/* 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([7, 7, -2/3*w^3 + 2/3*w^2 + 5*w - 7/3]) 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^5 + 3*x^4 - x^3 - 7*x^2 - 2*x + 1 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 1, e^4 + 2*e^3 - 3*e^2 - 4*e, -2*e^3 - 2*e^2 + 5*e + 1, e^4 + 3*e^3 - e^2 - 7*e - 2, e^4 + 3*e^3 - 6*e - 3, -2*e^4 - 3*e^3 + 7*e^2 + 8*e - 3, -3*e^4 - 10*e^3 + e^2 + 19*e + 4, 2*e^4 + 7*e^3 - 4*e^2 - 18*e + 1, 2*e^4 + e^3 - 8*e^2 + e + 4, -5*e^4 - 10*e^3 + 12*e^2 + 16*e - 4, -3*e^4 - 6*e^3 + 4*e^2 + 9*e + 7, -3*e^4 - 4*e^3 + 13*e^2 + 11*e - 8, -3*e^4 - e^3 + 13*e^2 - 2*e - 8, -2*e^3 - e^2 + 8*e, -3*e^4 - 6*e^3 + 6*e^2 + 10*e - 4, 6*e^4 + 9*e^3 - 19*e^2 - 19*e + 5, 6*e^4 + 17*e^3 - 9*e^2 - 32*e + 2, -e^4 - 2*e^3 + 2*e^2 + 3*e + 1, 3*e^4 + 6*e^3 - 8*e^2 - 10*e - 9, 10*e^4 + 19*e^3 - 21*e^2 - 34*e - 6, -5*e^4 - 8*e^3 + 9*e^2 + 5*e, 8*e^4 + 17*e^3 - 19*e^2 - 36*e, 4*e^4 + 4*e^3 - 19*e^2 - 8*e + 7, -e^3 + 3*e^2 + 13*e - 4, -2*e^4 - 6*e^3 + 5*e^2 + 21*e + 4, -4*e^4 - 11*e^3 + 6*e^2 + 20*e - 9, 2*e^4 + 4*e^3 - 4*e^2 - 7*e - 10, 2*e^3 + 2*e^2 - 7*e + 3, -4*e^4 - 14*e^3 - 3*e^2 + 23*e + 10, e^4 - 3*e^3 - 12*e^2 + 11*e + 11, 10*e^4 + 20*e^3 - 28*e^2 - 45*e + 6, 2*e^4 + 12*e^3 + 10*e^2 - 21*e - 14, 7*e^4 + 16*e^3 - 9*e^2 - 26*e - 2, -2*e^4 - 9*e^3 - e^2 + 30*e + 11, -6*e^4 - 12*e^3 + 23*e^2 + 36*e - 14, -e^4 - 7*e^3 - 7*e^2 + 18*e + 18, 5*e^4 + 10*e^3 - 11*e^2 - 28*e - 3, -3*e^4 - 11*e^3 - e^2 + 20*e - 4, 3*e^4 - 15*e^2 + 11*e + 11, 12*e^4 + 29*e^3 - 18*e^2 - 56*e - 5, -8*e^4 - 11*e^3 + 21*e^2 + 6*e - 10, 9*e^4 + 14*e^3 - 23*e^2 - 21*e + 8, -2*e^4 - e^3 + 6*e^2 - 4*e - 18, 9*e^4 + 10*e^3 - 38*e^2 - 16*e + 32, -4*e^4 - 9*e^3 + 13*e^2 + 27*e - 1, -2*e^4 - 4*e^3 + 2*e^2 + 9*e + 3, -9*e^4 - 16*e^3 + 24*e^2 + 32*e + 3, 11*e^4 + 20*e^3 - 24*e^2 - 34*e + 2, -8*e^4 - 19*e^3 + 6*e^2 + 