/* 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([11, 11, 2/3*w^2 + 1/3*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^8 - 4*x^7 - 13*x^6 + 48*x^5 + 46*x^4 - 110*x^3 - 59*x^2 + 26*x + 1 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 531/6224*e^7 - 1885/6224*e^6 - 1029/778*e^5 + 2969/778*e^4 + 20137/3112*e^3 - 3829/389*e^2 - 69441/6224*e + 17961/6224, 297/3112*e^7 - 1173/3112*e^6 - 1039/778*e^5 + 3763/778*e^4 + 8217/1556*e^3 - 5147/389*e^2 - 21803/3112*e + 13725/3112, 157/1556*e^7 - 156/389*e^6 - 995/778*e^5 + 3537/778*e^4 + 1718/389*e^3 - 3160/389*e^2 - 7811/1556*e - 893/778, -1, 531/6224*e^7 - 1885/6224*e^6 - 1029/778*e^5 + 2969/778*e^4 + 20137/3112*e^3 - 3829/389*e^2 - 63217/6224*e + 11737/6224, -21/389*e^7 + 485/1556*e^6 + 183/778*e^5 - 2549/778*e^4 + 1955/778*e^3 + 1713/389*e^2 - 2258/389*e + 1741/1556, -151/3112*e^7 + 895/3112*e^6 + 227/778*e^5 - 2775/778*e^4 + 2565/1556*e^3 + 3700/389*e^2 - 11883/3112*e - 13815/3112, -113/778*e^7 + 407/778*e^6 + 788/389*e^5 - 2350/389*e^4 - 3256/389*e^3 + 4970/389*e^2 + 9393/778*e - 2275/778, 1143/3112*e^7 - 4585/3112*e^6 - 1793/389*e^5 + 6681/389*e^4 + 23065/1556*e^3 - 13926/389*e^2 - 49205/3112*e + 17669/3112, -2219/6224*e^7 + 9149/6224*e^6 + 3421/778*e^5 - 13487/778*e^4 - 44017/3112*e^3 + 14741/389*e^2 + 118377/6224*e - 28729/6224, 605/3112*e^7 - 2303/3112*e^6 - 979/389*e^5 + 3278/389*e^4 + 13367/1556*e^3 - 6148/389*e^2 - 31735/3112*e + 5915/3112, 43/1556*e^7 - 327/1556*e^6 - 26/389*e^5 + 1053/389*e^4 - 885/778*e^3 - 3586/389*e^2 - 841/1556*e + 16887/1556, 411/6224*e^7 - 2637/6224*e^6 - 269/778*e^5 + 4087/778*e^4 - 4967/3112*e^3 - 5579/389*e^2 - 11657/6224*e + 54569/6224, -1751/3112*e^7 + 7725/3112*e^6 + 2402/389*e^5 - 11312/389*e^4 - 20177/1556*e^3 + 24460/389*e^2 + 29325/3112*e - 38929/3112, 1113/3112*e^7 - 3995/3112*e^6 - 1992/389*e^5 + 5988/389*e^4 + 33127/1556*e^3 - 13634/389*e^2 - 89219/3112*e + 18263/3112, -493/778*e^7 + 3961/1556*e^6 + 6177/778*e^5 - 23187/778*e^4 - 19629/778*e^3 + 24692/389*e^2 + 19141/778*e - 17899/1556, 1319/3112*e^7 - 5453/3112*e^6 - 2000/389*e^5 + 7868/389*e^4 + 23785/1556*e^3 - 15276/389*e^2 - 49101/3112*e + 7649/3112, 377/1556*e^7 - 1709/1556*e^6 - 1015/389*e^5 + 5125/389*e^4 + 3169/778*e^3 - 11592/389*e^2 + 7101/1556*e + 12141/1556, 335/1556*e^7 - 318/389*e^6 - 2133/778*e^5 + 7225/778*e^4 + 3532/389*e^3 - 7429/389*e^2 - 13753/1556*e + 4269/778, -903/3112*e^7 + 2977/3112*e^6 + 1829/389*e^5 - 4638/389*e^4 - 36653/1556*e^3 + 11201/389*e^2 + 104797/3112*e - 9973/3112, 193/389*e^7 - 1497/778*e^6 - 2647/389*e^5 + 8981/389*e^4 + 10809/389*e^3 - 19800/389*e^2 - 17833/389*e + 