/* 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([3, -9, -11, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([3, 3, w^3 - 2*w^2 - 8*w - 3]) primes_array = [ [3, 3, w^3 - 2*w^2 - 8*w - 3],\ [3, 3, w^3 - 3*w^2 - 5*w + 2],\ [13, 13, w^3 - 2*w^2 - 6*w + 1],\ [16, 2, 2],\ [17, 17, -2*w^3 + 5*w^2 + 14*w - 1],\ [17, 17, -w^3 + 3*w^2 + 5*w - 4],\ [17, 17, -w^3 + 2*w^2 + 8*w + 1],\ [17, 17, w - 1],\ [23, 23, 2*w^3 - 6*w^2 - 11*w + 7],\ [23, 23, w^3 - 3*w^2 - 7*w + 4],\ [23, 23, -w^2 + 2*w + 5],\ [23, 23, 3*w^3 - 8*w^2 - 20*w + 5],\ [61, 61, -w^3 + 2*w^2 + 9*w + 1],\ [61, 61, -2*w^3 + 5*w^2 + 13*w - 2],\ [61, 61, w^3 - 2*w^2 - 9*w - 2],\ [61, 61, 2*w^3 - 5*w^2 - 13*w + 1],\ [79, 79, 4*w^3 - 10*w^2 - 28*w + 5],\ [79, 79, w^3 - 3*w^2 - 4*w + 4],\ [79, 79, w^3 - 4*w^2 - 2*w + 10],\ [79, 79, 2*w^3 - 6*w^2 - 10*w + 5],\ [101, 101, -w^3 + 3*w^2 + 7*w - 5],\ [101, 101, w^2 - 2*w - 4],\ [101, 101, -3*w^3 + 8*w^2 + 20*w - 4],\ [101, 101, -2*w^3 + 6*w^2 + 11*w - 8],\ [139, 139, 4*w^3 - 11*w^2 - 26*w + 8],\ [139, 139, -3*w^3 + 9*w^2 + 17*w - 11],\ [139, 139, w^3 - 4*w^2 - 4*w + 8],\ [139, 139, -6*w^3 + 16*w^2 + 40*w - 13],\ [157, 157, w^3 - 3*w^2 - 7*w - 1],\ [157, 157, -3*w^3 + 9*w^2 + 17*w - 8],\ [157, 157, -4*w^3 + 11*w^2 + 26*w - 11],\ [157, 157, 3*w^3 - 8*w^2 - 20*w + 10],\ [173, 173, 3*w^3 - 8*w^2 - 18*w + 1],\ [173, 173, -3*w^3 + 7*w^2 + 23*w - 4],\ [173, 173, -w^3 + 4*w^2 + 2*w - 11],\ [173, 173, 5*w^3 - 13*w^2 - 33*w + 4],\ [179, 179, 5*w^3 - 14*w^2 - 31*w + 14],\ [179, 179, w^3 - w^2 - 11*w - 7],\ [179, 179, -4*w^3 + 10*w^2 + 29*w - 4],\ [179, 179, 4*w^3 - 11*w^2 - 24*w + 8],\ [211, 211, -2*w^3 + 5*w^2 + 16*w - 1],\ [211, 211, 2*w^3 - 4*w^2 - 15*w - 5],\ [211, 211, -w^3 + 4*w^2 + 2*w - 7],\ [211, 211, 5*w^3 - 13*w^2 - 33*w + 8],\ [233, 233, w^3 - 4*w^2 - 3*w + 7],\ [233, 233, 3*w^3 - 7*w^2 - 22*w - 5],\ [233, 233, -w^3 + 3*w^2 + 4*w + 2],\ [233, 233, -4*w^3 + 11*w^2 + 25*w - 10],\ [251, 251, -3*w^3 + 7*w^2 + 22*w - 4],\ [251, 251, 3*w^3 - 7*w^2 - 22*w - 4],\ [251, 251, w^3 - 3*w^2 - 