/* 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([45, 15, -14, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([5,5,2/3*w^2 - 5/3*w - 4]) primes_array = [ [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 = [ZF.ideal(I) for I in primes_array] heckePol = x^4 - 6*x^3 + 8*x^2 + 4*x - 6 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -1, 2*e^3 - 8*e^2 + 2*e + 8, -e^3 + 5*e^2 - 4*e - 4, e^2 - 3*e, -e^2 + 3*e - 1, -e^3 + 5*e^2 - 3*e, 2*e^3 - 8*e^2 + 2*e + 6, 2*e^3 - 7*e^2 - 3*e + 12, -2*e^2 + 3*e + 6, -2*e^2 + 6*e + 6, 2*e^3 - 7*e^2 - e + 6, -e^3 + 3*e^2 - e, -e^3 + 4*e^2 + 4*e - 6, 2*e^3 - 10*e^2 + 8*e + 6, -e^3 + 3*e^2 + 2*e - 6, e^3 - 3*e^2 + 2*e - 2, -e^3 + 2*e^2 + 3*e, -e^3 + 2*e^2 + 4*e + 6, -e^3 + e^2 + 4*e + 4, -2*e^3 + 10*e^2 - 6*e - 12, -e^3 + 2*e^2 + 6*e - 6, -e^3 + e^2 + 3*e + 12, -3*e^3 + 15*e^2 - 12*e - 12, -2*e^3 + 8*e^2 + 4*e - 18, -4*e + 4, -4*e + 4, -2*e^2 + 8*e - 8, -e^3 + 3*e^2 + 2*e - 6, e^3 - 3*e^2 - 8*e + 12, 2*e^3 - 9*e^2 - e + 12, -5*e^3 + 25*e^2 - 25*e - 18, e^3 + 2*e^2 - 16*e, -e^3 + 6*e^2 - 14*e + 6, -3*e^3 + 12*e^2 - 2*e - 12, 8*e - 12, -e^3 + 12*e^2 - 26*e - 6, -e^3 + 8*e^2 - 6*e - 12, -2*e^3 + 4*e^2 + 8*e, -5*e^3 + 22*e^2 - 13*e - 12, -2*e^3 + 12*e^2 - 12*e - 2, 3*e^3 - 7*e^2 - 18*e + 16, -2*e^3 + 12*e^2 - 12*e - 2, -3*e^3 + 9*e^2 + 6*e - 2, 5*e^3 - 25*e^2 + 10*e + 30, 5*e^2 - 14*e + 6, 6*e^3 - 30*e^2 + 18*e + 34, -4*e^3 + 17*e^2 - 10*e + 4, -5*e^3 + 13*e^2 + 16*e - 24, 4*e^3 - 19*e^2 + 21*e + 6, -5*e^3 + 18*e^2 - 4*e, e^3 - 3*e^2 - 6*e + 6, e^3 - 2*e^2 - 6*e, -2*e^3 + 12*e^2 - 6*e - 12, -5*e^3 + 22*e^2 - 5*e - 18, -2*e^3 + 8*e^2 - e + 18, -2*e^3 + 8*e^2 - 4*e - 6, -5*e^3 + 21*e^2 - 10*e - 18, 2*e^3 - 12*e^2 + 14*e + 8, -7*e^3 + 25*e^2 - 24, 6*e^3 - 25*e^2 + 2*e + 36, -4*e^3 + 15*e^2 + e - 24, e^3 - 5*e^2 - 5*e + 30, 5*e^3 - 16*e^2 - 4*e + 18, -5*e^3 + 21*e^2 + e - 24, -e^3 - 6*e^2 + 22*e + 12, -7*e^3 + 31*e^2 - 19*e - 12, -6*e^3 + 22*e^2 - 4*e - 6, 8*e^2 - 20*e - 12, -2*e^3 + 4*e^2 + 14*e - 30, -3*e^3 + e^2 + 35*e - 12, -3*e^3 + 17*e^2 - 26*e, -e^3 + 4*e^2 + 4*e - 6, -7*e^3 + 32*e^2 - 54, 7*e^3 - 31*e^2 + 54, -9*e^3 + 