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

NN := ideal<ZF | {21, 21, w^3 - w^2 - 5*w - 1}>;

primesArray := [
[3, 3, w - 1],
[4, 2, -w^3 + 2*w^2 + 4*w - 3],
[5, 5, w],
[7, 7, w - 2],
[11, 11, w^2 - 2*w - 4],
[23, 23, -w^2 + 2*w + 1],
[23, 23, w^3 - 2*w^2 - 3*w + 3],
[27, 3, -w^3 + w^2 + 6*w + 2],
[31, 31, -w^3 + 3*w^2 + w - 1],
[31, 31, -w^3 + 2*w^2 + 4*w - 4],
[37, 37, w^2 - 2*w - 6],
[37, 37, w^3 - 2*w^2 - 3*w + 2],
[43, 43, w^2 - 3*w - 2],
[61, 61, -w^3 + 2*w^2 + 2*w - 2],
[73, 73, w^3 - 3*w^2 - 2*w + 3],
[83, 83, -w - 3],
[89, 89, -w^3 + 3*w^2 + 2*w - 2],
[89, 89, 2*w - 1],
[101, 101, w^3 - 4*w^2 + w + 7],
[101, 101, 2*w^2 - 3*w - 3],
[103, 103, w^3 - 7*w - 4],
[107, 107, 3*w^3 - 2*w^2 - 17*w - 12],
[109, 109, -w^3 + 2*w^2 + 5*w - 2],
[113, 113, w^3 - 3*w^2 - 4*w + 4],
[125, 5, w^3 - 2*w^2 - 5*w + 4],
[139, 139, -w^3 + 2*w^2 + w - 4],
[139, 139, -2*w^2 + 3*w + 7],
[149, 149, -w^3 + 3*w^2 + w - 7],
[149, 149, -2*w^3 + 6*w^2 + 5*w - 16],
[157, 157, -2*w^3 + 6*w^2 + 3*w - 11],
[157, 157, 2*w^3 - 3*w^2 - 10*w + 1],
[163, 163, -w^3 + 4*w^2 + w - 9],
[163, 163, 2*w^3 - 5*w^2 - 6*w + 7],
[167, 167, -w^3 + 4*w^2 - 2*w - 6],
[169, 13, -w^3 + 4*w^2 + w - 8],
[169, 13, 2*w^2 - 3*w - 6],
[173, 173, w^3 - w^2 - 4*w - 4],
[181, 181, 2*w^3 - 4*w^2 - 7*w + 4],
[181, 181, w^2 - 2*w + 2],
[191, 191, 2*w^2 - 4*w - 3],
[197, 197, w^3 - 5*w^2 + 17],
[197, 197, -w^3 + w^2 + 4*w - 2],
[211, 211, 2*w^3 - 4*w^2 - 8*w + 3],
[211, 211, -w^3 + 6*w + 8],
[223, 223, w^3 - 4*w^2 - 2*w + 6],
[227, 227, 2*w^3 - 3*w^2 - 10*w - 2],
[229, 229, -w^3 + 3*w^2 + 3*w - 1],
[233, 233, -w^3 + w^2 + 5*w - 1],
[233, 233, -2*w^3 + 7*w^2 + 4*w - 17],
[257, 257, 2*w^3 - 5*w^2 - 5*w + 4],
[263, 263, w^2 - 6],
[263, 263, 3*w^3 - 9*w^2 - 8*w + 24],
[281, 281, 3*w^3 - 4*w^2 - 14*w - 2],
[281, 281, 2*w^3 - 3*w^2 - 8*w + 1],
[289, 17, 2*w^3 - 4*w^2 - 9*w + 9],
[289, 17, -2*w^3 + 5*w^2 + 4*w - 8],
[293, 293, -w - 4],
[307, 307, 3*w^3 - 3*w^2 - 15*w - 7],
[311, 311, w^2 - 8],
[311, 311, -w^3 + 5*w^2 - 2*w - 7],
[337, 337, w^2 - 4*w - 2],
[337, 337, -w^3 + 3*w^2 - 6],
[343, 7, -2*w^3 + 7*w^2 + 3*w - 16],
[347, 347, w^3 - 2*w^2 - 3*w - 3],
[349, 349, -2*w^3 + 5*w^2 + 2*w - 4],
[353, 353, -2*w^3 + 7*w^2 + 4*w - 14],
[353, 353, -w^3 + 4*w^2 - 14],
[359, 359, -w^3 + 3*w^2 - 2*w - 2],
[367, 367, w^2 - 5*w - 4],
[367, 367, w^2 - w - 8],
[379, 379, 3*w^3 - 2*w^2 - 19*w - 11],
[379, 379, -w^2 - w - 2],
[379, 379, 3*w^3 - 21*w - 19],
[379, 379, -2*w^3 + 3*w^2 + 10*w + 3],
[383, 383, 3*w^3 - 6*w^2 - 11*w + 7],
[383, 383, w^3 - 5*w^2 + w + 7],
[389, 389, w^2 - 4*w - 1],
[397, 397, -w^3 + w^2 + 6*w - 2],
[397, 397, 2*w^3 - 2*w^2 - 11*w - 8],
[401, 401, 3*w^2 - 4*w - 12],
[409, 409, -2*w^3 + 7*w^2 + 4*w - 16],
[409, 409, 3*w - 2],
[419, 419, 2*w^2 - w - 8],
[433, 433, -w^3 + 4*w^2 + w - 14],
[439, 439, w^3 - w^2 - 7*w - 1],
[439, 439, 3*w^3 - 7*w^2 - 9*w + 9],
[443, 443, -2*w^3 + 5*w^2 + 3*w - 4],
[449, 449, -2*w^3 + 5*w^2 + 4*w - 6],
[457, 457, -2*w^3 + 5*w^2 + 8*w - 12],
[461, 461, 2*w^3 - 3*w^2 - 6*w - 1],
[463, 463, 3*w - 1],
[463, 463, 2*w^3 + w^2 - 16*w - 18],
[479, 479, -w^3 + 5*w^2 + w - 9],
[487, 487, -3*w^3 + 8*w^2 + 7*w - 13],
[503, 503, 3*w^2 - 6*w - 11],
[503, 503, -w^3 + 5*w^2 + w - 13],
[509, 509, -w^3 + 2*w^2 + 6*w - 6],
[521, 521, 2*w^3 - 4*w^2 - 9*w + 6],
[523, 523, -w^3 + 5*w^2 - 8],
[523, 523, w^2 - 4*w - 7],
[529, 23, -w^3 + 4*w^2 - w - 9],
[541, 541, -w^3 + w^2 + 5*w - 3],
[541, 541, -w^3 + 6*w^2 - 3*w - 19],
[547, 547, w^3 - 2*w^2 - w - 2],
[547, 547, -w^3 + 5*w^2 - 14],
[557, 557, -2*w^3 + 4*w^2 + 6*w - 3],
[557, 557, w^3 - 3*w^2 - 5*w + 11],
[563, 563, w^3 - 5*w^2 + 2*w + 9],
[563, 563, -w^3 + 4*w^2 + 2*w - 4],
[569, 569, -2*w^3 + w^2 + 12*w + 12],
[571, 571, -w^2 + 3*w - 4],
[577, 577, w^2 - 2*w + 3],
[587, 587, 3*w^2 - 5*w - 8],
[587, 587, w^3 - 5*w^2 + w + 13],
[613, 613, w^3 + w^2 - 7*w - 11],
[617, 617, w^3 - 9*w - 2],
[643, 643, 2*w^2 - 5*w - 8],
[661, 661, -w^3 + 2*w^2 + 6*w - 2],
[661, 661, -2*w^3 + 6*w^2 + w - 9],
[673, 673, -2*w^3 + 5*w^2 + 8*w - 9],
[677, 677, w^3 - 5*w - 7],
[691, 691, 3*w^3 - 7*w^2 - 9*w + 11],
[701, 701, 3*w^2 - 4*w - 7],
[709, 709, -2*w^2 + 3*w + 12],
[709, 709, -w^3 + 3*w^2 - 9],
[719, 719, -2*w^2 + 6*w - 3],
[727, 727, w^3 - 3*w^2 - 2*w - 1],