4*w - 1],\ [251, 251, -w^3 + 3*w^2 + 4*w - 7],\ [257, 257, -w^3 + 2*w^2 + 7*w + 5],\ [257, 257, 2*w^3 - 5*w^2 - 15*w - 1],\ [257, 257, w^2 - 3*w - 2],\ [257, 257, -3*w^3 + 8*w^2 + 19*w - 8],\ [311, 311, -2*w^3 + 6*w^2 + 11*w - 11],\ [311, 311, w^2 - 2*w - 1],\ [311, 311, -3*w^3 + 8*w^2 + 20*w - 1],\ [311, 311, w^3 - 3*w^2 - 7*w + 8],\ [313, 313, -4*w^3 + 10*w^2 + 27*w - 1],\ [313, 313, -w^3 + 2*w^2 + 10*w - 1],\ [313, 313, -3*w^3 + 7*w^2 + 21*w - 2],\ [313, 313, w^2 - 4*w - 7],\ [367, 367, 2*w^3 - 4*w^2 - 17*w - 10],\ [367, 367, 4*w^3 - 10*w^2 - 29*w + 10],\ [367, 367, -4*w^3 + 11*w^2 + 24*w - 2],\ [367, 367, -3*w^3 + 8*w^2 + 18*w + 2],\ [373, 373, -3*w^3 + 6*w^2 + 24*w + 8],\ [373, 373, -9*w^3 + 23*w^2 + 62*w - 13],\ [373, 373, -6*w^3 + 15*w^2 + 42*w - 8],\ [373, 373, 5*w^3 - 12*w^2 - 36*w + 1],\ [389, 389, 3*w^3 - 8*w^2 - 18*w + 7],\ [389, 389, 3*w^3 - 7*w^2 - 23*w - 2],\ [389, 389, 2*w^3 - 5*w^2 - 12*w - 1],\ [389, 389, -2*w^3 + 4*w^2 + 17*w + 1],\ [467, 467, 6*w^3 - 16*w^2 - 39*w + 8],\ [467, 467, w^3 - w^2 - 9*w - 5],\ [467, 467, 2*w^3 - 4*w^2 - 15*w - 8],\ [467, 467, 2*w^3 - 7*w^2 - 8*w + 14],\ [491, 491, -6*w^3 + 18*w^2 + 33*w - 14],\ [491, 491, 9*w^3 - 24*w^2 - 60*w + 22],\ [491, 491, 4*w^3 - 11*w^2 - 26*w + 2],\ [491, 491, 2*w^3 - 6*w^2 - 13*w + 14],\ [523, 523, -w - 5],\ [523, 523, w^3 - 2*w^2 - 8*w - 7],\ [523, 523, w^3 - 3*w^2 - 5*w - 2],\ [523, 523, 2*w^3 - 5*w^2 - 14*w + 7],\ [547, 547, -4*w^3 + 12*w^2 + 23*w - 16],\ [547, 547, -2*w^3 + 7*w^2 + 10*w - 10],\ [547, 547, -9*w^3 + 24*w^2 + 60*w - 20],\ [547, 547, -5*w^3 + 14*w^2 + 32*w - 10],\ [563, 563, 3*w^3 - 8*w^2 - 17*w + 2],\ [563, 563, 4*w^3 - 9*w^2 - 31*w - 4],\ [563, 563, 4*w^3 - 9*w^2 - 31*w + 1],\ [563, 563, 3*w^3 - 8*w^2 - 17*w + 7],\ [569, 569, 3*w^2 - 6*w - 16],\ [569, 569, 8*w^3 - 22*w^2 - 49*w + 10],\ [569, 569, 3*w^3 - 9*w^2 - 21*w + 11],\ [569, 569, w^2 + 3*w - 2],\ [601, 601, -5*w^3 + 15*w^2 + 26*w - 13],\ [601, 601, 9*w^3 - 23*w^2 - 62*w + 14],\ [601, 601, 6*w^3 - 15*w^2 - 41*w + 2],\ [601, 601, w^3 - 4*w^2 - w + 11],\ [607, 607, w^3 - 3*w^2 - 4*w - 4],\ [607, 607, -2*w^3 + 5*w^2 + 15*w - 8],\ [607, 607, 3*w^3 - 7*w^2 - 22*w - 7],\ [607, 607, -3*w^3 + 8*w^2 + 19*w + 1],\ [625, 5, -5],\ [641, 641, -w^3 + 5*w^2 - 13],\ [641, 641, 9*w^3 - 24*w^2 - 57*w + 8],\ [641, 641, 4*w^3 - 11*w^2 - 23*w + 2],\ [641, 641, 8*w^3 - 24*w^2 - 43*w + 23],\ [647, 647, 6*w^3 - 15*w^2 - 42*w + 4],\ [647, 647, 5*w^3 - 13*w^2 - 31*w + 1],\ [647, 647, -3*w^3 + 9*w^2 + 15*w - 11],\ [647, 647, 4*w^3 - 9*w^2 - 32*w + 4],\ [701, 701, -5*w^3 + 13*w^2 + 33*w - 2],\ [701, 701, 3*w^2 - 7*w - 17],\ [701, 701, 5*w^3 - 12*w^2 - 34*w - 7],\ [701, 701, -w^3 + 4*w^2 + 2*w - 13],\ [719, 719, -w^3 + 12*w + 13],\ [719, 719, -7*w^3 + 19*w^2 + 42*w - 4],\ [719, 719, -8*w^3 + 21*w^2 + 54*w - 13],\ [719, 719, 5*w^3 - 15*w^2 - 27*w + 16],\ [757, 757, 2*w^3 - 4*w^2 - 18*w - 1],\ [757, 757, -4*w^3 + 10*w^2 + 26*w - 5],\ [757, 757, -2*w^3 + 4*w^2 + 18*w + 5],\ [757, 757, 4*w^3 - 10*w^2 - 26*w + 1],\ [797, 797, 2*w^3 - 5*w^2 - 16*w + 8],\ [797, 797, -w^3 + 5*w^2 + w - 13],\ [797, 797, -6*w^3 + 17*w^2 + 36*w - 16],\ [797, 797, 5*w^3 - 13*w^2 - 33*w + 1],\ [841, 29, -3*w^3 + 9*w^2 + 18*w - 10],\ [841, 29, -3*w^3 + 9*w^2 + 18*w - 11],\ [857, 857, -4*w^3 + 10*w^2 + 29*w - 2],\ [857, 857, w^3 - w^2 - 11*w - 5],\ [857, 857, -4*w^3 + 11*w^2 + 24*w - 10],\ [857, 857, w^3 - 2*w^2 - 6*w - 4],\ [859, 859, 5*w^3 - 13*w^2 - 32*w + 5],\ [859, 859, 3*w^3 - 7*w^2 - 20*w + 1],\ [859, 859, -3*w^3 + 7*w^2 + 24*w - 2],\ [859, 859, -w^3 + w^2 + 12*w + 8],\ [881, 881, 4*w^3 - 11*w^2 - 25*w + 13],\ [881, 881, w^2 - w - 10],\ [881, 881, 3*w^3 - 8*w^2 - 21*w + 1],\ [881, 881, -w^3 + 4*w^2 + 3*w - 4],\ [919, 919, 6*w^3 - 16*w^2 - 37*w + 7],\ [919, 919, -4*w^3 + 9*w^2 + 32*w + 2],\ [919, 919, 2*w^3 - 3*w^2 - 20*w - 11],\ [919, 919, 5*w^3 - 12*w^2 - 38*w + 5],\ [937, 937, 6*w^3 - 16*w^2 - 37*w + 8],\ [937, 937, 5*w^3 - 12*w^2 - 38*w + 4],\ [937, 937, -5*w^3 + 13*w^2 + 31*w - 4],\ [937, 937, 3*w^3 - 6*w^2 - 26*w - 7],\ [953, 953, w^3 - w^2 - 9*w - 11],\ [953, 953, 3*w^3 - 