/193456*e^10 - 9067/12091*e^9 - 470509/48364*e^8 + 634055/48364*e^7 + 18018503/193456*e^6 - 1354267/24182*e^5 - 36221769/96728*e^4 - 90674/12091*e^3 + 90007789/193456*e^2 + 893931/96728*e - 2472416/12091, -637/1712*e^10 + 63/107*e^9 + 4587/428*e^8 - 4849/428*e^7 - 192225/1712*e^6 + 12377/214*e^5 + 420407/856*e^4 - 3338/107*e^3 - 1222539/1712*e^2 - 11517/856*e + 28456/107, -47233/96728*e^10 + 2757/12091*e^9 + 288451/24182*e^8 - 47131/24182*e^7 - 9693477/96728*e^6 - 131074/12091*e^5 + 15995115/48364*e^4 + 1087592/12091*e^3 - 33872551/96728*e^2 - 3190093/48364*e + 842714/12091, -107289/386912*e^10 + 9113/24182*e^9 + 774783/96728*e^8 - 539733/96728*e^7 - 33005709/386912*e^6 + 311681/48364*e^5 + 73427299/193456*e^4 + 1624578/12091*e^3 - 207710543/386912*e^2 - 29114857/193456*e + 2444032/12091, -24241/386912*e^10 + 7557/12091*e^9 + 60663/96728*e^8 - 1324109/96728*e^7 + 1359611/386912*e^6 + 4860567/48364*e^5 - 8056869/193456*e^4 - 3305074/12091*e^3 + 21715913/386912*e^2 + 27901031/193456*e - 336715/12091, -61081/386912*e^10 + 21623/24182*e^9 + 349567/96728*e^8 - 1725013/96728*e^7 - 12461197/386912*e^6 + 5171305/48364*e^5 + 25221475/193456*e^4 - 2262463/12091*e^3 - 56257231/386912*e^2 + 21562615/193456*e + 1042470/12091, 411231/386912*e^10 - 26693/24182*e^9 - 2705793/96728*e^8 + 1632723/96728*e^7 + 101654283/386912*e^6 - 1989447/48364*e^5 - 195653221/193456*e^4 - 2542811/12091*e^3 + 486575161/386912*e^2 + 52426703/193456*e - 5473282/12091, -88195/386912*e^10 + 1757/24182*e^9 + 675909/96728*e^8 + 60553/96728*e^7 - 29250047/386912*e^6 - 1689341/48364*e^5 + 61822417/193456*e^4 + 2777231/12091*e^3 - 135875509/386912*e^2 - 30439699/193456*e + 815506/12091, 101/113*e^10 - 139/113*e^9 - 2696/113*e^8 + 2288/113*e^7 + 25853/113*e^6 - 7695/113*e^5 - 100860/113*e^4 - 16042/113*e^3 + 116849/113*e^2 + 19987/113*e - 36614/113, -230853/386912*e^10 + 8712/12091*e^9 + 1450579/96728*e^8 - 1208369/96728*e^7 - 51535785/386912*e^6 + 2884135/48364*e^5 + 93340615/193456*e^4 - 806474/12091*e^3 - 223193027/386912*e^2 + 16115555/193456*e + 2550463/12091, -158909/386912*e^10 + 4256/12091*e^9 + 1096939/96728*e^8 - 603449/96728*e^7 - 43614785/386912*e^6 + 1339203/48364*e^5 + 91607247/193456*e^4 + 7177/12091*e^3 - 283047627/386912*e^2 - 5688165/193456*e + 4022545/12091, 91423/48364*e^10 - 27371/12091*e^9 - 602857/12091*e^8 + 430583/12091*e^7 + 22836747/48364*e^6 - 1222249/12091*e^5 - 44345365/24182*e^4 - 4190662/12091*e^3 + 107370393/48364*e^2 + 9285383/24182*e - 9499034/12091, 154949/193456*e^10 - 12184/12091*e^9 - 1056747/48364*e^8 + 791305/48364*e^7 + 41693097/193456*e^6 - 1215611/24182*e^5 - 84997815/96728*e^4 - 1785264/12091*e^3 + 221583587/193456*e^2 + 15727261/96728*e - 5547238/12091, 2433/3424*e^10 - 48/107*e^9 - 15351/856*e^8 + 4877/856*e^7 + 