[751, 751, -2*w^3 + 3*w^2 + 8*w - 4],
[757, 757, -2*w^3 + 5*w^2 + 7*w - 6],
[757, 757, w^3 - w^2 - 2*w - 3],
[757, 757, -w^3 - w^2 + 10*w + 11],
[757, 757, 6*w^3 - 14*w^2 - 20*w + 23],
[761, 761, -4*w^3 + 10*w^2 + 13*w - 17],
[769, 769, w^3 - 2*w^2 - w - 3],
[769, 769, 5*w^3 - 8*w^2 - 22*w + 2],
[773, 773, -w^3 + 5*w^2 - 3*w - 11],
[787, 787, -2*w^3 + 8*w^2 - w - 13],
[787, 787, 2*w^3 - 2*w^2 - 9*w - 8],
[787, 787, 3*w^3 - 5*w^2 - 12*w + 3],
[787, 787, 4*w^3 - 5*w^2 - 21*w - 4],
[797, 797, 2*w^2 - w - 9],
[797, 797, -3*w^3 + 7*w^2 + 10*w - 16],
[821, 821, 4*w^3 - 3*w^2 - 24*w - 17],
[821, 821, 2*w^3 - w^2 - 14*w - 6],
[823, 823, 3*w^3 - 5*w^2 - 12*w + 1],
[827, 827, -w^3 + 5*w^2 - 9],
[827, 827, -2*w^3 + 6*w^2 + 2*w - 11],
[827, 827, -2*w^3 + 7*w^2 + 6*w - 13],
[827, 827, w^3 - w^2 - 8*w - 3],
[853, 853, -w^3 + 2*w^2 + 3*w - 8],
[857, 857, -w^3 - 2*w^2 + 11*w + 17],
[857, 857, 3*w^3 - w^2 - 18*w - 16],
[859, 859, -w^3 + w^2 + 7*w + 7],
[859, 859, 5*w^3 - 5*w^2 - 26*w - 12],
[859, 859, 2*w^3 - 4*w^2 - 4*w - 1],
[859, 859, -3*w^2 + 4*w + 3],
[863, 863, w^3 - 3*w^2 - 6*w + 3],
[877, 877, w^3 - 2*w^2 - 3*w - 4],
[877, 877, -w^3 + 5*w^2 - 2*w - 18],
[883, 883, 3*w^3 - 7*w^2 - 7*w + 13],
[883, 883, -4*w^3 + 9*w^2 + 14*w - 12],
[919, 919, -w^3 + 4*w^2 + 3*w - 2],
[919, 919, -w^3 + 3*w^2 + 2*w - 11],
[929, 929, 2*w^3 - 4*w^2 - 9*w + 1],
[937, 937, 3*w^3 - 9*w^2 - 4*w + 9],
[953, 953, -3*w^3 + 9*w^2 + 6*w - 14],
[961, 31, -3*w^3 + 6*w^2 + 11*w - 3],
[967, 967, -w^3 + 5*w^2 - w - 11],
[967, 967, 3*w^3 - 6*w^2 - 9*w + 1],
[977, 977, 2*w^3 - 6*w^2 - 3*w + 18],
[977, 977, 7*w^3 - 16*w^2 - 24*w + 26],
[991, 991, 3*w^2 - 3*w - 8],
[997, 997, 3*w^3 - 5*w^2 - 13*w - 1],
[1009, 1009, 3*w^3 - 12*w^2 - 3*w + 34],
[1013, 1013, -2*w^3 + 8*w^2 + w - 12],
[1013, 1013, -2*w^3 + 3*w^2 + 6*w - 2],
[1049, 1049, 3*w^3 - 5*w^2 - 14*w + 6],
[1069, 1069, w^3 + w^2 - 6*w - 3],
[1069, 1069, 2*w^3 - 8*w^2 - 2*w + 21],
[1087, 1087, 4*w^3 - 5*w^2 - 20*w - 8],
[1091, 1091, -2*w^3 + 8*w^2 - w - 16],
[1103, 1103, -3*w^3 + 6*w^2 + 13*w - 9],
[1117, 1117, 4*w^2 - 5*w - 16],
[1117, 1117, 6*w^3 - 15*w^2 - 18*w + 26],
[1123, 1123, -2*w^3 + 7*w^2 + 2*w - 6],
[1123, 1123, -3*w^3 + 7*w^2 + 5*w - 11],
[1129, 1129, -2*w^2 + 3*w - 2],
[1129, 1129, 5*w^3 - 9*w^2 - 21*w + 9],
[1129, 1129, 3*w^3 - 4*w^2 - 16*w - 2],
[1129, 1129, w^3 + 2*w^2 - 10*w - 12],
[1151, 1151, 2*w^3 + 2*w^2 - 17*w - 21],
[1153, 1153, 6*w^3 - 11*w^2 - 24*w + 7],
[1163, 1163, 3*w^3 - 7*w^2 - 8*w + 7],
[1163, 1163, -3*w^3 + 10*w^2 + 7*w - 28],
[1171, 1171, -2*w^3 + 4*w^2 + 9*w - 12],
[1187, 1187, -3*w^3 + 10*w^2 + 4*w - 22],
[1187, 1187, 5*w^3 - 9*w^2 - 22*w + 9],
[1193, 1193, 3*w^3 - 6*w^2 - 10*w + 8],
[1193, 1193, 3*w^2 - 3*w - 14],
[1193, 1193, 4*w - 3],
[1193, 1193, 3*w^3 - 10*w^2 - 7*w + 27],
[1201, 1201, 4*w^3 - 9*w^2 - 15*w + 18],
[1213, 1213, -w^3 + 4*w^2 - 4*w - 4],
[1213, 1213, w^3 - 9*w + 1],
[1217, 1217, w^3 - w^2 - w - 3],
[1217, 1217, -3*w^3 + 20*w + 18],
[1223, 1223, 6*w^3 - 11*w^2 - 24*w + 6],
[1223, 1223, 3*w^2 - 6*w - 13],
[1229, 1229, 3*w^3 - 6*w^2 - 13*w + 8],
[1231, 1231, -w^3 + 4*w^2 - w - 12],
[1259, 1259, -2*w^3 + 6*w^2 + 5*w - 8],
[1259, 1259, 3*w^2 - 6*w - 4],
[1277, 1277, -4*w^3 + 11*w^2 + 8*w - 19],
[1279, 1279, -3*w^3 + 5*w^2 + 11*w + 1],
[1283, 1283, -4*w^3 + 9*w^2 + 13*w - 14],
[1291, 1291, -2*w^3 + 6*w^2 + 6*w - 9],
[1291, 1291, -2*w^3 - 2*w^2 + 18*w + 21],
[1297, 1297, 3*w^3 - 8*w^2 - 5*w + 8],
[1319, 1319, -w^3 + 6*w^2 - 3*w - 9],
[1321, 1321, -4*w^3 + 9*w^2 + 15*w - 12],
[1327, 1327, w^2 + 2*w - 7],
[1331, 11, -2*w^3 + 5*w^2 + 2*w - 9],
[1367, 1367, -w^3 + 7*w^2 - 6*w - 11],
[1367, 1367, -w^3 + w^2 + 8*w - 3],
[1369, 37, -2*w^3 + 6*w^2 + 7*w - 9],
[1373, 1373, -2*w^3 + 6*w^2 + 2*w - 1],
[1409, 1409, 5*w^3 - 16*w^2 - 11*w + 38],
[1423, 1423, -2*w^3 + 3*w^2 + 11*w - 2],
[1433, 1433, -2*w^3 + w^2 + 9*w + 2],
[1439, 1439, w^3 - 3*w^2 - 6*w + 4],
[1439, 1439, -3*w^3 + 6*w^2 + 12*w - 4],
[1447, 1447, 4*w^3 - 13*w^2 - 7*w + 24],
[1453, 1453, -w^3 + 5*w^2 - 2*w - 16],
[1459, 1459, 3*w^3 - 7*w^2 - 4*w + 4],
[1471, 1471, -w^3 + 4*w^2 - 3*w - 8],
[1487, 1487, -2*w^2 + w + 14],
[1489, 1489, -3*w^3 + 7*w^2 + 5*w - 13],
[1489, 1489, -4*w^2 + 6*w + 21],
[1493, 1493, -2*w^3 + 7*w^2 + 2*w - 3],
