/*
  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![8, 1, -7, -1, 1];
F<w> := NumberField(g);
ZF := Integers(F);

NN := ideal<ZF | {8, 8, w}>;

primesArray := [
[2, 2, -w^2 + 2],
[2, 2, -w^3 + 2*w^2 + 4*w - 5],
[5, 5, -w^3 + 2*w^2 + 3*w - 1],
[13, 13, w^3 - 2*w^2 - 3*w + 5],
[17, 17, -w^2 - w + 3],
[19, 19, -w^3 + 3*w^2 + 2*w - 7],
[23, 23, w^3 - 2*w^2 - 3*w + 3],
[31, 31, -w^2 + w + 1],
[47, 47, -w^3 + w^2 + 4*w - 3],
[49, 7, 2*w^3 - 5*w^2 - 7*w + 11],
[53, 53, -3*w^3 + 9*w^2 + 10*w - 31],
[53, 53, w^3 - w^2 - 4*w + 1],
[61, 61, 3*w^3 - 6*w^2 - 13*w + 13],
[61, 61, 2*w^2 - 7],
[71, 71, w^2 - 3*w - 5],
[73, 73, 2*w - 3],
[73, 73, -2*w^3 + 6*w^2 + 6*w - 19],
[79, 79, 2*w^2 - 5],
[81, 3, -3],
[101, 101, 2*w^2 - 4*w - 9],
[107, 107, 2*w - 1],
[109, 109, 2*w^3 - 3*w^2 - 11*w + 7],
[109, 109, 2*w^2 - 2*w - 7],
[125, 5, -2*w^3 + 8*w^2 - 17],
[127, 127, 2*w^2 - 4*w - 7],
[127, 127, -w^2 + 3*w + 1],
[131, 131, w^3 - w^2 - 4*w - 3],
[137, 137, 4*w^3 - 10*w^2 - 14*w + 25],
[139, 139, -w^3 + 2*w^2 + w - 5],
[139, 139, 2*w^2 - 2*w - 5],
[149, 149, -w^3 + 4*w^2 - w - 7],
[149, 149, -2*w^3 + 5*w^2 + 9*w - 19],
[151, 151, -w^3 + 4*w^2 + w - 11],
[151, 151, w^2 + w + 1],
[157, 157, -2*w + 5],
[163, 163, 4*w^3 - 8*w^2 - 18*w + 19],
[163, 163, w^3 - 4*w^2 - w + 9],
[167, 167, -w^3 + 3*w^2 + 2*w - 9],
[167, 167, w^3 - 2*w^2 - 5*w + 1],
[173, 173, w^2 - 3*w - 7],
[173, 173, w^3 - 3*w^2 - 4*w + 5],
[181, 181, -w^3 + 4*w^2 + w - 13],
[191, 191, -w^3 + 2*w^2 + 3*w + 1],
[191, 191, -2*w^3 + 3*w^2 + 9*w - 3],
[193, 193, -w^3 + 4*w^2 + 3*w - 13],
[197, 197, 5*w^3 - 10*w^2 - 21*w + 21],
[211, 211, -w^3 + 3*w^2 + 4*w - 13],
[227, 227, w^3 - 4*w^2 + w + 5],
[229, 229, -w^3 + 5*w^2 - 2*w - 11],
[229, 229, -w^3 + 3*w^2 + 4*w - 3],
[239, 239, -2*w^3 + 4*w^2 + 8*w - 13],
[241, 241, 4*w^3 - 10*w^2 - 16*w + 31],
[241, 241, -5*w^3 + 12*w^2 + 21*w - 31],
[251, 251, -w^3 + 3*w^2 + 2*w - 11],
[263, 263, -2*w^3 + 2*w^2 + 10*w + 1],
[263, 263, -2*w - 5],
[269, 269, w^2 + w - 5],
[269, 269, 4*w^3 - 7*w^2 - 19*w + 15],
[271, 271, 2*w^3 - 5*w^2 - 5*w + 11],
[271, 271, -w^3 + 7*w + 3],
[277, 277, -2*w^3 + 4*w^2 + 6*w - 5],
[277, 277, 4*w^2 - 13],
[281, 281, w^3 - 5*w^2 + 11],
[307, 307, w^3 - 3*w - 3],
[313, 313, 5*w^3 - 10*w^2 - 23*w + 27],
[313, 313, -2*w^3 + 3*w^2 + 9*w - 7],
[317, 317, -3*w^3 + 6*w^2 + 11*w - 15],
[347, 347, -w^3 - w^2 + 1],
[347, 347, -2*w^3 + 6*w^2 + 6*w - 17],
[353, 353, -2*w^3 + 4*w^2 + 8*w - 5],
[353, 353, w^3 - 5*w - 1],
[359, 359, -2*w^2 + 1],
[367, 367, -w^3 + 4*w^2 + 3*w - 17],
[373, 373, 2*w^2 - 2*w - 13],
[397, 397, 5*w^3 - 13*w^2 - 18*w + 39],
[397, 397, 2*w^3 - 5*w^2 - 7*w + 9],
[401, 401, -4*w^3 + 12*w^2 + 8*w - 25],
[401, 401, -3*w^3 + 7*w^2 + 8*w - 13],
[421, 421, -4*w^3 + 11*w^2 + 13*w - 31],
[433, 433, 2*w^3 - 12*w - 15],
[433, 433, w^3 - w^2 - 6*w + 5],
[439, 439, 5*w^3 - 13*w^2 - 12*w + 19],
[439, 439, -2*w^3 + 3*w^2 + 7*w + 1],
[449, 449, -w^3 + 4*w^2 + 3*w - 11],
[461, 461, -4*w^3 + 11*w^2 + 7*w - 19],
[461, 461, -w^3 + w^2 + 2*w + 1],
[463, 463, -w^3 + 2*w^2 + 7*w - 1],
[463, 463, -4*w^3 + 11*w^2 + 7*w - 13],
[467, 467, 2*w^2 - 2*w - 3],
[467, 467, 2*w^3 - 4*w^2 - 6*w + 11],
[487, 487, -3*w^3 + 11*w^2 + 2*w - 23],
[487, 487, w^3 - w + 5],
[491, 491, w^3 - 2*w^2 - 3*w + 9],
[499, 499, w^3 - 3*w^2 - 4*w + 1],
[503, 503, -6*w^3 + 11*w^2 + 27*w - 21],
[503, 503, -3*w^3 + 8*w^2 + 5*w - 9],
[521, 521, 2*w^2 - 4*w - 11],
[541, 541, -3*w^3 + 7*w^2 + 8*w - 11],
[557, 557, 5*w^3 - 11*w^2 - 18*w + 21],
[557, 557, 4*w^3 - 7*w^2 - 17*w + 9],