43*e^2 - 28*e - 42, -2*e^3 + 16*e^2 - 22*e - 18, 9*e^3 - 40*e^2 + 17*e + 48, 4*e^3 - 6*e^2 - 22*e + 6, 6*e^3 - 18*e^2 - 4*e + 6, -2*e^3 + 14*e + 18, -2*e^3 + 14*e^2 - 6*e - 36, -10*e^3 + 42*e^2 - 23*e - 24, e^3 - 9*e^2 + 20*e - 16, -e^3 + 11*e^2 - 30*e - 4, 8*e^3 - 38*e^2 + 22*e + 26, 2*e^3 - 7*e^2 + 2*e + 20, -8*e^3 + 34*e^2 - 6*e - 30, -7*e^3 + 33*e^2 - 28*e - 24, -e^2 - 4*e + 6, -3*e^3 + 17*e^2 - 6*e - 48, 4*e^2 - 24, -4*e^3 + 11*e^2 + 13*e - 12, 5*e^3 - 17*e^2 + e + 18, -5*e^3 + 8*e^2 + 20*e + 12, 3*e^3 - 8*e^2 - 13*e + 18, -10*e^3 + 40*e^2 - 6*e - 38, -4*e^3 + 12*e^2 - 2*e + 10, e^3 - 14*e^2 + 25*e + 30, e^3 - 6*e^2 + 12*e + 24, -e^3 - 2*e^2 + 13*e + 24, 8*e^3 - 36*e^2 + 29*e + 24, 6*e^3 - 22*e^2 - 4*e + 30, 8*e^3 - 29*e^2 + 5*e + 6, -e^3 - 2*e^2 + 18*e + 18, 2*e^3 - 22*e^2 + 42*e + 8, 9*e^3 - 36*e^2 + 14*e + 24, -4*e^3 + 11*e^2 + e + 6, 2*e^3 - 11*e^2 + 14*e + 14, -10*e^2 + 28*e + 18, -2*e^3 + 6*e^2 + 7*e + 24, 2*e^3 - 12*e^2 + 14*e + 4, 5*e^3 - 13*e^2 - 6*e - 2, -3*e^3 + 6*e^2 + 13*e - 18, 6*e^3 - 23*e^2 - e + 36, -8*e^3 + 38*e^2 - 16*e - 52, -2*e^3 + 10*e^2 - 12*e - 4, 5*e^2 - 22*e + 16, 2*e^3 - 30*e + 10, -11*e^3 + 45*e^2 - 2*e - 72, -e^3 + 7*e^2 - 11*e, 2*e^3 - 4*e^2 + 2*e - 18, 6*e^3 - 28*e^2 + 14*e + 54, -e^3 - 4*e^2 + 10*e + 24, 6*e^3 - 26*e^2 + 6*e + 24, 5*e^3 - 2*e^2 - 50*e + 12, -10*e^2 + 31*e - 6, -2*e^3 - 5*e^2 + 39*e, 15*e^3 - 70*e^2 + 43*e + 48, -9*e^3 + 29*e^2 + 10*e - 22, -6*e^3 + 28*e^2 - 10*e - 28, 4*e^3 - 12*e^2 - 10*e + 2, -5*e^3 + 27*e^2 - 28*e - 34, e^3 - 10*e^2 + 26*e - 12, 5*e^3 - 25*e^2 + 16*e + 36, -e^3 + 3*e^2 + 12*e - 12, -4*e^3 + 18*e^2 - 8*e - 24, 2*e^3 + e^2 - 17*e - 12, -8*e^3 + 22*e^2 + 12*e - 4, 3*e^3 + e^2 - 34*e + 2, 4*e^2 - 17*e + 18, -10*e^2 + 30*e - 20, 2*e^3 - 18*e^2 + 16*e + 46, -5*e^3 + 26*e^2 - 10*e - 60, 9*e^3 - 33*e^2 + e + 24, 15*e^3 - 71*e^2 + 48*e + 48, 15*e^3 - 61*e^2 + 16*e + 54, 4*e^3 - 18*e^2 + 2*e + 36, -10*e^3 + 39*e^2 - 18*e - 18, -15*e^3 + 65*e^2 - 28*e - 52, 10*e^3 - 42*e^2 + 15*e + 42, 5*e^3 - 15*e^2 - 25*e + 30, -14*e^3 + 60*e^2 - 13*e - 78, 5*e^3 - 18*e^2 - 5*e + 42, 4*e^3 - 11*e^2 - 14*e + 14, -2*e^3 + 5*e^2 - 5*e, -14*e^3 + 48*e^2 + 11*e - 54, 5*e^3 - 29*e^2 + 30*e + 2, -5*e^3 + 24*e^2 - 10*e - 42, 9*e^3 - 44*e^2 + 38*e + 18, -6*e^3 + 31*e^2 - 8*e - 70, 9*e^3 - 41*e^2 + 25*e + 30, -4*e^3 + 24*e^2 - 31*e - 24, -e^3 + 10*e^2 - 30*e - 6, 8*e^3 - 31*e^2 + 21*e, -3*e^3 + 18*e^2 - 34*e, 7*e^3 - 38*e^2 + 34*e + 24, -10*e^3 + 47*e^2 - 8*e - 80, 6*e^3 - 18*e^2 - 10*e + 4, 4*e^3 - 24*e^2 + 6*e + 54, 3*e^3 - 23*e^2 + 38*e - 6, e^3 - 15*e^2 + 25*e + 30, 4*e^3 - 11*e^2 - 3*e - 12, 5*e^3 - 21*e^2 + 5*e + 42, -3*e^3 + 21*e^2 - 9*e - 54, 6*e^3 - 28*e^2 + 26*e + 36, -8*e^3 + 29*e^2 + 2*e - 54, 13*e^3 - 55*e^2 + 36*e + 36, -2*e^3 + 16*e^2 - 48*e + 6, e^3 - 4*e^2 + 20*e - 36, 2*e^3 - 3*e^2 - 7*e - 18, 4*e^3 - 16*e^2 - 14*e + 24, 10*e^3 - 40*e^2 + 10*e + 48, -17*e^3 + 79*e^2 - 35*e - 72, -8*e^3 + 16*e^2 + 34*e - 6, 2*e^3 + 2*e^2 - 36*e, -2*e^2 + 12*e, -14*e^3 + 42*e^2 + 30*e - 66, -18*e^3 + 83*e^2 - 53*e - 54, 6*e^3 - 25*e^2 - 7*e + 54, 3*e^3 - 10*e^2 - 8*e, 10*e^3 - 40*e^2 + 12*e + 52, 14*e^3 - 59*e^2 + 36*e + 34, 8*e^3 - 34*e^2 + 21*e + 12, 3*e^3 - 15*e^2 + 8*e + 10, 8*e^3 - 20*e^2 - 14*e - 2, -5*e^3 + 14*e^2 + 10*e - 30, 8*e^3 - 42*e^2 + 35*e + 36, 8*e^3 - 42*e^2 + 36*e + 42, 23*e^3 - 89*e^2 + 16*e + 92, -6*e^3 + 25*e^2 + 3*e - 60, 2*e^3 - 6*e^2 + 7*e - 42, -12*e^3 + 60*e^2 - 40*e - 58, 5*e^3 - 20*e^2 + 22*e, 7*e^3 - 28*e^2 + 7*e + 60, 4*e^3 - 26*e^2 + 44*e + 8, -2*e^3 + 14*e^2 - 8*e - 26, 12*e^3 - 44*e^2 + 4*e + 28, 10*e^3 - 32*e^2 - 14*e + 32, 11*e^3 - 36*e^2 - 8*e + 42, -2*e^3 - 2*e^2 + 22*e - 18, -15*e^3 + 69*e^2 - 40*e - 54, 2*e^3 - 6*e^2 + 6*e - 48, 3*e^3 - 8*e^2 - 26*e + 18, 12*e^3 - 36*e^2 - 36*e + 60, -2*e^3 + 13*e^2 - 17*e - 18, 2*e^3 - 30*e^2 + 62*e + 18, -7*e^3 + 22*e^2 + 6*e + 6, -e^3 + 11*e^2 - 44*e + 6, 2*e^3 - 10*e^2 + 6*e, -12*e^3 + 45*e^2 + 23*e - 90, 12*e^3 - 42*e^2 - 22*e + 84, -15*e^3 + 54*e^2 - 12*e - 24, -3*e^3 + 23*e^2 - 32*e - 22, 2*e^3 - 2*e^2 + 14*e - 46, 16*e^3 - 66*e^2 + 22*e + 66, -4*e^3 + 30*e^2 - 29*e - 36, 5*e^3 - 19*e^2 + 6*e - 22, -2*e^3 + 5*e^2 + 20*e - 34, 8*e^3 - 30*e^2 + 10*e - 14, 8*e^3 - 44*e^2 + 32*e + 52, 14*e^3 - 68*e^2 + 34*e + 60, 10*e^3 - 