/* 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 := PolynomialRing(Rationals()); g := P![45, 15, -14, -2, 1]; F := NumberField(g); ZF := Integers(F); NN := ideal; primesArray := [ [5, 5, 2/3*w^2 + 1/3*w - 5], [5, 5, 2/3*w^2 - 5/3*w - 4], [9, 3, -w + 3], [9, 3, w + 2], [11, 11, 2/3*w^2 + 1/3*w - 4], [16, 2, 2], [19, 19, 1/3*w^3 - 10/3*w - 3], [19, 19, 1/3*w^3 - w^2 - 7/3*w + 6], [29, 29, -1/3*w^3 + 2/3*w^2 + 8/3*w - 2], [29, 29, 1/3*w^3 - 1/3*w^2 - 3*w + 1], [31, 31, -1/3*w^3 + 1/3*w^2 + 3*w + 1], [31, 31, -1/3*w^3 + 2/3*w^2 + 8/3*w - 4], [49, 7, 1/3*w^3 - 10/3*w - 1], [49, 7, -1/3*w^3 + w^2 + 7/3*w - 4], [59, 59, -1/3*w^3 + 5/3*w^2 + 5/3*w - 11], [59, 59, -2/3*w^3 + 5/3*w^2 + 5*w - 13], [61, 61, -1/3*w^3 + 5/3*w^2 + 2/3*w - 9], [61, 61, -1/3*w^3 + 1/3*w^2 + 4*w + 2], [61, 61, 2/3*w^2 - 5/3*w - 1], [61, 61, -1/3*w^2 + 4/3*w + 6], [71, 71, -4/3*w^2 + 7/3*w + 11], [79, 79, -1/3*w^2 + 7/3*w - 3], [79, 79, -2/3*w^3 + 1/3*w^2 + 16/3*w - 4], [101, 101, 2/3*w^2 - 5/3*w - 6], [101, 101, -2/3*w^2 - 1/3*w + 7], [109, 109, -4/3*w^2 + 1/3*w + 9], [109, 109, 1/3*w^3 - 1/3*w^2 - 3*w - 4], [121, 11, -1/3*w^2 + 1/3*w + 6], [131, 131, -2/3*w^3 + 2/3*w^2 + 5*w - 7], [131, 131, 2/3*w^3 - 4/3*w^2 - 13/3*w - 2], [151, 151, -1/3*w^3 - 2/3*w^2 + 5*w + 7], [151, 151, 1/3*w^3 - 10/3*w + 2], [169, 13, 5/3*w^2 + 1/3*w - 11], [169, 13, 5/3*w^2 - 11/3*w - 9], [181, 181, -1/3*w^3 + 4/3*w^2 + 3*w - 8], [181, 181, -1/3*w^3 - 1/3*w^2 + 14/3*w + 4], [191, 191, -2/3*w^3 + w^2 + 17/3*w - 9], [191, 191, 1/3*w^3 - 2*w^2 - 7/3*w + 13], [191, 191, 2/3*w^3 - 1/3*w^2 - 22/3*w - 7], [191, 191, 2/3*w^3 - w^2 - 17/3*w - 3], [199, 199, 1/3*w^3 + w^2 - 13/3*w - 9], [199, 199, 2/3*w^2 - 5/3*w - 7], [199, 199, 1/3*w^3 - w^2 - 4/3*w + 6], [199, 199, -1/3*w^3 + 2*w^2 + 4/3*w - 12], [269, 269, -1/3*w^3 - 4/3*w^2 + 11/3*w + 14], [269, 269, 1/3*w^3 - 7/3*w^2 + 16], [271, 271, 2/3*w^2 + 1/3*w - 9], [271, 271, 2/3*w^2 - 5/3*w - 8], [281, 281, 1/3*w^3 + w^2 - 13/3*w - 11], [281, 281, -2/3*w^3 + 20/3*w + 3], [281, 281, -w^2 + 3*w + 2], [281, 281, -1/3*w^3 + 2*w^2 + 4/3*w - 14], [289, 17, w^3 - 8/3*w^2 - 16/3*w + 4], [289, 17, -w^3 + 1/3*w^2 + 23/3*w - 3], [331, 331, -2/3*w^3 + 2*w^2 + 11/3*w - 7], [331, 331, 2/3*w^3 - 17/3*w - 2], [359, 359, -1/3*w^3 - 1/3*w^2 + 11/3*w - 2], [359, 359, 1/3*w^3 + 4/3*w^2 - 17/3*w - 12], [361, 19, 4/3*w^2 - 4/3*w - 11], [389, 389, 5/3*w^2 - 8/3*w - 13], [389, 389, 5/3*w^2 - 2/3*w - 14], [401, 401, -1/3*w^3 + 5/3*w^2 + 11/3*w - 12], [401, 401, 1/3*w^3 + 2/3*w^2 - 6*w - 7], [409, 409, 1/3*w^3 + 1/3*w^2 - 14/3*w - 3], [409, 409, -1/3*w^3 + 4/3*w^2 + 3*w - 7], [421, 421, -1/3*w^3 + 5/3*w^2 + 11/3*w - 13], [421, 421, 1/3*w^3 + 2/3*w^2 - 6*w - 8], [431, 431, 2/3*w^2 + 4/3*w - 9], [431, 431, 2/3*w^2 - 8/3*w - 7], [449, 449, 2/3*w^3 - 17/3*w + 2], [449, 449, 1/3*w^3 + 4/3*w^2 - 20/3*w - 11], [461, 461, 1/3*w^2 + 5/3*w - 8], [461, 461, 1/3*w^3 + 1/3*w^2 - 17/3*w - 3], [461, 461, -1/3*w^3 + 4/3*w^2 + 4*w - 8], [461, 461, 1/3*w^2 - 7/3*w - 6], [479, 479, -1/3*w^3 + 2/3*w^2 + 5/3*w - 9], [479, 479, 4/3*w^3 + w^2 - 40/3*w - 18], [479, 479, 4/3*w^3 - 5*w^2 - 22/3*w + 29], [479, 479, 1/3*w^3 - 1/3*w^2 - 2*w - 7], [491, 491, 2/3*w^3 - 5/3*w^2 - 5*w + 8], [491, 491, -1/3*w^3 + 3*w^2 + 10/3*w - 24], [491, 491, 1/3*w^3 + 2*w^2 - 25/3*w - 18], [491, 491, 2/3*w^3 - 1/3*w^2 - 19/3*w - 2], [499, 499, -1/3*w^3 + 10/3*w^2 - 4*w - 17], [499, 499, 1/3*w^3 - 7/3*w - 9], [499, 499, -1/3*w^3 + w^2 + 4/3*w - 11], [499, 499, -w^3 + 5/3*w^2 + 22/3*w - 14], [509, 509, w^3 - 14/3*w^2 - 10/3*w + 24], [509, 509, -2/3*w^2 + 5/3*w + 11], [509, 509, 2/3*w^2 + 1/3*w - 12], [509, 509, -2/3*w^3 + 3*w^2 + 8/3*w - 18], [521, 521, 1/3*w^3 - 13/3*w + 1], [521, 521, w^3 + 2/3*w^2 - 32/3*w - 12], [521, 521, 2/3*w^3 + 7/3*w^2 - 13*w - 23], [521, 521, -1/3*w^3 + w^2 + 10/3*w - 3], [541, 541, 2/3*w^3 - 