/* 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^8 - 41*x^6 + 526*x^4 - 2336*x^2 + 2312 K. = NumberField(heckePol) hecke_eigenvalues_array = [1, 3/358*e^6 - 73/358*e^4 + 121/179*e^2 + 422/179, 1, e, -49/12172*e^7 + 1431/12172*e^5 - 1913/3043*e^3 - 3327/3043*e, -49/12172*e^7 + 1431/12172*e^5 - 1913/3043*e^3 - 3327/3043*e, 45/6086*e^7 - 1811/6086*e^5 + 10407/3043*e^3 - 30902/3043*e, 47/12172*e^7 - 1621/12172*e^5 + 4319/3043*e^3 - 18234/3043*e, 1/6086*e^7 + 95/6086*e^5 - 2406/3043*e^3 + 21561/3043*e, -7/179*e^6 + 230/179*e^4 - 1937/179*e^2 + 3878/179, 11/358*e^6 - 387/358*e^4 + 1816/179*e^2 - 3226/179, -93/6086*e^7 + 3337/6086*e^5 - 16639/3043*e^3 + 45809/3043*e, -47/12172*e^7 + 1621/12172*e^5 - 4319/3043*e^3 + 18234/3043*e, 3/358*e^6 - 73/358*e^4 - 58/179*e^2 + 2212/179, -141/6086*e^7 + 4863/6086*e^5 - 22871/3043*e^3 + 51587/3043*e, 24/3043*e^7 - 763/3043*e^5 + 6232/3043*e^3 - 14907/3043*e, 11/358*e^6 - 387/358*e^4 + 1637/179*e^2 - 1436/179, 11/358*e^6 - 387/358*e^4 + 1637/179*e^2 - 1436/179, 3/179*e^6 - 73/179*e^4 + 242/179*e^2 + 486/179, 3/179*e^6 - 73/179*e^4 + 242/179*e^2 + 486/179, -3/179*e^6 + 73/179*e^4 - 421/179*e^2 + 2020/179, 3/358*e^6 - 73/358*e^4 + 300/179*e^2 - 1368/179, 47/6086*e^7 - 1621/6086*e^5 + 8638/3043*e^3 - 36468/3043*e, 427/12172*e^7 - 14209/12172*e^5 + 31016/3043*e^3 - 63167/3043*e, 95/6086*e^7 - 3147/6086*e^5 + 11827/3043*e^3 - 2687/3043*e, -237/12172*e^7 + 7915/12172*e^5 - 16146/3043*e^3 + 11792/3043*e, -91/6086*e^7 + 3527/6086*e^5 - 18408/3043*e^3 + 40243/3043*e, 41/12172*e^7 - 2191/12172*e^5 + 8494/3043*e^3 - 43358/3043*e, 3/179*e^7 - 73/179*e^5 + 63/179*e^3 + 3529/179*e, -46/3043*e^7 + 1716/3043*e^5 - 19045/3043*e^3 + 58241/3043*e, -3/179*e^6 + 73/179*e^4 + 116/179*e^2 - 3350/179, -10/179*e^6 + 303/179*e^4 - 2000/179*e^2 + 886/179, 11/179*e^6 - 387/179*e^4 + 3632/179*e^2 - 6810/179, -14/179*e^6 + 460/179*e^4 - 3874/179*e^2 + 7398/179, 25/358*e^6 - 847/358*e^4 + 3753/179*e^2 - 6746/179, 5/358*e^6 - 241/358*e^4 + 1395/179*e^2 - 490/179, -17/179*e^6 + 533/179*e^4 - 3758/179*e^2 + 2616/179, -21/179*e^6 + 690/179*e^4 - 5811/179*e^2 + 10918/179, -18/179*e^6 + 617/179*e^4 - 5211/179*e^2 + 8540/179, 6/179*e^6 - 146/179*e^4 + 484/179*e^2 + 614/179, 23/3043*e^7 - 858/3043*e^5 + 8001/3043*e^3 + 8917/3043*e, 13/716*e^7 - 555/716*e^5 + 1724/179*e^3 - 5112/179*e, 9/358*e^6 - 219/358*e^4 + 542/179*e^2 - 1240/179, 9/358*e^6 - 219/358*e^4 + 542/179*e^2 - 1240/179, 49/3043*e^7 - 1431/3043*e^5 + 