[557, 557, 4*w^3 - 8*w^2 - 16*w + 15],
[557, 557, -3*w^3 + 6*w^2 + 11*w - 9],
[563, 563, -2*w^3 + 6*w^2 + 8*w - 13],
[569, 569, -2*w^3 + 3*w^2 + 7*w - 11],
[587, 587, 3*w^3 - 8*w^2 - 9*w + 15],
[601, 601, -3*w^2 + 5*w + 9],
[607, 607, -w^3 + w^2 - 5],
[619, 619, -2*w^3 + 4*w^2 + 6*w - 13],
[631, 631, -2*w^3 + 7*w^2 + 5*w - 23],
[643, 643, 2*w^3 - 2*w^2 - 12*w - 5],
[659, 659, -w^3 + 6*w^2 + 3*w - 11],
[659, 659, -3*w^2 + w + 9],
[661, 661, -2*w^3 + 4*w^2 + 8*w - 3],
[661, 661, -w^3 + 4*w^2 + 5*w - 7],
[673, 673, w^2 - w - 9],
[673, 673, 2*w^3 - 7*w^2 - 3*w + 17],
[677, 677, 9*w^3 - 20*w^2 - 37*w + 51],
[701, 701, -7*w^3 + 18*w^2 + 27*w - 57],
[709, 709, 4*w^3 - 6*w^2 - 14*w + 17],
[709, 709, w^3 + w^2 - 6*w - 17],
[719, 719, -2*w^3 + 6*w^2 + 4*w - 15],
[719, 719, -2*w^3 + 3*w^2 + 7*w + 3],
[727, 727, -w^3 + 3*w^2 + 6*w - 3],
[743, 743, -2*w^3 + 2*w^2 + 6*w - 1],
[757, 757, 6*w^3 - 16*w^2 - 22*w + 51],
[757, 757, w^3 + w^2 - 10*w - 11],
[761, 761, w^2 + w - 7],
[761, 761, 2*w^2 - 17],
[761, 761, 2*w^3 - 6*w^2 - 2*w + 13],
[761, 761, 2*w^2 - 4*w - 3],
[769, 769, -w^3 - w^2 + 4*w + 7],
[769, 769, w^3 + w^2 - 4*w - 1],
[787, 787, 3*w^3 - 6*w^2 - 11*w + 3],
[809, 809, -w^3 + 3*w^2 + 2*w - 1],
[809, 809, 2*w^3 - w^2 - 9*w - 3],
[809, 809, 2*w^3 - 7*w^2 - 3*w + 15],
[809, 809, 2*w^3 - 2*w^2 - 8*w - 1],
[811, 811, -8*w^3 + 19*w^2 + 33*w - 57],
[811, 811, -2*w^3 + 2*w^2 + 4*w - 11],
[823, 823, 2*w^3 - w^2 - 7*w + 1],
[823, 823, -3*w^3 + 8*w^2 + 7*w - 9],
[829, 829, -w^3 + 5*w - 1],
[853, 853, -w^3 + 5*w^2 - 2*w - 15],
[853, 853, -2*w^3 + 4*w^2 + 4*w - 9],
[853, 853, 2*w^3 - w^2 - 11*w - 3],
[853, 853, 2*w^3 - 5*w^2 - 7*w + 5],
[857, 857, -2*w^3 + 5*w^2 + 7*w - 7],
[859, 859, w^3 - 2*w^2 - w + 9],
[859, 859, w^3 - 2*w^2 - w - 1],
[877, 877, 2*w^3 - 6*w^2 - 8*w + 25],
[877, 877, -4*w^3 + 8*w^2 + 16*w - 19],
[881, 881, -4*w^2 + 6*w + 13],
[881, 881, w^3 + 2*w^2 - 7*w - 9],
[887, 887, -4*w^2 + 4*w + 11],
[887, 887, -w^3 - w^2 + 6*w + 11],
[887, 887, w^3 - 6*w^2 - w + 29],
[887, 887, 4*w^3 - 9*w^2 - 19*w + 31],
[907, 907, -3*w^3 + 9*w^2 + 12*w - 25],
[907, 907, -w^3 + 2*w^2 + 7*w - 7],
[929, 929, -7*w^3 + 13*w^2 + 32*w - 29],
[941, 941, -2*w^3 + 10*w^2 - 2*w - 23],
[941, 941, 4*w^3 - 9*w^2 - 13*w + 13],
[967, 967, -w^3 + 2*w^2 - w - 1],
[977, 977, w^3 - 5*w^2 + 15],
[983, 983, w^3 + 2*w^2 - 9*w - 11],
[983, 983, 2*w^3 - 5*w^2 - 5*w + 13],
[997, 997, -4*w^3 + 10*w^2 + 12*w - 23],
[1009, 1009, 2*w^2 + 2*w + 1],
[1019, 1019, 2*w^3 - 2*w^2 - 6*w + 3],
[1031, 1031, w^3 - 9*w - 7],
[1033, 1033, 2*w^3 - 2*w^2 - 8*w + 1],
[1063, 1063, -w^3 - w - 7],
[1063, 1063, 4*w^3 - 8*w^2 - 12*w + 5],
[1091, 1091, 2*w^3 - 2*w^2 - 4*w + 1],
[1093, 1093, 3*w^3 - 4*w^2 - 13*w - 1],
[1093, 1093, w^3 - w^2 - 4*w - 7],
[1097, 1097, w^3 + 3*w^2 - 2*w - 9],
[1109, 1109, w^2 + w - 9],
[1109, 1109, -2*w^3 + 5*w^2 + 3*w - 11],
[1123, 1123, -5*w^3 + 16*w^2 + 7*w - 27],
[1123, 1123, 8*w^3 - 17*w^2 - 35*w + 47],
[1163, 1163, 3*w^3 - 3*w^2 - 14*w - 5],
[1171, 1171, 2*w^3 - w^2 - 7*w - 1],
[1171, 1171, -3*w^3 + 6*w^2 + 9*w - 7],
[1181, 1181, 3*w^3 - 7*w^2 - 10*w + 21],
[1187, 1187, w^3 - 2*w^2 - 7*w + 3],
[1201, 1201, -3*w^3 + 5*w^2 + 10*w - 3],
[1201, 1201, -3*w^2 + 3*w + 19],
[1213, 1213, w^3 - 5*w^2 + 4*w + 7],
[1217, 1217, w^3 - 4*w^2 - 5*w + 5],
[1223, 1223, -w^3 - w^2 + 2*w + 5],
[1223, 1223, w^3 - 5*w^2 + 4*w + 5],
[1231, 1231, 7*w^3 - 15*w^2 - 28*w + 33],
[1237, 1237, w^3 - 5*w^2 + 2*w + 9],
[1249, 1249, -2*w^3 + 2*w^2 + 10*w - 3],
[1259, 1259, -4*w^3 + 8*w^2 + 16*w - 13],
