/* 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([9, 3, -1/3*w^3 + 1/3*w^2 + 3*w - 5/3]) 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^16 - 21*x^14 + 174*x^12 - 724*x^10 + 1587*x^8 - 1747*x^6 + 822*x^4 - 120*x^2 + 4 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -1/2*e^15 + 21/2*e^13 - 87*e^11 + 723/2*e^9 - 1573/2*e^7 + 841*e^5 - 354*e^3 + 30*e, 1/4*e^15 - 5*e^13 + 39*e^11 - 150*e^9 + 1171/4*e^7 - 260*e^5 + 67*e^3 + 5*e, -1, -1/4*e^14 + 5*e^12 - 39*e^10 + 301/2*e^8 - 1199/4*e^6 + 583/2*e^4 - 115*e^2 + 9, 1/4*e^14 - 5*e^12 + 79/2*e^10 - 315/2*e^8 + 1325/4*e^6 - 679/2*e^4 + 127*e^2 - 7, -1/4*e^14 + 9/2*e^12 - 63/2*e^10 + 112*e^8 - 885/4*e^6 + 479/2*e^4 - 115*e^2 + 9, 1/2*e^13 - 17/2*e^11 + 107/2*e^9 - 311/2*e^7 + 210*e^5 - 112*e^3 + 14*e, -3/2*e^15 + 31*e^13 - 252*e^11 + 2049/2*e^9 - 4357/2*e^7 + 4575/2*e^5 - 969*e^3 + 90*e, 1/2*e^12 - 17/2*e^10 + 105/2*e^8 - 285/2*e^6 + 158*e^4 - 46*e^2 + 4, -1/2*e^12 + 8*e^10 - 91/2*e^8 + 110*e^6 - 100*e^4 + 10*e^2 + 6, 1/4*e^14 - 5*e^12 + 39*e^10 - 301/2*e^8 + 1195/4*e^6 - 565/2*e^4 + 97*e^2 - 5, 1/2*e^14 - 19/2*e^12 + 141/2*e^10 - 523/2*e^8 + 508*e^6 - 478*e^4 + 162*e^2 - 8, -e^13 + 17*e^11 - 213/2*e^9 + 304*e^7 - 777/2*e^5 + 175*e^3 - 12*e, -1/4*e^15 + 6*e^13 - 113/2*e^11 + 265*e^9 - 2597/4*e^7 + 791*e^5 - 399*e^3 + 49*e, 1/2*e^14 - 10*e^12 + 78*e^10 - 301*e^8 + 1197/2*e^6 - 574*e^4 + 212*e^2 - 16, -1/4*e^14 + 13/2*e^12 - 127/2*e^10 + 296*e^8 - 2753/4*e^6 + 1507/2*e^4 - 313*e^2 + 23, 1/2*e^14 - 21/2*e^12 + 86*e^10 - 693/2*e^8 + 1417/2*e^6 - 674*e^4 + 222*e^2 - 8, e^6 - 11*e^4 + 32*e^2 - 12, 1/2*e^15 - 21/2*e^13 + 86*e^11 - 347*e^9 + 1431/2*e^7 - 1411/2*e^5 + 275*e^3 - 42*e, -1/4*e^15 + 11/2*e^13 - 95/2*e^11 + 204*e^9 - 1821/4*e^7 + 1007/2*e^5 - 245*e^3 + 57*e, 1/2*e^12 - 8*e^10 + 93/2*e^8 - 122*e^6 + 142*e^4 - 50*e^2, -3/4*e^14 + 13*e^12 - 167/2*e^10 + 491/2*e^8 - 1287/4*e^6 + 269/2*e^4 + 23*e^2 - 7, 1/2*e^13 - 15/2*e^11 + 77/2*e^9 - 155/2*e^7 + 42*e^5 + 26*e^3 - 14*e, 1/2*e^13 - 15/2*e^11 + 77/2*e^9 - 155/2*e^7 + 42*e^5 + 26*e^3 - 14*e, 1/2*e^15 - 10*e^13 + 77*e^11 - 569/2*e^9 + 1003/2*e^7 - 661/2*e^5 - 28*e^3 + 42*e, 3/2*e^15 - 32*e^13 + 268*e^11 - 2231/2*e^9 + 4797/2*e^7 - 4973/2*e^5 + 982*e^3 - 70*e, -11/4*e^15 + 57*e^13 - 466*e^11 + 1913*e^9 - 16513/4*e^7 + 4419*e^5 - 1906*e^3 + 177*e, 5/4*e^15 - 51/2*e^13 + 204*e^11 - 814*e^9 + 6791/4*e^7 - 3517/2*e^5 + 747*e^3 - 63*e, -3/4*e^15 + 33/2*e^13 - 285/2*e^11 + 1225/2*e^9 - 5483/4*e^7 + 1515*e^5 - 670*e^3 + 43*e, -1/4*e^15 + 11/2*e^13 - 93/2*e^11 + 377/2*e^9 - 1481/4*e^7 + 302*e^5 - 37*e^3 - 39*e, 5/4*e^15 - 26*e^13 + 423/2*e^11 - 852*e^9 + 7077/4*e^7 - 1781*e^5 + 714*e^3 - 81*e, 1/4*e^15 - 6*e^13 + 113/2*e^11 - 266*e^9 + 2657/4*e^7 - 867*e^5 + 547*e^3 - 129*e, 3/4*e^14 - 33/2*e^12 + 142*e^10 - 604*e^8 + 5277/4*e^6 - 2777/2*e^4 + 579*e^2 - 51, 1/4*e^14 - 9/2*e^12 + 32*e^10 - 118*e^8 + 963/4*e^6 - 487/2*e^4 + 73*e^2 + 11, 2*e^15 - 41*e^13 + 329*e^11 - 1309*e^9 + 2678*e^7 - 2597*e^5 + 886*e^3 - 28*e, -2*e^15 + 85/2*e^13 - 356*e^11 + 1492*e^9 - 3262*e^7 + 6969/2*e^5 - 1439*e^3 + 92*e, -1/2*e^15 + 11*e^13 - 96*e^11 + 423*e^9 - 1973/2*e^7 + 1149*e^5 - 526*e^3 + 26*e, 1/2*e^15 - 19/2*e^13 + 139/2*e^11 - 495/2*e^9 + 443*e^7 - 362*e^5 + 82*e^3 + 32*e, 5/4*e^15 - 53/2*e^13 + 222*e^11 - 1869/2*e^9 + 8267/4*e^7 - 2266*e^5 + 1018*e^3 - 127*e, -e^15 + 39/2*e^13 - 297/2*e^11 + 563*e^9 - 2225/2*e^7 + 2141/2*e^5 - 373*e^3 - 10*e, -1/2*e^14 + 21/2*e^12 - 171/2*e^10 + 679/2*e^8 - 676*e^6 + 616*e^4 - 186*e^2, e^14 - 19*e^12 + 279/2*e^10 - 502*e^8 + 1841/2*e^6 - 804*e^4 + 276*e^2 - 24, 3/2*e^15 - 63/2*e^13 + 521/2*e^11 - 2155/2*e^9 + 2328*e^7 - 2479*e^5 + 1080*e^3 - 132*e, 4*e^15 - 167/2*e^13 + 1369/2*e^11 - 5591/2*e^9 + 11861/2*e^7 - 6142*e^5 + 2516*e^3 - 234*e, -1/4*e^14 + 8*e^12 - 177/2*e^10 + 897/2*e^8 - 4433/4*e^6 + 2523/2*e^4 - 511*e^2 + 31, 3/4*e^14 - 12*e^12 + 135/2*e^10 - 309/2*e^8 + 407/4*e^6 + 135/2*e^4 - 59*e^2 + 27, -1/2*e^10 + 8*e^8 - 89/2*e^6 + 102*e^4 - 88*e^2 + 20, -7/4*e^14 + 33*e^12 - 481/2*e^10 + 1725/2*e^8 - 6391/4*e^6 + 2919/2*e^4 - 559*e^2 + 49, -3/4*e^14 + 15*e^12 - 235/2*e^10 + 915/2*e^8 - 3671/4*e^6 + 1737/2*e^4 - 281*e^2 + 5, -1/4*e^14 + 7/2*e^12 - 15*e^10 + 13*e^8 + 181/4*e^6 - 159/2*e^4 + 27*e^2 + 3, 5/2*e^15 - 105/2*e^13 + 434*e^11 - 3591/2*e^9 + 7793/2*e^7 - 4228*e^5 + 1938*e^3 - 230*e, 1/4*e^15 - 11/2*e^13 + 46*e^11 - 180*e^9 + 1267/4*e^7 - 297/2*e^5 - 151*e^3 + 89*e, -3/2*e^15 + 61/2*e^13 - 244*e^11 + 979*e^9 - 4141/2*e^7 + 4423/2*e^5 - 1043*e^3 + 174*e, 7/2*e^15 - 147/2*e^13 + 1215/2*e^11 - 5017/2*e^9 + 5396*e^7 - 5675*e^5 + 2358*e^3 - 224*e, -1/2*e^14 + 8*e^12 - 44*e^10 + 88*e^8 + 19/2*e^6 - 205*e^4 + 150*e^2 - 14, 1/2*e^14 - 19/2*e^12 + 71*e^10 - 535/2*e^8 + 1055/2*e^6 - 480*e^4 + 106*e^2 + 24, -3/2*e^12 + 49/2*e^10 - 291/2*e^8 + 775/2*e^6 - 451*e^4 + 168*e^2 - 12, 5/2*e^15 - 52*e^13 + 851/2*e^11 - 3479/2*e^9 + 3706*e^7 - 7725/2*e^5 + 1598*e^3 - 160*e, -7/4*e^15 + 37*e^13 - 308*e^11 + 2561/2*e^9 - 11073/4*e^7 + 5807/2*e^5 - 1153*e^3 + 57*e, 1/2*e^15 - 23/2*e^13 + 103*e^11 - 453*e^9 + 2025/2*e^7 - 2121/2*e^5 + 379*e^3 + 14*e, 1/4*e^15 - 6*e^13 + 56*e^11 - 517/2*e^9 + 2503/4*e^7 - 1577/2*e^5 + 493*e^3 - 123*e, 1/2*e^14 - 9*e^12 + 64*e^10 - 237*e^8 + 989/2*e^6 - 541*e^4 + 226*e^2 - 4, 2*e^14 - 38*e^12 + 280*e^10 - 1020*e^8 + 1929*e^6 - 1799*e^4 + 682*e^2 - 46, -3/4*e^14 + 13*e^12 - 165/2*e^10 + 463/2*e^8 - 1031/4*e^6 + 63/2*e^4 + 49*e^2 + 5, 1/4*e^14 - 3*e^12 + 11/2*e^10 + 111/2*e^8 - 1107/4*e^6 + 875/2*e^4 - 227*e^2 + 25, 9/4*e^15 - 93/2*e^13 + 755/2*e^11 - 3061/2*e^9 + 12989/4*e^7 - 3437*e^5 + 1543*e^3 - 201*e, 1/2*e^11 - 8*e^9 + 87/2*e^7 - 88*e^5 + 40*e^3 + 10*e, 11/4*e^15 - 115/2*e^13 + 947/2*e^11 - 1953*e^9 + 16911/4*e^7 - 9131/2*e^5 + 2047*e^3 - 203*e, 1/4*e^15 - 13/2*e^13 + 129/2*e^11 - 621/2*e^9 + 3037/4*e^7 - 891*e^5 + 412*e^3 - 61*e, -e^14 + 39/2*e^12 - 297/2*e^10 + 1127/2*e^8 - 2243/2*e^6 + 1126*e^4 - 496*e^2 + 46, e^10 - 14*e^8 + 65*e^6 - 118*e^4 + 84*e^2 - 16, e^14 - 21*e^12 + 171*e^10 - 679*e^8 + 1354*e^6 - 1252*e^4 + 424*e^2 - 28, -e^14 + 21*e^12 - 172*e^10 + 694*e^8 - 1430*e^6 + 1400*e^4 - 508*e^2 + 24, 1/2*e^15 - 19/2*e^13 + 137/2*e^11 - 232*e^9 + 360*e^7 - 375/2*e^5 - 14*e^3 - 12*e, 1/4*e^15 - 7/2*e^13 + 12*e^11 + 69/2*e^9 - 1253/4*e^7 + 735*e^5 - 684*e^3 + 173*e, 1/4*e^14 - 2*e^12 - 19/2*e^10 + 263/2*e^8 - 1683/4*e^6 + 987/2*e^4 - 179*e^2 + 17, 3/4*e^14 - 29/2*e^12 + 110*e^10 - 418*e^8 + 3309/4*e^6 - 1549/2*e^4 + 235*e^2 + 9, e^15 - 