[1499, 1499, 6*w^3 - 14*w^2 - 20*w + 21],
[1531, 1531, 3*w^3 - 7*w^2 - 8*w + 8],
[1531, 1531, 2*w^2 + w - 8],
[1531, 1531, -3*w^3 + 7*w^2 + 8*w - 11],
[1531, 1531, 2*w^3 - 3*w^2 - 6*w - 4],
[1553, 1553, -w^3 + 6*w^2 - 4*w - 12],
[1567, 1567, 4*w^3 - 5*w^2 - 20*w - 2],
[1571, 1571, 4*w^3 - 8*w^2 - 13*w + 13],
[1571, 1571, 5*w^3 - 5*w^2 - 25*w - 9],
[1579, 1579, -2*w^3 + 6*w^2 - 9],
[1579, 1579, -3*w^3 + 8*w^2 + 5*w - 9],
[1583, 1583, 4*w^2 - 4*w - 17],
[1597, 1597, 3*w^3 - 6*w^2 - 9*w + 2],
[1601, 1601, 2*w^2 - w - 11],
[1609, 1609, 4*w^3 - 5*w^2 - 18*w - 7],
[1613, 1613, -w^3 + 6*w^2 - 3*w - 16],
[1613, 1613, -2*w^3 + 8*w^2 - 13],
[1619, 1619, w^3 - 2*w^2 - 7*w + 1],
[1621, 1621, -w^3 + w^2 + 2*w + 12],
[1621, 1621, 6*w^3 - 11*w^2 - 25*w + 8],
[1637, 1637, 3*w^3 - 5*w^2 - 14*w - 1],
[1681, 41, -2*w^3 + 5*w^2 + 9*w - 4],
[1681, 41, w^3 - 4*w^2 + 5*w + 6],
[1693, 1693, 3*w^3 - 3*w^2 - 14*w - 2],
[1697, 1697, 2*w^3 + w^2 - 16*w - 21],
[1697, 1697, w^3 + w^2 - 8*w - 4],
[1721, 1721, -3*w^3 + 9*w^2 + 6*w - 13],
[1723, 1723, 2*w^3 - 2*w^2 - 12*w + 1],
[1723, 1723, 5*w^2 - 7*w - 26],
[1741, 1741, -2*w^3 + 2*w^2 + 9*w - 1],
[1753, 1753, -w^3 + 4*w^2 + 5*w - 3],
[1753, 1753, 3*w^3 + 2*w^2 - 24*w - 28],
[1759, 1759, -w^3 + 7*w + 11],
[1777, 1777, 2*w^3 - w^2 - 13*w - 4],
[1777, 1777, -2*w^3 + 6*w^2 + 5*w - 7],
[1787, 1787, -w^3 + 2*w^2 + 3*w - 9],
[1801, 1801, -2*w^3 + 3*w^2 + 8*w + 7],
[1861, 1861, -2*w^3 - w^2 + 14*w + 14],
[1867, 1867, -w^3 + w^2 + 8*w - 1],
[1871, 1871, -w^3 + 3*w^2 + 2*w - 12],
[1873, 1873, 3*w^3 - 8*w^2 - 9*w + 22],
[1877, 1877, -3*w^3 + 7*w^2 + 13*w - 7],
[1877, 1877, 3*w^3 - w^2 - 19*w - 11],
[1877, 1877, -7*w^3 + 17*w^2 + 23*w - 29],
[1877, 1877, 5*w^2 - 7*w - 8],
[1879, 1879, 4*w^3 - 8*w^2 - 16*w + 7],
[1931, 1931, -2*w^3 + 6*w^2 + 9*w - 9],
[1933, 1933, 5*w^3 - 13*w^2 - 14*w + 21],
[1951, 1951, -w^2 + w - 4],
[1973, 1973, w^3 - 6*w - 12],
[1973, 1973, 3*w^3 - 11*w^2 + 19],
[1993, 1993, -5*w^3 + 12*w^2 + 17*w - 19],
[1993, 1993, -6*w^3 + 15*w^2 + 19*w - 26],
[1999, 1999, -3*w^3 + 7*w^2 + 4*w - 9],
[1999, 1999, 3*w^3 - 8*w^2 - 11*w + 17]];
primes := [ideal<ZF | {F!x : x in I}> : I in primesArray];

heckePol := x^9 - 7*x^8 + 83*x^6 - 101*x^5 - 268*x^4 + 441*x^3 + 175*x^2 - 520*x + 200;
K<e> := NumberField(heckePol);

heckeEigenvaluesArray := [-1, e, -229/470*e^8 + 1473/470*e^7 + 75/47*e^6 - 17867/470*e^5 + 257/10*e^4 + 31156/235*e^3 - 50639/470*e^2 - 12879/94*e + 5190/47, -1, -9/235*e^8 + 23/235*e^7 + 57/47*e^6 - 812/235*e^5 - 43/5*e^4 + 5937/235*e^3 + 2991/235*e^2 - 1902/47*e + 504/47, 24/47*e^8 - 171/47*e^7 + 39/47*e^6 + 1805/47*e^5 - 49*e^4 - 4693/47*e^3 + 6594/47*e^2 + 2753/47*e - 3712/47, 123/235*e^8 - 706/235*e^7 - 215/47*e^6 + 10314/235*e^5 - 19/5*e^4 - 46594/235*e^3 + 23278/235*e^2 + 12505/47*e - 8768/47, 24/235*e^8 - 218/235*e^7 + 83/47*e^6 + 1382/235*e^5 - 117/5*e^4 + 2968/235*e^3 + 9649/235*e^2 - 2777/47*e + 724/47, -273/235*e^8 + 1716/235*e^7 + 225/47*e^6 - 21184/235*e^5 + 259/5*e^4 + 75984/235*e^3 - 56383/235*e^2 - 16146/47*e + 12468/47, -40/47*e^8 + 238/47*e^7 + 264/47*e^6 - 3165/47*e^5 + 19*e^4 + 12647/47*e^3 - 7089/47*e^2 - 14944/47*e + 10636/47, -142/235*e^8 + 859/235*e^7 + 163/47*e^6 - 11036/235*e^5 + 86/5*e^4 + 41816/235*e^3 - 24092/235*e^2 - 9204/47*e + 6260/47, 37/94*e^8 - 199/94*e^7 - 202/47*e^6 + 3051/94*e^5 + 13/2*e^4 - 7214/47*e^3 + 4655/94*e^2 + 19529/94*e - 6026/47, 12/235*e^8 - 109/235*e^7 + 18/47*e^6 + 1396/235*e^5 - 51/5*e^4 - 5566/235*e^3 + 9407/235*e^2 + 1455/47*e - 1800/47, 1/470*e^8 - 107/470*e^7 + 83/47*e^6 - 1137/470*e^5 - 133/10*e^4 + 9031/235*e^3 - 19/470*e^2 - 7011/94*e + 2698/47, 103/470*e^8 - 681/470*e^7 - 5/47*e^6 + 7439/470*e^5 - 179/10*e^4 - 10512/235*e^3 + 29533/470*e^2 + 3453/94*e - 2038/47, 63/47*e^8 - 396/47*e^7 - 256/47*e^6 + 4838/47*e^5 - 58*e^4 - 17072/47*e^3 + 12151/47*e^2 + 17878/47*e - 13316/47, -211/470*e^8 + 957/470*e^7 + 394/47*e^6 - 20003/470*e^5 - 357/10*e^4 + 59999/235*e^3 - 18081/470*e^2 - 37557/94*e + 11078/47, -379/470*e^8 + 2483/470*e^7 + 80/47*e^6 - 28737/470*e^5 + 497/10*e^4 + 46086/235*e^3 - 84919/470*e^2 - 17131/94*e + 7510/47, -14/47*e^8 + 135/47*e^7 - 293/47*e^6 - 814/47*e^5 + 78*e^4 - 2076/47*e^3 - 6032/47*e^2 + 8362/47*e - 3600/47, 79/470*e^8 - 463/470*e^7 - 70/47*e^6 + 7467/470*e^5 - 47/10*e^4 - 19281/235*e^3 + 30929/470*e^2 + 12387/94*e - 5502/47, -5/47*e^8 + 18/47*e^7 + 127/47*e^6 - 519/47*e^5 - 13*e^4 + 3596/47*e^3 - 751/47*e^2 - 6051/47*e + 4220/47, 66/235*e^8 - 482/235*e^7 + 5/47*e^6 + 5798/235*e^5 - 133/5*e^4 - 20508/235*e^3 + 23186/235*e^2 + 4642/47*e - 4448/47, -361/470*e^8 + 2437/470*e^7 + 23/47*e^6 - 27113/470*e^5 + 583/10*e^4 + 40149/235*e^3 - 91371/470*e^2 - 13233/94*e + 7194/47, 99/470*e^8 - 723/470*e^7 + 39/47*e^6 + 6817/470*e^5 - 237/10*e^4 - 5746/235*e^3 + 24909/470*e^2 - 933/94*e - 46/47, -473/470*e^8 + 3141/470*e^7 + 80/47*e^6 - 36069/470*e^5 + 659/10*e^4 + 56567/235*e^3 - 107103/470*e^2 - 20139/94*e + 8638/47, -100/47*e^8 + 595/47*e^7 + 660/47*e^6 - 7936/47*e^5 + 49*e^4 + 31923/47*e^3 - 18357/47*e^2 - 38300/47*e + 27248/47, -53/47*e^8 + 360/47*e^7 + 2/47*e^6 - 3894/47*e^5 + 91*e^4 + 10726/47*e^3 - 13328/47*e^2 - 7374/47*e + 8448/47, 13/235*e^8 + 19/235*e^7 - 145/47*e^6 + 1199/235*e^5 + 116/5*e^4 - 12414/235*e^3 - 5652/235*e^2 + 4408/47*e - 2138/47, -258/235*e^8 + 1521/235*e^7 + 365/47*e^6 - 20614/235*e^5 + 104/5*e^4 + 84419/235*e^3 - 46093/235*e^2 - 20402/47*e + 14260/47, 293/235*e^8 - 1741/235*e^7 - 430/47*e^6 + 24294/235*e^5 - 119/5*e^4 - 103904/235*e^3 + 58353/235*e^2 + 26608/47*e - 18946/47, -663/470*e^8 + 4201/470*e^7 + 290/47*e^6 - 53629/470*e^5 + 649/10*e^4 + 101297/235*e^3 - 154253/470*e^2 - 45597/94*e + 18094/47, 9/47*e^8 - 70/47*e^7 + 91/47*e^6 + 436/47*e^5 - 28*e^4 + 1113/47*e^3 + 1333/47*e^2 - 5060/47*e + 3120/47, -45/47*e^8 + 256/47*e^7 + 391/47*e^6 - 3637/47*e^5 + 3*e^4 + 15726/47*e^3 - 6618/47*e^2 - 19726/47*e + 12976/47, 214/235*e^8 - 1513/235*e^7 + 86/47*e^6 + 15417/235*e^5 - 447/5*e^4 - 36202/235*e^3 + 57269/235*e^2 + 2894/47*e - 5780/47, -112/235*e^8 + 469/235*e^7 + 490/47*e^6 - 11306/235*e^5 - 239/5*e^4 + 73021/235*e^3 - 13147/235*e^2 - 23920/47*e + 14920/47, 289/235*e^8 - 1783/235*e^7 - 295/47*e^6 + 22732/235*e^5 - 222/5*e^4 - 85207/235*e^3 + 56314/235*e^2 + 18650/47*e - 13928/47, -483/235*e^8 + 3036/235*e^7 + 380/47*e^6 - 36919/235*e^5 + 464/5*e^4 + 128739/235*e^3 - 95633/235*e^2 - 26310/47*e + 19904/47, 327/470*e^8 - 2089/470*e^7 - 72/47*e^6 + 22531/470*e^5 - 351/10*e^4 - 30188/235*e^3 + 42667/470*e^2 + 6925/94*e - 1542/47, 341/235*e^8 - 2177/235*e^7 - 217/47*e^6 + 25883/235*e^5 - 378/5*e^4 - 86688/235*e^3 + 71776/235*e^2 + 16824/47*e - 14114/47, -448/235*e^8 + 2816/235*e^7 + 409/47*e^6 - 35589/235*e^5 + 389/5*e^4 + 132754/235*e^3 - 91128/235*e^2 - 29645/47*e + 22268/47, -77/235*e^8 + 484/235*e^7 + 49/47*e^6 - 5746/235*e^5 + 91/5*e^4 + 19696/235*e^3 - 19217/235*e^2 - 4460/47*e + 3936/47, 909/470*e^8 - 5613/470*e^7 - 458/47*e^6 + 71907/470*e^5 - 747/10*e^4 - 136611/235*e^3 + 195169/470*e^2 + 62523/94*e - 24042/47, -273/235*e^8 + 1481/235*e^7 + 601/47*e^6 - 23064/235*e^5 - 86/5*e^4 + 110764/235*e^3 - 40168/235*e^2 - 30575/47*e + 19800/47, -83/235*e^8 + 421/235*e^7 + 228/47*e^6 - 7149/235*e^5 - 71/5*e^4 + 36579/235*e^3 - 8763/235*e^2 - 10052/47*e + 6716/47, 182/235*e^8 - 909/235*e^7 - 526/47*e^6 + 16081/235*e^5 + 169/5*e^4 - 86141/235*e^3 + 21452/235*e^2 + 25710/47*e - 15268/47, -502/235*e^8 + 3424/235*e^7 - 1/47*e^6 - 36936/235*e^5 + 846/5*e^4 + 100931/235*e^3 - 116892/235*e^2 - 13374/47*e + 13448/47, -93/470*e^8 + 1021/470*e^7 - 340/47*e^6 - 1889/470*e^5 + 749/10*e^4 - 28898/235*e^3 - 38653/470*e^2 + 29367/94*e - 6890/47, 539/470*e^8 - 3153/470*e^7 - 430/47*e^6 + 44687/470*e^5 - 147/10*e^4 - 96901/235*e^3 + 99739/470*e^2 + 49879/94*e - 17066/47, -114/47*e^8 + 730/47*e^7 + 414/47*e^6 - 8985/47*e^5 + 121*e^4 + 32103/47*e^3 - 25047/47*e^2 - 34074/47*e + 27220/47, 77/94*e^8 - 531/94*e^7 + 42/47*e^6 + 5417/94*e^5 - 143/2*e^4 - 6276/47*e^3 + 17995/94*e^2 + 4675/94*e - 4106/47, 221/235*e^8 - 1322/235*e^7 - 303/47*e^6 + 18033/235*e^5 - 103/5*e^4 - 74973/235*e^3 + 42331/235*e^2 + 18630/47*e - 13692/47, -151/235*e^8 + 882/235*e^7 + 220/47*e^6 - 12083/235*e^5 + 63/5*e^4 + 50338/235*e^3 - 30031/235*e^2 - 12516/47*e + 8832/47, -1227/470*e^8 + 7679/470*e^7 + 572/47*e^6 - 97621/470*e^5 + 1091/10*e^4 + 183218/235*e^3 - 267147/470*e^2 - 82821/94*e + 32194/47, 683/470*e^8 - 4461/470*e^7 - 228/47*e^6 + 55799/470*e^5 - 809/10*e^4 - 102567/235*e^3 + 171733/470*e^2 + 44779/94*e - 18466/47, -43/94*e^8 + 371/94*e^7 - 314/47*e^6 - 2433/94*e^5 + 183/2*e^4 - 1993/47*e^3 - 13659/94*e^2 + 20661/94*e - 4790/47, -1723/470*e^8 + 10461/470*e^7 + 999/47*e^6 - 136209/470*e^5 + 1099/10*e^4 + 264487/235*e^3 - 327283/470*e^2 - 122751/94*e + 44578/47, -22/235*e^8 + 239/235*e^7 - 127/47*e^6 - 1071/235*e^5 + 141/5*e^4 - 7264/235*e^3 - 5222/235*e^2 + 4500/47*e - 3374/47, 588/235*e^8 - 3696/235*e^7 - 528/47*e^6 + 46784/235*e^5 - 539/5*e^4 - 174739/235*e^3 + 127713/235*e^2 + 39335/47*e - 30108/47, -148/235*e^8 + 796/235*e^7 + 389/47*e^6 - 14084/235*e^5 - 76/5*e^4 + 75854/235*e^3 - 29383/235*e^2 - 22692/47*e + 14868/47, -89/235*e^8 + 358/235*e^7 + 360/47*e^6 - 7612/235*e^5 - 198/5*e^4 + 46412/235*e^3 + 2161/235*e^2 - 14704/47*e + 7052/47, 313/470*e^8 - 1531/470*e^7 - 435/47*e^6 + 25759/470*e^5 + 281/10*e^4 - 65677/235*e^3 + 28363/470*e^2 + 37681/94*e - 10550/47, -498/235*e^8 + 3231/235*e^7 + 287/47*e^6 - 38664/235*e^5 + 589/5*e^4 + 132054/235*e^3 - 110153/235*e^2 - 26848/47*e + 21778/47, -321/235*e^8 + 2387/235*e^7 - 317/47*e^6 - 21833/235*e^5 + 818/5*e^4 + 33388/235*e^3 - 84376/235*e^2 + 4730/47*e + 1996/47, -98/235*e^8 + 851/235*e^7 - 288/47*e^6 - 5839/235*e^5 + 434/5*e^4 - 6636/235*e^3 - 37148/235*e^2 + 8304/47*e - 2972/47, -161/470*e^8 + 1717/470*e^7 - 485/47*e^6 - 7293/470*e^5 + 1173/10*e^4 - 27541/235*e^3 - 89061/470*e^2 + 31791/94*e - 5174/47, 306/235*e^8 - 1722/235*e^7 - 528/47*e^6 + 24083/235*e^5 - 13/5*e^4 - 102453/235*e^3 + 40481/235*e^2 + 25470/47*e - 15820/47, 272/235*e^8 - 1374/235*e^7 - 767/47*e^6 + 24201/235*e^5 + 229/5*e^4 - 130001/235*e^3 + 35722/235*e^2 + 38808/47*e - 23598/47, e^8 - 6*e^7 - 6*e^6 + 78*e^5 - 28*e^4 - 300*e^3 + 185*e^2 + 336*e - 260, -237/235*e^8 + 1624/235*e^7 - 3/47*e^6 - 17466/235*e^5 + 396/5*e^4 + 46831/235*e^3 - 52132/235*e^2 - 5577/47*e + 5564/47, -107/235*e^8 + 404/235*e^7 + 474/47*e^6 - 9471/235*e^5 - 259/5*e^4 + 60166/235*e^3 - 2197/235*e^2 - 19824/47*e + 11444/47, -207/235*e^8 + 1234/235*e^7 + 277/47*e^6 - 16326/235*e^5 + 81/5*e^4 + 64406/235*e^3 - 29672/235*e^2 - 14747/47*e + 8772/47, -111/235*e^8 + 832/235*e^7 - 96/47*e^6 - 8213/235*e^5 + 288/5*e^4 + 17528/235*e^3 - 36196/235*e^2 - 1180/47*e + 3396/47, -96/47*e^8 + 637/47*e^7 + 173/47*e^6 - 7455/47*e^5 + 139*e^4 + 24365/47*e^3 - 24543/47*e^2 - 23326/47*e + 21616/47, 61/47*e^8 - 417/47*e^7 - 83/47*e^6 + 4997/47*e^5 - 98*e^4 - 17147/47*e^3 + 17876/47*e^2 + 17723/47*e - 17080/47, -5/47*e^8 + 18/47*e^7 + 127/47*e^6 - 472/47*e^5 - 17*e^4 + 3267/47*e^3 + 565/47*e^2 - 5393/47*e + 3468/47, 27/235*e^8 - 539/235*e^7 + 534/47*e^6 + 86/235*e^5 - 556/5*e^4 + 38119/235*e^3 + 38027/235*e^2 - 17606/47*e + 6948/47, -197/94*e^8 + 1339/94*e^7 + 72/47*e^6 - 15241/94*e^5 + 325/2*e^4 + 23672/47*e^3 - 52939/94*e^2 - 42833/94*e + 21282/47, 285/94*e^8 - 1825/94*e^7 - 400/47*e^6 + 21217/94*e^5 - 327/2*e^4 - 34054/47*e^3 + 57377/94*e^2 + 61027/94*e - 24954/47, 117/235*e^8 - 769/235*e^7 - 36/47*e^6 + 8676/235*e^5 - 161/5*e^4 - 26656/235*e^3 + 24097/235*e^2 + 4516/47*e - 3356/47, 239/235*e^8 - 1368/235*e^7 - 417/47*e^6 + 20127/235*e^5 - 52/5*e^4 - 91077/235*e^3 + 49274/235*e^2 + 24220/47*e - 17520/47, -389/235*e^8 + 2848/235*e^7 - 278/47*e^6 - 27942/235*e^5 + 927/5*e^4 + 57957/235*e^3 - 110109/235*e^2 - 2058/47*e + 7308/47, 169/470*e^8 - 1163/470*e^7 + 68/47*e^6 + 9007/470*e^5 - 347/10*e^4 - 86/235*e^3 + 21699/470*e^2 - 8543/94*e + 2318/47, -789/235*e^8 + 5228/235*e^7 + 297/47*e^6 - 61002/235*e^5 + 1102/5*e^4 + 198762/235*e^3 - 191574/235*e^2 - 37868/47*e + 34032/47, -62/235*e^8 + 54/235*e^7 + 612/47*e^6 - 8466/235*e^5 - 429/5*e^4 + 76776/235*e^3 + 2353/235*e^2 - 28456/47*e + 16350/47, 352/235*e^8 - 2179/235*e^7 - 318/47*e^6 + 26771/235*e^5 - 296/5*e^4 - 94336/235*e^3 + 67102/235*e^2 + 18804/47*e - 15012/47, -281/235*e^8 + 2102/235*e^7 - 257/47*e^6 - 20078/235*e^5 + 713/5*e^4 + 37473/235*e^3 - 77146/235*e^2 + 744/47*e + 2388/47, -313/235*e^8 + 1766/235*e^7 + 541/47*e^6 - 25054/235*e^5 + 39/5*e^4 + 108089/235*e^3 - 52333/235*e^2 - 27341/47*e + 19032/47, -127/470*e^8 + 1369/470*e^7 - 342/47*e^6 - 8351/470*e^5 + 881/10*e^4 - 9537/235*e^3 - 75607/470*e^2 + 15539/94*e - 1802/47, -363/94*e^8 + 2181/94*e^7 + 1165/47*e^6 - 29163/94*e^5 + 197/2*e^4 + 58888/47*e^3 - 69995/94*e^2 - 142789/94*e + 51666/47, 471/470*e^8 - 