8*w^2 - 22*w + 2],\ [953, 953, -2*w^3 + 7*w^2 + 8*w - 8],\ [953, 953, 6*w^3 - 16*w^2 - 39*w + 14],\ [991, 991, -7*w^3 + 19*w^2 + 46*w - 17],\ [991, 991, -7*w^3 + 20*w^2 + 42*w - 19],\ [991, 991, -5*w^3 + 15*w^2 + 28*w - 14],\ [991, 991, -2*w^3 + 8*w^2 + 7*w - 17],\ [997, 997, w^3 - w^2 - 11*w - 14],\ [997, 997, w^3 - 2*w^2 - 6*w + 5],\ [997, 997, -4*w^3 + 10*w^2 + 29*w - 11],\ [997, 997, -4*w^3 + 11*w^2 + 24*w - 1],\ [1013, 1013, -5*w^3 + 13*w^2 + 36*w - 13],\ [1013, 1013, -w^3 + 5*w^2 - 19],\ [1013, 1013, -7*w^3 + 19*w^2 + 44*w - 8],\ [1013, 1013, -w^3 + w^2 + 8*w + 2],\ [1031, 1031, 2*w^3 - 6*w^2 - 9*w + 10],\ [1031, 1031, 5*w^3 - 13*w^2 - 34*w - 2],\ [1031, 1031, 8*w^3 - 21*w^2 - 50*w + 2],\ [1031, 1031, 6*w^3 - 18*w^2 - 33*w + 13],\ [1069, 1069, -5*w^3 + 12*w^2 + 35*w + 2],\ [1069, 1069, w^2 - 5*w - 1],\ [1069, 1069, w^2 - 5*w - 8],\ [1069, 1069, 5*w^3 - 12*w^2 - 35*w + 5],\ [1091, 1091, w^2 + w - 5],\ [1091, 1091, w^3 - 13*w - 13],\ [1091, 1091, 6*w^3 - 17*w^2 - 35*w + 14],\ [1091, 1091, 7*w^3 - 18*w^2 - 49*w + 10],\ [1093, 1093, 7*w^3 - 18*w^2 - 47*w + 10],\ [1093, 1093, 3*w^3 - 6*w^2 - 23*w - 7],\ [1093, 1093, -2*w^3 + 5*w^2 + 17*w - 1],\ [1093, 1093, -2*w^3 + 7*w^2 + 7*w - 10],\ [1109, 1109, 5*w^3 - 11*w^2 - 39*w - 7],\ [1109, 1109, -6*w^3 + 14*w^2 + 45*w - 4],\ [1109, 1109, 3*w^3 - 8*w^2 - 16*w + 8],\ [1109, 1109, -5*w^3 + 14*w^2 + 31*w - 16],\ [1153, 1153, 3*w^3 - 8*w^2 - 20*w - 2],\ [1153, 1153, -6*w^3 + 16*w^2 + 38*w - 1],\ [1153, 1153, -w^3 + 3*w^2 + 7*w - 11],\ [1153, 1153, 2*w^3 - 6*w^2 - 11*w + 14],\ [1171, 1171, -3*w^3 + 8*w^2 + 21*w - 13],\ [1171, 1171, 4*w^3 - 11*w^2 - 25*w + 1],\ [1171, 1171, -5*w^3 + 13*w^2 + 33*w + 2],\ [1171, 1171, 2*w^3 - 5*w^2 - 16*w + 11],\ [1187, 1187, 4*w^3 - 9*w^2 - 32*w - 5],\ [1187, 1187, -5*w^3 + 13*w^2 + 31*w - 10],\ [1187, 1187, 4*w^3 - 10*w^2 - 25*w - 1],\ [1187, 1187, -3*w^3 + 6*w^2 + 26*w + 1],\ [1193, 1193, 8*w^3 - 21*w^2 - 53*w + 10],\ [1193, 1193, -w^3 + w^2 + 12*w + 2],\ [1193, 1193, -3*w^3 + 10*w^2 + 13*w - 17],\ [1193, 1193, -3*w^3 + 7*w^2 + 20*w + 5],\ [1231, 1231, 5*w^3 - 14*w^2 - 32*w + 13],\ [1231, 1231, -4*w^3 + 12*w^2 + 23*w - 13],\ [1231, 1231, -2*w^3 + 7*w^2 + 10*w - 13],\ [1231, 1231, -3*w^3 + 9*w^2 + 19*w - 10],\ [1249, 1249, -4*w^3 + 13*w^2 + 20*w - 17],\ [1249, 1249, -6*w^3 + 17*w^2 + 37*w - 17],\ [1249, 1249, -8*w^3 + 22*w^2 + 51*w - 19],\ [1249, 1249, 5*w^3 - 14*w^2 - 34*w + 11],\ [1303, 1303, w^3 - 2*w^2 - 11*w - 4],\ [1303, 1303, -w^3 + 4*w^2 + w - 5],\ [1303, 1303, -4*w^3 + 9*w^2 + 29*w + 5],\ [1303, 1303, 6*w^3 - 15*w^2 - 41*w + 8],\ [1327, 1327, 9*w^3 - 23*w^2 - 59*w + 1],\ [1327, 1327, 8*w^3 - 24*w^2 - 42*w + 19],\ [1327, 1327, 7*w^3 - 18*w^2 - 46*w + 4],\ [1327, 1327, 4*w^3 - 13*w^2 - 18*w + 16],\ [1381, 1381, w^3 - 5*w^2 - 3*w + 13],\ [1381, 1381, -4*w^3 + 13*w^2 + 20*w - 20],\ [1381, 1381, 5*w^3 - 14*w^2 - 31*w + 22],\ [1381, 1381, -14*w^3 + 37*w^2 + 94*w - 28],\ [1427, 1427, -3*w^3 + 9*w^2 + 16*w - 13],\ [1427, 1427, w^3 - 3*w^2 - 8*w + 7],\ [1427, 1427, 5*w^3 - 13*w^2 - 34*w + 4],\ [1427, 1427, w^3 - w^2 - 10*w - 4],\ [1459, 1459, -w^3 + 3*w^2 + 5*w - 10],\ [1459, 1459, -2*w^3 + 5*w^2 + 14*w + 5],\ [1459, 1459, -w^3 + 2*w^2 + 8*w - 5],\ [1459, 1459, w - 7],\ [1481, 1481, 5*w^3 - 14*w^2 - 31*w + 20],\ [1481, 1481, -7*w^3 + 20*w^2 + 40*w - 16],\ [1481, 1481, -2*w^3 + 2*w^2 + 21*w + 16],\ [1481, 1481, 9*w^3 - 23*w^2 - 63*w + 13],\ [1483, 1483, -6*w^3 + 15*w^2 + 42*w - 14],\ [1483, 1483, 3*w^3 - 6*w^2 - 24*w - 14],\ [1483, 1483, -2*w^3 + 6*w^2 + 10*w + 1],\ [1483, 1483, -11*w^3 + 30*w^2 + 72*w - 31],\ [1499, 1499, -5*w^3 + 10*w^2 + 40*w + 8],\ [1499, 1499, 10*w^3 - 25*w^2 - 70*w + 8],\ [1499, 1499, 5*w^3 - 15*w^2 - 25*w + 17],\ [1499, 1499, 5*w - 2],\ [1543, 1543, 5*w^3 - 12*w^2 - 35*w - 1],\ [1543, 1543, 5*w^3 - 12*w^2 - 35*w + 4],\ [1543, 1543, w^2 - 5*w - 7],\ [1543, 1543, w^2 - 5*w - 2],\ [1559, 1559, -2*w^3 + 7*w^2 + 9*w - 7],\ [1559, 1559, w^3 - 4*w^2 - 5*w + 14],\ [1559, 1559, 4*w^3 - 11*w^2 - 27*w + 4],\ [1559, 1559, 5*w^3 - 14*w^2 - 31*w + 17],\ [1583, 1583, -6*w^3 + 16*w^2 + 38*w - 