/* 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([-1, 10, -9, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([1, 1, 1]) primes_array = [ [4, 2, -2/5*w^3 + 3/5*w^2 + 17/5*w - 9/5],\ [9, 3, -2/5*w^3 + 3/5*w^2 + 22/5*w - 9/5],\ [9, 3, 2/5*w^3 - 3/5*w^2 - 22/5*w + 14/5],\ [17, 17, w + 1],\ [17, 17, -4/5*w^3 + 6/5*w^2 + 39/5*w - 13/5],\ [17, 17, -4/5*w^3 + 6/5*w^2 + 39/5*w - 28/5],\ [17, 17, -w + 2],\ [23, 23, -1/5*w^3 + 4/5*w^2 + 6/5*w - 22/5],\ [23, 23, -1/5*w^3 - 1/5*w^2 + 11/5*w + 3/5],\ [23, 23, -1/5*w^3 + 4/5*w^2 + 6/5*w - 12/5],\ [23, 23, -1/5*w^3 - 1/5*w^2 + 11/5*w + 13/5],\ [25, 5, -4/5*w^3 + 6/5*w^2 + 39/5*w - 33/5],\ [25, 5, -w^3 + w^2 + 10*w - 2],\ [49, 7, -4/5*w^3 + 6/5*w^2 + 34/5*w - 23/5],\ [49, 7, 4/5*w^3 - 6/5*w^2 - 34/5*w + 13/5],\ [79, 79, 3/5*w^3 - 7/5*w^2 - 28/5*w + 21/5],\ [79, 79, 1/5*w^3 + 1/5*w^2 - 16/5*w - 13/5],\ [79, 79, -1/5*w^3 + 4/5*w^2 + 11/5*w - 27/5],\ [79, 79, 3/5*w^3 - 2/5*w^2 - 33/5*w + 11/5],\ [103, 103, -1/5*w^3 + 4/5*w^2 + 1/5*w - 17/5],\ [103, 103, -w^3 + 2*w^2 + 9*w - 7],\ [103, 103, w^3 - w^2 - 10*w + 3],\ [103, 103, 1/5*w^3 + 1/5*w^2 - 6/5*w - 13/5],\ [113, 113, w^2 - 7],\ [113, 113, -7/5*w^3 + 13/5*w^2 + 67/5*w - 49/5],\ [113, 113, 7/5*w^3 - 8/5*w^2 - 72/5*w + 24/5],\ [113, 113, -3/5*w^3 + 2/5*w^2 + 33/5*w + 19/5],\ [121, 11, 6/5*w^3 - 9/5*w^2 - 61/5*w + 32/5],\ [121, 11, -2/5*w^3 + 3/5*w^2 + 27/5*w - 14/5],\ [127, 127, -1/5*w^3 - 1/5*w^2 + 6/5*w - 12/5],\ [127, 127, -w^3 + w^2 + 10*w + 2],\ [127, 127, -w^3 + 2*w^2 + 9*w - 12],\ [127, 127, 1/5*w^3 - 4/5*w^2 - 1/5*w - 8/5],\ [169, 13, -4/5*w^3 + 6/5*w^2 + 44/5*w - 23/5],\ [191, 191, 2/5*w^3 + 2/5*w^2 - 27/5*w - 26/5],\ [191, 191, -2/5*w^3 + 8/5*w^2 + 17/5*w - 24/5],\ [191, 191, -2/5*w^3 - 2/5*w^2 + 27/5*w + 1/5],\ [191, 191, 2/5*w^3 - 8/5*w^2 - 17/5*w + 49/5],\ [199, 199, -w - 4],\ [199, 199, 4/5*w^3 - 6/5*w^2 - 39/5*w - 2/5],\ [199, 199, -4/5*w^3 + 6/5*w^2 + 39/5*w - 43/5],\ [199, 199, w - 5],\ [233, 233, -w^3 + 2*w^2 + 9*w - 6],\ [233, 233, 1/5*w^3 + 1/5*w^2 - 6/5*w - 18/5],\ [233, 233, -1/5*w^3 + 4/5*w^2 + 1/5*w - 22/5],\ [233, 233, w^3 - w^2 - 10*w + 4],\ [257, 257, -9/5*w^3 + 16/5*w^2 + 79/5*w - 63/5],\ [257, 257, w^3 - w^2 - 8*w + 3],\ [257, 257, 2/5*w^3 - 