/* This code can be loaded, or copied and paste using cpaste, into Sage. It will load the data associated to the HMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data. */ P. = PolynomialRing(QQ) g = P([41, 9, -14, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([16, 2, 2]) primes_array = [ [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 = [ZF.ideal(I) for I in primes_array] heckePol = x^11 - x^10 - 53*x^9 + 46*x^8 + 1006*x^7 - 720*x^6 - 8252*x^5 + 4144*x^4 + 28752*x^3 - 3520*x^2 - 35840*x - 15360 K. = NumberField(heckePol) hecke_eigenvalues_array = [1, 1, e, 781/692704*e^10 + 3883/1385408*e^9 - 84647/1385408*e^8 - 171237/1385408*e^7 + 775117/692704*e^6 + 1278823/692704*e^5 - 1361663/173176*e^4 - 3711511/346352*e^3 + 1459625/86588*e^2 + 1835407/86588*e + 93110/21647, 781/692704*e^10 + 3883/1385408*e^9 - 84647/1385408*e^8 - 171237/1385408*e^7 + 775117/692704*e^6 + 1278823/692704*e^5 - 1361663/173176*e^4 - 3711511/346352*e^3 + 1459625/86588*e^2 + 1835407/86588*e + 93110/21647, -3019/5541632*e^10 - 3389/5541632*e^9 + 150175/5541632*e^8 + 108239/2770816*e^7 - 1226461/2770816*e^6 - 137875/173176*e^5 + 3355213/1385408*e^4 + 2103165/346352*e^3 - 277443/346352*e^2 - 1383593/86588*e - 233667/21647, -3019/5541632*e^10 - 3389/5541632*e^9 + 150175/5541632*e^8 + 108239/2770816*e^7 - 1226461/2770816*e^6 - 137875/173176*e^5 + 3355213/1385408*e^4 + 2103165/346352*e^3 - 277443/346352*e^2 - 1383593/86588*e - 233667/21647, 10663/5541632*e^10 - 41635/5541632*e^9 - 554935/5541632*e^8 + 959703/2770816*e^7 + 5245565/2770816*e^6 - 3798443/692704*e^5 - 21539113/1385408*e^4 + 5856529/173176*e^3 + 17935679/346352*e^2 - 2696077/43294*e - 1226802/21647, 10663/5541632*e^10 - 41635/5541632*e^9 - 554935/5541632*e^8 + 959703/2770816*e^7 + 5245565/2770816*e^6 - 3798443/692704*e^5 - 21539113/1385408*e^4 + 5856529/173176*e^3 + 17935679/346352*e^2 - 2696077/43294*e - 1226802/21647, -1737/5541632*e^10 + 10469/5541632*e^9 + 94865/5541632*e^8 - 238717/2770816*e^7 - 961171/2770816*e^6 + 1007575/692704*e^5 + 4535023/1385408*e^4 - 950311/86588*e^3 - 5335893/346352*e^2 + 1249283/43294*e + 631320/21647, -1737/5541632*e^10 + 10469/5541632*e^9 + 94865/5541632*e^8 - 238717/2770816*e^7 - 961171/2770816*e^6 + 1007575/692704*e^5 + 4535023/1385408*e^4 - 950311/86588*e^3 - 5335893/346352*e^2 + 1249283/43294*e + 631320/21647, 12121/2770816*e^10 + 9247/2770816*e^9 - 602709/2770816*e^8 - 271317/1385408*e^7 + 5125007/1385408*e^6 + 159275/43294*e^5 - 16914823/692704*e^4 - 4393159/173176*e^3 + 8692781/173176*e^2 + 2491217/43294*e + 249328/21647, 12121/2770816*e^10 + 9247/2770816*e^9 - 602709/2770816*e^8 - 271317/1385408*e^7 + 5125007/1385408*e^6 + 159275/43294*e^5 - 16914823/692704*e^4 - 4393159/173176*e^3 + 8692781/173176*e^2 + 2491217/43294*e + 249328/21647, 5995/2770816*e^10 - 16043/2770816*e^9 - 306127/2770816*e^8 + 387193/1385408*e^7 + 2691833/1385408*e^6 - 814439/173176*e^5 - 