/* 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([18, 0, -12, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([7,7,-1/3*w^3 + 1/3*w^2 + 3*w - 3]) primes_array = [ [2, 2, -1/3*w^3 - 1/3*w^2 + 3*w + 4],\ [7, 7, 1/3*w^3 + 1/3*w^2 - 3*w - 3],\ [7, 7, -1/3*w^2 + w + 1],\ [7, 7, 1/3*w^2 + w - 1],\ [7, 7, 1/3*w^3 - 1/3*w^2 - 3*w + 3],\ [9, 3, w - 3],\ [41, 41, 1/3*w^3 - 1/3*w^2 - 3*w + 1],\ [41, 41, -1/3*w^2 + w + 3],\ [41, 41, 1/3*w^2 + w - 3],\ [41, 41, -1/3*w^3 - 1/3*w^2 + 3*w + 1],\ [47, 47, 1/3*w^3 + 1/3*w^2 - 4*w - 1],\ [47, 47, -1/3*w^3 + 1/3*w^2 + 2*w - 3],\ [47, 47, 1/3*w^3 + 1/3*w^2 - 2*w - 3],\ [47, 47, 1/3*w^3 - 1/3*w^2 - 4*w + 1],\ [89, 89, -1/3*w^3 + 2/3*w^2 + 3*w - 3],\ [89, 89, 2/3*w^2 + w - 5],\ [89, 89, 2/3*w^2 - w - 5],\ [89, 89, 1/3*w^3 + 2/3*w^2 - 3*w - 3],\ [97, 97, 2/3*w^3 - 1/3*w^2 - 6*w + 5],\ [97, 97, -w^3 - 5/3*w^2 + 10*w + 15],\ [97, 97, -5/3*w^3 - 5/3*w^2 + 16*w + 21],\ [97, 97, -2/3*w^3 - 1/3*w^2 + 6*w + 5],\ [103, 103, -4/3*w^3 - 4/3*w^2 + 13*w + 17],\ [103, 103, 1/3*w^3 + w^2 - 5*w - 7],\ [103, 103, -w^3 - w^2 + 9*w + 11],\ [103, 103, -2/3*w^3 - 4/3*w^2 + 7*w + 11],\ [137, 137, -1/3*w^3 - 1/3*w^2 + 3*w - 1],\ [137, 137, 1/3*w^2 + w - 5],\ [137, 137, 1/3*w^2 - w - 5],\ [137, 137, 1/3*w^3 - 1/3*w^2 - 3*w - 1],\ [151, 151, w^2 - w - 5],\ [151, 151, 1/3*w^3 + w^2 - 3*w - 7],\ [151, 151, -1/3*w^3 + w^2 + 3*w - 7],\ [151, 151, w^2 + w - 5],\ [191, 191, 1/3*w^3 + 2/3*w^2 - 4*w - 3],\ [191, 191, 1/3*w^3 + 2/3*w^2 - 2*w - 5],\ [191, 191, -1/3*w^3 + 2/3*w^2 + 2*w - 5],\ [191, 191, -1/3*w^3 + 2/3*w^2 + 4*w - 3],\ [193, 193, 2/3*w^3 + w^2 - 8*w - 7],\ [193, 193, -1/3*w^3 - 1/3*w^2 + 4*w + 7],\ [193, 193, -7/3*w^3 - 13/3*w^2 + 26*w + 37],\ [193, 193, -2/3*w^3 + w^2 + 8*w - 7],\ [199, 199, 5/3*w^3 + 2*w^2 - 17*w - 23],\ [199, 199, -2/3*w^3 - 5/3*w^2 + 9*w + 13],\ [199, 199, -2/3*w^3 - 1/3*w^2 + 5*w + 5],\ [199, 199, -w^3 - 2*w^2 + 11*w + 17],\ [233, 233, 1/3*w^3 - 4/3*w^2 - 3*w + 5],\ [233, 233, 1/3*w^3 - 4/3*w^2 - 5*w + 7],\ [233, 233, 4/3*w^2 + w - 11],\ [233, 233, 1/3*w^3 + 4/3*w^2 - 3*w - 5],\ [239, 