8/5*w^2 - 17/5*w + 59/5],\ [257, 257, -9/5*w^3 + 11/5*w^2 + 84/5*w - 23/5],\ [263, 263, 7/5*w^3 - 13/5*w^2 - 57/5*w + 39/5],\ [263, 263, -7/5*w^3 + 8/5*w^2 + 77/5*w - 14/5],\ [263, 263, -7/5*w^3 + 13/5*w^2 + 72/5*w - 64/5],\ [263, 263, -7/5*w^3 + 8/5*w^2 + 62/5*w - 24/5],\ [311, 311, 1/5*w^3 + 1/5*w^2 - 11/5*w - 33/5],\ [311, 311, 1/5*w^3 - 4/5*w^2 - 6/5*w - 8/5],\ [311, 311, -1/5*w^3 - 1/5*w^2 + 11/5*w - 17/5],\ [311, 311, -1/5*w^3 + 4/5*w^2 + 6/5*w - 42/5],\ [313, 313, -9/5*w^3 + 11/5*w^2 + 94/5*w - 33/5],\ [313, 313, -11/5*w^3 + 19/5*w^2 + 96/5*w - 52/5],\ [313, 313, -11/5*w^3 + 19/5*w^2 + 101/5*w - 67/5],\ [313, 313, -9/5*w^3 + 16/5*w^2 + 89/5*w - 63/5],\ [337, 337, -4/5*w^3 + 1/5*w^2 + 44/5*w + 2/5],\ [337, 337, w^2 - 2*w - 5],\ [337, 337, w^2 - 6],\ [337, 337, -4/5*w^3 + 11/5*w^2 + 34/5*w - 43/5],\ [361, 19, 2/5*w^3 + 2/5*w^2 - 17/5*w - 26/5],\ [361, 19, 12/5*w^3 - 18/5*w^2 - 112/5*w + 59/5],\ [367, 367, -3/5*w^3 + 7/5*w^2 + 18/5*w - 31/5],\ [367, 367, 7/5*w^3 - 8/5*w^2 - 67/5*w + 29/5],\ [367, 367, -7/5*w^3 + 13/5*w^2 + 62/5*w - 39/5],\ [367, 367, 3/5*w^3 - 2/5*w^2 - 23/5*w - 9/5],\ [433, 433, w^3 - w^2 - 11*w + 9],\ [433, 433, 2/5*w^3 - 3/5*w^2 - 32/5*w + 19/5],\ [433, 433, 1/5*w^3 + 1/5*w^2 - 6/5*w - 38/5],\ [433, 433, w^3 - 2*w^2 - 10*w + 2],\ [439, 439, -11/5*w^3 + 14/5*w^2 + 111/5*w - 47/5],\ [439, 439, -1/5*w^3 + 4/5*w^2 + 21/5*w - 27/5],\ [439, 439, -3/5*w^3 + 7/5*w^2 + 28/5*w - 56/5],\ [439, 439, -11/5*w^3 + 19/5*w^2 + 106/5*w - 67/5],\ [503, 503, -2/5*w^3 + 8/5*w^2 + 17/5*w - 34/5],\ [503, 503, -2/5*w^3 + 8/5*w^2 + 17/5*w - 39/5],\ [503, 503, 2/5*w^3 + 2/5*w^2 - 27/5*w - 16/5],\ [503, 503, 2/5*w^3 + 2/5*w^2 - 27/5*w - 11/5],\ [521, 521, -2/5*w^3 + 8/5*w^2 + 12/5*w - 39/5],\ [521, 521, -2/5*w^3 + 8/5*w^2 + 12/5*w - 29/5],\ [521, 521, 2/5*w^3 + 2/5*w^2 - 22/5*w - 11/5],\ [521, 521, 2/5*w^3 + 2/5*w^2 - 22/5*w - 21/5],\ [569, 569, 2*w^3 - 4*w^2 - 17*w + 14],\ [569, 569, 6/5*w^3 - 4/5*w^2 - 51/5*w - 3/5],\ [569, 569, -6/5*w^3 + 14/5*w^2 + 41/5*w - 52/5],\ [569, 569, 2*w^3 - 2*w^2 - 19*w + 5],\ [599, 599, -11/5*w^3 + 14/5*w^2 + 101/5*w - 22/5],\ [599, 599, -7/5*w^3 + 8/5*w^2 + 57/5*w - 34/5],\ [599, 599, -7/5*w^3 + 13/5*w^2 + 52/5*w - 24/5],\ [599, 