9588761/692704*e^4 + 5520191/173176*e^3 + 6983069/173176*e^2 - 1495463/21647*e - 1150172/21647, 5995/2770816*e^10 - 16043/2770816*e^9 - 306127/2770816*e^8 + 387193/1385408*e^7 + 2691833/1385408*e^6 - 814439/173176*e^5 - 9588761/692704*e^4 + 5520191/173176*e^3 + 6983069/173176*e^2 - 1495463/21647*e - 1150172/21647, -12391/2770816*e^10 + 16607/2770816*e^9 + 614763/2770816*e^8 - 352165/1385408*e^7 - 5400929/1385408*e^6 + 321505/86588*e^5 + 19868345/692704*e^4 - 3791655/173176*e^3 - 14014003/173176*e^2 + 1870339/43294*e + 1331448/21647, -12391/2770816*e^10 + 16607/2770816*e^9 + 614763/2770816*e^8 - 352165/1385408*e^7 - 5400929/1385408*e^6 + 321505/86588*e^5 + 19868345/692704*e^4 - 3791655/173176*e^3 - 14014003/173176*e^2 + 1870339/43294*e + 1331448/21647, 3965/2770816*e^10 - 14077/2770816*e^9 - 196257/2770816*e^8 + 378491/1385408*e^7 + 1685227/1385408*e^6 - 866919/173176*e^5 - 6011899/692704*e^4 + 6141475/173176*e^3 + 4758197/173176*e^2 - 3378527/43294*e - 1116410/21647, 3965/2770816*e^10 - 14077/2770816*e^9 - 196257/2770816*e^8 + 378491/1385408*e^7 + 1685227/1385408*e^6 - 866919/173176*e^5 - 6011899/692704*e^4 + 6141475/173176*e^3 + 4758197/173176*e^2 - 3378527/43294*e - 1116410/21647, -3715/5541632*e^10 - 241/5541632*e^9 + 175475/5541632*e^8 - 4835/2770816*e^7 - 1400881/2770816*e^6 + 114495/692704*e^5 + 4091725/1385408*e^4 - 418741/173176*e^3 - 1094683/346352*e^2 + 253291/43294*e - 129540/21647, -3715/5541632*e^10 - 241/5541632*e^9 + 175475/5541632*e^8 - 4835/2770816*e^7 - 1400881/2770816*e^6 + 114495/692704*e^5 + 4091725/1385408*e^4 - 418741/173176*e^3 - 1094683/346352*e^2 + 253291/43294*e - 129540/21647, 293/2770816*e^10 + 8503/2770816*e^9 - 15005/2770816*e^8 - 230015/1385408*e^7 + 45435/1385408*e^6 + 1112535/346352*e^5 + 958161/692704*e^4 - 552816/21647*e^3 - 3111021/173176*e^2 + 2886167/43294*e + 1228878/21647, 293/2770816*e^10 + 8503/2770816*e^9 - 15005/2770816*e^8 - 230015/1385408*e^7 + 45435/1385408*e^6 + 1112535/346352*e^5 + 958161/692704*e^4 - 552816/21647*e^3 - 3111021/173176*e^2 + 2886167/43294*e + 1228878/21647, -1279/173176*e^10 - 871/346352*e^9 + 32639/86588*e^8 + 24203/173176*e^7 - 2274117/346352*e^6 - 435947/173176*e^5 + 7722551/173176*e^4 + 737819/43294*e^3 - 8712329/86588*e^2 - 1999807/43294*e + 471040/21647, -1279/173176*e^10 - 871/346352*e^9 + 32639/86588*e^8 + 24203/173176*e^7 - 2274117/346352*e^6 - 435947/173176*e^5 + 7722551/173176*e^4 + 737819/43294*e^3 - 8712329/86588*e^2 - 1999807/43294*e + 471040/21647, 3573/1385408*e^10 - 21759/1385408*e^9 - 185491/1385408*e^8 + 271485/346352*e^7 + 1781067/692704*e^6 - 4688347/346352*e^5 - 7846877/346352*e^4 + 16001791/173176*e^3 + 4072429/43294*e^2 - 4353740/21647*e - 3441866/21647, -1069/173176*e^10 + 1607/1385408*e^9 + 454437/1385408*e^8 - 112199/1385408*e^7 - 4151853/692704*e^6 + 1090085/692704*e^5 + 7529347/173176*e^4 - 3178937/346352*e^3 - 2353178/21647*e^2 + 450659/86588*e + 