/* 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([14, 14, w]) 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^7 - 3*x^6 - 22*x^5 + 61*x^4 + 92*x^3 - 218*x^2 - 100*x + 172 K. = NumberField(heckePol) hecke_eigenvalues_array = [1, 1, e, -44/3361*e^6 + 773/6722*e^5 + 253/6722*e^4 - 7827/3361*e^3 + 21721/6722*e^2 + 21728/3361*e - 18919/3361, 107/6722*e^6 - 367/6722*e^5 - 784/3361*e^4 + 5819/6722*e^3 - 2454/3361*e^2 - 1059/3361*e + 13952/3361, -175/3361*e^6 + 506/3361*e^5 + 3444/3361*e^4 - 9360/3361*e^3 - 6265/3361*e^2 + 21337/3361*e - 10394/3361, -47/3361*e^6 + 291/6722*e^5 + 2791/6722*e^4 - 3090/3361*e^3 - 22859/6722*e^2 + 10071/3361*e + 23866/3361, 243/6722*e^6 - 645/6722*e^5 - 2660/3361*e^4 + 12901/6722*e^3 + 12080/3361*e^2 - 20278/3361*e - 17002/3361, 19/6722*e^6 + 203/3361*e^5 - 1315/6722*e^4 - 9835/6722*e^3 + 16813/6722*e^2 + 27391/3361*e - 18411/3361, 91/3361*e^6 - 532/3361*e^5 - 1522/3361*e^4 + 10917/3361*e^3 + 569/3361*e^2 - 35160/3361*e + 11858/3361, -262/3361*e^6 + 239/3361*e^5 + 6635/3361*e^4 - 3066/3361*e^3 - 40973/3361*e^2 - 4143/3361*e + 70826/3361, -953/6722*e^6 + 1493/3361*e^5 + 19965/6722*e^4 - 54717/6722*e^3 - 66383/6722*e^2 + 54727/3361*e + 19348/3361, 417/6722*e^6 - 111/6722*e^5 - 5851/3361*e^4 + 313/6722*e^3 + 40066/3361*e^2 + 5202/3361*e - 44446/3361, -19/6722*e^6 - 203/3361*e^5 + 1315/6722*e^4 + 9835/6722*e^3 - 16813/6722*e^2 - 24030/3361*e + 15050/3361, -129/3361*e^6 - 280/3361*e^5 + 4152/3361*e^4 + 5392/3361*e^3 - 34195/3361*e^2 - 10545/3361*e + 41620/3361, 47/3361*e^6 - 291/6722*e^5 - 2791/6722*e^4 + 3090/3361*e^3 + 22859/6722*e^2 - 13432/3361*e - 13783/3361, 55/6722*e^6 - 63/6722*e^5 + 131/3361*e^4 + 541/6722*e^3 - 10779/3361*e^2 + 3225/3361*e + 24008/3361, -317/6722*e^6 + 151/3361*e^5 + 6373/6722*e^4 - 3607/6722*e^3 - 12693/6722*e^2 - 6977/3361*e - 8761/3361, 374/3361*e^6 - 1529/6722*e^5 - 17275/6722*e^4 + 14434/3361*e^3 + 82571/6722*e^2 - 33443/3361*e - 35807/3361, 1205/6722*e^6 - 1454/3361*e^5 - 25731/6722*e^4 + 53407/6722*e^3 + 96915/6722*e^2 - 62561/3361*e - 45071/3361, 592/3361*e^6 - 617/3361*e^5 - 15146/3361*e^4 + 9673/3361*e^3 + 89758/3361*e^2 - 17655/3361*e - 112108/3361, 727/6722*e^6 + 145/6722*e^5 - 10918/3361*e^4 - 5193/6722*e^3 + 85947/3361*e^2 + 4741/3361*e - 129732/3361, -847/6722*e^6 + 149/3361*e^5 + 22181/6722*e^4 - 265/6722*e^3 - 139219/6722*e^2 - 26138/3361*e + 98128/3361, -353/3361*e^6 + 771/3361*e^5 + 8157/3361*e^4 - 13983/3361*e^3 - 41542/3361*e^2 + 20934/3361*e + 79134/3361, 323/6722*e^6 + 90/3361*e^5 - 8911/6722*e^4 - 5867/6722*e^3 + 63995/6722*e^2 + 21995/3361*e - 60912/3361, 62/3361*e^6 - 621/3361*e^5 + 662/3361*e^4 + 13015/3361*e^3 - 33407/3361*e^2 - 42533/3361*e + 81504/3361, -857/3361*e^6 + 4591/6722*e^5 + 36017/6722*e^4 - 41612/3361*e^3 - 127909/6722*e^2 + 89241/3361*e + 47586/3361, -670/3361*e^6 + 1073/3361*e^5 + 14530/3361*e^4 - 17590/3361*e^3 - 54235/3361*e^2 + 20424/3361*e + 28002/3361, 1205/6722*e^6 - 1454/3361*e^5 - 25731/6722*e^4 + 53407/6722*e^3 + 83471/6722*e^2 - 55839/3361*e + 1983/3361, -573/3361*e^6 + 1023/3361*e^5 + 13831/3361*e^4 - 19508/3361*e^3 - 66223/3361*e^2 + 52271/3361*e + 14788/3361, 54/3361*e^6 - 1407/6722*e^5 - 1991/6722*e^4 + 15564/3361*e^3 + 5883/6722*e^2 - 59054/3361*e - 3822/3361, -666/3361*e^6 + 3909/6722*e^5 + 29037/6722*e^4 - 37350/3361*e^3 - 119611/6722*e^2 + 90863/3361*e + 43777/3361, -1059/6722*e^6 - 524/3361*e^5 + 31193/6722*e^4 + 25271/6722*e^3 - 235539/6722*e^2 - 45902/3361*e + 162394/3361, -579/3361*e^6 + 4443/6722*e^5 + 22655/6722*e^4 - 40283/3361*e^3 - 63639/6722*e^2 + 79372/3361*e + 36499/3361, -361/6722*e^6 - 496/3361*e^5 + 11541/6722*e^4 + 18815/6722*e^3 - 97621/6722*e^2 - 2835/3361*e + 70846/3361, -443/6722*e^6 + 263/6722*e^5 + 4628/3361*e^4 + 409/6722*e^3 - 12299/3361*e^2 - 23226/3361*e - 11024/3361, 337/6722*e^6 - 468/3361*e^5 - 8111/6722*e^4 + 19081/6722*e^3 + 53741/6722*e^2 - 37071/3361*e - 67756/3361, 2307/6722*e^6 - 3124/3361*e^5 - 48225/6722*e^4 + 114845/6722*e^3 + 157877/6722*e^2 - 117412/3361*e - 37389/3361, 701/3361*e^6 - 2767/6722*e^5 - 31759/6722*e^4 + 25778/3361*e^3 + 135561/6722*e^2 - 66898/3361*e - 47748/3361, -328/3361*e^6 - 43/6722*e^5 + 18691/6722*e^4 + 3679/3361*e^3 - 138431/6722*e^2 - 42132/3361*e + 107987/3361, -209/3361*e^6 + 1151/6722*e^5 + 5403/6722*e^4 - 9450/3361*e^3 + 36795/6722*e^2 + 15822/3361*e - 72220/3361, 549/6722*e^6 - 2951/6722*e^5 - 3520/3361*e^4 + 54043/6722*e^3 - 20758/3361*e^2 - 54278/3361*e + 83082/3361, 363/3361*e^6 - 1088/3361*e^5 - 5665/3361*e^4 + 18359/3361*e^3 - 11876/3361*e^2 - 17928/3361*e + 56092/3361, 771/6722*e^6 - 961/3361*e^5 - 16921/6722*e^4 + 39605/6722*e^3 + 58523/6722*e^2 - 76704/3361*e + 9126/3361, 129/3361*e^6 + 280/3361*e^5 - 4152/3361*e^4 - 8753/3361*e^3 + 40917/3361*e^2 + 54238/3361*e - 95396/3361, -483/3361*e^6 + 1531/3361*e^5 + 9371/3361*e^4 - 30539/3361*e^3 - 26030/3361*e^2 + 96130/3361*e + 42028/3361, 1427/6722*e^6 - 1879/6722*e^5 - 17806/3361*e^4 + 32247/6722*e^3 + 98477/3361*e^2 - 31211/3361*e - 102222/3361, -655/3361*e^6 + 1195/6722*e^5 + 33175/6722*e^4 - 11026/3361*e^3 - 191421/6722*e^2 + 35016/3361*e + 146816/3361, 413/6722*e^6 + 344/3361*e^5 - 13371/6722*e^4 - 13537/6722*e^3 + 114271/6722*e^2 - 1449/3361*e - 