/* 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([14, -4, -10, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([18,6,w - 2]) primes_array = [ [2, 2, -w - 2],\ [7, 7, -2/3*w^3 + 2/3*w^2 + 5*w - 7/3],\ [7, 7, -1/3*w^3 + 1/3*w^2 + w - 5/3],\ [9, 3, -1/3*w^3 + 1/3*w^2 + 3*w - 5/3],\ [9, 3, w + 1],\ [17, 17, w + 3],\ [17, 17, -1/3*w^3 + 1/3*w^2 + 3*w - 11/3],\ [31, 31, 1/3*w^3 - 1/3*w^2 - w - 1/3],\ [31, 31, -2/3*w^3 + 2/3*w^2 + 5*w - 1/3],\ [41, 41, -2/3*w^3 + 5/3*w^2 + 4*w - 19/3],\ [41, 41, w^2 - 5],\ [41, 41, 2*w + 3],\ [41, 41, 2/3*w^3 + 4/3*w^2 - 5*w - 29/3],\ [47, 47, -2/3*w^3 + 5/3*w^2 + 3*w - 19/3],\ [47, 47, 1/3*w^3 + 2/3*w^2 - 3*w - 13/3],\ [49, 7, -1/3*w^3 + 1/3*w^2 + 2*w - 11/3],\ [73, 73, -1/3*w^3 + 1/3*w^2 + 5*w + 19/3],\ [73, 73, -2/3*w^3 - 1/3*w^2 + 4*w + 11/3],\ [73, 73, -1/3*w^3 + 4/3*w^2 + 2*w - 17/3],\ [103, 103, -1/3*w^3 + 4/3*w^2 + w - 23/3],\ [103, 103, w^2 - w - 3],\ [113, 113, -2/3*w^3 + 2/3*w^2 + 5*w + 11/3],\ [113, 113, 1/3*w^3 - 1/3*w^2 - w - 13/3],\ [127, 127, 2/3*w^3 + 1/3*w^2 - 9*w - 41/3],\ [127, 127, -2/3*w^3 + 5/3*w^2 + 5*w - 31/3],\ [127, 127, -1/3*w^3 + 1/3*w^2 - 11/3],\ [127, 127, 4/3*w^3 + 5/3*w^2 - 10*w - 43/3],\ [151, 151, -1/3*w^3 + 4/3*w^2 + w - 29/3],\ [151, 151, 2/3*w^3 - 2/3*w^2 - 6*w - 5/3],\ [167, 167, -2/3*w^3 + 5/3*w^2 + 2*w - 19/3],\ [167, 167, 2/3*w^3 + 1/3*w^2 - 6*w - 11/3],\ [191, 191, -w^3 + 2*w^2 + 6*w - 5],\ [191, 191, 1/3*w^3 + 2/3*w^2 - 2*w - 19/3],\ [193, 193, -1/3*w^3 + 1/3*w^2 + 5*w + 13/3],\ [193, 193, 2/3*w^3 + 7/3*w^2 - 2*w - 23/3],\ [199, 199, 1/3*w^3 + 2/3*w^2 + 2*w + 11/3],\ [199, 199, 1/3*w^3 + 2/3*w^2 - 5*w - 31/3],\ [223, 223, -2/3*w^3 + 5/3*w^2 + 5*w - 13/3],\ [223, 223, 4/3*w^3 - 7/3*w^2 - 8*w + 17/3],\ [223, 223, 2/3*w^3 + 1/3*w^2 - 4*w - 17/3],\ [223, 223, w^3 - w^2 - 7*w - 1],\ [233, 233, -1/3*w^3 + 1/3*w^2 + w - 17/3],\ [233, 233, -2/3*w^3 + 2/3*w^2 + 5*w - 19/3],\ [239, 239, 5/3*w^3 + 7/3*w^2 - 10*w - 41/3],\ [239, 239, -5/3*w^3 - 7/3*w^2 + 12*w + 59/3],\ [241, 241, -1/3*w^3 + 7/3*w^2 + w - 23/3],\ [241, 241, 5/3*w^3 + 10/3*w^2 - 10*w - 59/3],\ [257, 257, -1/3*w^3 + 1/3*w^2 + 4*w - 5/3],\ [257, 257, 1/3*w^3 - 1/3*w^2 - 4*w - 1/3],\ [257, 257, 2/3*w^3 + 1/3*w^2 - 7*w - 23/3],\ [257, 257, -4/3*w^3 + 1/3*w^2 + 10*w + 13/3],\ [263, 263, -4/3*w^3 + 7/3*w^2 + 9*w - 23/3],\ [263, 263, 1/3*w^3 + 2/3*w^2 - w - 13/3],\ [271, 271, 5/3*w^3 - 5/3*w^2 - 12*w + 19/3],\ [271, 271, w^3 - w^2 - 4*w + 5],\ [281, 281, w^2 + 5*w + 5],\ [281, 281, -1/3*w^3 - 5/3*w^2 + 2*w + 25/3],\ [289, 17, w^3 - w^2 - 6*w + 3],\ [311, 311, 1/3*w^3 - 7/3*w^2 + 41/3],\ [311, 311, -2*w + 5],\ [311, 311, -w^3 - 2*w^2 + 7*w + 15],\ [311, 311, 2/3*w^3 - 2/3*w^2 - 6*w - 11/3],\ [313, 313, w^3 - w^2 - 5*w + 1],\ [313, 313, -4/3*w^3 + 4/3*w^2 + 9*w - 5/3],\ [337, 337, 4/3*w^3 - 4/3*w^2 - 11*w + 5/3],\ [337, 337, 2/3*w^3 + 1/3*w^2 - 6*w - 29/3],\ [359, 359, -w^3 - w^2 + 12*w + 19],\ [359, 359, -1/3*w^3 + 4/3*w^2 + 5*w + 1/3],\ [359, 359, -1/3*w^3 - 8/3*w^2 - 4*w + 1/3],\ [359, 359, w^2 - 3*w - 9],\ [361, 19, 2*w^2 - w - 13],\ [361, 19, -w^3 + 3*w^2 + 5*w - 9],\ [409, 409, -w - 5],\ [409, 409, -1/3*w^3 + 1/3*w^2 + 3*w - 17/3],\ [431, 431, -w^3 - 3*w^2 + 2*w + 9],\ [431, 431, 2/3*w^3 + 7/3*w^2 - w - 23/3],\ [433, 433, -1/3*w^3 + 1/3*w^2 + 6*w + 19/3],\ [433, 433, 2/3*w^3 + 7/3*w^2 - 3*w - 29/3],\ [439, 439, 2/3*w^3 + 4/3*w^2 - 8*w - 47/3],\ [439, 439, 4/3*w^3 - 10/3*w^2 - 8*w + 29/3],\ [439, 439, 2*w^2 - 13],\ [439, 439, 5*w + 9],\ [449, 449, w^2 - 11],\ [449, 449, 2/3*w^3 - 5/3*w^2 - 4*w + 1/3],\ [457, 457, -w^3 - w^2 + 10*w + 17],\ [457, 457, -4/3*w^3 + 4/3*w^2 + 7*w + 1/3],\ [457, 457, 4/3*w^3 + 5/3*w^2 - 5*w - 19/3],\ [457, 457, -w^3 + 2*w^2 + 7*w - 13],\ [463, 463, w^3 - 2*w^2 - 5*w + 9],\ [463, 