20*e^13 + 317/2*e^11 - 640*e^9 + 2797/2*e^7 - 1595*e^5 + 812*e^3 - 130*e, -1/4*e^15 + 9/2*e^13 - 63/2*e^11 + 111*e^9 - 837/4*e^7 + 397/2*e^5 - 89*e^3 + 41*e, 1/4*e^15 - 5*e^13 + 40*e^11 - 165*e^9 + 1479/4*e^7 - 418*e^5 + 174*e^3 + 17*e, 21/4*e^15 - 219/2*e^13 + 1797/2*e^11 - 7367/2*e^9 + 31493/4*e^7 - 8245*e^5 + 3423*e^3 - 317*e, -5/4*e^14 + 24*e^12 - 357/2*e^10 + 1303/2*e^8 - 4821/4*e^6 + 2045/2*e^4 - 273*e^2 - 1, -e^14 + 20*e^12 - 309/2*e^10 + 580*e^8 - 2173/2*e^6 + 923*e^4 - 258*e^2 + 12, e^12 - 33/2*e^10 + 99*e^8 - 535/2*e^6 + 330*e^4 - 160*e^2 - 16, -e^14 + 22*e^12 - 189*e^10 + 800*e^8 - 1728*e^6 + 1766*e^4 - 656*e^2 + 46, -e^12 + 17*e^10 - 108*e^8 + 323*e^6 - 461*e^4 + 254*e^2 + 2, -5/4*e^14 + 23*e^12 - 166*e^10 + 1223/2*e^8 - 4947/4*e^6 + 2627/2*e^4 - 591*e^2 + 65, 2*e^15 - 41*e^13 + 330*e^11 - 1325*e^9 + 2771*e^7 - 2841*e^5 + 1162*e^3 - 100*e, -1/2*e^15 + 21/2*e^13 - 173/2*e^11 + 354*e^9 - 748*e^7 + 1525/2*e^5 - 302*e^3 + 44*e, -e^15 + 43/2*e^13 - 361/2*e^11 + 1491/2*e^9 - 3117/2*e^7 + 1491*e^5 - 432*e^3 - 22*e, 7/4*e^15 - 71/2*e^13 + 284*e^11 - 2287/2*e^9 + 9729/4*e^7 - 2586*e^5 + 1136*e^3 - 153*e, -17/4*e^15 + 87*e^13 - 700*e^11 + 2815*e^9 - 23647/4*e^7 + 6100*e^5 - 2514*e^3 + 259*e, -3*e^15 + 61*e^13 - 975/2*e^11 + 1949*e^9 - 8157/2*e^7 + 4213*e^5 - 1752*e^3 + 162*e, 7/4*e^15 - 71/2*e^13 + 565/2*e^11 - 1121*e^9 + 9263/4*e^7 - 4669/2*e^5 + 899*e^3 - 19*e, -5/2*e^15 + 103/2*e^13 - 420*e^11 + 1730*e^9 - 7541/2*e^7 + 8179/2*e^5 - 1776*e^3 + 166*e, 5/2*e^15 - 52*e^13 + 855/2*e^11 - 1770*e^9 + 3869*e^7 - 4225*e^5 + 1884*e^3 - 172*e, 9/4*e^15 - 97/2*e^13 + 821/2*e^11 - 3455/2*e^9 + 15053/4*e^7 - 3984*e^5 + 1666*e^3 - 185*e, 5/4*e^15 - 51/2*e^13 + 413/2*e^11 - 1699/2*e^9 + 7465/4*e^7 - 2072*e^5 + 973*e^3 - 153*e, -5/2*e^15 + 101/2*e^13 - 400*e^11 + 3159/2*e^9 - 6489/2*e^7 + 3237*e^5 - 1206*e^3 + 38*e, -1/2*e^12 + 8*e^10 - 91/2*e^8 + 110*e^6 - 98*e^4 - 2*e^2 + 2, e^14 - 18*e^12 + 122*e^10 - 390*e^8 + 602*e^6 - 421*e^4 + 138*e^2 - 46, -1/2*e^14 + 10*e^12 - 155/2*e^10 + 295*e^8 - 580*e^6 + 579*e^4 - 264*e^2 + 4, 1/4*e^14 - 9/2*e^12 + 57/2*e^10 - 68*e^8 + 1/4*e^6 + 415/2*e^4 - 201*e^2 + 23, 5*e^12 - 