/*
  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![2, 4, -5, -1, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {19, 19, -w^3 + 3*w - 1}>;

primesArray := [
[2, 2, w],
[4, 2, -w^3 + 4*w + 1],
[5, 5, w + 1],
[13, 13, -w^2 + 3],
[17, 17, -w^3 + w^2 + 3*w - 1],
[19, 19, -w^3 + 3*w - 1],
[23, 23, -w + 3],
[31, 31, -w^2 - 2*w + 1],
[41, 41, w^3 + w^2 - 5*w - 3],
[43, 43, 2*w - 1],
[53, 53, -w - 3],
[53, 53, w^3 - w^2 - 4*w + 1],
[61, 61, w^3 - 3*w - 5],
[67, 67, w^3 + w^2 - 5*w - 1],
[81, 3, -3],
[83, 83, -w^3 + 5*w - 3],
[89, 89, w^2 + 1],
[97, 97, w^3 - w^2 - 5*w + 1],
[97, 97, 3*w^3 - 5*w^2 - 14*w + 21],
[97, 97, w^3 - 3*w - 3],
[97, 97, w^3 - 7*w - 3],
[103, 103, w^3 - w^2 - 3*w + 5],
[107, 107, -2*w^3 + 2*w^2 + 8*w - 7],
[109, 109, 3*w^3 - 3*w^2 - 13*w + 11],
[113, 113, 2*w^3 - 2*w^2 - 10*w + 7],
[113, 113, w^3 + w^2 - 5*w - 7],
[121, 11, 2*w^2 - w - 9],
[121, 11, 2*w^2 - w - 7],
[125, 5, -w^3 + 2*w^2 + 3*w - 7],
[131, 131, 4*w^3 - 5*w^2 - 18*w + 19],
[137, 137, w^3 + w^2 - 6*w - 5],
[137, 137, 3*w^3 - 13*w - 3],
[139, 139, 3*w^3 - 5*w^2 - 13*w + 19],
[149, 149, 2*w^3 - 9*w + 1],
[163, 163, -2*w^2 + 11],
[163, 163, -w^3 + w^2 + 6*w - 3],
[163, 163, w^3 - 2*w^2 - 5*w + 5],
[163, 163, 3*w^3 - 3*w^2 - 14*w + 15],
[173, 173, 2*w^3 - 10*w + 1],
[173, 173, 2*w^3 - 3*w^2 - 8*w + 13],
[179, 179, 2*w^3 + w^2 - 8*w - 1],
[181, 181, 2*w^3 - 4*w^2 - 9*w + 15],
[193, 193, w^2 - 7],
[199, 199, 2*w^2 - 5],
[211, 211, -2*w^3 + 8*w - 3],
[211, 211, -2*w^3 + w^2 + 8*w - 3],
[223, 223, 3*w - 1],
[223, 223, -2*w^3 - w^2 + 8*w + 5],
[229, 229, -w^3 + 3*w^2 + 4*w - 11],
[233, 233, -w^3 + 3*w^2 - 5],
[233, 233, w^3 + 2*w^2 - 5*w - 3],
[239, 239, 2*w^3 - 7*w - 1],
[241, 241, w^3 - 2*w^2 - 3*w + 11],
[251, 251, 2*w^2 - w - 5],
[251, 251, 2*w^2 + 2*w - 7],
[271, 271, -2*w^3 + 2*w^2 + 7*w - 9],
[283, 283, 6*w^3 - 6*w^2 - 28*w + 23],
[293, 293, 4*w^3 - 4*w^2 - 17*w + 17],
[293, 293, 2*w^3 - 2*w^2 - 7*w + 5],
[307, 307, 6*w^3 - 7*w^2 - 28*w + 29],
[311, 311, w^3 - 2*w^2 - 3*w + 1],
[311, 311, 2*w^2 - 2*w - 7],
[311, 311, 2*w^3 - 4*w^2 - 8*w + 17],
[311, 311, -w^3 + 3*w^2 + 4*w - 9],
[347, 347, -w^3 - w^2 + 6*w - 1],
[347, 347, -3*w^3 + 5*w^2 + 15*w - 21],
[349, 349, 2*w^3 + 2*w^2 - 11*w - 7],
[349, 349, 3*w^3 - w^2 - 15*w + 3],
[353, 353, w^3 + w^2 - 3*w - 5],
[353, 353, -4*w^3 + 16*w + 5],
[361, 19, 6*w^3 - 8*w^2 - 27*w + 31],
[367, 367, 3*w^3 - 3*w^2 - 13*w + 9],
[367, 367, -2*w^2 - w + 9],
[373, 373, -2*w^3 + w^2 + 10*w - 7],
[379, 379, w^3 + 2*w^2 - 7*w - 7],
[383, 383, -w^3 + 2*w^2 + 3*w - 9],
[389, 389, -2*w^3 + 3*w^2 + 10*w - 9],
[389, 389, w^2 - 2*w - 5],
[397, 397, 2*w^3 - w^2 - 10*w - 1],
[397, 397, w - 5],
[409, 409, w^3 - w^2 - 6*w - 3],
[419, 419, w^3 - 7*w + 1],
[419, 419, -3*w^3 + 2*w^2 + 13*w - 11],
[421, 421, w^3 + w^2 - 4*w + 3],
[421, 421, 3*w^3 + w^2 - 14*w - 3],
[431, 431, w^2 + 2*w - 7],
[449, 449, w^3 + w^2 - 3*w - 9],
[457, 457, -2*w^3 + w^2 + 8*w - 9],
[457, 457, 2*w^3 - 2*w^2 - 7*w + 11],
[463, 463, -w^3 - w^2 + 8*w - 3],
[463, 463, 3*w^3 - 3*w^2 - 15*w + 13],
[487, 487, 2*w^3 - 2*w^2 - 7*w + 1],
[487, 487, w^2 - 2*w - 7],
[499, 499, 3*w^3 - 3*w^2 - 12*w + 11],
[503, 503, -3*w^3 + w^2 + 13*w + 5],
[509, 509, -w^3 - w^2 + 7*w + 5],
[521, 521, 2*w^3 + 2*w^2 - 9*w - 5],
[523, 523, -2*w^2 - 1],
[541, 541, 2*w^3 - 2*w^2 - 8*w + 3],
[541, 541, w^3 - 2*w^2 - 7*w + 5],
[547, 547, 3*w^3 - 4*w^2 - 13*w + 13],
[563, 563, w^3 + 3*w^2 - 3*w - 11],
[571, 571, -w^3 + w - 3],
[571, 571, 2*w^3 + w^2 - 10*w - 1],
[587, 587, 3*w^3 - 15*w + 1],
[587, 587, 3*w^3 - w^2 - 14*w - 1],
[593, 593, 3*w^3 - 2*w^2 - 15*w + 7],
[593, 593, -2*w^3 + w^2 + 6*w - 1],
[599, 599, -w^3 + w^2 + 4*w + 3],
[599, 599, 2*w^3 + 2*w^2 - 11*w - 3],
[607, 607, -w - 5],
[607, 607, -w^3 + 4*w^2 + 5*w - 19],
[613, 613, 2*w^3 + w^2 - 8*w + 1],
[617, 617, 3*w^3 - w^2 - 12*w + 5],
[617, 617, -2*w^3 + 12*w - 3],
[619, 619, w^2 - 4*w - 3],
[631, 631, -3*w^2 - 4*w + 7],
[631, 631, -6*w^3 + 4*w^2 + 27*w - 15],
[643, 643, -w^3 + 2*w^2 + 7*w - 7],
[643, 643, 3*w^2 - 11],
[647, 647, 4*w^3 - 4*w^2 - 17*w + 15],
[653, 653, -2*w^3 - 2*w^2 + 10*w + 7],
[653, 653, w^3 - 3*w^2 - 6*w + 7],
[659, 659, -3*w^3 + 2*w^2 + 15*w - 11],
[673, 673, w^3 + w^2 - 3*w - 7],
[677, 677, w^3 - 3*w^2 - 3*w + 13],
[677, 677, 2*w^3 - 2*w^2 - 11*w + 9],
[709, 709, w^3 + w^2 - 2*w - 5],
[751, 751, w^3 - 5*w^2 - 4*w + 21],
[757, 757, -2*w^3 + 2*w^2 + 12*w - 1],
[757, 757, -w^3 + w^2 + 2*w - 7],
[761, 761, 4*w^3 - w^2 - 20*w + 3],
[787, 787, 4*w + 3],
[797, 797, 5*w^3 - 4*w^2 - 23*w + 17],
[809, 809, -2*w^3 + 9*w - 5],
[821, 821, 3*w^2 - 2*w - 9],
[823, 823, -w^2 - 3],
[863, 863, -w^3 + w^2 + 5*w - 9],
[881, 881, -4*w^3 + 5*w^2 + 16*w - 21],
[881, 881, -5*w^3 + 4*w^2 + 23*w - 13],
[887, 887, 2*w^3 - 2*w^2 - 11*w + 7],
[907, 907, -3*w^3 + 2*w^2 + 13*w - 3],
[907, 907, 2*w^2 + 2*w - 9],
[911, 911, -3*w^3 + w^2 + 15*w + 3],
[919, 919, 3*w^2 - 7],
[919, 919, 2*w^3 - 7*w + 7],
[937, 937, 4*w^3 - 4*w^2 - 18*w + 13],
[937, 937, 3*w^3 - w^2 - 13*w + 7],
[977, 977, -4*w^3 + 2*w^2 + 19*w - 9],
[983, 983, -w^3 + 4*w^2 + 5*w - 13],
[983, 983, -2*w^3 + 2*w^2 + 9*w - 3],
[991, 991, -w^3 + 4*w^2 + 3*w - 19],
[991, 991, 2*w - 7],
[1019, 1019, -5*w^3 + 5*w^2 + 23*w - 23],
[1031, 1031, -2*w^3 + 4*w + 3],
[1039, 1039, -3*w^3 + w^2 + 12*w - 3],
[1051, 1051, -4*w^3 - 2*w^2 + 23*w + 9],
[1051, 1051, 5*w^3 - 5*w^2 - 21*w + 21],
[1051, 1051, 4*w^3 - 6*w^2 - 20*w + 23],
[1051, 1051, 4*w^2 + 2*w - 11],
[1061, 1061, -w^3 + 3*w^2 + 8*w - 7],
[1061, 1061, 5*w^3 - 3*w^2 - 24*w + 13],
[1063, 1063, -w^3 - w^2 + 8*w + 5],
[1069, 1069, 2*w^2 - 4*w - 5],
[1087, 1087, 2*w^3 - 2*w^2 - 10*w + 3],
[1091, 1091, 3*w^3 - 17*w + 3],
[1091, 1091, 3*w^3 + w^2 - 12*w - 7],
[1093, 1093, 6*w^3 - 8*w^2 - 26*w + 29],
[1093, 1093, 6*w^3 - 6*w^2 - 26*w + 25],
[1093, 1093, -w^3 + 3*w^2 + 6*w - 15],
[1093, 1093, 2*w^3 - 4*w^2 - 6*w + 13],
[1117, 1117, 2*w^3 + w^2 - 12*w - 7],
[1129, 1129, -w^3 + 3*w^2 + 7*w - 13],
[1129, 1129, 2*w^2 - 3*w + 3],
[1163, 1163, 2*w^3 + 3*w^2 - 10*w - 13],
[1163, 1163, -2*w^3 + 2*w^2 + 6*w - 9],
[1171, 1171, 3*w^2 - 2*w - 7],
[1171, 1171, -3*w^3 + 11*w + 1],
[1181, 1181, -5*w^3 + 6*w^2 + 23*w - 29],
[1187, 1187, 4*w^3 - 2*w^2 - 20*w + 5],
[1187, 1187, 2*w^3 - 3*w^2 - 10*w + 17],
[1201, 1201, 5*w^3 - 3*w^2 - 22*w + 9],
[1213, 1213, 2*w^3 + 2*w^2 - 13*w - 7],
[1213, 1213, 3*w^3 - 11*w + 1],
[1217, 1217, -2*w^3 + 4*w^2 + 11*w - 11],
[1223, 1223, 2*w^3 - w^2 - 12*w + 7],
[1223, 1223, w^3 + 2*w^2 - 5*w - 13],
[1229, 1229, 2*w^3 - 6*w - 5],
[1229, 1229, 3*w^3 + 2*w^2 - 11*w - 7],
[1237, 1237, -w^3 + w^2 + w - 5],
[1237, 1237, -2*w^3 + 10*w - 5],
[1249, 1249, -3*w^3 + 3*w^2 + 13*w - 17],
[1249, 1249, 2*w^3 - 12*w + 1],
[1249, 1249, 4*w^3 - 5*w^2 - 18*w + 17],
[1249, 1249, 4*w^3 - 3*w^2 - 18*w + 15],
[1277, 1277, -3*w^3 + 2*w^2 + 11*w - 3],
[1279, 1279, w^3 + w^2 - 3*w - 11],
[1279, 1279, w^2 - 6*w - 1],
[1279, 1279, -3*w^3 + 4*w^2 + 11*w - 9],
[1279, 1279, 2*w^3 - 11*w + 5],
[1283, 1283, 2*w^3 + 2*w^2 - 9*w - 1],
[1283, 1283, -2*w^3 + 13*w - 5],
[1291, 1291, 3*w^3 - 5*w^2 - 16*w + 19],
[1291, 1291, -2*w^3 + 13*w + 3],
[1301, 1301, -w^3 + 3*w^2 + 2*w - 11],
[1301, 1301, w^3 + 3*w^2 - 7*w - 5],
[1319, 1319, 2*w^3 - 2*w^2 - 8*w + 13],