599, -11/5*w^3 + 19/5*w^2 + 96/5*w - 82/5],\ [601, 601, 7/5*w^3 - 13/5*w^2 - 67/5*w + 39/5],\ [601, 601, -1/5*w^3 + 4/5*w^2 + 16/5*w - 32/5],\ [601, 601, 1/5*w^3 + 1/5*w^2 - 21/5*w - 13/5],\ [601, 601, 7/5*w^3 - 8/5*w^2 - 72/5*w + 34/5],\ [607, 607, -4/5*w^3 + 6/5*w^2 + 49/5*w - 33/5],\ [607, 607, 8/5*w^3 - 12/5*w^2 - 83/5*w + 36/5],\ [607, 607, -8/5*w^3 + 12/5*w^2 + 83/5*w - 51/5],\ [607, 607, 4/5*w^3 - 6/5*w^2 - 49/5*w + 18/5],\ [641, 641, -3/5*w^3 + 7/5*w^2 + 18/5*w - 36/5],\ [641, 641, -7/5*w^3 + 8/5*w^2 + 67/5*w - 34/5],\ [641, 641, -7/5*w^3 + 13/5*w^2 + 62/5*w - 34/5],\ [641, 641, 3/5*w^3 - 2/5*w^2 - 23/5*w - 14/5],\ [647, 647, 8/5*w^3 - 7/5*w^2 - 93/5*w + 6/5],\ [647, 647, -8/5*w^3 + 7/5*w^2 + 93/5*w - 36/5],\ [647, 647, 8/5*w^3 - 17/5*w^2 - 83/5*w + 56/5],\ [647, 647, -8/5*w^3 + 17/5*w^2 + 83/5*w - 86/5],\ [673, 673, -2*w^3 + 3*w^2 + 18*w - 11],\ [673, 673, -6/5*w^3 + 9/5*w^2 + 46/5*w - 17/5],\ [673, 673, -6/5*w^3 + 9/5*w^2 + 46/5*w - 32/5],\ [673, 673, -2*w^3 + 3*w^2 + 18*w - 8],\ [719, 719, -2/5*w^3 + 3/5*w^2 + 2/5*w - 14/5],\ [719, 719, 7/5*w^3 - 8/5*w^2 - 82/5*w + 14/5],\ [719, 719, -7/5*w^3 + 13/5*w^2 + 77/5*w - 69/5],\ [719, 719, -9/5*w^3 + 11/5*w^2 + 99/5*w - 53/5],\ [727, 727, 4/5*w^3 - 6/5*w^2 - 49/5*w + 23/5],\ [727, 727, -8/5*w^3 + 12/5*w^2 + 83/5*w - 41/5],\ [727, 727, -8/5*w^3 + 12/5*w^2 + 83/5*w - 46/5],\ [727, 727, -4/5*w^3 + 6/5*w^2 + 49/5*w - 28/5],\ [751, 751, 14/5*w^3 - 16/5*w^2 - 144/5*w + 43/5],\ [751, 751, 2/5*w^3 + 2/5*w^2 - 42/5*w - 1/5],\ [751, 751, 2/5*w^3 - 8/5*w^2 - 32/5*w + 39/5],\ [751, 751, 14/5*w^3 - 26/5*w^2 - 134/5*w + 103/5],\ [809, 809, 2*w^3 - 3*w^2 - 18*w + 9],\ [809, 809, -6/5*w^3 + 9/5*w^2 + 46/5*w - 22/5],\ [809, 809, 6/5*w^3 - 9/5*w^2 - 46/5*w + 27/5],\ [809, 809, -2*w^3 + 3*w^2 + 18*w - 10],\ [823, 823, 3/5*w^3 - 2/5*w^2 - 23/5*w - 44/5],\ [823, 823, 12/5*w^3 - 18/5*w^2 - 112/5*w + 39/5],\ [823, 823, -12/5*w^3 + 18/5*w^2 + 112/5*w - 79/5],\ [823, 823, 7/5*w^3 - 18/5*w^2 - 57/5*w + 94/5],\ [841, 29, -6/5*w^3 + 9/5*w^2 + 66/5*w - 32/5],\ [841, 29, 6/5*w^3 - 9/5*w^2 - 66/5*w + 37/5],\ [857, 857, -w^3 + 3*w^2 + 6*w - 11],\ [857, 857, 9/5*w^3 - 6/5*w^2 - 89/5*w + 3/5],\ [857, 857, -9/5*w^3 + 21/5*w^2 + 74/5*w - 83/5],\ [857, 