83*e^10 + 504*e^8 - 1387*e^6 + 1723*e^4 - 800*e^2 + 48, -1/4*e^14 + 7/2*e^12 - 31/2*e^10 + 18*e^8 + 155/4*e^6 - 257/2*e^4 + 131*e^2 - 9, 3/4*e^14 - 33/2*e^12 + 281/2*e^10 - 583*e^8 + 4883/4*e^6 - 2399/2*e^4 + 421*e^2 - 15, 3/4*e^14 - 12*e^12 + 68*e^10 - 319/2*e^8 + 437/4*e^6 + 197/2*e^4 - 95*e^2 - 1, -11/2*e^15 + 113*e^13 - 1825/2*e^11 + 7365/2*e^9 - 7766*e^7 + 16155/2*e^5 - 3393*e^3 + 340*e, -e^15 + 20*e^13 - 313/2*e^11 + 1217/2*e^9 - 2445/2*e^7 + 2347/2*e^5 - 410*e^3 + 38*e, 1/2*e^14 - 27/2*e^12 + 136*e^10 - 1301/2*e^8 + 3077/2*e^6 - 1669*e^4 + 636*e^2 - 44, 3/4*e^14 - 25/2*e^12 + 149/2*e^10 - 184*e^8 + 491/4*e^6 + 329/2*e^4 - 175*e^2 + 7, -11/4*e^14 + 113/2*e^12 - 905/2*e^10 + 1785*e^8 - 14363/4*e^6 + 6825/2*e^4 - 1195*e^2 + 73, -3/2*e^12 + 57/2*e^10 - 407/2*e^8 + 1343/2*e^6 - 997*e^4 + 528*e^2 - 42, 1/4*e^14 - 9*e^12 + 106*e^10 - 1123/2*e^8 + 5751/4*e^6 - 3357/2*e^4 + 685*e^2 - 41, -e^15 + 45/2*e^13 - 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195/2*e^11 + 442*e^9 - 1056*e^7 + 1195*e^5 - 424*e^3 - 48*e, 33/4*e^15 - 341/2*e^13 + 2771/2*e^11 - 5623*e^9 + 47545/4*e^7 - 24519/2*e^5 + 4919*e^3 - 373*e, -1/2*e^13 + 9*e^11 - 123/2*e^9 + 204*e^7 - 362*e^5 + 384*e^3 - 204*e, e^14 - 21*e^12 + 345/2*e^10 - 702*e^8 + 2957/2*e^6 - 1533*e^4 + 634*e^2 - 16, -5/4*e^14 + 26*e^12 - 211*e^10 + 1689/2*e^8 - 6911/4*e^6 + 3343/2*e^4 - 583*e^2 + 57, -3*e^15 + 123/2*e^13 - 494*e^11 + 1968*e^9 - 4017*e^7 + 7647/2*e^5 - 1201*e^3 + 8*e, 3*e^15 - 63*e^13 + 520*e^11 - 2135*e^9 + 4510*e^7 - 4485*e^5 + 1512*e^3 + 4*e, 2*e^14 - 43*e^12 + 729/2*e^10 - 1544*e^8 + 6799/2*e^6 - 3630*e^4 + 1484*e^2 - 96, -3/4*e^14 + 15*e^12 - 237/2*e^10 + 953/2*e^8 - 4171/4*e^6 + 2407/2*e^4 - 607*e^2 + 73, -3*e^15 + 66*e^13 - 1133/2*e^11 + 2391*e^9 - 10251/2*e^7 + 5135*e^5 - 1796*e^3 + 78*e, -3*e^15 + 129/2*e^13 - 544*e^11 + 4549/2*e^9 - 4877*e^7 + 4926*e^5 - 1716*e^3 + 16*e, 1/2*e^14 - 25/2*e^12 + 243/2*e^10 - 1165/2*e^8 + 1437*e^6 - 1696*e^4 + 714*e^2 - 16, 1/2*e^14 - 4*e^12 - 24*e^10 + 340*e^8 - 2503/2*e^6 + 1861*e^4 - 978*e^2 + 110, -5/4*e^14 + 22*e^12 - 295/2*e^10 + 965/2*e^8 - 3261/4*e^6 + 1333/2*e^4 - 189*e^2 - 9, -3/2*e^14 + 