[1321, 1321, w^3 + 2*w^2 - 7*w - 9],
[1321, 1321, -6*w^3 + 8*w^2 + 28*w - 37],
[1361, 1361, -w^3 + w + 7],
[1361, 1361, -4*w^3 + 2*w^2 + 17*w - 5],
[1367, 1367, -w^3 + w^2 + 8*w - 1],
[1381, 1381, 3*w^3 - w^2 - 11*w + 5],
[1427, 1427, w^3 + 3*w^2 - 5*w - 5],
[1427, 1427, -w^3 + 4*w^2 + 3*w - 13],
[1427, 1427, 6*w^3 - 7*w^2 - 26*w + 33],
[1427, 1427, -4*w^3 + w^2 + 18*w + 7],
[1429, 1429, 3*w^3 - 3*w^2 - 17*w + 17],
[1433, 1433, -w^3 + 5*w - 7],
[1451, 1451, -3*w^3 + w^2 + 15*w - 7],
[1451, 1451, -w^3 + 5*w^2 + 5*w - 19],
[1459, 1459, -5*w + 9],
[1471, 1471, -4*w^3 + 8*w^2 + 19*w - 29],
[1483, 1483, w^3 + 3*w^2 - 6*w - 5],
[1483, 1483, -3*w^3 - w^2 + 12*w - 1],
[1487, 1487, -2*w^3 + 2*w^2 + 11*w - 15],
[1489, 1489, 2*w^3 - 5*w^2 - 10*w + 23],
[1493, 1493, 3*w^3 - 5*w^2 - 12*w + 25],
[1493, 1493, 3*w^3 - 6*w^2 - 15*w + 25],
[1499, 1499, 2*w^2 + 2*w - 13],
[1499, 1499, w^3 + 3*w^2 - 5*w - 11],
[1523, 1523, -w^3 + 3*w^2 + 5*w - 5],
[1523, 1523, 4*w^3 - w^2 - 14*w + 9],
[1523, 1523, -3*w^3 + w^2 + 14*w - 7],
[1523, 1523, -2*w^3 + 3*w^2 + 6*w - 11],
[1543, 1543, -w^3 + 3*w^2 + w - 9],
[1543, 1543, -4*w^3 + 7*w^2 + 20*w - 29],
[1559, 1559, 2*w^2 - 13],
[1559, 1559, -4*w^2 - w + 17],
[1571, 1571, 5*w - 3],
[1579, 1579, 2*w^2 + 2*w - 11],
[1579, 1579, w^3 + w^2 - 7*w - 11],
[1583, 1583, 2*w^3 - 3*w^2 - 10*w + 7],
[1597, 1597, -3*w^3 + w^2 + 7*w + 1],
[1601, 1601, -5*w^3 + 3*w^2 + 23*w - 13],
[1601, 1601, 5*w^3 - w^2 - 20*w + 9],
[1607, 1607, 2*w^3 - w^2 - 10*w - 5],
[1609, 1609, 3*w^3 - 8*w^2 - 13*w + 37],
[1609, 1609, 3*w^3 - 2*w^2 - 11*w + 7],
[1613, 1613, 2*w^3 - 4*w^2 - 12*w + 13],
[1621, 1621, 5*w - 1],
[1621, 1621, -2*w^3 + 5*w^2 + 8*w - 17],
[1627, 1627, 3*w^3 + w^2 - 14*w - 1],
[1627, 1627, -2*w^3 + 2*w^2 + 9*w + 1],
[1637, 1637, 7*w^3 - 12*w^2 - 31*w + 49],
[1657, 1657, -2*w^3 + 2*w^2 + 9*w - 1],
[1657, 1657, -5*w^3 + w^2 + 21*w - 7],
[1663, 1663, 9*w^3 - 11*w^2 - 39*w + 45],
[1667, 1667, -4*w^3 + 3*w^2 + 16*w - 7],
[1669, 1669, -w^3 - w^2 - w - 3],
[1693, 1693, -3*w^3 + w^2 + 11*w - 1],
[1693, 1693, w^3 + 2*w^2 - 11*w - 5],
[1709, 1709, 3*w^3 + 3*w^2 - 16*w - 5],
[1721, 1721, w^3 - 4*w^2 - 3*w + 11],
[1747, 1747, 2*w^3 - 2*w^2 - 11*w + 1],
[1747, 1747, w^3 + 3*w^2 - 4*w - 7],
[1753, 1753, -6*w^3 + 6*w^2 + 28*w - 21],
[1787, 1787, w^3 + 3*w^2 - 7*w - 13],
[1787, 1787, -w^3 + w^2 + 8*w - 5],
[1789, 1789, 2*w^3 + 3*w^2 - 12*w - 7],
[1789, 1789, 4*w^2 - 15],
[1801, 1801, w^3 + 3*w^2 - 7*w - 7],
[1811, 1811, -3*w^3 + 2*w^2 + 11*w - 5],
[1823, 1823, -w^3 + 3*w^2 + 6*w - 5],
[1831, 1831, 5*w^3 - 4*w^2 - 21*w + 17],
[1867, 1867, 3*w^3 - w^2 - 10*w + 5],
[1871, 1871, 2*w^3 + 2*w^2 - 6*w - 7],
[1873, 1873, -3*w^3 + 3*w^2 + 10*w - 7],
[1879, 1879, 2*w^3 - 4*w^2 - 7*w + 17],
[1889, 1889, 3*w^3 - 17*w - 3],
[1907, 1907, -4*w^3 - 2*w^2 + 19*w + 5],
[1907, 1907, 6*w^3 - 8*w^2 - 29*w + 33],
[1913, 1913, -w^3 + w^2 + 8*w - 3],
[1913, 1913, w^3 + 2*w^2 - 9*w + 3],
[1933, 1933, w^2 + 4*w - 9],
[1933, 1933, 6*w^3 - 6*w^2 - 26*w + 23],
[1951, 1951, w^3 + 2*w^2 - 3*w - 11],
[1951, 1951, -2*w^3 + 2*w^2 + 10*w - 1],
[1973, 1973, -5*w^3 + 7*w^2 + 23*w - 25],
[1979, 1979, -3*w^3 + 5*w^2 + 11*w - 19],
[1987, 1987, 2*w^3 - 2*w^2 - 6*w + 11],
[1993, 1993, -w^3 + 3*w - 7],
[1993, 1993, w^3 + w^2 - 2*w - 9],
[1997, 1997, 5*w^3 - w^2 - 19*w - 5],
[1999, 1999, -3*w^3 + 3*w^2 + 15*w - 19],
[2011, 2011, 5*w^3 - 6*w^2 - 23*w + 21],
[2039, 2039, -2*w^3 + 4*w^2 + 8*w - 9],
[2039, 2039, -3*w^3 + 4*w^2 + 11*w - 17],
[2053, 2053, -2*w^3 + 3*w^2 + 8*w - 5],
[2069, 2069, 5*w^3 - 6*w^2 - 21*w + 19],
[2069, 2069, w^3 - 2*w^2 - 5*w - 3],
[2069, 2069, 5*w^3 - 10*w^2 - 23*w + 43],
[2069, 2069, 3*w^3 - 2*w^2 - 13*w + 1],
[2081, 2081, 7*w^3 - 10*w^2 - 31*w + 37],
[2081, 2081, -3*w^3 + 2*w^2 + 11*w - 15],
[2099, 2099, -4*w^3 + 5*w^2 + 14*w - 13],
[2111, 2111, w^3 + 3*w^2 - 6*w - 9],
[2129, 2129, 4*w^3 - 4*w^2 - 20*w + 15],
[2129, 2129, 4*w^2 - 3*w - 15],
[2141, 2141, -w^3 + w^2 + w - 7],
[2153, 2153, 7*w^3 - 11*w^2 - 30*w + 45],
[2153, 2153, -4*w^3 + 8*w^2 + 17*w - 37],
[2153, 2153, 4*w^3 + w^2 - 14*w - 3],
[2153, 2153, -3*w^3 + 4*w^2 + 13*w - 11],
[2161, 2161, 3*w^3 - 7*w^2 - 11*w + 27],
[2179, 2179, w^3 + 3*w^2 - 5*w - 9],
[2179, 2179, -2*w^3 + 14*w - 7],
[2197, 13, w^3 + 3*w^2 - 6*w - 7],
[2203, 2203, 6*w^3 - 9*w^2 - 28*w + 33],
[2203, 2203, 3*w^3 + 3*w^2 - 13*w - 7],
[2207, 2207, -4*w^3 + 16*w - 5],
[2221, 2221, 5*w^3 - 3*w^2 - 21*w + 13],
[2221, 2221, -3*w^3 + 3*w^2 + 16*w - 13],
[2237, 2237, w^3 - w^2 - 3*w - 5],
[2239, 2239, 3*w^3 - w^2 - 16*w + 9],
[2239, 2239, -4*w^3 + 8*w^2 + 18*w - 31],
[2243, 2243, -2*w^3 + 2*w^2 + 12*w - 5],
[2251, 2251, 3*w^3 + 3*w^2 - 14*w - 7],
[2251, 2251, 4*w^3 + 2*w^2 - 15*w - 1],
[2267, 2267, w^3 - 5*w^2 + 15],
[2269, 2269, 3*w^3 - 3*w^2 - 11*w + 3],
[2273, 2273, -w^3 + 5*w^2 + 2*w - 17],
[2281, 2281, -3*w^3 - w^2 + 11*w + 7],
[2287, 2287, -3*w^3 + 4*w^2 + 17*w - 19],
[2287, 2287, 4*w^2 + w - 11],
[2287, 2287, w^3 - 5*w - 7],
[2287, 2287, -5*w^3 + 21*w - 3],
[2293, 2293, w^3 + w^2 - 8*w - 7],
[2293, 2293, -2*w^3 - 2*w^2 + 7*w + 9],
[2293, 2293, -4*w^3 + 6*w^2 + 16*w - 25],
[2293, 2293, -5*w^3 + w^2 + 20*w - 7],
[2309, 2309, 2*w^3 + 2*w^2 - 12*w - 1],
[2311, 2311, -2*w^3 - w^2 + 10*w - 3],
[2333, 2333, -5*w^3 + 7*w^2 + 25*w - 29],
[2341, 2341, 6*w^3 - 7*w^2 - 24*w + 27],
[2341, 2341, -w^3 + 5*w^2 + 6*w - 11],
[2347, 2347, -5*w^3 + 7*w^2 + 23*w - 33],
[2347, 2347, 4*w^3 - 2*w^2 - 16*w + 3],
[2347, 2347, -6*w^3 + 8*w^2 + 26*w - 37],
[2347, 2347, -w^3 - w^2 + 4*w - 5],
[2351, 2351, -3*w^2 - 2*w + 13],
[2357, 2357, 6*w^3 - 4*w^2 - 29*w + 15],
[2357, 2357, 3*w^3 - 4*w^2 - 13*w + 21],
[2371, 2371, 3*w^3 - 13*w + 9],
[2371, 2371, -7*w^3 + 29*w + 9],
[2377, 2377, w^3 - 3*w^2 - 7*w + 15],
[2377, 2377, 4*w^3 - 6*w^2 - 21*w + 25],
[2399, 2399, -3*w^3 + w^2 + 10*w - 1],
[2401, 7, -7],
[2411, 2411, 4*w^3 + w^2 - 16*w + 1],
[2417, 2417, 3*w^3 + 2*w^2 - 15*w - 3],
[2423, 2423, 5*w^3 + w^2 - 20*w - 3],
[2437, 2437, -2*w^3 + 3*w^2 + 12*w - 11],
[2437, 2437, 7*w^3 - 13*w^2 - 32*w + 55],
[2437, 2437, -3*w^3 + w^2 + 14*w - 9],
[2437, 2437, 3*w^3 - 3*w^2 - 9*w + 5],
[2459, 2459, 5*w^2 - 2*w - 23],
[2459, 2459, 5*w^3 - 4*w^2 - 23*w + 19],
[2467, 2467, 4*w^3 + 4*w^2 - 15*w - 11],
[2473, 2473, -w - 7],
[2503, 2503, -4*w^3 + w^2 + 16*w - 11],
[2521, 2521, 3*w^3 - 7*w^2 - 16*w + 27],
[2531, 2531, -2*w^2 + w - 3],
[2539, 2539, w^3 - 3*w^2 - 2*w + 13],
[2543, 2543, -w^3 + 3*w^2 + 5*w - 3],
[2549, 2549, 3*w^3 - 9*w - 5],
[2549, 2549, -3*w^3 + w^2 + 10*w - 3],
[2551, 2551, 2*w^3 - 4*w^2 - 9*w + 21],
[2557, 2557, 3*w^3 - 4*w^2 - 15*w + 11],
[2579, 2579, 6*w^3 - 8*w^2 - 27*w + 29],
[2591, 2591, 2*w^3 - 6*w^2 - 8*w + 23],
[2609, 2609, 6*w^3 - 5*w^2 - 26*w + 17],
[2617, 2617, 7*w^3 - 7*w^2 - 32*w + 31],
[2633, 2633, -5*w^3 + 3*w^2 + 22*w - 15],
[2659, 2659, -6*w^3 - w^2 + 26*w + 13],
[2659, 2659, w^3 + 3*w^2 - 7*w - 17],
[2663, 2663, 2*w^3 - 2*w^2 - 12*w - 5],
[2683, 2683, 4*w^3 - 3*w^2 - 22*w + 21],
[2683, 2683, -w^3 + 3*w^2 + 5*w - 1],
[2687, 2687, -w^3 - w^2 + 3*w - 5],
[2687, 2687, -2*w^3 - w^2 + 12*w - 3],
[2687, 2687, -3*w^3 + 5*w^2 + 15*w - 15],
[2687, 2687, 3*w^3 + 3*w^2 - 16*w - 9],
[2693, 2693, 2*w^3 + 3*w^2 - 10*w - 7],
[2711, 2711, 6*w^3 - 8*w^2 - 28*w + 29],