4883/778, 209/3112*e^7 - 739/3112*e^6 - 416/389*e^5 + 1288/389*e^4 + 7079/1556*e^3 - 4472/389*e^2 + 4597/3112*e + 31183/3112, -1449/3112*e^7 + 5935/3112*e^6 + 2175/389*e^5 - 8537/389*e^4 - 25307/1556*e^3 + 16671/389*e^2 + 65539/3112*e - 1963/3112, 2219/3112*e^7 - 9149/3112*e^6 - 3421/389*e^5 + 13487/389*e^4 + 44017/1556*e^3 - 29093/389*e^2 - 124601/3112*e + 25617/3112, 3485/6224*e^7 - 15375/6224*e^6 - 2413/389*e^5 + 11563/389*e^4 + 38587/3112*e^3 - 27593/389*e^2 - 15039/6224*e + 116939/6224, -579/1556*e^7 + 610/389*e^6 + 3387/778*e^5 - 14833/778*e^4 - 3925/389*e^3 + 18351/389*e^2 + 2929/1556*e - 12901/778, -1141/6224*e^7 + 4027/6224*e^6 + 2299/778*e^5 - 6557/778*e^4 - 48943/3112*e^3 + 9391/389*e^2 + 173863/6224*e - 19887/6224, 523/1556*e^7 - 1987/1556*e^6 - 1827/389*e^5 + 6113/389*e^4 + 13951/778*e^3 - 14486/389*e^2 - 26585/1556*e + 5827/1556, 1611/3112*e^7 - 6009/3112*e^6 - 2812/389*e^5 + 8856/389*e^4 + 45349/1556*e^3 - 18170/389*e^2 - 116473/3112*e - 4979/3112, 1971/3112*e^7 - 7643/3112*e^6 - 6683/778*e^5 + 23063/778*e^4 + 49863/1556*e^3 - 26342/389*e^2 - 106217/3112*e + 52467/3112, 2227/3112*e^7 - 9047/3112*e^6 - 7073/778*e^5 + 26799/778*e^4 + 47091/1556*e^3 - 28341/389*e^2 - 108329/3112*e + 22191/3112, -6885/6224*e^7 + 27263/6224*e^6 + 5659/389*e^5 - 20491/389*e^4 - 161699/3112*e^3 + 46733/389*e^2 + 397079/6224*e - 90075/6224, -165/1556*e^7 + 261/778*e^6 + 1457/778*e^5 - 3187/778*e^4 - 4033/389*e^3 + 2823/389*e^2 + 17991/1556*e + 4804/389, -2295/3112*e^7 + 8569/3112*e^6 + 4032/389*e^5 - 12753/389*e^4 - 67385/1556*e^3 + 28562/389*e^2 + 192525/3112*e - 34693/3112, 303/3112*e^7 - 513/3112*e^6 - 752/389*e^5 + 503/389*e^4 + 18497/1556*e^3 + 474/389*e^2 - 58613/3112*e + 21853/3112, -151/778*e^7 + 895/778*e^6 + 454/389*e^5 - 5550/389*e^4 + 2565/389*e^3 + 14022/389*e^2 - 11883/778*e - 6035/778, -187/389*e^7 + 2911/1556*e^6 + 5075/778*e^5 - 17067/778*e^4 - 20565/778*e^3 + 17699/389*e^2 + 14477/389*e - 7985/1556, -4605/6224*e^7 + 19767/6224*e^6 + 3496/389*e^5 - 15163/389*e^4 - 83059/3112*e^3 + 37193/389*e^2 + 189215/6224*e - 147667/6224, -157/389*e^7 + 624/389*e^6 + 1990/389*e^5 - 7074/389*e^4 - 6872/389*e^3 + 13418/389*e^2 + 7811/389*e - 2104/389, -593/389*e^7 + 2456/389*e^6 + 7224/389*e^5 - 28830/389*e^4 - 22180/389*e^3 + 61320/389*e^2 + 28135/389*e - 9498/389, 1589/1556*e^7 - 6873/1556*e^6 - 4697/389*e^5 + 20819/389*e^4 + 25809/778*e^3 - 49034/389*e^2 - 49967/1556*e + 37313/1556, 507/778*e^7 - 901/389*e^6 - 3897/389*e^5 + 10981/389*e^4 + 19084/389*e^3 - 25652/389*e^2 - 60685/778*e + 5756/389, 2353/3112*e^7 - 9191/3112*e^6 - 3751/389*e^5 + 13237/389*e^4 + 51355/1556*e^3 - 