541781/3424*e^6 - 1195/428*e^5 - 963643/1712*e^4 - 12396/107*e^3 + 2294631/3424*e^2 + 240553/1712*e - 23245/107, 52279/48364*e^10 - 16256/12091*e^9 - 346407/12091*e^8 + 257249/12091*e^7 + 13195043/48364*e^6 - 721420/12091*e^5 - 25675477/24182*e^4 - 2639978/12091*e^3 + 60572129/48364*e^2 + 5166751/24182*e - 5021684/12091, 18969/12091*e^10 - 19525/12091*e^9 - 506446/12091*e^8 + 288298/12091*e^7 + 4843037/12091*e^6 - 514531/12091*e^5 - 18916054/12091*e^4 - 4848260/12091*e^3 + 23035539/12091*e^2 + 4862655/12091*e - 8415056/12091, -20129/24182*e^10 + 13798/12091*e^9 + 258328/12091*e^8 - 240616/12091*e^7 - 4763545/24182*e^6 + 1085344/12091*e^5 + 9208217/12091*e^4 - 394650/12091*e^3 - 24639387/24182*e^2 - 788777/12091*e + 4621840/12091, 67957/96728*e^10 - 7851/12091*e^9 - 472995/24182*e^8 + 213469/24182*e^7 + 19002281/96728*e^6 - 6290/12091*e^5 - 39305991/48364*e^4 - 3139010/12091*e^3 + 103783619/96728*e^2 + 12699945/48364*e - 4663688/12091, 138221/193456*e^10 - 9449/12091*e^9 - 909243/48364*e^8 + 588849/48364*e^7 + 34379729/193456*e^6 - 823525/24182*e^5 - 67552735/96728*e^4 - 1403936/12091*e^3 + 179260155/193456*e^2 + 11793917/96728*e - 4688584/12091, -111095/96728*e^10 + 16004/12091*e^9 + 745165/24182*e^8 - 526307/24182*e^7 - 28915715/96728*e^6 + 934527/12091*e^5 + 58638181/48364*e^4 + 1303418/12091*e^3 - 161103601/96728*e^2 - 6980735/48364*e + 8242408/12091, 82533/193456*e^10 - 3270/12091*e^9 - 507987/48364*e^8 + 136865/48364*e^7 + 17371689/193456*e^6 + 184109/24182*e^5 - 29904695/96728*e^4 - 1279700/12091*e^3 + 70768419/193456*e^2 + 11761357/96728*e - 1062382/12091, -9997/12091*e^10 + 18097/12091*e^9 + 281968/12091*e^8 - 323772/12091*e^7 - 2920591/12091*e^6 + 1367468/12091*e^5 + 12625584/12091*e^4 + 937993/12091*e^3 - 17341693/12091*e^2 - 2467624/12091*e + 6989738/12091, 82469/193456*e^10 - 2450/12091*e^9 - 502843/48364*e^8 + 49817/48364*e^7 + 16767689/193456*e^6 + 570185/24182*e^5 - 26476295/96728*e^4 - 1830310/12091*e^3 + 41186563/193456*e^2 + 8526205/96728*e - 185804/12091, -166041/193456*e^10 + 140/12091*e^9 + 1144215/48364*e^8 + 318083/48364*e^7 - 44640173/193456*e^6 - 2898149/24182*e^5 + 87872035/96728*e^4 + 6965368/12091*e^3 - 219849535/193456*e^2 - 40751969/96728*e + 5124074/12091, -88355/193456*e^10 + 3807/12091*e^9 + 543677/48364*e^8 - 205431/48364*e^7 - 18572319/193456*e^6 + 170583/24182*e^5 + 31798945/96728*e^4 + 659456/12091*e^3 - 73830581/193456*e^2 - 8832083/96728*e + 1174528/12091, -162909/386912*e^10 + 23489/24182*e^9 + 983163/96728*e^8 - 1836281/96728*e^7 - 34354977/386912*e^6 + 5446257/48364*e^5 + 64739343/193456*e^4 - 2406047/12091*e^3 - 177814571/386912*e^2 + 12848131/193456*e + 2125160/12091, 4345/12091*e^10 - 8082/12091*e^9 - 109226/12091*e^8 + 140114/12091*e^7 + 990773/12091*e^6 - 603910/12091*e^5 - 