[2719, 2719, w^3 - 5*w^2 + w + 13],
[2729, 2729, 4*w^3 - 3*w^2 - 16*w + 9],
[2729, 2729, 2*w^2 + 5*w - 5],
[2741, 2741, 3*w^3 + w^2 - 12*w + 3],
[2741, 2741, w^3 - 9*w + 3],
[2749, 2749, w^3 - w^2 - 4*w - 5],
[2749, 2749, -2*w^3 + 13*w - 3],
[2789, 2789, -3*w^3 + 4*w^2 + 11*w - 19],
[2789, 2789, 3*w^3 - w^2 - 17*w + 11],
[2791, 2791, 2*w^3 + 2*w^2 - 9*w - 15],
[2791, 2791, w^3 - 9*w + 1],
[2791, 2791, 7*w^3 - 11*w^2 - 33*w + 47],
[2791, 2791, 3*w^3 - 17*w - 1],
[2801, 2801, 2*w^2 - 4*w - 7],
[2801, 2801, 3*w^3 - w^2 - 7*w + 1],
[2803, 2803, -w^3 + 2*w^2 - w - 5],
[2809, 53, -2*w^3 + 4*w^2 + 7*w - 7],
[2819, 2819, 4*w^2 - 2*w - 13],
[2833, 2833, 2*w^3 + w^2 - 6*w - 7],
[2843, 2843, 6*w^3 - 8*w^2 - 25*w + 35],
[2843, 2843, 4*w^3 - 2*w^2 - 19*w + 11],
[2861, 2861, 8*w^3 - 11*w^2 - 36*w + 49],
[2879, 2879, w^3 - w^2 - 5*w - 5],
[2879, 2879, w^3 + w^2 - w - 13],
[2887, 2887, 7*w^3 + 2*w^2 - 35*w - 9],
[2887, 2887, -4*w^3 + 5*w^2 + 20*w - 15],
[2939, 2939, 4*w^3 - 2*w^2 - 18*w + 1],
[2939, 2939, -w^3 + w^2 + 9*w - 7],
[2953, 2953, -5*w^3 + 9*w^2 + 22*w - 33],
[2963, 2963, w^3 - 5*w^2 - 5*w + 17],
[3001, 3001, 4*w^2 + w - 19],
[3037, 3037, w^3 + w^2 - 7],
[3037, 3037, w^3 + 4*w^2 - 9*w - 9],
[3041, 3041, -5*w^3 + 7*w^2 + 22*w - 33],
[3041, 3041, -4*w^3 - w^2 + 16*w + 9],
[3041, 3041, -2*w^3 - 4*w^2 + 14*w + 13],
[3041, 3041, -2*w^3 + 3*w^2 + 6*w - 13],
[3049, 3049, -w^3 + 3*w^2 + 7*w - 3],
[3067, 3067, w^3 + w^2 - 4*w - 11],
[3067, 3067, -3*w^3 + 6*w^2 + 13*w - 29],
[3079, 3079, 2*w^3 + 5*w^2 - 6*w - 17],
[3079, 3079, 2*w^3 + 3*w^2 - 10*w - 9],
[3079, 3079, w^3 + 3*w^2 - 7*w - 15],
[3079, 3079, -5*w^3 + w^2 + 21*w + 9],
[3089, 3089, -4*w^3 + w^2 + 16*w - 3],
[3089, 3089, 5*w^3 - 2*w^2 - 25*w + 5],
[3109, 3109, -w^2 - 5],
[3109, 3109, w^2 - 2*w - 11],
[3119, 3119, 5*w^3 - 9*w^2 - 24*w + 31],
[3119, 3119, 2*w^3 - 4*w - 5],
[3137, 3137, -w^3 + 3*w^2 + 2*w - 15],
[3167, 3167, -2*w^3 - 2*w^2 + 15*w + 7],
[3167, 3167, 4*w^3 - 4*w^2 - 21*w + 19],
[3169, 3169, -5*w^2 - 4*w + 9],
[3181, 3181, -3*w^3 + 2*w^2 + 9*w - 3],
[3187, 3187, -4*w^3 + 2*w^2 + 16*w - 7],
[3187, 3187, 2*w^3 + 2*w^2 - 10*w + 1],
[3191, 3191, -5*w^3 + 4*w^2 + 23*w - 23],
[3191, 3191, 5*w^3 + w^2 - 18*w - 5],
[3203, 3203, -2*w^3 + 6*w^2 + 10*w - 27],
[3229, 3229, 4*w^3 + w^2 - 18*w - 1],
[3229, 3229, 7*w^3 - 5*w^2 - 31*w + 17],
[3257, 3257, 5*w^3 - 11*w^2 - 23*w + 47],
[3271, 3271, 6*w^3 - 11*w^2 - 30*w + 43],
[3271, 3271, 6*w - 1],
[3271, 3271, -5*w^3 - w^2 + 21*w + 11],
[3271, 3271, 2*w^3 - 13*w + 1],
[3299, 3299, -w^3 + 3*w^2 + 8*w - 15],
[3299, 3299, -2*w^2 + 6*w + 5],
[3301, 3301, -8*w^3 - w^2 + 34*w + 13],
[3307, 3307, -w^3 + 2*w^2 + 9*w - 3],
[3307, 3307, -8*w^3 + 6*w^2 + 35*w - 25],
[3313, 3313, 6*w^3 - 6*w^2 - 25*w + 31],
[3323, 3323, -6*w^3 + w^2 + 26*w - 3],
[3323, 3323, -2*w^2 - 3*w + 15],
[3347, 3347, 2*w^3 - 6*w^2 - 5*w + 17],
[3373, 3373, 4*w^3 - 4*w^2 - 18*w + 11],
[3373, 3373, 4*w^3 - 6*w^2 - 20*w + 19],
[3389, 3389, 4*w^2 - 11],
[3389, 3389, 3*w^3 - 7*w^2 - 15*w + 21],
[3391, 3391, 4*w^3 - 15*w + 1],
[3391, 3391, 4*w^3 - 7*w^2 - 16*w + 29],
[3433, 3433, -5*w^2 + 2*w + 19],
[3433, 3433, -w^3 + 4*w^2 + 7*w - 17],
[3449, 3449, 2*w^2 - 3*w - 11],
[3449, 3449, 3*w^3 - w^2 - 15*w - 7],
[3463, 3463, 4*w^2 - w - 13],
[3463, 3463, -5*w^3 - 3*w^2 + 23*w + 7],
[3467, 3467, 3*w^3 + 2*w^2 - 13*w - 1],
[3469, 3469, 4*w^2 - 3*w - 9],
[3491, 3491, w^3 - 5*w^2 - 7*w + 11],
[3499, 3499, 5*w^3 - 2*w^2 - 23*w + 1],
[3499, 3499, -8*w^3 + 9*w^2 + 34*w - 37],
[3511, 3511, w^3 - 5*w^2 - 8*w + 11],
[3511, 3511, -2*w^3 + 6*w^2 + 4*w - 13],
[3517, 3517, w^3 + 4*w^2 - 3*w - 9],
[3527, 3527, w^2 - 4*w - 7],
[3529, 3529, -8*w^3 + 10*w^2 + 38*w - 39],
[3529, 3529, 2*w^3 - 5*w - 7],
[3539, 3539, 6*w^3 - 4*w^2 - 28*w + 11],
[3539, 3539, 4*w^2 - w - 9],
[3541, 3541, 6*w^3 - 23*w - 9],
[3547, 3547, -3*w^3 - 2*w^2 + 11*w + 9],
[3557, 3557, -3*w^3 + 2*w^2 + 15*w + 3],
[3571, 3571, 3*w^3 - w^2 - 15*w + 11],
[3581, 3581, 6*w^3 - 2*w^2 - 28*w + 1],
[3593, 3593, 5*w^3 - w^2 - 24*w + 5],
[3593, 3593, -2*w^3 + 3*w^2 + 4*w - 9],
[3607, 3607, 3*w^3 - 4*w^2 - 17*w + 11],
[3607, 3607, -w^3 - 5*w^2 + 6*w + 21],
[3617, 3617, 2*w^3 + 4*w^2 - 7*w - 7],
[3617, 3617, 2*w^2 + 4*w - 11],
[3623, 3623, -5*w^3 + 4*w^2 + 25*w - 17],
[3631, 3631, 8*w^3 - 14*w^2 - 36*w + 57],
[3631, 3631, -2*w^3 + 4*w^2 + 13*w - 7],
[3637, 3637, 6*w^3 - 3*w^2 - 26*w + 7],
[3637, 3637, w^3 + 2*w^2 - w - 9],
[3659, 3659, 4*w^3 - 4*w^2 - 14*w + 13],
[3677, 3677, -w^3 + w^2 + 3*w - 11],
[3691, 3691, -4*w^3 + 5*w^2 + 14*w - 19],
[3697, 3697, -4*w^3 + 18*w - 3],
[3719, 3719, w^3 + 5*w^2 - 2*w - 9],
[3733, 3733, 3*w^2 + 2*w - 15],
[3733, 3733, -5*w^3 + 5*w^2 + 22*w - 15],
[3767, 3767, w^3 + w^2 - w - 9],
[3767, 3767, -3*w^3 + 3*w^2 + 13*w - 5],
[3793, 3793, 2*w^2 + 3*w - 13],
[3793, 3793, 5*w^3 - 3*w^2 - 25*w + 9],
[3797, 3797, -9*w^3 - w^2 + 39*w + 15],
[3797, 3797, 4*w^3 - 6*w^2 - 21*w + 21],
[3803, 3803, -6*w^3 + 4*w^2 + 26*w - 15],
[3803, 3803, 2*w - 9],
[3823, 3823, -5*w^3 + 10*w^2 + 23*w - 39],
[3833, 3833, w^3 + w^2 - 5*w - 11],
[3847, 3847, 3*w^3 - 5*w^2 - 11*w + 21],
[3851, 3851, 4*w^2 - 2*w - 9],
[3851, 3851, -2*w^3 + 6*w^2 + 9*w - 21],
[3853, 3853, -w^3 + w^2 + 7*w - 13],
[3863, 3863, 4*w^3 - 6*w^2 - 18*w + 19],
[3881, 3881, -4*w^3 + 14*w + 7],
[3889, 3889, -3*w^3 + w^2 + 12*w - 13],
[3889, 3889, -4*w^3 + 2*w^2 + 21*w - 9],
[3889, 3889, 5*w^3 - 6*w^2 - 25*w + 25],
[3889, 3889, 3*w^3 - 7*w^2 - 12*w + 21],
[3907, 3907, -3*w^3 + 9*w^2 + 14*w - 39],
[3917, 3917, 3*w^3 + 3*w^2 - 13*w - 17],
[3917, 3917, 9*w^3 - 11*w^2 - 40*w + 41],
[3917, 3917, -w^3 + w^2 + 4*w - 11],
[3917, 3917, 3*w^3 - 3*w^2 - 11*w - 1],
[3923, 3923, -2*w^3 + 4*w^2 + 12*w - 21],
[3923, 3923, w^3 + 3*w^2 - 11*w - 7],
[3931, 3931, -3*w^3 + 19*w - 7],
[3947, 3947, -4*w^3 + 4*w^2 + 22*w - 9],
[3947, 3947, -5*w^3 - w^2 + 17*w + 7],
[3947, 3947, -w^3 - 4*w^2 + 3*w + 17],
[3947, 3947, -2*w^3 - 4*w^2 + 12*w + 3]];
primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x^8 + 6*x^7 + 7*x^6 - 18*x^5 - 39*x^4 - x^3 + 33*x^2 + 14*x + 1;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [e, 2*e^7 + 10*e^6 + 5*e^5 - 37*e^4 - 42*e^3 + 24*e^2 + 36*e + 5, -e^6 - 4*e^5 + e^4 + 16*e^3 + 6*e^2 - 13*e - 3, -2*e^7 - 9*e^6 - e^5 + 36*e^4 + 26*e^3 - 31*e^2 - 24*e - 1, -e^7 - 5*e^6 - e^5 + 22*e^4 + 15*e^3 - 22*e^2 - 12*e - 2, 1, e^7 + 7*e^6 + 9*e^5 - 25*e^4 - 48*e^3 + 15*e^2 + 40*e + 5, -3*e^7 - 15*e^6 - 8*e^5 + 54*e^4 + 64*e^3 - 33*e^2 - 54*e - 9, -e^6 - 4*e^5 + 2*e^4 + 21*e^3 + 7*e^2 - 27*e - 8, -8*e^7 - 38*e^6 - 11*e^5 + 149*e^4 + 135*e^3 - 114*e^2 - 119*e - 14, -4*e^7 - 22*e^6 - 18*e^5 + 75*e^4 + 113*e^3 - 34*e^2 - 95*e - 21, 4*e^7 + 17*e^6 - 3*e^5 - 72*e^4 - 29*e^3 + 72*e^2 + 22*e - 9, -e^7 - 4*e^6 + 4*e^5 + 23*e^4 - 8*e^3 - 41*e^2 + 9*e + 16, e^7 + 6*e^6 + 6*e^5 - 22*e^4 - 36*e^3 + 17*e^2 + 32*e - 4, 4*e^7 + 16*e^6 - 4*e^5 - 62*e^4 - 22*e^3 + 47*e^2 + 15*e + 4, 3*e^6 + 12*e^5 - e^4 - 43*e^3 - 22*e^2 + 31*e + 8, e^6 + 3*e^5 - 5*e^4 - 16*e^3 + 6*e^2 + 22*e - 1, 3*e^7 + 18*e^6 + 20*e^5 - 57*e^4 - 111*e^3 + 14*e^2 + 94*e + 21, 5*e^7 + 22*e^6 - e^5 - 95*e^4 - 57*e^3 + 96*e^2 + 62*e - 10, 9*e^7 + 42*e^6 + 9*e^5 - 166*e^4 - 136*e^3 + 129*e^2 + 121*e + 22, -11*e^7 - 52*e^6 - 16*e^5 + 198*e^4 + 182*e^3 - 