463, 2/3*w^3 + 1/3*w^2 - 5*w - 5/3],\ [463, 463, 5/3*w^3 - 11/3*w^2 - 9*w + 43/3],\ [463, 463, 2/3*w^3 + 4/3*w^2 - 5*w - 23/3],\ [487, 487, -4/3*w^3 - 8/3*w^2 + 7*w + 37/3],\ [487, 487, w^3 + w^2 - 8*w - 9],\ [487, 487, -2/3*w^3 - 4/3*w^2 + 4*w + 17/3],\ [487, 487, 5/3*w^3 - 11/3*w^2 - 8*w + 37/3],\ [503, 503, 2/3*w^3 + 4/3*w^2 - 4*w - 29/3],\ [503, 503, 2/3*w^3 + 1/3*w^2 - 10*w - 47/3],\ [503, 503, 1/3*w^3 - 1/3*w^2 + w + 17/3],\ [503, 503, -4/3*w^3 - 8/3*w^2 + 5*w + 31/3],\ [521, 521, -1/3*w^3 + 4/3*w^2 + 9*w + 31/3],\ [521, 521, w^3 - 6*w - 3],\ [529, 23, -1/3*w^3 + 1/3*w^2 + 2*w - 17/3],\ [529, 23, 1/3*w^3 - 1/3*w^2 - 2*w - 13/3],\ [569, 569, -4/3*w^3 - 5/3*w^2 + 7*w + 25/3],\ [569, 569, -1/3*w^3 - 5/3*w^2 - 2*w - 5/3],\ [577, 577, -1/3*w^3 + 7/3*w^2 + 3*w - 23/3],\ [577, 577, -4/3*w^3 + 10/3*w^2 + 9*w - 47/3],\ [599, 599, -4/3*w^3 - 8/3*w^2 + 6*w + 37/3],\ [599, 599, 2/3*w^3 + 4/3*w^2 - 3*w - 23/3],\ [601, 601, -2/3*w^3 + 8/3*w^2 + 4*w - 43/3],\ [601, 601, -2/3*w^3 + 8/3*w^2 + 4*w - 25/3],\ [617, 617, -1/3*w^3 + 7/3*w^2 + 2*w - 23/3],\ [617, 617, w^3 - 3*w^2 - 6*w + 15],\ [625, 5, -5],\ [631, 631, -2*w^3 + 2*w^2 + 14*w - 1],\ [631, 631, -w^3 + 10*w - 1],\ [641, 641, -w^2 - 1],\ [641, 641, -2/3*w^3 + 5/3*w^2 + 4*w - 37/3],\ [641, 641, 2/3*w^3 - 8/3*w^2 - 5*w + 37/3],\ [641, 641, w^3 - 3*w^2 - 7*w + 11],\ [647, 647, -1/3*w^3 - 2/3*w^2 - 3*w - 17/3],\ [647, 647, 1/3*w^3 + 2/3*w^2 - 6*w - 37/3],\ [673, 673, 2/3*w^3 - 2/3*w^2 - 7*w - 5/3],\ [673, 673, 2/3*w^3 - 5/3*w^2 - 3*w + 1/3],\ [673, 673, -1/3*w^3 + 1/3*w^2 + 5*w - 11/3],\ [673, 673, 1/3*w^3 + 2/3*w^2 - 3*w - 31/3],\ [719, 719, -w^3 - 2*w^2 + 4*w + 9],\ [719, 719, -w^3 - 2*w^2 + 5*w + 11],\ [727, 727, -w^3 + 3*w^2 + 4*w - 13],\ [727, 727, -1/3*w^3 + 4/3*w^2 + 4*w - 23/3],\ [727, 727, 1/3*w^3 + 5/3*w^2 - 4*w - 25/3],\ [727, 727, -2/3*w^3 - 1/3*w^2 + 4*w + 23/3],\ [743, 743, 1/3*w^3 + 2/3*w^2 + 3*w + 23/3],\ [743, 743, -1/3*w^3 + 7/3*w^2 + 2*w - 53/3],\ [751, 751, -2/3*w^3 + 5/3*w^2 + 2*w - 25/3],\ [751, 751, -2/3*w^3 - 1/3*w^2 + 6*w + 5/3],\ [761, 761, -1/3*w^3 + 7/3*w^2 + w - 29/3],\ [761, 761, -2/3*w^3 + 8/3*w^2 + 3*w - 37/3],\ [769, 769, -4/3*w^3 + 13/3*w^2 + 6*w - 59/3],\ [769, 769, -7/3*w^3 + 7/3*w^2 + 16*w - 5/3],\ [823, 823, -4/3*w^3 + 1/3*w^2 + 11*w + 25/3],\ [823, 823, w^3 - 2*w^2 - 3*w + 1],\ [857, 857, w^2 - 3*w - 5],\ [857, 857, -2/3*w^3 - 1/3*w^2 + 8*w - 1/3],\ [857, 857, 1/3*w^3 + 2/3*w^2 - 5*w - 13/3],\ [857, 857, w^2 - 4*w - 9],\ [863, 863, -4/3*w^3 + 7/3*w^2 + 8*w - 5/3],\ [863, 863, 2/3*w^3 + 1/3*w^2 - 4*w - 29/3],\ [881, 881, -5/3*w^3 - 4/3*w^2 + 11*w + 41/3],\ [881, 881, -4/3*w^3 - 5/3*w^2 + 6*w + 19/3],\ [887, 887, -4/3*w^3 + 4/3*w^2 + 10*w + 1/3],\ [887, 887, 2/3*w^3 - 2/3*w^2 - 2*w - 5/3],\ [911, 911, w^3 - 9*w - 1],\ [911, 911, 5/3*w^3 + 10/3*w^2 - 12*w - 65/3],\ [911, 911, 1/3*w^3 - 1/3*w^2 + w + 23/3],\ [911, 911, -2/3*w^3 + 5/3*w^2 + w - 25/3],\ [919, 919, -2/3*w^3 + 8/3*w^2 - 37/3],\ [919, 919, 2/3*w^3 + 4/3*w^2 - 8*w - 23/3],\ [929, 929, -2*w^3 - 3*w^2 + 11*w + 17],\ [929, 929, 1/3*w^3 - 1/3*w^2 - 4*w - 19/3],\ [937, 937, 4/3*w^3 - 1/3*w^2 - 9*w - 13/3],\ [937, 937, 3*w - 1],\ [937, 937, -w^3 + w^2 + 7*w - 9],\ [937, 937, w^3 - w^2 - 9*w + 1],\ [961, 31, 4/3*w^3 - 4/3*w^2 - 8*w + 11/3],\ [967, 967, w^2 - 3*w - 11],\ [967, 967, 1/3*w^3 + 2/3*w^2 - w - 19/3],\ [967, 967, 1/3*w^3 + 5/3*w^2 + 6*w + 23/3],\ [967, 967, 4/3*w^3 - 7/3*w^2 - 9*w + 17/3],\ [977, 977, w^3 - 4*w^2 - 5*w + 23],\ [977, 977, 2/3*w^3 - 11/3*w^2 - 3*w + 31/3],\ [983, 983, 4/3*w^3 - 4/3*w^2 - 6*w + 23/3],\ [983, 983, -2*w^3 + 2*w^2 + 14*w - 9],\ [991, 991, 2/3*w^3 + 1/3*w^2 - 5*w + 1/3],\ [991, 991, -w^3 + 2*w^2 + 5*w - 11],\ [1009, 1009, -1/3*w^3 + 1/3*w^2 + 9*w + 37/3],\ [1009, 1009, 