/* 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![41, 9, -14, -1, 1]; F := NumberField(g); ZF := Integers(F); NN := ideal; primesArray := [ [4, 2, 1/6*w^3 - 7/3*w - 17/6], [4, 2, w - 3], [5, 5, -1/6*w^3 + w^2 + 1/3*w - 25/6], [9, 3, 1/6*w^3 - 7/3*w + 13/6], [9, 3, -w - 2], [11, 11, -1/6*w^3 + 7/3*w + 11/6], [11, 11, -w + 2], [41, 41, -w], [41, 41, 1/6*w^3 - 7/3*w + 1/6], [59, 59, -1/6*w^3 + 1/3*w + 23/6], [59, 59, -1/3*w^3 + 11/3*w + 11/3], [61, 61, -5/3*w^3 - 3*w^2 + 46/3*w + 79/3], [61, 61, 5/6*w^3 + w^2 - 23/3*w - 55/6], [61, 61, w^3 + 2*w^2 - 9*w - 17], [61, 61, -1/6*w^3 + 10/3*w + 35/6], [71, 71, -1/2*w^3 + 2*w^2 + 4*w - 33/2], [71, 71, 1/6*w^3 - w^2 - 4/3*w + 67/6], [79, 79, 1/2*w^3 - 3*w + 1/2], [79, 79, -2/3*w^3 + 19/3*w - 2/3], [89, 89, 1/2*w^3 + w^2 - 5*w - 15/2], [89, 89, 1/3*w^3 - 11/3*w + 7/3], [101, 101, -5/6*w^3 - w^2 + 23/3*w + 61/6], [101, 101, 1/2*w^3 - w^2 - 3*w + 9/2], [109, 109, 1/2*w^3 - w^2 - 4*w + 11/2], [109, 109, -2/3*w^3 - w^2 + 16/3*w + 28/3], [121, 11, -1/2*w^3 + 4*w + 1/2], [131, 131, 2*w - 7], [131, 131, -7/6*w^3 - 2*w^2 + 28/3*w + 89/6], [139, 139, -1/6*w^3 + w^2 + 4/3*w - 31/6], [139, 139, 1/3*w^3 + w^2 - 8/3*w - 29/3], [149, 149, 1/6*w^3 - 2*w^2 + 5/3*w + 37/6], [151, 151, -7/6*w^3 + 3*w^2 + 28/3*w - 133/6], [151, 151, 5/3*w^3 + 3*w^2 - 40/3*w - 67/3], [169, 13, -1/6*w^3 - 2/3*w + 29/6], [169, 13, 7/6*w^3 - 4*w^2 - 19/3*w + 139/6], [181, 181, -2/3*w^3 + 13/3*w + 10/3], [181, 181, 5/6*w^3 - 23/3*w - 19/6], [191, 191, 5/6*w^3 + w^2 - 32/3*w - 97/6], [191, 191, w^3 - 9*w - 5], [191, 191, -w^2 + 4*w - 2], [191, 191, 5/6*w^3 + w^2 - 17/3*w - 43/6], [199, 199, 1/2*w^3 - 2*w - 7/2], [199, 199, 7/6*w^3 - 5*w^2 - 7/3*w + 109/6], [211, 211, -1/6*w^3 + w^2 + 7/3*w - 79/6], [211, 211, 1/2*w^3 + 2*w^2 - 6*w - 37/2], [229, 229, -1/2*w^3 + 5*w - 5/2], [229, 229, 1/2*w^3 - 2*w^2 - 2*w + 23/2], [229, 229, 1/6*w^3 + w^2 - 10/3*w - 53/6], [229, 229, -7/6*w^3 - 2*w^2 + 34/3*w + 107/6], [239, 239, 2*w^3 + 3*w^2 - 22*w - 36], [239, 239, -7/3*w^3 - 3*w^2 + 74/3*w + 113/3], [241, 241, -1/3*w^3 - w^2 + 2/3*w + 11/3], [241, 241, -1/2*w^3 + w^2 + 6*w - 23/2], [271, 271, -5/6*w^3 - w^2 + 20/3*w + 49/6], [271, 271, 1/6*w^3 - 1/3*w - 35/6], [281, 281, -1/6*w^3 - w^2 + 7/3*w + 11/6], [281, 281, -w^3 + 9*w - 1], [281, 281, -1/2*w^3 + 8*w + 19/2], [281, 281, w^3 - 4*w^2 - 4*w + 20], [311, 311, 2*w^2 - 13], [311, 311, -1/3*w^3 - 2*w^2 + 8/3*w + 50/3], [331, 331, 1/2*w^3 + w^2 - 4*w - 5/2], [331, 331, -1/2*w^3 - w^2 + 5*w + 27/2], [331, 331, 1/6*w^3 - 2*w^2 + 2/3*w + 73/6], [331, 331, 5/6*w^3 + 2*w^2 - 26/3*w - 103/6], [349, 349, -1/2*w^3 - w^2 + 4*w + 21/2], [349, 349, 1/6*w^3 + w^2 - 1/3*w - 59/6], [361, 19, 2/3*w^3 - 16/3*w - 7/3], [361, 19, 1/6*w^3 - 4/3*w - 29/6], [379, 379, 1/6*w^3 + w^2 - 10/3*w - 17/6], [379, 379, -5/6*w^3 - 2*w^2 + 23/3*w + 115/6], [379, 379, -1/3*w^3 + 2*w^2 + 5/3*w - 31/3], [379, 379, 1/3*w^3 + w^2 - 14/3*w - 35/3], [389, 389, -1/3*w^3 + 2/3*w + 14/3], [389, 389, 1/2*w^3 + 2*w^2 - 4*w - 35/2], [401, 401, 1/3*w^3 + 2*w^2 - 14/3*w - 38/3], [401, 401, 5/6*w^3 - 4*w^2 - 5/3*w + 101/6], [401, 401, -1/3*w^3 - 2*w^2 + 14/3*w + 50/3], [401, 401, -5/6*w^3 + 2*w^2 + 5/3*w - 29/6], [409, 409, -1/2*w^3 + 6*w - 7/2], [409, 409, 5/6*w^3 + 2*w^2 - 26/3*w - 91/6], [439, 439, 1/3*w^3 + 2*w^2 - 14/3*w - 32/3], [439, 439, 1/3*w^3 + 2*w^2 - 14/3*w - 56/3], [449, 449, -11/6*w^3 - 3*w^2 + 47/3*w + 157/6], [449, 449, -7/6*w^3 + 3*w^2 + 25/3*w - 109/6], [461, 461, 1/6*w^3 + 2*w^2 - 4/3*w - 77/6], [461, 461, 2/3*w^3 + 2*w^2 - 22/3*w - 55/3], [479, 479, 2/3*w^3 - 2*w^2 - 13/3*w + 32/3], [479, 479, -7/6*w^3 - 2*w^2 + 31/3*w + 113/6], [491, 491, 1/3*w^3 + 2*w^2 - 11/3*w - 35/3], [491, 491, 1/6*w^3 + 2*w^2 - 7/3*w - 107/6], [499, 499, 4/3*w^3 + 2*w^2 - 38/3*w - 53/3], [499, 499, 5/6*w^3 - 4*w^2 - 2/3*w + 101/6], [509, 509, -2/3*w^3 + 31/3*w + 40/3], [509, 509, 1/6*w^3 - 19/3*w + 85/6], [521, 521, -2/3*w^3 - 2*w^2 + 19/3*w + 52/3], [521, 521, -w^2 - 2*w + 10], [529, 23, -1/3*w^3 + 2*w^2 + 5/3*w - 49/3], [529, 23, 5/6*w^3 + 2*w^2 - 23/3*w - 79/6], [541, 541, -1/6*w^3 + 10/3*w - 13/6], [541, 541, 1/6*w^3 - 10/3*w - 11/6], [569, 569, 1/2*w^3 + w^2 - 5*w - 9/2], [569, 569, -1/6*w^3 + w^2 + 1/3*w - 61/6], [599, 599, 1/6*w^3 + w^2 - 1/3*w - 65/6], [599, 599, -1/6*w^3 + w^2 + 7/3*w - 25/6], [619, 619, 7/2*w^3 + 6*w^2 - 33*w - 113/2], [619, 619, -7/6*w^3 - 2*w^2 + 31/3*w + 89/6], [631, 631, -1/2*w^3 + 3*w^2 + w - 29/2], [631, 631, -1/6*w^3 + w^2 - 8/3*w + 29/6], [631, 631, -2/3*w^3 + 25/3*w + 16/3], [631, 631, -11/6*w^3 - 3*w^2 + 47/3*w + 145/6], [659, 659, 5/6*w^3 - 3*w^2 - 20/3*w + 155/6], [659, 659, 7/6*w^3 - 2*w^2 - 16/3*w + 49/6], [659, 659, -7/6*w^3 + 34/3*w + 29/6], [659, 659, -5/6*w^3 + w^2 + 14/3*w - 35/6], [661, 661, 1/3*w^3 - 20/3*w + 28/3], [661, 661, 1/3*w^3 - 20/3*w - 26/3], [691, 691, 1/2*w^3 + 2*w^2 - 5*w - 35/2], [691, 691, 2*w^2 - 15], [691, 691, 1/2*w^3 + 2*w^2 - 6*w - 31/2], [691, 691, 2*w^2 - w - 12], [701, 701, 1/3*w^3 + 2*w^2 - 11/3*w - 53/3], [701, 701, 1/6*w^3 + 2*w^2 - 7/3*w - 71/6], [709, 709, -11/6*w^3 - 3*w^2 + 50/3*w + 151/6], [709, 709, 7/6*w^3 + w^2 - 25/3*w - 71/6], [709, 709, 7/6*w^3 - w^2 - 31/3*w + 19/6], [709, 709, 13/6*w^3 + 4*w^2 - 58/3*w - 209/6], [739, 739, 7/6*w^3 - 4*w^2 - 28/3*w + 199/6], [739, 739, 5/3*w^3 - 5*w^2 - 40/3*w + 119/3], [739, 739, 5/6*w^3 - 4*w^2 - 8/3*w + 107/6], [739, 739, -5/6*w^3 + w^2 + 26/3*w - 35/6], [809, 809, 11/6*w^3 + 3*w^2 - 56/3*w - 175/6], [809, 809, -5/6*w^3 + 2*w^2 + 17/3*w - 89/6], [809, 809, -4/3*w^3 + 4*w^2 + 14/3*w - 49/3], [809, 809, -5/6*w^3 + w^2 + 11/3*w - 23/6], [811, 811, -1/3*w^3 + 17/3*w + 17/3], [811, 811, -1/6*w^3 + 13/3*w - 37/6], [821, 821, w^3 - w^2 - 8*w + 3], [821, 821, -2*w^3 - 3*w^2 + 18*w + 28], [821, 821, 7/6*w^3 + w^2 - 28/3*w - 71/6], [821, 821, 1/2*w^3 - w^2 - 7*w + 35/2], [829, 829, 5/6*w^3 + w^2 - 20/3*w - 73/6], [829, 829, 1/6*w^3 + w^2 - 1/3*w - 71/6], [839, 839, 1/2*w^3 - 10*w + 33/2], [839, 839, 1/2*w^3 - 10*w - 31/2], [841, 29, 5/6*w^3 - 20/3*w - 19/6], [841, 29, 1/6*w^3 - 4/3*w - 35/6], [859, 859, -1/6*w^3 + 2*w^2 + 7/3*w - 121/6], [859, 859, -2*w^3 - 4*w^2 + 16*w + 27], [859, 859, 1/2*w^3 - w^2 - 4*w - 1/2], [859, 859, 4/3*w^3 - 4*w^2 - 32/3*w + 97/3], [881, 881, -5/6*w^3 + w^2 + 14/3*w - 11/6], [881, 881, 4/3*w^3 + w^2 - 38/3*w - 38/3], [911, 911, 2*w^2 - 3*w - 4], [911, 911, -2/3*w^3 + 19/3*w - 20/3], [911, 911, 2/3*w^3 + w^2 - 22/3*w - 46/3], [911, 911, -2/3*w^3 + 4*w^2 - 2/3*w - 35/3], [919, 919, -1/6*w^3 + 3*w^2 - 11/3*w - 43/6], [919, 919, -13/6*w^3 - 4*w^2 + 55/3*w + 179/6], [919, 919, 5/6*w^3 - 2*w^2 - 8/3*w + 47/6], [919, 919, 4/3*w^3 - 4*w^2 - 29/3*w + 88/3], [929, 929, -7/6*w^3 + 3*w^2 + 10/3*w - 61/6], [929, 929, -1/2*w^3 + 2*w^2 + 4*w - 25/2], [929, 929, -2/3*w^3 + 22/3*w + 19/3], [929, 929, 2*w^2 - 4*w - 3], [961, 31, 5/6*w^3 - 20/3*w - 13/6], [961, 31, -5/6*w^3 + 20/3*w + 7/6], [971, 971, -7/6*w^3 + 6*w^2 + 4/3*w - 139/6], [971, 971, -2/3*w^3 + 2*w^2 + 1/3*w - 14/3], [991, 991, 7/3*w^3 + 4*w^2 - 59/3*w - 95/3], [991, 991, -1/6*w^3 + w^2 - 11/3*w + 47/6], [1009, 1009, -7/6*w^3 - w^2 + 31/3*w + 35/6], [1009, 1009, -5/6*w^3 + w^2 + 17/3*w - 53/6], [1021, 1021, -11/6*w^3 - 3*w^2 + 44/3*w + 139/6], [1021, 1021, 4/3*w^3 - 3*w^2 - 32/3*w + 64/3], [1021, 1021, -w^3 + 11*w + 3], [1021, 1021, 1/2*w^3 - w - 7/2], [1031, 1031, -w^3 + 6*w + 2], [1031, 1031, 4/3*w^3 - 38/3*w - 5/3], [1049, 1049, -w^3 + 4*w^2 + 3*w - 19], [1049, 1049, -5/2*w^3 - 4*w^2 + 25*w + 79/2], [1049, 1049, -2*w^3 - 4*w^2 + 18*w + 31], [1049, 1049, -w^3 + 4*w^2 + 6*w - 28], [1051, 1051, -3/2*w^3 - 2*w^2 + 13*w + 33/2], [1051, 1051, 1/6*w^3 - w^2 + 5/3*w - 17/6], [1061, 1061, 7/6*w^3 - 5*w^2 - 13/3*w + 157/6], [1061, 1061, -1/2*w^3 + 9*w + 23/2], [1091, 1091, -4/3*w^3 + 2*w^2 + 17/3*w - 16/3], [1091, 1091, -1/6*w^3 + 2*w^2 - 8/3*w - 13/6], [1109, 1109, -1/6*w^3 + 2*w^2 - 2/3*w - 91/6], [1109, 1109, -5/6*w^3 - 2*w^2 + 26/3*w + 85/6], [1151, 1151, -1/2*w^3 + 5*w - 13/2], [1151, 1151, -7/6*w^3 - w^2 + 31/3*w + 59/6], [1171, 1171, 5/6*w^3 - w^2 - 17/3*w + 23/6], [1171, 1171, 7/6*w^3 + w^2 - 31/3*w - 65/6], [1181, 1181, w^2 - 6*w + 10], [1181, 1181, -7/6*w^3 - w^2 + 46/3*w + 143/6], [1229, 1229, -5/3*w^3 - 3*w^2 + 46/3*w + 73/3], [1229, 1229, 1/6*w^3 - w^2 - 13/3*w + 109/6], [1229, 1229, 5/6*w^3 - 3*w^2 - 14/3*w + 119/6], [1229, 1229, -1/6*w^3 + w^2 + 13/3*w + 17/6], [1231, 1231, -2/3*w^3 + 25/3*w - 8/3], [1231, 1231, -1/6*w^3 - 5/3*w - 13/6], [1231, 1231, 1/2*w^3 - w - 3/2], [1231, 1231, w^3 - 11*w - 1], [1249, 1249, 1/3*w^3 + 3*w^2 - 14/3*w - 89/3], [1249, 1249, 7/6*w^3 - 2*w^2 - 25/3*w + 43/6], [1279, 1279, -17/6*w^3 - 5*w^2 + 80/3*w + 265/6], [1279, 1279, 4/3*w^3 - 5*w^2 - 20/3*w + 88/3], [1289, 1289, 5/6*w^3 + 2*w^2 - 23/3*w - 127/6], [1289, 1289, 1/2*w^3 + w^2 - 2*w - 21/2], [1291, 1291, -1/3*w^3 + 26/3*w - 46/3], [1291, 1291, -2/3*w^3 + 34/3*w + 43/3], [1301, 1301, 19/6*w^3 + 5*w^2 - 88/3*w - 275/6], [1301, 1301, -5/3*w^3 + 5*w^2 + 28/3*w - 83/3], [1321, 1321, -2*w^3 - 4*w^2 + 19*w + 34], [1321, 1321, -7/6*w^3 + 2*w^2 + 28/3*w - 97/6], [1321, 1321, 5/3*w^3 + 2*w^2 - 46/3*w - 64/3], [1321, 1321, 5/6*w^3 - 4*w^2 - 11/3*w + 149/6], [1381, 1381, -7/6*w^3 - 3*w^2 + 34/3*w + 167/6], [1381, 1381, 1/3*w^3 - 3*w^2 - 2/3*w + 49/3], [1399, 1399, 7/6*w^3 - 4*w^2 - 22/3*w + 163/6], [1399, 1399, 13/6*w^3 + 4*w^2 - 58/3*w - 191/6], [1409, 1409, -3/2*w^3 + 4*w^2 + 10*w - 45/2], [1409, 1409, 2*w^2 - 9], [1409, 1409, -5/2*w^3 - 4*w^2 + 22*w + 73/2], [1409, 1409, 1/3*w^3 + 2*w^2 - 8/3*w - 62/3], [1439, 1439, 7/6*w^3 - 37/3*w + 7/6], [1439, 1439, -1/2*w^3 - 3*w^2 + 7*w + 33/2], [1459, 1459, 2*w^2 - 2*w - 17], [1459, 1459, -5/6*w^3 + 26/3*w + 55/6], [1459, 1459, 2/3*w^3 + 2*w^2 - 22/3*w - 37/3], [1459, 1459, -1/2*w^3 + 2*w + 19/2], [1511, 1511, 3/2*w^3 - 6*w^2 - 8*w + 75/2], [1511, 1511, -19/6*w^3 - 6*w^2 + 88/3*w + 305/6], [1531, 1531, 5/2*w^3 + 3*w^2 - 29*w - 87/2], [1531, 1531, -13/6*w^3 - 3*w^2 + 61/3*w + 179/6], [1549, 1549, 1/2*w^3 + 2*w^2 - 6*w - 21/2], [1549, 1549, w^3 - 10*w + 2], [1579, 1579, -1/2*w^3 + w^2 + 3*w - 21/2], [1579, 1579, 5/6*w^3 + w^2 - 23/3*w - 25/6], [1601, 1601, 1/3*w^3 + w^2 - 20/3*w - 5/3], [1601, 1601, -7/6*w^3 - 3*w^2 + 31/3*w + 131/6], [1609, 1609, 5/6*w^3 - w^2 - 23/3*w + 23/6], [1609, 1609, -11/6*w^3 - 3*w^2 + 50/3*w + 175/6], [1609, 1609, -5/6*w^3 - w^2 + 17/3*w + 67/6], [1609, 1609, -w^3 + 3*w^2 + 6*w - 15], [1619, 1619, 1/3*w^3 + 2*w^2 - 5/3*w - 53/3], [1619, 1619, 2/3*w^3 - w^2 - 16/3*w + 2/3], [1619, 1619, 3/2*w^3 + 2*w^2 - 12*w - 39/2], [1619, 1619, 1/3*w^3 - 2*w^2 - 14/3*w + 70/3], [1621, 1621, 1/6*w^3 + 3*w^2 - 4/3*w - 113/6], [1621, 1621, -1/3*w^3 - 3*w^2 + 8/3*w + 77/3], [1681, 41, w^3 - 8*w - 4], [1699, 1699, 5/6*w^3 + w^2 - 29/3*w - 37/6], [1699, 1699, -1/6*w^3 + w^2 - 5/3*w - 49/6], [1709, 1709, -1/6*w^3 - 2*w^2 + 13/3*w + 35/6], [1709, 1709, -3/2*w^3 - w^2 + 14*w + 15/2], [1721, 1721, -5/6*w^3 - w^2 + 35/3*w + 103/6], [1721, 1721, 5/3*w^3 + 2*w^2 - 43/3*w - 61/3], [1721, 1721, -7/6*w^3 + 2*w^2 + 25/3*w - 55/6], [1721, 1721, -1/6*w^3 - w^2 + 19/3*w - 19/6], [1741, 1741, 1/6*w^3 - 3*w^2 + 5/3*w + 115/6], [1741, 1741, -1/2*w^3 + 4*w^2 - w - 25/2], [1741, 1741, 7/6*w^3 + 3*w^2 - 37/3*w - 149/6], [1741, 1741, -11/6*w^3 + 6*w^2 + 17/3*w - 131/6], [1789, 1789, 1/6*w^3 - w^2 - 13/3*w + 103/6], [1789, 1789, w^3 + 2*w^2 - 8*w - 18], [1789, 1789, -2*w^3 - 3*w^2 + 18*w + 30], [1789, 1789, -2/3*w^3 + 2*w^2 + 16/3*w - 35/3], [1801, 1801, -7/6*w^3 - w^2 + 28/3*w + 47/6], [1801, 1801, -w^3 + w^2 + 8*w - 7], [1811, 1811, 4/3*w^3 - 29/3*w - 26/3], [1811, 1811, -7/6*w^3 + w^2 + 31/3*w - 43/6], [1831, 1831, -1/3*w^3 + 2/3*w + 32/3], [1831, 1831, -3/2*w^3 - 2*w^2 + 12*w + 33/2], [1849, 43, -7/6*w^3 - 2*w^2 + 31/3*w + 125/6], [1849, 43, -1/2*w^3 + 3*w^2 + 5*w - 43/2], [1871, 1871, -3/2*w^3 - 2*w^2 + 12*w + 29/2], [1871, 1871, 7/6*w^3 - 2*w^2 - 28/3*w + 91/6], [1879, 1879, 3/2*w^3 + 3*w^2 - 13*w - 53/2], [1879, 1879, -5/6*w^3 + 3*w^2 + 17/3*w - 107/6], [1889, 1889, -1/2*w^3 - w^2 + 6*w + 5/2], [1889, 1889, w^2 - 2*w - 12], [1901, 1901, w^2 + 2*w + 2], [1901, 1901, 1/2*w^3 - 3*w^2 + w + 13/2], [1901, 