13],\ [1583, 1583, 2*w^2 - 6*w - 7],\ [1583, 1583, -2*w^3 + 4*w^2 + 14*w + 7],\ [1583, 1583, 4*w^3 - 10*w^2 - 30*w + 1],\ [1621, 1621, -4*w^3 + 9*w^2 + 28*w + 5],\ [1621, 1621, 2*w^3 - 3*w^2 - 21*w - 14],\ [1621, 1621, 4*w^3 - 9*w^2 - 33*w + 5],\ [1621, 1621, 7*w^3 - 18*w^2 - 45*w + 2],\ [1637, 1637, -5*w^3 + 14*w^2 + 34*w - 8],\ [1637, 1637, w^3 - 5*w^2 - 3*w + 19],\ [1637, 1637, 2*w^3 - 7*w^2 - 8*w + 20],\ [1637, 1637, w^3 - w^2 - 9*w + 1],\ [1693, 1693, -w^3 + 6*w^2 - w - 22],\ [1693, 1693, -9*w^3 + 24*w^2 + 61*w - 19],\ [1693, 1693, -8*w^3 + 23*w^2 + 47*w - 19],\ [1693, 1693, -8*w^3 + 22*w^2 + 51*w - 17],\ [1699, 1699, -8*w^3 + 20*w^2 + 55*w - 4],\ [1699, 1699, 11*w^3 - 28*w^2 - 76*w + 16],\ [1699, 1699, -2*w^3 + 7*w^2 + 6*w - 14],\ [1699, 1699, -6*w^3 + 18*w^2 + 31*w - 16],\ [1733, 1733, 3*w^3 - 10*w^2 - 18*w + 20],\ [1733, 1733, 8*w^3 - 22*w^2 - 53*w + 14],\ [1733, 1733, -3*w^3 + 11*w^2 + 13*w - 17],\ [1733, 1733, 8*w^3 - 23*w^2 - 48*w + 26],\ [1777, 1777, -3*w^2 + 9*w + 19],\ [1777, 1777, 9*w^3 - 24*w^2 - 57*w + 11],\ [1777, 1777, 3*w^3 - 6*w^2 - 21*w - 2],\ [1777, 1777, -w^3 + 5*w^2 - w - 14],\ [1811, 1811, 6*w^3 - 16*w^2 - 42*w + 17],\ [1811, 1811, -5*w^3 + 13*w^2 + 30*w - 2],\ [1811, 1811, -8*w^3 + 22*w^2 + 50*w - 11],\ [1811, 1811, -5*w^3 + 11*w^2 + 40*w + 7],\ [1849, 43, -4*w^3 + 12*w^2 + 24*w - 17],\ [1849, 43, -4*w^3 + 12*w^2 + 24*w - 11],\ [1871, 1871, 2*w^2 - 5*w - 8],\ [1871, 1871, 5*w^3 - 14*w^2 - 30*w + 14],\ [1871, 1871, w^2 - 8],\ [1871, 1871, -5*w^3 + 13*w^2 + 35*w - 5],\ [1873, 1873, -3*w^2 + 9*w + 16],\ [1873, 1873, -3*w^3 + 5*w^2 + 29*w + 8],\ [1873, 1873, 5*w^3 - 12*w^2 - 32*w - 1],\ [1873, 1873, -6*w^3 + 14*w^2 + 47*w + 1],\ [1889, 1889, -4*w^3 + 11*w^2 + 27*w - 2],\ [1889, 1889, 6*w^3 - 17*w^2 - 34*w + 14],\ [1889, 1889, 6*w^3 - 14*w^2 - 41*w - 8],\ [1889, 1889, 8*w^3 - 20*w^2 - 57*w + 8],\ [1933, 1933, 2*w^3 - 8*w^2 - 7*w + 20],\ [1933, 1933, -8*w^3 + 21*w^2 + 56*w - 25],\ [1933, 1933, 5*w^3 - 14*w^2 - 33*w + 23],\ [1933, 1933, 9*w^3 - 25*w^2 - 55*w + 8],\ [1949, 