7652/3043*e^3 + 13308/3043*e, 49/3043*e^7 - 1431/3043*e^5 + 7652/3043*e^3 + 13308/3043*e, -97/6086*e^7 + 2957/6086*e^5 - 10058/3043*e^3 + 17382/3043*e, -55/12172*e^7 + 861/12172*e^5 + 2262/3043*e^3 - 10193/3043*e, -11/358*e^7 + 387/358*e^5 - 1816/179*e^3 + 3047/179*e, -9/716*e^7 + 219/716*e^5 - 92/179*e^3 - 1528/179*e, -43/6086*e^7 + 2001/6086*e^5 - 15219/3043*e^3 + 64895/3043*e, 66/3043*e^7 - 2859/3043*e^5 + 35396/3043*e^3 - 108701/3043*e, 5/358*e^6 - 241/358*e^4 + 1574/179*e^2 - 5502/179, -17/358*e^6 + 533/358*e^4 - 1700/179*e^2 + 234/179, 19/358*e^6 - 701/358*e^4 + 3690/179*e^2 - 9738/179, 37/358*e^6 - 1139/358*e^4 + 4058/179*e^2 - 3626/179, -138/3043*e^7 + 5148/3043*e^5 - 54092/3043*e^3 + 144293/3043*e, 37/12172*e^7 - 2571/12172*e^5 + 13306/3043*e^3 - 68222/3043*e, -2/3043*e^7 - 190/3043*e^5 + 6581/3043*e^3 - 28427/3043*e, 243/12172*e^7 - 7345/12172*e^5 + 11971/3043*e^3 - 4926/3043*e, 137/12172*e^7 - 5243/12172*e^5 + 14726/3043*e^3 - 67394/3043*e, -149/6086*e^7 + 4103/6086*e^5 - 9709/3043*e^3 - 23525/3043*e, 8/179*e^6 - 314/179*e^4 + 3390/179*e^2 - 6938/179, 33/358*e^6 - 1161/358*e^4 + 5627/179*e^2 - 12184/179, -20/179*e^6 + 606/179*e^4 - 4537/179*e^2 + 7858/179, 31/358*e^6 - 993/358*e^4 + 3458/179*e^2 - 1248/179, 3/716*e^7 - 73/716*e^5 + 150/179*e^3 - 1937/179*e, 189/3043*e^7 - 6389/3043*e^5 + 55163/3043*e^3 - 102558/3043*e, -327/12172*e^7 + 11537/12172*e^5 - 26553/3043*e^3 + 33565/3043*e, 33/12172*e^7 - 2951/12172*e^5 + 15075/3043*e^3 - 71785/3043*e, 7/358*e^6 - 409/358*e^4 + 3027/179*e^2 - 7130/179, 3/179*e^6 - 73/179*e^4 - 116/179*e^2 + 4066/179, -4/179*e^6 + 157/179*e^4 - 2232/179*e^2 + 9376/179, 4/179*e^6 - 157/179*e^4 + 1874/179*e^2 - 7228/179, -709/12172*e^7 + 23935/12172*e^5 - 53887/3043*e^3 + 123883/3043*e, -113/3043*e^7 + 4480/3043*e^5 - 49629/3043*e^3 + 123820/3043*e, 149/12172*e^7 - 4103/12172*e^5 + 6376/3043*e^3 - 26275/3043*e, -11/179*e^7 + 387/179*e^5 - 3632/179*e^3 + 8242/179*e, -46/3043*e^7 + 1716/3043*e^5 - 19045/3043*e^3 + 49112/3043*e, 185/6086*e^7 - 6769/6086*e^5 + 32641/3043*e^3 - 55362/3043*e, -5/358*e^7 + 241/358*e^5 - 1753/179*e^3 + 6576/179*e, -233/6086*e^7 + 8295/6086*e^5 - 41916/3043*e^3 + 128086/3043*e, 21/179*e^6 - 690/179*e^4 + 5274/179*e^2 - 4832/179, 9/179*e^6 - 219/179*e^4 + 726/179*e^2 + 742/179, 31/179*e^6 - 993/179*e^4 + 7990/179*e^2 - 11446/179, 2*e^2 - 30, -17/179*e^6 + 533/179*e^4 - 4116/179*e^2 + 6196/179, -37/358*e^6 + 1139/358*e^4 - 4237/179*e^2 + 7206/179, -45/3043*e^7 + 1811/3043*e^5 - 23857/3043*e^3 + 92234/3043*e, -415/12172*e^7 + 15349/12172*e^5 - 39366/3043*e^3 + 113415/3043*e, 7/358*e^6 - 51/358*e^4 - 1269/179*e^2 + 8264/179, -17/358*e^6 + 533/358*e^4 - 1879/179*e^2 + 4172/179, -4/179*e^6 + 157/179*e^4 - 1516/179*e^2 + 1142/179, 37/358*e^6 - 1139/358*e^4 + 3521/179*e^2 + 670/179, -37/12172*e^7 + 2571/12172*e^5 - 13306/3043*e^3 + 59093/3043*e, 245/6086*e^7 - 7155/6086*e^5 + 19130/3043*e^3 + 33270/3043*e, 17/358*e^6 - 533/358*e^4 + 1521/179*e^2 + 124/179, 21/358*e^6 - 869/358*e^4 + 5143/179*e^2 - 12440/179, -28/3043*e^7 + 383/3043*e^5 + 6930/3043*e^3 - 78463/3043*e, 353/12172*e^7 - 9067/12172*e^5 + 4404/3043*e^3 + 82406/3043*e, -515/6086*e^7 + 18021/6086*e^5 - 84615/3043*e^3 + 191701/3043*e, 233/6086*e^7 - 8295/6086*e^5 + 41916/3043*e^3 - 118957/3043*e, 18/179*e^6 - 617/179*e^4 + 5748/179*e^2 - 9972/179, 607/12172*e^7 - 21453/12172*e^5 + 48787/3043*e^3 - 85412/3043*e, 103/6086*e^7 - 2387/6086*e^5 + 1708/3043*e^3 + 41995/3043*e, 91/3043*e^7 - 3527/3043*e^5 + 39859/3043*e^3 - 138303/3043*e, 121/3043*e^7 - 3720/3043*e^5 + 26348/3043*e^3 - 13155/3043*e, -43/358*e^6 + 1285/358*e^4 - 4479/179*e^2 + 2782/179, -3/179*e^6 + 73/179*e^4 - 600/179*e^2 + 3810/179, 3/179*e^6 - 73/179*e^4 + 242/179*e^2 + 486/179, -6/179*e^6 + 146/179*e^4 - 126/179*e^2 - 5626/179, 195/6086*e^7 - 5819/6086*e^5 + 17710/3043*e^3 + 23313/3043*e, 227/6086*e^7 - 8865/6086*e^5 + 50266/3043*e^3 - 169205/3043*e, 25/358*e^6 - 847/358*e^4 + 3574/179*e^2 - 7104/179, 33/358*e^6 - 1161/358*e^4 + 5627/179*e^2 - 14332/179, -7/179*e^6 + 230/179*e^4 - 1400/179*e^2 - 1492/179, -16/179*e^6 + 449/179*e^4 - 2842/179*e^2 + 5284/179, -7/179*e^6 + 230/179*e^4 - 1400/179*e^2 - 1492/179, -339/12172*e^7 + 10397/12172*e^5 - 18203/3043*e^3 + 1575/3043*e, -319/12172*e^7 + 12297/12172*e^5 - 36177/3043*e^3 + 138067/3043*e, -8/179*e^6 + 314/179*e^4 - 3927/179*e^2 + 13024/179, -15/358*e^6 + 365/358*e^4 - 784/179*e^2 + 1828/179, 277/6086*e^7 - 10201/6086*e^5 + 54729/3043*e^3 - 189678/3043*e, -219/12172*e^7 + 9625/12172*e^5 - 31714/3043*e^3 + 90207/3043*e, -33/358*e^6 + 1161/358*e^4 - 5269/179*e^2 + 9320/179, -19/358*e^6 + 701/358*e^4 - 3511/179*e^2 + 5442/179, 7/179*e^6 - 230/179*e^4 + 1758/179*e^2 - 3520/179, -2*e^2 + 4, 65/3043*e^7 - 2954/3043*e^5 + 40208/3043*e^3 - 151823/3043*e, 283/6086*e^7 - 9631/6086*e^5 + 43336/3043*e^3 - 99871/3043*e, -5/358*e^6 + 241/358*e^4 - 1932/179*e^2 + 11946/179, -7/179*e^6 + 230/179*e^4 - 2295/179*e^2 + 3162/179, 25/3043*e^7 - 668/3043*e^5 + 4463/3043*e^3 - 20473/3043*e, 3/716*e^7 - 73/716*e^5 + 329/179*e^3 - 4264/179*e, -49/3043*e^7 + 1431/3043*e^5 - 7652/3043*e^3 - 4179/3043*e, 48/3043*e^7 - 1526/3043*e^5 + 12464/3043*e^3 - 2427/3043*e, 145/12172*e^7 - 4483/12172*e^5 + 14231/3043*e^3 - 108956/3043*e, -2/3043*e^7 - 190/3043*e^5 + 6581/3043*e^3 - 28427/3043*e, -9/358*e^6 + 219/358*e^4 - 5/179*e^2 - 3414/179, -8/179*e^6 + 314/179*e^4 - 3748/179*e^2 + 10160/179, -205/12172*e^7 + 10955/12172*e^5 - 42470/3043*e^3 + 180274/3043*e, 341/12172*e^7 - 10207/12172*e^5 + 15797/3043*e^3 + 1728/3043*e, -25/716*e^7 + 847/716*e^5 - 1608/179*e^3 + 330/179*e, -20/3043*e^7 + 1143/3043*e^5 - 16351/3043*e^3 + 41331/3043*e, 1/716*e^7 - 263/716*e^5 + 1661/179*e^3 - 9715/179*e, 599/12172*e^7 - 22213/12172*e^5 + 58411/3043*e^3 - 162527/3043*e, 127/12172*e^7 - 6193/12172*e^5 + 23713/3043*e^3 - 108253/3043*e, 333/6086*e^7 - 10967/6086*e^5 + 44756/3043*e^3 - 71656/3043*e, 45/6086*e^7 - 1811/6086*e^5 + 10407/3043*e^3 - 49160/3043*e, -143/12172*e^7 + 4673/12172*e^5 - 10551/3043*e^3 + 69657/3043*e, -405/12172*e^7 + 16299/12172*e^5 - 48353/3043*e^3 + 154274/3043*e, 361/12172*e^7 - 8307/12172*e^5 + 866/3043*e^3 + 89532/3043*e, 233/3043*e^7 - 8295/3043*e^5 + 83832/3043*e^3 - 237914/3043*e, -217/12172*e^7 + 9815/12172*e^5 - 34120/3043*e^3 + 102639/3043*e, 8/179*e^6 - 314/179*e^4 + 3748/179*e^2 - 5148/179, -4/179*e^6 + 157/179*e^4 - 1158/179*e^2 + 784/179, 8/179*e^6 - 314/179*e^4 + 3032/179*e^2 - 4432/179, 17/358*e^6 - 533/358*e^4 + 1879/179*e^2 - 5604/179, -313/12172*e^7 + 12867/12172*e^5 - 40352/3043*e^3 + 144933/3043*e, -87/6086*e^7 + 3907/6086*e^5 - 28032/3043*e^3 + 117358/3043*e, 2*e^2 - 30, -34/179*e^6 + 1066/179*e^4 - 7516/179*e^2 + 3800/179, 7/358*e^6 - 51/358*e^4 - 911/179*e^2 + 4684/179, -19/358*e^6 + 701/358*e^4 - 2795/179*e^2 + 430/179, 15/358*e^6 - 723/358*e^4 + 4185/179*e^2 - 6482/179, 163/12172*e^7 - 2773/12172*e^5 - 7423/3043*e^3 + 112480/3043*e, 523/12172*e^7 - 17261/12172*e^5 + 37248/3043*e^3 - 96332/3043*e, 53/358*e^6 - 1767/358*e^4 + 7448/179*e^2 - 8774/179, -19/358*e^6 + 343/358*e^4 + 606/179*e^2 - 10310/179, -33/179*e^6 + 1161/179*e^4 - 10896/179*e^2 + 21862/179, -28/179*e^6 + 920/179*e^4 - 7032/179*e^2 + 7278/179, 193/6086*e^7 - 6009/6086*e^5 + 22522/3043*e^3 - 19809/3043*e, 327/12172*e^7 - 11537/12172*e^5 + 32639/3043*e^3 - 140070/3043*e, -9/179*e^6 + 398/179*e^4 - 5022/179*e^2 + 12146/179, -35/358*e^6 + 971/358*e^4 - 