239, 1/3*w^3 + w^2 - 4*w - 5],\ [239, 239, 4/3*w^3 + 4/3*w^2 - 14*w - 17],\ [239, 239, 4/3*w^3 + 2/3*w^2 - 12*w - 13],\ [239, 239, -1/3*w^3 + w^2 + 4*w - 5],\ [241, 241, -2/3*w^3 + 6*w + 1],\ [241, 241, 2/3*w^3 - 1/3*w^2 - 6*w + 3],\ [241, 241, -2/3*w^3 - 1/3*w^2 + 6*w + 3],\ [241, 241, 2/3*w^3 - 6*w + 1],\ [281, 281, -w^3 - w^2 + 9*w + 13],\ [281, 281, -2/3*w^3 - 2/3*w^2 + 5*w + 7],\ [281, 281, -2/3*w^3 + 2/3*w^2 + 5*w - 7],\ [281, 281, -7/3*w^3 - 3*w^2 + 23*w + 31],\ [289, 17, w^2 - 5],\ [289, 17, w^2 - 7],\ [337, 337, -w^3 + 4/3*w^2 + 8*w - 7],\ [337, 337, -2*w + 7],\ [337, 337, 2/3*w^3 - 2*w^2 - 4*w + 11],\ [337, 337, 1/3*w^3 + 2/3*w^2 - 6*w + 1],\ [383, 383, 2/3*w^3 + 5/3*w^2 - 8*w - 11],\ [383, 383, -w^3 - 2/3*w^2 + 10*w + 11],\ [383, 383, -5/3*w^3 - 4/3*w^2 + 16*w + 19],\ [383, 383, -4/3*w^3 - 7/3*w^2 + 14*w + 19],\ [431, 431, -2/3*w^3 + 1/3*w^2 + 4*w - 5],\ [431, 431, -2/3*w^3 - 1/3*w^2 + 8*w - 1],\ [431, 431, 2/3*w^3 - 1/3*w^2 - 8*w - 1],\ [431, 431, 2/3*w^3 + 1/3*w^2 - 4*w - 5],\ [433, 433, 2/3*w^3 + 7/3*w^2 - 10*w - 15],\ [433, 433, -3*w^3 - 10/3*w^2 + 30*w + 39],\ [433, 433, -1/3*w^3 - 4/3*w^2 + 4*w + 9],\ [433, 433, -4/3*w^3 - 5/3*w^2 + 12*w + 15],\ [439, 439, -4/3*w^3 - 1/3*w^2 + 11*w + 13],\ [439, 439, 1/3*w^3 + 2/3*w^2 - 5*w - 5],\ [439, 439, -3*w^3 - 10/3*w^2 + 29*w + 37],\ [439, 439, -4/3*w^3 - 7/3*w^2 + 13*w + 19],\ [479, 479, 1/3*w^2 - 2*w - 5],\ [479, 479, 2/3*w^3 + 1/3*w^2 - 6*w + 1],\ [479, 479, 2/3*w^3 - 1/3*w^2 - 6*w - 1],\ [479, 479, -1/3*w^2 - 2*w + 5],\ [487, 487, 1/3*w^3 + 4/3*w^2 - 3*w - 7],\ [487, 487, 4/3*w^2 - w - 9],\ [487, 487, -4/3*w^2 - w + 9],\ [487, 487, 1/3*w^3 - 4/3*w^2 - 3*w + 7],\ [521, 521, 2/3*w^3 - 2/3*w^2 - 5*w - 3],\ [521, 521, 5/3*w^3 + 7/3*w^2 - 17*w - 21],\ [521, 521, -7/3*w^3 - 11/3*w^2 + 25*w + 33],\ [521, 521, -4/3*w^3 - 2/3*w^2 + 13*w + 15],\ [529, 23, -1/3*w^2 - 3],\ [529, 23, 1/3*w^2 - 7],\ [569, 569, 2/3*w^3 + 2/3*w^2 - 5*w + 1],\ [569, 569, 1/3*w^3 - 2/3*w^2 - 5*w + 9],\ [569, 569, -1/3*w^3 - 2/3*w^2 + 5*w + 9],\ [569, 569, -2/3*w^3 + 2/3*w^2 + 5*w + 1],\ [577, 