857, -w^3 + 9*w + 3],\ [881, 881, 7/5*w^3 - 18/5*w^2 - 67/5*w + 64/5],\ [881, 881, -w^3 + 13*w + 4],\ [881, 881, w^3 - 3*w^2 - 10*w + 16],\ [881, 881, -7/5*w^3 + 3/5*w^2 + 82/5*w - 14/5],\ [887, 887, 8/5*w^3 - 7/5*w^2 - 78/5*w + 21/5],\ [887, 887, -4/5*w^3 + 11/5*w^2 + 24/5*w - 48/5],\ [887, 887, -4/5*w^3 + 1/5*w^2 + 34/5*w + 17/5],\ [887, 887, -8/5*w^3 + 17/5*w^2 + 68/5*w - 56/5],\ [911, 911, 2*w^3 - 3*w^2 - 20*w + 4],\ [911, 911, 2/5*w^3 - 3/5*w^2 - 32/5*w - 16/5],\ [911, 911, 2/5*w^3 - 3/5*w^2 - 32/5*w + 49/5],\ [911, 911, -2*w^3 + 3*w^2 + 20*w - 17],\ [919, 919, -w^3 + w^2 + 10*w - 10],\ [919, 919, 1/5*w^3 + 1/5*w^2 - 6/5*w - 48/5],\ [919, 919, w^3 - 3*w^2 - 7*w + 15],\ [919, 919, -w^3 + 3*w^2 + 7*w - 9],\ [937, 937, 13/5*w^3 - 22/5*w^2 - 123/5*w + 76/5],\ [937, 937, 12/5*w^3 - 18/5*w^2 - 122/5*w + 49/5],\ [937, 937, -12/5*w^3 + 18/5*w^2 + 122/5*w - 79/5],\ [937, 937, 4/5*w^3 - 6/5*w^2 - 54/5*w + 43/5],\ [953, 953, w^3 - 3*w^2 - 6*w + 9],\ [953, 953, -9/5*w^3 + 21/5*w^2 + 74/5*w - 93/5],\ [953, 953, 9/5*w^3 - 6/5*w^2 - 89/5*w - 7/5],\ [953, 953, w^3 - 9*w - 1],\ [961, 31, 8/5*w^3 - 12/5*w^2 - 68/5*w + 31/5],\ [961, 31, -8/5*w^3 + 12/5*w^2 + 68/5*w - 41/5],\ [991, 991, 7/5*w^3 - 18/5*w^2 - 52/5*w + 74/5],\ [991, 991, -7/5*w^3 + 18/5*w^2 + 52/5*w - 64/5],\ [991, 991, -8/5*w^3 + 12/5*w^2 + 73/5*w - 76/5],\ [991, 991, -7/5*w^3 + 3/5*w^2 + 67/5*w + 11/5],\ [1031, 1031, -16/5*w^3 + 24/5*w^2 + 156/5*w - 67/5],\ [1031, 1031, -4*w - 1],\ [1031, 1031, 4*w - 5],\ [1031, 1031, -16/5*w^3 + 24/5*w^2 + 156/5*w - 97/5],\ [1039, 1039, -8/5*w^3 + 17/5*w^2 + 78/5*w - 96/5],\ [1039, 1039, -4/5*w^3 + 1/5*w^2 + 54/5*w - 28/5],\ [1039, 1039, 1/5*w^3 - 9/5*w^2 - 1/5*w + 67/5],\ [1039, 1039, 8/5*w^3 - 7/5*w^2 - 88/5*w - 9/5],\ [1049, 1049, -9/5*w^3 + 16/5*w^2 + 84/5*w - 48/5],\ [1049, 1049, -1/5*w^3 + 4/5*w^2 - 4/5*w - 22/5],\ [1049, 1049, 1/5*w^3 + 1/5*w^2 - 1/5*w - 23/5],\ [1049, 1049, 9/5*w^3 - 11/5*w^2 - 89/5*w + 43/5],\ [1063, 1063, -9/5*w^3 + 11/5*w^2 + 79/5*w - 33/5],\ [1063, 1063, -9/5*w^3 + 16/5*w^2 + 74/5*w - 58/5],\ [1063, 1063, 9/5*w^3 - 11/5*w^2 - 79/5*w + 23/5],\ [1063, 1063, 9/5*w^3 - 16/5*w^2 - 74/5*w + 48/5],\ [1153, 1153, -7/5*w^3 + 8/5*w^2 + 67/5*w - 44/5],\ [1153, 