3397/470*e^7 + 177/47*e^6 + 30823/470*e^5 - 1033/10*e^4 - 22224/235*e^3 + 92101/470*e^2 - 8233/94*e + 1758/47, 553/235*e^8 - 3476/235*e^7 - 463/47*e^6 + 43104/235*e^5 - 519/5*e^4 - 156664/235*e^3 + 114748/235*e^2 + 34727/47*e - 26268/47, -150/47*e^8 + 916/47*e^7 + 849/47*e^6 - 11904/47*e^5 + 100*e^4 + 46028/47*e^3 - 28875/47*e^2 - 52656/47*e + 38804/47, 33/235*e^8 - 241/235*e^7 - 21/47*e^6 + 3369/235*e^5 - 44/5*e^4 - 14484/235*e^3 + 9948/235*e^2 + 3308/47*e - 2600/47, -314/235*e^8 + 1638/235*e^7 + 798/47*e^6 - 27442/235*e^5 - 173/5*e^4 + 141022/235*e^3 - 50904/235*e^2 - 41151/47*e + 27924/47, 182/235*e^8 - 1379/235*e^7 + 179/47*e^6 + 13496/235*e^5 - 496/5*e^4 - 28096/235*e^3 + 60462/235*e^2 + 800/47*e - 4364/47, -409/235*e^8 + 2638/235*e^7 + 209/47*e^6 - 30112/235*e^5 + 457/5*e^4 + 92692/235*e^3 - 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1713/10*e^4 - 145479/235*e^3 + 251441/470*e^2 + 42363/94*e - 15642/47, 659/470*e^8 - 3303/470*e^7 - 951/47*e^6 + 58647/470*e^5 + 603/10*e^4 - 157866/235*e^3 + 83359/470*e^2 + 93475/94*e - 29450/47, 131/47*e^8 - 857/47*e^7 - 216/47*e^6 + 9443/47*e^5 - 169*e^4 - 27024/47*e^3 + 24348/47*e^2 + 19576/47*e - 16564/47, -12/47*e^8 + 62/47*e^7 + 98/47*e^6 - 691/47*e^5 - 5*e^4 + 1853/47*e^3 + 933/47*e^2 - 366/47*e - 964/47, 1274/235*e^8 - 8008/235*e^7 - 1097/47*e^6 + 99407/235*e^5 - 1142/5*e^4 - 358117/235*e^3 + 249569/235*e^2 + 74878/47*e - 55740/47, -363/235*e^8 + 2416/235*e^7 + 137/47*e^6 - 28599/235*e^5 + 519/5*e^4 + 96344/235*e^3 - 92978/235*e^2 - 19562/47*e + 17884/47, -111/94*e^8 + 691/94*e^7 + 230/47*e^6 - 8307/94*e^5 + 95/2*e^4 + 14028/47*e^3 - 18007/94*e^2 - 25875/94*e + 7738/47, -603/235*e^8 + 4126/235*e^7 - 129/47*e^6 - 41009/235*e^5 + 1074/5*e^4 + 86169/235*e^3 - 122258/235*e^2 - 1474/47*e + 5944/47, 424/235*e^8 - 2833/235*e^7 - 69/47*e^6 + 30682/235*e^5 - 627/5*e^4 - 83787/235*e^3 + 87354/235*e^2 + 10990/47*e - 10396/47, -88/235*e^8 + 956/235*e^7 - 555/47*e^6 - 3814/235*e^5 + 654/5*e^4 - 32816/235*e^3 - 43918/235*e^2 + 18705/47*e - 10112/47, -23/10*e^8 + 151/10*e^7 + 6*e^6 - 1809/10*e^5 + 1333/10*e^4 + 3112/5*e^3 - 5153/10*e^2 - 1271/2*e + 490, -3/47*e^8 + 39/47*e^7 - 46/47*e^6 - 725/47*e^5 + 31*e^4 + 4188/47*e^3 - 8309/47*e^2 - 7541/47*e + 10992/47, -318/47*e^8 + 2066/47*e^7 + 905/47*e^6 - 24774/47*e^5 + 384*e^4 + 84707/47*e^3 - 72683/47*e^2 - 85087/47*e + 71556/47, -1047/235*e^8 + 6514/235*e^7 + 1038/47*e^6 - 83496/235*e^5 + 866/5*e^4 + 317961/235*e^3 - 224272/235*e^2 - 73216/47*e + 56752/47, -1764/235*e^8 + 10853/235*e^7 + 1772/47*e^6 - 136827/235*e^5 + 1332/5*e^4 + 506592/235*e^3 - 329324/235*e^2 - 111754/47*e + 81676/47, 39/10*e^8 - 213/10*e^7 - 41*e^6 + 3247/10*e^5 + 431/10*e^4 - 7621/5*e^3 + 5629/10*e^2 + 4135/2*e - 1330, 289/235*e^8 - 1783/235*e^7 - 295/47*e^6 + 22732/235*e^5 - 227/5*e^4 - 85912/235*e^3 + 61954/235*e^2 + 19120/47*e - 16748/47, -343/470*e^8 + 1921/470*e^7 + 248/47*e^6 - 23139/470*e^5 - 1/10*e^4 + 38207/235*e^3 - 8053/470*e^2 - 12249/94*e + 1614/47, -272/235*e^8 + 1374/235*e^7 + 720/47*e^6 - 22791/235*e^5 - 214/5*e^4 + 116841/235*e^3 - 29612/235*e^2 - 34014/47*e + 21436/47, -261/235*e^8 + 2077/235*e^7 - 509/47*e^6 - 15558/235*e^5 + 868/5*e^4 - 4077/235*e^3 - 68126/235*e^2 + 16846/47*e - 7004/47, 1819/235*e^8 - 11568/235*e^7 - 1196/47*e^6 + 137507/235*e^5 - 1962/5*e^4 - 459997/235*e^3 + 370579/235*e^2 + 88754/47*e - 71220/47, -926/235*e^8 + 5787/235*e^7 + 867/47*e^6 - 73728/235*e^5 + 818/5*e^4 + 279188/235*e^3 - 199781/235*e^2 - 64173/47*e + 48472/47, 851/470*e^8 - 5517/470*e^7 - 196/47*e^6 + 63593/470*e^5 - 1063/10*e^4 - 100874/235*e^3 + 175121/470*e^2 + 36949/94*e - 13958/47, -721/235*e^8 + 4532/235*e^7 + 587/47*e^6 - 55598/235*e^5 + 678/5*e^4 + 196283/235*e^3 - 142811/235*e^2 - 39728/47*e + 30600/47, 1214/235*e^8 - 7463/235*e^7 - 1234/47*e^6 + 94542/235*e^5 - 922/5*e^4 - 351672/235*e^3 + 232379/235*e^2 + 77144/47*e - 56046/47, -437/235*e^8 + 2109/235*e^7 + 1342/47*e^6 - 38226/235*e^5 - 489/5*e^4 + 207121/235*e^3 - 43397/235*e^2 - 60377/47*e + 37632/47, -4097/470*e^8 + 26189/470*e^7 + 1357/47*e^6 - 313841/470*e^5 + 4401/10*e^4 + 534663/235*e^3 - 835367/470*e^2 - 212235/94*e + 82850/47, 951/235*e^8 - 5877/235*e^7 - 947/47*e^6 + 74208/235*e^5 - 723/5*e^4 - 275783/235*e^3 + 