/* 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([25, 5, -2/3*w^2 + 5/3*w + 5]) 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 - 20*x^2 + 54 K. = NumberField(heckePol) hecke_eigenvalues_array = [0, e, 4, -4, 1/3*e^3 - 14/3*e, e^2 - 11, e, -e, 1/3*e^3 - 14/3*e, -1/3*e^3 + 14/3*e, 1/3*e^3 - 17/3*e, 1/3*e^3 - 17/3*e, 1/3*e^3 - 11/3*e, -1/3*e^3 + 11/3*e, e^2 - 12, -e^2 + 12, 8, -1/3*e^3 + 11/3*e, -1/3*e^3 + 11/3*e, 8, 2*e^2 - 18, -2/3*e^3 + 25/3*e, 2/3*e^3 - 25/3*e, -e^2 + 18, -e^2 + 18, 2, -2, 2*e^2 - 20, -6, -6, -1/3*e^3 + 2/3*e, -1/3*e^3 + 2/3*e, 2*e, -2*e, 0, 0, -3*e, 2/3*e^3 - 46/3*e, 2/3*e^3 - 46/3*e, -3*e, -4, 4, -4, 4, 2*e^2 - 12, -2*e^2 + 12, -2*e^2 + 22, -2*e^2 + 22, 12, -2/3*e^3 + 43/3*e, -2/3*e^3 + 43/3*e, 12, 2/3*e^3 - 28/3*e, -2/3*e^3 + 28/3*e, -e^3 + 12*e, -e^3 + 12*e, 4*e^2 - 42, -4*e^2 + 42, -4*e^2 + 34, -2*e^2, 2*e^2, -1/3*e^3 + 38/3*e, -1/3*e^3 + 38/3*e, e^3 - 25*e, -e^3 + 25*e, -5*e, -5*e, -4*e^2 + 30, -4*e^2 + 30, 2/3*e^3 - 31/3*e, -2/3*e^3 + 31/3*e, 3*e^2 - 24, -4/3*e^3 + 74/3*e, -4/3*e^3 + 74/3*e, 3*e^2 - 24, e^2 - 18, 4/3*e^3 - 65/3*e, -4/3*e^3 + 65/3*e, -e^2 + 18, -1/3*e^3 + 23/3*e, -e^2 - 18, -e^2 - 18, -1/3*e^3 + 23/3*e, -2*e^2 + 26, e^2 + 2, -e^2 - 2, 2*e^2 - 26, -e^2 - 12, -2*e^2 + 36, 2*e^2 - 36, e^2 + 12, 10*e, 1/3*e^3 + 4/3*e, 1/3*e^3 + 4/3*e, 10*e, 5/3*e^3 - 70/3*e, -e^2 + 4, -e^2 + 4, 5/3*e^3 - 70/3*e, -2*e^3 + 27*e, 2*e^3 - 27*e, -1/3*e^3 - 7/3*e, -1/3*e^3 - 7/3*e, -e^3 + 17*e, e^3 - 17*e, -2*e^2 + 44, 2/3*e^3 - 37/3*e, 2/3*e^3 - 37/3*e, -2*e^2 + 44, -e^3 + 11*e, e^3 - 11*e, -e^2 + 20, -e^2 + 20, 5/3*e^3 - 76/3*e, -5/3*e^3 + 76/3*e, -10, -10, 4*e^2 - 26, 4*e^2 - 26, 2*e^2 - 18, e^3 - 27*e, e^3 - 27*e, 2*e^2 - 18, -4/3*e^3 + 62/3*e, 4/3*e^3 - 62/3*e, -5/3*e^3 + 85/3*e, -e^3 + 14*e, e^3 - 14*e, 5/3*e^3 - 85/3*e, 26, -26, 4, 4, -6*e, -4*e^2 + 54, -4*e^2 + 54, -6*e, 1/3*e^3 - 8/3*e, -14, 14, -1/3*e^3 + 8/3*e, -2*e^2 + 2, -2*e^2 + 2, -2/3*e^3 + 25/3*e, -2/3*e^3 + 25/3*e, -4*e^2 + 18, 3*e^2 - 66, -3*e^2 + 66, 4*e^2 - 18, -2*e^2 - 14, -1/3*e^3 + 26/3*e, 1/3*e^3 - 26/3*e, -1/3*e^3 + 44/3*e, -1/3*e^3 + 44/3*e, -2*e^2 + 34, -1/3*e^3 + 20/3*e, 1/3*e^3 - 20/3*e, 2*e^2 - 34, 2/3*e^3 - 46/3*e, 2/3*e^3 - 46/3*e, 2*e^2 + 