2/3*w^3 + 7/3*w^2 - 6*w - 47/3],\ [1031, 1031, -4/3*w^3 + 10/3*w^2 + 7*w - 47/3],\ [1031, 1031, w^3 - w^2 - 9*w - 3],\ [1031, 1031, 1/3*w^3 - 7/3*w^2 + 53/3],\ [1031, 1031, 1/3*w^3 + 5/3*w^2 - 3*w - 19/3],\ [1033, 1033, -4/3*w^3 - 5/3*w^2 + 5*w + 13/3],\ [1033, 1033, 2*w^3 + 2*w^2 - 14*w - 19],\ [1039, 1039, -4/3*w^3 + 10/3*w^2 + 10*w - 53/3],\ [1039, 1039, -2/3*w^3 + 8/3*w^2 + 6*w - 19/3],\ [1063, 1063, -1/3*w^3 - 8/3*w^2 + 4*w + 37/3],\ [1063, 1063, -2/3*w^3 + 5/3*w^2 + 2*w - 43/3],\ [1063, 1063, -5/3*w^3 + 14/3*w^2 + 8*w - 61/3],\ [1063, 1063, 2/3*w^3 + 4/3*w^2 - 5*w - 41/3],\ [1097, 1097, -4/3*w^3 + 7/3*w^2 + 8*w - 47/3],\ [1097, 1097, 5/3*w^3 - 8/3*w^2 - 8*w + 19/3],\ [1097, 1097, -2/3*w^3 + 8/3*w^2 + 4*w - 31/3],\ [1097, 1097, -2/3*w^3 + 8/3*w^2 + 4*w - 37/3],\ [1129, 1129, 2/3*w^3 + 10/3*w^2 - w - 29/3],\ [1129, 1129, -2/3*w^3 + 2/3*w^2 + 10*w + 29/3],\ [1151, 1151, -w^3 + w^2 + 15*w + 17],\ [1151, 1151, -2/3*w^3 + 5/3*w^2 + 6*w - 1/3],\ [1153, 1153, w^3 - w^2 - 9*w + 3],\ [1153, 1153, -3*w - 1],\ [1201, 1201, 1/3*w^3 + 8/3*w^2 - 4*w - 43/3],\ [1201, 1201, -5/3*w^3 - 13/3*w^2 + 7*w + 53/3],\ [1231, 1231, 2/3*w^3 + 1/3*w^2 - 3*w - 17/3],\ [1231, 1231, -5/3*w^3 + 8/3*w^2 + 11*w - 19/3],\ [1279, 1279, 4/3*w^3 - 1/3*w^2 - 10*w - 1/3],\ [1279, 1279, -4/3*w^3 + 7/3*w^2 + 6*w - 29/3],\ [1279, 1279, 2/3*w^3 + 1/3*w^2 - 7*w + 1/3],\ [1279, 1279, -1/3*w^3 + 4/3*w^2 - w - 29/3],\ [1297, 1297, -2*w^3 - 3*w^2 + 9*w + 11],\ [1297, 1297, w^3 + 3*w^2 - 1],\ [1303, 1303, 8/3*w^3 - 11/3*w^2 - 17*w + 19/3],\ [1303, 1303, 4/3*w^3 + 2/3*w^2 - 13*w - 19/3],\ [1319, 1319, 5/3*w^3 - 8/3*w^2 - 9*w + 37/3],\ [1319, 1319, 4/3*w^3 - 1/3*w^2 - 9*w + 5/3],\ [1321, 1321, -1/3*w^3 + 1/3*w^2 + 5*w - 5/3],\ [1321, 1321, 2/3*w^3 - 2/3*w^2 - 7*w + 1/3],\ [1327, 1327, 2/3*w^3 + 1/3*w^2 - 11*w - 53/3],\ [1327, 1327, -1/3*w^3 + 1/3*w^2 - 2*w - 23/3],\ [1361, 1361, 2/3*w^3 + 1/3*w^2 - 8*w - 41/3],\ [1361, 1361, -5/3*w^3 - 7/3*w^2 + 7*w + 29/3],\ [1367, 1367, -1/3*w^3 + 7/3*w^2 + 3*w - 41/3],\ [1367, 1367, 4/3*w^3 - 10/3*w^2 - 9*w + 29/3],\ [1369, 37, -4/3*w^3 + 10/3*w^2 + 9*w - 65/3],\ [1369, 37, 1/3*w^3 - 7/3*w^2 - 3*w + 5/3],\ [1409, 1409, -2/3*w^3 - 13/3*w^2 - w + 29/3],\ [1409, 1409, -4/3*w^3 - 2/3*w^2 + 5*w + 1/3],\ [1423, 1423, 2/3*w^3 + 1/3*w^2 + 19/3],\ [1423, 1423, 7/3*w^3 - 16/3*w^2 - 12*w + 59/3],\ [1423, 1423, -4/3*w^3 - 2/3*w^2 + 9*w + 37/3],\ [1423, 1423, 7/3*w^3 - 13/3*w^2 - 13*w + 29/3],\ [1433, 1433, 1/3*w^3 - 1/3*w^2 - w - 19/3],\ [1433, 1433, -2*w^3 - 2*w^2 + 13*w + 15],\ [1433, 1433, 2/3*w^3 - 2/3*w^2 - 5*w - 17/3],\ [1433, 1433, -2/3*w^3 + 11/3*w^2 + 2*w - 61/3],\ [1439, 1439, 2/3*w^3 + 4/3*w^2 - 6*w - 23/3],\ [1439, 1439, -4/3*w^3 + 10/3*w^2 + 6*w - 41/3],\ [1447, 1447, -5/3*w^3 + 11/3*w^2 + 7*w - 37/3],\ [1447, 1447, 2/3*w^3 - 5/3*w^2 - 8*w + 31/3],\ [1471, 1471, 5/3*w^3 - 2/3*w^2 - 14*w + 1/3],\ [1471, 1471, -w^3 + 2*w^2 + 2*w - 9],\ [1481, 1481, -1/3*w^3 - 5/3*w^2 + 7*w + 43/3],\ [1481, 1481, -8/3*w^3 + 17/3*w^2 + 17*w - 73/3],\ [1489, 1489, 4*w + 5],\ [1489, 1489, 4/3*w^3 - 4/3*w^2 - 12*w + 23/3],\ [1511, 1511, w^3 - 4*w^2 - 3*w + 9],\ [1511, 1511, 3*w^2 - 3*w - 23],\ [1543, 1543, 2/3*w^3 + 1/3*w^2 - 6*w + 1/3],\ [1543, 1543, -2/3*w^3 + 5/3*w^2 + 2*w - 31/3],\ [1553, 1553, -7/3*w^3 + 10/3*w^2 + 13*w - 41/3],\ [1553, 1553, 2*w^3 - w^2 - 13*w + 3],\ [1559, 1559, 2*w^2 - 15],\ [1559, 1559, -4/3*w^3 + 10/3*w^2 + 8*w - 23/3],\ [1567, 1567, -1/3*w^3 - 2/3*w^2 - 4*w - 23/3],\ [1567, 1567, -1/3*w^3 - 2/3*w^2 + 7*w + 43/3],\ [1601, 1601, -2/3*w^3 + 2/3*w^2 + 5*w - 25/3],\ [1601, 1601, -1/3*w^3 + 1/3*w^2 + w - 23/3],\ [1607, 1607, -7/3*w^3 + 10/3*w^2 + 18*w - 29/3],\ [1607, 1607, -2*w^3 + 4*w^2 + 12*w - 19],\ [1607, 1607, -2/3*w^3 - 4/3*w^2 + 4*w + 