1901, -1/6*w^3 + 4*w^2 - 11/3*w - 73/6], [1901, 1901, 1/6*w^3 - w^2 - 10/3*w + 103/6], [1931, 1931, 7/6*w^3 - w^2 - 28/3*w + 13/6], [1931, 1931, 4/3*w^3 + w^2 - 32/3*w - 38/3], [1931, 1931, -7/6*w^3 - 3*w^2 + 31/3*w + 137/6], [1931, 1931, 1/2*w^3 - 3*w^2 - 3*w + 43/2], [1949, 1949, 4/3*w^3 - 3*w^2 - 32/3*w + 58/3], [1949, 1949, 11/6*w^3 + 3*w^2 - 44/3*w - 151/6], [1951, 1951, 11/6*w^3 - 5*w^2 - 20/3*w + 113/6], [1951, 1951, -4/3*w^3 + 26/3*w - 1/3], [1999, 1999, -1/6*w^3 + 3*w^2 - 2/3*w - 151/6], [1999, 1999, 1/2*w^3 + 2*w^2 - 4*w - 49/2]]; primes := [ideal : I in primesArray]; heckePol := x^11 + x^10 - 27*x^9 - 22*x^8 + 259*x^7 + 134*x^6 - 1067*x^5 - 98*x^4 + 1688*x^3 - 683*x^2 - 190*x + 52; K := NumberField(heckePol); heckeEigenvaluesArray := [e, -1, -1, -29/11672*e^10 - 157/5836*e^9 + 917/11672*e^8 + 7235/11672*e^7 - 1283/1459*e^6 - 27223/5836*e^5 + 50089/11672*e^4 + 149967/11672*e^3 - 101353/11672*e^2 - 51531/5836*e + 11137/2918, -367/5836*e^10 + 555/11672*e^9 + 17927/11672*e^8 - 6545/5836*e^7 - 144625/11672*e^6 + 104951/11672*e^5 + 419789/11672*e^4 - 150779/5836*e^3 - 252865/11672*e^2 + 51043/5836*e + 1703/2918, -51/5836*e^10 - 551/11672*e^9 + 3175/11672*e^8 + 6787/5836*e^7 - 36755/11672*e^6 - 107733/11672*e^5 + 194639/11672*e^4 + 70665/2918*e^3 - 421333/11672*e^2 - 30165/5836*e + 20607/2918, -15/11672*e^10 + 925/5836*e^9 - 1035/11672*e^8 - 43147/11672*e^7 + 3814/1459*e^6 + 79921/2918*e^5 - 263477/11672*e^4 - 750841/11672*e^3 + 756667/11672*e^2 - 8341/5836*e - 8427/2918, 285/11672*e^10 - 67/5836*e^9 - 6597/11672*e^8 + 2753/11672*e^7 + 6320/1459*e^6 - 9573/5836*e^5 - 147125/11672*e^4 + 40729/11672*e^3 + 122869/11672*e^2 + 21333/5836*e + 5459/2918, -559/11672*e^10 - 29/2918*e^9 + 13953/11672*e^8 + 2013/11672*e^7 - 58927/5836*e^6 + 473/2918*e^5 + 388449/11672*e^4 - 121639/11672*e^3 - 397165/11672*e^2 + 145923/5836*e - 3571/2918, -1867/11672*e^10 + 357/5836*e^9 + 46257/11672*e^8 - 17195/11672*e^7 - 48287/1459*e^6 + 38167/2918*e^5 + 1241059/11672*e^4 - 548669/11672*e^3 - 1187813/11672*e^2 + 233877/5836*e + 25527/2918, 174/1459*e^10 + 241/5836*e^9 - 17631/5836*e^8 - 1099/1459*e^7 + 151501/5836*e^6 + 12571/5836*e^5 - 509111/5836*e^4 + 37277/2918*e^3 + 545985/5836*e^2 - 89487/2918*e - 14881/1459, 553/5836*e^10 - 603/5836*e^9 - 3227/1459*e^8 + 14577/5836*e^7 + 94751/5836*e^6 - 118255/5836*e^5 - 102333/2918*e^4 + 331369/5836*e^3 - 57291/2918*e^2 - 17291/1459*e + 18000/1459, 341/11672*e^10 - 29/1459*e^9 - 8569/11672*e^8 + 5485/11672*e^7 + 38259/5836*e^6 - 25829/5836*e^5 - 301303/11672*e^4 + 245487/11672*e^3 + 502721/11672*e^2 - 234853/5836*e - 23191/2918, 1233/11672*e^10 - 167/5836*e^9 - 28725/11672*e^8 + 7733/11672*e^7 + 26728/1459*e^6 - 33399/5836*e^5 - 527161/11672*e^4 + 197769/11672*e^3 + 129869/11672*e^2 + 57093/5836*e + 4635/2918, 29/5836*e^10 + 2087/11672*e^9 - 3293/11672*e^8 - 24743/5836*e^7 + 57003/11672*e^6 + 372971/11672*e^5 - 408027/11672*e^4 - 435931/5836*e^3 + 1076647/11672*e^2 - 76395/5836*e - 14979/2918, -115/2918*e^10 - 327/5836*e^9 + 6015/5836*e^8 + 2145/1459*e^7 - 56903/5836*e^6 - 70937/5836*e^5 + 243157/5836*e^4 + 45369/1459*e^3 - 432091/5836*e^2 + 5598/1459*e + 12309/1459, -99/11672*e^10 - 921/11672*e^9 + 1691/5836*e^8 + 19869/11672*e^7 - 40523/11672*e^6 - 131985/11672*e^5 + 26248/1459*e^4 + 274089/11672*e^3 - 104649/2918*e^2 - 4498/1459*e + 7061/1459, -101/5836*e^10 - 47/1459*e^9 + 1785/5836*e^8 + 4973/5836*e^7 - 2227/2918*e^6 - 22163/2918*e^5 - 49735/5836*e^4 + 160165/5836*e^3 + 191873/5836*e^2 - 52933/1459*e - 2467/1459, 703/5836*e^10 - 1731/11672*e^9 - 32837/11672*e^8 + 20019/5836*e^7 + 246025/11672*e^6 - 311261/11672*e^5 - 612501/11672*e^4 + 220595/2918*e^3 + 139371/11672*e^2 - 213111/5836*e + 13411/2918, -973/11672*e^10 - 121/11672*e^9 + 10931/5836*e^8 + 2867/11672*e^7 - 150831/11672*e^6 - 14327/11672*e^5 + 145777/5836*e^4 + 25269/11672*e^3 + 45923/2918*e^2 - 30045/1459*e - 8799/1459, 2037/11672*e^10 - 141/5836*e^9 - 49117/11672*e^8 + 8189/11672*e^7 + 97177/2918*e^6 - 47105/5836*e^5 - 1106845/11672*e^4 + 386877/11672*e^3 + 711649/11672*e^2 - 56669/5836*e - 14643/2918, -285/5836*e^10 + 1727/11672*e^9 + 11735/11672*e^8 - 20261/5836*e^7 - 64645/11672*e^6 + 314043/11672*e^5 - 1927/11672*e^4 - 431741/5836*e^3 + 546499/11672*e^2 + 192233/5836*e - 38639/2918, -1641/11672*e^10 + 131/1459*e^9 + 38507/11672*e^8 - 23469/11672*e^7 - 143947/5836*e^6 + 21962/1459*e^5 + 690019/11672*e^4 - 421081/11672*e^3 - 43975/11672*e^2 - 110639/5836*e + 16515/2918, -72/1459*e^10 - 451/11672*e^9 + 14239/11672*e^8 + 2771/2918*e^7 - 118387/11672*e^6 - 83907/11672*e^5 + 378821/11672*e^4 + 53953/2918*e^3 - 360637/11672*e^2 - 94733/5836*e - 2325/2918, -441/11672*e^10 + 3325/11672*e^9 + 2241/2918*e^8 - 79145/11672*e^7 - 45753/11672*e^6 + 613487/11672*e^5 - 16439/2918*e^4 - 1623047/11672*e^3 + 346685/5836*e^2 + 122937/2918*e + 284/1459, -289/11672*e^10 + 141/11672*e^9 + 1945/2918*e^8 - 3365/11672*e^7 - 73257/11672*e^6 + 26679/11672*e^5 + 35712/1459*e^4 - 84743/11672*e^3 - 201621/5836*e^2 + 16020/1459*e + 10591/1459, -755/5836*e^10 - 3923/11672*e^9 + 40251/11672*e^8 + 44975/5836*e^7 - 375103/11672*e^6 - 636737/11672*e^5 + 1472427/11672*e^4 + 340993/2918*e^3 - 2182505/11672*e^2 + 26499/5836*e + 25623/2918, 475/11672*e^10 + 580/1459*e^9 - 16831/11672*e^8 - 108241/11672*e^7 + 108761/5836*e^6 + 398401/5836*e^5 - 1249973/11672*e^4 - 1818119/11672*e^3 + 2768731/11672*e^2 - 133689/5836*e - 39535/2918, -425/5836*e^10 + 919/2918*e^9 + 8609/5836*e^8 - 41681/5836*e^7 - 10991/1459*e^6 + 149425/2918*e^5 - 49571/5836*e^4 - 667885/5836*e^3 + 582007/5836*e^2 - 41795/2918*e - 16997/1459, 1025/5836*e^10 + 1519/11672*e^9 - 49679/11672*e^8 - 18255/5836*e^7 + 403019/11672*e^6 + 263201/11672*e^5 - 1278167/11672*e^4 - 138711/2918*e^3 + 1408753/11672*e^2 + 14075/5836*e - 49067/2918, -179/2918*e^10 - 781/2918*e^9 + 5157/2918*e^8 + 8921/1459*e^7 - 53845/2918*e^6 - 64342/1459*e^5 + 251615/2918*e^4 + 151383/1459*e^3 - 240928/1459*e^2 - 64163/2918*e + 46322/1459, -90/1459*e^10 + 315/2918*e^9 + 3629/2918*e^8 - 3557/1459*e^7 - 17573/2918*e^6 + 50103/2918*e^5 - 32169/2918*e^4 - 46342/1459*e^3 + 277857/2918*e^2 - 62158/1459*e - 18414/1459, -121/5836*e^10 - 153/5836*e^9 + 2391/2918*e^8 + 1913/5836*e^7 - 65415/5836*e^6 + 7929/5836*e^5 + 92207/1459*e^4 - 156199/5836*e^3 - 367179/2918*e^2 + 219069/2918*e + 19854/1459, -127/11672*e^10 - 109/1459*e^9 + 2909/11672*e^8 + 21421/11672*e^7 - 12161/5836*e^6 - 21214/1459*e^5 + 106157/11672*e^4 + 441625/11672*e^3 - 207297/11672*e^2 - 21209/5836*e - 56175/2918, 703/11672*e^10 + 1323/11672*e^9 - 10033/5836*e^8 - 32505/11672*e^7 + 212741/11672*e^6 + 250701/11672*e^5 - 513863/5836*e^4 - 572815/11672*e^3 + 498709/2918*e^2 - 35940/1459*e - 30569/1459, -1131/5836*e^10 - 287/2918*e^9 + 27009/5836*e^8 + 13709/5836*e^7 - 53386/1459*e^6 - 23846/1459*e^5 + 640371/5836*e^4 + 184875/5836*e^3 - 605821/5836*e^2 - 13797/2918*e + 25823/1459, -164/1459*e^10 + 287/1459*e^9 + 8007/2918*e^8 - 13709/2918*e^7 - 31833/1459*e^6 + 108515/2918*e^5 + 170833/2918*e^4 - 298677/2918*e^3 - 23176/1459*e^2 + 87413/2918*e + 19845/1459, -1211/5836*e^10 + 1025/5836*e^9 + 7196/1459*e^8 - 24793/5836*e^7 - 222489/5836*e^6 + 205553/5836*e^5 + 147886/1459*e^4 - 610783/5836*e^3 - 53833/1459*e^2 + 101235/2918*e + 2764/1459, -521/2918*e^10 + 547/2918*e^9 + 6099/1459*e^8 - 12599/2918*e^7 - 91173/2918*e^6 + 95925/2918*e^5 + 109764/1459*e^4 - 244795/2918*e^3 - 7384/1459*e^2 - 2385/1459*e + 25050/1459, 2049/11672*e^10 - 303/11672*e^9 - 12437/2918*e^8 + 10025/11672*e^7 + 398439/11672*e^6 - 125563/11672*e^5 - 583281/5836*e^4 + 562689/11672*e^3 + 430601/5836*e^2 - 102471/2918*e - 16644/1459, -142/1459*e^10 - 481/1459*e^9 + 8125/2918*e^8 + 22203/2918*e^7 - 41957/1459*e^6 - 159641/2918*e^5 + 381303/2918*e^4 + 348885/2918*e^3 - 340620/1459*e^2 + 52503/2918*e + 34851/1459, 259/2918*e^10 + 641/2918*e^9 - 3466/1459*e^8 - 7178/1459*e^7 + 64249/2918*e^6 + 99121/2918*e^5 - 245099/2918*e^4 - 208887/2918*e^3 + 336479/2918*e^2 + 3343/2918*e - 7499/1459, -1515/11672*e^10 - 1361/11672*e^9 + 19953/5836*e^8 + 30825/11672*e^7 - 374659/11672*e^6 - 199469/11672*e^5 + 385057/2918*e^4 + 240237/11672*e^3 - 631875/2918*e^2 + 174781/2918*e + 33292/1459, -223/11672*e^10 + 1107/5836*e^9 + 2121/11672*e^8 - 51627/11672*e^7 + 7285/2918*e^6 + 48073/1459*e^5 - 387801/11672*e^4 - 926937/11672*e^3 + 1117431/11672*e^2 + 38627/5836*e - 6227/2918, -145/11672*e^10 - 111/11672*e^9 + 1563/5836*e^8 + 1159/11672*e^7 - 14845/11672*e^6 + 3521/11672*e^5 - 14351/2918*e^4 - 8845/11672*e^3 + 50274/1459*e^2 - 31951/1459*e - 4985/1459, -1481/5836*e^10 - 691/5836*e^9 + 9104/1459*e^8 + 15601/5836*e^7 - 303561/5836*e^6 - 94985/5836*e^5 + 506909/2918*e^4 + 87657/5836*e^3 - 302897/1459*e^2 + 140767/2918*e + 40748/1459, 357/11672*e^10 - 762/1459*e^9 - 1629/11672*e^8 + 142161/11672*e^7 - 47657/5836*e^6 - 525283/5836*e^5 + 1081965/11672*e^4 + 2388275/11672*e^3 - 3272191/11672*e^2 + 295977/5836*e + 71587/2918, 1007/5836*e^10 - 167/1459*e^9 - 23893/5836*e^8 + 16925/5836*e^7 + 89809/2918*e^6 - 36317/1459*e^5 - 416739/5836*e^4 + 411587/5836*e^3 - 91881/5836*e^2 + 11864/1459*e + 20942/1459, 701/11672*e^10 - 431/5836*e^9 - 15827/11672*e^8 + 19713/11672*e^7 + 13958/1459*e^6 - 18983/1459*e^5 - 231129/11672*e^4 + 442527/11672*e^3 - 128861/11672*e^2 - 180569/5836*e + 27321/2918, 907/11672*e^10 - 493/11672*e^9 - 5145/2918*e^8 + 10379/11672*e^7 + 143269/11672*e^6 - 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127096/1459*e^3 + 2708245/11672*e^2 - 457893/5836*e - 191591/2918, -4957/11672*e^10 - 1903/11672*e^9 + 16153/1459*e^8 + 46947/11672*e^7 - 1172597/11672*e^6 - 334617/11672*e^5 + 1099583/2918*e^4 + 581777/11672*e^3 - 2964213/5836*e^2 + 131027/2918*e + 120124/1459, -320/1459*e^10 + 2579/2918*e^9 + 12741/2918*e^8 - 29993/1459*e^7 - 61347/2918*e^6 + 448059/2918*e^5 - 100275/2918*e^4 - 534547/1459*e^3 + 852249/2918*e^2 - 44143/1459*e + 48330/1459, -1357/11672*e^10 - 843/1459*e^9 + 34759/11672*e^8 + 154211/11672*e^7 - 153055/5836*e^6 - 139546/1459*e^5 + 1133051/11672*e^4 + 2700995/11672*e^3 - 1650447/11672*e^2 - 509665/5836*e + 61097/2918, -501/2918*e^10 + 256/1459*e^9 + 5330/1459*e^8 - 5499/1459*e^7 - 32614/1459*e^6 + 71391/2918*e^5 + 32522/1459*e^4 - 37895/1459*e^3 + 301601/2918*e^2 - 440167/2918*e - 7920/1459, 7285/11672*e^10 - 5089/11672*e^9 - 43213/2918*e^8 + 122485/11672*e^7 + 1330037/11672*e^6 - 1006115/11672*e^5 - 877245/2918*e^4 + 2857571/11672*e^3 + 655879/5836*e^2 - 73785/2918*e - 42202/1459, 1813/5836*e^10 + 1569/5836*e^9 - 22803/2918*e^8 - 37755/5836*e^7 + 397219/5836*e^6 + 273655/5836*e^5 - 717053/2918*e^4 - 545957/5836*e^3 + 468106/1459*e^2 - 82784/1459*e + 5122/1459, 551/1459*e^10 + 2499/11672*e^9 - 114581/11672*e^8 - 13769/2918*e^7 + 1036347/11672*e^6 + 325701/11672*e^5 - 3894537/11672*e^4 - 112127/5836*e^3 + 5462571/11672*e^2 - 546325/5836*e - 214857/2918, -1343/5836*e^10 + 2715/5836*e^9 + 6378/1459*e^8 - 59579/5836*e^7 - 100467/5836*e^6 + 408913/5836*e^5 - 99695/1459*e^4 - 761817/5836*e^3 + 1082483/2918*e^2 - 235426/1459*e - 27040/1459, 9135/11672*e^10 - 10515/11672*e^9 - 104305/5836*e^8 + 247963/11672*e^7 + 1477983/11672*e^6 - 1949279/11672*e^5 - 744557/2918*e^4 + 5220199/11672*e^3 - 464967/2918*e^2 - 127947/2918*e + 36845/1459, 791/2918*e^10 - 4957/5836*e^9 - 35283/5836*e^8 + 59745/2918*e^7 + 232147/5836*e^6 - 949103/5836*e^5 - 275435/5836*e^4 + 649307/1459*e^3 - 1142523/5836*e^2 - 370471/2918*e + 22997/1459, 777/11672*e^10 - 7063/5836*e^9 - 4747/11672*e^8 + 328977/11672*e^7 - 22777/1459*e^6 - 610295/2918*e^5 + 2182703/11672*e^4 + 5787103/11672*e^3 - 6661985/11672*e^2 + 21793/5836*e + 147053/2918, 1083/2918*e^10 + 2117/2918*e^9 - 27403/2918*e^8 - 25846/1459*e^7 + 237357/2918*e^6 + 202315/1459*e^5 - 845039/2918*e^4 - 539626/1459*e^3 + 580839/1459*e^2 + 468229/2918*e - 97992/1459, 25/5836*e^10 + 321/5836*e^9 - 663/1459*e^8 - 7847/5836*e^7 + 45927/5836*e^6 + 64897/5836*e^5 - 127921/2918*e^4 - 208571/5836*e^3 + 215421/2918*e^2 + 55341/1459*e - 69118/1459, -10755/11672*e^10 - 155/1459*e^9 + 264615/11672*e^8 + 23581/11672*e^7 - 1087985/5836*e^6 - 13785/5836*e^5 + 6765153/11672*e^4 - 711497/11672*e^3 - 6009991/11672*e^2 + 328219/5836*e + 144001/2918, 3253/5836*e^10 + 5393/11672*e^9 - 162407/11672*e^8 - 65465/5836*e^7 + 1398045/11672*e^6 + 955173/11672*e^5 - 4995757/11672*e^4 - 957095/5836*e^3 + 6750249/11672*e^2 - 458579/5836*e - 135703/2918, -1651/2918*e^10 - 115/11672*e^9 + 158563/11672*e^8 - 98/1459*e^7 - 1254531/11672*e^6 + 90925/11672*e^5 + 3651185/11672*e^4 - 68593/1459*e^3 - 2864369/11672*e^2 - 179321/5836*e + 214291/2918, -2105/11672*e^10 + 2389/5836*e^9 + 44425/11672*e^8 - 106133/11672*e^7 - 64153/2918*e^6 + 368649/5836*e^5 + 29525/11672*e^4 - 1464849/11672*e^3 + 2305775/11672*e^2 - 512025/5836*e - 129191/2918, 4243/11672*e^10 + 241/2918*e^9 - 104081/11672*e^8 - 21961/11672*e^7 + 418263/5836*e^6 + 17228/1459*e^5 - 2390981/11672*e^4 - 301433/11672*e^3 + 1499669/11672*e^2 + 440125/5836*e - 110589/2918, 2083/11672*e^10 + 6749/5836*e^9 - 63451/11672*e^8 - 317425/11672*e^7 + 179027/2918*e^6 + 1176357/5836*e^5 - 3725359/11672*e^4 - 5446317/11672*e^3 + 8029163/11672*e^2 - 75249/5836*e - 247335/2918, -5209/11672*e^10 - 1277/1459*e^9 + 136639/11672*e^8 + 235995/11672*e^7 - 634491/5836*e^6 - 415111/2918*e^5 + 5130067/11672*e^4 + 3230539/11672*e^3 - 8316195/11672*e^2 + 968437/5836*e + 144487/2918, 85/5836*e^10 + 1675/5836*e^9 - 3633/2918*e^8 - 39519/5836*e^7 + 136893/5836*e^6 + 288931/5836*e^5 - 234536/1459*e^4 - 549235/5836*e^3 + 539399/1459*e^2 - 165794/1459*e - 9148/1459, 3977/11672*e^10 - 759/11672*e^9 - 50275/5836*e^8 + 19045/11672*e^7 + 871527/11672*e^6 - 196509/11672*e^5 - 1505929/5836*e^4 + 864131/11672*e^3 + 420777/1459*e^2 - 230365/2918*e - 33574/1459, -621/11672*e^10 - 549/2918*e^9 + 18429/11672*e^8 + 45051/11672*e^7 - 98777/5836*e^6 - 117577/5836*e^5 + 952555/11672*e^4 - 145847/11672*e^3 - 1888413/11672*e^2 + 1116017/5836*e + 26377/2918, -3031/11672*e^10 - 568/1459*e^9 + 76825/11672*e^8 + 102349/11672*e^7 - 336097/5836*e^6 - 171393/2918*e^5 + 2468397/11672*e^4 + 1134045/11672*e^3 - 3621229/11672*e^2 + 614335/5836*e + 122685/2918, -3591/11672*e^10 - 7941/11672*e^9 + 11521/1459*e^8 + 185913/11672*e^7 - 819431/11672*e^6 - 1371539/11672*e^5 + 766551/2918*e^4 + 3285467/11672*e^3 - 2241391/5836*e^2 - 185317/2918*e + 68176/1459, 321/5836*e^10 + 8557/5836*e^9 - 7163/2918*e^8 - 198917/5836*e^7 + 216899/5836*e^6 + 1468351/5836*e^5 - 357320/1459*e^4 - 3467429/5836*e^3 + 1825009/2918*e^2 + 79869/2918*e - 98623/1459, -164/1459*e^10 + 3755/11672*e^9 + 24733/11672*e^8 - 19545/2918*e^7 - 89797/11672*e^6 + 470535/11672*e^5 - 499917/11672*e^4 - 58151/1459*e^3 + 2503529/11672*e^2 - 1020095/5836*e - 28883/2918, -1104/1459*e^10 + 433/5836*e^9 + 111111/5836*e^8 - 6631/2918*e^7 - 944595/5836*e^6 + 185425/5836*e^5 + 3097855/5836*e^4 - 262850/1459*e^3 - 3073219/5836*e^2 + 389944/1459*e + 66797/1459, 207/2918*e^10 + 5/5836*e^9 - 13745/5836*e^8 - 427/2918*e^7 + 167205/5836*e^6 + 4547/5836*e^5 - 877717/5836*e^4 + 24551/1459*e^3 + 1689347/5836*e^2 - 340841/2918*e - 23907/1459, -1279/2918*e^10 + 3747/5836*e^9 + 58397/5836*e^8 - 43951/2918*e^7 - 415685/5836*e^6 + 689113/5836*e^5 + 859493/5836*e^4 - 483275/1459*e^3 + 472881/5836*e^2 + 426329/2918*e - 76421/1459, -637/2918*e^10 + 13213/11672*e^9 + 44497/11672*e^8 - 39247/1459*e^7 - 92675/11672*e^6 + 2414515/11672*e^5 - 1648443/11672*e^4 - 3017599/5836*e^3 + 7089329/11672*e^2 - 12619/5836*e - 222539/2918, -1479/11672*e^10 + 3665/5836*e^9 + 38013/11672*e^8 - 173763/11672*e^7 - 40630/1459*e^6 + 333679/2918*e^5 + 943803/11672*e^4 - 3489689/11672*e^3 - 170469/11672*e^2 + 570047/5836*e + 92353/2918, -1351/5836*e^10 - 412/1459*e^9 + 38091/5836*e^8 + 41327/5836*e^7 - 194757/2918*e^6 - 160785/2918*e^5 + 1756095/5836*e^4 + 720039/5836*e^3 - 3133153/5836*e^2 + 93640/1459*e + 123995/1459, -853/11672*e^10 - 6167/11672*e^9 + 12153/5836*e^8 + 137947/11672*e^7 - 246109/11672*e^6 - 961063/11672*e^5 + 139796/1459*e^4 + 2095615/11672*e^3 - 542405/2918*e^2 - 19199/1459*e + 16155/1459, -8199/11672*e^10 + 1125/2918*e^9 + 187113/11672*e^8 - 104755/11672*e^7 - 670979/5836*e^6 + 211871/2918*e^5 + 3002233/11672*e^4 - 