26222/389*e^2 - 146907/3112*e - 7845/3112, -2299/6224*e^7 + 8129/6224*e^6 + 2288/389*e^5 - 6695/389*e^4 - 87205/3112*e^3 + 19150/389*e^2 + 204617/6224*e - 112725/6224, -3685/3112*e^7 + 14381/3112*e^6 + 12315/778*e^5 - 42655/778*e^4 - 93653/1556*e^3 + 45722/389*e^2 + 258647/3112*e - 29733/3112, 349/6224*e^7 + 657/6224*e^6 - 781/389*e^5 - 462/389*e^4 + 53483/3112*e^3 + 1621/389*e^2 - 231903/6224*e - 21381/6224, -1429/1556*e^7 + 3095/778*e^6 + 8323/778*e^5 - 36579/778*e^4 - 11534/389*e^3 + 39825/389*e^2 + 64207/1556*e - 4577/389, 2059/3112*e^7 - 8855/3112*e^6 - 5723/778*e^5 + 25417/778*e^4 + 25327/1556*e^3 - 25461/389*e^2 - 45481/3112*e + 52903/3112, -809/1556*e^7 + 3203/1556*e^6 + 2597/389*e^5 - 9290/389*e^4 - 19011/778*e^3 + 19068/389*e^2 + 66483/1556*e + 11817/1556, 6053/6224*e^7 - 23867/6224*e^6 - 9809/778*e^5 + 34911/778*e^4 + 139199/3112*e^3 - 36045/389*e^2 - 383991/6224*e + 118063/6224, -6135/6224*e^7 + 23405/6224*e^6 + 5229/389*e^5 - 17469/389*e^4 - 164289/3112*e^3 + 39193/389*e^2 + 466941/6224*e - 50465/6224, 11/389*e^7 + 561/1556*e^6 - 1763/778*e^5 - 3481/778*e^4 + 17685/778*e^3 + 5549/389*e^2 - 16137/389*e - 7951/1556, -335/6224*e^7 + 1661/6224*e^6 + 218/389*e^5 - 1049/389*e^4 - 9009/3112*e^3 + 1371/389*e^2 + 86885/6224*e + 12079/6224, 335/778*e^7 - 2933/1556*e^6 - 3877/778*e^5 + 17173/778*e^4 + 11405/778*e^3 - 18748/389*e^2 - 16087/778*e + 15131/1556, 997/3112*e^7 - 5085/3112*e^6 - 2385/778*e^5 + 15875/778*e^4 + 5281/1556*e^3 - 21037/389*e^2 - 15519/3112*e + 51213/3112, -1615/3112*e^7 + 8681/3112*e^6 + 1411/389*e^5 - 12605/389*e^4 + 17299/1556*e^3 + 27130/389*e^2 - 89275/3112*e - 45045/3112, 727/1556*e^7 - 2109/1556*e^6 - 3244/389*e^5 + 6902/389*e^4 + 35933/778*e^3 - 18924/389*e^2 - 114237/1556*e + 16881/1556, -737/1556*e^7 + 3343/1556*e^6 + 2074/389*e^5 - 10087/389*e^4 - 10795/778*e^3 + 24046/389*e^2 + 29323/1556*e - 38467/1556, -4551/3112*e^7 + 18705/3112*e^6 + 7039/389*e^5 - 27756/389*e^4 - 87789/1556*e^3 + 61568/389*e^2 + 209581/3112*e - 72181/3112, 2239/3112*e^7 - 8505/3112*e^6 - 3807/389*e^5 + 12782/389*e^4 + 59093/1556*e^3 - 29936/389*e^2 - 178837/3112*e + 78125/3112, -899/778*e^7 + 8001/1556*e^6 + 9891/778*e^5 - 46401/778*e^4 - 23163/778*e^3 + 47086/389*e^2 + 29687/778*e - 7423/1556, -261/1556*e^7 + 408/389*e^6 + 777/778*e^5 - 10657/778*e^4 + 2419/389*e^3 + 16673/389*e^2 - 35677/1556*e - 20017/778, 8679/6224*e^7 - 36093/6224*e^6 - 6672/389*e^5 + 26702/389*e^4 + 169321/3112*e^3 - 57331/389*e^2 - 464589/6224*e + 85985/6224, -89/3112*e^7 + 713/3112*e^6 - 299/778*e^5 - 1311/778*e^4 + 9467/1556*e^3 - 1753/389*e^2 + 6083/3112*e + 49687/3112, 2883/3112*e^7 - 10797/3112*e^6 - 5033/389*e^5 + 15755/389*e^4 + 85209/1556*e^3 - 32418/389*e^2 - 270897/3112*e + 36121/3112, -123/778*e^7 + 85/778*e^6 + 1560/389*e^5 - 162/389*e^4 - 11961/389*e^3 - 2680/389*e^2 + 48181/778*e + 5703/778, 163/1556*e^7 - 353/1556*e^6 - 768/389*e^5 + 762/389*e^4 + 10993/778*e^3 + 302/389*e^2 - 71073/1556*e - 14275/1556, -6065/3112*e^7 + 24103/3112*e^6 + 9885/389*e^5 - 35655/389*e^4 - 142643/1556*e^3 + 76408/389*e^2 + 401595/3112*e - 76747/3112, 2945/3112*e^7 - 12535/3112*e^6 - 4129/389*e^5 + 18043/389*e^4 + 39207/1556*e^3 - 38260/389*e^2 - 84883/3112*e + 113627/3112, -946/389*e^7 + 3693/389*e^6 + 12402/389*e^5 - 43650/389*e^4 - 43917/389*e^3 + 94616/389*e^2 + 51567/389*e - 10133/389, 2071/3112*e^7 - 8313/3112*e^6 - 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11551/389*e^2 + 4515/389*e + 35175/1556, 13713/6224*e^7 - 55739/6224*e^6 - 10943/389*e^5 + 41938/389*e^4 + 285255/3112*e^3 - 94978/389*e^2 - 567387/6224*e + 238695/6224, 724/389*e^7 - 11701/1556*e^6 - 18257/778*e^5 + 68189/778*e^4 + 58987/778*e^3 - 67838/389*e^2 - 28146/389*e - 2025/1556, -333/3112*e^7 + 3437/3112*e^6 - 839/778*e^5 - 10561/778*e^4 + 29687/1556*e^3 + 17323/389*e^2 - 56089/3112*e - 177637/3112, 5367/1556*e^7 - 10569/778*e^6 - 35213/778*e^5 + 126283/778*e^4 + 62768/389*e^3 - 140110/389*e^2 - 325233/1556*e + 14998/389, -1043/778*e^7 + 9775/1556*e^6 + 10185/778*e^5 - 57141/778*e^4 - 11681/778*e^3 + 62573/389*e^2 + 16871/778*e - 60693/1556, 2859/3112*e^7 - 7991/3112*e^6 - 12485/778*e^5 + 24255/778*e^4 + 128891/1556*e^3 - 26116/389*e^2 - 307265/3112*e - 28289/3112, -6361/3112*e^7 + 23441/3112*e^6 + 22093/778*e^5 - 67947/778*e^4 - 181693/1556*e^3 + 70757/389*e^2 + 533963/3112*e - 142929/3112, 1001/389*e^7 - 14301/1556*e^6 - 28951/778*e^5 + 83899/778*e^4 + 125689/778*e^3 - 89044/389*e^2 - 90240/389*e + 62239/1556, -18083/6224*e^7 + 70625/6224*e^6 + 15575/389*e^5 - 53706/389*e^4 - 506261/3112*e^3 + 126489/389*e^2 + 1476161/6224*e - 424469/6224, -9473/3112*e^7 + 40557/3112*e^6 + 28317/778*e^5 - 121629/778*e^4 - 163021/1556*e^3 + 138443/389*e^2 + 322347/3112*e - 175605/3112, -2635/3112*e^7 + 6957/3112*e^6 + 6315/389*e^5 - 11660/389*e^4 - 147849/1556*e^3 + 33168/389*e^2 + 436121/3112*e - 62193/3112, -2119/3112*e^7 + 6145/3112*e^6 + 4603/389*e^5 - 9232/389*e^4 - 99341/1556*e^3 + 17876/389*e^2 + 276653/3112*e + 68875/3112, 7989/3112*e^7 - 32637/3112*e^6 - 24561/778*e^5 + 95547/778*e^4 + 154121/1556*e^3 - 101333/389*e^2 - 413967/3112*e + 195341/3112, -14875/6224*e^7 + 59401/6224*e^6 + 12159/389*e^5 - 45284/389*e^4 - 332445/3112*e^3 + 107661/389*e^2 + 753385/6224*e - 322429/6224, 23/3112*e^7 - 971/3112*e^6 + 357/778*e^5 + 5575/778*e^4 - 8181/1556*e^3 - 19233/389*e^2 - 39965/3112*e + 185331/3112, -9583/3112*e^7 + 38571/3112*e^6 + 30229/778*e^5 - 113485/778*e^4 - 200815/1556*e^3 + 121490/389*e^2 + 530397/3112*e - 33387/3112, 141/3112*e^7 + 1895/3112*e^6 - 2175/778*e^5 - 8579/778*e^4 + 38133/1556*e^3 + 25313/389*e^2 - 91703/3112*e - 202271/3112, 91/1556*e^7 + 337/778*e^6 - 2435/778*e^5 - 2717/778*e^4 + 7807/389*e^3 - 8/389*e^2 + 14323/1556*e + 4237/389, -19573/6224*e^7 + 80219/6224*e^6 + 31121/778*e^5 - 120047/778*e^4 - 428191/3112*e^3 + 135815/389*e^2 + 1085255/6224*e - 267375/6224, -3487/1556*e^7 + 14377/1556*e^6 + 11363/389*e^5 - 44166/389*e^4 - 82729/778*e^3 + 107662/389*e^2 + 226477/1556*e - 69597/1556, -2077/6224*e^7 - 905/6224*e^6 + 4308/389*e^5 - 591/389*e^4 - 266227/3112*e^3 + 4688/389*e^2 + 688063/6224*e + 17629/6224, -5937/1556*e^7 + 11117/778*e^6 + 41095/778*e^5 - 132271/778*e^4 - 80378/389*e^3 + 141870/389*e^2 + 394315/1556*e - 13149/389, 1619/778*e^7 - 12203/1556*e^6 - 22253/778*e^5 + 72093/778*e^4 + 90233/778*e^3 - 80175/389*e^2 - 137545/778*e + 29481/1556, 242/389*e^7 - 4385/1556*e^6 - 4943/778*e^5 + 26503/778*e^4 + 1237/778*e^3 - 31188/389*e^2 + 19593/389*e + 46419/1556, 1895/3112*e^7 - 8223/3112*e^6 - 4683/778*e^5 + 20641/778*e^4 + 9379/1556*e^3 - 5867/389*e^2 + 36395/3112*e - 143329/3112, -16197/6224*e^7 + 61023/6224*e^6 + 13752/389*e^5 - 44643/389*e^4 - 422443/3112*e^3 + 93763/389*e^2 + 1111863/6224*e - 443451/6224, -1957/1556*e^7 + 3619/778*e^6 + 14697/778*e^5 - 44599/778*e^4 - 35565/389*e^3 + 55705/389*e^2 + 239723/1556*e - 19235/389, -5647/3112*e^7 + 26515/3112*e^6 + 14605/778*e^5 - 79773/778*e^4 - 48351/1556*e^3 + 93138/389*e^2 + 52909/3112*e - 131859/3112, 1879/778*e^7 - 12575/1556*e^6 - 28165/778*e^5 + 71905/778*e^4 + 128997/778*e^3 - 67995/389*e^2 - 198429/778*e + 33189/1556, -32831/6224*e^7 + 133493/6224*e^6 + 25711/389*e^5 - 97776/389*e^4 - 687113/3112*e^3 + 208221/389*e^2 + 1875189/6224*e - 431833/6224, 91/389*e^7 - 27/1556*e^6 - 6239/778*e^5 + 2747/778*e^4 + 53509/778*e^3 - 9757/389*e^2 - 50251/389*e + 12165/1556, -4199/3112*e^7 + 19303/3112*e^6 + 10527/778*e^5 - 55821/778*e^4 - 23331/1556*e^3 + 58479/389*e^2 - 79627/3112*e - 99223/3112, -267/3112*e^7 + 3695/3112*e^6 - 1675/778*e^5 - 10157/778*e^4 + 48629/1556*e^3 + 7578/389*e^2 - 146687/3112*e + 35473/3112, 15489/6224*e^7 - 62659/6224*e^6 - 12288/389*e^5 + 46813/389*e^4 + 325055/3112*e^3 - 105255/389*e^2 - 708075/6224*e + 232783/6224] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([11, 11, 2/3*w^2 + 1/3*w - 4])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]