8, -5/3*e^3 + 100/3*e, 8/3*e^3 - 103/3*e, 8/3*e^3 - 103/3*e, -5/3*e^3 + 100/3*e, -2/3*e^3 + 22/3*e, -2/3*e^3 + 22/3*e, 3*e^2 + 2, -3*e^2 - 2, 30, -30, -5/3*e^3 + 82/3*e, 5/3*e^3 - 82/3*e, 5/3*e^3 - 82/3*e, -5/3*e^3 + 82/3*e, 2*e^2 - 6, 2*e^2 - 6, e^2 + 6, -e^2 - 6, -1/3*e^3 - 7/3*e, -1/3*e^3 - 7/3*e, -3*e^2 + 36, -3*e^2 + 36, 4/3*e^3 - 71/3*e, -4/3*e^3 + 71/3*e, 2/3*e^3 - 4/3*e, -2/3*e^3 + 4/3*e, -2/3*e^3 + 67/3*e, 2/3*e^3 - 67/3*e, -2*e^3 + 27*e, -2*e^3 + 27*e, -7*e^2 + 52, -7*e^2 + 52, 2*e^3 - 21*e, 2*e^2 + 14, 2*e^2 + 14, 2*e^3 - 21*e, 1/3*e^3 - 29/3*e, 1/3*e^3 - 29/3*e, -6*e^2 + 80, 5/3*e^3 - 94/3*e, -5/3*e^3 + 94/3*e, 6*e^2 - 80, -4/3*e^3 + 95/3*e, 4/3*e^3 - 95/3*e, -4*e^2 + 40, 2*e^2 + 20, -2*e^2 - 20, 4*e^2 - 40, 8/3*e^3 - 112/3*e, 7*e^2 - 72, -7*e^2 + 72, -8/3*e^3 + 112/3*e, -2/3*e^3 - 14/3*e, -2/3*e^3 - 14/3*e, -e^3 + 15*e, -e^3 + 15*e, 1/3*e^3 - 59/3*e, 3*e^2 - 6, -3*e^2 + 6, -1/3*e^3 + 59/3*e, -2/3*e^3 + 46/3*e, -2/3*e^3 + 46/3*e, 9*e^2 - 88, -9*e^2 + 88, 5/3*e^3 - 91/3*e, 5/3*e^3 - 91/3*e, 4*e^2 - 46, -4*e^2 + 46, 2*e^2 - 14, -2*e^2 + 14, -10/3*e^3 + 152/3*e, 24, 24, -10/3*e^3 + 152/3*e, -4*e^3 + 50*e, -4*e^2 + 14, 4*e^2 - 14, 4*e^3 - 50*e, 5*e^2 - 14, 5/3*e^3 - 55/3*e, 5/3*e^3 - 55/3*e, 5*e^2 - 14, -15*e, 15*e, 1/3*e^3 - 26/3*e, 1/3*e^3 - 26/3*e, 4/3*e^3 - 44/3*e, -1/3*e^3 - 4/3*e, 1/3*e^3 + 4/3*e, -4/3*e^3 + 44/3*e, 6*e^2 - 30, -3*e^2 + 48, -3*e^2 + 48, 6*e^2 - 30, 7/3*e^3 - 74/3*e, 5*e^2 - 48, 5*e^2 - 48, 7/3*e^3 - 74/3*e, -2*e^2 + 86, 2*e^2 - 86, -8/3*e^3 + 118/3*e, 8/3*e^3 - 118/3*e, -1/3*e^3 + 56/3*e, -1/3*e^3 + 56/3*e, -10*e^2 + 112, 10*e^2 - 112, e^2 + 8, 2*e^2 + 28, e^2 - 28, -e^2 + 28, -6*e^2 + 48, -6*e^2 + 48, 6*e^2 - 92, 3*e^3 - 36*e, -3*e^3 + 36*e, -6*e^2 + 92, -6*e^2 + 84, -6*e^2 + 84, -7/3*e^3 + 83/3*e, -7/3*e^3 + 83/3*e, 56, 56, -e^3 + 18*e, -2*e^3 + 19*e, -2*e^3 + 19*e, -e^3 + 18*e, 1/3*e^3 - 20/3*e, -1/3*e^3 + 20/3*e, -e^3 + 15*e, e^3 - 15*e, -10*e^2 + 96, -10*e^2 + 96, -2/3*e^3 - 26/3*e, 0, 0, -2/3*e^3 - 26/3*e, -6*e^2 + 30, 6*e^2 - 30, 50, 50, 10/3*e^3 - 116/3*e, -2*e^2 - 28, 2*e^2 + 28, -10/3*e^3 + 116/3*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 + 1/3*w - 5])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]