1153, 3/5*w^3 - 2/5*w^2 - 23/5*w - 24/5],\ [1153, 1153, -3/5*w^3 + 7/5*w^2 + 18/5*w - 46/5],\ [1153, 1153, 7/5*w^3 - 13/5*w^2 - 62/5*w + 24/5],\ [1193, 1193, w^3 - w^2 - 8*w - 2],\ [1193, 1193, -9/5*w^3 + 16/5*w^2 + 79/5*w - 38/5],\ [1193, 1193, -9/5*w^3 + 11/5*w^2 + 84/5*w - 48/5],\ [1193, 1193, -w^3 + 2*w^2 + 7*w - 10],\ [1223, 1223, w^2 - 4*w - 3],\ [1223, 1223, -12/5*w^3 + 23/5*w^2 + 112/5*w - 89/5],\ [1223, 1223, 12/5*w^3 - 13/5*w^2 - 122/5*w + 34/5],\ [1223, 1223, w^2 + 2*w - 6],\ [1231, 1231, 4/5*w^3 - 11/5*w^2 - 44/5*w + 18/5],\ [1231, 1231, -8/5*w^3 + 17/5*w^2 + 78/5*w - 101/5],\ [1231, 1231, -8/5*w^3 + 7/5*w^2 + 88/5*w + 14/5],\ [1231, 1231, 6/5*w^3 - 4/5*w^2 - 46/5*w - 3/5],\ [1249, 1249, 1/5*w^3 - 4/5*w^2 - 16/5*w + 42/5],\ [1249, 1249, -7/5*w^3 + 8/5*w^2 + 72/5*w - 44/5],\ [1249, 1249, 7/5*w^3 - 13/5*w^2 - 67/5*w + 29/5],\ [1249, 1249, 1/5*w^3 + 1/5*w^2 - 21/5*w - 23/5],\ [1297, 1297, -13/5*w^3 + 17/5*w^2 + 123/5*w - 61/5],\ [1297, 1297, -w^3 + 2*w^2 + 6*w - 8],\ [1297, 1297, w^3 - w^2 - 7*w - 1],\ [1297, 1297, 13/5*w^3 - 22/5*w^2 - 118/5*w + 66/5],\ [1303, 1303, 12/5*w^3 - 13/5*w^2 - 117/5*w + 34/5],\ [1303, 1303, -4/5*w^3 + 1/5*w^2 + 29/5*w + 12/5],\ [1303, 1303, -4/5*w^3 + 11/5*w^2 + 19/5*w - 38/5],\ [1303, 1303, -12/5*w^3 + 23/5*w^2 + 107/5*w - 84/5],\ [1327, 1327, -3/5*w^3 + 2/5*w^2 + 28/5*w - 36/5],\ [1327, 1327, -3/5*w^3 + 7/5*w^2 + 23/5*w - 61/5],\ [1327, 1327, 3/5*w^3 - 2/5*w^2 - 28/5*w - 34/5],\ [1327, 1327, -3/5*w^3 + 7/5*w^2 + 23/5*w + 9/5],\ [1361, 1361, 3/5*w^3 + 3/5*w^2 - 48/5*w + 16/5],\ [1361, 1361, 9/5*w^3 - 21/5*w^2 - 84/5*w + 118/5],\ [1361, 1361, -9/5*w^3 + 6/5*w^2 + 99/5*w + 22/5],\ [1361, 1361, -12/5*w^3 + 13/5*w^2 + 132/5*w - 49/5],\ [1369, 37, 6/5*w^3 - 9/5*w^2 - 41/5*w + 22/5],\ [1369, 37, 14/5*w^3 - 21/5*w^2 - 129/5*w + 68/5],\ [1433, 1433, -8/5*w^3 + 17/5*w^2 + 53/5*w - 36/5],\ [1433, 1433, 16/5*w^3 - 29/5*w^2 - 141/5*w + 122/5],\ [1433, 1433, -16/5*w^3 + 19/5*w^2 + 151/5*w - 32/5],\ [1433, 1433, 8/5*w^3 - 7/5*w^2 - 63/5*w + 26/5],\ [1439, 1439, 9/5*w^3 - 11/5*w^2 - 94/5*w + 53/5],\ [1439, 1439, -3/5*w^3 + 7/5*w^2 + 38/5*w - 51/5],\ [1439, 1439, 3/5*w^3 - 2/5*w^2 - 43/5*w - 9/5],\ [1439, 1439, 9/5*w^3 - 16/5*w^2 - 89/5*w + 43/5],\ [1447, 1447, 11/5*w^3 - 14/5*w^2 - 116/5*w + 32/5],\ [1447, 1447, -w^3 + w^2 + 13*w - 7],\ [1447, 1447, -w^3 + 2*w^2 + 12*w - 6],\ [1447, 1447, -11/5*w^3 + 19/5*w^2 + 111/5*w - 87/5],\ [1481, 1481, 1/5*w^3 - 4/5*w^2 - 16/5*w + 52/5],\ [1481, 1481, 7/5*w^3 - 13/5*w^2 - 67/5*w + 19/5],\ [1481, 1481, -7/5*w^3 + 8/5*w^2 + 72/5*w - 54/5],\ [1481, 1481, 1/5*w^3 + 1/5*w^2 - 21/5*w - 33/5],\ [1511, 1511, 6/5*w^3 - 4/5*w^2 - 56/5*w + 27/5],\ [1511, 1511, -6/5*w^3 + 14/5*w^2 + 46/5*w - 77/5],\ [1511, 1511, -6/5*w^3 + 4/5*w^2 + 56/5*w + 23/5],\ [1511, 1511, 6/5*w^3 - 14/5*w^2 - 46/5*w + 27/5],\ [1543, 1543, -8/5*w^3 + 17/5*w^2 + 68/5*w - 51/5],\ [1543, 1543, -4/5*w^3 + 1/5*w^2 + 34/5*w + 22/5],\ [1543, 1543, -4/5*w^3 + 11/5*w^2 + 24/5*w - 53/5],\ [1543, 1543, 8/5*w^3 - 7/5*w^2 - 78/5*w + 26/5],\ [1559, 1559, -12/5*w^3 + 18/5*w^2 + 107/5*w - 44/5],\ [1559, 1559, 8/5*w^3 - 12/5*w^2 - 63/5*w + 21/5],\ [1559, 1559, -8/5*w^3 + 12/5*w^2 + 63/5*w - 46/5],\ [1559, 1559, -12/5*w^3 + 18/5*w^2 + 107/5*w - 69/5],\ [1583, 1583, w^2 + w - 8],\ [1583, 1583, 8/5*w^3 - 7/5*w^2 - 83/5*w + 26/5],\ [1583, 1583, -8/5*w^3 + 17/5*w^2 + 73/5*w - 56/5],\ [1583, 1583, w^2 - 3*w - 6],\ [1609, 1609, -6/5*w^3 + 9/5*w^2 + 71/5*w - 52/5],\ [1609, 1609, 2*w^3 - 3*w^2 - 21*w + 8],\ [1609, 1609, -2*w^3 + 3*w^2 + 21*w - 14],\ [1609, 1609, -6/5*w^3 + 9/5*w^2 + 71/5*w - 22/5],\ [1663, 1663, -8/5*w^3 + 17/5*w^2 + 78/5*w - 56/5],\ [1663, 1663, -9/5*w^3 + 11/5*w^2 + 84/5*w - 53/5],\ [1663, 1663, -4/5*w^3 + 11/5*w^2 + 44/5*w - 63/5],\ [1663, 1663, 8/5*w^3 - 7/5*w^2 - 88/5*w + 31/5],\ [1681, 41, 2*w^3 - 3*w^2 - 17*w + 6],\ [1681, 41, -2*w^3 + 3*w^2 + 17*w - 12],\ [1759, 1759, 1/5*w^3 + 1/5*w^2 - 26/5*w - 13/5],\ [1759, 1759, -11/5*w^3 + 19/5*w^2 + 106/5*w - 57/5],\ [1759, 1759, 11/5*w^3 - 14/5*w^2 - 111/5*w + 57/5],\ [1759, 1759, -1/5*w^3 + 4/5*w^2 + 21/5*w - 37/5],\ [1777, 1777, -9/5*w^3 + 6/5*w^2 + 89/5*w - 18/5],\ [1777, 1777, 1/5*w^3 + 6/5*w^2 - 6/5*w - 48/5],\ [1777, 1777, w^3 - 9*w - 6],\ [1777, 1777, -18/5*w^3 + 27/5*w^2 + 168/5*w - 86/5],\ [1823, 1823, -14/5*w^3 + 26/5*w^2 + 139/5*w - 123/5],\ [1823, 1823, -6/5*w^3 + 4/5*w^2 + 81/5*w - 37/5],\ [1823, 1823, 6/5*w^3 - 14/5*w^2 - 71/5*w + 42/5],\ [1823, 1823, 