17/3*w - 3], [541, 541, -1/3*w^3 + 4/3*w^2 + 2*w - 14], [541, 541, -1/3*w^3 + 4/3*w^2 + w - 1], [541, 541, -1/3*w^3 + 1/3*w^2 + 5*w - 4], [569, 569, 1/3*w^3 + 11/3*w^2 - 12*w - 26], [569, 569, -w^3 + 10/3*w^2 + 23/3*w - 21], [571, 571, w^3 - 7/3*w^2 - 23/3*w + 17], [571, 571, 2/3*w^3 - 3*w^2 - 11/3*w + 17], [599, 599, 1/3*w^3 + 2/3*w^2 - 4*w - 1], [599, 599, 1/3*w^3 - 5/3*w^2 - 5/3*w + 4], [601, 601, 1/3*w^3 - 7/3*w - 6], [601, 601, -2/3*w^3 + 2*w^2 + 11/3*w - 9], [601, 601, 2/3*w^3 - 17/3*w - 4], [601, 601, -1/3*w^3 + w^2 + 4/3*w - 8], [619, 619, -2/3*w^3 + 10/3*w^2 + 19/3*w - 26], [619, 619, 2/3*w^3 + 4/3*w^2 - 11*w - 17], [631, 631, 1/3*w^3 - 7/3*w^2 - w + 14], [631, 631, 1/3*w^3 + 4/3*w^2 - 14/3*w - 11], [659, 659, -2/3*w^3 + 2/3*w^2 + 6*w + 1], [659, 659, 2/3*w^3 - 4/3*w^2 - 16/3*w + 7], [661, 661, -2/3*w^3 + 13/3*w^2 + 16/3*w - 32], [661, 661, -2/3*w^3 - 7/3*w^2 + 12*w + 23], [691, 691, 1/3*w^3 - 11/3*w^2 - 11/3*w + 29], [691, 691, -2/3*w^3 + 10/3*w^2 + 10/3*w - 23], [701, 701, 2/3*w^3 - 4/3*w^2 - 13/3*w - 3], [701, 701, 2/3*w^3 - 4/3*w^2 - 16/3*w - 1], [701, 701, -2/3*w^3 + 2/3*w^2 + 6*w - 7], [701, 701, -2/3*w^3 + 2/3*w^2 + 5*w - 8], [709, 709, -4/3*w^3 + 31/3*w - 2], [709, 709, -w^3 + 1/3*w^2 + 32/3*w + 4], [719, 719, -2/3*w^3 + w^2 + 17/3*w - 2], [719, 719, 1/3*w^3 - 2*w^2 - 4/3*w + 9], [719, 719, 1/3*w^3 + w^2 - 13/3*w - 6], [719, 719, 2/3*w^3 - w^2 - 17/3*w + 4], [739, 739, 2/3*w^3 + 2/3*w^2 - 19/3*w - 11], [739, 739, -2/3*w^3 + 8/3*w^2 + 3*w - 16], [751, 751, -1/3*w^3 + w^2 + 4/3*w - 9], [751, 751, 1/3*w^3 - 7/3*w - 7], [761, 761, 1/3*w^3 - 16/3*w - 4], [761, 761, w^3 - 1/3*w^2 - 29/3*w - 12], [761, 761, -w^3 + 8/3*w^2 + 22/3*w - 21], [761, 761, -1/3*w^3 + w^2 + 13/3*w - 9], [769, 769, w^3 - 7/3*w^2 - 23/3*w + 8], [769, 769, 1/3*w^3 + 4/3*w^2 - 14/3*w - 14], [769, 769, -1/3*w^3 + 7/3*w^2 + w - 17], [769, 769, 1/3*w^3 - 3*w^2 + 11/3*w + 13], [811, 811, 1/3*w^3 + w^2 - 10/3*w - 12], [811, 811, -1/3*w^3 + 2*w^2 + 1/3*w - 14], [821, 821, -1/3*w^3 + 13/3*w - 3], [821, 821, -1/3*w^3 + w^2 + 10/3*w - 1], [839, 839, -w^3 - 5/3*w^2 + 32/3*w + 18], [839, 839, 1/3*w^3 + 3*w^2 - 7/3*w - 22], [839, 839, 1/3*w^3 - 4*w^2 + 14/3*w + 21], [839, 839, -w^3 + 14/3*w^2 + 13/3*w - 26], [841, 29, -5/3*w^2 + 5/3*w + 11], [859, 859, -w^3 + 5/3*w^2 + 25/3*w - 1], [859, 859, -w^3 + 4/3*w^2 + 26/3*w - 8], [911, 911, -1/3*w^3 + 1/3*w^2 + 5*w + 1], [911, 911, 1/3*w^3 - 2/3*w^2 - 14/3*w + 6], [919, 919, 2/3*w^3 - 2/3*w^2 - 5*w - 7], [919, 919, -2/3*w^3 + 7/3*w^2 + 10/3*w - 7], [919, 919, 2/3*w^3 + 1/3*w^2 - 6*w - 2], [919, 919, -2/3*w^3 + 4/3*w^2 + 13/3*w - 12], [941, 941, 5/3*w^2 + 1/3*w - 9], [941, 941, 5/3*w^2 - 11/3*w - 7], [961, 31, 5/3*w^2 - 5/3*w - 13], [971, 971, -1/3*w^3 + w^2 + 13/3*w - 8], [971, 971, 2/3*w^3 - 2/3*w^2 - 5*w + 2], [971, 971, -2/3*w^3 + 4/3*w^2 + 13/3*w - 3], [971, 971, 1/3*w^3 - 16/3*w - 3], [991, 991, 10/3*w^2 - 22/3*w - 19], [991, 991, 10/3*w^2 + 2/3*w - 23], [1009, 1009, -2*w^2 + 3*w + 16], [1009, 1009, 2*w^2 - w - 17], [1019, 1019, 1/3*w^3 + w^2 - 19/3*w - 14], [1019, 1019, -1/3*w^3 + 2*w^2 + 10/3*w - 19], [1021, 1021, 2/3*w^3 - 3*w^2 - 14/3*w + 19], [1021, 1021, 11/3*w^2 + 4/3*w - 27], [1021, 1021, 11/3*w^2 - 26/3*w - 22], [1021, 1021, -2/3*w^3 - w^2 + 26/3*w + 12], [1031, 1031, -2/3*w^3 + 5/3*w^2 + 4*w + 1], [1031, 1031, -2/3*w^3 + 1/3*w^2 + 16/3*w - 6], [1049, 1049, -1/3*w^3 - 2/3*w^2 + 4*w - 1], [1049, 1049, 1/3*w^3 + 5/3*w^2 - 6*w - 14], [1051, 1051, 1/3*w^3 - 16/3*w - 2], [1051, 1051, -1/3*w^3 + w^2 + 13/3*w - 7], [1061, 1061, 11/3*w^2 + 1/3*w - 27], [1061, 1061, 11/3*w^2 - 23/3*w - 23], [1069, 1069, w^2 + 2*w - 11], [1069, 1069, w^2 - 4*w - 8], [1109, 1109, w^3 - 5/3*w^2 - 19/3*w - 1], [1109, 1109, -w^3 - w^2 + 12*w + 16], [1129, 1129, -w^3 + 5/3*w^2 + 25/3*w - 11], [1129, 1129, -w^3 + 4/3*w^2 + 26/3*w + 2], [1151, 