/* 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([14,14,1/3*w^3 - 1/3*w^2 - 3*w + 2/3]) 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^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, e, -1, 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, -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, -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, -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, -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, -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, -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, 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, 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, -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, 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, 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, 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, -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, 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, 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, -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, -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, -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, 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, -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, 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, -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, 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, -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, 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, 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, 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, -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, -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, -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, 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, 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, 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, -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, -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, 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, 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, -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, -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, 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, -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, 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, -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, -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, 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, -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, 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, 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, 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, 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, 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, -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, -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, -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, 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, -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, 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, -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, -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, -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, -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, -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, 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, -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, 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, 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, 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, -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, 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, 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, 336/3361*e^6 + 3153/6722*e^5 - 12015/6722*e^4 - 30743/3361*e^3 + 22041/6722*e^2 + 75787/3361*e - 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61504/3361*e^2 - 177666/3361*e - 29660/3361, 608/3361*e^6 + 4265/6722*e^5 - 27023/6722*e^4 - 41546/3361*e^3 + 131591/6722*e^2 + 95526/3361*e - 92701/3361, -1957/6722*e^6 - 8597/6722*e^5 + 18988/3361*e^4 + 163345/6722*e^3 - 44105/3361*e^2 - 183461/3361*e + 104920/3361, 699/6722*e^6 + 3853/3361*e^5 + 91/6722*e^4 - 146571/6722*e^3 - 200835/6722*e^2 + 179617/3361*e + 179724/3361, 43/6722*e^6 + 1027/6722*e^5 - 692/3361*e^4 - 26211/6722*e^3 - 8305/3361*e^2 + 67143/3361*e + 170076/3361, -1086/3361*e^6 - 144/3361*e^5 + 29170/3361*e^4 - 684/3361*e^3 - 197518/3361*e^2 - 8304/3361*e + 249396/3361, -1451/3361*e^6 - 9985/6722*e^5 + 54557/6722*e^4 + 95181/3361*e^3 - 74987/6722*e^2 - 201075/3361*e - 128837/3361, 1803/6722*e^6 + 3043/6722*e^5 - 23388/3361*e^4 - 70411/6722*e^3 + 144195/3361*e^2 + 192491/3361*e - 184242/3361, 2515/6722*e^6 + 3732/3361*e^5 - 48823/6722*e^4 - 142679/6722*e^3 + 103481/6722*e^2 + 168158/3361*e + 83715/3361, 1845/6722*e^6 - 331/6722*e^5 - 25549/3361*e^4 + 16073/6722*e^3 + 172507/3361*e^2 - 84046/3361*e - 271994/3361, -1276/3361*e^6 - 2806/3361*e^5 + 25515/3361*e^4 + 45489/3361*e^3 - 56436/3361*e^2 - 28493/3361*e - 47862/3361, -1828/3361*e^6 - 2155/3361*e^5 + 43907/3361*e^4 + 37658/3361*e^3 - 228787/3361*e^2 - 98504/3361*e + 275772/3361, 1805/6722*e^6 + 5123/6722*e^5 - 20450/3361*e^4 - 100863/6722*e^3 + 94488/3361*e^2 + 126987/3361*e - 186180/3361, -1275/6722*e^6 + 1595/6722*e^5 + 19268/3361*e^4 - 36957/6722*e^3 - 135416/3361*e^2 + 31985/3361*e + 69208/3361, 805/3361*e^6 + 311/3361*e^5 - 21220/3361*e^4 + 637/3361*e^3 + 