64097/3361, 649/6722*e^6 - 1380/3361*e^5 - 12369/6722*e^4 + 50749/6722*e^3 + 19201/6722*e^2 - 35887/3361*e + 19792/3361, -967/6722*e^6 + 741/6722*e^5 + 11263/3361*e^4 - 5723/6722*e^3 - 53272/3361*e^2 - 20647/3361*e + 59802/3361, -489/6722*e^6 + 1049/6722*e^5 + 4274/3361*e^4 - 14343/6722*e^3 - 1695/3361*e^2 - 10646/3361*e - 20226/3361, 188/3361*e^6 - 582/3361*e^5 - 5582/3361*e^4 + 12360/3361*e^3 + 49079/3361*e^2 - 47006/3361*e - 108908/3361, -1534/3361*e^6 + 7853/6722*e^5 + 64277/6722*e^4 - 71676/3361*e^3 - 212681/6722*e^2 + 141843/3361*e + 82432/3361, -804/3361*e^6 + 1903/6722*e^5 + 38233/6722*e^4 - 17747/3361*e^3 - 187301/6722*e^2 + 55430/3361*e + 55785/3361, 345/6722*e^6 - 1267/3361*e^5 - 4773/6722*e^4 + 53503/6722*e^3 - 21259/6722*e^2 - 97711/3361*e + 48849/3361, 786/3361*e^6 - 4795/6722*e^5 - 29727/6722*e^4 + 42808/3361*e^3 + 60983/6722*e^2 - 78318/3361*e - 17540/3361, -977/6722*e^6 + 529/3361*e^5 + 23395/6722*e^4 - 16821/6722*e^3 - 116985/6722*e^2 + 8099/3361*e + 45965/3361, 583/3361*e^6 + 681/6722*e^5 - 32761/6722*e^4 - 9726/3361*e^3 + 230631/6722*e^2 + 34760/3361*e - 124915/3361, -129/6722*e^6 - 140/3361*e^5 + 7513/6722*e^4 + 8753/6722*e^3 - 108137/6722*e^2 - 17036/3361*e + 121640/3361, 121/3361*e^6 + 395/6722*e^5 - 11619/6722*e^4 - 2843/3361*e^3 + 127643/6722*e^2 - 5976/3361*e - 93336/3361, 186/3361*e^6 - 365/6722*e^5 - 6111/6722*e^4 - 1287/3361*e^3 - 2143/6722*e^2 + 53895/3361*e + 29408/3361, -225/6722*e^6 + 2091/6722*e^5 - 1147/3361*e^4 - 41323/6722*e^3 + 54790/3361*e^2 + 58610/3361*e - 121436/3361, 1233/3361*e^6 - 6919/6722*e^5 - 51623/6722*e^4 + 62971/3361*e^3 + 169619/6722*e^2 - 122755/3361*e - 40215/3361, -129/3361*e^6 - 280/3361*e^5 + 4152/3361*e^4 + 5392/3361*e^3 - 34195/3361*e^2 - 10545/3361*e + 34898/3361, 248/3361*e^6 - 1607/6722*e^5 - 11509/6722*e^4 + 18450/3361*e^3 + 52039/6722*e^2 - 69302/3361*e - 3362/3361, 226/3361*e^6 + 230/3361*e^5 - 4851/3361*e^4 - 10671/3361*e^3 + 18846/3361*e^2 + 79363/3361*e - 41390/3361, 1270/3361*e^6 - 3288/3361*e^5 - 26338/3361*e^4 + 58324/3361*e^3 + 82437/3361*e^2 - 115666/3361*e - 48062/3361, 656/3361*e^6 - 3275/6722*e^5 - 27299/6722*e^4 + 29613/3361*e^3 + 85285/6722*e^2 - 63620/3361*e + 29379/3361, 1181/6722*e^6 - 1475/6722*e^5 - 12831/3361*e^4 + 17361/6722*e^3 + 48364/3361*e^2 + 21890/3361*e - 11732/3361, -2151/6722*e^6 + 1975/6722*e^5 + 26409/3361*e^4 - 31791/6722*e^3 - 139669/3361*e^2 + 33979/3361*e + 118134/3361, 807/3361*e^6 - 2391/3361*e^5 - 15344/3361*e^4 + 43259/3361*e^3 + 26874/3361*e^2 - 87466/3361*e + 49314/3361, 1571/6722*e^6 - 3755/6722*e^5 - 18013/3361*e^4 + 67029/6722*e^3 + 82233/3361*e^2 - 67377/3361*e - 87152/3361, 1701/6722*e^6 - 4515/6722*e^5 - 18620/3361*e^4 + 76863/6722*e^3 + 74477/3361*e^2 - 54560/3361*e - 31628/3361, 277/3361*e^6 + 966/3361*e^5 - 9619/3361*e^4 - 20619/3361*e^3 + 88564/3361*e^2 + 62428/3361*e - 140228/3361, -712/3361*e^6 + 1060/3361*e^5 + 15491/3361*e^4 - 15131/3361*e^3 - 53722/3361*e^2 - 11695/3361*e - 4876/3361, 1933/6722*e^6 - 3803/6722*e^5 - 20634/3361*e^4 + 60079/6722*e^3 + 72580/3361*e^2 - 31790/3361*e - 68220/3361, 295/3361*e^6 - 949/3361*e^5 - 7150/3361*e^4 + 18179/3361*e^3 + 34088/3361*e^2 - 35680/3361*e - 20506/3361, 1358/3361*e^6 - 4761/6722*e^5 - 63265/6722*e^4 + 43729/3361*e^3 + 292843/6722*e^2 - 118790/3361*e - 121137/3361, -343/3361*e^6 + 454/3361*e^5 + 10649/3361*e^4 - 9607/3361*e^3 - 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105285/6722*e^3 - 64744/3361*e^2 + 66004/3361*e - 12702/3361, -6049/6722*e^6 + 15973/6722*e^5 + 64362/3361*e^4 - 289637/6722*e^3 - 228937/3361*e^2 + 293065/3361*e + 171308/3361, -2167/3361*e^6 + 13703/6722*e^5 + 88923/6722*e^4 - 127523/3361*e^3 - 255315/6722*e^2 + 253381/3361*e - 11687/3361, 2114/3361*e^6 - 7188/3361*e^5 - 40528/3361*e^4 + 137268/3361*e^3 + 81731/3361*e^2 - 333844/3361*e + 10210/3361, -103/6722*e^6 - 3793/6722*e^5 + 6660/3361*e^4 + 81973/6722*e^3 - 100321/3361*e^2 - 140174/3361*e + 177110/3361, 899/3361*e^6 - 4565/6722*e^5 - 37939/6722*e^4 + 39153/3361*e^3 + 140327/6722*e^2 - 36956/3361*e - 115538/3361, -632/3361*e^6 + 409/6722*e^5 + 33883/6722*e^4 + 3072/3361*e^3 - 219351/6722*e^2 - 48145/3361*e + 132491/3361, -845/3361*e^6 + 4940/3361*e^5 + 11252/3361*e^4 - 94170/3361*e^3 + 50413/3361*e^2 + 216533/3361*e - 136998/3361, -2376/3361*e^6 + 7427/3361*e^5 + 47163/3361*e^4 - 133612/3361*e^3 - 122704/3361*e^2 + 225510/3361*e + 13562/3361, 156/3361*e^6 + 2449/3361*e^5 - 8851/3361*e^4 - 51386/3361*e^3 + 107087/3361*e^2 + 135624/3361*e - 120834/3361, -4687/6722*e^6 + 3876/3361*e^5 + 107163/6722*e^4 - 121145/6722*e^3 - 518683/6722*e^2 + 21856/3361*e + 357258/3361, -842/3361*e^6 + 1820/3361*e^5 + 16705/3361*e^4 - 31687/3361*e^3 - 38210/3361*e^2 + 63501/3361*e - 89036/3361, 4821/6722*e^6 - 6336/3361*e^5 - 103347/6722*e^4 + 225493/6722*e^3 + 378285/6722*e^2 - 193965/3361*e - 110672/3361, 464/3361*e^6 - 1937/3361*e^5 - 8056/3361*e^4 + 37013/3361*e^3 - 866/3361*e^2 - 113941/3361*e - 5206/3361, 21/3361*e^6 + 6735/6722*e^5 - 21127/6722*e^4 - 63408/3361*e^3 + 369197/6722*e^2 + 138736/3361*e - 407047/3361, 2495/6722*e^6 - 3415/3361*e^5 - 60529/6722*e^4 + 127205/6722*e^3 + 338035/6722*e^2 - 164442/3361*e - 243088/3361, -1700/3361*e^6 + 3589/6722*e^5 + 