577, -w^3 + 1/3*w^2 + 8*w + 3],\ [577, 577, -1/3*w^3 - 1/3*w^2 + 6*w + 7],\ [577, 577, 1/3*w^3 - 1/3*w^2 - 6*w + 7],\ [577, 577, w^3 + 1/3*w^2 - 8*w + 3],\ [617, 617, -2/3*w^3 - 5/3*w^2 + 5*w + 7],\ [617, 617, -5/3*w^2 + 3*w + 5],\ [617, 617, -8/3*w^3 - 13/3*w^2 + 27*w + 37],\ [617, 617, -w^3 - 5/3*w^2 + 9*w + 15],\ [625, 5, -5],\ [631, 631, -1/3*w^3 - 5/3*w^2 + 3*w + 7],\ [631, 631, -5/3*w^2 - w + 13],\ [631, 631, 5/3*w^2 - w - 13],\ [631, 631, 1/3*w^3 - 5/3*w^2 - 3*w + 7],\ [673, 673, 2/3*w^3 + 1/3*w^2 - 8*w - 1],\ [673, 673, -2/3*w^3 - 1/3*w^2 + 4*w + 3],\ [673, 673, -2/3*w^3 + 1/3*w^2 + 4*w - 3],\ [673, 673, 2/3*w^3 - 1/3*w^2 - 8*w + 1],\ [719, 719, 1/3*w^3 - 1/3*w^2 - 6*w + 9],\ [719, 719, w^3 - 1/3*w^2 - 8*w - 5],\ [719, 719, w^3 + 1/3*w^2 - 8*w + 5],\ [719, 719, -1/3*w^3 - 1/3*w^2 + 6*w + 9],\ [727, 727, 2/3*w^3 + 1/3*w^2 - 5*w - 1],\ [727, 727, -1/3*w^3 - 1/3*w^2 + 5*w + 3],\ [727, 727, 1/3*w^3 - 1/3*w^2 - 5*w + 3],\ [727, 727, -2/3*w^3 + 1/3*w^2 + 5*w - 1],\ [761, 761, -2/3*w^3 + 1/3*w^2 + 3*w + 3],\ [761, 761, 7/3*w^3 + 10/3*w^2 - 23*w - 33],\ [761, 761, 3*w^3 + 10/3*w^2 - 29*w - 39],\ [761, 761, -2*w^3 - 5/3*w^2 + 17*w + 21],\ [769, 769, -4/3*w^3 - w^2 + 12*w + 13],\ [769, 769, -w^3 - 2/3*w^2 + 10*w + 13],\ [769, 769, -w^3 - 8/3*w^2 + 12*w + 19],\ [769, 769, -2*w^3 - 3*w^2 + 22*w + 29],\ [809, 809, -2/3*w^3 - 2/3*w^2 + 7*w + 3],\ [809, 809, w^2 + w - 11],\ [809, 809, w^2 - w - 11],\ [809, 809, 2/3*w^3 - 2/3*w^2 - 7*w + 3],\ [823, 823, 1/3*w^3 - 5*w - 1],\ [823, 823, 2/3*w^3 - 5*w - 1],\ [823, 823, 2/3*w^3 - 5*w + 1],\ [823, 823, -1/3*w^3 + 5*w - 1],\ [857, 857, -5/3*w^2 + w + 15],\ [857, 857, -1/3*w^3 - 5/3*w^2 + 3*w + 5],\ [857, 857, 1/3*w^3 - 5/3*w^2 - 3*w + 5],\ [857, 857, 5/3*w^2 + w - 15],\ [863, 863, -2/3*w^3 - 5/3*w^2 + 10*w + 15],\ [863, 863, -5/3*w^3 - 8/3*w^2 + 18*w + 27],\ [863, 863, -3*w^3 - 14/3*w^2 + 32*w + 45],\ [863, 863, -5/3*w^2 + 4*w + 9],\ [911, 911, 1/3*w^3 - 2/3*w^2 - 4*w - 1],\ [911, 911, -1/3*w^3 + 2/3*w^2 + 2*w - 9],\ [911, 911, 1/3*w^3 + 2/3*w^2 - 2*w - 9],\ [911, 911, -1/3*w^3 - 2/3*w^2 + 4*w - 1],\ [919, 919, w^3 + 1/3*w^2 - 9*w - 1],\ [919, 919, -w^3 - 2/3*w^2 + 9*w + 7],\ [919, 919, w^3 - 2/3*w^2 - 9*w + 7],\ [919, 919, -w^3 + 1/3*w^2 + 9*w - 1],\ [953, 953, -w^3 - w^2 + 9*w + 5],\ [953, 953, -w^2 - 3*w + 7],\ [953, 953, w^2 - 3*w - 7],\ [953, 953, w^3 - w^2 - 9*w + 5],\ [961, 31, 4/3*w^2 - 7],\ [961, 31, 4/3*w^2 - 9],\ [967, 967, -w^3 - 1/3*w^2 + 9*w + 5],\ [967, 967, w^3 + 2/3*w^2 - 9*w - 5],\ [967, 967, -w^3 + 2/3*w^2 + 9*w - 5],\ [967, 967, w^3 - 1/3*w^2 - 9*w + 5],\ [1009, 1009, 1/3*w^3 + 5/3*w^2 - 4*w - 9],\ [1009, 1009, -8/3*w^3 - 10/3*w^2 + 26*w + 33],\ [1009, 1009, 4/3*w^3 + 8/3*w^2 - 16*w - 21],\ [1009, 1009, 7/3*w^3 + 5/3*w^2 - 22*w - 27],\ [1049, 1049, -2/3*w^3 + 2/3*w^2 + 5*w - 9],\ [1049, 1049, -1/3*w^3 - 2/3*w^2 + 5*w - 1],\ [1049, 1049, 1/3*w^3 - 2/3*w^2 - 5*w - 1],\ [1049, 1049, 2/3*w^3 + 2/3*w^2 - 5*w - 9],\ [1063, 1063, w^3 + 2/3*w^2 - 9*w - 13],\ [1063, 1063, 2*w^3 + w^2 - 17*w - 19],\ [1063, 1063, -2/3*w^3 - w^2 + 9*w + 11],\ [1063, 1063, -3*w^3 - 14/3*w^2 + 31*w + 43],\ [1097, 1097, -2/3*w^3 + 1/3*w^2 + 7*w + 1],\ [1097, 1097, 1/3*w^3 + 1/3*w^2 - w - 5],\ [1097, 1097, -1/3*w^3 + 1/3*w^2 + w - 5],\ [1097, 1097, 2/3*w^3 + 1/3*w^2 - 7*w + 1],\ [1103, 1103, 2/3*w^2 + 2*w - 7],\ [1103, 1103, 2/3*w^3 + 2/3*w^2 - 6*w - 1],\ [1103, 1103, -2/3*w^3 + 2/3*w^2 + 6*w - 1],\ [1103, 1103, 2/3*w^2 - 2*w - 7],\ [1151, 1151, -2/3*w^3 + 4*w - 7],\ [1151, 1151, 2/3*w^3 - 8*w - 7],\ [1151, 1151, -2/3*w^3 + 8*w - 7],\ [1151, 1151, 2/3*w^3 - 4*w - 7],\ [1153, 1153, -1/3*w^3 + 6*w - 5],\ [1153, 1153, -w^3 + 8*w + 5],\ [1153, 1153, -w^3 + 8*w - 5],\ [1153, 1153, 1/3*w^3 - 6*w - 5],\ [1193, 1193, -1/3*w^3 - 2/3*w^2 + 5*w - 3],\ [1193, 1193, 2/3*w^3 + 2/3*w^2 - 5*w - 11],\ [1193, 1193, -2/3*w^3 + 2/3*w^2 + 5*w - 11],\ [1193, 1193, 1/3*w^3 - 2/3*w^2 - 5*w - 3],\ [1201, 1201, -7/3*w^3 - 4/3*w^2 + 20*w + 23],\ [1201, 1201, -w^3 + 2/3*w^2 + 8*w - 1],\ [1201, 1201, w^3 + 2/3*w^2 - 8*w - 1],\ [1201, 1201, 1/3*w^3 + 2/3*w^2 - 6*w - 7],\ [1249, 1249, -2/3*w^3 + 2*w^2 + 6*w - 11],\ [1249, 1249, 2*w^2 + 2*w - 13],\ [1249, 