1151, 1/3*w^3 + w^2 - 16/3*w - 7], [1151, 1151, -1/3*w^3 + 2*w^2 + 7/3*w - 11], [1171, 1171, w^3 - 8/3*w^2 - 16/3*w + 1], [1171, 1171, -w^3 + 1/3*w^2 + 23/3*w - 6], [1201, 1201, -1/3*w^3 + 2/3*w^2 + 14/3*w - 4], [1201, 1201, -1/3*w^3 - 4/3*w^2 + 8/3*w + 13], [1201, 1201, 1/3*w^3 - 7/3*w^2 + w + 14], [1201, 1201, 1/3*w^3 - 1/3*w^2 - 5*w + 1], [1231, 1231, -1/3*w^3 + 5/3*w^2 + 8/3*w - 8], [1231, 1231, 1/3*w^3 + 2/3*w^2 - 5*w - 4], [1249, 1249, -4/3*w^3 + 7/3*w^2 + 9*w + 4], [1249, 1249, 4/3*w^2 - 13/3*w - 9], [1249, 1249, 4/3*w^2 + 5/3*w - 12], [1249, 1249, -4/3*w^3 + 5/3*w^2 + 29/3*w - 14], [1259, 1259, 2/3*w^3 - w^2 - 20/3*w + 11], [1259, 1259, -2/3*w^3 + w^2 + 20/3*w + 4], [1279, 1279, -2/3*w^3 - 1/3*w^2 + 5*w + 8], [1279, 1279, 1/3*w^3 - w^2 - 7/3*w + 12], [1279, 1279, -2*w^2 + 3*w + 13], [1279, 1279, -2/3*w^3 + 7/3*w^2 + 7/3*w - 12], [1289, 1289, w^3 + 1/3*w^2 - 28/3*w - 8], [1289, 1289, -2/3*w^3 + 3*w^2 + 8/3*w - 19], [1289, 1289, 2/3*w^3 + w^2 - 20/3*w - 14], [1289, 1289, 5/3*w^3 - 11/3*w^2 - 11*w - 1], [1291, 1291, -w^3 + 2/3*w^2 + 25/3*w - 7], [1291, 1291, w^3 - 7/3*w^2 - 20/3*w + 1], [1301, 1301, w^3 - 10/3*w^2 - 14/3*w + 16], [1301, 1301, -w^3 + 14/3*w^2 + 25/3*w - 34], [1319, 1319, -5/3*w^3 + 6*w^2 + 17/3*w - 14], [1319, 1319, 1/3*w^3 - 2/3*w^2 - 8/3*w - 4], [1319, 1319, -1/3*w^3 + 1/3*w^2 + 3*w - 7], [1319, 1319, -5/3*w^3 - w^2 + 38/3*w + 4], [1361, 1361, w^3 - 4*w^2 - 6*w + 23], [1361, 1361, w^3 + w^2 - 11*w - 14], [1369, 37, -w^3 + 7*w - 4], [1369, 37, -1/3*w^3 - 2*w^2 + 10/3*w + 16], [1381, 1381, -2/3*w^3 + 20/3*w + 1], [1381, 1381, 2/3*w^3 - 2*w^2 - 14/3*w + 7], [1399, 1399, -w^3 + 4/3*w^2 + 20/3*w + 4], [1399, 1399, -w^3 + 5/3*w^2 + 19/3*w - 11], [1429, 1429, -2/3*w^3 + 2/3*w^2 + 4*w - 7], [1429, 1429, w^3 + 1/3*w^2 - 19/3*w + 1], [1451, 1451, w^3 - 4/3*w^2 - 23/3*w + 9], [1451, 1451, -1/3*w^3 + 2*w^2 - 2/3*w - 12], [1451, 1451, -1/3*w^3 - w^2 + 7/3*w + 11], [1451, 1451, 1/3*w^3 - 8/3*w^2 + 10/3*w + 12], [1459, 1459, -2/3*w^3 + 8/3*w^2 + 5*w - 16], [1459, 1459, -1/3*w^3 + 8/3*w^2 + 2/3*w - 16], [1459, 1459, -1/3*w^3 - 5/3*w^2 + 5*w + 13], [1459, 1459, 2/3*w^3 + 2/3*w^2 - 25/3*w - 9], [1471, 1471, -2/3*w^3 + 3*w^2 + 5/3*w - 16], [1471, 1471, -13/3*w^2 - 5/3*w + 33], [1471, 1471, -13/3*w^2 + 31/3*w + 27], [1471, 1471, 2/3*w^3 + w^2 - 17/3*w - 12], [1489, 1489, 1/3*w^3 - 7/3*w^2 - 4*w + 17], [1489, 1489, 1/3*w^3 + 4/3*w^2 - 23/3*w - 11], [1531, 1531, -w^3 + 3*w^2 + 7*w - 17], [1531, 1531, w^3 - 10*w - 8], [1549, 1549, w^3 + 2/3*w^2 - 35/3*w - 13], [1549, 1549, -2/3*w^3 + 5*w^2 + 17/3*w - 36], [1549, 1549, -2/3*w^3 - 3*w^2 + 41/3*w + 26], [1549, 1549, -w^3 + 11/3*w^2 + 22/3*w - 23], [1571, 1571, -w^3 + 3*w^2 + 7*w - 23], [1571, 1571, -1/3*w^3 - 2*w^2 + 4/3*w + 17], [1571, 1571, -1/3*w^3 + 1/3*w^2 + 6*w - 13], [1571, 1571, -2/3*w^3 + 4*w^2 + 8/3*w - 23], [1601, 1601, -w^3 + 4/3*w^2 + 26/3*w - 11], [1601, 1601, -w^3 + 8/3*w^2 + 25/3*w - 24], [1601, 1601, -1/3*w^3 - 7/3*w^2 + 23/3*w + 18], [1601, 1601, -w^3 + 5/3*w^2 + 25/3*w + 2], [1609, 1609, -5/3*w^3 + 2/3*w^2 + 12*w - 8], [1609, 1609, 2/3*w^3 + 4/3*w^2 - 7*w - 17], [1619, 1619, w^3 - 4/3*w^2 - 23/3*w - 3], [1619, 1619, -w^3 + 5/3*w^2 + 22/3*w - 11], [1621, 1621, 7/3*w^2 - 13/3*w - 11], [1621, 1621, -2/3*w^3 + 8/3*w^2 + 6*w - 17], [1669, 1669, 5/3*w^2 + 1/3*w - 16], [1669, 1669, 5/3*w^2 - 11/3*w - 14], [1681, 41, 2*w^2 - 2*w - 17], [1681, 41, 2*w^2 - 2*w - 13], [1699, 1699, 1/3*w^3 - 2*w^2 + 5/3*w + 11], [1699, 1699, -1/3*w^3 - w^2 + 4/3*w + 11], [1721, 1721, 1/3*w^2 + 8/3*w - 11], [1721, 1721, 1/3*w^2 - 10/3*w - 8], [1789, 1789, -2/3*w^2 - 7/3*w - 4], [1789, 1789, -w^3 + 2*w^2 + 8*w - 13], [1789, 1789, 4/3*w^2 - 13/3*w - 8], [1789, 1789, 2/3*w^2 - 11/3*w + 7], [1811, 1811, 2/3*w^2 - 11/3*w - 9], [1811, 1811, 2/3*w^2 + 7/3*w - 12], [1831, 1831, 4/3*w^2 + 5/3*w - 9], [1831, 