11/3],\ [1607, 1607, -4/3*w^3 - 5/3*w^2 + 11*w + 43/3],\ [1657, 1657, -4/3*w^3 + 1/3*w^2 + 6*w - 5/3],\ [1657, 1657, 8/3*w^3 - 11/3*w^2 - 18*w + 43/3],\ [1697, 1697, 2/3*w^3 - 2/3*w^2 - 8*w - 11/3],\ [1697, 1697, -2/3*w^3 - 1/3*w^2 + 10*w + 41/3],\ [1697, 1697, -w^3 - 3*w^2 + 7*w + 17],\ [1697, 1697, -2/3*w^3 - 1/3*w^2 + 13*w + 59/3],\ [1721, 1721, -2/3*w^3 - 7/3*w^2 - 4*w - 19/3],\ [1721, 1721, -5/3*w^3 - 7/3*w^2 + 5*w + 11/3],\ [1753, 1753, -7/3*w^3 - 14/3*w^2 + 15*w + 85/3],\ [1753, 1753, -5/3*w^3 - 13/3*w^2 + 11*w + 71/3],\ [1753, 1753, 1/3*w^3 + 2/3*w^2 - 6*w - 25/3],\ [1753, 1753, 1/3*w^3 + 8/3*w^2 - 2*w - 43/3],\ [1759, 1759, -1/3*w^3 + 4/3*w^2 + 4*w - 29/3],\ [1759, 1759, -w^3 + 2*w^2 + 8*w - 3],\ [1777, 1777, -2/3*w^3 + 11/3*w^2 + 4*w - 31/3],\ [1777, 1777, -5/3*w^3 + 14/3*w^2 + 12*w - 67/3],\ [1777, 1777, -4/3*w^3 + 13/3*w^2 + 8*w - 71/3],\ [1777, 1777, w^3 - 4*w^2 - 8*w + 13],\ [1783, 1783, -5/3*w^3 + 2/3*w^2 + 13*w + 29/3],\ [1783, 1783, 4/3*w^3 - 7/3*w^2 - 5*w - 1/3],\ [1831, 1831, -1/3*w^3 - 5/3*w^2 + 25/3],\ [1831, 1831, 4/3*w^3 + 2/3*w^2 - 7*w - 25/3],\ [1831, 1831, -7/3*w^3 + 13/3*w^2 + 16*w - 47/3],\ [1831, 1831, 3*w^3 - 5*w^2 - 19*w + 15],\ [1847, 1847, -4/3*w^3 - 2/3*w^2 + 8*w + 31/3],\ [1847, 1847, -8/3*w^3 - 10/3*w^2 + 19*w + 89/3],\ [1889, 1889, -2/3*w^3 - 1/3*w^2 + 10*w + 53/3],\ [1889, 1889, 2/3*w^3 + 7/3*w^2 + 3*w + 13/3],\ [1889, 1889, 3*w^3 - 2*w^2 - 24*w + 1],\ [1889, 1889, -5/3*w^3 - 7/3*w^2 + 5*w + 17/3],\ [1913, 1913, 5/3*w^3 - 5/3*w^2 - 9*w + 1/3],\ [1913, 1913, -4/3*w^3 + 7/3*w^2 + 9*w - 47/3],\ [1951, 1951, -7/3*w^3 - 8/3*w^2 + 17*w + 67/3],\ [1951, 1951, 4/3*w^3 - 10/3*w^2 - 10*w + 59/3],\ [1993, 1993, -8/3*w^3 + 8/3*w^2 + 19*w - 19/3],\ [1993, 1993, 5/3*w^3 - 5/3*w^2 - 7*w + 13/3],\ [1999, 1999, 2/3*w^3 + 1/3*w^2 - 3*w - 41/3],\ [1999, 1999, -5/3*w^3 + 8/3*w^2 + 11*w + 5/3]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^8 - 4*x^7 - 27*x^6 + 117*x^5 + 133*x^4 - 843*x^3 + 673*x^2 - 6*x - 76 K. = NumberField(heckePol) hecke_eigenvalues_array = [1, e, -4052/86739*e^7 + 27575/173478*e^6 + 231031/173478*e^5 - 13981/2991*e^4 - 491295/57826*e^3 + 996537/28913*e^2 - 2279659/173478*e - 539263/86739, -5042/86739*e^7 + 30245/173478*e^6 + 294199/173478*e^5 - 15178/2991*e^4 - 690377/57826*e^3 + 1065552/28913*e^2 - 755797/173478*e - 661813/86739, 1, -683/173478*e^7 + 3308/86739*e^6 + 21965/173478*e^5 - 6835/5982*e^4 - 51121/57826*e^3 + 508031/57826*e^2 - 267875/173478*e - 484292/86739, -430/28913*e^7 + 1456/28913*e^6 + 11966/28913*e^5 - 1245/997*e^4 - 78012/28913*e^3 + 213466/28913*e^2 - 60700/28913*e - 60238/28913, -9151/173478*e^7 + 17779/86739*e^6 + 268639/173478*e^5 - 34367/5982*e^4 - 623465/57826*e^3 + 2288167/57826*e^2 - 1305901/173478*e - 326764/86739, 2363/86739*e^7 - 6253/86739*e^6 - 80819/86739*e^5 + 6691/2991*e^4 + 242819/28913*e^3 - 501610/28913*e^2 - 725455/86739*e + 635086/86739, -2365/57826*e^7 + 4004/28913*e^6 + 65813/57826*e^5 - 8343/1994*e^4 - 342327/57826*e^3 + 1810149/57826*e^2 - 1519283/57826*e - 35546/28913, 6859/86739*e^7 - 19325/86739*e^6 - 204454/86739*e^5 + 19523/2991*e^4 + 495347/28913*e^3 - 1395048/28913*e^2 + 387286/86739*e + 1132058/86739, -7823/86739*e^7 + 26758/86739*e^6 + 228725/86739*e^5 - 27160/2991*e^4 - 504425/28913*e^3 + 1904707/28913*e^2 - 2161322/86739*e - 375238/86739, -18271/173478*e^7 + 29185/86739*e^6 + 538567/173478*e^5 - 60077/5982*e^4 - 1218025/57826*e^3 + 4343307/57826*e^2 - 4190917/173478*e - 1366987/86739, -35093/173478*e^7 + 51479/86739*e^6 + 1019867/173478*e^5 - 104725/5982*e^4 - 2297455/57826*e^3 + 7451423/57826*e^2 - 6170189/173478*e - 1599479/86739, 2098/86739*e^7 - 10039/173478*e^6 - 119321/173478*e^5 + 5147/2991*e^4 + 274057/57826*e^3 - 388950/28913*e^2 - 