/* 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([7, 2, -7, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([28,14,2*w^3 - 7*w^2 - 5*w + 13]) primes_array = [ [4, 2, w^3 - 3*w^2 - 3*w + 4],\ [7, 7, w],\ [7, 7, w^3 - 3*w^2 - 4*w + 5],\ [9, 3, w^3 - 4*w^2 - w + 9],\ [17, 17, 2*w^3 - 6*w^2 - 7*w + 8],\ [17, 17, -w^3 + 3*w^2 + 4*w - 3],\ [17, 17, -w + 2],\ [23, 23, 2*w^3 - 7*w^2 - 4*w + 12],\ [23, 23, -w^2 + 2*w + 3],\ [31, 31, -2*w^3 + 7*w^2 + 5*w - 12],\ [31, 31, -w^3 + 4*w^2 + 2*w - 8],\ [41, 41, 3*w^3 - 10*w^2 - 7*w + 16],\ [41, 41, 2*w^3 - 7*w^2 - 5*w + 10],\ [49, 7, 2*w^3 - 6*w^2 - 6*w + 9],\ [71, 71, w^2 - 2*w - 2],\ [71, 71, 2*w^3 - 7*w^2 - 4*w + 13],\ [73, 73, 3*w^3 - 11*w^2 - 5*w + 19],\ [73, 73, -4*w^3 + 13*w^2 + 10*w - 17],\ [79, 79, 3*w^3 - 9*w^2 - 10*w + 13],\ [79, 79, -2*w^3 + 6*w^2 + 5*w - 8],\ [97, 97, 2*w^3 - 6*w^2 - 8*w + 9],\ [97, 97, 2*w - 1],\ [113, 113, 2*w^3 - 6*w^2 - 7*w + 6],\ [113, 113, -w^3 + 3*w^2 + 2*w - 1],\ [137, 137, w^3 - 2*w^2 - 5*w + 2],\ [137, 137, 2*w^3 - 7*w^2 - 3*w + 12],\ [137, 137, -3*w^3 + 10*w^2 + 7*w - 17],\ [137, 137, -w^3 + 2*w^2 + 6*w - 2],\ [167, 167, -2*w^3 + 7*w^2 + 6*w - 10],\ [167, 167, 3*w^3 - 9*w^2 - 10*w + 10],\ [169, 13, -2*w^3 + 7*w^2 + 2*w - 9],\ [169, 13, -2*w^3 + 5*w^2 + 10*w - 4],\ [193, 193, -2*w^3 + 8*w^2 + 3*w - 13],\ [193, 193, -3*w^3 + 11*w^2 + 6*w - 22],\ [199, 199, 5*w^3 - 16*w^2 - 14*w + 26],\ [199, 199, w^3 - 2*w^2 - 7*w + 3],\ [223, 223, -3*w^3 + 8*w^2 + 12*w - 8],\ [223, 223, 3*w^3 - 11*w^2 - 6*w + 17],\ [223, 223, 2*w^3 - 8*w^2 - 3*w + 18],\ [223, 223, -4*w^3 + 13*w^2 + 9*w - 18],\ [233, 233, -3*w^3 + 10*w^2 + 6*w - 16],\ [233, 233, -2*w^3 + 5*w^2 + 9*w - 6],\ [241, 241, -3*w^3 + 9*w^2 + 8*w - 10],\ [241, 241, 4*w^3 - 12*w^2 - 13*w + 15],\ [257, 257, 2*w^3 - 8*w^2 - w + 16],\ [257, 257, 4*w^3 - 13*w^2 - 11*w + 18],\ [257, 257, -w^3 + 5*w^2 - 2*w - 9],\ [257, 257, -w^3 + 2*w^2 + 4*w + 2],\ [263, 263, 4*w^3 - 14*w^2 - 9*w + 27],\ [263, 263, 5*w^3 - 15*w^2 - 17*w + 25],\ [263, 263, -2*w^3 + 7*w^2 + 6*w - 16],\ [263, 263, -2*w^3 + 7*w^2 + 6*w - 9],\ [271, 271, -w - 4],\ [271, 271, -w^3 + 3*w^2 + 4*w - 9],\ [271, 271, 5*w^3 - 16*w^2 - 14*w + 24],\ [271, 271, -4*w^3 + 14*w^2 + 9*w - 24],\ [281, 281, -2*w^3 + 6*w^2 + 5*w - 4],\ [281, 281, -3*w^3 + 9*w^2 + 10*w - 9],\ [281, 281, 3*w^3 - 10*w^2 - 8*w + 12],\ [281, 281, w^2 - w - 8],\ [311, 311, w^2 - 5],\ [311, 311, -4*w^3 + 13*w^2 + 12*w - 20],\ [313, 313, 6*w^3 - 19*w^2 - 18*w + 31],\ [313, 313, -2*w^3 + 5*w^2 + 6*w - 6],\ [337, 337, 3*w^3 - 11*w^2 - 3*w + 15],\ [337, 337, w^3 - w^2 - 9*w - 5],\ [353, 353, -w^3 + 2*w^2 + 5*w - 4],\ [353, 353, w^3 - w^2 - 8*w - 3],\ [353, 353, 3*w^3 - 10*w^2 - 7*w + 19],\ [353, 353, -4*w^3 + 14*w^2 + 7*w - 22],\ [361, 19, -3*w^3 + 11*w^2 + 6*w - 18],\ [361, 19, 2*w^3 - 8*w^2 - 3*w + 17],\ [367, 367, -4*w^3 + 12*w^2 + 13*w - 18],\ [367, 367, 3*w^3 - 9*w^2 - 8*w + 13],\ [383, 383, 5*w^3 - 17*w^2 - 12*w + 30],\ [383, 383, 2*w^2 - 3*w - 5],\ [383, 383, 3*w^3 - 9*w^2 - 11*w + 11],\ [383, 383, -w^3 + 3*w^2 + w - 1],\ [401, 401, 3*w^3 - 11*w^2 - 8*w + 23],\ [401, 401, 4*w^3 - 14*w^2 - 11*w + 22],\ [431, 431, 2*w^3 - 5*w^2 - 10*w + 8],\ [431, 431, 6*w^3 - 20*w^2 - 15*w + 29],\ [433, 433, -4*w^3 + 12*w^2 + 13*w - 17],\ [433, 433, -3*w^3 + 9*w^2 + 8*w - 12],\ [433, 433, 3*w^3 - 11*w^2 - 6*w + 20],\ [433, 433, -2*w^3 + 8*w^2 + 3*w - 15],\ [439, 439, -3*w^3 + 11*w^2 + 6*w - 19],\ [439, 439, -2*w^3 + 8*w^2 + 3*w - 16],\ [449, 449, w^3 - 4*w^2 + w + 11],\ [449, 449, -w^3 + 2*w^2 + 7*w - 6],\ [457, 457, w^2 - 4*w - 3],\ [457, 457, 4*w^3 - 15*w^2 - 6*w + 27],\ [457, 457, w^2 - 4*w - 2],\ [457, 457, -2*w^3 + 6*w^2 + 8*w - 15],\ [479, 479, -4*w^3 + 14*w^2 + 9*w - 29],\ [479, 479, -w^3 + 5*w^2 - 6],\ [487, 487, -w^3 + 6*w^2 - 3*w - 16],\ [487, 487, -5*w^3 + 18*w^2 + 9*w - 29],\ [503, 503, -2*w^3 + 7*w^2 + 8*w - 15],\ [503, 503, 4*w^3 - 13*w^2 - 14*w + 20],\ [521, 521, 3*w^3 - 10*w^2 - 9*w + 10],\ [521, 521, -2*w^3 + 7*w^2 + 3*w - 16],\ [529, 23, w^3 - 3*w^2 - 3*w - 1],\ [599, 599, -4*w^3 + 12*w^2 + 14*w - 15],\ [599, 599, 2*w^3 - 6*w^2 - 4*w + 5],\ [599, 599, 4*w^3 - 13*w^2 - 12*w + 19],\ [599, 599, w^2 - 6],\ [601, 601, -4*w^3 + 12*w^2 + 11*w - 19],\ [601, 601, 5*w^3 - 15*w^2 - 16*w + 24],\ [607, 607, -w^3 + 4*w^2 + w - 13],\ [607, 607, -w^3 + 4*w^2 + w - 2],\ [617, 617, -4*w^3 + 13*w^2 + 11*w - 16],\ [617, 617, 4*w^3 - 13*w^2 - 13*w + 20],\ [625, 5, -5],\ [631, 631, -3*w^3 + 8*w^2 + 11*w - 9],\ [631, 631, 5*w^3 - 16*w^2 - 13*w + 24],\ [631, 631, w^3 - 3*w^2 - 4*w - 1],\ [631, 631, w - 6],\ [641, 641, -3*w^3 + 12*w^2 + w - 17],\ [641, 641, w^3 - 6*w^2 + 5*w + 18],\ [673, 673, 4*w^3 - 15*w^2 - 6*w + 26],\ [673, 673, -2*w^3 + 9*w^2 - 19],\ [719, 719, 2*w^2 - 4*w - 5],\ [719, 719, 4*w^3 - 14*w^2 - 8*w + 25],\ [727, 727, 3*w^3 - 8*w^2 - 11*w + 8],\ [727, 727, 6*w^3 - 18*w^2 - 19*w + 20],\ [727, 727, -5*w^3 + 14*w^2 + 19*w - 17],\ [727, 727, -5*w^3 + 16*w^2 + 13*w - 23],\ [743, 743, 4*w^3 - 14*w^2 - 7*w + 23],\ [743, 743, w^3 - w^2 - 8*w - 2],\ [751, 751, 3*w^3 - 12*w^2 - 3*w + 23],\ [751, 751, 3*w^3 - 12*w^2 - 3*w + 22],\ [761, 761, 3*w^3 - 10*w^2 - 6*w + 22],\ [761, 761, 3*w^3 - 10*w^2 - 6*w + 18],\ [761, 761, -5*w^3 + 16*w^2 + 17*w - 25],\ [761, 761, -2*w^3 + 5*w^2 + 9*w - 8],\ [809, 809, -3*w^3 + 8*w^2 + 13*w - 3],\ [809, 809, -2*w^3 + 6*w^2 + 3*w - 12],\ [823, 823, -w^3 + 4*w^2 + 2*w - 2],\ [823, 823, 2*w^3 - 7*w^2 - 5*w + 18],\ [839, 839, 4*w^3 - 13*w^2 - 14*w + 27],\ [839, 839, -7*w^3 + 23*w^2 + 19*w - 41],\ [857, 857, -3*w^3 + 10*w^2 + 9*w - 12],\ [857, 857, -w^3 + 4*w^2 + 3*w - 13],\ [863, 863, 3*w^3 - 11*w^2 - 2*w + 20],\ [863, 863, -2*w^3 + 4*w^2 + 13*w - 5],\ [863, 863, 6*w^3 - 19*w^2 - 18*w + 27],\ [863, 863, -2*w^3 + 5*w^2 + 6*w - 2],\ [881, 881, -3*w^3 + 10*w^2 + 5*w - 17],\ [881, 881, -3*w^3 + 8*w^2 + 13*w - 12],\ [887, 887, -3*w^3 + 9*w^2 + 11*w - 9],\ [887, 887, w^3 - 3*w^2 - w - 1],\ [911, 911, 4*w^3 - 14*w^2 - 10*w + 17],\ [911, 911, 5*w^3 - 17*w^2 - 12*w + 22],\ [919, 919, -4*w^3 + 15*w^2 + 7*w - 30],\ [919, 919, -2*w^2 + 7*w + 2],\ [919, 919, w^3 - 5*w^2 + 4*w + 13],\ [919, 919, 3*w^3 - 12*w^2 - 4*w + 20],\ [929, 929, -4*w^3 + 13*w^2 + 9*w - 22],\ [929, 929, 3*w^3 - 8*w^2 - 12*w + 12],\ [961, 31, 4*w^3 - 12*w^2 - 12*w + 17],\ [967, 967, -2*w^3 + 6*w^2 + 7*w - 2],\ [967, 967, -3*w^3 + 8*w^2 + 15*w - 6],\ [967, 967, w^3 - 2*w^2 - 5*w - 6],\ [967, 967, 7*w^3 - 22*w^2 - 21*w + 36],\ [983, 983, 5*w^3 - 17*w^2 - 13*w + 25],\ [983, 983, w^3 - 5*w^2 - w + 15],\ [991, 991, -6*w^3 + 21*w^2 + 13*w - 34],\ [991, 991, 7*w^3 - 22*w^2 - 21*w + 33],\ [1009, 1009, w^2 - 2*w + 3],\ [1009, 1009, -2*w^3 + 7*w^2 + 4*w - 18],\ [1031, 1031, -4*w^3 + 15*w^2 + 4*w - 26],\ [1031, 1031, 3*w^2 - 8*w - 9],\ [1033, 1033, 2*w^3 - 4*w^2 - 13*w + 3],\ [1033, 1033, -5*w^3 + 15*w^2 + 19*w - 23],\ [1033, 1033, w^3 - w^2 - 8*w - 10],\ [1033, 1033, 4*w^3 - 14*w^2 - 7*w + 15],\ [1049, 1049, -7*w^3 + 24*w^2 + 16*w - 34],\ [1049, 1049, -5*w^3 + 16*w^2 + 18*w - 24],\ [1063, 1063, w^3 - 4*w^2 + 2*w + 8],\ [1063, 1063, w^3 - 2*w^2 - 4*w - 8],\ [1063, 1063, 7*w^3 - 24*w^2 - 17*w + 39],\ [1063, 1063, w^3 - 2*w^2 - 7*w - 6],\ [1103, 1103, w^3 - 5*w^2 + 3*w + 17],\ [1103, 1103, -w^3 + 5*w^2 - 3*w - 3],\ [1103, 1103, -w^3 + 5*w^2 - 2*w - 6],\ [1103, 1103, -2*w^3 + 8*w^2 + w - 19],\ [1129, 1129, -6*w^3 + 18*w^2 + 20*w - 27],\ [1129, 1129, -4*w^3 + 12*w^2 + 10*w - 17],\ [1151, 1151, w^3 - w^2 - 7*w - 1],\ [1151, 1151, 5*w^3 - 17*w^2 - 11*w + 29],\ [1153, 1153, -2*w^3 + 8*w^2 + 3*w - 23],\ [1153, 1153, -6*w^3 + 18*w^2 + 20*w - 25],\ [1193, 1193, -2*w^3 + 5*w^2 + 9*w - 10],\ [1193, 1193, 3*w^3 - 10*w^2 - 6*w + 20],\ [1201, 1201, 6*w^3 - 19*w^2 - 16*w + 24],\ [1201, 1201, 4*w^3 - 11*w^2 - 14*w + 9],\ [1217, 1217, 7*w^3 - 22*w^2 - 21*w + 30],\ [1217, 1217, 7*w^3 - 23*w^2 - 18*w + 39],\ [1223, 1223, -2*w^3 + 9*w^2 - 15],\ [1223, 1223, -3*w^3 + 9*w^2 + 13*w - 9],\ [1223, 1223, -5*w^3 + 17*w^2 + 12*w - 34],\ [1223, 1223, 4*w^3 - 15*w^2 - 6*w + 30],\ [1231, 1231, -3*w^3 + 7*w^2 + 12*w - 3],\ [1231, 1231, -8*w^3 + 26*w^2 + 21*w - 38],\ [1289, 1289, -4*w^3 + 14*w^2 + 7*w - 24],\ [1289, 1289, -w^3 + w^2 + 8*w + 1],\ [1297, 1297, -4*w^3 + 12*w^2 + 11*w - 15],\ [1297, 1297, -5*w^3 + 15*w^2 + 16*w - 20],\ [1303, 1303, -3*w^3 + 10*w^2 + 7*w - 23],\ [1303, 1303, -w^3 + 2*w^2 + 5*w - 8],\ [1319, 1319, -8*w^3 + 28*w^2 + 15*w - 43],\ [1319, 1319, w^3 + w^2 - 12*w - 12],\ [1321, 1321, w^2 - 2*w - 10],\ [1321, 1321, 2*w^3 - 7*w^2 - 4*w + 5],\ [1367, 1367, -5*w^3 + 17*w^2 + 14*w - 26],\ [1367, 1367, 2*w^3 - 8*w^2 - 5*w + 19],\ [1399, 1399, -2*w^3 + 7*w^2 + 3*w - 4],\ [1399, 1399, w^3 - 2*w^2 - 6*w - 6],\ [1409, 1409, w^3 - 2*w^2 - 3*w - 3],\ [1409, 1409, 3*w^3 - 10*w^2 - 5*w + 18],\ [1409, 1409, -5*w^3 + 16*w^2 + 15*w - 22],\ [1409, 1409, -3*w^3 + 8*w^2 + 13*w - 13],\ [1423, 1423, 7*w^3 - 24*w^2 - 18*w + 44],\ [1423, 1423, -8*w^3 + 26*w^2 + 21*w - 40],\ [1433, 1433, -7*w^3 + 24*w^2 + 17*w - 45],\ [1433, 1433, -3*w^3 + 12*w^2 + 3*w - 29],\ [1439, 1439, -2*w^3 + 6*w^2 + 4*w - 3],\ [1439, 1439, -4*w^3 + 12*w^2 + 14*w - 13],\ [1471, 1471, -w - 6],\ [1471, 1471, -w^3 + 3*w^2 + 4*w - 11],\ [1471, 1471, w^3 - 2*w^2 - 8*w + 4],\ [1471, 1471, w^2 - 5*w - 4],\ [1489, 1489, -2*w^3 + 9*w^2 + 2*w - 17],\ [1489, 1489, -6*w^3 + 21*w^2 + 14*w - 38],\ [1543, 1543, -7*w^3 + 24*w^2 + 19*w - 45],\ [1543, 1543, 2*w^3 - 3*w^2 - 15*w - 4],\ [1543, 1543, -5*w^3 + 18*w^2 + 6*w - 26],\ [1543, 1543, -3*w^3 + 12*w^2 + 7*w - 20],\ [1553, 1553, -4*w^3 + 14*w^2 + 11*w - 20],\ [1553, 1553, -3*w^3 + 11*w^2 + 8*w - 25],\ [1559, 1559, 2*w^2 - 4*w - 3],\ [1559, 1559, 4*w^3 - 14*w^2 - 8*w + 27],\ [1567, 1567, -4*w^3 + 15*w^2 + 3*w - 20],\ [1567, 1567, w^3 - 12*w - 10],\ [1601, 1601, -3*w^3 + 10*w^2 + 10*w - 12],\ [1601, 1601, 2*w^3 - 7*w^2 - 7*w + 18],\ [1607, 1607, -7*w^3 + 23*w^2 + 20*w - 36],\ [1607, 1607, -6*w^3 + 19*w^2 + 18*w - 26],\ [1607, 1607, 2*w^2 - w - 9],\ [1607, 1607, -2*w^3 + 5*w^2 + 6*w - 1],\ [1609, 1609, -4*w^3 + 15*w^2 + 8*w - 24],\ [1609, 1609, 4*w^3 - 15*w^2 - 8*w + 31],\ [1663, 1663, -6*w^3 + 19*w^2 + 13*w - 26],\ [1663, 1663, -7*w^3 + 20*w^2 + 26*w - 26],\ [1681, 41, -5*w^3 + 15*w^2 + 15*w - 17],\ [1697, 1697, -w^3 + 9*w + 6],\ [1697, 1697, -7*w^3 + 24*w^2 + 15*w - 39],\ [1721, 1721, -5*w^3 + 18*w^2 + 13*w - 38],\ [1721, 1721, -w^3 + 6*w^2 - 5*w - 20],\ [1721, 1721, -w^3 + w^2 + 6*w + 11],\ [1721, 1721, 6*w^3 - 20*w^2 - 15*w + 24],\ [1753, 1753, -3*w^3 + 9*w^2 + 13*w - 17],\ [1753, 1753, w^3 - 3*w^2 - 7*w + 3],\ [1753, 1753, -6*w^3 + 22*w^2 + 12*w - 45],\ [1753, 1753, -6*w^3 + 21*w^2 + 16*w - 40],\ [1759, 1759, -2*w^3 + 6*w^2 + w - 8],\ [1759, 1759, 7*w^3 - 21*w^2 - 26*w + 33],\ [1759, 1759, -3*w^3 + 10*w^2 + 10*w - 26],\ [1759, 1759, -5*w^3 + 17*w^2 + 12*w - 37],\ [1783, 1783, -5*w^3 + 18*w^2 + 11*w - 29],\ [1783, 1783, 4*w^3 - 15*w^2 - 7*w + 26],\ [1783, 1783, 3*w^3 - 12*w^2 - 5*w + 26],\ [1783, 1783, -3*w^3 + 12*w^2 + 4*w - 24],\ [1801, 1801, 8*w^3 - 24*w^2 - 27*w + 33],\ [1801, 1801, 4*w^3 - 12*w^2 - 16*w + 19],\ [1801, 1801, 4*w - 1],\ [1801, 1801, 7*w^3 - 21*w^2 - 23*w + 33],\ [1831, 1831, w^3 - 2*w^2 - 8*w + 2],\ [1831, 1831, w^2 - 5*w - 2],\ [1847, 1847, 6*w^3 - 20*w^2 - 15*w + 25],\ [1847, 1847, w^3 - w^2 - 6*w - 10],\ [1849, 43, -6*w^3 + 21*w^2 + 14*w - 37],\ [1849, 43, -2*w^3 + 9*w^2 + 2*w - 18],\ [1871, 1871, -4*w^3 + 13*w^2 + 8*w - 22],\ [1871, 1871, 4*w^3 - 13*w^2 - 12*w + 15],\ [1871, 1871, 4*w^3 - 11*w^2 - 16*w + 17],\ [1871, 1871, w^2 - 10],\ [1873, 1873, -w^3 + 5*w^2 - 20],\ [1873, 1873, -4*w^3 + 14*w^2 + 9*w - 15],\ [1913, 1913, -2*w^3 + 6*w^2 + 3*w - 4],\ [1913, 1913, 5*w^3 - 15*w^2 - 18*w + 19],\ [1913, 1913, 6*w^3 - 20*w^2 - 11*w + 30],\ [1913, 1913, 9*w^3 - 30*w^2 - 23*w + 45],\ [1993, 1993, -8*w^3 + 28*w^2 + 17*w - 43],\ [1993, 1993, 4*w^3 - 13*w^2 - 16*w + 19],\ [1993, 1993, -6*w^3 + 21*w^2 + 14*w - 36],\ [1993, 1993, -2*w^3 + 9*w^2 + 2*w - 19],\ [1999, 1999, -7*w^3 + 22*w^2 + 20*w - 30],\ [1999, 1999, 4*w^3 - 11*w^2 - 13*w + 10]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^4 - 7*x^2 + 2 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1, e^2 - 2, -1, e, 0, 2*e^3 - 14*e, -e^3 + 8*e, e^3 - 5*e, -e^3 + 7*e, -2*e^2 + 10, e^2 - 4, 2*e^3 - 9*e, -3*e^3 + 17*e, 4, -3*e^3 + 19*e, 3*e^3 - 25*e, -2*e^2 + 10, 2*e^2 + 2, 0, 0, e^2 - 6, 2*e^2, 4*e^3 - 30*e, 2*e, -2*e^3 + 15*e, -5*e^3 + 29*e, -3*e^3 + 25*e, e^3 + e, 7*e^3 - 41*e, e^3 - 13*e, -4*e^2 + 18, -e^2 + 20, 2*e^2 - 18, -4*e^2 + 10, -3*e^2 + 18, 4*e^2 - 20, -4*e^2 + 16, -6*e^2 + 22, 4*e^2 - 14, -2*e^2 + 28, -6*e^3 + 31*e, -3*e^3 + 25*e, 12, -20, -6*e^3 + 32*e, 6*e^3 - 44*e, -e^3 - 2*e, -2*e^3 + 12*e, -3*e^3 + 9*e, 2*e^3 - 17*e, 3*e^3 - 31*e, e^3 + 5*e, -3*e^2 + 24, -e^2 + 4, -2*e^2 + 6, 2*e^2 - 2, 8*e^3 - 51*e, 5*e^3 - 45*e, -3*e^3 + 9*e, -3*e^3 + 17*e, -8*e^3 + 51*e, e^3 + e, 14, 2*e^2 - 22, 5*e^2 - 18, 6*e^2 - 12, 2*e^3 - 20*e, 7*e^3 - 46*e, -8*e^3 + 48*e, 10*e^3 - 68*e, 5*e^2 - 12, -8*e^2 + 38, 3*e^2 + 10, 3*e^2 + 10, e^3 - 16*e, 2*e, -2*e^3 + 6*e, 6*e^3 - 34*e, -9*e^3 + 52*e, -4*e^3 + 18*e, -8*e^3 + 52*e, -6*e^3 + 32*e, -9*e^2 + 40, -2*e^2 + 2, -6*e^2 + 18, 2*e^2 + 2, 2*e^2 + 16, -3*e^2 + 18, 9*e^3 - 50*e, 2*e^3 - 20*e, 10*e^2 - 42, -4*e^2 + 10, -5*e^2 + 28, 5*e^2 - 16, e^3 - 10*e, -4*e^3 + 16*e, -4*e^2 + 8, 0, -e^3 + 11*e, -12*e^3 + 81*e, e^3 + 9*e, -2*e^3 + 7*e, e^2 - 12, -13*e^3 + 85*e, -11*e^3 + 73*e, -9*e^3 + 61*e, -5*e^3 + 21*e, 11*e^2 - 28, -4*e^2 + 10, -8*e^2 + 16, 4*e^2 - 40, 15*e^3 - 85*e, -2*e^3 + 21*e, -10*e^2 + 28, 36, 5*e^2 - 30, -5*e^2 + 30, -5*e^2 + 30, 4*e^3 - 34*e, 4*e^3 - 34*e, e^2 + 22, -2*e^2 - 28, 12*e^3 - 70*e, 6*e^3 - 34*e, -2*e^2 - 16, 9*e^2 - 10, -3*e^2 + 30, 2*e^2 + 24, 5*e^3 - 27*e, -e^3 + 17*e, 7*e^2 - 4, 18, -4*e^3 + 11*e, 5*e^3 - 37*e, 3*e, 10*e^3 - 63*e, -9*e^3 + 65*e, 5*e^3 - 51*e, -7*e^2 + 22, -6*e^2 + 28, -13*e^3 + 101*e, 11*e^3 - 91*e, -17*e^3 + 101*e, 4*e^3 - 37*e, -8*e^3 + 64*e, 3*e^3 - 14*e, -6*e^3 + 34*e, 12*e^3 - 90*e, 19*e^3 - 110*e, 8*e^3 - 56*e, 6*e^3 - 21*e, -10*e^3 + 75*e, -4*e^3 + 22*e, 7*e^3 - 32*e, 10*e^2 - 20, 9*e^2 - 50, -14*e^2 + 52, 2*e^2 + 12, -16*e, -15*e^3 + 110*e, -2*e^2 + 10, 48, -6*e^2, -5*e^2 + 54, 4*e^2 - 8, -6*e^3 + 