3678556/12091*e^4 + 12752/12091*e^3 + 3902849/12091*e^2 + 206454/12091*e - 1401022/12091, 82731/193456*e^10 + 1750/12091*e^9 - 659925/48364*e^8 - 322313/48364*e^7 + 29578119/193456*e^6 + 2325291/24182*e^5 - 65860089/96728*e^4 - 5767598/12091*e^3 + 178791501/193456*e^2 + 36321627/96728*e - 4323680/12091, 284377/386912*e^10 - 8518/12091*e^9 - 1756495/96728*e^8 + 1032469/96728*e^7 + 61058445/386912*e^6 - 1601587/48364*e^5 - 108130307/193456*e^4 - 585090/12091*e^3 + 258610319/386912*e^2 + 10322449/193456*e - 3018581/12091, 168931/386912*e^10 - 4226/12091*e^9 - 1216293/96728*e^8 + 399495/96728*e^7 + 50453023/386912*e^6 + 664303/48364*e^5 - 107212113/193456*e^4 - 2679084/12091*e^3 + 291456533/386912*e^2 + 37787499/193456*e - 3896991/12091, -59357/386912*e^10 + 7324/12091*e^9 + 204955/96728*e^8 - 1248217/96728*e^7 - 374433/386912*e^6 + 4695071/48364*e^5 - 11863089/193456*e^4 - 3664552/12091*e^3 + 47475349/386912*e^2 + 43260939/193456*e - 827405/12091, -34315/193456*e^10 - 5439/12091*e^9 + 202333/48364*e^8 + 447449/48364*e^7 - 5800103/193456*e^6 - 1257581/24182*e^5 + 7032729/96728*e^4 + 594165/12091*e^3 - 25696909/193456*e^2 - 3646931/96728*e + 816928/12091, 10578/12091*e^10 - 4201/12091*e^9 - 293440/12091*e^8 + 8540/12091*e^7 + 2896328/12091*e^6 + 887763/12091*e^5 - 11582132/12091*e^4 - 6112758/12091*e^3 + 14561394/12091*e^2 + 5097567/12091*e - 5525406/12091, 55333/96728*e^10 + 1273/12091*e^9 - 401439/24182*e^8 - 150259/24182*e^7 + 16420521/96728*e^6 + 1098364/12091*e^5 - 33717679/48364*e^4 - 5098582/12091*e^3 + 88402643/96728*e^2 + 13696473/48364*e - 4619994/12091, -109043/96728*e^10 + 17831/12091*e^9 + 731373/24182*e^8 - 558579/24182*e^7 - 28387743/96728*e^6 + 722534/12091*e^5 + 56627281/48364*e^4 + 3327784/12091*e^3 - 137766117/96728*e^2 - 12544223/48364*e + 6184410/12091, -166575/193456*e^10 + 11516/12091*e^9 + 1105521/48364*e^8 - 671203/48364*e^7 - 41929467/193456*e^6 + 506049/24182*e^5 + 80065701/96728*e^4 + 3091386/12091*e^3 - 176065961/193456*e^2 - 20149047/96728*e + 3393198/12091, 8899/193456*e^10 - 1421/12091*e^9 - 106173/48364*e^8 + 132151/48364*e^7 + 6354047/193456*e^6 - 410471/24182*e^5 - 18414065/96728*e^4 + 145102/12091*e^3 + 72676117/193456*e^2 + 3701035/96728*e - 2507588/12091, -73415/48364*e^10 + 23377/12091*e^9 + 497565/12091*e^8 - 373363/12091*e^7 - 19500227/48364*e^6 + 1051885/12091*e^5 + 39341985/24182*e^4 + 4057102/12091*e^3 - 98853089/48364*e^2 - 9156605/24182*e + 9112910/12091, 161253/386912*e^10 - 10204/12091*e^9 - 1031427/96728*e^8 + 1482201/96728*e^7 + 38700809/386912*e^6 - 3624011/48364*e^5 - 76505703/193456*e^4 + 694764/12091*e^3 + 188094243/386912*e^2 - 7350291/193456*e - 1770617/12091];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
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;