145*e^2 - 158*e - 20, -e^6 - 3*e^5 + 7*e^4 + 18*e^3 - 13*e^2 - 16*e + 4, 2*e^7 + 14*e^6 + 21*e^5 - 40*e^4 - 101*e^3 + 3*e^2 + 80*e + 17, 4*e^7 + 20*e^6 + 10*e^5 - 77*e^4 - 91*e^3 + 56*e^2 + 87*e + 5, 7*e^7 + 31*e^6 - e^5 - 132*e^4 - 73*e^3 + 131*e^2 + 63*e - 8, 3*e^7 + 15*e^6 + 5*e^5 - 60*e^4 - 50*e^3 + 48*e^2 + 37*e + 8, e^7 + 7*e^6 + 12*e^5 - 19*e^4 - 68*e^3 - 10*e^2 + 72*e + 11, -3*e^7 - 15*e^6 - 5*e^5 + 63*e^4 + 52*e^3 - 70*e^2 - 43*e + 11, -4*e^7 - 18*e^6 - 3*e^5 + 67*e^4 + 50*e^3 - 47*e^2 - 38*e - 5, -e^6 - 4*e^5 + 12*e^3 + 9*e^2 - 5*e - 11, e^7 + 9*e^6 + 20*e^5 - 19*e^4 - 91*e^3 - 23*e^2 + 83*e + 18, -5*e^6 - 18*e^5 + 12*e^4 + 75*e^3 + 8*e^2 - 65*e - 13, e^7 + 10*e^6 + 25*e^5 - 19*e^4 - 117*e^3 - 38*e^2 + 107*e + 31, -7*e^7 - 29*e^6 + 6*e^5 + 119*e^4 + 48*e^3 - 104*e^2 - 39*e - 12, e^7 + 7*e^6 + 10*e^5 - 25*e^4 - 60*e^3 + 15*e^2 + 67*e + 1, 6*e^7 + 28*e^6 + 5*e^5 - 111*e^4 - 75*e^3 + 98*e^2 + 50*e - 5, -3*e^7 - 16*e^6 - 11*e^5 + 59*e^4 + 80*e^3 - 40*e^2 - 76*e - 13, 2*e^7 + 7*e^6 - 3*e^5 - 24*e^4 - 15*e^3 + 23*e + 18, -4*e^7 - 12*e^6 + 25*e^5 + 70*e^4 - 61*e^3 - 104*e^2 + 67*e + 21, 11*e^7 + 55*e^6 + 24*e^5 - 212*e^4 - 218*e^3 + 155*e^2 + 181*e + 22, -2*e^7 - 14*e^6 - 17*e^5 + 52*e^4 + 92*e^3 - 36*e^2 - 81*e - 6, 7*e^7 + 33*e^6 + 7*e^5 - 132*e^4 - 102*e^3 + 105*e^2 + 78*e + 14, -10*e^7 - 47*e^6 - 14*e^5 + 179*e^4 + 164*e^3 - 133*e^2 - 140*e - 17, 11*e^7 + 49*e^6 - e^5 - 209*e^4 - 117*e^3 + 207*e^2 + 98*e - 18, 4*e^7 + 14*e^6 - 13*e^5 - 62*e^4 + 13*e^3 + 60*e^2 - 19*e + 3, 7*e^7 + 27*e^6 - 15*e^5 - 120*e^4 - 10*e^3 + 134*e^2 - 3*e - 28, 6*e^6 + 22*e^5 - 15*e^4 - 97*e^3 - 5*e^2 + 97*e + 8, -13*e^7 - 55*e^6 + 7*e^5 + 226*e^4 + 109*e^3 - 202*e^2 - 84*e, -e^7 - 3*e^6 + 4*e^5 + 10*e^4 - 9*e^3 - e^2 + 12*e - 14, -e^7 - 5*e^6 - e^5 + 18*e^4 + 3*e^3 - 18*e^2 + 12*e + 6, -8*e^7 - 32*e^6 + 13*e^5 + 140*e^4 + 36*e^3 - 131*e^2 - 26*e - 18, -2*e^7 - 6*e^6 + 8*e^5 + 23*e^4 - 15*e^3 - 13*e^2 + 19*e - 14, 4*e^7 + 22*e^6 + 20*e^5 - 72*e^4 - 129*e^3 + 24*e^2 + 127*e + 22, 15*e^7 + 72*e^6 + 26*e^5 - 268*e^4 - 258*e^3 + 177*e^2 + 213*e + 43, 6*e^7 + 33*e^6 + 27*e^5 - 117*e^4 - 184*e^3 + 62*e^2 + 176*e + 25, -e^7 - 4*e^6 - 2*e^5 + 5*e^4 + 7*e^3 + 13*e^2 + 5*e - 3, e^7 + 9*e^6 + 18*e^5 - 25*e^4 - 81*e^3 + 8*e^2 + 66*e - 8, -3*e^7 - 7*e^6 + 24*e^5 + 41*e^4 - 78*e^3 - 68*e^2 + 89*e + 20, 2*e^7 + 8*e^6 - 3*e^5 - 33*e^4 - 3*e^3 + 33*e^2 - 15*e + 5, 9*e^7 + 46*e^6 + 20*e^5 - 185*e^4 - 185*e^3 + 150*e^2 + 163*e + 26, 9*e^7 + 36*e^6 - 14*e^5 - 154*e^4 - 28*e^3 + 167*e^2 + 4*e - 36, 3*e^7 + 9*e^6 - 19*e^5 - 51*e^4 + 58*e^3 + 80*e^2 - 82*e - 30, 4*e^7 + 15*e^6 - 10*e^5 - 64*e^4 + 6*e^3 + 58*e^2 - 24*e - 5, 2*e^7 + 14*e^6 + 22*e^5 - 38*e^4 - 109*e^3 - 14*e^2 + 85*e + 30, 3*e^7 + 13*e^6 - e^5 - 51*e^4 - 20*e^3 + 44*e^2 + 7*e - 11, -5*e^7 - 28*e^6 - 23*e^5 + 104*e^4 + 161*e^3 - 59*e^2 - 151*e - 39, -2*e^7 - 15*e^6 - 21*e^5 + 51*e^4 + 102*e^3 - 22*e^2 - 79*e - 32, 8*e^6 + 27*e^5 - 27*e^4 - 124*e^3 + 11*e^2 + 131*e + 16, -8*e^7 - 35*e^6 - e^5 + 143*e^4 + 101*e^3 - 123*e^2 - 112*e - 11, 4*e^7 + 15*e^6 - 7*e^5 - 61*e^4 - 18*e^3 + 51*e^2 + 24*e - 2, 11*e^7 + 46*e^6 - 6*e^5 - 185*e^4 - 95*e^3 + 155*e^2 + 89*e + 7, -e^7 - 7*e^6 - 7*e^5 + 29*e^4 + 31*e^3 - 38*e^2 - 16*e + 5, -6*e^7 - 23*e^6 + 12*e^5 + 98*e^4 + 15*e^3 - 90*e^2 - 22*e - 12, 3*e^7 + 6*e^6 - 33*e^5 - 58*e^4 + 97*e^3 + 125*e^2 - 89*e - 45, -3*e^7 - 7*e^6 + 29*e^5 + 60*e^4 - 79*e^3 - 125*e^2 + 69*e + 36, -16*e^7 - 76*e^6 - 23*e^5 + 298*e^4 + 278*e^3 - 229*e^2 - 247*e - 33, 8*e^7 + 34*e^6 - 5*e^5 - 138*e^4 - 51*e^3 + 128*e^2 + 12*e - 14, 14*e^7 + 67*e^6 + 19*e^5 - 261*e^4 - 222*e^3 + 196*e^2 + 177*e + 32, 10*e^7 + 56*e^6 + 49*e^5 - 192*e^4 - 307*e^3 + 90*e^2 + 268*e + 48, -2*e^7 - 9*e^6 - 3*e^5 + 34*e^4 + 46*e^3 - 16*e^2 - 57*e - 19, -12*e^7 - 69*e^6 - 62*e^5 + 238*e^4 + 371*e^3 - 117*e^2 - 304*e - 63, 7*e^7 + 28*e^6 - 6*e^5 - 103*e^4 - 33*e^3 + 66*e^2 - 3*e + 20, 5*e^7 + 32*e^6 + 40*e^5 - 104*e^4 - 230*e^3 + 21*e^2 + 232*e + 52, 12*e^7 + 58*e^6 + 17*e^5 - 229*e^4 - 190*e^3 + 190*e^2 + 143*e - 3, -9*e^7 - 40*e^6 + e^5 + 171*e^4 + 102*e^3 - 168*e^2 - 105*e + 22, -3*e^7 - 12*e^6 + 4*e^5 + 51*e^4 + 22*e^3 - 41*e^2 - 25*e - 12, 3*e^7 + 9*e^6 - 17*e^5 - 53*e^4 + 26*e^3 + 74*e^2 - 15*e - 5, 12*e^7 + 53*e^6 + e^5 - 217*e^4 - 142*e^3 + 184*e^2 + 133*e + 10, 3*e^7 + 12*e^6 - 6*e^5 - 53*e^4 - 7*e^3 + 40*e^2 - 2*e + 35, -e^7 - 6*e^6 - 5*e^5 + 22*e^4 + 26*e^3 - 13*e^2 - 3*e - 8, 2*e^7 - 34*e^5 - 22*e^4 + 119*e^3 + 70*e^2 - 97*e - 26, 19*e^7 + 88*e^6 + 22*e^5 - 338*e^4 - 303*e^3 + 233*e^2 + 269*e + 62, -9*e^7 - 44*e^6 - 24*e^5 + 154*e^4 + 204*e^3 - 73*e^2 - 198*e - 34, 6*e^7 + 28*e^6 + 5*e^5 - 120*e^4 - 95*e^3 + 127*e^2 + 88*e - 19, -5*e^7 - 23*e^6 - 9*e^5 + 74*e^4 + 82*e^3 - 12*e^2 - 55*e - 24, -6*e^7 - 30*e^6 - 19*e^5 + 101*e^4 + 141*e^3 - 45*e^2 - 134*e - 34, -7*e^7 - 38*e^6 - 26*e^5 + 141*e^4 + 178*e^3 - 97*e^2 - 143*e - 10, 2*e^7 - e^6 - 36*e^5 - 11*e^4 + 145*e^3 + 61*e^2 - 157*e - 55, -e^7 - 20*e^6 - 60*e^5 + 47*e^4 + 268*e^3 + 43*e^2 - 246*e - 53, -e^7 - 11*e^6 - 26*e^5 + 31*e^4 + 126*e^3 + 3*e^2 - 108*e - 12, -17*e^7 - 76*e^6 - 6*e^5 + 305*e^4 + 216*e^3 - 238*e^2 - 196*e - 44, -5*e^7 - 25*e^6 - 10*e^5 + 101*e^4 + 108*e^3 - 75*e^2 - 114*e - 8, -6*e^7 - 24*e^6 + 7*e^5 + 105*e^4 + 57*e^3 - 106*e^2 - 96*e + 11, -6*e^7 - 31*e^6 - 20*e^5 + 106*e^4 + 134*e^3 - 49*e^2 - 93*e - 37, -10*e^7 - 40*e^6 + 14*e^5 + 173*e^4 + 60*e^3 - 161*e^2 - 55*e - 21, -3*e^7 - 8*e^6 + 22*e^5 + 50*e^4 - 54*e^3 - 66*e^2 + 44*e - 13, 9*e^7 + 41*e^6 + 6*e^5 - 161*e^4 - 122*e^3 + 119*e^2 + 113*e + 41, -2*e^7 + 32*e^5 + 20*e^4 - 107*e^3 - 68*e^2 + 87*e + 40, 6*e^7 + 35*e^6 + 38*e^5 - 107*e^4 - 219*e^3 + 2*e^2 + 182*e + 55, -2*e^7 - 10*e^6 - 5*e^5 + 33*e^4 + 32*e^3 - 11*e^2 - 13*e - 16, -24*e^7 - 111*e^6 - 22*e^5 + 440*e^4 + 359*e^3 - 355*e^2 - 323*e - 32, 14*e^7 + 59*e^6 - 12*e^5 - 256*e^4 - 115*e^3 + 249*e^2 + 116*e + 1, -6*e^7 - 30*e^6 - 11*e^5 + 123*e^4 + 116*e^3 - 102*e^2 - 103*e - 9, -9*e^7 - 45*e^6 - 27*e^5 + 150*e^4 + 198*e^3 - 64*e^2 - 178*e - 23, -16*e^7 - 91*e^6 - 78*e^5 + 323*e^4 + 489*e^3 - 171*e^2 - 405*e - 77, -10*e^7 - 59*e^6 - 63*e^5 + 193*e^4 + 369*e^3 - 58*e^2 - 307*e - 73, -6*e^7 - 13*e^6 + 50*e^5 + 80*e^4 - 149*e^3 - 141*e^2 + 136*e + 47, -9*e^7 - 55*e^6 - 63*e^5 + 182*e^4 + 368*e^3 - 64*e^2 - 350*e - 73, 5*e^7 + 10*e^6 - 50*e^5 - 74*e^4 + 170*e^3 + 151*e^2 - 189*e - 67, -11*e^7 - 49*e^6 + 204*e^4 + 117*e^3 - 196*e^2 - 93*e + 32, 4*e^7 + 12*e^6 - 22*e^5 - 63*e^4 + 56*e^3 + 97*e^2 - 74*e - 46, 21*e^7 + 93*e^6 + 2*e^5 - 381*e^4 - 238*e^3 + 341*e^2 + 205*e + 3, 8*e^7 + 33*e^6 - 8*e^5 - 139*e^4 - 51*e^3 + 126*e^2 + 32*e + 25, -e^7 - 19*e^6 - 63*e^5 + 31*e^4 + 290*e^3 + 91*e^2 - 290*e - 75, -15*e^7 - 71*e^6 - 23*e^5 + 269*e^4 + 250*e^3 - 194*e^2 - 188*e - 26, 5*e^7 + 11*e^6 - 43*e^5 - 71*e^4 + 133*e^3 + 128*e^2 - 151*e - 54, 4*e^7 + 21*e^6 + 13*e^5 - 83*e^4 - 107*e^3 + 71*e^2 + 103*e - 24, -22*e^7 - 105*e^6 - 31*e^5 + 414*e^4 + 374*e^3 - 331*e^2 - 338*e - 31, -13*e^7 - 58*e^6 - 6*e^5 + 220*e^4 + 148*e^3 - 149*e^2 - 98*e - 48, -5*e^7 - 23*e^6 - 4*e^5 + 91*e^4 + 72*e^3 - 73*e^2 - 63*e - 9, -5*e^7 - 18*e^6 + 13*e^5 + 80*e^4 + 12*e^3 - 72*e^2 - 23*e + 3, -8*e^7 - 45*e^6 - 38*e^5 + 159*e^4 + 241*e^3 - 92*e^2 - 200*e - 3, -4*e^7 - 24*e^6 - 34*e^5 + 57*e^4 + 181*e^3 + 46*e^2 - 154*e - 40, 6*e^7 + 35*e^6 + 32*e^5 - 128*e^4 - 204*e^3 + 82*e^2 + 189*e - 2, -7*e^7 - 46*e^6 - 57*e^5 + 152*e^4 + 296*e^3 - 74*e^2 - 229*e - 21, -22*e^7 - 102*e^6 - 26*e^5 + 387*e^4 + 338*e^3 - 268*e^2 - 271*e - 54, -12*e^7 - 52*e^6 + 7*e^5 + 228*e^4 + 117*e^3 - 223*e^2 - 127*e - 6, 7*e^7 + 35*e^6 + 18*e^5 - 132*e^4 - 162*e^3 + 92*e^2 + 183*e + 19, 2*e^7 - 10*e^6 - 74*e^5 - 16*e^4 + 261*e^3 + 128*e^2 - 200*e - 65, -3*e^7 - 2*e^6 + 48*e^5 + 44*e^4 - 175*e^3 - 121*e^2 + 173*e + 34, -6*e^7 - 28*e^6 - 2*e^5 + 117*e^4 + 64*e^3 - 113*e^2 - 35*e + 19, 21*e^7 + 102*e^6 + 40*e^5 - 386*e^4 - 394*e^3 + 258*e^2 + 339*e + 68, 3*e^7 + 6*e^6 - 29*e^5 - 43*e^4 + 91*e^3 + 85*e^2 - 81*e - 24, 13*e^7 + 51*e^6 - 23*e^5 - 214*e^4 - 28*e^3 + 200*e^2 - 9*e + 10, 18*e^7 + 80*e^6 + 9*e^5 - 312*e^4 - 227*e^3 + 262*e^2 + 204*e - 10, -14*e^7 - 57*e^6 + 16*e^5 + 236*e^4 + 68*e^3 - 226*e^2 - 28*e + 21, -9*e^7 - 42*e^6 - 8*e^5 + 169*e^4 + 126*e^3 - 155*e^2 - 101*e + 30, 4*e^7 + 21*e^6 + 14*e^5 - 73*e^4 - 105*e^3 + 17*e^2 + 107*e + 37, 12*e^7 + 43*e^6 - 40*e^5 - 209*e^4 + 18*e^3 + 245*e^2 + 10*e - 13, -3*e^7 + 4*e^6 + 72*e^5 + 37*e^4 - 274*e^3 - 152*e^2 + 272*e + 64, 10*e^7 + 53*e^6 + 29*e^5 - 205*e^4 - 215*e^3 + 168*e^2 + 176*e + 8, -19*e^7 - 89*e^6 - 31*e^5 + 326*e^4 + 343*e^3 - 181*e^2 - 320*e - 77, -13*e^7 - 69*e^6 - 54*e^5 + 234*e^4 + 367*e^3 - 107*e^2 - 341*e - 53, -2*e^7 - 6*e^6 + 7*e^5 + 24*e^4 + 8*e^3 - 9*e^2 - 42*e, -24*e^7 - 106*e^6 - 2*e^5 + 437*e^4 + 284*e^3 - 379*e^2 - 252*e - 22, -18*e^7 - 90*e^6 - 40*e^5 + 346*e^4 + 368*e^3 - 248*e^2 - 344*e - 46, 9*e^7 + 39*e^6 + 3*e^5 - 146*e^4 - 101*e^3 + 111*e^2 + 84*e - 39, -3*e^7 - 23*e^6 - 46*e^5 + 49*e^4 + 223*e^3 + 57*e^2 - 191*e - 38, -9*e^7 - 28*e^6 + 47*e^5 + 147*e^4 - 109*e^3 - 207*e^2 + 143*e + 52, 17*e^7 + 87*e^6 + 54*e^5 - 312*e^4 - 424*e^3 + 165*e^2 + 410*e + 67, e^7 + 21*e^6 + 66*e^5 - 46*e^4 - 307*e^3 - 66*e^2 + 313*e + 60, -8*e^7 - 45*e^6 - 36*e^5 + 157*e^4 + 216*e^3 - 75*e^2 - 154*e - 57, 5*e^7 + 30*e^6 + 30*e^5 - 110*e^4 - 185*e^3 + 81*e^2 + 187*e + 22, e^7 - 3*e^6 - 29*e^5 - 5*e^4 + 117*e^3 + 56*e^2 - 129*e - 66, -11*e^7 - 50*e^6 - 6*e^5 + 196*e^4 + 137*e^3 - 138*e^2 - 93*e - 31, -10*e^7 - 52*e^6 - 41*e^5 + 158*e^4 + 256*e^3 - 20*e^2 - 211*e - 48, -5*e^7 - 41*e^6 - 84*e^5 + 92*e^4 + 390*e^3 + 75*e^2 - 348*e - 71, 15*e^7 + 75*e^6 + 35*e^5 - 289*e^4 - 311*e^3 + 223*e^2 + 269*e + 37, -18*e^7 - 88*e^6 - 40*e^5 + 321*e^4 + 355*e^3 - 179*e^2 - 280*e - 69, 15*e^7 + 81*e^6 + 58*e^5 - 291*e^4 - 390*e^3 + 176*e^2 + 319*e + 30, 14*e^7 + 66*e^6 + 21*e^5 - 248*e^4 - 228*e^3 + 169*e^2 + 159*e + 29, -18*e^7 - 88*e^6 - 36*e^5 + 331*e^4 + 342*e^3 - 210*e^2 - 287*e - 68, -13*e^7 - 48*e^6 + 32*e^5 + 207*e^4 - 2*e^3 - 203*e^2 + 47*e + 22, 11*e^7 + 50*e^6 + e^5 - 209*e^4 - 110*e^3 + 194*e^2 + 50*e - 9, 9*e^7 + 37*e^6 - 11*e^5 - 156*e^4 - 42*e^3 + 134*e^2 + 5*e + 24, 17*e^7 + 95*e^6 + 92*e^5 - 299*e^4 - 555*e^3 + 59*e^2 + 492*e + 103, -e^7 - 13*e^6 - 36*e^5 + 32*e^4 + 172*e^3 + 13*e^2 - 163*e - 16, 11*e^7 + 47*e^6 - 7*e^5 - 197*e^4 - 89*e^3 + 172*e^2 + 59*e, -2*e^7 + 10*e^6 + 73*e^5 + 6*e^4 - 290*e^3 - 125*e^2 + 281*e + 93, 28*e^7 + 117*e^6 - 22*e^5 - 484*e^4 - 193*e^3 + 443*e^2 + 127*e + 4, -14*e^7 - 72*e^6 - 47*e^5 + 242*e^4 + 321*e^3 - 96*e^2 - 258*e - 64, 11*e^7 + 34*e^6 - 65*e^5 - 204*e^4 + 134*e^3 + 318*e^2 - 121*e - 61, 11*e^6 + 44*e^5 - 8*e^4 - 175*e^3 - 88*e^2 + 151*e + 55, -18*e^7 - 86*e^6 - 31*e^5 + 325*e^4 + 327*e^3 - 228*e^2 - 294*e - 25, 14*e^7 + 52*e^6 - 34*e^5 - 223*e^4 + 3*e^3 + 213*e^2 - 47*e - 24, 10*e^6 + 44*e^5 + 2*e^4 - 161*e^3 - 82*e^2 + 105*e + 46, 2*e^7 + 5*e^6 - 15*e^5 - 31*e^4 + 39*e^3 + 47*e^2 - 31*e - 12, -19*e^7 - 103*e^6 - 73*e^5 + 381*e^4 + 518*e^3 - 234*e^2 - 452*e - 84, -17*e^7 - 91*e^6 - 75*e^5 + 311*e^4 + 522*e^3 - 123*e^2 - 519*e - 110, 14*e^7 + 54*e^6 - 34*e^5 - 252*e^4 - 15*e^3 + 286*e^2 + 13*e - 28, 6*e^7 + 40*e^6 + 61*e^5 - 103*e^4 - 305*e^3 - 48*e^2 + 267*e + 64, -18*e^7 - 85*e^6 - 20*e^5 + 335*e^4 + 261*e^3 - 284*e^2 - 189*e + 18, -27*e^7 - 129*e^6 - 41*e^5 + 489*e^4 + 434*e^3 - 347*e^2 - 329*e - 68, 6*e^7 + 27*e^6 + 8*e^5 - 92*e^4 - 92*e^3 + 41*e^2 + 79*e + 17, 20*e^7 + 109*e^6 + 80*e^5 - 391*e^4 - 529*e^3 + 232*e^2 + 437*e + 76, 14*e^7 + 80*e^6 + 86*e^5 - 248*e^4 - 524*e^3 + 20*e^2 + 501*e + 113, 10*e^7 + 34*e^6 - 42*e^5 - 168*e^4 + 82*e^3 + 229*e^2 - 112*e - 41, 26*e^7 + 138*e^6 + 97*e^5 - 492*e^4 - 683*e^3 + 259*e^2 + 586*e + 117, -11*e^7 - 46*e^6 + 6*e^5 + 182*e^4 + 84*e^3 - 151*e^2 - 74*e - 30, 9*e^7 + 28*e^6 - 46*e^5 - 142*e^4 + 102*e^3 + 172*e^2 - 121*e - 18, -26*e^7 - 118*e^6 - 20*e^5 + 464*e^4 + 377*e^3 - 352*e^2 - 334*e - 55, 3*e^7 + 15*e^6 + 7*e^5 - 50*e^4 - 57*e^3 - 4*e^2 + 49*e + 61, 16*e^7 + 85*e^6 + 52*e^5 - 327*e^4 - 409*e^3 + 217*e^2 + 387*e + 71, -16*e^7 - 71*e^6 + 7*e^5 + 307*e^4 + 134*e^3 - 310*e^2 - 101*e + 6, -8*e^7 - 34*e^6 + 6*e^5 + 147*e^4 + 69*e^3 - 130*e^2 - 57*e - 47, -22*e^7 - 99*e^6 - 6*e^5 + 398*e^4 + 248*e^3 - 316*e^2 - 173*e - 48, -13*e^7 - 62*e^6 - 24*e^5 + 230*e^4 + 236*e^3 - 169*e^2 - 214*e - 24, 6*e^7 + 17*e^6 - 38*e^5 - 85*e^4 + 112*e^3 + 87*e^2 - 147*e + 6, -3*e^7 - 17*e^6 - 16*e^5 + 62*e^4 + 106*e^3 - 55*e^2 - 94*e + 31, 45*e^7 + 225*e^6 + 111*e^5 - 833*e^4 - 941*e^3 + 533*e^2 + 812*e + 142, -4*e^7 - 22*e^6 - 30*e^5 + 49*e^4 + 176*e^3 + 72*e^2 - 162*e - 77, -12*e^7 - 54*e^6 - 2*e^5 + 233*e^4 + 146*e^3 - 254*e^2 - 116*e + 43, -19*e^7 - 88*e^6 - 16*e^5 + 349*e^4 + 270*e^3 - 282*e^2 - 237*e - 15, 5*e^7 + 14*e^6 - 22*e^5 - 60*e^4 + 18*e^3 + 50*e^2 + 29*e - 10, -2*e^7 - 14*e^6 - 12*e^5 + 64*e^4 + 70*e^3 - 65*e^2 - 53*e - 24, 9*e^7 + 54*e^6 + 60*e^5 - 175*e^4 - 345*e^3 + 56*e^2 + 309*e + 68, 11*e^7 + 59*e^6 + 45*e^5 - 201*e^4 - 306*e^3 + 73*e^2 + 301*e + 90, 41*e^7 + 199*e^6 + 70*e^5 - 771*e^4 - 726*e^3 + 588*e^2 + 630*e + 79, e^7 - 16*e^6 - 76*e^5 + 21*e^4 + 304*e^3 + 80*e^2 - 259*e - 29, -31*e^7 - 138*e^6 - 8*e^5 + 557*e^4 + 368*e^3 - 473*e^2 - 303*e - 20, -19*e^7 - 80*e^6 + 9*e^5 + 311*e^4 + 132*e^3 - 248*e^2 - 59*e - 18, 13*e^7 + 78*e^6 + 85*e^5 - 266*e^4 - 518*e^3 + 111*e^2 + 490*e + 91, 18*e^7 + 80*e^6 + 8*e^5 - 301*e^4 - 199*e^3 + 197*e^2 + 118*e + 43, -48*e^7 - 231*e^6 - 80*e^5 + 889*e^4 + 857*e^3 - 654*e^2 - 744*e - 93, -16*e^7 - 79*e^6 - 26*e^5 + 316*e^4 + 280*e^3 - 261*e^2 - 263*e - 31, -28*e^7 - 135*e^6 - 44*e^5 + 523*e^4 + 470*e^3 - 395*e^2 - 369*e - 50, -46*e^7 - 219*e^6 - 67*e^5 + 842*e^4 + 756*e^3 - 627*e^2 - 639*e - 94, 13*e^7 + 80*e^6 + 90*e^5 - 269*e^4 - 519*e^3 + 113*e^2 + 478*e + 84, -6*e^7 - 17*e^6 + 38*e^5 + 108*e^4 - 65*e^3 - 175*e^2 + 17*e + 42, -12*e^7 - 53*e^6 - 6*e^5 + 202*e^4 + 153*e^3 - 136*e^2 - 127*e - 33, 6*e^7 + 42*e^6 + 70*e^5 - 103*e^4 - 332*e^3 - 51*e^2 + 261*e + 67, -6*e^7 - 43*e^6 - 58*e^5 + 150*e^4 + 303*e^3 - 84*e^2 - 273*e - 33, 13*e^7 + 73*e^6 + 58*e^5 - 266*e^4 - 381*e^3 + 165*e^2 + 339*e + 59, -31*e^7 - 140*e^6 - 26*e^5 + 528*e^4 + 430*e^3 - 361*e^2 - 369*e - 83, -32*e^7 - 160*e^6 - 84*e^5 + 591*e^4 + 725*e^3 - 357*e^2 - 691*e - 136, -11*e^7 - 47*e^6 + 6*e^5 + 189*e^4 + 70*e^3 - 173*e^2 - 30*e - 12, 4*e^7 + 20*e^6 + 14*e^5 - 72*e^4 - 110*e^3 + 60*e^2 + 117*e - 1, 8*e^7 + 32*e^6 - 20*e^5 - 159*e^4 - 10*e^3 + 194*e^2 + 9*e + 18, 5*e^7 + 31*e^6 + 48*e^5 - 67*e^4 - 242*e^3 - 67*e^2 + 222*e + 38, 27*e^7 + 107*e^6 - 47*e^5 - 472*e^4 - 108*e^3 + 470*e^2 + 92*e + 15, 6*e^7 + 47*e^6 + 76*e^5 - 151*e^4 - 377*e^3 + 48*e^2 + 313*e + 58, 2*e^7 + 20*e^6 + 49*e^5 - 39*e^4 - 203*e^3 - 29*e^2 + 144*e + 12, -36*e^7 - 161*e^6 - 12*e^5 + 646*e^4 + 433*e^3 - 548*e^2 - 338*e + 20, -15*e^7 - 55*e^6 + 50*e^5 + 277*e^4 - 29*e^3 - 363*e^2 + 4*e + 81, -15*e^7 - 77*e^6 - 45*e^5 + 286*e^4 + 362*e^3 - 173*e^2 - 343*e - 73, -17*e^7 - 76*e^6 - 11*e^5 + 297*e^4 + 241*e^3 - 220*e^2 - 227*e - 41, -9*e^7 - 30*e^6 + 36*e^5 + 140*e^4 - 60*e^3 - 152*e^2 + 68*e + 7, 3*e^7 + 15*e^6 + 4*e^5 - 77*e^4 - 75*e^3 + 115*e^2 + 104*e - 39, -10*e^7 - 49*e^6 - 20*e^5 + 183*e^4 + 192*e^3 - 97*e^2 - 164*e - 65, -21*e^7 - 111*e^6 - 83*e^5 + 380*e^4 + 563*e^3 - 183*e^2 - 507*e - 92, -10*e^7 - 58*e^6 - 60*e^5 + 191*e^4 + 359*e^3 - 66*e^2 - 331*e - 75, 15*e^7 + 91*e^6 + 86*e^5 - 344*e^4 - 532*e^3 + 240*e^2 + 470*e + 64, -13*e^7 - 59*e^6 - 9*e^5 + 228*e^4 + 180*e^3 - 156*e^2 - 177*e - 58, -e^7 - 3*e^6 - 3*e^4 + 12*e^3 + 70*e^2 - 7*e - 48, -12*e^7 - 73*e^6 - 76*e^5 + 256*e^4 + 448*e^3 - 132*e^2 - 405*e - 68, 6*e^7 + 41*e^6 + 52*e^5 - 146*e^4 - 280*e^3 + 88*e^2 + 247*e + 38, -11*e^7 - 55*e^6 - 31*e^5 + 193*e^4 + 230*e^3 - 128*e^2 - 178*e - 10, 21*e^7 + 104*e^6 + 50*e^5 - 380*e^4 - 427*e^3 + 224*e^2 + 386*e + 102, -20*e^7 - 79*e^6 + 33*e^5 + 336*e^4 + 60*e^3 - 345*e^2 - 16*e + 55, -23*e^7 - 94*e^6 + 29*e^5 + 401*e^4 + 119*e^3 - 376*e^2 - 63*e - 3, 9*e^7 + 47*e^6 + 25*e^5 - 189*e^4 - 216*e^3 + 171*e^2 + 223*e - 4, 5*e^7 + 15*e^6 - 18*e^5 - 39*e^4 + 60*e^3 - 10*e^2 - 96*e + 13, 14*e^6 + 59*e^5 - 17*e^4 - 248*e^3 - 51*e^2 + 243*e + 38, 16*e^7 + 75*e^6 + 13*e^5 - 296*e^4 - 206*e^3 + 223*e^2 + 145*e + 60, 20*e^7 + 108*e^6 + 82*e^5 - 382*e^4 - 563*e^3 + 187*e^2 + 506*e + 114, 39*e^7 + 191*e^6 + 85*e^5 - 702*e^4 - 765*e^3 + 438*e^2 + 672*e + 106, 38*e^7 + 196*e^6 + 110*e^5 - 730*e^4 - 858*e^3 + 480*e^2 + 741*e + 141, -16*e^7 - 70*e^6 - 10*e^5 + 252*e^4 + 206*e^3 - 132*e^2 - 169*e - 61, -7*e^7 - 19*e^6 + 56*e^5 + 127*e^4 - 178*e^3 - 254*e^2 + 191*e + 96, 9*e^7 + 47*e^6 + 46*e^5 - 133*e^4 - 303*e^3 - 35*e^2 + 315*e + 104, 25*e^7 + 106*e^6 - 11*e^5 - 423*e^4 - 198*e^3 + 362*e^2 + 131*e + 22, 19*e^7 + 87*e^6 + 19*e^5 - 335*e^4 - 294*e^3 + 234*e^2 + 272*e + 40, -12*e^7 - 41*e^6 + 52*e^5 + 213*e^4 - 81*e^3 - 281*e^2 + 71*e + 27, 23*e^7 + 98*e^6 - 11*e^5 - 400*e^4 - 182*e^3 + 362*e^2 + 109*e + 1, 7*e^7 + 29*e^6 - 13*e^5 - 136*e^4 - 23*e^3 + 156*e^2 + 32*e - 4, 9*e^7 + 48*e^6 + 36*e^5 - 170*e^4 - 245*e^3 + 95*e^2 + 195*e + 56, -2*e^7 + 8*e^6 + 62*e^5 + e^4 - 228*e^3 - 71*e^2 + 192*e + 58, -14*e^7 - 58*e^6 + 13*e^5 + 223*e^4 + 48*e^3 - 167*e^2 + 33*e - 32, 9*e^7 + 52*e^6 + 51*e^5 - 180*e^4 - 318*e^3 + 76*e^2 + 271*e + 47, -12*e^7 - 49*e^6 + 17*e^5 + 215*e^4 + 68*e^3 - 202*e^2 - 61*e - 6, -7*e^7 - 19*e^6 + 38*e^5 + 83*e^4 - 91*e^3 - 76*e^2 + 89*e + 15, 10*e^7 + 62*e^6 + 73*e^5 - 190*e^4 - 392*e^3 + 15*e^2 + 335*e + 91, -3*e^7 - 23*e^6 - 39*e^5 + 71*e^4 + 208*e^3 - 18*e^2 - 230*e - 20, 3*e^7 + 32*e^6 + 76*e^5 - 75*e^4 - 353*e^3 - 73*e^2 + 340*e + 92, 2*e^7 + 2*e^6 - 17*e^5 + 5*e^4 + 55*e^3 - 52*e^2 - 66*e + 21, -5*e^7 - 28*e^6 - 13*e^5 + 132*e^4 + 126*e^3 - 145*e^2 - 120*e - 13, -2*e^7 - 8*e^6 + 5*e^5 + 42*e^4 + 25*e^3 - 40*e^2 - 91*e - 3, -27*e^7 - 113*e^6 + 17*e^5 + 460*e^4 + 220*e^3 - 380*e^2 - 177*e - 48, -10*e^7 - 32*e^6 + 45*e^5 + 153*e^4 - 102*e^3 - 213*e^2 + 121*e + 60, 52*e^7 + 241*e^6 + 61*e^5 - 911*e^4 - 796*e^3 + 618*e^2 + 654*e + 137, 49*e^7 + 239*e^6 + 96*e^5 - 903*e^4 - 914*e^3 + 626*e^2 + 766*e + 129, -33*e^7 - 166*e^6 - 97*e^5 + 588*e^4 + 766*e^3 - 309*e^2 - 722*e - 137, -9*e^7 - 24*e^6 + 68*e^5 + 158*e^4 - 188*e^3 - 291*e^2 + 181*e + 75, 9*e^7 + 35*e^6 - 14*e^5 - 141*e^4 - 24*e^3 + 121*e^2 + e + 43, -12*e^7 - 35*e^6 + 75*e^5 + 200*e^4 - 190*e^3 - 317*e^2 + 177*e + 70, 6*e^6 + 23*e^5 - e^4 - 75*e^3 - 50*e^2 + 63*e + 42, -16*e^7 - 71*e^6 + 5*e^5 + 302*e^4 + 131*e^3 - 310*e^2 - 75*e + 22, -20*e^7 - 89*e^6 - 5*e^5 + 357*e^4 + 248*e^3 - 268*e^2 - 230*e - 61, -24*e^7 - 122*e^6 - 62*e^5 + 459*e^4 + 497*e^3 - 349*e^2 - 412*e - 25, e^7 + 20*e^6 + 61*e^5 - 42*e^4 - 256*e^3 - 38*e^2 + 201*e + 31, 30*e^7 + 140*e^6 + 31*e^5 - 552*e^4 - 448*e^3 + 439*e^2 + 367*e + 31, -11*e^7 - 62*e^6 - 58*e^5 + 214*e^4 + 371*e^3 - 92*e^2 - 312*e - 72, 12*e^7 + 56*e^6 + 8*e^5 - 226*e^4 - 158*e^3 + 173*e^2 + 121*e + 52, 2*e^7 + 4*e^6 - 6*e^5 + 2*e^4 - 9*e^3 - 59*e^2 + 43*e + 33, 17*e^7 + 69*e^6 - 17*e^5 - 270*e^4 - 80*e^3 + 191*e^2 - 15*e + 47, -14*e^7 - 56*e^6 + 33*e^5 + 264*e^4 + 3*e^3 - 312*e^2 + 16*e + 30, 35*e^7 + 167*e^6 + 53*e^5 - 653*e^4 - 619*e^3 + 507*e^2 + 564*e + 66, 7*e^7 + 27*e^6 - 14*e^5 - 115*e^4 - 9*e^3 + 121*e^2 + 4*e - 55, 23*e^7 + 95*e^6 - 27*e^5 - 404*e^4 - 111*e^3 + 415*e^2 + 54*e - 71, 20*e^7 + 86*e^6 - 341*e^4 - 221*e^3 + 288*e^2 + 221*e + 25, 26*e^7 + 115*e^6 + 13*e^5 - 437*e^4 - 316*e^3 + 318*e^2 + 232*e + 15, 28*e^7 + 122*e^6 - 10*e^5 - 504*e^4 - 236*e^3 + 450*e^2 + 125*e - 9, 15*e^7 + 40*e^6 - 106*e^5 - 239*e^4 + 285*e^3 + 379*e^2 - 266*e - 74, 24*e^7 + 122*e^6 + 59*e^5 - 466*e^4 - 476*e^3 + 371*e^2 + 364*e - 8, -16*e^7 - 92*e^6 - 88*e^5 + 302*e^4 + 502*e^3 - 125*e^2 - 397*e - 80, -5*e^7 - 17*e^6 + 23*e^5 + 83*e^4 - 63*e^3 - 99*e^2 + 112*e - 2, -13*e^7 - 68*e^6 - 36*e^5 + 250*e^4 + 244*e^3 - 188*e^2 - 151*e - 6, -7*e^7 - 32*e^6 - 4*e^5 + 130*e^4 + 95*e^3 - 105*e^2 - 75*e - 24, e^7 - 3*e^6 - 20*e^5 + 21*e^4 + 72*e^3 - 82*e^2 - 62*e + 57, 28*e^7 + 117*e^6 - 20*e^5 - 481*e^4 - 213*e^3 + 439*e^2 + 172*e - 26, 3*e^7 - 14*e^6 - 107*e^5 - 10*e^4 + 420*e^3 + 166*e^2 - 371*e - 99, 25*e^7 + 110*e^6 + 3*e^5 - 433*e^4 - 256*e^3 + 344*e^2 + 183*e + 34, 36*e^7 + 165*e^6 + 34*e^5 - 637*e^4 - 525*e^3 + 479*e^2 + 431*e + 51, -9*e^7 - 37*e^6 + 14*e^5 + 166*e^4 + 25*e^3 - 194*e^2 + 10*e + 15, 5*e^7 + 27*e^6 + 20*e^5 - 98*e^4 - 130*e^3 + 64*e^2 + 96*e + 56, -7*e^7 - 22*e^6 + 25*e^5 + 81*e^4 - 49*e^3 - 66*e^2 + 50*e + 12, -11*e^7 - 68*e^6 - 82*e^5 + 213*e^4 + 454*e^3 - 58*e^2 - 393*e - 51, -4*e^7 - 24*e^6 - 26*e^5 + 96*e^4 + 179*e^3 - 105*e^2 - 199*e + 39, 12*e^7 + 55*e^6 + 7*e^5 - 222*e^4 - 144*e^3 + 202*e^2 + 71*e - 25, -12*e^7 - 63*e^6 - 36*e^5 + 248*e^4 + 302*e^3 - 192*e^2 - 306*e - 29, -46*e^7 - 242*e^6 - 157*e^5 + 880*e^4 + 1139*e^3 - 520*e^2 - 958*e - 170, -4*e^7 - 34*e^6 - 67*e^5 + 82*e^4 + 294*e^3 + 27*e^2 - 247*e - 17, -27*e^7 - 126*e^6 - 30*e^5 + 484*e^4 + 396*e^3 - 343*e^2 - 307*e - 69, 4*e^7 + 9*e^6 - 34*e^5 - 68*e^4 + 86*e^3 + 148*e^2 - 63*e - 50, 26*e^7 + 113*e^6 - 9*e^5 - 480*e^4 - 255*e^3 + 478*e^2 + 251*e - 24, 14*e^7 + 49*e^6 - 61*e^5 - 255*e^4 + 119*e^3 + 350*e^2 - 150*e - 86, -8*e^7 - 60*e^6 - 102*e^5 + 181*e^4 + 557*e^3 + 20*e^2 - 572*e - 132, 10*e^7 + 42*e^6 - 5*e^5 - 160*e^4 - 62*e^3 + 121*e^2 + 28*e + 12, 44*e^7 + 214*e^6 + 87*e^5 - 806*e^4 - 845*e^3 + 541*e^2 + 742*e + 125, -50*e^7 - 235*e^6 - 64*e^5 + 922*e^4 + 849*e^3 - 697*e^2 - 798*e - 101, 26*e^7 + 119*e^6 + 26*e^5 - 460*e^4 - 395*e^3 + 348*e^2 + 360*e + 66, -5*e^6 - 25*e^5 - 6*e^4 + 106*e^3 + 79*e^2 - 100*e - 39, 24*e^7 + 129*e^6 + 97*e^5 - 454*e^4 - 656*e^3 + 237*e^2 + 566*e + 137, -4*e^7 - 28*e^6 - 45*e^5 + 72*e^4 + 211*e^3 + 31*e^2 - 144*e - 55, 14*e^7 + 47*e^6 - 48*e^5 - 