[1283, 1283, w^3 - 2*w^2 - 3*w - 3],
[1289, 1289, -w^3 + w^2 + 4*w - 7],
[1291, 1291, 2*w^3 - 5*w^2 - 9*w + 9],
[1297, 1297, -10*w^3 + 24*w^2 + 38*w - 63],
[1301, 1301, 3*w^3 - 8*w^2 - 11*w + 17],
[1301, 1301, 2*w^2 - 4*w - 1],
[1307, 1307, w^3 - w^2 + 7],
[1327, 1327, -6*w^3 + 12*w^2 + 24*w - 31],
[1327, 1327, -w^3 + 2*w^2 - w - 5],
[1327, 1327, 8*w^3 - 16*w^2 - 34*w + 35],
[1327, 1327, 3*w^3 - 8*w^2 - 3*w + 15],
[1367, 1367, -w^3 + 2*w^2 + 7*w - 5],
[1369, 37, 7*w^3 - 17*w^2 - 18*w + 19],
[1369, 37, w^3 - 7*w^2 + 6*w + 19],
[1381, 1381, 6*w^2 - 6*w - 35],
[1427, 1427, -2*w^3 + 3*w^2 + 11*w + 1],
[1427, 1427, -2*w^3 + 7*w^2 + 7*w - 13],
[1427, 1427, 3*w^3 - 8*w^2 - 9*w + 9],
[1427, 1427, -12*w^3 + 26*w^2 + 50*w - 65],
[1433, 1433, w^3 - 7*w^2 - 4*w + 11],
[1439, 1439, -5*w^3 + 12*w^2 + 21*w - 39],
[1453, 1453, -w^3 - w^2 - 2*w - 7],
[1453, 1453, 2*w^3 - 4*w^2 - 6*w - 1],
[1459, 1459, 3*w^2 - 7*w - 15],
[1483, 1483, 4*w^3 - 15*w^2 - 9*w + 55],
[1483, 1483, w^3 - 3*w - 5],
[1493, 1493, -2*w^3 + 8*w^2 + 2*w - 23],
[1499, 1499, -w^3 + 9*w + 1],
[1499, 1499, w^3 - 4*w^2 + 3*w + 3],
[1499, 1499, 5*w^3 - 12*w^2 - 13*w + 17],
[1499, 1499, w^3 + w^2 - 8*w - 15],
[1511, 1511, -7*w^3 + 17*w^2 + 26*w - 47],
[1531, 1531, w^3 - 4*w^2 - 7*w + 13],
[1543, 1543, 4*w^3 - 7*w^2 - 21*w + 21],
[1543, 1543, 5*w^2 + 3*w - 7],
[1579, 1579, 4*w^3 - 9*w^2 - 13*w + 17],
[1583, 1583, -2*w^3 + 6*w^2 + 6*w - 23],
[1597, 1597, -4*w^3 + 11*w^2 + 13*w - 25],
[1609, 1609, 4*w^3 - 11*w^2 - 11*w + 27],
[1609, 1609, -4*w^3 + 13*w^2 + 5*w - 21],
[1637, 1637, -6*w^3 + 16*w^2 + 20*w - 45],
[1667, 1667, 5*w^2 - 3*w - 13],
[1667, 1667, -5*w^2 - w + 11],
[1697, 1697, -w^3 + 3*w^2 + 8*w + 1],
[1699, 1699, -w^3 + 4*w^2 - w - 13],
[1699, 1699, 5*w^3 - 14*w^2 - 9*w + 25],
[1721, 1721, 2*w^3 - 7*w^2 - w + 17],
[1723, 1723, -3*w^3 + 6*w^2 + 9*w - 11],
[1733, 1733, w^3 - w^2 - 8*w + 3],
[1747, 1747, w^3 - 2*w^2 - 7*w - 5],
[1753, 1753, -w^3 + 3*w^2 - 11],
[1759, 1759, -w^3 + 6*w^2 - w - 15],
[1759, 1759, -4*w^3 + 8*w^2 + 14*w - 19],
[1783, 1783, 3*w^3 - 6*w^2 - 7*w + 13],
[1783, 1783, -5*w^2 - 3*w + 13],
[1787, 1787, -2*w^3 + 7*w^2 + 5*w - 21],
[1787, 1787, w^2 - 3*w - 11],
[1787, 1787, -2*w - 7],
[1787, 1787, -w^3 + 3*w^2 + 4*w - 15],
[1789, 1789, w^3 - w^2 - 8*w - 1],
[1789, 1789, -4*w^2 + 8*w + 13],
[1801, 1801, -3*w^3 + 9*w^2 + 6*w - 11],
[1823, 1823, -2*w^3 + 5*w^2 + 5*w - 15],
[1831, 1831, 3*w^3 - 5*w^2 - 12*w + 9],
[1831, 1831, 3*w^3 - 3*w^2 - 18*w + 1],
[1831, 1831, w^3 - 5*w^2 - 2*w + 5],
[1831, 1831, w^3 - 5*w^2 - 2*w + 13],
[1847, 1847, 2*w^3 - 2*w^2 - 8*w - 9],
[1847, 1847, -3*w^3 + 5*w^2 + 14*w - 17],
[1849, 43, 3*w^3 - 3*w^2 - 12*w + 5],
[1849, 43, 3*w^3 - 2*w^2 - 19*w - 5],
[1861, 1861, 4*w^3 - 13*w^2 - 5*w + 27],
[1867, 1867, w^3 + 2*w^2 - 5*w - 5],
[1871, 1871, -w^3 + 5*w^2 + 2*w - 15],
[1871, 1871, 2*w^3 - w^2 - 15*w + 1],
[1873, 1873, w^3 - 7*w - 11],
[1873, 1873, -4*w^3 + 9*w^2 + 11*w - 17],
[1877, 1877, -4*w - 1],
[1877, 1877, 4*w + 9],
[1889, 1889, -3*w^3 + 7*w^2 + 6*w - 7],
[1901, 1901, 2*w^3 - 8*w^2 - 2*w + 17],
[1901, 1901, -3*w^2 + 7*w + 7],
[1913, 1913, 4*w^3 - 14*w^2 - 2*w + 27],
[1931, 1931, w^2 + 3*w - 7],
[1931, 1931, 3*w^3 - 3*w^2 - 12*w - 5],
[1933, 1933, -2*w^3 + 7*w^2 + 7*w - 17],
[1951, 1951, -2*w^3 + 6*w^2 + 4*w - 17],
[1951, 1951, -5*w^3 + 13*w^2 + 20*w - 43],
[1973, 1973, -2*w^3 + 9*w^2 - w - 19],
[1979, 1979, -4*w^3 + 10*w^2 + 18*w - 37],
[1979, 1979, -2*w^3 + 6*w^2 + 8*w - 11],
[1987, 1987, -w^3 + 3*w^2 + 6*w - 13],