91507/173478*e + 739838/86739, -7445/173478*e^7 + 42019/173478*e^6 + 101236/86739*e^5 - 40951/5982*e^4 - 170652/28913*e^3 + 2764145/57826*e^2 - 2504338/86739*e - 747740/86739, 1257/28913*e^7 - 8647/57826*e^6 - 75473/57826*e^5 + 4393/997*e^4 + 517555/57826*e^3 - 965996/28913*e^2 + 680995/57826*e + 436846/28913, 6734/86739*e^7 - 50579/173478*e^6 - 405313/173478*e^5 + 24946/2991*e^4 + 974903/57826*e^3 - 1698682/28913*e^2 + 1939507/173478*e + 587389/86739, -3475/173478*e^7 - 1009/173478*e^6 + 46670/86739*e^5 + 13/5982*e^4 - 90954/28913*e^3 + 99875/57826*e^2 - 469178/86739*e + 487154/86739, 9173/57826*e^7 - 12975/28913*e^6 - 277051/57826*e^5 + 26617/1994*e^4 + 2017741/57826*e^3 - 5741495/57826*e^2 + 785883/57826*e + 694357/28913, 5465/173478*e^7 - 39349/173478*e^6 - 69652/86739*e^5 + 38557/5982*e^4 + 71111/28913*e^3 - 2626115/57826*e^2 + 3353008/86739*e + 451712/86739, -4845/28913*e^7 + 15733/28913*e^6 + 136171/28913*e^5 - 15964/997*e^4 - 831928/28913*e^3 + 3380189/28913*e^2 - 1539893/28913*e - 413132/28913, 8522/86739*e^7 - 65915/173478*e^6 - 463675/173478*e^5 + 33253/2991*e^4 + 815425/57826*e^3 - 2301706/28913*e^2 + 9230119/173478*e + 156865/86739, 2727/57826*e^7 - 3810/28913*e^6 - 67549/57826*e^5 + 8255/1994*e^4 + 248779/57826*e^3 - 1877971/57826*e^2 + 2051819/57826*e + 25534/28913, -6685/173478*e^7 + 20059/86739*e^6 + 208891/173478*e^5 - 37313/5982*e^4 - 474873/57826*e^3 + 2313391/57826*e^2 - 3814129/173478*e + 401498/86739, 5798/86739*e^7 - 27970/86739*e^6 - 156236/86739*e^5 + 26479/2991*e^4 + 281105/28913*e^3 - 1688629/28913*e^2 + 2966765/86739*e - 451064/86739, 14447/173478*e^7 - 27805/173478*e^6 - 201889/86739*e^5 + 28045/5982*e^4 + 443023/28913*e^3 - 1966955/57826*e^2 + 646510/86739*e + 132368/86739, -37781/173478*e^7 + 119725/173478*e^6 + 530995/86739*e^5 - 123637/5982*e^4 - 1091021/28913*e^3 + 8979321/57826*e^2 - 5890099/86739*e - 1905158/86739, 9835/173478*e^7 - 28595/173478*e^6 - 127094/86739*e^5 + 31061/5982*e^4 + 175007/28913*e^3 - 2341107/57826*e^2 + 3675569/86739*e - 9398/86739, -50669/173478*e^7 + 152875/173478*e^6 + 755503/86739*e^5 - 157057/5982*e^4 - 1809385/28913*e^3 + 11312907/57826*e^2 - 2321599/86739*e - 3806798/86739, 19235/173478*e^7 - 65803/173478*e^6 - 281419/86739*e^5 + 64723/5982*e^4 + 656921/28913*e^3 - 4419271/57826*e^2 + 857371/86739*e + 1595750/86739, 19091/86739*e^7 - 139103/173478*e^6 - 1118065/173478*e^5 + 68410/2991*e^4 + 2570865/57826*e^3 - 4666821/28913*e^2 + 6239113/173478*e + 2944999/86739, -16023/57826*e^7 + 25917/28913*e^6 + 462293/57826*e^5 - 51667/1994*e^4 - 3043979/57826*e^3 + 10735635/57826*e^2 - 3880307/57826*e - 635571/28913, 8915/57826*e^7 - 30859/57826*e^6 - 137827/28913*e^5 + 30855/1994*e^4 + 1034619/28913*e^3 - 6399849/57826*e^2 + 360275/28913*e + 525938/28913, -6124/86739*e^7 + 24905/86739*e^6 + 167863/86739*e^5 - 25568/2991*e^4 - 292213/28913*e^3 + 1797218/28913*e^2 - 3716782/86739*e + 33964/86739, 159/997*e^7 - 441/997*e^6 - 4420/997*e^5 + 13107/997*e^4 + 27214/997*e^3 - 98103/997*e^2 + 40530/997*e + 18504/997, -18616/86739*e^7 + 57521/86739*e^6 + 552202/86739*e^5 - 57911/2991*e^4 - 1307473/28913*e^3 + 4074285/28913*e^2 - 2123590/86739*e - 1985516/86739, 7391/86739*e^7 - 76007/173478*e^6 - 434617/173478*e^5 + 38221/2991*e^4 + 954045/57826*e^3 - 2676270/28913*e^2 + 4771543/173478*e + 2498122/86739, -2647/86739*e^7 + 19405/173478*e^6 + 207971/173478*e^5 - 9971/2991*e^4 - 738247/57826*e^3 + 699267/28913*e^2 + 4108051/173478*e + 28051/86739, 20506/86739*e^7 - 67955/86739*e^6 - 596728/86739*e^5 + 69713/2991*e^4 + 1284601/28913*e^3 - 4981435/28913*e^2 + 6448966/86739*e + 1241690/86739, 12415/173478*e^7 - 37331/173478*e^6 - 162992/86739*e^5 + 38531/5982*e^4 + 281932/28913*e^3 - 2768039/57826*e^2 + 2383106/86739*e + 691750/86739, 19495/173478*e^7 - 45781/86739*e^6 - 549229/173478*e^5 + 90053/5982*e^4 + 1033039/57826*e^3 - 6142387/57826*e^2 + 11484367/173478*e + 1135216/86739, 19804/86739*e^7 - 59123/86739*e^6 - 572755/86739*e^5 + 58151/2991*e^4 + 1299705/28913*e^3 - 4012538/28913*e^2 + 2666488/86739*e + 2653010/86739, -4415/28913*e^7 + 14277/28913*e^6 + 124205/28913*e^5 - 14719/997*e^4 - 753916/28913*e^3 + 3166723/28913*e^2 - 1479193/28913*e - 410720/28913, 25040/86739*e^7 - 85459/86739*e^6 - 724379/86739*e^5 + 86017/2991*e^4 + 1578157/28913*e^3 - 5987041/28913*e^2 + 6784403/86739*e + 2183194/86739, 53683/173478*e^7 - 166577/173478*e^6 - 782378/86739*e^5 + 172067/5982*e^4 + 1771689/28913*e^3 - 12515699/57826*e^2 + 4894439/86739*e + 4234288/86739, 3685/28913*e^7 - 9788/28913*e^6 - 107925/28913*e^5 + 9939/997*e^4 + 711578/28913*e^3 - 2086209/28913*e^2 + 965983/28913*e - 112464/28913, 6181/86739*e^7 - 31553/86739*e^6 - 173887/86739*e^5 + 30776/2991*e^4 + 324842/28913*e^3 - 2081122/28913*e^2 + 3765172/86739*e + 979790/86739, 8369/86739*e^7 - 57617/173478*e^6 - 504379/173478*e^5 + 29506/2991*e^4 + 1194171/57826*e^3 - 2134647/28913*e^2 + 2679481/173478*e + 2101381/86739, 914/86739*e^7 + 7529/86739*e^6 - 23552/86739*e^5 - 5747/2991*e^4 + 46398/28913*e^3 + 213147/28913*e^2 - 161452/86739*e + 274354/86739, -2707/57826*e^7 + 18983/57826*e^6 + 36522/28913*e^5 - 19651/1994*e^4 - 103412/28913*e^3 + 4202599/57826*e^2 - 2075788/28913*e + 103622/28913, -12649/28913*e^7 + 40275/28913*e^6 + 362888/28913*e^5 - 40391/997*e^4 - 2370400/28913*e^3 + 8463450/28913*e^2 - 2962260/28913*e - 797408/28913, 27514/86739*e^7 - 204751/173478*e^6 - 1592771/173478*e^5 + 103637/2991*e^4 + 3377947/57826*e^3 - 7294125/28913*e^2 + 19368743/173478*e + 2742653/86739, 9056/86739*e^7 - 24478/86739*e^6 - 258599/86739*e^5 + 25687/2991*e^4 + 549808/28913*e^3 - 1892095/28913*e^2 + 2381771/86739*e + 1970890/86739, 269/86739*e^7 + 9713/86739*e^6 - 5603/86739*e^5 - 9110/2991*e^4 + 7392/28913*e^3 + 580097/28913*e^2 + 94454/86739*e - 1117088/86739, 6647/28913*e^7 - 42459/57826*e^6 - 380837/57826*e^5 + 21877/997*e^4 + 2458505/57826*e^3 - 4695411/28913*e^2 + 3313527/57826*e + 429426/28913, -2310/28913*e^7 + 3115/28913*e^6 + 73696/28913*e^5 - 3790/997*e^4 - 638961/28913*e^3 + 974626/28913*e^2 + 939362/28913*e - 228124/28913, 13385/173478*e^7 - 50029/173478*e^6 - 195988/86739*e^5 + 48133/5982*e^4 + 440362/28913*e^3 - 3178235/57826*e^2 + 1779847/86739*e - 272434/86739, 6589/173478*e^7 - 42617/173478*e^6 - 74264/86739*e^5 + 41765/5982*e^4 - 12975/28913*e^3 - 2748279/57826*e^2 + 6018374/86739*e - 743882/86739, -9931/173478*e^7 + 13048/86739*e^6 + 314551/173478*e^5 - 26609/5982*e^4 - 850837/57826*e^3 + 1906219/57826*e^2 + 1218437/173478*e + 360926/86739, -81115/173478*e^7 + 298193/173478*e^6 + 1177379/86739*e^5 - 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111077/5982*e^4 - 1531415/57826*e^3 + 6794711/57826*e^2 - 9909673/173478*e + 233057/86739, -2512/28913*e^7 + 6892/28913*e^6 + 61566/28913*e^5 - 8131/997*e^4 - 209773/28913*e^3 + 1973629/28913*e^2 - 2050382/28913*e + 759702/28913, -49235/173478*e^7 + 195625/173478*e^6 + 757336/86739*e^5 - 198883/5982*e^4 - 1777859/28913*e^3 + 13891335/57826*e^2 - 6944635/86739*e + 179956/86739, -62363/173478*e^7 + 265897/173478*e^6 + 862135/86739*e^5 - 263047/5982*e^4 - 1568178/28913*e^3 + 17913349/57826*e^2 - 17753422/86739*e - 1189820/86739, 38506/86739*e^7 - 239653/173478*e^6 - 2318309/173478*e^5 + 120299/2991*e^4 + 5681583/57826*e^3 - 8559807/28913*e^2 + 3792923/173478*e + 8981741/86739, -751/28913*e^7 - 11993/57826*e^6 + 35477/57826*e^5 + 4793/997*e^4 - 216151/57826*e^3 - 643303/28913*e^2 + 1246399/57826*e - 268195/28913, 72173/173478*e^7 - 287011/173478*e^6 - 1097473/86739*e^5 + 284425/5982*e^4 + 2706644/28913*e^3 - 19661749/57826*e^2 + 3076885/86739*e + 7466576/86739, 24271/57826*e^7 - 90117/57826*e^6 - 355793/28913*e^5 + 88903/1994*e^4 + 2467796/28913*e^3 - 18343073/57826*e^2 + 1719805/28913*e + 1804062/28913, -30356/86739*e^7 + 219425/173478*e^6 + 1736959/173478*e^5 - 110173/2991*e^4 - 3854011/57826*e^3 + 7868992/28913*e^2 - 11396353/173478*e - 8529226/86739, -33607/173478*e^7 + 71165/173478*e^6 + 461084/86739*e^5 - 69701/5982*e^4 - 896630/28913*e^3 + 4608105/57826*e^2 - 5083127/86739*e + 3700340/86739, -2246/86739*e^7 - 19351/173478*e^6 + 95821/173478*e^5 + 9194/2991*e^4 - 76253/57826*e^3 - 551357/28913*e^2 - 2116735/173478*e + 1500560/86739, 78359/173478*e^7 - 250669/173478*e^6 - 1136746/86739*e^5 + 255523/5982*e^4 + 2520243/28913*e^3 - 18224157/57826*e^2 + 8820718/86739*e + 3593984/86739, -17981/86739*e^7 + 99311/173478*e^6 + 1120837/173478*e^5 - 48850/2991*e^4 - 2840049/57826*e^3 + 3233158/28913*e^2 - 2427931/173478*e + 1936766/86739, -23833/173478*e^7 + 81641/173478*e^6 + 350909/86739*e^5 - 78059/5982*e^4 - 797162/28913*e^3 + 5096401/57826*e^2 - 2404319/86739*e - 559978/86739, -51947/86739*e^7 + 380165/173478*e^6 + 3013663/173478*e^5 - 192754/2991*e^4 - 6364827/57826*e^3 + 13517905/28913*e^2 - 39527785/173478*e - 2764591/86739, -6569/28913*e^7 + 25067/28913*e^6 + 182936/28913*e^5 - 24248/997*e^4 - 1094541/28913*e^3 + 4873604/28913*e^2 - 2311088/28913*e - 1376528/28913, -44456/86739*e^7 + 331049/173478*e^6 + 2489431/173478*e^5 - 169639/2991*e^4 - 4779411/57826*e^3 + 12171671/28913*e^2 - 40805791/173478*e - 4670770/86739, -65479/57826*e^7 + 97813/28913*e^6 + 1909017/57826*e^5 - 200795/1994*e^4 - 12765227/57826*e^3 + 43168215/57826*e^2 - 14588069/57826*e - 2993048/28913, 62683/173478*e^7 - 85414/86739*e^6 - 1780915/173478*e^5 + 176423/5982*e^4 + 3735985/57826*e^3 - 12743583/57826*e^2 + 16858753/173478*e + 1376971/86739, -53253/57826*e^7 + 165121/57826*e^6 + 776395/28913*e^5 - 167831/1994*e^4 - 5160409/28913*e^3 + 35483199/57826*e^2 - 6512130/28913*e - 1226130/28913, -39943/173478*e^7 + 79709/173478*e^6 + 544805/86739*e^5 - 86933/5982*e^4 - 1145770/28913*e^3 + 6900233/57826*e^2 - 2280644/86739*e - 2416594/86739, -104959/173478*e^7 + 158602/86739*e^6 + 3089695/173478*e^5 - 317051/5982*e^4 - 7535995/57826*e^3 + 22319695/57826*e^2 + 1440197/173478*e - 9208453/86739, -49310/86739*e^7 + 349397/173478*e^6 + 2858023/173478*e^5 - 177085/2991*e^4 - 6103173/57826*e^3 + 12575765/28913*e^2 - 32110441/173478*e - 5813098/86739, 13621/86739*e^7 - 54728/86739*e^6 - 384961/86739*e^5 + 53639/2991*e^4 + 785530/28913*e^3 - 3593336/28913*e^2 + 5648521/86739*e - 1637128/86739, -67777/57826*e^7 + 108562/28913*e^6 + 2014923/57826*e^5 - 220595/1994*e^4 - 14130753/57826*e^3 + 47110485/57826*e^2 - 10993741/57826*e - 4828005/28913, 3044/2991*e^7 - 10117/2991*e^6 - 88877/2991*e^5 + 292502/2991*e^4 + 201316/997*e^3 - 701489/997*e^2 + 588779/2991*e + 387022/2991, -151369/173478*e^7 + 267433/86739*e^6 + 4433635/173478*e^5 - 534407/5982*e^4 - 10135515/57826*e^3 + 37122863/57826*e^2 - 26436859/173478*e - 10359313/86739, 62371/57826*e^7 - 215091/57826*e^6 - 918862/28913*e^5 + 215817/1994*e^4 + 6332053/28913*e^3 - 45304381/57826*e^2 + 6051618/28913*e + 3878348/28913, 77713/173478*e^7 - 131032/86739*e^6 - 2291959/173478*e^5 + 268283/5982*e^4 + 5239313/57826*e^3 - 19497731/57826*e^2 + 14288455/173478*e + 8576101/86739, 11812/86739*e^7 - 72002/86739*e^6 - 339865/86739*e^5 + 69860/2991*e^4 + 655422/28913*e^3 - 4625061/28913*e^2 + 7577770/86739*e + 1852946/86739, -28550/86739*e^7 + 172499/173478*e^6 + 1775227/173478*e^5 - 86998/2991*e^4 - 4653315/57826*e^3 + 6147620/28913*e^2 + 4553069/173478*e - 