26*e + 19, 10*e^4 + 25*e^3 - 21*e^2 - 60*e - 1, 5*e^4 + 10*e^3 - 14*e^2 - 36*e - 1, e^4 + 5*e^3 + 10*e^2 - 4*e - 22, 3*e^4 + 12*e^3 - e^2 - 33*e - 16, -5*e^4 - 12*e^3 + 8*e^2 + 17*e - 9, 12*e^4 + 29*e^3 - 25*e^2 - 65*e - 6, -13*e^4 - 19*e^3 + 44*e^2 + 42*e - 10, -7*e^4 - 22*e^3 + 8*e^2 + 53*e + 4, -9*e^4 - 8*e^3 + 34*e^2 + 6*e - 29, -5*e^4 - 6*e^3 + 17*e^2 - 2*e - 25, -13*e^4 - 27*e^3 + 25*e^2 + 44*e + 3, -6*e^4 - 14*e^3 + 16*e^2 + 27*e - 13, -11*e^4 - 21*e^3 + 22*e^2 + 45*e + 15, -13*e^4 - 25*e^3 + 30*e^2 + 44*e + 3, -14*e^4 - 32*e^3 + 21*e^2 + 64*e + 12, -17*e^4 - 36*e^3 + 38*e^2 + 69*e, -e^4 + 4*e^3 + 14*e^2 - 6*e - 15, 6*e^4 + 6*e^3 - 33*e^2 - 12*e + 18, -6*e^4 - 7*e^3 + 12*e^2 + 3*e - 5, -10*e^4 - 25*e^3 + 19*e^2 + 56*e + 2, 10*e^4 + 20*e^3 - 25*e^2 - 28*e + 17, 8*e^4 + 17*e^3 - 11*e^2 - 28*e - 6, -7*e^3 - 6*e^2 + 19*e + 14, 6*e^4 + 11*e^3 - 24*e^2 - 22*e + 9, -5*e^4 - 6*e^3 + 24*e^2 + 11*e - 29, 5*e^4 + 11*e^3 - 7*e^2 - 17*e - 26, 3*e^4 + 13*e^3 + 8*e^2 - 33*e - 12, 2*e^4 + 3*e^3 + 2*e^2 + 6*e - 14, -2*e^3 - 7*e^2 + 10*e + 24, -17*e^4 - 36*e^3 + 38*e^2 + 74*e - 9, -2*e^4 + 16*e^3 + 24*e^2 - 47*e - 12, 3*e^4 + 12*e^3 + 4*e^2 - 26*e - 21, 6*e^4 + 14*e^3 - 3*e^2 - 18*e - 8, 8*e^4 + 8*e^3 - 30*e^2 - 16*e + 13, 5*e^4 + 9*e^3 - 5*e^2 - 4*e + 5, -7*e^4 - 11*e^3 + 29*e^2 + 30*e - 19, -5*e^4 - 16*e^3 + 2*e^2 + 39*e + 9, 4*e^4 + 25*e^3 + 14*e^2 - 49*e - 14, -17*e^4 - 28*e^3 + 54*e^2 + 47*e - 31, 2*e^4 + 4*e^3 + 14*e^2 + 4*e - 38, -4*e^4 - 8*e^3 + 12*e^2 + 6*e - 15, -2*e^4 - 11*e^3 - 11*e^2 + 20*e + 29, 2*e^4 + 13*e^3 + 12*e^2 - 42*e - 29, 16*e^4 + 30*e^3 - 29*e^2 - 47*e - 16, 5*e^4 + 21*e^3 - 7*e^2 - 54*e + 5, -8*e^4 - 13*e^3 + 23*e^2 + 18*e - 8, 5*e^4 + 19*e^3 - 3*e^2 - 56*e - 19, 16*e^4 + 28*e^3 - 53*e^2 - 65*e + 16, -11*e^4 - 24*e^3 + 21*e^2 + 31*e - 2, 5*e^4 + 13*e^3 - 5*e^2 - 10*e - 16, -6*e^4 - 14*e^3 + 7*e^2 + 17*e + 6, -e^4 - 9*e^3 - 15*e^2 + 10*e + 14, 2*e^4 - 3*e^3 - 16*e^2 + 5*e - 15, 9*e^4 + 32*e^3 - 11*e^2 - 71*e - 5, -3*e^4 - 14*e^3 - 10*e^2 + 36*e + 15, 13*e^4 + 24*e^3 - 40*e^2 - 44*e + 26, -9*e^4 - 15*e^3 + 22*e^2 + 6*e - 6, 15*e^4 + 31*e^3 - 36*e^2 - 56*e + 9, -3*e^4 - 17*e^3 + 47*e - 2, 10*e^4 + 20*e^3 - 15*e^2 - 33*e - 27, -10*e^4 - 34*e^3 + 12*e^2 + 80*e + 17, -9*e^4 - 13*e^3 + 15*e^2 + 12*e + 23, e^4 - 2*e^3 - 7*e^2 + 2*e - 12, -16*e^4 - 31*e^3 + 53*e^2 + 74*e - 20, 2*e^4 + 5*e^3 - 13*e^2 - 22*e + 9, 8*e^4 + 2*e^3 - 43*e^2 + 4*e + 31, 7*e^4 + 14*e^3 - 17*e^2 - 30*e + 11, -8*e^4 - 17*e^3 + 14*e^2 + 42*e - 5, 8*e^4 + 16*e^3 - 8*e^2 - 22*e - 24, 5*e^4 + 24*e^3 - 12*e^2 - 76*e + 8, -17*e^4 - 31*e^3 + 35*e^2 + 47*e - 7, -8*e^4 - 15*e^3 + 41*e^2 + 38*e - 38, -13*e^4 - 32*e^3 + 28*e^2 + 75*e + 7, 5*e^4 + 13*e^3 - 3*e^2 - 18*e + 1, -4*e^4 - 9*e^3 - e^2 - 3*e + 29, 3*e^4 - 4*e^3 - 19*e^2 + 31*e + 17, -5*e^4 + 5*e^3 + 34*e^2 - 2*e - 22, -16*e^4 - 26*e^3 + 44*e^2 + 46*e - 32, -9*e^4 - 23*e^3 + 21*e^2 + 53*e - 14, -19*e^4 - 38*e^3 + 44*e^2 + 68*e - 8, -22*e^4 - 39*e^3 + 46*e^2 + 70*e + 20, -12*e^4 - 35*e^3 + 29*e^2 + 96*e - 5, 8*e^4 + 25*e^3 - e^2 - 35*e - 9, -3*e^4 - 5*e^3 + 20*e^2 + 9*e - 32, 6*e^4 + 3*e^3 - 34*e^2 - 13*e + 42, 5*e^4 + 3*e^3 - 26*e^2 + 27, 8*e^4 - 3*e^3 - 38*e^2 + 26*e + 19, -13*e^4 - 41*e^3 + 15*e^2 + 103*e + 16, e^4 + 5*e^3 + 23*e^2 + 4*e - 46, 13*e^4 + 27*e^3 - 38*e^2 - 50*e + 15, -2*e^4 - 14*e^3 - 10*e^2 + 40*e + 11, 25*e^4 + 47*e^3 - 65*e^2 - 87*e + 10, -12*e^4 - 33*e^3 + 29*e^2 + 68*e - 11, 5*e^4 + 32*e^3 + 8*e^2 - 88*e - 17, 5*e^4 + 6*e^3 - 19*e^2 - 11*e + 24, 6*e^4 + 25*e^3 - 10*e^2 - 81*e + 1, 3*e^4 + 19*e^3 - 7*e^2 - 76*e - 4, 15*e^4 + 21*e^3 - 45*e^2 - 49*e - 14, -5*e^4 - 8*e^3 + 8*e^2 - 8*e - 2, 16*e^4 + 16*e^3 - 60*e^2 - 33*e + 26, -e^4 + 16*e^3 + 28*e^2 - 23*e - 