14/5*w^3 - 16/5*w^2 - 149/5*w + 28/5],\ [1847, 1847, 4/5*w^3 - 16/5*w^2 - 39/5*w + 88/5],\ [1847, 1847, -16/5*w^3 + 29/5*w^2 + 151/5*w - 112/5],\ [1847, 1847, 16/5*w^3 - 19/5*w^2 - 161/5*w + 52/5],\ [1847, 1847, -17/5*w^3 + 28/5*w^2 + 167/5*w - 124/5],\ [1849, 43, -8/5*w^3 + 12/5*w^2 + 88/5*w - 61/5],\ [1849, 43, 8/5*w^3 - 12/5*w^2 - 88/5*w + 31/5],\ [1871, 1871, -6/5*w^3 + 4/5*w^2 + 66/5*w - 27/5],\ [1871, 1871, 2/5*w^3 + 2/5*w^2 - 32/5*w - 31/5],\ [1871, 1871, 2/5*w^3 - 8/5*w^2 - 22/5*w + 59/5],\ [1871, 1871, 6/5*w^3 - 14/5*w^2 - 56/5*w + 37/5],\ [1873, 1873, -1/5*w^3 + 9/5*w^2 - 4/5*w - 47/5],\ [1873, 1873, -w^3 + 11*w + 1],\ [1873, 1873, -w^3 + 3*w^2 + 8*w - 11],\ [1873, 1873, 1/5*w^3 + 6/5*w^2 - 11/5*w - 43/5],\ [1889, 1889, -16/5*w^3 + 29/5*w^2 + 156/5*w - 122/5],\ [1889, 1889, -17/5*w^3 + 28/5*w^2 + 152/5*w - 74/5],\ [1889, 1889, -18/5*w^3 + 32/5*w^2 + 163/5*w - 116/5],\ [1889, 1889, 16/5*w^3 - 19/5*w^2 - 166/5*w + 47/5],\ [1951, 1951, 8/5*w^3 - 12/5*w^2 - 63/5*w + 41/5],\ [1951, 1951, -12/5*w^3 + 18/5*w^2 + 107/5*w - 64/5],\ [1951, 1951, 12/5*w^3 - 18/5*w^2 - 107/5*w + 49/5],\ [1951, 1951, -8/5*w^3 + 12/5*w^2 + 63/5*w - 26/5],\ [1993, 1993, 4/5*w^3 - 11/5*w^2 - 34/5*w + 88/5],\ [1993, 1993, 13/5*w^3 - 22/5*w^2 - 133/5*w + 56/5],\ [1993, 1993, 13/5*w^3 - 22/5*w^2 - 128/5*w + 66/5],\ [1993, 1993, -3/5*w^3 + 7/5*w^2 + 43/5*w - 51/5],\ [1999, 1999, -7/5*w^3 + 13/5*w^2 + 77/5*w - 49/5],\ [1999, 1999, -9/5*w^3 + 16/5*w^2 + 94/5*w - 68/5],\ [1999, 1999, 9/5*w^3 - 11/5*w^2 - 99/5*w + 33/5],\ [1999, 1999, -7/5*w^3 + 8/5*w^2 + 82/5*w - 34/5]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^2 + x - 10 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -e, -e, e - 2, e - 2, e - 2, e - 2, 4, 4, 4, 4, -e - 4, -e - 4, e + 10, e + 10, -4*e, -4*e, -4*e, -4*e, 4, 4, 4, 4, -2*e + 4, -2*e + 4, -2*e + 4, -2*e + 4, 2*e - 8, 2*e - 8, -12, -12, -12, -12, 4*e - 10, 4*e + 12, 4*e + 12, 4*e + 12, 4*e + 12, 0, 0, 0, 0, 3*e + 4, 3*e + 4, 3*e + 4, 3*e + 4, -5*e - 12, -5*e - 12, -5*e - 12, -5*e - 12, -16, -16, -16, -16, 12, 12, 12, 12, 5*e - 6, 5*e - 6, 5*e - 6, 5*e - 6, e + 18, e + 18, e + 18, e + 18, 2*e - 8, 2*e - 8, 8, 8, 8, 8, -5*e - 16, -5*e - 16, -5*e - 16, -5*e - 16, 4*e, 