2963/179*e^2 + 7368/179, 3/179*e^6 - 73/179*e^4 - 116/179*e^2 + 6214/179, -91/358*e^6 + 2811/358*e^4 - 10353/179*e^2 + 11424/179, 40/3043*e^7 - 2286/3043*e^5 + 38788/3043*e^3 - 170909/3043*e, -975/12172*e^7 + 35181/12172*e^5 - 86877/3043*e^3 + 220152/3043*e, 26/179*e^6 - 752/179*e^4 + 4842/179*e^2 - 2948/179, 5/179*e^6 - 62/179*e^4 - 1506/179*e^2 + 9760/179, -14/179*e^6 + 460/179*e^4 - 4232/179*e^2 + 9904/179, -43/179*e^6 + 1464/179*e^4 - 12896/179*e^2 + 25612/179, -1265/12172*e^7 + 44147/12172*e^5 - 103167/3043*e^3 + 252441/3043*e, 243/12172*e^7 - 7345/12172*e^5 + 11971/3043*e^3 + 4203/3043*e, 21/3043*e^7 - 1048/3043*e^5 + 17625/3043*e^3 - 104714/3043*e, -225/12172*e^7 + 9055/12172*e^5 - 30582/3043*e^3 + 150287/3043*e, -21/179*e^6 + 690/179*e^4 - 5990/179*e^2 + 13782/179, -53/358*e^6 + 1767/358*e^4 - 6553/179*e^2 + 3762/179, 147/6086*e^7 - 4293/6086*e^5 + 11478/3043*e^3 + 1704/3043*e, -145/12172*e^7 + 4483/12172*e^5 - 8145/3043*e^3 + 57225/3043*e, 47/358*e^6 - 1621/358*e^4 + 6848/179*e^2 - 12840/179, -3/358*e^6 + 73/358*e^4 + 416/179*e^2 - 11520/179, 151/6086*e^7 - 3913/6086*e^5 + 4897/3043*e^3 + 48389/3043*e, 141/3043*e^7 - 4863/3043*e^5 + 48785/3043*e^3 - 160991/3043*e, 22/179*e^6 - 774/179*e^4 + 7443/179*e^2 - 15768/179, -75/358*e^6 + 2541/358*e^4 - 11080/179*e^2 + 17732/179, -609/12172*e^7 + 21263/12172*e^5 - 46381/3043*e^3 + 82109/3043*e, 1/6086*e^7 + 95/6086*e^5 - 8492/3043*e^3 + 109808/3043*e, 423/12172*e^7 - 14589/12172*e^5 + 35828/3043*e^3 - 115418/3043*e, 471/6086*e^7 - 16115/6086*e^5 + 71802/3043*e^3 - 111851/3043*e, -61/12172*e^7 + 291/12172*e^5 + 12523/3043*e^3 - 123564/3043*e, -365/6086*e^7 + 14013/6086*e^5 - 77312/3043*e^3 + 236787/3043*e, 22/179*e^6 - 595/179*e^4 + 3147/179*e^2 - 374/179, -11/358*e^6 + 387/358*e^4 - 2174/179*e^2 + 5374/179, 229/12172*e^7 - 8675/12172*e^5 + 25770/3043*e^3 - 116294/3043*e, -49/716*e^7 + 1431/716*e^5 - 2092/179*e^3 - 2074/179*e, -53/358*e^6 + 1767/358*e^4 - 8164/179*e^2 + 17724/179, -33/358*e^6 + 803/358*e^4 - 1152/179*e^2 - 10728/179, 5/179*e^6 - 241/179*e^4 + 3864/179*e^2 - 17448/179, 35/179*e^6 - 1150/179*e^4 + 9506/179*e^2 - 11156/179, 1087/12172*e^7 - 36713/12172*e^5 + 79947/3043*e^3 - 150818/3043*e, 237/3043*e^7 - 7915/3043*e^5 + 67627/3043*e^3 - 123243/3043*e, -59/358*e^6 + 1913/358*e^4 - 7153/179*e^2 + 5066/179, 39/358*e^6 - 1307/358*e^4 + 5511/179*e^2 - 10624/179, -879/12172*e^7 + 32129/12172*e^5 - 83688/3043*e^3 + 263062/3043*e, 215/6086*e^7 - 10005/6086*e^5 + 70009/3043*e^3 - 263615/3043*e, 17/179*e^6 - 533/179*e^4 + 3042/179*e^2 + 5260/179, -28/179*e^6 + 920/179*e^4 - 8106/179*e^2 + 19092/179, 617/6086*e^7 - 20503/6086*e^5 + 88729/3043*e^3 - 180396/3043*e, -11/12172*e^7 + 5041/12172*e^5 - 32412/3043*e^3 + 153763/3043*e, 13/12172*e^7 - 4851/12172*e^5 + 33049/3043*e^3 - 208277/3043*e, -303/3043*e^7 + 10774/3043*e^5 - 106066/3043*e^3 + 262374/3043*e, -2/179*e^6 - 11/179*e^4 + 1390/179*e^2 - 3188/179, -16/179*e^6 + 449/179*e^4 - 1768/179*e^2 - 7604/179, -611/12172*e^7 + 21073/12172*e^5 - 50061/3043*e^3 + 139666/3043*e, 465/6086*e^7 - 16685/6086*e^5 + 83195/3043*e^3 - 210787/3043*e, -1103/12172*e^7 + 35193/12172*e^5 - 63742/3043*e^3 + 36147/3043*e, -1063/12172*e^7 + 38993/12172*e^5 - 96647/3043*e^3 + 205669/3043*e, 9/358*e^6 - 577/358*e^4 + 4480/179*e^2 - 15202/179, 27/358*e^6 - 1015/358*e^4 + 4848/179*e^2 - 9090/179, 89/358*e^6 - 2643/358*e^4 + 8900/179*e^2 - 5858/179, -15/179*e^6 + 544/179*e^4 - 6043/179*e^2 + 18334/179, -13/179*e^6 + 376/179*e^4 - 3137/179*e^2 + 9708/179, -33/358*e^6 + 803/358*e^4 - 794/179*e^2 - 12160/179, 18/179*e^6 - 617/179*e^4 + 5032/179*e^2 - 4960/179, 85/358*e^6 - 2665/358*e^4 + 9395/179*e^2 - 7972/179, 3/358*e^6 + 285/358*e^4 - 3817/179*e^2 + 13310/179, -17/358*e^6 + 533/358*e^4 - 1163/179*e^2 - 2988/179, 615/6086*e^7 - 20693/6086*e^5 + 93541/3043*e^3 - 205260/3043*e, 143/6086*e^7 - 4673/6086*e^5 + 24145/3043*e^3 - 96712/3043*e, -49/12172*e^7 + 1431/12172*e^5 - 1913/3043*e^3 + 24060/3043*e, -259/12172*e^7 + 5825/12172*e^5 - 1852/3043*e^3 - 21498/3043*e, 4/179*e^6 - 157/179*e^4 + 1695/179*e^2 - 10808/179, -21/179*e^6 + 690/179*e^4 - 5453/179*e^2 + 14856/179, 779/12172*e^7 - 29457/12172*e^5 + 82268/3043*e^3 - 254761/3043*e, -175/12172*e^7 + 1633/12172*e^5 + 21859/3043*e^3 - 214459/3043*e, -687/12172*e^7 + 26025/12172*e^5 - 74267/3043*e^3 + 245420/3043*e, -347/12172*e^7 + 9637/12172*e^5 - 14665/3043*e^3 + 3578/3043*e, -497/12172*e^7 + 19731/12172*e^5 - 56354/3043*e^3 + 154486/3043*e, -655/6086*e^7 + 22979/6086*e^5 - 109892/3043*e^3 + 264849/3043*e, -3/179*e^6 + 73/179*e^4 + 116/179*e^2 - 5498/179, -7/179*e^6 + 230/179*e^4 - 2116/179*e^2 + 8890/179, 13/358*e^6 - 197/358*e^4 - 490/179*e^2 + 3022/179, 101/358*e^6 - 3293/358*e^4 + 13322/179*e^2 - 20638/179, 25/179*e^6 - 847/179*e^4 + 6790/179*e^2 - 7764/179, -229/6086*e^7 + 8675/6086*e^5 - 48497/3043*e^3 + 165642/3043*e, 251/3043*e^7 - 9628/3043*e^5 + 100678/3043*e^3 - 228554/3043*e, 229/12172*e^7 - 8675/12172*e^5 + 19684/3043*e^3 - 18918/3043*e, 1553/12172*e^7 - 53303/12172*e^5 + 124906/3043*e^3 - 309334/3043*e, 79/716*e^7 - 2877/716*e^5 + 7351/179*e^3 - 20876/179*e, 252/3043*e^7 - 9533/3043*e^5 + 104995/3043*e^3 - 322367/3043*e, -23/358*e^6 + 679/358*e^4 - 2479/179*e^2 + 14068/179, -31/358*e^6 + 993/358*e^4 - 3279/179*e^2 - 8418/179, -7/179*e^6 + 409/179*e^4 - 6412/179*e^2 + 21062/179, 77/358*e^6 - 2709/358*e^4 + 12891/179*e^2 - 26520/179, -33/179*e^6 + 1161/179*e^4 - 10538/179*e^2 + 25800/179, -45/179*e^6 + 1453/179*e^4 - 12222/179*e^2 + 22782/179, 14/179*e^6 - 460/179*e^4 + 4590/179*e^2 - 12768/179, -34/179*e^6 + 1066/179*e^4 - 7516/179*e^2 + 3800/179, 57/358*e^6 - 1745/358*e^4 + 6237/179*e^2 - 4870/179, -59/179*e^6 + 1913/179*e^4 - 15022/179*e^2 + 22304/179, -37/179*e^6 + 1139/179*e^4 - 7400/179*e^2 - 2056/179, -59/358*e^6 + 1913/358*e^4 - 7511/179*e^2 + 17238/179, 33/179*e^6 - 982/179*e^4 + 6600/179*e^2 - 4678/179, -83/358*e^6 + 2855/358*e^4 - 12417/179*e^2 + 26392/179, -13/179*e^6 + 555/179*e^4 - 7254/179*e^2 + 22238/179, -71/358*e^6 + 2205/358*e^4 - 7995/179*e^2 + 12686/179, -33/358*e^6 + 1161/358*e^4 - 4911/179*e^2 + 5740/179, 29/358*e^6 - 825/358*e^4 + 2005/179*e^2 + 380/179, 55/12172*e^7 - 861/12172*e^5 - 8348/3043*e^3 + 134956/3043*e, 1197/12172*e^7 - 38435/12172*e^5 + 75423/3043*e^3 - 93916/3043*e, -99/358*e^6 + 3483/358*e^4 - 15449/179*e^2 + 26886/179, -17/358*e^6 + 533/358*e^4 - 1163/179*e^2 - 7284/179, -377/6086*e^7 + 12873/6086*e^5 - 57569/3043*e^3 + 151506/3043*e, -951/12172*e^7 + 37461/12172*e^5 - 109663/3043*e^3 + 354121/3043*e, 759/6086*e^7 - 25271/6086*e^5 + 112237/3043*e^3 - 259110/3043*e, -28/3043*e^7 + 383/3043*e^5 + 3887/3043*e^3 - 20646/3043*e, 31/179*e^6 - 993/179*e^4 + 7632/179*e^2 - 1422/179, 15/179*e^6 - 544/179*e^4 + 5148/179*e^2 - 15112/179, -285/6086*e^7 + 9441/6086*e^5 - 38524/3043*e^3 + 56749/3043*e, -319/6086*e^7 + 12297/6086*e^5 - 72354/3043*e^3 + 267005/3043*e, -1459/12172*e^7 + 50061/12172*e^5 - 110182/3043*e^3 + 193748/3043*e, -77/12172*e^7 - 1229/12172*e^5 + 16556/3043*e^3 - 52612/3043*e, 101/358*e^6 - 3293/358*e^4 + 13859/179*e^2 - 27082/179, 25/358*e^6 - 847/358*e^4 + 3037/179*e^2 - 3882/179, 3/179*e^6 - 73/179*e^4 + 1316/179*e^2 - 12402/179, -89/358*e^6 + 3001/358*e^4 - 13017/179*e^2 + 27696/179, -79/358*e^6 + 2519/358*e^4 - 8258/179*e^2 - 4430/179, -35/179*e^6 + 1150/179*e^4 - 10043/179*e^2 + 18316/179] 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]