27, -28*e^4 - 55*e^3 + 71*e^2 + 108*e - 9, 3*e^4 + 29*e^3 + 27*e^2 - 56*e - 26, -22*e^4 - 54*e^3 + 37*e^2 + 98*e, 26*e^4 + 56*e^3 - 65*e^2 - 111*e + 21, 13*e^4 + 34*e^3 - 24*e^2 - 68*e + 14, -7*e^4 - 10*e^3 + 23*e^2 + 19*e + 18, -31*e^4 - 60*e^3 + 81*e^2 + 125*e - 10, 15*e^4 + 31*e^3 - 26*e^2 - 48*e - 16, -13*e^3 + 5*e^2 + 55*e - 26, 9*e^4 + 19*e^3 - 23*e^2 - 35*e + 7, 3*e^4 + 19*e^3 + 7*e^2 - 59*e - 8, 7*e^4 + 13*e^3 - 16*e^2 - 27*e - 17, 11*e^3 + 24*e^2 - 25*e - 48, 14*e^4 + 31*e^3 - 37*e^2 - 67*e + 16, 32*e^4 + 64*e^3 - 79*e^2 - 150*e - 4, 13*e^4 + 30*e^3 - 23*e^2 - 59*e - 6, -4*e^4 - 10*e^3 + 6*e^2 + 29*e + 8, 14*e^4 + 36*e^3 - 18*e^2 - 61*e + 8, 11*e^4 + 5*e^3 - 69*e^2 - 25*e + 69, -2*e^4 - 7*e^3 - 5*e^2 - 15*e + 10, -5*e^4 + 13*e^3 + 46*e^2 - 27*e - 31, 13*e^4 + 14*e^3 - 33*e^2 - 10*e + 4, 13*e^4 + 23*e^3 - 15*e^2 - 31*e - 38, 20*e^4 + 43*e^3 - 39*e^2 - 105*e - 24, -18*e^4 - 44*e^3 + 26*e^2 + 71*e + 12, -7*e^4 - 17*e^3 - 2*e^2 + 32*e + 39, 10*e^4 + 2*e^3 - 45*e^2 + e + 8, 8*e^4 + 13*e^3 - 6*e^2 - 10*e - 53, -e^4 + 14*e^3 + 21*e^2 - 30*e - 31, 9*e^4 + 16*e^3 - 23*e^2 - 45*e + 13, 12*e^4 + 22*e^3 - 35*e^2 - 39*e + 6, 6*e^4 - 9*e^3 - 26*e^2 + 57*e + 33, -9*e^4 - 12*e^3 + 45*e^2 + 31*e - 35, 8*e^4 + 35*e^3 - 14*e^2 - 103*e - 6, 2*e^4 + e^3 - 14*e^2 + 15*e + 31, -10*e^4 - 15*e^3 + 21*e^2 + 6*e - 5, 21*e^4 + 58*e^3 - 31*e^2 - 113*e + 8, -16*e^4 - 34*e^3 + 40*e^2 + 88*e + 2, -8*e^3 - 9*e^2 + 4*e - 8, 18*e^4 + 35*e^3 - 52*e^2 - 81*e - 3, 5*e^4 + 8*e^3 + 3*e^2 + 8*e - 27, -11*e^4 - 25*e^3 + 21*e^2 + 37*e - 20, 21*e^4 + 39*e^3 - 61*e^2 - 81*e + 5, 16*e^4 + 23*e^3 - 40*e^2 - 35*e - 19, -20*e^4 - 32*e^3 + 63*e^2 + 66*e - 27, -15*e^4 - 50*e^3 + 6*e^2 + 108*e + 1, -6*e^4 - 23*e^3 + 12*e^2 + 62*e - 1, -24*e^4 - 30*e^3 + 84*e^2 + 66*e - 29, -3*e^4 + 3*e^3 + 13*e^2 + 17, -6*e^4 - 19*e^3 - 16*e^2 + 29*e + 36, 32*e^4 + 63*e^3 - 94*e^2 - 141*e + 10, -23*e^4 - 60*e^3 + 44*e^2 + 126*e, -3*e^4 - 27*e^3 - 13*e^2 + 77*e + 29, 15*e^4 + 31*e^3 - 34*e^2 - 82*e - 22, 12*e^4 + 13*e^3 - 59*e^2 - 38*e + 24, -4*e^4 - 17*e^3 - 5*e^2 + 50*e - 3, 5*e^4 + 13*e^3 - 14*e^2 - 43*e - 6, 27*e^4 + 44*e^3 - 81*e^2 - 71*e + 55, -7*e^4 - 6*e^3 + 19*e^2 - 17*e - 9, -e^4 + 5*e^3 + 21*e^2 - 27*e - 40, 20*e^4 + 59*e^3 - 29*e^2 - 122*e - 25, 10*e^4 + 32*e^3 - 9*e^2 - 50*e, -5*e^4 - 20*e^3 + 7*e^2 + 52*e - 34, 16*e^4 + 16*e^3 - 54*e^2 - 6*e + 28, 3*e^4 + 11*e^3 + 17*e^2 - 16*e - 61, -12*e^4 - 29*e^3 + 18*e^2 + 52*e + 27, 2*e^4 - 8*e^3 - 22*e^2 + e + 22, -10*e^4 - 22*e^3 + 15*e^2 + 50*e - 6, -3*e^4 - 3*e^3 + 3*e^2 + e, -25*e^4 - 41*e^3 + 62*e^2 + 85*e + 32, -4*e^4 + 4*e^3 + 38*e^2 + 2*e - 37, 22*e^4 + 22*e^3 - 88*e^2 - 49*e + 50, -15*e^4 - 24*e^3 + 55*e^2 + 56*e + 2, -4*e^4 - 31*e^3 - 7*e^2 + 90*e - 11, -e^3 - 10*e^2 - 33*e + 23, -19*e^4 - 47*e^3 + 45*e^2 + 121*e + 2, 8*e^4 + 11*e^3 - 38*e^2 - 29*e + 5, -12*e^4 - 29*e^3 + 22*e^2 + 76*e + 12, 17*e^4 + 14*e^3 - 74*e^2 - 43*e + 41, -6*e^4 + 12*e^3 + 33*e^2 - 50*e - 1, e^4 - 8*e^3 - e^2 + 58*e - 9, 33*e^4 + 76*e^3 - 50*e^2 - 142*e - 29, -20*e^4 - 55*e^3 + 27*e^2 + 131*e + 7, 7*e^4 + 22*e^3 + 9*e^2 - 51*e - 47, -6*e^4 - e^3 + 31*e^2 + 22*e, 19*e^4 + 50*e^3 - 14*e^2 - 86*e - 17, -21*e^4 - 43*e^3 + 53*e^2 + 70*e - 46, -6*e^4 - 6*e^3 + 18*e^2 - 6*e - 16, -10*e^4 + 4*e^3 + 69*e^2 - 2*e - 48, 10*e^4 + 26*e^3 - 21*e^2 - 65*e - 2, 20*e^4 + 42*e^3 - 43*e^2 - 94*e - 23, -5*e^4 - 26*e^3 + 5*e^2 + 83*e + 7, 5*e^4 + 10*e^3 - 16*e^2 - 17*e - 23, -2*e^4 - e^3 + 2*e^2 + e + 20, 13*e^4 + 22*e^3 - 16*e^2 - 12*e - 44, 2*e^4 - e^3 - 18*e^2 + 11*e + 41, -12*e^4 - 7*e^3 + 36*e^2 - 5*e + 15, -12*e^4 - 19*e^3 + 13*e^2 + 25*e + 54, -6*e^4 + 4*e^3 + 31*e^2 - e - 11, 10*e^4 + 26*e^3 - 39*e^2 - 41*e + 74, -5*e^4 + 19*e^3 + 