6055708/86739, -6070/86739*e^7 + 41779/173478*e^6 + 365399/173478*e^5 - 22838/2991*e^4 - 855863/57826*e^3 + 1969560/28913*e^2 - 2187755/173478*e - 5739323/86739, 17669/57826*e^7 - 50549/57826*e^6 - 258016/28913*e^5 + 53349/1994*e^4 + 1694364/28913*e^3 - 11771157/57826*e^2 + 2501120/28913*e + 1070386/28913, 119/997*e^7 + 525/1994*e^6 - 7889/1994*e^5 - 6876/997*e^4 + 85011/1994*e^3 + 37244/997*e^2 - 318437/1994*e + 32284/997, -23/173478*e^7 + 34639/173478*e^6 + 14911/86739*e^5 - 29965/5982*e^4 + 31714/28913*e^3 + 1502889/57826*e^2 - 5288668/86739*e + 2563510/86739, -107519/173478*e^7 + 337303/173478*e^6 + 1554580/86739*e^5 - 341899/5982*e^4 - 3347496/28913*e^3 + 24099763/57826*e^2 - 15112945/86739*e - 2812412/86739, 29309/86739*e^7 - 203459/173478*e^6 - 1835221/173478*e^5 + 100777/2991*e^4 + 4804017/57826*e^3 - 6966726/28913*e^2 + 333019/173478*e + 6785749/86739, 7600/86739*e^7 - 19010/86739*e^6 - 282766/86739*e^5 + 18434/2991*e^4 + 1064089/28913*e^3 - 1240371/28913*e^2 - 10346453/86739*e + 3034790/86739, -3594/28913*e^7 + 2218/28913*e^6 + 96786/28913*e^5 - 1572/997*e^4 - 672476/28913*e^3 + 323198/28913*e^2 + 812573/28913*e - 828648/28913, 12043/57826*e^7 - 14472/28913*e^6 - 370365/57826*e^5 + 28365/1994*e^4 + 2935139/57826*e^3 - 6102527/57826*e^2 - 2161543/57826*e + 2227399/28913, -29693/173478*e^7 + 135103/173478*e^6 + 427738/86739*e^5 - 130825/5982*e^4 - 894337/28913*e^3 + 8667821/57826*e^2 - 6428689/86739*e - 815786/86739, 31675/86739*e^7 - 110615/86739*e^6 - 932551/86739*e^5 + 109946/2991*e^4 + 2177089/28913*e^3 - 7635452/28913*e^2 + 3198487/86739*e + 5360498/86739, -26086/86739*e^7 + 107021/86739*e^6 + 711664/86739*e^5 - 108545/2991*e^4 - 1196422/28913*e^3 + 7720267/28913*e^2 - 17467822/86739*e - 1317368/86739, -16489/86739*e^7 + 198673/173478*e^6 + 841997/173478*e^5 - 98600/2991*e^4 - 984791/57826*e^3 + 6705598/28913*e^2 - 33902447/173478*e - 1125560/86739, -25023/57826*e^7 + 42499/28913*e^6 + 765191/57826*e^5 - 85933/1994*e^4 - 5790275/57826*e^3 + 18127103/57826*e^2 - 686067/57826*e - 1710422/28913, 37725/57826*e^7 - 128411/57826*e^6 - 538688/28913*e^5 + 129225/1994*e^4 + 3445630/28913*e^3 - 27352061/57826*e^2 + 5169373/28913*e + 2688476/28913, 15927/57826*e^7 - 54333/57826*e^6 - 200965/28913*e^5 + 54125/1994*e^4 + 944233/28913*e^3 - 11346387/57826*e^2 + 3651684/28913*e + 379926/28913, 34893/57826*e^7 - 50468/28913*e^6 - 1016991/57826*e^5 + 99045/1994*e^4 + 7108901/57826*e^3 - 20157109/57826*e^2 + 3169969/57826*e + 972918/28913, 29228/86739*e^7 - 117391/86739*e^6 - 874811/86739*e^5 + 117619/2991*e^4 + 1962272/28913*e^3 - 8150455/28913*e^2 + 9221318/86739*e + 1871026/86739, 91519/86739*e^7 - 320108/86739*e^6 - 2705602/86739*e^5 + 321194/2991*e^4 + 6233715/28913*e^3 - 22428889/28913*e^2 + 16394689/86739*e + 12410990/86739, 154847/173478*e^7 - 246560/86739*e^6 - 4591205/173478*e^5 + 497989/5982*e^4 + 10673705/57826*e^3 - 35105727/57826*e^2 + 26492111/173478*e + 9058838/86739, -225697/173478*e^7 + 351718/86739*e^6 + 6564157/173478*e^5 - 709547/5982*e^4 - 14865527/57826*e^3 + 49968999/57826*e^2 - 38708365/173478*e - 14452474/86739, -6521/86739*e^7 + 110459/173478*e^6 + 305509/173478*e^5 - 58378/2991*e^4 - 55393/57826*e^3 + 4318859/28913*e^2 - 22559563/173478*e - 4272400/86739, 4895/57826*e^7 - 891/28913*e^6 - 165803/57826*e^5 + 2429/1994*e^4 + 1616271/57826*e^3 - 575571/57826*e^2 - 3463739/57826*e - 1031846/28913, 9487/86739*e^7 - 70181/86739*e^6 - 263062/86739*e^5 + 69632/2991*e^4 + 337979/28913*e^3 - 4669314/28913*e^2 + 11689393/86739*e - 1633690/86739] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([2,2,-1/3*w^3 + 1/3*w^2 + 3*w - 8/3])] = -1 AL_eigenvalues[ZF.ideal([9,3,-w - 1])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]