1007838/21647, -1069/173176*e^10 + 1607/1385408*e^9 + 454437/1385408*e^8 - 112199/1385408*e^7 - 4151853/692704*e^6 + 1090085/692704*e^5 + 7529347/173176*e^4 - 3178937/346352*e^3 - 2353178/21647*e^2 + 450659/86588*e + 1007838/21647, -3883/5541632*e^10 - 59197/5541632*e^9 + 50207/5541632*e^8 + 1645887/2770816*e^7 + 1077027/2770816*e^6 - 1899571/173176*e^5 - 11507427/1385408*e^4 + 26444517/346352*e^3 + 17918645/346352*e^2 - 14130353/86588*e - 2613965/21647, -3883/5541632*e^10 - 59197/5541632*e^9 + 50207/5541632*e^8 + 1645887/2770816*e^7 + 1077027/2770816*e^6 - 1899571/173176*e^5 - 11507427/1385408*e^4 + 26444517/346352*e^3 + 17918645/346352*e^2 - 14130353/86588*e - 2613965/21647, -6619/1385408*e^10 - 5021/1385408*e^9 + 310895/1385408*e^8 + 165319/692704*e^7 - 2480957/692704*e^6 - 431413/86588*e^5 + 7523053/346352*e^4 + 3386443/86588*e^3 - 3140039/86588*e^2 - 2217588/21647*e - 544920/21647, 347/173176*e^10 + 2335/346352*e^9 - 39161/346352*e^8 - 113887/346352*e^7 + 91439/43294*e^6 + 972409/173176*e^5 - 1269599/86588*e^4 - 3326079/86588*e^3 + 1212021/43294*e^2 + 1862791/21647*e + 654238/21647, 347/173176*e^10 + 2335/346352*e^9 - 39161/346352*e^8 - 113887/346352*e^7 + 91439/43294*e^6 + 972409/173176*e^5 - 1269599/86588*e^4 - 3326079/86588*e^3 + 1212021/43294*e^2 + 1862791/21647*e + 654238/21647, 10535/5541632*e^10 + 49513/5541632*e^9 - 489571/5541632*e^8 - 1305911/2770816*e^7 + 3550401/2770816*e^6 + 2893133/346352*e^5 - 7167401/1385408*e^4 - 19534891/346352*e^3 - 3116165/346352*e^2 + 10674421/86588*e + 1365355/21647, 10535/5541632*e^10 + 49513/5541632*e^9 - 489571/5541632*e^8 - 1305911/2770816*e^7 + 3550401/2770816*e^6 + 2893133/346352*e^5 - 7167401/1385408*e^4 - 19534891/346352*e^3 - 3116165/346352*e^2 + 10674421/86588*e + 1365355/21647, -2789/2770816*e^10 - 6171/2770816*e^9 + 120665/2770816*e^8 + 232069/1385408*e^7 - 933691/1385408*e^6 - 614983/173176*e^5 + 3161091/692704*e^4 + 4353161/173176*e^3 - 2081509/173176*e^2 - 2159811/43294*e - 165542/21647, -2789/2770816*e^10 - 6171/2770816*e^9 + 120665/2770816*e^8 + 232069/1385408*e^7 - 933691/1385408*e^6 - 614983/173176*e^5 + 3161091/692704*e^4 + 4353161/173176*e^3 - 2081509/173176*e^2 - 2159811/43294*e - 165542/21647, -4051/2770816*e^10 - 31565/2770816*e^9 + 184703/2770816*e^8 + 828851/1385408*e^7 - 1207405/1385408*e^6 - 1864959/173176*e^5 + 947933/692704*e^4 + 13138391/173176*e^3 + 4807825/173176*e^2 - 7488287/43294*e - 2317272/21647, 619/346352*e^10 + 2301/346352*e^9 - 28597/346352*e^8 - 31485/86588*e^7 + 112085/86588*e^6 + 143112/21647*e^5 - 320797/43294*e^4 - 973451/21647*e^3 + 208827/43294*e^2 + 1997134/21647*e + 1184598/21647, -4051/2770816*e^10 - 31565/2770816*e^9 + 184703/2770816*e^8 + 828851/1385408*e^7 - 1207405/1385408*e^6 - 1864959/173176*e^5 + 947933/692704*e^4 + 13138391/173176*e^3 + 4807825/173176*e^2 - 7488287/43294*e - 2317272/21647, 619/346352*e^10 + 2301/346352*e^9 - 28597/346352*e^8 - 