62*e^2 - 41*e - 49, 14*e^4 + 19*e^3 - 34*e^2 - 26*e - 11, 3*e^4 + 18*e^3 - 11*e^2 - 57*e + 16, -10*e^4 - 37*e^3 + 17*e^2 + 108*e + 17, 2*e^4 + 4*e^3 - 10*e^2 + 8*e + 26, -14*e^4 - 30*e^3 + 34*e^2 + 77*e + 34, -26*e^4 - 60*e^3 + 54*e^2 + 117*e, -3*e^4 + 3*e^3 + 5*e^2 - 25*e + 19, -6*e^4 - 18*e^3 + 16*e^2 + 38*e - 13, -2*e^4 - 10*e^3 + 11*e - 45, -22*e^4 - 37*e^3 + 79*e^2 + 82*e - 32, -15*e^4 - 19*e^3 + 50*e^2 + 38*e + 23, -7*e^4 - 18*e^3 + 26*e^2 + 28*e - 47, -18*e^4 - 64*e^3 + 23*e^2 + 147*e + 5, -9*e^4 - 30*e^3 + 6*e^2 + 63*e + 1, -7*e^4 - 8*e^3 + 31*e^2 + 25*e + 8, 11*e^4 + 40*e^3 - 7*e^2 - 85*e - 30, -11*e^4 - 22*e^3 + 37*e^2 + 52*e - 29, 37*e^4 + 88*e^3 - 75*e^2 - 190*e - 12, 26*e^4 + 60*e^3 - 56*e^2 - 142*e - 26, -11*e^4 - 16*e^3 + 72*e^2 + 54*e - 62, -27*e^4 - 76*e^3 + 27*e^2 + 133*e + 43, -23*e^4 - 42*e^3 + 69*e^2 + 100*e - 30, 23*e^4 + 45*e^3 - 42*e^2 - 89*e - 30, -23*e^4 - 35*e^3 + 61*e^2 + 55*e - 44, 27*e^4 + 40*e^3 - 92*e^2 - 99*e + 20, -6*e^4 - 42*e^3 - 29*e^2 + 87*e + 52, 2*e^4 - 12*e^3 - 8*e^2 + 29*e - 50, 25*e^4 + 49*e^3 - 52*e^2 - 94*e - 45, 17*e^4 + 38*e^3 - 19*e^2 - 52*e - 15, -22*e^4 - 50*e^3 + 52*e^2 + 116*e - 1, -17*e^4 - 26*e^3 + 64*e^2 + 80*e - 29, 42*e^4 + 101*e^3 - 82*e^2 - 210*e - 8, 13*e^3 + e^2 - 58*e - 3, 8*e^4 + 35*e^3 + 10*e^2 - 60*e - 13, -25*e^4 - 71*e^3 + 19*e^2 + 141*e + 41, -5*e^4 - 41*e^3 - 29*e^2 + 112*e + 32, -11*e^4 - 33*e^3 + 22*e^2 + 86*e, 3*e^4 + 19*e^3 + 4*e^2 - 61*e + 12, 28*e^4 + 42*e^3 - 92*e^2 - 69*e + 68, 4*e^4 + 5*e^3 - 25*e^2 - 38*e + 23, 14*e^4 + 18*e^3 - 72*e^2 - 53*e + 78, 6*e^4 + 6*e^3 + 10*e^2 + 21*e - 69, -21*e^3 - 31*e^2 + 73*e + 54, 8*e^4 + 9*e^3 - 51*e^2 - 2*e + 78, 18*e^4 + 67*e^3 - 8*e^2 - 135*e + 9, 20*e^4 + 51*e^3 - 10*e^2 - 91*e - 42] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} 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]