83717/6722*e^4 - 31388/3361*e^3 - 434293/6722*e^2 + 70433/3361*e + 189036/3361, -1059/3361*e^6 - 1048/3361*e^5 + 34554/3361*e^4 + 21910/3361*e^3 - 289315/3361*e^2 - 54833/3361*e + 425618/3361, 2883/6722*e^6 - 3669/6722*e^5 - 33343/3361*e^4 + 72479/6722*e^3 + 146722/3361*e^2 - 124275/3361*e - 7358/3361, -127/3361*e^6 - 1359/6722*e^5 + 16695/6722*e^4 + 12317/3361*e^3 - 230247/6722*e^2 - 24060/3361*e + 192350/3361, 2499/6722*e^6 - 5495/3361*e^5 - 42055/6722*e^4 + 208275/6722*e^3 - 28843/6722*e^2 - 211567/3361*e + 189966/3361, -539/3361*e^6 + 8629/6722*e^5 + 15703/6722*e^4 - 89999/3361*e^3 + 46777/6722*e^2 + 299778/3361*e - 51104/3361, 1179/3361*e^6 - 2756/3361*e^5 - 24816/3361*e^4 + 54129/3361*e^3 + 78507/3361*e^2 - 141004/3361*e + 61076/3361, -872/3361*e^6 - 590/3361*e^5 + 26034/3361*e^4 + 15683/3361*e^3 - 193890/3361*e^2 - 73235/3361*e + 231262/3361, 1772/3361*e^6 - 4413/3361*e^5 - 40385/3361*e^4 + 89111/3361*e^3 + 182417/3361*e^2 - 261205/3361*e - 180688/3361, -1511/6722*e^6 + 2607/3361*e^5 + 27451/6722*e^4 - 94549/6722*e^3 - 24517/6722*e^2 + 62951/3361*e - 135677/3361, -1499/3361*e^6 + 8995/6722*e^5 + 61555/6722*e^4 - 79887/3361*e^3 - 176565/6722*e^2 + 128837/3361*e - 69423/3361, 787/6722*e^6 - 2559/3361*e^5 - 3523/6722*e^4 + 95005/6722*e^3 - 192307/6722*e^2 - 93793/3361*e + 339805/3361, 2096/3361*e^6 - 5273/3361*e^5 - 42997/3361*e^4 + 91748/3361*e^3 + 129485/3361*e^2 - 168516/3361*e + 31650/3361, 2333/6722*e^6 - 9761/6722*e^5 - 21209/3361*e^4 + 188065/6722*e^3 + 36047/3361*e^2 - 217023/3361*e - 18890/3361, -649/6722*e^6 + 1380/3361*e^5 + 12369/6722*e^4 - 64193/6722*e^3 - 25923/6722*e^2 + 126634/3361*e - 2987/3361, 3155/6722*e^6 - 3793/3361*e^5 - 70829/6722*e^4 + 140419/6722*e^3 + 307887/6722*e^2 - 139186/3361*e - 146569/3361, -1072/3361*e^6 + 1417/6722*e^5 + 56579/6722*e^4 - 11339/3361*e^3 - 365129/6722*e^2 + 7807/3361*e + 222264/3361, -727/6722*e^6 + 1608/3361*e^5 + 18475/6722*e^4 - 75471/6722*e^3 - 87869/6722*e^2 + 180114/3361*e - 21513/3361, -621/6722*e^6 - 2833/6722*e^5 + 8665/3361*e^4 + 73089/6722*e^3 - 58506/3361*e^2 - 193158/3361*e + 94238/3361, -453/3361*e^6 + 580/3361*e^5 + 10125/3361*e^4 - 10689/3361*e^3 - 35039/3361*e^2 + 11040/3361*e - 110220/3361, 35/3361*e^6 + 571/3361*e^5 - 1361/3361*e^4 - 18294/3361*e^3 + 11336/3361*e^2 + 111351/3361*e - 74552/3361, -2551/6722*e^6 + 5647/3361*e^5 + 37163/6722*e^4 - 213553/6722*e^3 + 113023/6722*e^2 + 262905/3361*e - 196715/3361, 3049/6722*e^6 - 2449/3361*e^5 - 73045/6722*e^4 + 79245/6722*e^3 + 400889/6722*e^2 - 54960/3361*e - 326179/3361, 479/3361*e^6 - 732/3361*e^5 - 14401/3361*e^4 + 16689/3361*e^3 + 113945/3361*e^2 - 95988/3361*e - 229214/3361, 507/6722*e^6 + 1879/3361*e^5 - 19523/6722*e^4 - 81299/6722*e^3 + 207711/6722*e^2 + 136364/3361*e - 135017/3361, -5673/6722*e^6 + 5724/3361*e^5 + 127643/6722*e^4 - 204419/6722*e^3 - 558015/6722*e^2 + 178839/3361*e + 274143/3361, -2309/6722*e^6 + 4164/3361*e^5 + 42349/6722*e^4 - 158741/6722*e^3 - 71907/6722*e^2 + 193070/3361*e + 126713/3361, -2915/6722*e^6 + 10061/6722*e^5 + 26667/3361*e^4 - 183279/6722*e^3 - 30332/3361*e^2 + 195424/3361*e - 8688/3361, 4753/6722*e^6 - 12533/6722*e^5 - 49055/3361*e^4 + 218591/6722*e^3 + 146585/3361*e^2 - 172592/3361*e - 38058/3361, 883/3361*e^6 - 767/3361*e^5 - 20604/3361*e^4 + 3919/3361*e^3 + 90765/3361*e^2 + 111496/3361*e - 57642/3361, 148/3361*e^6 - 1989/6722*e^5 + 5871/6722*e^4 + 15022/3361*e^3 - 244167/6722*e^2 - 18698/3361*e + 365210/3361, -4241/6722*e^6 + 11091/6722*e^5 + 41597/3361*e^4 - 200233/6722*e^3 - 86333/3361*e^2 + 207197/3361*e - 74916/3361, 2353/6722*e^6 - 156/3361*e^5 - 60961/6722*e^4 - 11565/6722*e^3 + 365217/6722*e^2 + 51502/3361*e - 266818/3361, 2516/3361*e^6 - 5143/3361*e^5 - 55968/3361*e^4 + 90685/3361*e^3 + 238629/3361*e^2 - 203592/3361*e - 177330/3361, -1247/6722*e^6 + 2895/6722*e^5 + 16707/3361*e^4 - 40865/6722*e^3 - 115421/3361*e^2 - 19038/3361*e + 136184/3361, 2883/6722*e^6 - 3669/6722*e^5 - 36704/3361*e^4 + 65757/6722*e^3 + 220664/3361*e^2 - 33528/3361*e - 296404/3361, -677/6722*e^6 - 5091/6722*e^5 + 13787/3361*e^4 + 107737/6722*e^3 - 128745/3361*e^2 - 138388/3361*e + 67838/3361, 1702/3361*e^6 - 1027/6722*e^5 - 92131/6722*e^4 + 4703/3361*e^3 + 611897/6722*e^2 - 16728/3361*e - 323991/3361, 2012/3361*e^6 - 8660/3361*e^5 - 37714/3361*e^4 + 167247/3361*e^3 + 59930/3361*e^2 - 390721/3361*e + 46558/3361, 3593/6722*e^6 - 9371/6722*e^5 - 38985/3361*e^4 + 174793/6722*e^3 + 156070/3361*e^2 - 195695/3361*e - 171032/3361, 695/3361*e^6 - 185/3361*e^5 - 15022/3361*e^4 - 1719/3361*e^3 + 61852/3361*e^2 + 64394/3361*e - 184004/3361, -1031/6722*e^6 + 81/6722*e^5 + 14716/3361*e^4 - 5497/6722*e^3 - 109538/3361*e^2 + 74597/3361*e + 121818/3361, -2512/3361*e^6 + 12049/6722*e^5 + 105191/6722*e^4 - 103723/3361*e^3 - 347237/6722*e^2 + 146313/3361*e + 68748/3361, 3229/6722*e^6 - 7243/6722*e^5 - 35941/3361*e^4 + 131125/6722*e^3 + 154932/3361*e^2 - 132097/3361*e - 188026/3361, -819/6722*e^6 + 1427/6722*e^5 + 13571/3361*e^4 - 31033/6722*e^3 - 118515/3361*e^2 + 91000/3361*e + 70996/3361] 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, -w - 2])] = -1 AL_eigenvalues[ZF.ideal([7, 7, -2/3*w^3 + 2/3*w^2 + 5*w - 7/3])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]