31485/86588*e^7 + 112085/86588*e^6 + 143112/21647*e^5 - 320797/43294*e^4 - 973451/21647*e^3 + 208827/43294*e^2 + 1997134/21647*e + 1184598/21647, 27/43294*e^10 + 6257/692704*e^9 - 14957/692704*e^8 - 303769/692704*e^7 + 38841/346352*e^6 + 2512423/346352*e^5 + 104423/43294*e^4 - 8094579/173176*e^3 - 980419/43294*e^2 + 4257813/43294*e + 1165450/21647, 27/43294*e^10 + 6257/692704*e^9 - 14957/692704*e^8 - 303769/692704*e^7 + 38841/346352*e^6 + 2512423/346352*e^5 + 104423/43294*e^4 - 8094579/173176*e^3 - 980419/43294*e^2 + 4257813/43294*e + 1165450/21647, -18589/5541632*e^10 + 15529/5541632*e^9 + 931877/5541632*e^8 - 186065/2770816*e^7 - 8392575/2770816*e^6 + 111939/692704*e^5 + 32247915/1385408*e^4 + 224599/86588*e^3 - 23847505/346352*e^2 - 258905/43294*e + 846358/21647, -18589/5541632*e^10 + 15529/5541632*e^9 + 931877/5541632*e^8 - 186065/2770816*e^7 - 8392575/2770816*e^6 + 111939/692704*e^5 + 32247915/1385408*e^4 + 224599/86588*e^3 - 23847505/346352*e^2 - 258905/43294*e + 846358/21647, 1817/2770816*e^10 + 29975/2770816*e^9 - 146541/2770816*e^8 - 710209/1385408*e^7 + 1533591/1385408*e^6 + 1500095/173176*e^5 - 4339015/692704*e^4 - 10543637/173176*e^3 - 1714179/173176*e^2 + 6327891/43294*e + 2072440/21647, 8461/692704*e^10 - 1071/692704*e^9 - 424879/692704*e^8 + 650/21647*e^7 + 3679313/346352*e^6 + 16207/173176*e^5 - 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1038420/21647*e - 27396/21647, -1481/346352*e^10 + 1349/346352*e^9 + 50725/346352*e^8 + 6405/173176*e^7 - 211777/173176*e^6 - 151539/43294*e^5 - 180231/86588*e^4 + 659047/21647*e^3 + 595658/21647*e^2 - 1038420/21647*e - 27396/21647, -81967/2770816*e^10 + 5847/2770816*e^9 + 4090387/2770816*e^8 + 121795/1385408*e^7 - 35183169/1385408*e^6 - 318931/86588*e^5 + 120264769/692704*e^4 + 5030593/173176*e^3 - 71339779/173176*e^2 - 3653241/43294*e + 3328720/21647, -81967/2770816*e^10 + 5847/2770816*e^9 + 4090387/2770816*e^8 + 121795/1385408*e^7 - 35183169/1385408*e^6 - 318931/86588*e^5 + 120264769/692704*e^4 + 5030593/173176*e^3 - 71339779/173176*e^2 - 3653241/43294*e + 3328720/21647, 42057/5541632*e^10 + 25127/5541632*e^9 - 2327869/5541632*e^8 - 790225/2770816*e^7 + 21990519/2770816*e^6 + 2034083/346352*e^5 - 80654751/1385408*e^4 - 16420489/346352*e^3 + 46800425/346352*e^2 + 12751809/86588*e - 202995/21647, 42057/5541632*e^10 + 25127/5541632*e^9 - 2327869/5541632*e^8 - 790225/2770816*e^7 + 21990519/2770816*e^6 + 2034083/346352*e^5 - 80654751/1385408*e^4 - 16420489/346352*e^3 + 46800425/346352*e^2 + 12751809/86588*e - 202995/21647, 11277/1385408*e^10 - 14803/1385408*e^9 - 564067/1385408*e^8 + 141139/346352*e^7 + 4865725/692704*e^6 - 1759189/346352*e^5 - 16618855/346352*e^4 + 4117435/173176*e^3 + 9670393/86588*e^2 - 1475309/43294*e - 817602/21647, 43141/2770816*e^10 - 45961/2770816*e^9 - 2131893/2770816*e^8 + 1112917/1385408*e^7 + 18208959/1385408*e^6 - 4776329/346352*e^5 - 62958507/692704*e^4 + 