[1997, 1997, -4*w^3 + 11*w^2 + 13*w - 29],
[1997, 1997, 4*w - 1],
[1997, 1997, 9*w^3 - 23*w^2 - 22*w + 35],
[1997, 1997, -6*w^3 + 18*w^2 + 8*w - 31],
[1999, 1999, 6*w^3 - 19*w^2 - 9*w + 37]];
primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x^10 - 36*x^8 + 400*x^6 - 1648*x^4 + 2048*x^2 - 512;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [0, -1/176*e^8 + 31/176*e^6 - 16/11*e^4 + 79/22*e^2 - 13/11, e, 9/704*e^9 - 39/88*e^7 + 199/44*e^5 - 669/44*e^3 + 98/11*e, 3/704*e^9 - 13/88*e^7 + 35/22*e^5 - 311/44*e^3 + 128/11*e, 3/176*e^9 - 13/22*e^7 + 269/44*e^5 - 245/11*e^3 + 226/11*e, 1/176*e^8 - 21/88*e^6 + 141/44*e^4 - 155/11*e^2 + 112/11, 7/704*e^9 - 17/44*e^7 + 211/44*e^5 - 953/44*e^3 + 273/11*e, 5/704*e^9 - 9/44*e^7 + 29/22*e^5 - 27/44*e^3 - 47/11*e, -e, -1/176*e^8 + 21/88*e^6 - 141/44*e^4 + 166/11*e^2 - 134/11, 2, -1/2*e^3 + 7*e, -7/704*e^9 + 17/44*e^7 - 211/44*e^5 + 953/44*e^3 - 240/11*e, 3/176*e^8 - 41/88*e^6 + 115/44*e^4 - 3/11*e^2 - 16/11, 15/704*e^9 - 65/88*e^7 + 339/44*e^5 - 1313/44*e^3 + 398/11*e, 5/704*e^9 - 9/44*e^7 + 29/22*e^5 - 5/44*e^3 - 124/11*e, 1/88*e^8 - 31/88*e^6 + 117/44*e^4 - 24/11*e^2 - 40/11, -1/44*e^8 + 31/44*e^6 - 64/11*e^4 + 158/11*e^2 - 30/11, -3/704*e^9 + 13/88*e^7 - 35/22*e^5 + 311/44*e^3 - 128/11*e, -1/88*e^8 + 21/44*e^6 - 141/22*e^4 + 321/11*e^2 - 268/11, -3/88*e^8 + 93/88*e^6 - 373/44*e^4 + 193/11*e^2 + 10/11, 3/176*e^8 - 41/88*e^6 + 115/44*e^4 - 14/11*e^2 + 50/11, 3/704*e^9 - 13/88*e^7 + 35/22*e^5 - 333/44*e^3 + 172/11*e, 3/176*e^8 - 13/22*e^6 + 70/11*e^4 - 289/11*e^2 + 248/11, -5/176*e^8 + 83/88*e^6 - 397/44*e^4 + 313/11*e^2 - 208/11, -9/352*e^9 + 39/44*e^7 - 199/22*e^5 + 669/22*e^3 - 196/11*e, -1/88*e^8 + 31/88*e^6 - 117/44*e^4 + 24/11*e^2 + 194/11, -1/176*e^9 + 21/88*e^7 - 141/44*e^5 + 155/11*e^3 - 90/11*e, -9/352*e^9 + 39/44*e^7 - 199/22*e^5 + 669/22*e^3 - 240/11*e, -5/176*e^8 + 47/44*e^6 - 135/11*e^4 + 500/11*e^2 - 318/11, -1/176*e^8 + 21/88*e^6 - 141/44*e^4 + 166/11*e^2 - 134/11, -5/176*e^8 + 83/88*e^6 - 397/44*e^4 + 335/11*e^2 - 296/11, -1/22*e^8 + 135/88*e^6 - 655/44*e^4 + 514/11*e^2 - 280/11, 15/704*e^9 - 65/88*e^7 + 339/44*e^5 - 1269/44*e^3 + 244/11*e, -1/88*e^8 + 5/22*e^6 + 13/22*e^4 - 163/11*e^2 + 172/11, 5/176*e^8 - 83/88*e^6 + 397/44*e^4 - 335/11*e^2 + 340/11, -9/704*e^9 + 39/88*e^7 - 199/44*e^5 + 647/44*e^3 + 1/11*e, -3/64*e^9 + 13/8*e^7 - 67/4*e^5 + 237/4*e^3 - 39*e, 1/22*e^9 - 73/44*e^7 + 205/11*e^5 - 811/11*e^3 + 687/11*e, 9/176*e^9 - 39/22*e^7 + 807/44*e^5 - 735/11*e^3 + 623/11*e, 1/176*e^9 - 21/88*e^7 + 141/44*e^5 - 321/22*e^3 + 145/11*e, 1/176*e^8 - 5/44*e^6 - 1/22*e^4 + 10/11*e^2 + 200/11, 5/176*e^8 - 9/11*e^6 + 58/11*e^4 - 27/11*e^2 - 232/11, -1/88*e^8 + 31/88*e^6 - 117/44*e^4 + 24/11*e^2 + 106/11, -1/176*e^8 - 1/88*e^6 + 167/44*e^4 - 329/11*e^2 + 350/11, -3/176*e^8 + 63/88*e^6 - 423/44*e^4 + 465/11*e^2 - 204/11, 3/64*e^9 - 7/4*e^7 + 81/4*e^5 - 325/4*e^3 + 65*e, -3/64*e^9 + 13/8*e^7 - 67/4*e^5 + 239/4*e^3 - 48*e, -21/704*e^9 + 91/88*e^7 - 117/11*e^5 + 1671/44*e^3 - 412/11*e, -1/88*e^8 + 21/44*e^6 - 141/22*e^4 + 321/11*e^2 - 312/11, -49/704*e^9 + 27/11*e^7 - 1147/44*e^5 + 4251/44*e^3 - 888/11*e, 5/352*e^9 - 9/22*e^7 + 29/11*e^5 - 8/11*e^3 - 171/11*e, -1/704*e^9 + 1/11*e^7 - 41/22*e^5 + 595/44*e^3 - 303/11*e, 3/88*e^8 - 93/88*e^6 + 395/44*e^4 - 292/11*e^2 + 232/11, 3/88*e^8 - 13/11*e^6 + 269/22*e^4 - 501/11*e^2 + 408/11, -25/704*e^9 + 14/11*e^7 - 609/44*e^5 + 2269/44*e^3 - 370/11*e, -1/176*e^9 + 5/44*e^7 + 6/11*e^5 - 295/22*e^3 + 405/11*e, 37/704*e^9 - 41/22*e^7 + 439/22*e^5 - 