54*e^2 + 68*e + 36, 18*e^3 - 66*e^2 + 78, 12*e^3 - 50*e^2 + 24*e + 60, -15*e^3 + 62*e^2 - 26*e - 72, 2*e^3 - 31*e^2 + 66*e + 34, -3*e^3 + 21*e^2 - 18*e - 2, 13*e^3 - 42*e^2 - 22*e + 54, 15*e^3 - 57*e^2 + 14*e + 20, -4*e^3 + 15*e^2 - 5*e - 54, -21*e^3 + 96*e^2 - 52*e - 84, 5*e^3 - 33*e^2 + 48*e + 50, 15*e^3 - 48*e^2 - 15*e + 48, 5*e^3 - 22*e^2 + 20*e + 12, -13*e^3 + 48*e^2 + e - 90, -10*e^3 + 34*e^2 + 5*e - 54, 6*e^3 - 20*e^2 + 2*e - 12, e^3 - 2*e^2 - 11*e + 42, -5*e^3 + 23*e^2 - 29*e + 18, -7*e^3 + 38*e^2 - 36*e - 6, 6*e^3 - 31*e^2 + 18*e + 66, -e^3 - 3*e^2 + 26*e - 42, -2*e^3 - 6*e^2 + 48*e - 18, 8*e^3 - 44*e^2 + 50*e + 18, -20*e^3 + 84*e^2 - 33*e - 78, -22*e^3 + 98*e^2 - 58*e - 66, -12*e^3 + 62*e^2 - 62*e - 54, -17*e^3 + 72*e^2 - 21*e - 66, -5*e^3 + 21*e^2 - 4*e + 14, 6*e^3 - 22*e^2 - 28, 3*e^3 - 20*e^2 + 24*e + 42, e^3 + 6*e^2 - 40*e, -11*e^3 + 64*e^2 - 69*e - 54, 10*e^2 - 19*e + 6, -5*e^3 + 15*e^2 + 2*e - 26, -12*e^3 + 42*e^2 + 28*e - 74, 30*e - 46, -18*e^3 + 66*e^2 - 20*e - 14, -2*e^3 - 3*e^2 + 24*e - 8, 10*e^3 - 28*e^2 + 6*e - 44, -10*e^3 + 36*e^2 + 20*e - 54, 4*e^3 - 12*e^2 + 18, 7*e^3 - 33*e^2 - 8*e + 76, -4*e^3 + 23*e^2 - 31*e, -6*e^3 + 28*e^2 - 21*e + 18, -2*e^3 + e^2 + 32*e - 2, 12*e^2 - 24*e - 24, 11*e^3 - 55*e^2 + 48*e + 66, -9*e^3 + 32*e^2 - 4*e - 42, 4*e^3 + 6*e^2 - 53*e - 12, 2*e^3 + 6*e^2 - 40*e + 32, 12*e^3 - 60*e^2 + 56*e + 14, -13*e^3 + 55*e^2 - 25*e - 6, 25*e^3 - 116*e^2 + 76*e + 84, 7*e^3 - 27*e^2 + 9*e, 7*e^3 - 17*e^2 - 35*e + 6, 6*e^3 - 31*e^2 + 27*e + 12, -10*e^3 + 22*e^2 + 57*e - 42, 2*e^3 - 16*e^2 + 28*e - 30, -10*e^3 + 21*e^2 + 25*e + 18, e^3 - 11*e^2 + 4*e + 60, -5*e^3 + 15*e^2 - 4*e + 60, 2*e^3 - 10*e^2 - 16*e + 72, -2*e^3 - 6*e^2 + 16*e + 30, -4*e^3 + 32*e + 48, 13*e^3 - 58*e^2 + 50*e + 12, -10*e^3 + 40*e^2 - 16*e - 30, -7*e^3 + 25*e^2 - 20*e - 6, -11*e^3 + 59*e^2 - 58*e - 38, 9*e^3 - 25*e^2 - 36*e + 28, 22*e^3 - 84*e^2 + 16*e + 84, -2*e^3 - 8*e^2 + 58*e + 14, -14*e^3 + 56*e^2 + 4*e - 76, 2*e^3 + 8*e^2 - 56*e] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([5,5,2/3*w^2 - 5/3*w - 4])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]