209*e^4 + 35*e^3 + 209*e^2 + 6*e + 12, -21*e^7 - 89*e^6 + 14*e^5 + 389*e^4 + 204*e^3 - 398*e^2 - 214*e + 61, -7*e^7 - 28*e^6 + 5*e^5 + 97*e^4 + 46*e^3 - 18*e^2 - 26*e - 57, 27*e^7 + 138*e^6 + 83*e^5 - 481*e^4 - 603*e^3 + 243*e^2 + 494*e + 123, -14*e^7 - 69*e^6 - 33*e^5 + 251*e^4 + 286*e^3 - 137*e^2 - 213*e - 83, -31*e^7 - 151*e^6 - 54*e^5 + 587*e^4 + 552*e^3 - 465*e^2 - 487*e - 63, 19*e^7 + 83*e^6 - 4*e^5 - 346*e^4 - 185*e^3 + 318*e^2 + 118*e + 5, -10*e^7 - 51*e^6 - 21*e^5 + 228*e^4 + 246*e^3 - 247*e^2 - 275*e + 16, -24*e^7 - 109*e^6 - 23*e^5 + 422*e^4 + 383*e^3 - 303*e^2 - 388*e - 64, 6*e^7 + 31*e^6 + 27*e^5 - 95*e^4 - 190*e^3 - 3*e^2 + 209*e + 59, 7*e^7 + 35*e^6 + 16*e^5 - 133*e^4 - 137*e^3 + 106*e^2 + 99*e - 41, -4*e^7 - 24*e^6 - 17*e^5 + 99*e^4 + 115*e^3 - 72*e^2 - 83*e - 72, -13*e^7 - 60*e^6 - 14*e^5 + 227*e^4 + 194*e^3 - 132*e^2 - 149*e - 91, -12*e^7 - 48*e^6 + e^5 + 158*e^4 + 106*e^3 - 44*e^2 - 70*e - 87, -8*e^7 - 36*e^6 - 9*e^5 + 144*e^4 + 154*e^3 - 127*e^2 - 190*e + 6, -15*e^7 - 73*e^6 - 22*e^5 + 295*e^4 + 239*e^3 - 276*e^2 - 157*e + 57, e^7 - 8*e^6 - 58*e^5 - 14*e^4 + 253*e^3 + 122*e^2 - 264*e - 34, 6*e^7 + 46*e^6 + 83*e^5 - 108*e^4 - 374*e^3 - 72*e^2 + 313*e + 82, -7*e^7 - 33*e^6 - 21*e^5 + 98*e^4 + 164*e^3 - 14*e^2 - 176*e - 21, -39*e^7 - 181*e^6 - 33*e^5 + 717*e^4 + 525*e^3 - 604*e^2 - 382*e + 15, 10*e^7 + 53*e^6 + 36*e^5 - 195*e^4 - 269*e^3 + 105*e^2 + 238*e + 112, 20*e^7 + 112*e^6 + 97*e^5 - 387*e^4 - 607*e^3 + 182*e^2 + 496*e + 109, -16*e^7 - 68*e^6 + 3*e^5 + 272*e^4 + 175*e^3 - 214*e^2 - 185*e - 31, 4*e^7 - 15*e^6 - 128*e^5 - 27*e^4 + 474*e^3 + 198*e^2 - 408*e - 78, 12*e^7 + 59*e^6 + 19*e^5 - 240*e^4 - 220*e^3 + 186*e^2 + 202*e + 62, -28*e^7 - 129*e^6 - 10*e^5 + 536*e^4 + 323*e^3 - 513*e^2 - 265*e + 20, -15*e^7 - 52*e^6 + 56*e^5 + 256*e^4 - 64*e^3 - 330*e^2 + 57*e + 100, -28*e^7 - 131*e^6 - 34*e^5 + 496*e^4 + 421*e^3 - 318*e^2 - 313*e - 99, 23*e^7 + 122*e^6 + 100*e^5 - 390*e^4 - 649*e^3 + 87*e^2 + 576*e + 139, 15*e^7 + 81*e^6 + 56*e^5 - 288*e^4 - 370*e^3 + 148*e^2 + 267*e + 47, -4*e^7 - 21*e^6 + 2*e^5 + 123*e^4 + 47*e^3 - 210*e^2 - 55*e + 78, 57*e^7 + 268*e^6 + 71*e^5 - 1053*e^4 - 937*e^3 + 825*e^2 + 858*e + 113, 3*e^7 + 8*e^6 - 16*e^5 - 40*e^4 + 16*e^3 + 33*e^2 + 11*e + 55, 21*e^7 + 105*e^6 + 48*e^5 - 411*e^4 - 444*e^3 + 324*e^2 + 397*e + 32, 55*e^7 + 273*e^6 + 128*e^5 - 1025*e^4 - 1136*e^3 + 681*e^2 + 979*e + 159, -28*e^6 - 119*e^5 + 21*e^4 + 504*e^3 + 204*e^2 - 446*e - 128, 25*e^7 + 116*e^6 + 12*e^5 - 496*e^4 - 345*e^3 + 487*e^2 + 327*e - 34, 15*e^7 + 65*e^6 - 267*e^4 - 192*e^3 + 229*e^2 + 220*e + 32, 34*e^7 + 158*e^6 + 36*e^5 - 613*e^4 - 518*e^3 + 453*e^2 + 448*e + 60, -15*e^7 - 106*e^6 - 147*e^5 + 353*e^4 + 760*e^3 - 153*e^2 - 656*e - 122, 6*e^7 + 23*e^6 - 9*e^5 - 79*e^4 + e^3 + 40*e^2 - 26*e - 8, 7*e^7 + 51*e^6 + 83*e^5 - 152*e^4 - 423*e^3 + 14*e^2 + 385*e + 83, 9*e^7 + 53*e^6 + 46*e^5 - 209*e^4 - 306*e^3 + 181*e^2 + 302*e - 12, 17*e^7 + 68*e^6 - 25*e^5 - 283*e^4 - 61*e^3 + 257*e^2 + 30*e + 5, 4*e^7 - 3*e^6 - 90*e^5 - 62*e^4 + 332*e^3 + 200*e^2 - 323*e - 58, 5*e^7 + 16*e^6 - 17*e^5 - 62*e^4 + 24*e^3 + 51*e^2 - 16*e + 7, -43*e^7 - 194*e^6 - 27*e^5 + 764*e^4 + 592*e^3 - 597*e^2 - 520*e - 15, 30*e^7 + 157*e^6 + 100*e^5 - 570*e^4 - 722*e^3 + 363*e^2 + 603*e + 67, -3*e^7 - 29*e^6 - 67*e^5 + 62*e^4 + 289*e^3 + 40*e^2 - 219*e - 1, 21*e^7 + 91*e^6 - 6*e^5 - 377*e^4 - 199*e^3 + 342*e^2 + 146*e + 16, 33*e^7 + 147*e^6 + 18*e^5 - 562*e^4 - 423*e^3 + 380*e^2 + 333*e + 102, 7*e^7 + 28*e^6 - 20*e^5 - 147*e^4 + 6*e^3 + 206*e^2 - 31*e - 41, -11*e^7 - 66*e^6 - 69*e^5 + 217*e^4 + 385*e^3 - 80*e^2 - 298*e - 40, -3*e^7 - 9*e^6 + 8*e^5 + 29*e^4 - 25*e^2 - 36*e + 42, 2*e^7 + 32*e^6 + 98*e^5 - 66*e^4 - 465*e^3 - 104*e^2 + 492*e + 141, -8*e^7 - 25*e^6 + 40*e^5 + 138*e^4 - 50*e^3 - 199*e^2 - 13*e + 71, 16*e^7 + 65*e^6 - 7*e^5 - 241*e^4 - 127*e^3 + 183*e^2 + 104*e - 27, 6*e^7 + 31*e^6 + 21*e^5 - 127*e^4 - 212*e^3 + 78*e^2 + 281*e + 36, 20*e^7 + 96*e^6 + 25*e^5 - 379*e^4 - 305*e^3 + 283*e^2 + 232*e + 90, 27*e^7 + 120*e^6 + 12*e^5 - 470*e^4 - 338*e^3 + 355*e^2 + 271*e + 69, -34*e^7 - 146*e^6 + 7*e^5 + 578*e^4 + 313*e^3 - 461*e^2 - 198*e - 11, -28*e^7 - 145*e^6 - 78*e^5 + 549*e^4 + 620*e^3 - 368*e^2 - 514*e - 68, 6*e^7 + 32*e^6 + 17*e^5 - 143*e^4 - 169*e^3 + 156*e^2 + 174*e - 45, -11*e^7 - 73*e^6 - 101*e^5 + 209*e^4 + 502*e^3 + 4*e^2 - 422*e - 88, 3*e^7 + 10*e^6 - 5*e^5 - 38*e^4 - 25*e^3 + 10*e^2 + 15*e + 40, 25*e^7 + 146*e^6 + 144*e^5 - 486*e^4 - 823*e^3 + 215*e^2 + 654*e + 119, 3*e^7 + 3*e^6 - 41*e^5 - 33*e^4 + 177*e^3 + 129*e^2 - 221*e - 109, 33*e^7 + 144*e^6 - 4*e^5 - 597*e^4 - 354*e^3 + 542*e^2 + 312*e - 6, 24*e^7 + 128*e^6 + 86*e^5 - 474*e^4 - 629*e^3 + 314*e^2 + 584*e + 103, 2*e^7 - 6*e^6 - 66*e^5 - 47*e^4 + 221*e^3 + 210*e^2 - 172*e - 116, 41*e^7 + 194*e^6 + 52*e^5 - 771*e^4 - 680*e^3 + 619*e^2 + 606*e + 35, -22*e^7 - 106*e^6 - 23*e^5 + 448*e^4 + 358*e^3 - 412*e^2 - 327*e - 24, 18*e^7 + 88*e^6 + 33*e^5 - 348*e^4 - 355*e^3 + 272*e^2 + 338*e + 24, 9*e^7 + 46*e^6 + 32*e^5 - 146*e^4 - 213*e^3 + 37*e^2 + 189*e + 50, -31*e^7 - 167*e^6 - 128*e^5 + 573*e^4 + 832*e^3 - 277*e^2 - 674*e - 116, 20*e^7 + 109*e^6 + 86*e^5 - 383*e^4 - 581*e^3 + 175*e^2 + 515*e + 135, -45*e^7 - 209*e^6 - 52*e^5 + 801*e^4 + 697*e^3 - 586*e^2 - 593*e - 49, -e^7 + 4*e^6 + 40*e^5 + 28*e^4 - 144*e^3 - 130*e^2 + 134*e + 113, -24*e^7 - 101*e^6 + 7*e^5 + 387*e^4 + 202*e^3 - 295*e^2 - 132*e + 12, 8*e^7 + 35*e^6 + 13*e^5 - 113*e^4 - 164*e^3 - 3*e^2 + 197*e + 77, -5*e^7 - 5*e^6 + 64*e^5 + 64*e^4 - 209*e^3 - 172*e^2 + 196*e + 95, -23*e^7 - 97*e^6 + 27*e^5 + 436*e^4 + 137*e^3 - 480*e^2 - 92*e + 78, 4*e^7 + 28*e^6 + 50*e^5 - 67*e^4 - 256*e^3 - 52*e^2 + 209*e + 30, -14*e^7 - 52*e^6 + 34*e^5 + 217*e^4 - 16*e^3 - 203*e^2 + 34*e - 2, -13*e^7 - 58*e^6 + e^5 + 239*e^4 + 124*e^3 - 198*e^2 - 72*e - 29, -49*e^7 - 216*e^6 + e^5 + 888*e^4 + 520*e^3 - 809*e^2 - 439*e - 2, 14*e^7 + 61*e^6 + 15*e^5 - 200*e^4 - 203*e^3 + 43*e^2 + 162*e + 90, 20*e^7 + 104*e^6 + 74*e^5 - 341*e^4 - 498*e^3 + 86*e^2 + 407*e + 122, 23*e^7 + 84*e^6 - 71*e^5 - 382*e^4 + 82*e^3 + 423*e^2 - 164*e - 53, 7*e^7 + 41*e^6 + 27*e^5 - 163*e^4 - 151*e^3 + 171*e^2 + 56*e - 56, -3*e^7 - 21*e^6 - 42*e^5 + 35*e^4 + 184*e^3 + 50*e^2 - 148*e - 11, 30*e^7 + 153*e^6 + 100*e^5 - 529*e^4 - 753*e^3 + 231*e^2 + 700*e + 128, -17*e^7 - 61*e^6 + 63*e^5 + 307*e^4 - 70*e^3 - 387*e^2 + 69*e + 44, 35*e^7 + 133*e^6 - 88*e^5 - 602*e^4 + 15*e^3 + 669*e^2 - 85*e - 81, -3*e^7 - 23*e^6 - 53*e^5 + 41*e^4 + 278*e^3 + 88*e^2 - 327*e - 69, 44*e^7 + 219*e^6 + 107*e^5 - 815*e^4 - 925*e^3 + 535*e^2 + 830*e + 151, -8*e^7 - 53*e^6 - 69*e^5 + 181*e^4 + 402*e^3 - 61*e^2 - 384*e - 82, 34*e^7 + 179*e^6 + 122*e^5 - 647*e^4 - 898*e^3 + 354*e^2 + 825*e + 161, -7*e^7 - 60*e^6 - 108*e^5 + 179*e^4 + 494*e^3 - 35*e^2 - 390*e - 71, -38*e^7 - 200*e^6 - 154*e^5 + 663*e^4 + 1036*e^3 - 246*e^2 - 944*e - 189, -40*e^7 - 188*e^6 - 48*e^5 + 734*e^4 + 630*e^3 - 575*e^2 - 555*e - 58, 14*e^7 + 92*e^6 + 112*e^5 - 316*e^4 - 631*e^3 + 119*e^2 + 564*e + 116, 39*e^7 + 166*e^6 - 18*e^5 - 694*e^4 - 366*e^3 + 646*e^2 + 323*e - 20, 12*e^7 + 72*e^6 + 70*e^5 - 255*e^4 - 415*e^3 + 128*e^2 + 350*e + 82, 7*e^7 + 18*e^6 - 56*e^5 - 111*e^4 + 177*e^3 + 178*e^2 - 181*e - 26, -e^7 - 20*e^6 - 61*e^5 + 45*e^4 + 287*e^3 + 41*e^2 - 336*e - 25, 11*e^7 + 52*e^6 + 24*e^5 - 177*e^4 - 224*e^3 + 58*e^2 + 230*e + 86, 22*e^7 + 127*e^6 + 123*e^5 - 440*e^4 - 773*e^3 + 209*e^2 + 750*e + 130, -18*e^7 - 79*e^6 + 6*e^5 + 343*e^4 + 189*e^3 - 356*e^2 - 199*e + 14, -12*e^7 - 70*e^6 - 69*e^5 + 223*e^4 + 381*e^3 - 55*e^2 - 283*e - 55, 26*e^7 + 121*e^6 + 19*e^5 - 493*e^4 - 367*e^3 + 427*e^2 + 355*e + 12, -34*e^7 - 155*e^6 - 15*e^5 + 627*e^4 + 403*e^3 - 547*e^2 - 271*e + 18, -43*e^7 - 202*e^6 - 42*e^5 + 805*e^4 + 629*e^3 - 646*e^2 - 509*e - 42, -21*e^7 - 109*e^6 - 83*e^5 + 353*e^4 + 572*e^3 - 79*e^2 - 514*e - 145, -11*e^7 - 74*e^6 - 105*e^5 + 206*e^4 + 514*e^3 + 32*e^2 - 425*e - 133, 5*e^7 + 26*e^6 + 10*e^5 - 120*e^4 - 123*e^3 + 127*e^2 + 158*e - 23, 14*e^7 + 44*e^6 - 67*e^5 - 211*e^4 + 152*e^3 + 264*e^2 - 188*e - 44, -18*e^7 - 59*e^6 + 63*e^5 + 252*e^4 - 73*e^3 - 243*e^2 + 64*e + 10, -39*e^7 - 182*e^6 - 62*e^5 + 664*e^4 + 678*e^3 - 393*e^2 - 612*e - 102, 40*e^7 + 191*e^6 + 64*e^5 - 718*e^4 - 669*e^3 + 471*e^2 + 518*e + 103, -39*e^7 - 174*e^6 - 17*e^5 + 682*e^4 + 477*e^3 - 555*e^2 - 389*e + 1, 30*e^7 + 148*e^6 + 67*e^5 - 551*e^4 - 601*e^3 + 357*e^2 + 527*e + 95, -8*e^7 - 32*e^6 + 13*e^5 + 132*e^4 + 2*e^3 - 120*e^2 + 48*e - 35, -8*e^7 - 23*e^6 + 32*e^5 + 87*e^4 - 46*e^3 - 55*e^2 + 34*e + 13, 14*e^7 + 67*e^6 + 25*e^5 - 242*e^4 - 232*e^3 + 157*e^2 + 176*e + 43, 30*e^7 + 125*e^6 - 43*e^5 - 567*e^4 - 146*e^3 + 628*e^2 + 119*e - 30, -35*e^7 - 141*e^6 + 46*e^5 + 587*e^4 + 161*e^3 - 527*e^2 - 96*e - 55, 18*e^7 + 75*e^6 - 21*e^5 - 316*e^4 - 66*e^3 + 310*e^2 - 8*e - 30, 15*e^7 + 74*e^6 + 45*e^5 - 242*e^4 - 329*e^3 + 89*e^2 + 250*e + 48, 11*e^7 + 75*e^6 + 108*e^5 - 234*e^4 - 593*e^3 + 5*e^2 + 582*e + 160, -9*e^7 - 31*e^6 + 40*e^5 + 162*e^4 - 64*e^3 - 189*e^2 + 71*e - 46, 4*e^7 + 29*e^6 + 41*e^5 - 87*e^4 - 172*e^3 + 26*e^2 + 94*e + 41, 15*e^7 + 90*e^6 + 87*e^5 - 335*e^4 - 543*e^3 + 234*e^2 + 531*e + 65, -16*e^7 - 63*e^6 + 26*e^5 + 263*e^4 + 54*e^3 - 244*e^2 - 55*e - 3, -21*e^7 - 91*e^6 + 7*e^5 + 372*e^4 + 174*e^3 - 322*e^2 - 99*e - 14, -11*e^7 - 43*e^6 + 24*e^5 + 195*e^4 + 26*e^3 - 188*e^2 - 32*e - 13, -22*e^7 - 127*e^6 - 127*e^5 + 413*e^4 + 757*e^3 - 129*e^2 - 694*e - 157, -12*e^7 - 50*e^6 + 24*e^5 + 250*e^4 + 59*e^3 - 298*e^2 - 81*e + 4, -7*e^7 - 23*e^6 + 48*e^5 + 163*e^4 - 100*e^3 - 289*e^2 + 76*e + 88, 11*e^7 + 50*e^6 - 11*e^5 - 251*e^4 - 94*e^3 + 330*e^2 + 89*e - 76, -3*e^7 + 3*e^6 + 42*e^5 - 31*e^4 - 157*e^3 + 90*e^2 + 158*e - 8, 34*e^7 + 166*e^6 + 64*e^5 - 644*e^4 - 653*e^3 + 468*e^2 + 588*e + 81, -18*e^7 - 112*e^6 - 129*e^5 + 378*e^4 + 741*e^3 - 150*e^2 - 657*e - 117, 41*e^7 + 209*e^6 + 111*e^5 - 780*e^4 - 886*e^3 + 528*e^2 + 736*e + 129, 3*e^7 + 18*e^6 + 29*e^5 - 40*e^4 - 169*e^3 - 41*e^2 + 228*e + 64, -6*e^7 - 32*e^6 - 11*e^5 + 148*e^4 + 123*e^3 - 170*e^2 - 136*e - 28, 33*e^7 + 161*e^6 + 84*e^5 - 558*e^4 - 703*e^3 + 243*e^2 + 634*e + 148, 32*e^7 + 165*e^6 + 102*e^5 - 597*e^4 - 772*e^3 + 343*e^2 + 659*e + 120, -34*e^7 - 170*e^6 - 86*e^5 + 625*e^4 + 729*e^3 - 368*e^2 - 635*e - 115, -35*e^7 - 174*e^6 - 92*e^5 + 618*e^4 + 749*e^3 - 311*e^2 - 602*e - 151, -52*e^7 - 268*e^6 - 150*e^5 + 994*e^4 + 1157*e^3 - 656*e^2 - 964*e - 117, -19*e^7 - 107*e^6 - 98*e^5 + 367*e^4 + 618*e^3 - 167*e^2 - 513*e - 85, 28*e^7 + 155*e^6 + 114*e^5 - 574*e^4 - 765*e^3 + 371*e^2 + 639*e + 110, 28*e^7 + 108*e^6 - 62*e^5 - 502*e^4 - 76*e^3 + 594*e^2 + 91*e - 101, 38*e^7 + 157*e^6 - 35*e^5 - 661*e^4 - 276*e^3 + 634*e^2 + 263*e - 50, -8*e^7 - 25*e^6 + 37*e^5 + 116*e^4 - 85*e^3 - 158*e^2 + 71*e + 80, -37*e^7 - 157*e^6 + 5*e^5 + 604*e^4 + 352*e^3 - 451*e^2 - 267*e - 35, -2*e^7 + 8*e^6 + 69*e^5 + 13*e^4 - 280*e^3 - 107*e^2 + 306*e + 87, 5*e^7 + 33*e^6 + 30*e^5 - 141*e^4 - 162*e^3 + 186*e^2 + 125*e - 58, 24*e^7 + 84*e^6 - 85*e^5 - 401*e^4 + 92*e^3 + 481*e^2 - 119*e - 100, -31*e^7 - 154*e^6 - 64*e^5 + 582*e^4 + 562*e^3 - 383*e^2 - 396*e - 116, -34*e^7 - 196*e^6 - 185*e^5 + 667*e^4 + 1112*e^3 - 304*e^2 - 957*e - 197, -52*e^7 - 241*e^6 - 66*e^5 + 913*e^4 + 847*e^3 - 639*e^2 - 785*e - 111, -31*e^7 - 143*e^6 - 21*e^5 + 564*e^4 + 370*e^3 - 500*e^2 - 254*e + 55, 23*e^7 + 134*e^6 + 132*e^5 - 442*e^4 - 753*e^3 + 181*e^2 + 608*e + 109, -6*e^7 - 37*e^6 - 36*e^5 + 118*e^4 + 173*e^3 - 13*e^2 - 95*e - 120, -15*e^7 - 60*e^6 + 24*e^5 + 259*e^4 + 78*e^3 - 192*e^2 - 71*e - 105, -18*e^7 - 63*e^6 + 76*e^5 + 336*e^4 - 107*e^3 - 458*e^2 + 89*e + 55, -e^7 - 12*e^6 - 30*e^5 + 47*e^4 + 165*e^3 - 59*e^2 - 190*e + 36, -15*e^7 - 75*e^6 - 29*e^5 + 303*e^4 + 315*e^3 - 192*e^2 - 312*e - 129, 9*e^7 + 46*e^6 + 30*e^5 - 175*e^4 - 264*e^3 + 138*e^2 + 333*e - 5, -4*e^7 - 18*e^6 - 9*e^5 + 54*e^4 + 82*e^3 - 8*e^2 - 67*e + 56, -20*e^7 - 112*e^6 - 92*e^5 + 410*e^4 + 619*e^3 - 249*e^2 - 573*e - 83, -21*e^7 - 80*e^6 + 58*e^5 + 376*e^4 - 35*e^3 - 459*e^2 + 88*e + 115, -12*e^7 - 45*e^6 + 36*e^5 + 224*e^4 - 5*e^3 - 290*e^2 + 110, -e^7 - 3*e^6 + 10*e^5 + 10*e^4 - 59*e^3 + 15*e^2 + 110*e - 6, e^7 + 40*e^6 + 142*e^5 - 69*e^4 - 602*e^3 - 145*e^2 + 567*e + 138, -21*e^7 - 72*e^6 + 69*e^5 + 331*e^4 - 23*e^3 - 359*e^2 - 56*e + 25, -16*e^7 - 73*e^6 - 16*e^5 + 261*e^4 + 191*e^3 - 168*e^2 - 76*e - 17, -4*e^7 - e^6 + 64*e^5 + 37*e^4 - 240*e^3 - 101*e^2 + 243*e + 12, 46*e^7 + 220*e^6 + 73*e^5 - 844*e^4 - 791*e^3 + 627*e^2 + 666*e + 49, 19*e^7 + 70*e^6 - 58*e^5 - 339*e^4 + 31*e^3 + 433*e^2 - 32*e - 88, 3*e^7 + 3*e^6 - 53*e^5 - 65*e^4 + 226*e^3 + 236*e^2 - 268*e - 142, 33*e^7 + 154*e^6 + 24*e^5 - 635*e^4 - 457*e^3 + 594*e^2 + 409*e - 38, 27*e^7 + 135*e^6 + 73*e^5 - 505*e^4 - 645*e^3 + 331*e^2 + 663*e + 91, 45*e^7 + 213*e^6 + 56*e^5 - 837*e^4 - 714*e^3 + 665*e^2 + 607*e + 29, -13*e^7 - 66*e^6 - 42*e^5 + 245*e^4 + 363*e^3 - 143*e^2 - 392*e, 35*e^7 + 174*e^6 + 84*e^5 - 634*e^4 - 698*e^3 + 369*e^2 + 564*e + 122, 29*e^7 + 117*e^6 - 47*e^5 - 526*e^4 - 129*e^3 + 566*e^2 + 108*e - 12, -33*e^7 - 173*e^6 - 114*e^5 + 610*e^4 + 803*e^3 - 311*e^2 - 650*e - 140, -7*e^7 - 60*e^6 - 101*e^5 + 201*e^4 + 486*e^3 - 95*e^2 - 415*e - 43, -38*e^7 - 168*e^6 - 11*e^5 + 651*e^4 + 427*e^3 - 468*e^2 - 345*e - 138, 12*e^7 + 57*e^6 + 26*e^5 - 188*e^4 - 233*e^3 + 20*e^2 + 200*e + 104, -30*e^7 - 165*e^6 - 145*e^5 + 551*e^4 + 944*e^3 - 197*e^2 - 920*e - 188, -e^7 - 11*e^6 - 26*e^5 + 30*e^4 + 129*e^3 + 15*e^2 - 137*e - 25, -24*e^7 - 117*e^6 - 33*e^5 + 474*e^4 + 379*e^3 - 420*e^2 - 260*e + 17, 37*e^7 + 154*e^6 - 31*e^5 - 628*e^4 - 242*e^3 + 528*e^2 + 125*e + 43, -7*e^7 - 41*e^6 - 53*e^5 + 96*e^4 + 283*e^3 + 109*e^2 - 235*e - 114, -22*e^7 - 113*e^6 - 64*e^5 + 421*e^4 + 492*e^3 - 316*e^2 - 421*e - 23, -38*e^7 - 154*e^6 + 38*e^5 + 624*e^4 + 229*e^3 - 518*e^2 - 104*e - 47, 15*e^7 + 84*e^6 + 74*e^5 - 304*e^4 - 508*e^3 + 155*e^2 + 478*e + 110, 20*e^7 + 103*e^6 + 55*e^5 - 404*e^4 - 485*e^3 + 296*e^2 + 479*e + 40, 37*e^7 + 164*e^6 + 9*e^5 - 654*e^4 - 418*e^3 + 570*e^2 + 360*e, 27*e^7 + 128*e^6 + 33*e^5 - 517*e^4 - 457*e^3 + 432*e^2 + 433*e - 15, -24*e^7 - 106*e^6 - 11*e^5 + 399*e^4 + 284*e^3 - 251*e^2 - 204*e - 111, 15*e^7 + 72*e^6 + 35*e^5 - 254*e^4 - 303*e^3 + 180*e^2 + 287*e - 36, -20*e^7 - 104*e^6 - 76*e^5 + 344*e^4 + 512*e^3 - 107*e^2 - 404*e - 133];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {19, 19, -w^3 + 3*w - 1}>] := -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;