177216/235*e^2 + 61717/47*e - 43668/47, -1627/235*e^8 + 10529/235*e^7 + 826/47*e^6 - 122691/235*e^5 + 1991/5*e^4 + 397026/235*e^3 - 349552/235*e^2 - 73652/47*e + 61596/47, -1/235*e^8 + 342/235*e^7 - 589/47*e^6 + 4897/235*e^5 + 468/5*e^4 - 72582/235*e^3 + 3309/235*e^2 + 30276/47*e - 20248/47, -42/235*e^8 + 499/235*e^7 - 345/47*e^6 - 891/235*e^5 + 366/5*e^4 - 30104/235*e^3 - 14477/235*e^2 + 16692/47*e - 8552/47, -363/235*e^8 + 2416/235*e^7 + 43/47*e^6 - 25779/235*e^5 + 549/5*e^4 + 67909/235*e^3 - 72768/235*e^2 - 7953/47*e + 6228/47, 877/235*e^8 - 5479/235*e^7 - 776/47*e^6 + 68106/235*e^5 - 771/5*e^4 - 247491/235*e^3 + 174862/235*e^2 + 53990/47*e - 41404/47, 1902/235*e^8 - 11989/235*e^7 - 1565/47*e^6 + 148651/235*e^5 - 1836/5*e^4 - 536996/235*e^3 + 404957/235*e^2 + 115820/47*e - 90532/47, 80/47*e^8 - 429/47*e^7 - 904/47*e^6 + 6612/47*e^5 + 38*e^4 - 31263/47*e^3 + 7786/47*e^2 + 42296/47*e - 23998/47, -1216/235*e^8 + 8147/235*e^7 + 244/47*e^6 - 91093/235*e^5 + 1843/5*e^4 + 270663/235*e^3 - 280986/235*e^2 - 42912/47*e + 39990/47, 144/235*e^8 - 1073/235*e^7 + 216/47*e^6 + 7117/235*e^5 - 352/5*e^4 + 11933/235*e^3 + 7369/235*e^2 - 13748/47*e + 11112/47, 418/235*e^8 - 2426/235*e^7 - 548/47*e^6 + 30924/235*e^5 - 164/5*e^4 - 115079/235*e^3 + 57858/235*e^2 + 24433/47*e - 14760/47, 163/47*e^8 - 1085/47*e^7 - 258/47*e^6 + 12539/47*e^5 - 237*e^4 - 40206/47*e^3 + 40237/47*e^2 + 37989/47*e - 33984/47, 454/235*e^8 - 3223/235*e^7 + 117/47*e^6 + 34407/235*e^5 - 897/5*e^4 - 91592/235*e^3 + 122974/235*e^2 + 10750/47*e - 14896/47, 189/235*e^8 - 953/235*e^7 - 398/47*e^6 + 12352/235*e^5 + 138/5*e^4 - 44542/235*e^3 - 12286/235*e^2 + 7136/47*e + 1824/47, 2016/235*e^8 - 12672/235*e^7 - 1676/47*e^6 + 156273/235*e^5 - 1878/5*e^4 - 558853/235*e^3 + 407256/235*e^2 + 118762/47*e - 90524/47, 240/47*e^8 - 1569/47*e^7 - 503/47*e^6 + 18097/47*e^5 - 316*e^4 - 57270/47*e^3 + 53109/47*e^2 + 51500/47*e - 44170/47, -878/235*e^8 + 5586/235*e^7 + 657/47*e^6 - 69084/235*e^5 + 949/5*e^4 + 248464/235*e^3 - 206803/235*e^2 - 53277/47*e + 44656/47, -1616/235*e^8 + 10057/235*e^7 + 1477/47*e^6 - 125563/235*e^5 + 1383/5*e^4 + 457528/235*e^3 - 319681/235*e^2 - 98227/47*e + 74704/47, 108/47*e^8 - 746/47*e^7 + 199/47*e^6 + 7206/47*e^5 - 209*e^4 - 13669/47*e^3 + 22999/47*e^2 - 1594/47*e - 3544/47, 1698/235*e^8 - 10371/235*e^7 - 1871/47*e^6 + 133849/235*e^5 - 1179/5*e^4 - 512874/235*e^3 + 329168/235*e^2 + 116794/47*e - 86252/47, 116/235*e^8 - 192/235*e^7 - 954/47*e^6 + 13338/235*e^5 + 687/5*e^4 - 113103/235*e^3 - 18889/235*e^2 + 40855/47*e - 20220/47, -774/235*e^8 + 4798/235*e^7 + 672/47*e^6 - 58552/235*e^5 + 667/5*e^4 + 206022/235*e^3 - 145799/235*e^2 - 43064/47*e + 33004/47, -201/94*e^8 + 1109/94*e^7 + 1091/47*e^6 - 17649/94*e^5 - 39/2*e^4 + 43666/47*e^3 - 36977/94*e^2 - 125487/94*e + 42146/47, 648/235*e^8 - 3771/235*e^7 - 955/47*e^6 + 50474/235*e^5 - 149/5*e^4 - 203744/235*e^3 + 80983/235*e^2 + 47832/47*e - 27170/47, -347/94*e^8 + 1973/94*e^7 + 1507/47*e^6 - 28273/94*e^5 + 39/2*e^4 + 61961/47*e^3 - 57139/94*e^2 - 158563/94*e + 53750/47, -89/235*e^8 + 1298/235*e^7 - 1003/47*e^6 - 3382/235*e^5 + 1092/5*e^4 - 62158/235*e^3 - 71394/235*e^2 + 31826/47*e - 15696/47, -1263/235*e^8 + 7771/235*e^7 + 1231/47*e^6 - 97109/235*e^5 + 989/5*e^4 + 353054/235*e^3 - 236853/235*e^2 - 75060/47*e + 56064/47, -671/235*e^8 + 4587/235*e^7 + 51/47*e^6 - 51348/235*e^5 + 1128/5*e^4 + 154683/235*e^3 - 175721/235*e^2 - 26169/47*e + 27988/47, -449/235*e^8 + 2688/235*e^7 + 525/47*e^6 - 33512/235*e^5 + 187/5*e^4 + 122212/235*e^3 - 46929/235*e^2 - 26112/47*e + 13394/47, 2699/470*e^8 - 17133/470*e^7 - 1207/47*e^6 + 220297/470*e^5 - 2587/10*e^4 - 422296/235*e^3 + 627399/470*e^2 + 196629/94*e - 76606/47, 1501/470*e^8 - 9267/470*e^7 - 813/47*e^6 + 120723/470*e^5 - 1093/10*e^4 - 236149/235*e^3 + 304711/470*e^2 + 111931/94*e - 40994/47, 1349/470*e^8 - 8513/470*e^7 - 645/47*e^6 + 110247/470*e^5 - 1187/10*e^4 - 214371/235*e^3 + 303369/470*e^2 + 100833/94*e - 39182/47, 2601/470*e^8 - 15577/470*e^7 - 1680/47*e^6 + 206703/470*e^5 - 1283/10*e^4 - 412219/235*e^3 + 453951/470*e^2 + 195909/94*e - 66342/47, 933/470*e^8 - 5831/470*e^7 - 487/47*e^6 + 75639/470*e^5 - 679/10*e^4 - 146407/235*e^3 + 173563/470*e^2 + 67125/94*e - 21706/47, 72/235*e^8 - 1359/235*e^7 + 1283/47*e^6 + 151/235*e^5 - 1281/5*e^4 + 97734/235*e^3 + 66782/235*e^2 - 46824/47*e + 22946/47, -681/470*e^8 + 2837/470*e^7 + 1381/47*e^6 - 60893/470*e^5 - 1497/10*e^4 + 185724/235*e^3 + 6359/470*e^2 - 116329/94*e + 30066/47, 1877/470*e^8 - 12839/470*e^7 + 80/47*e^6 + 134541/470*e^5 - 3221/10*e^4 - 169738/235*e^3 + 409427/470*e^2 + 34569/94*e - 18246/47, -262/235*e^8 + 1479/235*e^7 + 547/47*e^6 - 23351/235*e^5 - 19/5*e^4 + 112751/235*e^3 - 53537/235*e^2 - 31086/47*e + 22004/47, 456/235*e^8 - 2967/235*e^7 - 350/47*e^6 + 38478/235*e^5 - 543/5*e^4 - 149938/235*e^3 + 131866/235*e^2 + 35832/47*e - 31552/47, 169/94*e^8 - 975/94*e^7 - 741/47*e^6 + 14271/94*e^5 - 23/2*e^4 - 31999/47*e^3 + 29313/94*e^2 + 82587/94*e - 26010/47, -31/470*e^8 + 1437/470*e^7 - 1022/47*e^6 + 9867/470*e^5 + 1903/10*e^4 - 98541/235*e^3 - 90121/470*e^2 + 81981/94*e - 21598/47, -58/235*e^8 + 566/235*e^7 - 228/47*e^6 - 4789/235*e^5 + 379/5*e^4 + 4969/235*e^3 - 53183/235*e^2 + 1404/47*e + 6256/47, -861/235*e^8 + 5177/235*e^7 + 1035/47*e^6 - 66793/235*e^5 + 453/5*e^4 + 254483/235*e^3 - 133336/235*e^2 - 56280/47*e + 35620/47, 3253/470*e^8 - 20951/470*e^7 - 1050/47*e^6 + 254509/470*e^5 - 3729/10*e^4 - 445067/235*e^3 + 738133/470*e^2 + 185993/94*e - 74822/47, 343/470*e^8 - 3331/470*e^7 + 692/47*e^6 + 23139/470*e^5 - 1979/10*e^4 + 9733/235*e^3 + 201223/470*e^2 - 27419/94*e - 1426/47, -743/235*e^8 + 4536/235*e^7 + 930/47*e^6 - 61604/235*e^5 + 474/5*e^4 + 253644/235*e^3 - 162603/235*e^2 - 62206/47*e + 46308/47, 691/235*e^8 - 4377/235*e^7 - 585/47*e^6 + 54928/235*e^5 - 648/5*e^4 - 203048/235*e^3 + 142911/235*e^2 + 46172/47*e - 32774/47, -444/235*e^8 + 2388/235*e^7 + 885/47*e^6 - 34262/235*e^5 - 113/5*e^4 + 150247/235*e^3 - 45379/235*e^2 - 39124/47*e + 23266/47, -353/235*e^8 + 2991/235*e^7 - 882/47*e^6 - 22814/235*e^5 + 1459/5*e^4 - 1276/235*e^3 - 146043/235*e^2 + 20496/47*e + 28/47, 149/47*e^8 - 950/47*e^7 - 457/47*e^6 + 11020/47*e^5 - 153*e^4 - 35185/47*e^3 + 24664/47*e^2 + 30794/47*e - 19160/47, -52/235*e^8 - 76/235*e^7 + 768/47*e^6 - 10201/235*e^5 - 519/5*e^4 + 102061/235*e^3 - 18047/235*e^2 - 38876/47*e + 28198/47, -213/94*e^8 + 1359/94*e^7 + 341/47*e^6 - 16131/94*e^5 + 233/2*e^4 + 26991/47*e^3 - 43517/94*e^2 - 52533/94*e + 20326/47, -2649/470*e^8 + 16013/470*e^7 + 1456/47*e^6 - 202417/470*e^5 + 1687/10*e^4 + 374706/235*e^3 - 446929/470*e^2 - 162719/94*e + 56782/47, 2997/470*e^8 - 19879/470*e^7 - 443/47*e^6 + 224571/470*e^5 - 4211/10*e^4 - 341203/235*e^3 + 654167/470*e^2 + 112465/94*e - 49606/47, 2371/470*e^8 - 15407/470*e^7 - 560/47*e^6 + 176813/470*e^5 - 2843/10*e^4 - 276354/235*e^3 + 456441/470*e^2 + 94631/94*e - 36026/47, -266/235*e^8 + 1672/235*e^7 + 306/47*e^6 - 23503/235*e^5 + 258/5*e^4 + 102543/235*e^3 - 88476/235*e^2 - 28234/47*e + 26176/47, -2473/235*e^8 + 15041/235*e^7 + 2753/47*e^6 - 193379/235*e^5 + 1649/5*e^4 + 736789/235*e^3 - 461553/235*e^2 - 166289/47*e + 120628/47, 487/94*e^8 - 2853/94*e^7 - 1781/47*e^6 + 38857/94*e^5 - 165/2*e^4 - 80486/47*e^3 + 82679/94*e^2 + 199963/94*e - 66770/47, 76/235*e^8 - 612/235*e^7 + 114/47*e^6 + 6648/235*e^5 - 303/5*e^4 - 20368/235*e^3 + 51431/235*e^2 + 5596/47*e - 8580/47, -743/235*e^8 + 5006/235*e^7 + 131/47*e^6 - 55964/235*e^5 + 1149/5*e^4 + 165519/235*e^3 - 176468/235*e^2 - 26110/47*e + 26756/47, -253/235*e^8 + 1926/235*e^7 - 309/47*e^6 - 17134/235*e^5 + 719/5*e^4 + 20569/235*e^3 - 78148/235*e^2 + 7476/47*e + 3546/47, 979/470*e^8 - 6053/470*e^7 - 570/47*e^6 + 81617/470*e^5 - 727/10*e^4 - 167611/235*e^3 + 232849/470*e^2 + 83395/94*e - 31642/47, 935/94*e^8 - 5951/94*e^7 - 1652/47*e^6 + 72049/94*e^5 - 985/2*e^4 - 124961/47*e^3 + 196367/94*e^2 + 255269/94*e - 100914/47, -162/235*e^8 + 179/235*e^7 + 1543/47*e^6 - 21431/235*e^5 - 1104/5*e^4 + 190761/235*e^3 + 16003/235*e^2 - 69533/47*e + 37648/47, 579/235*e^8 - 2968/235*e^7 - 1505/47*e^6 + 49027/235*e^5 + 418/5*e^4 - 246822/235*e^3 + 62789/235*e^2 + 69534/47*e - 42200/47];
heckeEigenvalues := AssociativeArray();
for i := 1 to #heckeEigenvaluesArray do
  heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i];
end for;

ALEigenvalues := AssociativeArray();
ALEigenvalues[ideal<ZF | {3, 3, w - 1}>] := 1;
ALEigenvalues[ideal<ZF | {7, 7, w - 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;