2396839/11672*e^3 + 83235/11672*e^2 + 2227/5836*e + 57933/2918, -765/5836*e^10 + 9243/11672*e^9 + 33035/11672*e^8 - 108291/5836*e^7 - 207001/11672*e^6 + 1637575/11672*e^5 + 141649/11672*e^4 - 2060085/5836*e^3 + 1619883/11672*e^2 + 420007/5836*e - 14793/2918, -1141/2918*e^10 - 4031/5836*e^9 + 57015/5836*e^8 + 22868/1459*e^7 - 479295/5836*e^6 - 640409/5836*e^5 + 1576749/5836*e^4 + 359859/1459*e^3 - 1761451/5836*e^2 - 149695/1459*e + 57918/1459, -725/11672*e^10 - 18063/11672*e^9 + 16569/5836*e^8 + 425987/11672*e^7 - 511925/11672*e^6 - 3186359/11672*e^5 + 424437/1459*e^4 + 7472543/11672*e^3 - 2122001/2918*e^2 + 64931/1459*e + 42189/1459, -277/5836*e^10 + 30/1459*e^9 + 7149/5836*e^8 - 1529/5836*e^7 - 31763/2918*e^6 - 2337/2918*e^5 + 225979/5836*e^4 + 120249/5836*e^3 - 277033/5836*e^2 - 197995/2918*e + 40471/1459, -81/2918*e^10 + 618/1459*e^9 + 247/2918*e^8 - 29901/2918*e^7 + 11475/1459*e^6 + 118765/1459*e^5 - 236317/2918*e^4 - 652737/2918*e^3 + 649765/2918*e^2 + 110488/1459*e - 34986/1459, -1181/11672*e^10 + 3769/5836*e^9 + 23559/11672*e^8 - 174857/11672*e^7 - 27473/2918*e^6 + 320857/2918*e^5 - 280683/11672*e^4 - 2911255/11672*e^3 + 2089537/11672*e^2 - 203063/5836*e + 76519/2918, -145/2918*e^10 - 7517/5836*e^9 + 13547/5836*e^8 + 45079/1459*e^7 - 212065/5836*e^6 - 1389221/5836*e^5 + 1421519/5836*e^4 + 1753627/2918*e^3 - 3609091/5836*e^2 - 135099/1459*e + 93862/1459, -1270/1459*e^10 + 1595/5836*e^9 + 123655/5836*e^8 - 10476/1459*e^7 - 1000601/5836*e^6 + 417521/5836*e^5 + 3022179/5836*e^4 - 824621/2918*e^3 - 2471929/5836*e^2 + 685049/2918*e + 36335/1459, -623/2918*e^10 - 1463/2918*e^9 + 8416/1459*e^8 + 33073/2918*e^7 - 161485/2918*e^6 - 226281/2918*e^5 + 333287/1459*e^4 + 417205/2918*e^3 - 523711/1459*e^2 + 132317/1459*e + 7904/1459, 1037/2918*e^10 - 725/1459*e^9 - 11641/1459*e^8 + 17323/1459*e^7 + 79723/1459*e^6 - 278363/2918*e^5 - 142587/1459*e^4 + 398567/1459*e^3 - 315459/2918*e^2 - 282471/2918*e + 37658/1459, 292/1459*e^10 + 437/2918*e^9 - 7573/1459*e^8 - 8401/2918*e^7 + 134601/2918*e^6 + 19101/1459*e^5 - 241171/1459*e^4 + 19575/2918*e^3 + 617911/2918*e^2 - 147809/2918*e - 46472/1459, -397/5836*e^10 - 1129/5836*e^9 + 7459/2918*e^8 + 23881/5836*e^7 - 191475/5836*e^6 - 147811/5836*e^5 + 249922/1459*e^4 + 177125/5836*e^3 - 907437/2918*e^2 + 289697/2918*e + 35792/1459, -847/1459*e^10 + 388/1459*e^9 + 39227/2918*e^8 - 18447/2918*e^7 - 144220/1459*e^6 + 156235/2918*e^5 + 685921/2918*e^4 - 487051/2918*e^3 - 42760/1459*e^2 + 124311/2918*e - 23311/1459, 573/1459*e^10 - 4011/5836*e^9 - 50489/5836*e^8 + 45487/2918*e^7 + 335425/5836*e^6 - 660155/5836*e^5 - 553905/5836*e^4 + 363228/1459*e^3 - 705835/5836*e^2 + 154907/1459*e - 42087/1459, -539/1459*e^10 + 855/5836*e^9 + 54037/5836*e^8 - 11739/2918*e^7 - 459553/5836*e^6 + 226035/5836*e^5 + 1529673/5836*e^4 - 193369/1459*e^3 - 1605645/5836*e^2 + 81135/1459*e + 74430/1459, 83/11672*e^10 - 255/5836*e^9 - 5945/11672*e^8 + 6863/11672*e^7 + 25003/2918*e^6 + 1501/2918*e^5 - 585083/11672*e^4 - 207951/11672*e^3 + 1063953/11672*e^2 + 31369/5836*e + 20951/2918, 1509/5836*e^10 - 569/1459*e^9 - 33025/5836*e^8 + 49961/5836*e^7 + 107205/2918*e^6 - 171461/2918*e^5 - 291375/5836*e^4 + 655223/5836*e^3 - 756347/5836*e^2 + 292855/2918*e - 17139/1459, 2883/5836*e^10 - 6869/5836*e^9 - 34035/2918*e^8 + 163889/5836*e^7 + 521053/5836*e^6 - 1294239/5836*e^5 - 331085/1459*e^4 + 3592841/5836*e^3 + 65495/2918*e^2 - 741181/2918*e + 2222/1459, 256/1459*e^10 - 448/1459*e^9 - 5680/1459*e^8 + 11447/1459*e^7 + 37378/1459*e^6 - 98395/1459*e^5 - 48889/1459*e^4 + 294285/1459*e^3 - 166695/1459*e^2 - 96871/1459*e + 66384/1459, 3513/5836*e^10 + 378/1459*e^9 - 87337/5836*e^8 - 34439/5836*e^7 + 368971/2918*e^6 + 103031/2918*e^5 - 2489103/5836*e^4 - 132949/5836*e^3 + 2945325/5836*e^2 - 358761/2918*e - 112183/1459, -85/2918*e^10 + 6863/5836*e^9 - 4435/5836*e^8 - 80119/2918*e^7 + 162455/5836*e^6 + 1197741/5836*e^5 - 1375823/5836*e^4 - 721150/1459*e^3 + 3678669/5836*e^2 + 22675/2918*e - 59031/1459]; 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;