1831, -w^3 + 5/3*w^2 + 25/3*w - 2], [1861, 1861, 14/3*w^2 + 1/3*w - 33], [1861, 1861, 14/3*w^2 - 29/3*w - 28], [1871, 1871, -w^3 + 2/3*w^2 + 28/3*w - 3], [1871, 1871, 1/3*w^3 + w^2 - 22/3*w - 7], [1871, 1871, -1/3*w^3 + 2*w^2 + 13/3*w - 13], [1871, 1871, -w^3 + 7/3*w^2 + 23/3*w - 6], [1879, 1879, -w^3 + 8/3*w^2 + 22/3*w - 13], [1879, 1879, -w^3 + 1/3*w^2 + 29/3*w + 4], [1889, 1889, -5/3*w^3 + 2*w^2 + 38/3*w - 16], [1889, 1889, 5/3*w^3 - 3*w^2 - 35/3*w - 3], [1901, 1901, w^2 - 3*w - 11], [1901, 1901, w^2 + w - 13], [1931, 1931, 2/3*w^3 + 2*w^2 - 38/3*w - 21], [1931, 1931, w^3 - 2/3*w^2 - 25/3*w - 9], [1931, 1931, -w^3 + 7/3*w^2 + 20/3*w - 17], [1931, 1931, -2/3*w^3 + 4*w^2 + 20/3*w - 31], [1949, 1949, 2/3*w^3 + 5/3*w^2 - 28/3*w - 21], [1949, 1949, -1/3*w^3 + 3*w^2 + 1/3*w - 17], [1951, 1951, -1/3*w^3 + 8/3*w^2 + 2/3*w - 19], [1951, 1951, 1/3*w^3 + 5/3*w^2 - 5*w - 16], [1999, 1999, -5/3*w^3 + 3*w^2 + 38/3*w - 23], [1999, 1999, -1/3*w^3 - 5/3*w^2 + 4*w + 19], [1999, 1999, 1/3*w^3 - 8/3*w^2 + 1/3*w + 21], [1999, 1999, 5/3*w^3 - 2*w^2 - 41/3*w - 9]]; primes := [ideal : I in primesArray]; heckePol := x^10 - 11*x^9 + 13*x^8 + 200*x^7 - 504*x^6 - 1059*x^5 + 3342*x^4 + 1360*x^3 - 5392*x^2 + 128*x + 512; K := NumberField(heckePol); heckeEigenvaluesArray := [1, 1, e, e, -911/256104*e^9 + 1835/85368*e^8 + 26785/256104*e^7 - 39929/64026*e^6 - 32450/32013*e^5 + 1373509/256104*e^4 + 501913/128052*e^3 - 445016/32013*e^2 - 50297/10671*e + 164974/32013, -865/2048832*e^9 + 4741/682944*e^8 - 54313/2048832*e^7 - 26785/512208*e^6 + 85937/256104*e^5 - 145789/2048832*e^4 - 161629/1024416*e^3 + 62663/256104*e^2 - 146029/42684*e + 53371/32013, -e + 2, -e + 2, 847/512208*e^9 - 3713/170736*e^8 + 22021/512208*e^7 + 111485/256104*e^6 - 46645/32013*e^5 - 1416173/512208*e^4 + 1394423/128052*e^3 + 661841/128052*e^2 - 211472/10671*e + 79976/32013, 847/512208*e^9 - 3713/170736*e^8 + 22021/512208*e^7 + 111485/256104*e^6 - 46645/32013*e^5 - 1416173/512208*e^4 + 1394423/128052*e^3 + 661841/128052*e^2 - 211472/10671*e + 79976/32013, 4873/512208*e^9 - 7147/85368*e^8 - 11143/256104*e^7 + 854437/512208*e^6 - 40666/32013*e^5 - 5196299/512208*e^4 + 4562123/512208*e^3 + 4083091/256104*e^2 - 206573/21342*e + 140546/32013, 4873/512208*e^9 - 7147/85368*e^8 - 11143/256104*e^7 + 854437/512208*e^6 - 40666/32013*e^5 - 5196299/512208*e^4 + 4562123/512208*e^3 + 4083091/256104*e^2 - 206573/21342*e + 140546/32013, -6203/1024416*e^9 + 19507/341472*e^8 + 8785/1024416*e^7 - 148993/128052*e^6 + 142717/128052*e^5 + 8180593/1024416*e^4 - 3731669/512208*e^3 - 1253647/64026*e^2 + 219005/21342*e + 255766/32013, -6203/1024416*e^9 + 19507/341472*e^8 + 8785/1024416*e^7 - 148993/128052*e^6 + 142717/128052*e^5 + 8180593/1024416*e^4 - 3731669/512208*e^3 - 1253647/64026*e^2 + 219005/21342*e + 255766/32013, 325/170736*e^9 + 43/170736*e^8 - 8399/56912*e^7 + 5359/28456*e^6 + 26365/10671*e^5 - 443615/170736*e^4 - 52676/3557*e^3 + 110019/14228*e^2 + 293782/10671*e - 38966/10671, 325/170736*e^9 + 43/170736*e^8 - 8399/56912*e^7 + 5359/28456*e^6 + 26365/10671*e^5 - 443615/170736*e^4 - 52676/3557*e^3 + 110019/14228*e^2 + 293782/10671*e - 38966/10671, -1181/341472*e^9 + 3027/113824*e^8 + 11929/341472*e^7 - 86155/170736*e^6 + 6649/42684*e^5 + 737335/341472*e^4 - 138409/85368*e^3 + 310499/85368*e^2 - 2072/3557*e - 89420/10671, -589/42684*e^9 + 6897/56912*e^8 + 3241/56912*e^7 - 136043/56912*e^6 + 91967/42684*e^5 + 194733/14228*e^4 - 880591/56912*e^3 - 509083/28456*e^2 + 186800/10671*e + 7046/3557, -589/42684*e^9 + 6897/56912*e^8 + 3241/56912*e^7 - 136043/56912*e^6 + 91967/42684*e^5 + 194733/14228*e^4 - 880591/56912*e^3 - 509083/28456*e^2 + 186800/10671*e + 7046/3557, -1181/341472*e^9 + 3027/113824*e^8 + 11929/341472*e^7 - 86155/170736*e^6 + 6649/42684*e^5 + 737335/341472*e^4 - 138409/85368*e^3 + 310499/85368*e^2 - 2072/3557*e - 89420/10671, 13417/1024416*e^9 - 33913/341472*e^8 - 177971/1024416*e^7 + 65603/32013*e^6 + 68869/128052*e^5 - 13031483/1024416*e^4 + 91579/512208*e^3 + 643075/32013*e^2 - 222437/21342*e - 41774/32013, 277/128052*e^9 - 139/28456*e^8 - 26983/256104*e^7 + 24023/256104*e^6 + 62687/32013*e^5 - 112799/128052*e^4 - 2988677/256104*e^3 + 372437/128052*e^2 + 90310/10671*e - 120214/32013, 277/128052*e^9 - 139/28456*e^8 - 26983/256104*e^7 + 24023/256104*e^6 + 62687/32013*e^5 - 112799/128052*e^4 - 2988677/256104*e^3 + 372437/128052*e^2 + 90310/10671*e - 120214/32013, 5833/1024416*e^9 - 11023/341472*e^8 - 188813/1024416*e^7 + 491699/512208*e^6 + 278815/128052*e^5 - 9251579/1024416*e^4 - 2761057/256104*e^3 + 7059725/256104*e^2 + 156152/10671*e - 331868/32013, 5833/1024416*e^9 - 11023/341472*e^8 - 188813/1024416*e^7 + 491699/512208*e^6 + 278815/128052*e^5 - 9251579/1024416*e^4 - 2761057/256104*e^3 + 7059725/256104*e^2 + 156152/10671*e - 331868/32013, -1293/56912*e^9 + 11671/56912*e^8 + 3079/56912*e^7 - 28377/7114*e^6 + 14240/3557*e^5 + 1338503/56912*e^4 - 750743/28456*e^3 - 271621/7114*e^2 + 97415/3557*e + 15656/3557, -1293/56912*e^9 + 11671/56912*e^8 + 3079/56912*e^7 - 28377/7114*e^6 + 14240/3557*e^5 + 1338503/56912*e^4 - 750743/28456*e^3 - 271621/7114*e^2 + 97415/3557*e + 15656/3557, 12245/512208*e^9 - 34957/170736*e^8 - 75199/512208*e^7 + 264313/64026*e^6 - 182245/64026*e^5 - 12366847/512208*e^4 + 5730755/256104*e^3 + 975928/32013*e^2 - 106647/3557*e + 359194/32013, -2567/256104*e^9 + 3805/56912*e^8 + 98273/512208*e^7 - 679513/512208*e^6 - 68666/32013*e^5 + 2115661/256104*e^4 + 6992923/512208*e^3 - 3248179/256104*e^2 - 439675/21342*e - 132434/32013, -2567/256104*e^9 + 3805/56912*e^8 + 98273/512208*e^7 - 679513/512208*e^6 - 68666/32013*e^5 + 2115661/256104*e^4 + 6992923/512208*e^3 - 3248179/256104*e^2 - 439675/21342*e - 132434/32013, -6931/1024416*e^9 + 23933/341472*e^8 - 52297/1024416*e^7 - 704405/512208*e^6 + 393107/128052*e^5 + 7876697/1024416*e^4 - 5992919/256104*e^3 - 2228075/256104*e^2 + 480754/10671*e - 108082/32013, -6931/1024416*e^9 + 23933/341472*e^8 - 52297/1024416*e^7 - 704405/512208*e^6 + 393107/128052*e^5 + 7876697/1024416*e^4 - 5992919/256104*e^3 - 2228075/256104*e^2 + 480754/10671*e - 108082/32013, 6385/1024416*e^9 - 3907/113824*e^8 - 158915/1024416*e^7 + 71069/128052*e^6 + 312229/128052*e^5 - 1872755/1024416*e^4 - 9056153/512208*e^3 - 329749/64026*e^2 + 629567/21342*e - 36752/32013, 6385/1024416*e^9 - 3907/113824*e^8 - 158915/1024416*e^7 + 71069/128052*e^6 + 312229/128052*e^5 - 1872755/1024416*e^4 - 9056153/512208*e^3 - 329749/64026*e^2 + 629567/21342*e - 36752/32013, 18389/1024416*e^9 - 20325/113824*e^8 + 84059/1024416*e^7 + 1723897/512208*e^6 - 367499/64026*e^5 - 19539679/1024416*e^4 + 4810583/128052*e^3 + 7359889/256104*e^2 - 1116143/21342*e - 74230/32013, 18389/1024416*e^9 - 20325/113824*e^8 + 84059/1024416*e^7 + 1723897/512208*e^6 - 367499/64026*e^5 - 19539679/1024416*e^4 + 4810583/128052*e^3 + 7359889/256104*e^2 - 1116143/21342*e - 74230/32013, 5611/341472*e^9 - 59059/341472*e^8 + 60293/341472*e^7 + 505255/170736*e^6 - 48085/7114*e^5 - 4840385/341472*e^4 + 1671785/42684*e^3 + 1277383/85368*e^2 - 943795/21342*e - 3008/3557, 212/32013*e^9 - 10733/170736*e^8 - 15007/512208*e^7 + 755873/512208*e^6 - 170375/128052*e^5 - 354877/32013*e^4 + 5168629/512208*e^3 + 6655793/256104*e^2 - 102470/10671*e - 148436/32013, 212/32013*e^9 - 10733/170736*e^8 - 15007/512208*e^7 + 755873/512208*e^6 - 170375/128052*e^5 - 354877/32013*e^4 + 5168629/512208*e^3 + 6655793/256104*e^2 - 102470/10671*e - 148436/32013, 5611/341472*e^9 - 59059/341472*e^8 + 60293/341472*e^7 + 505255/170736*e^6 - 48085/7114*e^5 - 4840385/341472*e^4 + 1671785/42684*e^3 + 1277383/85368*e^2 - 943795/21342*e - 3008/3557, -5947/1024416*e^9 + 27019/341472*e^8 - 186439/1024416*e^7 - 45155/32013*e^6 + 645677/128052*e^5 + 8351249/1024416*e^4 - 16894705/512208*e^3 - 544741/32013*e^2 + 1165487/21342*e + 379022/32013, -6385/1024416*e^9 + 3907/113824*e^8 + 158915/1024416*e^7 - 71069/128052*e^6 - 312229/128052*e^5 + 1872755/1024416*e^4 + 9056153/512208*e^3 + 329749/64026*e^2 - 608225/21342*e - 91300/32013, -6385/1024416*e^9 + 3907/113824*e^8 + 158915/1024416*e^7 - 71069/128052*e^6 - 312229/128052*e^5 + 1872755/1024416*e^4 + 9056153/512208*e^3 + 329749/64026*e^2 - 608225/21342*e - 91300/32013, -5947/1024416*e^9 + 27019/341472*e^8 - 186439/1024416*e^7 - 45155/32013*e^6 + 645677/128052*e^5 + 8351249/1024416*e^4 - 16894705/512208*e^3 - 544741/32013*e^2 + 1165487/21342*e + 379022/32013, 4717/341472*e^9 - 11313/113824*e^8 - 78059/341472*e^7 + 179125/85368*e^6 + 79033/42684*e^5 - 5017511/341472*e^4 - 1813967/170736*e^3 + 1473295/42684*e^2 + 168629/7114*e - 112880/10671, 4717/341472*e^9 - 11313/113824*e^8 - 78059/341472*e^7 + 179125/85368*e^6 + 79033/42684*e^5 - 5017511/341472*e^4 - 1813967/170736*e^3 + 1473295/42684*e^2 + 168629/7114*e - 112880/10671, 1165/128052*e^9 - 10429/170736*e^8 - 73607/512208*e^7 + 507061/512208*e^6 + 218207/128052*e^5 - 470555/128052*e^4 - 7199767/512208*e^3 - 1649183/256104*e^2 + 361525/10671*e + 397628/32013, 1165/128052*e^9 - 10429/170736*e^8 - 73607/512208*e^7 + 507061/512208*e^6 + 218207/128052*e^5 - 470555/128052*e^4 - 7199767/512208*e^3 - 1649183/256104*e^2 + 361525/10671*e + 397628/32013, -17803/512208*e^9 + 54383/170736*e^8 + 13949/512208*e^7 - 762475/128052*e^6 + 211522/32013*e^5 + 17158529/512208*e^4 - 10675963/256104*e^3 - 1602161/32013*e^2 + 200963/3557*e + 236548/32013, -4847/256104*e^9 + 25223/170736*e^8 + 112961/512208*e^7 - 1556185/512208*e^6 - 7643/32013*e^5 + 5024221/256104*e^4 - 966245/512208*e^3 - 10000267/256104*e^2 - 10007/21342*e + 758716/32013, -4847/256104*e^9 + 25223/170736*e^8 + 112961/512208*e^7 - 1556185/512208*e^6 - 7643/32013*e^5 + 5024221/256104*e^4 - 966245/512208*e^3 - 10000267/256104*e^2 - 10007/21342*e + 758716/32013, -17803/512208*e^9 + 54383/170736*e^8 + 13949/512208*e^7 - 762475/128052*e^6 + 211522/32013*e^5 + 17158529/512208*e^4 - 10675963/256104*e^3 - 1602161/32013*e^2 + 200963/3557*e + 236548/32013, -2995/341472*e^9 + 30577/341472*e^8 - 12631/341472*e^7 - 79463/42684*e^6 + 144209/42684*e^5 + 1247411/113824*e^4 - 4186165/170736*e^3 - 219203/21342*e^2 + 251471/7114*e - 130244/10671, -2995/341472*e^9 + 30577/341472*e^8 - 12631/341472*e^7 - 79463/42684*e^6 + 144209/42684*e^5 + 1247411/113824*e^4 - 4186165/170736*e^3 - 219203/21342*e^2 + 251471/7114*e - 130244/10671, -235/21342*e^9 + 15019/170736*e^8 + 3329/56912*e^7 - 75735/56912*e^6 + 11335/42684*e^5 + 100781/21342*e^4 + 1565/56912*e^3 + 144985/28456*e^2 + 85432/10671*e - 200780/10671, -235/21342*e^9 + 15019/170736*e^8 + 3329/56912*e^7 - 75735/56912*e^6 + 11335/42684*e^5 + 100781/21342*e^4 + 1565/56912*e^3 + 144985/28456*e^2 + 85432/10671*e - 200780/10671, -253/1024416*e^9 - 15983/341472*e^8 + 403355/1024416*e^7 + 109115/256104*e^6 - 1008607/128052*e^5 + 2423063/1024416*e^4 + 23646935/512208*e^3 - 2722873/128052*e^2 - 1351087/21342*e + 581474/32013, -253/1024416*e^9 - 15983/341472*e^8 + 403355/1024416*e^7 + 109115/256104*e^6 - 1008607/128052*e^5 + 2423063/1024416*e^4 + 23646935/512208*e^3 - 2722873/128052*e^2 - 1351087/21342*e + 581474/32013, 3229/170736*e^9 - 35099/170736*e^8 + 13719/56912*e^7 + 51395/14228*e^6 - 95450/10671*e^5 - 3128279/170736*e^4 + 1565103/28456*e^3 + 87915/3557*e^2 - 751757/10671*e + 159016/10671, -18115/1024416*e^9 + 67459/341472*e^8 - 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181147/341472*e^7 + 588605/85368*e^6 + 28309/42684*e^5 - 4906845/113824*e^4 + 1360097/170736*e^3 + 2534699/42684*e^2 - 517079/21342*e + 330874/10671, 4863/113824*e^9 - 112835/341472*e^8 - 181147/341472*e^7 + 588605/85368*e^6 + 28309/42684*e^5 - 4906845/113824*e^4 + 1360097/170736*e^3 + 2534699/42684*e^2 - 517079/21342*e + 330874/10671, -3411/56912*e^9 + 106363/170736*e^8 - 85693/170736*e^7 - 120580/10671*e^6 + 484825/21342*e^5 + 3479145/56912*e^4 - 11797555/85368*e^3 - 889238/10671*e^2 + 1774807/10671*e + 165218/10671, -8437/170736*e^9 + 73723/170736*e^8 + 34627/170736*e^7 - 348185/42684*e^6 + 38607/7114*e^5 + 8203967/170736*e^4 - 2678609/85368*e^3 - 1836995/21342*e^2 + 298273/10671*e + 260734/3557, 4465/170736*e^9 - 40561/170736*e^8 - 10825/170736*e^7 + 404305/85368*e^6 - 17620/3557*e^5 - 5030771/170736*e^4 + 414166/10671*e^3 + 2147017/42684*e^2 - 825376/10671*e + 129902/3557, 4465/170736*e^9 - 40561/170736*e^8 - 10825/170736*e^7 + 404305/85368*e^6 - 17620/3557*e^5 - 5030771/170736*e^4 + 414166/10671*e^3 + 2147017/42684*e^2 - 825376/10671*e + 129902/3557, 1216/32013*e^9 - 65791/170736*e^8 + 155731/512208*e^7 + 3446659/512208*e^6 - 1843207/128052*e^5 - 1024796/32013*e^4 + 46951415/512208*e^3 + 5832823/256104*e^2 - 1316669/10671*e + 231398/32013, 1216/32013*e^9 - 65791/170736*e^8 + 155731/512208*e^7 + 3446659/512208*e^6 - 1843207/128052*e^5 - 1024796/32013*e^4 + 46951415/512208*e^3 + 5832823/256104*e^2 - 1316669/10671*e + 231398/32013, 1687/32013*e^9 - 42377/85368*e^8 + 13553/256104*e^7 + 2409041/256104*e^6 - 412846/32013*e^5 - 1763243/32013*e^4 + 23882353/256104*e^3 + 11930651/128052*e^2 - 1968851/10671*e - 611194/32013, -4307/128052*e^9 + 20455/85368*e^8 + 129701/256104*e^7 - 1207021/256104*e^6 - 140615/64026*e^5 + 2796481/128052*e^4 + 1336675/256104*e^3 + 2399087/128052*e^2 + 56719/10671*e - 2239660/32013, -4307/128052*e^9 + 20455/85368*e^8 + 129701/256104*e^7 - 1207021/256104*e^6 - 140615/64026*e^5 + 2796481/128052*e^4 + 1336675/256104*e^3 + 2399087/128052*e^2 + 56719/10671*e - 2239660/32013, 1687/32013*e^9 - 42377/85368*e^8 + 13553/256104*e^7 + 2409041/256104*e^6 - 412846/32013*e^5 - 1763243/32013*e^4 + 23882353/256104*e^3 + 11930651/128052*e^2 - 1968851/10671*e - 611194/32013, -12035/1024416*e^9 + 22673/113824*e^8 - 721871/1024416*e^7 - 96970/32013*e^6 + 2114113/128052*e^5 + 11922601/1024416*e^4 - 50670089/512208*e^3 - 279365/32013*e^2 + 2986175/21342*e + 1014622/32013, -12035/1024416*e^9 + 22673/113824*e^8 - 721871/1024416*e^7 - 96970/32013*e^6 + 2114113/128052*e^5 + 11922601/1024416*e^4 - 50670089/512208*e^3 - 279365/32013*e^2 + 2986175/21342*e + 1014622/32013, -19337/1024416*e^9 + 84289/341472*e^8 - 568277/1024416*e^7 - 540781/128052*e^6 + 2108455/128052*e^5 + 16725499/1024416*e^4 - 54204623/512208*e^3 + 1078703/64026*e^2 + 3338083/21342*e - 1026464/32013, -19337/1024416*e^9 + 84289/341472*e^8 - 568277/1024416*e^7 - 540781/128052*e^6 + 2108455/128052*e^5 + 16725499/1024416*e^4 - 54204623/512208*e^3 + 1078703/64026*e^2 + 3338083/21342*e - 1026464/32013, -803/256104*e^9 - 1703/56912*e^8 + 281009/512208*e^7 - 332833/512208*e^6 - 1073783/128052*e^5 + 3147529/256104*e^4 + 21900127/512208*e^3 - 9678949/256104*e^2 - 732971/10671*e - 112562/32013, -803/256104*e^9 - 1703/56912*e^8 + 281009/512208*e^7 - 332833/512208*e^6 - 1073783/128052*e^5 + 3147529/256104*e^4 + 21900127/512208*e^3 - 9678949/256104*e^2 - 732971/10671*e - 112562/32013, -9757/341472*e^9 + 35935/113824*e^8 - 106771/341472*e^7 - 1055585/170736*e^6 + 572561/42684*e^5 + 13289111/341472*e^4 - 1918871/21342*e^3 - 6876263/85368*e^2 + 494105/3557*e + 156614/10671, -6181/341472*e^9 + 42895/341472*e^8 + 112279/341472*e^7 - 58001/21342*e^6 - 31243/14228*e^5 + 5802287/341472*e^4 + 786649/170736*e^3 - 207755/10671*e^2 + 456127/21342*e - 32226/3557, -6181/341472*e^9 + 42895/341472*e^8 + 112279/341472*e^7 - 58001/21342*e^6 - 31243/14228*e^5 + 5802287/341472*e^4 + 786649/170736*e^3 - 207755/10671*e^2 + 456127/21342*e - 32226/3557, -9757/341472*e^9 + 35935/113824*e^8 - 106771/341472*e^7 - 1055585/170736*e^6 + 572561/42684*e^5 + 13289111/341472*e^4 - 1918871/21342*e^3 - 6876263/85368*e^2 + 494105/3557*e + 156614/10671, -6869/113824*e^9 + 51691/113824*e^8 + 290617/341472*e^7 - 815171/85368*e^6 - 149713/42684*e^5 + 20647933/341472*e^4 + 1845397/170736*e^3 - 3784559/42684*e^2 - 652621/21342*e - 460340/10671, -6869/113824*e^9 + 51691/113824*e^8 + 290617/341472*e^7 - 815171/85368*e^6 - 149713/42684*e^5 + 20647933/341472*e^4 + 1845397/170736*e^3 - 3784559/42684*e^2 - 652621/21342*e - 460340/10671, -6097/341472*e^9 + 42731/341472*e^8 + 35489/113824*e^7 - 39255/14228*e^6 - 73643/42684*e^5 + 6717299/341472*e^4 - 56517/56912*e^3 - 198895/3557*e^2 + 1114487/21342*e + 669838/10671, -6097/341472*e^9 + 42731/341472*e^8 + 35489/113824*e^7 - 39255/14228*e^6 - 73643/42684*e^5 + 6717299/341472*e^4 - 56517/56912*e^3 - 198895/3557*e^2 + 1114487/21342*e + 669838/10671, 61043/1024416*e^9 - 189685/341472*e^8 + 8897/1024416*e^7 + 5459233/512208*e^6 - 1793011/128052*e^5 - 62678521/1024416*e^4 + 23895421/256104*e^3 + 24496927/256104*e^2 - 390854/3557*e - 441484/32013, 61043/1024416*e^9 - 189685/341472*e^8 + 8897/1024416*e^7 + 5459233/512208*e^6 - 1793011/128052*e^5 - 62678521/1024416*e^4 + 23895421/256104*e^3 + 24496927/256104*e^2 - 390854/3557*e - 441484/32013, -8/32013*e^9 - 313/14228*e^8 + 24403/128052*e^7 + 31627/128052*e^6 - 125740/32013*e^5 - 5333/32013*e^4 + 3162707/128052*e^3 - 100139/64026*e^2 - 68822/3557*e - 507412/32013, -917/32013*e^9 + 11219/56912*e^8 + 309691/512208*e^7 - 2396549/512208*e^6 - 743347/128052*e^5 + 1158757/32013*e^4 + 17289983/512208*e^3 - 23403257/256104*e^2 - 797323/10671*e + 1120640/32013, -917/32013*e^9 + 11219/56912*e^8 + 309691/512208*e^7 - 2396549/512208*e^6 - 743347/128052*e^5 + 1158757/32013*e^4 + 17289983/512208*e^3 - 23403257/256104*e^2 - 797323/10671*e + 1120640/32013, -8/32013*e^9 - 313/14228*e^8 + 24403/128052*e^7 + 31627/128052*e^6 - 125740/32013*e^5 - 5333/32013*e^4 + 3162707/128052*e^3 - 100139/64026*e^2 - 68822/3557*e - 507412/32013, 45167/1024416*e^9 - 43185/113824*e^8 - 194497/1024416*e^7 + 1790045/256104*e^6 - 637921/128052*e^5 - 36879085/1024416*e^4 + 13844135/512208*e^3 + 4039475/128052*e^2 - 202313/21342*e + 1007744/32013, 45167/1024416*e^9 - 43185/113824*e^8 - 194497/1024416*e^7 + 1790045/256104*e^6 - 637921/128052*e^5 - 36879085/1024416*e^4 + 13844135/512208*e^3 + 4039475/128052*e^2 - 202313/21342*e + 1007744/32013, -1343/256104*e^9 + 6773/170736*e^8 + 29507/512208*e^7 - 404551/512208*e^6 + 4498/32013*e^5 + 1362973/256104*e^4 - 2321027/512208*e^3 - 3233317/256104*e^2 + 113957/7114*e + 165334/32013, -1343/256104*e^9 + 6773/170736*e^8 + 29507/512208*e^7 - 404551/512208*e^6 + 4498/32013*e^5 + 1362973/256104*e^4 - 2321027/512208*e^3 - 3233317/256104*e^2 + 113957/7114*e + 165334/32013, 5275/170736*e^9 - 29947/170736*e^8 - 144107/170736*e^7 + 334271/85368*e^6 + 232279/21342*e^5 - 1505531/56912*e^4 - 693934/10671*e^3 + 2020613/42684*e^2 + 345398/3557*e - 174416/10671, -512/32013*e^9 + 11417/85368*e^8 + 18323/256104*e^7 - 593629/256104*e^6 + 135871/64026*e^5 + 224251/32013*e^4 - 3563345/256104*e^3 + 4949423/128052*e^2 + 91440/3557*e - 2552884/32013, -512/32013*e^9 + 11417/85368*e^8 + 18323/256104*e^7 - 593629/256104*e^6 + 135871/64026*e^5 + 224251/32013*e^4 - 3563345/256104*e^3 + 4949423/128052*e^2 + 91440/3557*e - 2552884/32013, 5275/170736*e^9 - 29947/170736*e^8 - 144107/170736*e^7 + 334271/85368*e^6 + 232279/21342*e^5 - 1505531/56912*e^4 - 693934/10671*e^3 + 2020613/42684*e^2 + 345398/3557*e - 174416/10671]; heckeEigenvalues := AssociativeArray(); for i := 1 to #heckeEigenvaluesArray do heckeEigenvalues[primes[i]] := heckeEigenvaluesArray[i]; end for; ALEigenvalues := AssociativeArray(); ALEigenvalues[ideal] := -1; ALEigenvalues[ideal] := -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;