3271/44*e^3 + 673/11*e, -31/704*e^9 + 69/44*e^7 - 749/44*e^5 + 2913/44*e^3 - 747/11*e, -9/176*e^8 + 145/88*e^6 - 653/44*e^4 + 504/11*e^2 - 414/11, -5/88*e^8 + 177/88*e^6 - 937/44*e^4 + 824/11*e^2 - 482/11, 5/176*e^8 - 47/44*e^6 + 135/11*e^4 - 500/11*e^2 + 362/11, -9/704*e^9 + 39/88*e^7 - 105/22*e^5 + 955/44*e^3 - 417/11*e, 15/352*e^9 - 65/44*e^7 + 667/44*e^5 - 1181/22*e^3 + 587/11*e, 25/704*e^9 - 14/11*e^7 + 609/44*e^5 - 2269/44*e^3 + 414/11*e, 1/44*e^8 - 73/88*e^6 + 399/44*e^4 - 356/11*e^2 + 294/11, -3/176*e^8 + 41/88*e^6 - 93/44*e^4 - 129/11*e^2 + 412/11, 7/176*e^8 - 125/88*e^6 + 679/44*e^4 - 645/11*e^2 + 564/11, -1/22*e^9 + 73/44*e^7 - 205/11*e^5 + 1633/22*e^3 - 797/11*e, 1/352*e^9 + 3/44*e^7 - 177/44*e^5 + 769/22*e^3 - 813/11*e, -13/176*e^8 + 49/22*e^6 - 186/11*e^4 + 365/11*e^2 - 48/11, -13/352*e^9 + 15/11*e^7 - 691/44*e^5 + 1465/22*e^3 - 882/11*e, 17/176*e^8 - 35/11*e^6 + 327/11*e^4 - 1018/11*e^2 + 694/11, 7/352*e^9 - 17/22*e^7 + 411/44*e^5 - 821/22*e^3 + 293/11*e, -47/704*e^9 + 25/11*e^7 - 1005/44*e^5 + 3589/44*e^3 - 876/11*e, 5/176*e^8 - 83/88*e^6 + 375/44*e^4 - 214/11*e^2 - 122/11, 9/176*e^8 - 39/22*e^6 + 199/11*e^4 - 680/11*e^2 + 370/11, 1/176*e^8 - 5/44*e^6 - 6/11*e^4 + 142/11*e^2 - 218/11, 19/704*e^9 - 43/44*e^7 + 469/44*e^5 - 1669/44*e^3 + 268/11*e, 17/352*e^9 - 151/88*e^7 + 819/44*e^5 - 806/11*e^3 + 809/11*e, -29/704*e^9 + 133/88*e^7 - 761/44*e^5 + 3219/44*e^3 - 911/11*e, 17/352*e^9 - 151/88*e^7 + 819/44*e^5 - 1601/22*e^3 + 754/11*e, 1/176*e^8 - 21/88*e^6 + 119/44*e^4 - 45/11*e^2 - 174/11, -29/704*e^9 + 61/44*e^7 - 607/44*e^5 + 2295/44*e^3 - 834/11*e, -15/176*e^9 + 65/22*e^7 - 667/22*e^5 + 2307/22*e^3 - 811/11*e, -7/88*e^8 + 57/22*e^6 - 525/22*e^4 + 795/11*e^2 - 512/11, 1/176*e^8 - 21/88*e^6 + 141/44*e^4 - 155/11*e^2 + 200/11, 13/176*e^9 - 109/44*e^7 + 263/11*e^5 - 838/11*e^3 + 554/11*e, -17/352*e^9 + 151/88*e^7 - 819/44*e^5 + 1623/22*e^3 - 908/11*e, -7/176*e^8 + 57/44*e^6 - 257/22*e^4 + 326/11*e^2 + 184/11, -1/176*e^8 + 5/44*e^6 + 6/11*e^4 - 109/11*e^2 + 64/11, -5/176*e^8 + 9/11*e^6 - 127/22*e^4 + 148/11*e^2 - 164/11, -1/44*e^8 + 73/88*e^6 - 421/44*e^4 + 444/11*e^2 - 228/11, -15/704*e^9 + 65/88*e^7 - 82/11*e^5 + 1005/44*e^3 + 31/11*e, -37/704*e^9 + 41/22*e^7 - 867/44*e^5 + 3007/44*e^3 - 365/11*e, 3/88*e^9 - 93/88*e^7 + 373/44*e^5 - 353/22*e^3 - 197/11*e, 1/88*e^8 - 5/22*e^6 - 12/11*e^4 + 251/11*e^2 - 414/11, 3/176*e^8 - 13/22*e^6 + 59/11*e^4 - 69/11*e^2 - 258/11, 1/44*e^8 - 31/44*e^6 + 64/11*e^4 - 136/11*e^2 - 146/11, 1/88*e^8 - 9/88*e^6 - 169/44*e^4 + 339/11*e^2 - 62/11, -1/22*e^8 + 135/88*e^6 - 633/44*e^4 + 371/11*e^2 + 226/11, 5/704*e^9 - 9/44*e^7 + 69/44*e^5 - 291/44*e^3 + 261/11*e, -1/176*e^8 + 21/88*e^6 - 141/44*e^4 + 166/11*e^2 - 90/11, 3/176*e^9 - 63/88*e^7 + 423/44*e^5 - 476/11*e^3 + 402/11*e, 7/88*e^9 - 239/88*e^7 + 1193/44*e^5 - 1997/22*e^3 + 787/11*e, -15/352*e^9 + 65/44*e^7 - 164/11*e^5 + 1027/22*e^3 - 114/11*e, -37/352*e^9 + 41/11*e^7 - 439/11*e^5 + 3271/22*e^3 - 1412/11*e, -1/176*e^8 + 5/44*e^6 + 1/22*e^4 - 54/11*e^2 + 416/11, 45/704*e^9 - 195/88*e^7 + 503/22*e^5 - 3631/44*e^3 + 897/11*e, -13/88*e^8 + 425/88*e^6 - 1939/44*e^4 + 1390/11*e^2 - 668/11, 5/88*e^8 - 83/44*e^6 + 397/22*e^4 - 659/11*e^2 + 548/11, 9/176*e^9 - 39/22*e^7 + 199/11*e^5 - 1327/22*e^3 + 337/11*e, 3/352*e^9 - 15/88*e^7 - 25/44*e^5 + 136/11*e^3 - 85/11*e, -1/44*e^8 + 51/88*e^6 - 113/44*e^4 - 40/11*e^2 + 234/11, -1/88*e^8 + 5/22*e^6 + 12/11*e^4 - 262/11*e^2 + 238/11, -35/704*e^9 + 37/22*e^7 - 725/44*e^5 + 2367/44*e^3 - 408/11*e, -1/22*e^8 + 