51*e, -e^3 + 17*e, 2*e^2 - 6, e^2 - 28, 2*e^2 - 22, -8*e^2 + 14, -9*e^3 + 69*e, 2*e^3 - e, -7*e^2 + 36, -4*e^2 + 22, -4*e^2 + 18, 2*e^2 - 26, 8*e^3 - 67*e, -3*e^3 + 35*e, -8*e^2 + 60, -e^2 - 6, 18*e^2 - 68, 3*e^2 - 50, 5*e^3 - 18*e, -5*e^3 + 18*e, -8*e^3 + 76*e, 19*e^3 - 106*e, 5*e^2 + 20, -7*e^2 - 4, 4*e^3 - 34*e, -7*e^3 + 52*e, -6*e^2 + 52, -6*e^2 - 12, 7*e^3 - 45*e, 3*e^3 - 21*e, -e^2 + 18, 12*e^2 - 64, 12*e^3 - 78*e, 3*e^3 - 28*e, 14*e^3 - 97*e, 7*e^3 - 57*e, 2*e^3 - 31*e, 11*e^3 - 59*e, -12*e^2 + 34, 3*e^2 - 4, -19*e^3 + 117*e, -e^3 + e, -2*e^2 - 20, -2*e^2 + 12, -10*e^2 + 8, -11*e^2 + 50, -10*e^3 + 87*e, -11*e^3 + 57*e, -5*e^2 + 52, -6*e^2 - 2, 13*e^3 - 85*e, 7*e^3 - 33*e, -16*e^2 + 36, -10*e^2 + 72, 3*e^3 - 42*e, -2*e, -10*e^3 + 64*e, 7*e^3 - 32*e, -9*e^2 + 18, -7*e^2 + 30, -17*e^3 + 121*e, -8*e^3 + 39*e, 7*e^3 - 40*e, 2*e^3 - 38*e, e^2 + 4, -3*e^2 - 52, 2*e^2 + 26, -2*e^2 - 14, -14*e^2 + 56, -16*e^2 + 60, -11*e^2 + 54, 2*e^2 - 40, 44, 14*e^2 - 52, 11*e^3 - 54*e, -13*e^3 + 90*e, -8*e^3 + 27*e, -14*e^3 + 103*e, -2*e^2 + 22, 14*e^2 - 74, 20*e^3 - 124*e, -6*e^3 + 40*e, 8*e^3 - 33*e, -14*e^3 + 109*e, 18*e^3 - 101*e, 11*e^3 - 69*e, 12*e^2 - 10, 7*e^2 + 8, 5*e^2 - 32, -e^2 + 60, 8*e^2 - 66, 5*e^3 - 56*e, -11*e^3 + 88*e, 7*e^3 - 43*e, -23*e^3 + 129*e, -11*e^3 + 65*e, -22*e^3 + 151*e, 4*e^2 + 10, -5*e^2 + 68, 16*e^2 - 58, 14*e^2 - 54, 8*e^2 - 32, -2*e^2 + 68, 16*e^2 - 40, 4*e^2 - 16, 12*e^2 - 84, 14*e^2 - 68, -8*e^2 + 68, 7*e^2 - 14, -e^2 - 40, -16*e^2 + 62, -14*e^2 + 26, 7*e^2 - 8, -20*e^2 + 68, -8*e^2 + 44, -8*e^3 + 73*e, -10*e^3 + 61*e, -8*e^2 - 6, -8*e^2 + 58, -2*e^3 - 2*e, 13*e^3 - 62*e, -20*e^3 + 114*e, 18*e^3 - 136*e, 4*e^2 + 6, 3*e^2 - 48, -5*e^3 + 51*e, -6*e^3 + 61*e, -21*e^3 + 119*e, 13*e^3 - 61*e, -4*e^2 + 2, 3*e^2 + 28, 20*e^2 - 86, -8*e^2 + 18, 11*e^2 - 56, 6*e^2 - 22] 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,w^3 - 3*w^2 - 3*w + 4])] = 1 AL_eigenvalues[ZF.ideal([7,7,w^3 - 3*w^2 - 4*w + 5])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]