24*e^12 - 267/2*e^10 + 287*e^8 - 95*e^6 - 336*e^4 + 200*e^2 + 10, 2*e^15 - 43*e^13 + 364*e^11 - 1537*e^9 + 3369*e^7 - 3601*e^5 + 1574*e^3 - 252*e, -15/4*e^15 + 81*e^13 - 1375/2*e^11 + 2905*e^9 - 25463/4*e^7 + 6775*e^5 - 2749*e^3 + 151*e, -5/2*e^15 + 109/2*e^13 - 468*e^11 + 2005*e^9 - 8917/2*e^7 + 9631/2*e^5 - 2030*e^3 + 194*e, 1/2*e^15 - 15/2*e^13 + 73/2*e^11 - 103/2*e^9 - 56*e^7 + 82*e^5 + 218*e^3 - 196*e, 2*e^14 - 39*e^12 + 295*e^10 - 1098*e^8 + 2097*e^6 - 1943*e^4 + 748*e^2 - 104, -5/4*e^14 + 53/2*e^12 - 443/2*e^10 + 929*e^8 - 8229/4*e^6 + 4617/2*e^4 - 1083*e^2 + 87, 13/4*e^14 - 64*e^12 + 493*e^10 - 3781/2*e^8 + 15035/4*e^6 - 7141/2*e^4 + 1181*e^2 - 45, -3/2*e^14 + 25*e^12 - 149*e^10 + 370*e^8 - 543/2*e^6 - 225*e^4 + 226*e^2 + 8, -e^15 + 43/2*e^13 - 182*e^11 + 771*e^9 - 1718*e^7 + 3893/2*e^5 - 1008*e^3 + 172*e, -3/2*e^15 + 63/2*e^13 - 511/2*e^11 + 1003*e^9 - 1945*e^7 + 3329/2*e^5 - 395*e^3 - 36*e, 29/4*e^15 - 152*e^13 + 1249*e^11 - 10191/2*e^9 + 42971/4*e^7 - 21959/2*e^5 + 4397*e^3 - 391*e, -7*e^15 + 289/2*e^13 - 1172*e^11 + 4742*e^9 - 9976*e^7 + 20427/2*e^5 - 4043*e^3 + 288*e, -15/4*e^15 + 151/2*e^13 - 600*e^11 + 4817/2*e^9 - 20601/4*e^7 + 5595*e^5 - 2566*e^3 + 305*e, -3*e^15 + 64*e^13 - 538*e^11 + 2263*e^9 - 4978*e^7 + 5406*e^5 - 2372*e^3 + 240*e, 3/2*e^14 - 57/2*e^12 + 421/2*e^10 - 1539/2*e^8 + 1443*e^6 - 1239*e^4 + 292*e^2 + 6, -e^14 + 18*e^12 - 241/2*e^10 + 366*e^8 - 931/2*e^6 + 89*e^4 + 198*e^2 - 40, 1/4*e^14 - 5*e^12 + 41*e^10 - 367/2*e^8 + 1967/4*e^6 - 1501/2*e^4 + 499*e^2 - 59, -7/4*e^14 + 39*e^12 - 338*e^10 + 2879/2*e^8 - 12581/4*e^6 + 6713/2*e^4 - 1453*e^2 + 117, -9/4*e^15 + 101/2*e^13 - 895/2*e^11 + 3973/2*e^9 - 18481/4*e^7 + 5342*e^5 - 2573*e^3 + 337*e, -9/4*e^15 + 93/2*e^13 - 753/2*e^11 + 3021/2*e^9 - 12397/4*e^7 + 2951*e^5 - 892*e^3 - 39*e, 5/2*e^15 - 54*e^13 + 909/2*e^11 - 1877*e^9 + 3919*e^7 - 3784*e^5 + 1234*e^3 - 32*e, 13/4*e^15 - 137/2*e^13 + 1137/2*e^11 - 4717/2*e^9 + 20409/4*e^7 - 5399*e^5 + 2228*e^3 - 189*e, -7/4*e^14 + 67/2*e^12 - 256*e^10 + 1015*e^8 - 8869/4*e^6 + 4979/2*e^4 - 1101*e^2 + 55, 1/2*e^14 - 8*e^12 + 89/2*e^10 - 97*e^8 + 52*e^6 + 15*e^4 + 80*e^2 - 44, -3/4*e^15 + 16*e^13 - 138*e^11 + 1241/2*e^9 - 6193/4*e^7 + 4159/2*e^5 - 1329*e^3 + 313*e, 11/4*e^15 - 113/2*e^13 + 459*e^11 - 1885*e^9 + 16517/4*e^7 - 9249/2*e^5 + 2221*e^3 - 237*e, -7/2*e^15 + 75*e^13 - 635*e^11 + 5397/2*e^9 - 12025/2*e^7 + 13239/2*e^5 - 2946*e^3 + 306*e, -3*e^15 + 131/2*e^13 - 1123/2*e^11 + 4785/2*e^9 - 10555/2*e^7 + 5672*e^5 - 2454*e^3 + 330*e, 3/4*e^14 - 17*e^12 + 153*e^10 - 1391/2*e^8 + 6689/4*e^6 - 3985/2*e^4 + 897*e^2 - 45, 5/4*e^14 - 39/2*e^12 + 107*e^10 - 243*e^8 + 679/4*e^6 + 271/2*e^4 - 197*e^2 + 15, -39/4*e^15 + 200*e^13 - 1612*e^11 + 12977/2*e^9 - 54485/4*e^7 + 28075/2*e^5 - 5805*e^3 + 597*e, -11/4*e^15 + 119/2*e^13 - 508*e^11 + 2174*e^9 - 19529/4*e^7 + 10933/2*e^5 - 2545*e^3 + 253*e, e^15 - 33/2*e^13 + 98*e^11 - 493/2*e^9 + 178*e^7 + 283*e^5 - 508*e^3 + 200*e, -27/4*e^15 + 287/2*e^13 - 1201*e^11 + 5020*e^9 - 43717/4*e^7 + 23321/2*e^5 - 4977*e^3 + 493*e, -7/4*e^14 + 73/2*e^12 - 603/2*e^10 + 1256*e^8 - 11015/4*e^6 + 5925/2*e^4 - 1227*e^2 + 89, 3*e^14 - 123/2*e^12 + 489*e^10 - 3799/2*e^8 + 3714*e^6 - 3355*e^4 + 1052*e^2 - 38, -3/4*e^14 + 12*e^12 - 67*e^10 + 293/2*e^8 - 213/4*e^6 - 405/2*e^4 + 203*e^2 - 51, -1/4*e^14 + 3/2*e^12 + 45/2*e^10 - 251*e^8 + 3623/4*e^6 - 2713/2*e^4 + 733*e^2 - 75, 7/2*e^14 - 71*e^12 + 563*e^10 - 2210*e^8 + 8909/2*e^6 - 4280*e^4 + 1536*e^2 - 104, 1/4*e^14 - 7/2*e^12 + 11*e^10 + 45*e^8 - 1317/4*e^6 + 1255/2*e^4 - 401*e^2 + 75, -5/4*e^14 + 23*e^12 - 161*e^10 + 1085/2*e^8 - 3691/4*e^6 + 1535/2*e^4 - 243*e^2 - 39, 2*e^14 - 42*e^12 + 346*e^10 - 1417*e^8 + 3006*e^6 - 3113*e^4 + 1310*e^2 - 122, 1/2*e^14 - 19/2*e^12 + 145/2*e^10 - 585/2*e^8 + 675*e^6 - 848*e^4 + 458*e^2 - 30, 3/4*e^14 - 14*e^12 + 96*e^10 - 575/2*e^8 + 1249/4*e^6 + 169/2*e^4 - 269*e^2 + 61, 3/2*e^14 - 59/2*e^12 + 441/2*e^10 - 1555/2*e^8 + 1290*e^6 - 841*e^4 + 64*e^2 + 58, 3/4*e^14 - 35/2*e^12 + 311/2*e^10 - 660*e^8 + 5519/4*e^6 - 2653/2*e^4 + 479*e^2 - 17, -5*e^15 + 205/2*e^13 - 1643/2*e^11 + 3259*e^9 - 13283/2*e^7 + 12913/2*e^5 - 2328*e^3 + 166*e, -7/2*e^15 + 149/2*e^13 - 1253/2*e^11 + 5297/2*e^9 - 5902*e^7 + 6589*e^5 - 3064*e^3 + 332*e, -7/4*e^14 + 75/2*e^12 - 631/2*e^10 + 1321*e^8 - 