31/22*e^6 - 128/11*e^4 + 349/11*e^2 - 214/11, 1/22*e^8 - 135/88*e^6 + 655/44*e^4 - 536/11*e^2 + 654/11, -19/176*e^8 + 311/88*e^6 - 1425/44*e^4 + 1053/11*e^2 - 698/11, -3/352*e^9 + 37/88*e^7 - 305/44*e^5 + 927/22*e^3 - 806/11*e, -35/704*e^9 + 159/88*e^7 - 445/22*e^5 + 3577/44*e^3 - 1013/11*e, -31/704*e^9 + 127/88*e^7 - 595/44*e^5 + 1945/44*e^3 - 505/11*e, -5/44*e^8 + 343/88*e^6 - 1731/44*e^4 + 1450/11*e^2 - 832/11, 3/176*e^8 - 15/44*e^6 - 7/11*e^4 + 184/11*e^2 - 214/11, 13/176*e^8 - 229/88*e^6 + 1195/44*e^4 - 1036/11*e^2 + 730/11, -5/176*e^9 + 83/88*e^7 - 397/44*e^5 + 659/22*e^3 - 329/11*e, -47/704*e^9 + 25/11*e^7 - 497/22*e^5 + 3325/44*e^3 - 634/11*e, 43/704*e^9 - 95/44*e^7 + 509/22*e^5 - 3915/44*e^3 + 1050/11*e, -15/176*e^9 + 65/22*e^7 - 339/11*e^5 + 1291/11*e^3 - 1383/11*e, -43/704*e^9 + 179/88*e^7 - 853/44*e^5 + 2639/44*e^3 - 280/11*e, -1/22*e^9 + 73/44*e^7 - 205/11*e^5 + 1633/22*e^3 - 709/11*e, -1/352*e^9 + 27/88*e^7 - 307/44*e^5 + 947/22*e^3 - 540/11*e, -9/176*e^8 + 167/88*e^6 - 961/44*e^4 + 944/11*e^2 - 634/11, -9/88*e^8 + 39/11*e^6 - 398/11*e^4 + 1360/11*e^2 - 982/11, -1/88*e^8 + 5/22*e^6 + 1/11*e^4 - 53/11*e^2 - 202/11, 1/8*e^8 - 33/8*e^6 + 153/4*e^4 - 110*e^2 + 46, 15/704*e^9 - 19/22*e^7 + 126/11*e^5 - 2545/44*e^3 + 937/11*e, 83/704*e^9 - 367/88*e^7 + 1955/44*e^5 - 7233/44*e^3 + 1521/11*e, 1/11*e^8 - 135/44*e^6 + 655/22*e^4 - 1061/11*e^2 + 824/11, 17/176*e^8 - 35/11*e^6 + 643/22*e^4 - 864/11*e^2 + 144/11, -7/64*e^9 + 31/8*e^7 - 165/4*e^5 + 605/4*e^3 - 132*e, 15/352*e^9 - 65/44*e^7 + 339/22*e^5 - 1313/22*e^3 + 785/11*e, -83/704*e^9 + 345/88*e^7 - 409/11*e^5 + 5055/44*e^3 - 696/11*e, -3/176*e^9 + 41/88*e^7 - 115/44*e^5 + 17/22*e^3 - 39/11*e, -1/176*e^9 + 5/44*e^7 + 13/44*e^5 - 76/11*e^3 + 31/11*e, -35/704*e^9 + 37/22*e^7 - 184/11*e^5 + 2565/44*e^3 - 474/11*e, -7/64*e^9 + 31/8*e^7 - 83/2*e^5 + 617/4*e^3 - 115*e, -1/32*e^9 + e^7 - 35/4*e^5 + 45/2*e^3 - 4*e, -1/22*e^8 + 31/22*e^6 - 128/11*e^4 + 305/11*e^2 - 38/11, -1/22*e^8 + 113/88*e^6 - 325/44*e^4 - 58/11*e^2 + 358/11, 31/704*e^9 - 69/44*e^7 + 190/11*e^5 - 3177/44*e^3 + 868/11*e, 5/64*e^9 - 23/8*e^7 + 131/4*e^5 - 527/4*e^3 + 110*e, 3/704*e^9 - 3/11*e^7 + 213/44*e^5 - 949/44*e^3 - 81/11*e, -23/352*e^9 + 203/88*e^7 - 1099/44*e^5 + 2245/22*e^3 - 1398/11*e, 37/352*e^9 - 153/44*e^7 + 1437/44*e^5 - 2193/22*e^3 + 642/11*e, 71/704*e^9 - 163/44*e^7 + 460/11*e^5 - 7177/44*e^3 + 1339/11*e, 1/176*e^8 + 3/22*e^6 - 83/11*e^4 + 615/11*e^2 - 636/11, -13/176*e^8 + 49/22*e^6 - 383/22*e^4 + 508/11*e^2 - 620/11, 27/704*e^9 - 117/88*e^7 + 597/44*e^5 - 2007/44*e^3 + 206/11*e, -23/352*e^9 + 24/11*e^7 - 228/11*e^5 + 1343/22*e^3 - 155/11*e, 49/704*e^9 - 205/88*e^7 + 491/22*e^5 - 2975/44*e^3 + 206/11*e, -7/176*e^8 + 57/44*e^6 - 134/11*e^4 + 469/11*e^2 - 344/11, -1/11*e^8 + 135/44*e^6 - 322/11*e^4 + 907/11*e^2 - 318/11, 1/44*e^9 - 31/44*e^7 + 267/44*e^5 - 246/11*e^3 + 536/11*e, 35/704*e^9 - 37/22*e^7 + 725/44*e^5 - 2389/44*e^3 + 507/11*e, -107/704*e^9 + 115/22*e^7 - 2339/44*e^5 + 8159/44*e^3 - 1500/11*e, -7/44*e^8 + 57/11*e^6 - 514/11*e^4 + 1392/11*e^2 - 474/11, 1/44*e^8 - 51/88*e^6 + 113/44*e^4 - 4/11*e^2 + 140/11, 3/88*e^8 - 41/44*e^6 + 52/11*e^4 + 126/11*e^2 - 560/11, -1/44*e^8 + 51/88*e^6 - 113/44*e^4 - 18/11*e^2 - 118/11, 25/704*e^9 - 101/88*e^7 + 233/22*e^5 - 1587/44*e^3 + 491/11*e, 9/704*e^9 - 39/88*e^7 + 221/44*e^5 - 1219/44*e^3 + 659/11*e, 23/352*e^9 - 107/44*e^7 + 1231/44*e^5 - 2443/22*e^3 + 980/11*e, 19/176*e^8 - 311/88*e^6 + 1403/44*e^4 - 888/11*e^2 + 170/11, 23/176*e^8 - 373/88*e^6 + 