1949, 3*w^3 - 7*w^2 - 24*w - 7],\ [1949, 1949, -7*w^3 + 22*w^2 + 35*w - 23],\ [1949, 1949, -3*w^3 + 7*w^2 + 20*w + 8],\ [1949, 1949, -14*w^3 + 37*w^2 + 93*w - 28],\ [1951, 1951, -2*w^3 + 8*w^2 + 7*w - 19],\ [1951, 1951, -2*w^3 + 7*w^2 + 12*w - 11],\ [1951, 1951, -7*w^3 + 19*w^2 + 47*w - 16],\ [1951, 1951, -7*w^3 + 20*w^2 + 42*w - 17],\ [1973, 1973, -9*w^3 + 24*w^2 + 57*w - 17],\ [1973, 1973, 14*w^3 - 36*w^2 - 97*w + 23],\ [1973, 1973, -3*w^3 + 6*w^2 + 21*w + 8],\ [1973, 1973, -3*w^2 + 9*w + 13]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, -2, -4, -1, 6, -6, -6, 6, 0, 0, 6, -6, -10, -10, -10, -10, -10, -10, 8, 8, 6, 12, -12, -6, -4, -4, -4, -4, -22, 14, -22, 14, 6, 24, -6, -24, 0, 12, -12, 0, 14, -4, 14, -4, 0, 0, -6, 6, -18, 18, -12, 12, -6, 0, 0, 6, 24, 6, -6, -24, -28, -28, -28, -28, 8, 8, 8, 8, -4, 32, -4, 32, -30, 18, 30, -18, 30, -30, 12, -12, -42, -12, 42, 12, 20, -16, 20, -16, 8, -28, 8, -28, 12, -36, 36, -12, 12, -12, 42, -42, 8, 8, 8, 8, 32, 32, -4, -4, 14, -6, 6, 18, -18, 24, -12, 12, -24, 42, -42, 30, -30, 30, -24, -30, 24, 2, 2, 2, 2, 30, 6, -30, -6, -58, -22, 12, -12, -18, 18, 14, 14, -40, -40, -6, 6, 36, -36, -34, -34, -16, -16, 38, 2, 2, 38, 6, -36, 36, -6, -52, -52, -16, -16, -46, 26, -46, 26, -30, 30, -24, 24, -48, 30, 48, -30, 44, 8, 8, 44, -24, 36, 24, -36, 14, 14, 14, 14, -6, 6, 54, -54, -34, -34, 38, 38, 56, 20, 20, 56, -24, -48, 48, 24, 36, -36, 6, -6, 8, -64, 8, -64, 26, -46, -46, 26, -28, -28, -10, -10, -22, -40, -22, -40, -22, -22, -22, -22, -36, 36, 42, -42, -52, 56, 56, -52, 66, -66, 30, -30, -28, -28, -28, -28, 60, -60, 24, -24, 68, 68, 14, 14, 6, 48, -6, -48, 48, -18, -48, 18, -16, 56, 56, -16, -6, 78, -78, 6, 38, 38, 2, 2, -64, -64, -46, -46, -30, -12, 12, 30, -40, -4, -4, -40, 36, -36, 6, -6, 50, 86, 12, -60, 60, -12, 38, 74, 38, 74, -12, 30, -30, 12, 26, 62, 62, 26, -54, 54, 54, -54, -28, 8, -28, 8, 42, 54, -42, -54] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, w^3 - 2*w^2 - 8*w - 3])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]