11507/4*e^6 + 6193/2*e^4 - 1363*e^2 + 121, -9/4*e^14 + 45*e^12 - 705/2*e^10 + 2759/2*e^8 - 11353/4*e^6 + 5843/2*e^4 - 1215*e^2 + 79, 1/2*e^14 - 17*e^12 + 393/2*e^10 - 1040*e^8 + 2702*e^6 - 3275*e^4 + 1462*e^2 - 114, 9/4*e^14 - 42*e^12 + 593/2*e^10 - 1965/2*e^8 + 6033/4*e^6 - 1659/2*e^4 - 61*e^2 + 73, -2*e^13 + 65/2*e^11 - 187*e^9 + 891/2*e^7 - 338*e^5 - 120*e^3 + 118*e, -25/4*e^15 + 255/2*e^13 - 2041/2*e^11 + 8143/2*e^9 - 33801/4*e^7 + 8570*e^5 - 3434*e^3 + 293*e, 5/2*e^15 - 52*e^13 + 843/2*e^11 - 1676*e^9 + 3348*e^7 - 2999*e^5 + 766*e^3 + 64*e, -15/4*e^15 + 153/2*e^13 - 614*e^11 + 2470*e^9 - 20909/4*e^7 + 11099/2*e^5 - 2505*e^3 + 293*e, 25/4*e^15 - 259/2*e^13 + 2107/2*e^11 - 8539/2*e^9 + 35913/4*e^7 - 9159*e^5 + 3600*e^3 - 325*e, 9/4*e^15 - 50*e^13 + 439*e^11 - 1935*e^9 + 17951/4*e^7 - 5202*e^5 + 2490*e^3 - 295*e, 17/4*e^15 - 91*e^13 + 767*e^11 - 3231*e^9 + 28475/4*e^7 - 7792*e^5 + 3548*e^3 - 447*e, 19/4*e^15 - 199/2*e^13 + 1645/2*e^11 - 6831/2*e^9 + 29883/4*e^7 - 8176*e^5 + 3727*e^3 - 423*e, -1/4*e^14 + 2*e^12 + 23/2*e^10 - 319/2*e^8 + 2187/4*e^6 - 1355/2*e^4 + 187*e^2 + 15, 5/4*e^14 - 23*e^12 + 323/2*e^10 - 1085/2*e^8 + 3481/4*e^6 - 1045/2*e^4 - 7*e^2 + 9, -5/4*e^14 + 35/2*e^12 - 151/2*e^10 + 66*e^8 + 1067/4*e^6 - 1213/2*e^4 + 395*e^2 - 97, 5/4*e^14 - 49/2*e^12 + 377/2*e^10 - 728*e^8 + 5921/4*e^6 - 2937/2*e^4 + 507*e^2 + 33, e^14 - 45/2*e^12 + 399/2*e^10 - 1763/2*e^8 + 4027/2*e^6 - 2208*e^4 + 902*e^2 - 48, -1/2*e^12 + 9*e^10 - 117/2*e^8 + 170*e^6 - 242*e^4 + 210*e^2 - 66, 6*e^15 - 125*e^13 + 1025*e^11 - 8397/2*e^9 + 8939*e^7 - 18425/2*e^5 + 3616*e^3 - 304*e, 11/2*e^15 - 225/2*e^13 + 1807/2*e^11 - 7233/2*e^9 + 7507*e^7 - 7525*e^5 + 2880*e^3 - 256*e, -e^12 + 31/2*e^10 - 84*e^8 + 385/2*e^6 - 189*e^4 + 98*e^2 - 36, 3*e^12 - 89/2*e^10 + 228*e^8 - 971/2*e^6 + 417*e^4 - 122*e^2 + 4, -11/2*e^15 + 227/2*e^13 - 1839/2*e^11 + 7423/2*e^9 - 7781*e^7 + 7957*e^5 - 3224*e^3 + 288*e, -2*e^15 + 75/2*e^13 - 547/2*e^11 + 998*e^9 - 3903/2*e^7 + 4075/2*e^5 - 1094*e^3 + 306*e] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([9, 3, -1/3*w^3 + 1/3*w^2 + 3*w - 5/3])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]