1703/44*e^4 - 1310/11*e^2 + 970/11, 1/32*e^9 - 9/8*e^7 + 47/4*e^5 - 33*e^3 - 21*e, -3/176*e^9 + 41/88*e^7 - 93/44*e^5 - 247/22*e^3 + 621/11*e, -1/22*e^9 + 73/44*e^7 - 809/44*e^5 + 734/11*e^3 - 181/11*e, 1/176*e^9 - 4/11*e^7 + 153/22*e^5 - 474/11*e^3 + 838/11*e, -21/704*e^9 + 51/44*e^7 - 611/44*e^5 + 2287/44*e^3 - 49/11*e, 15/176*e^8 - 65/22*e^6 + 328/11*e^4 - 1027/11*e^2 + 316/11, -15/88*e^8 + 249/44*e^6 - 590/11*e^4 + 1856/11*e^2 - 1116/11, 5/44*e^8 - 321/88*e^6 + 1423/44*e^4 - 1010/11*e^2 + 436/11, 47/704*e^9 - 25/11*e^7 + 497/22*e^5 - 3281/44*e^3 + 458/11*e, -1/176*e^8 + 4/11*e^6 - 131/22*e^4 + 166/11*e^2 + 460/11, 1/44*e^8 - 5/11*e^6 - 13/11*e^4 + 315/11*e^2 - 366/11, -2/11*e^8 + 529/88*e^6 - 2477/44*e^4 + 1880/11*e^2 - 1318/11, 1/44*e^8 - 73/88*e^6 + 399/44*e^4 - 334/11*e^2 + 294/11, -9/352*e^9 + 67/88*e^7 - 255/44*e^5 + 164/11*e^3 - 251/11*e, 9/704*e^9 - 25/44*e^7 + 353/44*e^5 - 1571/44*e^3 + 175/11*e, 5/352*e^9 - 47/88*e^7 + 259/44*e^5 - 379/22*e^3 - 138/11*e, -3/352*e^9 + 13/44*e^7 - 129/44*e^5 + 179/22*e^3 - 14/11*e, -61/704*e^9 + 123/44*e^7 - 1097/44*e^5 + 3009/44*e^3 - 278/11*e, -37/704*e^9 + 41/22*e^7 - 867/44*e^5 + 2963/44*e^3 - 376/11*e, 87/704*e^9 - 183/44*e^7 + 1777/44*e^5 - 5697/44*e^3 + 819/11*e, -13/88*e^8 + 109/22*e^6 - 1041/22*e^4 + 1577/11*e^2 - 668/11, -17/176*e^8 + 269/88*e^6 - 1165/44*e^4 + 809/11*e^2 - 518/11, 3/44*e^9 - 26/11*e^7 + 1087/44*e^5 - 1035/11*e^3 + 970/11*e, 13/176*e^8 - 251/88*e^6 + 1503/44*e^4 - 1454/11*e^2 + 862/11, -29/352*e^9 + 255/88*e^7 - 1357/44*e^5 + 1307/11*e^3 - 1525/11*e, 21/704*e^9 - 91/88*e^7 + 245/22*e^5 - 2199/44*e^3 + 830/11*e, -25/352*e^9 + 28/11*e^7 - 310/11*e^5 + 2555/22*e^3 - 1400/11*e, 1/44*e^8 - 51/88*e^6 + 69/44*e^4 + 216/11*e^2 - 80/11, 7/176*e^8 - 57/44*e^6 + 123/11*e^4 - 271/11*e^2 + 80/11, 1/44*e^8 - 73/88*e^6 + 399/44*e^4 - 312/11*e^2 + 96/11, -1/8*e^8 + 17/4*e^6 - 41*e^4 + 118*e^2 - 56, 25/176*e^8 - 101/22*e^6 + 455/11*e^4 - 1279/11*e^2 + 424/11, 7/88*e^8 - 195/88*e^6 + 555/44*e^4 + 52/11*e^2 - 654/11, 3/8*e^6 - 39/4*e^4 + 50*e^2 - 10, -15/176*e^8 + 119/44*e^6 - 251/11*e^4 + 609/11*e^2 - 470/11, -7/352*e^9 + 23/44*e^7 - 125/44*e^5 + 183/22*e^3 - 700/11*e, 51/704*e^9 - 221/88*e^7 + 281/11*e^5 - 3681/44*e^3 + 559/11*e, 67/704*e^9 - 283/88*e^7 + 1369/44*e^5 - 4093/44*e^3 + 237/11*e, 43/704*e^9 - 179/88*e^7 + 831/44*e^5 - 2133/44*e^3 - 83/11*e, 103/704*e^9 - 461/88*e^7 + 2517/44*e^5 - 9717/44*e^3 + 2026/11*e, 13/88*e^8 - 207/44*e^6 + 449/11*e^4 - 1214/11*e^2 + 800/11, -1/176*e^8 + 21/88*e^6 - 185/44*e^4 + 353/11*e^2 - 178/11, -1/88*e^8 + 21/44*e^6 - 76/11*e^4 + 398/11*e^2 - 290/11, -75/704*e^9 + 325/88*e^7 - 1673/44*e^5 + 5905/44*e^3 - 1143/11*e, 5/704*e^9 - 29/88*e^7 + 53/11*e^5 - 995/44*e^3 + 173/11*e, 9/176*e^9 - 89/44*e^7 + 276/11*e^5 - 1120/11*e^3 + 590/11*e, 3/88*e^8 - 93/88*e^6 + 351/44*e^4 - 28/11*e^2 - 626/11, -9/176*e^8 + 89/44*e^6 - 276/11*e^4 + 1131/11*e^2 - 876/11, 3/22*e^8 - 52/11*e^6 + 1065/22*e^4 - 1817/11*e^2 + 1148/11, -7/88*e^8 + 261/88*e^6 - 1501/44*e^4 + 1444/11*e^2 - 820/11, 5/88*e^8 - 177/88*e^6 + 915/44*e^4 - 714/11*e^2 + 284/11, -39/704*e^9 + 191/88*e^7 - 1207/44*e^5 + 5693/44*e^3 - 1829/11*e, 1/704*e^9 - 19/88*e^7 + 225/44*e^5 - 1299/44*e^3 + 369/11*e, 1/176*e^9 - 4/11*e^7 + 153/22*e^5 - 474/11*e^3 + 860/11*e, 7/704*e^9 - 7/11*e^7 + 541/44*e^5 - 3461/44*e^3 + 1483/11*e, -1/176*e^8 + 4/11*e^6 - 153/22*e^4 + 474/11*e^2 - 596/11, 1/88*e^8 - 5/22*e^6 - 12/11*e^4 + 262/11*e^2 - 656/11, 13/176*e^8 - 87/44*e^6 + 109/11*e^4 + 86/11*e^2 - 18/11, 1/704*e^9 + 7/44*e^7 - 62/11*e^5 + 1913/44*e^3 - 874/11*e, 39/704*e^9 - 79/44*e^7 + 345/22*e^5 - 1491/44*e^3 - 250/11*e, -25/176*e^9 + 213/44*e^7 - 532/11*e^5 + 3625/22*e^3 - 1315/11*e, -13/88*e^8 + 109/22*e^6 - 526/11*e^4 + 1698/11*e^2 - 1196/11, -1/16*e^8 + 2*e^6 - 17*e^4 + 37*e^2 - 36, -31/176*e^9 + 265/44*e^7 - 2655/44*e^5 + 2242/11*e^3 - 1459/11*e, 1/704*e^9 - 1/11*e^7 + 15/11*e^5 - 23/44*e^3 - 445/11*e, 71/704*e^9 - 315/88*e^7 + 427/11*e^5 - 6693/44*e^3 + 1515/11*e, 1/64*e^9 - 3/8*e^7 + e^5 + 21/4*e^3 + 18*e, 1/8*e^8 - 35/8*e^6 + 179/4*e^4 - 142*e^2 + 60, 3/176*e^8 - 19/88*e^6 - 193/44*e^4 + 448/11*e^2 - 214/11, 39/176*e^8 - 79/11*e^6 + 712/11*e^4 - 2019/11*e^2 + 980/11, -65/704*e^9 + 75/22*e^7 - 1711/44*e^5 + 6819/44*e^3 - 1424/11*e, -1/44*e^8 + 95/88*e^6 - 729/44*e^4 + 906/11*e^2 - 536/11, -1/44*e^8 + 51/88*e^6 - 113/44*e^4 - 18/11*e^2 - 184/11, -1/704*e^9 + 15/44*e^7 - 103/11*e^5 + 3059/44*e^3 - 1381/11*e, -13/176*e^9 + 109/44*e^7 - 515/22*e^5 + 706/11*e^3 - 48/11*e, -3/44*e^8 + 93/44*e^6 - 192/11*e^4 + 496/11*e^2 + 20/11, 25/176*e^8 - 415/88*e^6 + 1919/44*e^4 - 1257/11*e^2 + 204/11, -5/88*e^8 + 83/44*e^6 - 193/11*e^4 + 538/11*e^2 - 460/11, -1/44*e^8 + 73/88*e^6 - 421/44*e^4 + 488/11*e^2 - 844/11, 21/176*e^8 - 353/88*e^6 + 1707/44*e^4 - 1341/11*e^2 + 438/11, 14, 19/176*e^8 - 311/88*e^6 + 1403/44*e^4 - 855/11*e^2 + 82/11, -1/22*e^9 + 31/22*e^7 - 245/22*e^5 + 217/11*e^3 + 116/11*e, 25/176*e^8 - 101/22*e^6 + 921/22*e^4 - 1444/11*e^2 + 1128/11, -15/176*e^8 + 271/88*e^6 - 1477/44*e^4 + 1313/11*e^2 - 448/11, 1/16*e^8 - 15/8*e^6 + 55/4*e^4 - 21*e^2 + 8, -13/176*e^8 + 109/44*e^6 - 537/22*e^4 + 904/11*e^2 - 224/11, -7/88*e^9 + 125/44*e^7 - 1347/44*e^5 + 1235/11*e^3 - 908/11*e, -47/352*e^9 + 389/88*e^7 - 1845/44*e^5 + 2973/22*e^3 - 1202/11*e, 1/16*e^8 - 9/4*e^6 + 25*e^4 - 100*e^2 + 74, -3/44*e^8 + 41/22*e^6 - 115/11*e^4 + 34/11*e^2 - 398/11, -13/704*e^9 + 19/44*e^7 - 5/22*e^5 - 1197/44*e^3 + 978/11*e, -23/704*e^9 + 59/44*e^7 - 393/22*e^5 + 3785/44*e^3 - 1117/11*e, 1/11*e^8 - 135/44*e^6 + 655/22*e^4 - 973/11*e^2 + 384/11, 37/176*e^8 - 645/88*e^6 + 3303/44*e^4 - 2743/11*e^2 + 1680/11, 1/44*e^8 - 5/11*e^6 - 13/11*e^4 + 348/11*e^2 - 762/11, 1/11*e^8 - 31/11*e^6 + 256/11*e^4 - 698/11*e^2 + 626/11, 31/176*e^8 - 265/44*e^6 + 661/11*e^4 - 2132/11*e^2 + 1338/11, 7/88*e^8 - 103/44*e^6 + 180/11*e^4 - 146/11*e^2 - 786/11, 23/704*e^9 - 107/88*e^7 + 599/44*e^5 - 2003/44*e^3 - 214/11*e, -7/176*e^8 + 103/88*e^6 - 349/44*e^4 + 18/11*e^2 + 866/11, 3/8*e^6 - 39/4*e^4 + 44*e^2 + 18, 7/44*e^8 - 57/11*e^6 + 514/11*e^4 - 1403/11*e^2 + 254/11, -7/704*e^9 + 17/44*e^7 - 111/22*e^5 + 1349/44*e^3 - 1021/11*e, 27/352*e^9 - 267/88*e^7 + 1689/44*e^5 - 3811/22*e^3 + 1952/11*e, -13/88*e^8 + 109/22*e^6 - 526/11*e^4 + 1654/11*e^2 - 690/11, 1/32*e^9 - 9/8*e^7 + 47/4*e^5 - 65/2*e^3 - 30*e, -81/704*e^9 + 351/88*e^7 - 445/11*e^5 + 5735/44*e^3 - 563/11*e, -15/352*e^9 + 19/11*e^7 - 252/11*e^5 + 1256/11*e^3 - 1797/11*e, -27/352*e^9 + 117/44*e^7 - 1227/44*e^5 + 2403/22*e^3 - 1380/11*e, -5/64*e^9 + 23/8*e^7 - 33*e^5 + 559/4*e^3 - 157*e, -15/176*e^9 + 271/88*e^7 - 1499/44*e^5 + 1478/11*e^3 - 1702/11*e, 5/176*e^8 - 25/44*e^6 - 8/11*e^4 + 182/11*e^2 + 406/11, 1/16*e^8 - 9/4*e^6 + 25*e^4 - 96*e^2 + 38, -17/88*e^8 + 269/44*e^6 - 566/11*e^4 + 1310/11*e^2 - 178/11, -1/22*e^8 + 21/11*e^6 - 271/11*e^4 + 1064/11*e^2 - 654/11, -17/88*e^8 + 70/11*e^6 - 654/11*e^4 + 2058/11*e^2 - 1520/11];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

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