8278619/86588*e^3 + 42682901/173176*e^2 - 4210611/21647*e - 5826342/21647, 43141/2770816*e^10 - 45961/2770816*e^9 - 2131893/2770816*e^8 + 1112917/1385408*e^7 + 18208959/1385408*e^6 - 4776329/346352*e^5 - 62958507/692704*e^4 + 8278619/86588*e^3 + 42682901/173176*e^2 - 4210611/21647*e - 5826342/21647, 11277/1385408*e^10 - 14803/1385408*e^9 - 564067/1385408*e^8 + 141139/346352*e^7 + 4865725/692704*e^6 - 1759189/346352*e^5 - 16618855/346352*e^4 + 4117435/173176*e^3 + 9670393/86588*e^2 - 1475309/43294*e - 817602/21647, -3647/1385408*e^10 + 255/43294*e^9 + 52787/692704*e^8 - 159507/1385408*e^7 - 16879/86588*e^6 - 592285/692704*e^5 - 3240189/346352*e^4 + 7649173/346352*e^3 + 6065473/86588*e^2 - 5941215/86588*e - 2338386/21647, -3647/1385408*e^10 + 255/43294*e^9 + 52787/692704*e^8 - 159507/1385408*e^7 - 16879/86588*e^6 - 592285/692704*e^5 - 3240189/346352*e^4 + 7649173/346352*e^3 + 6065473/86588*e^2 - 5941215/86588*e - 2338386/21647, -105541/5541632*e^10 - 242091/5541632*e^9 + 5639273/5541632*e^8 + 5605709/2770816*e^7 - 50892507/2770816*e^6 - 11115455/346352*e^5 + 175204723/1385408*e^4 + 69465525/346352*e^3 - 87856381/346352*e^2 - 36823941/86588*e - 3364017/21647, -105541/5541632*e^10 - 242091/5541632*e^9 + 5639273/5541632*e^8 + 5605709/2770816*e^7 - 50892507/2770816*e^6 - 11115455/346352*e^5 + 175204723/1385408*e^4 + 69465525/346352*e^3 - 87856381/346352*e^2 - 36823941/86588*e - 3364017/21647, 6715/692704*e^10 + 1601/692704*e^9 - 338271/692704*e^8 - 57163/346352*e^7 + 2951391/346352*e^6 + 130197/43294*e^5 - 10205859/173176*e^4 - 292742/21647*e^3 + 2840479/21647*e^2 + 23260/21647*e - 46200/21647, 6715/692704*e^10 + 1601/692704*e^9 - 338271/692704*e^8 - 57163/346352*e^7 + 2951391/346352*e^6 + 130197/43294*e^5 - 10205859/173176*e^4 - 292742/21647*e^3 + 2840479/21647*e^2 + 23260/21647*e - 46200/21647, 25933/2770816*e^10 - 60689/2770816*e^9 - 1294381/2770816*e^8 + 1403077/1385408*e^7 + 10979455/1385408*e^6 - 5631509/346352*e^5 - 36143827/692704*e^4 + 9075749/86588*e^3 + 21402461/173176*e^2 - 4642028/21647*e - 2703302/21647, 25933/2770816*e^10 - 60689/2770816*e^9 - 1294381/2770816*e^8 + 1403077/1385408*e^7 + 10979455/1385408*e^6 - 5631509/346352*e^5 - 36143827/692704*e^4 + 9075749/86588*e^3 + 21402461/173176*e^2 - 4642028/21647*e - 2703302/21647, -44677/2770816*e^10 + 14093/2770816*e^9 + 2310145/2770816*e^8 - 375655/1385408*e^7 - 20627211/1385408*e^6 + 383819/86588*e^5 + 73153139/692704*e^4 - 3640033/173176*e^3 - 43680301/173176*e^2 - 421683/43294*e + 2231230/21647, -44677/2770816*e^10 + 14093/2770816*e^9 + 2310145/2770816*e^8 - 375655/1385408*e^7 - 20627211/1385408*e^6 + 383819/86588*e^5 + 73153139/692704*e^4 - 3640033/173176*e^3 - 43680301/173176*e^2 - 421683/43294*e + 2231230/21647] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([4, 2, 1/6*w^3 - 7/3*w - 17/6])] = -1 AL_eigenvalues[ZF.ideal([4, 2, w - 3])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]