133010/3361*e^2 - 67211/3361*e - 121582/3361, 1346/3361*e^6 + 6689/6722*e^5 - 46391/6722*e^4 - 55955/3361*e^3 + 249/6722*e^2 + 74671/3361*e + 174360/3361, 1207/3361*e^6 + 6615/6722*e^5 - 49793/6722*e^4 - 63693/3361*e^3 + 152969/6722*e^2 + 162164/3361*e + 53866/3361, -5311/6722*e^6 - 5700/3361*e^5 + 115679/6722*e^4 + 204647/6722*e^3 - 429437/6722*e^2 - 204343/3361*e + 91415/3361, -191/6722*e^6 - 341/6722*e^5 - 1616/3361*e^4 + 901/6722*e^3 + 66826/3361*e^2 + 24338/3361*e - 208158/3361, 3767/6722*e^6 + 8837/6722*e^5 - 42176/3361*e^4 - 162205/6722*e^3 + 190778/3361*e^2 + 166854/3361*e - 218642/3361, -943/6722*e^6 + 4053/6722*e^5 + 16270/3361*e^4 - 90821/6722*e^3 - 142245/3361*e^2 + 189123/3361*e + 211318/3361, 1523/3361*e^6 + 889/3361*e^5 - 35888/3361*e^4 - 8381/3361*e^3 + 177536/3361*e^2 - 55166/3361*e - 222442/3361, -1679/6722*e^6 - 1801/6722*e^5 + 24050/3361*e^4 + 30937/6722*e^3 - 174241/3361*e^2 - 69294/3361*e + 191804/3361, -2583/3361*e^6 - 4242/3361*e^5 + 57421/3361*e^4 + 68917/3361*e^3 - 235650/3361*e^2 - 63128/3361*e + 246678/3361, -2673/6722*e^6 - 1867/3361*e^5 + 68603/6722*e^4 + 61247/6722*e^3 - 423727/6722*e^2 - 41564/3361*e + 240798/3361, 827/3361*e^6 - 336/3361*e^5 - 23804/3361*e^4 + 11848/3361*e^3 + 172113/3361*e^2 - 36181/3361*e - 251604/3361, 725/6722*e^6 + 568/3361*e^5 - 24351/6722*e^4 - 31575/6722*e^3 + 234337/6722*e^2 + 91012/3361*e - 255512/3361, -575/3361*e^6 - 3103/3361*e^5 + 4594/3361*e^4 + 60043/3361*e^3 + 103772/3361*e^2 - 153172/3361*e - 297270/3361, 343/3361*e^6 + 4269/6722*e^5 - 4493/6722*e^4 - 39856/3361*e^3 - 162985/6722*e^2 + 74355/3361*e + 256180/3361, 1894/3361*e^6 + 3575/3361*e^5 - 44937/3361*e^4 - 61162/3361*e^3 + 235183/3361*e^2 + 90764/3361*e - 296128/3361, 1647/6722*e^6 + 2131/6722*e^5 - 24004/3361*e^4 - 47855/6722*e^3 + 183079/3361*e^2 + 112419/3361*e - 234738/3361, -2797/6722*e^6 - 8337/6722*e^5 + 31959/3361*e^4 + 147775/6722*e^3 - 156610/3361*e^2 - 127790/3361*e + 219792/3361, 1939/3361*e^6 + 3321/3361*e^5 - 40445/3361*e^4 - 53966/3361*e^3 + 129242/3361*e^2 + 46988/3361*e - 13628/3361, -3147/6722*e^6 - 9349/6722*e^5 + 32042/3361*e^4 + 173217/6722*e^3 - 92294/3361*e^2 - 189459/3361*e + 1016/3361, 580/3361*e^6 + 1581/3361*e^5 - 13431/3361*e^4 - 31982/3361*e^3 + 57735/3361*e^2 + 60922/3361*e + 25422/3361, -97/3361*e^6 + 3311/3361*e^5 + 10782/3361*e^4 - 65777/3361*e^3 - 156062/3361*e^2 + 189814/3361*e + 201430/3361, 523/6722*e^6 + 3080/3361*e^5 + 597/6722*e^4 - 128707/6722*e^3 - 170837/6722*e^2 + 189937/3361*e + 229272/3361, 1683/6722*e^6 + 5961/6722*e^5 - 18174/3361*e^4 - 105285/6722*e^3 + 64744/3361*e^2 + 66004/3361*e + 12702/3361, -847/6722*e^6 - 3659/6722*e^5 + 2688/3361*e^4 + 67485/6722*e^3 + 86677/3361*e^2 - 67970/3361*e - 211084/3361, 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, 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, -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, 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, -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, 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, 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, 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, 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, -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, 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, -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, -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, -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, 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, -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, 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, -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, -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, 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, -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, 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, 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, -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, 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, 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, -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, -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, -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, 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, -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, 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, -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, 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, 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, -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, 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, 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, -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, 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, -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, 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, -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, 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, -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, 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, 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, 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, -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, -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, -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, -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, 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, -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] 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([7,7,-1/3*w^3 + 1/3*w^2 + w - 5/3])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]