4*e, 4*e, 4*e, 8*e + 4, 8*e + 4, 8*e + 4, 8*e + 4, -3*e + 2, -3*e + 2, -3*e + 2, -3*e + 2, -5*e, -5*e, -5*e, -5*e, -20, -20, -20, -20, -3*e - 18, -3*e - 18, -3*e - 18, -3*e - 18, -12, -12, -12, -12, 2*e + 32, 2*e + 32, 2*e + 32, 2*e + 32, -4*e - 32, -4*e - 32, -4*e - 32, -4*e - 32, -7*e - 26, -7*e - 26, -7*e - 26, -7*e - 26, -4*e - 20, -4*e - 20, -4*e - 20, -4*e - 20, -4*e + 28, -4*e + 28, -4*e + 28, -4*e + 28, 12*e + 12, 12*e + 12, 12*e + 12, 12*e + 12, 5*e + 10, 5*e + 10, 5*e + 10, 5*e + 10, 8*e + 4, 8*e + 4, 8*e + 4, 8*e + 4, 4*e + 22, 4*e + 22, -4*e - 2, -4*e - 2, -4*e - 2, -4*e - 2, -e + 32, -e + 32, -e + 32, -e + 32, 16*e + 8, 16*e + 8, 16*e + 8, 16*e + 8, 32, 32, 32, 32, 40, 40, 40, 40, -4*e - 2, -4*e - 2, -4*e - 2, -4*e - 2, 15*e + 4, 15*e + 4, 15*e + 4, 15*e + 4, -10*e + 12, -10*e + 12, -8*e + 12, -8*e + 12, -8*e + 12, -8*e + 12, 32, 32, 32, 32, 4*e - 20, 4*e - 20, 4*e - 20, 4*e - 20, 11*e + 20, 11*e + 20, 11*e + 20, 11*e + 20, -12*e + 4, -12*e + 4, -12*e + 4, -12*e + 4, -15*e - 6, -15*e - 6, -15*e - 6, -15*e - 6, -6, -6, -6, -6, -12*e - 16, -12*e - 16, -12*e - 16, -12*e - 16, -8*e - 28, -8*e - 28, -8*e - 28, -8*e - 28, e + 50, e + 50, e + 50, e + 50, 16*e + 18, 16*e + 18, 16*e + 18, 16*e + 18, 8*e - 36, 8*e - 36, 8*e - 36, 8*e - 36, -4*e + 28, -4*e + 28, -4*e + 28, -4*e + 28, 7*e - 28, 7*e - 28, 7*e - 28, 7*e - 28, -e - 60, -e - 60, 3*e + 4, 3*e + 4, 3*e + 4, 3*e + 4, 4*e - 40, 4*e - 40, 4*e - 40, 4*e - 40, -4*e - 32, -4*e - 32, -4*e - 32, -4*e - 32, -11*e + 22, -11*e + 22, -11*e + 22, -11*e + 22, 12*e - 28, 12*e - 28, 12*e - 28, 12*e - 28, -12*e + 4, -12*e + 4, -12*e + 4, -12*e + 4, -4*e, -4*e, -4*e, -4*e, -12*e - 16, -12*e - 16, -12*e - 16, -12*e - 16, 5*e - 10, 5*e - 10, 5*e - 10, 5*e - 10, 8*e - 16, 8*e - 16, 8*e - 16, 8*e - 16, 82, 82, -20, -20, -20, -20, 6*e + 28, 6*e + 28, 6*e + 28, 6*e + 28, 8*e + 44, 8*e + 44, 8*e + 44, 8*e + 44, -32, -32, -32, -32, -e + 80, -e + 80, -8*e - 28, -8*e - 28, -8*e - 28, -8*e - 28, 3*e - 16, 3*e - 16, 3*e - 16, 3*e - 16, -4*e - 10, -4*e - 10, -4*e - 10, -4*e - 10, -8, -8, -8, -8, 3*e + 24, 3*e + 24, 3*e + 24, 3*e + 24, -20*e - 20, -20*e - 20, -20*e - 20, -20*e - 20] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]