1249, 2*w^2 - 2*w - 13],\ [1249, 1249, 2/3*w^3 + 2*w^2 - 6*w - 11],\ [1289, 1289, w^3 - 2/3*w^2 - 11*w + 3],\ [1289, 1289, 1/3*w^3 + w^2 - 5*w - 11],\ [1289, 1289, -1/3*w^3 + w^2 + 5*w - 11],\ [1289, 1289, -w^3 - 2/3*w^2 + 11*w + 3],\ [1297, 1297, -1/3*w^3 + 4*w - 7],\ [1297, 1297, -1/3*w^3 + 2*w - 7],\ [1297, 1297, 1/3*w^3 - 2*w - 7],\ [1297, 1297, 1/3*w^3 - 4*w - 7],\ [1303, 1303, 1/3*w^3 - 2/3*w^2 - 5*w + 13],\ [1303, 1303, -11/3*w^3 - 13/3*w^2 + 37*w + 49],\ [1303, 1303, -w^3 - 7/3*w^2 + 11*w + 19],\ [1303, 1303, -1/3*w^3 - 2/3*w^2 + 5*w + 13],\ [1399, 1399, 4/3*w^3 + 2/3*w^2 - 11*w + 1],\ [1399, 1399, -1/3*w^3 - 2/3*w^2 + 7*w + 9],\ [1399, 1399, 1/3*w^3 - 2/3*w^2 - 7*w + 9],\ [1399, 1399, -4/3*w^3 + 2/3*w^2 + 11*w + 1],\ [1433, 1433, w^3 - 9*w - 7],\ [1433, 1433, 4/3*w^3 + 11/3*w^2 - 17*w - 25],\ [1433, 1433, -4/3*w^3 - 7/3*w^2 + 13*w + 17],\ [1433, 1433, -w^3 + 9*w - 7],\ [1439, 1439, -1/3*w^3 - 4/3*w^2 + 6*w + 11],\ [1439, 1439, -2*w^3 - 3*w^2 + 22*w + 31],\ [1439, 1439, 4/3*w^3 + 3*w^2 - 16*w - 25],\ [1439, 1439, -5/3*w^3 - 10/3*w^2 + 20*w + 29],\ [1447, 1447, 1/3*w^2 + w - 9],\ [1447, 1447, 1/3*w^3 - 1/3*w^2 - 3*w - 5],\ [1447, 1447, -1/3*w^3 - 1/3*w^2 + 3*w - 5],\ [1447, 1447, 1/3*w^2 - w - 9],\ [1481, 1481, -2/3*w^3 + 5/3*w^2 + 7*w - 9],\ [1481, 1481, 1/3*w^3 + 5/3*w^2 - w - 11],\ [1481, 1481, -1/3*w^3 + 5/3*w^2 + w - 11],\ [1481, 1481, -2/3*w^3 - 5/3*w^2 + 7*w + 9],\ [1487, 1487, 2/3*w^3 + 8/3*w^2 - 10*w - 15],\ [1487, 1487, -w^3 - 1/3*w^2 + 10*w + 9],\ [1487, 1487, -w^3 + 1/3*w^2 + 10*w - 9],\ [1487, 1487, -2*w^3 - 10/3*w^2 + 20*w + 27],\ [1489, 1489, -1/3*w^3 + 5/3*w^2 + 2*w - 9],\ [1489, 1489, -1/3*w^3 + 5/3*w^2 + 4*w - 11],\ [1489, 1489, 1/3*w^3 + 5/3*w^2 - 4*w - 11],\ [1489, 1489, 1/3*w^3 + 5/3*w^2 - 2*w - 9],\ [1543, 1543, -4*w^3 - 13/3*w^2 + 39*w + 49],\ [1543, 1543, 4*w^3 + 5*w^2 - 41*w - 55],\ [1543, 1543, 2/3*w^3 - 2/3*w^2 - 9*w + 1],\ [1543, 1543, 4/3*w^3 + 5/3*w^2 - 15*w - 17],\ [1583, 1583, -1/3*w^3 + w^2 + 4*w + 1],\ [1583, 1583, 1/3*w^3 + w^2 - 2*w - 13],\ [1583, 1583, -1/3*w^3 + w^2 + 2*w - 13],\ [1583, 1583, -1/3*w^3 - w^2 + 4*w - 1],\ [1721, 1721, w^3 - 1/3*w^2 - 7*w + 9],\ [1721, 1721, 2/3*w^3 + 1/3*w^2 - 9*w + 5],\ [1721, 1721, -2/3*w^3 + 1/3*w^2 + 9*w + 5],\ [1721, 1721, w^3 + 1/3*w^2 - 7*w - 9],\ [1777, 1777, -8/3*w^3 - 3*w^2 + 28*w + 37],\ [1777, 1777, -w^3 - 2/3*w^2 + 8*w + 7],\ [1777, 1777, -w^3 + 2/3*w^2 + 8*w - 7],\ [1777, 1777, -2/3*w^3 - 3*w^2 + 10*w + 19],\ [1783, 1783, -1/3*w^2 - w - 5],\ [1783, 1783, -1/3*w^3 + 1/3*w^2 + 3*w - 9],\ [1783, 1783, 1/3*w^3 + 1/3*w^2 - 3*w - 9],\ [1783, 1783, -1/3*w^2 + w - 5],\ [1823, 1823, 2/3*w^3 - 4/3*w^2 - 4*w + 9],\ [1823, 1823, 2/3*w^3 - 4/3*w^2 - 8*w + 7],\ [1823, 1823, 2/3*w^3 + 4/3*w^2 - 8*w - 7],\ [1823, 1823, 2/3*w^3 + 4/3*w^2 - 4*w - 9],\ [1831, 1831, -w - 7],\ [1831, 1831, -1/3*w^3 + 3*w - 7],\ [1831, 1831, 1/3*w^3 - 3*w - 7],\ [1831, 1831, w - 7],\ [1871, 1871, -4*w^3 - 13/3*w^2 + 38*w + 49],\ [1871, 1871, -7/3*w^3 - 10/3*w^2 + 22*w + 31],\ [1871, 1871, -7/3*w^3 - 4/3*w^2 + 20*w + 25],\ [1871, 1871, 2/3*w^3 + 1/3*w^2 - 4*w - 7],\ [1873, 1873, -1/3*w^2 + 4*w - 3],\ [1873, 1873, 4/3*w^3 + 1/3*w^2 - 12*w - 7],\ [1873, 1873, 4/3*w^3 - 1/3*w^2 - 12*w + 7],\ [1873, 1873, 1/3*w^2 + 4*w + 3],\ [1879, 1879, -1/3*w^3 + 7/3*w^2 + 5*w - 11],\ [1879, 1879, 2/3*w^3 + 7/3*w^2 - 5*w - 17],\ [1879, 1879, -2/3*w^3 + 7/3*w^2 + 5*w - 17],\ [1879, 1879, 1/3*w^3 + 7/3*w^2 - 5*w - 11],\ [1913, 1913, 1/3*w^3 + 1/3*w^2 - w - 7],\ [1913, 1913, -2/3*w^3 - 1/3*w^2 + 7*w - 3],\ [1913, 1913, 2/3*w^3 - 1/3*w^2 - 7*w - 3],\ [1913, 1913, -1/3*w^3 + 1/3*w^2 + w - 7]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^8 - 13*x^6 + 54*x^4 - 71*x^2 + 1 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -1/2*e^6 + 5*e^4 - 12*e^2 + 5/2, -1/2*e^6 + 4*e^4 - 8*e^2 + 9/2, e^2 - 3, -1, -1/2*e^7 + 7*e^5 - 31*e^3 + 87/2*e, -1/2*e^7 + 8*e^5 - 38*e^3 + 105/2*e, -3/2*e^7 + 17*e^5 - 60*e^3 + 131/2*e, 3/2*e^7 - 20*e^5 + 84*e^3 - 215/2*e, -e^7 + 12*e^5 - 47*e^3 + 60*e, e^7 - 13*e^5 + 54*e^3 - 70*e, 2*e^5 - 16*e^3 + 26*e, -1/2*e^7 + 8*e^5 - 42*e^3 + 141/2*e, 4*e^5 - 33*e^3 + 63*e, 2*e^7 - 25*e^5 + 100*e^3 - 129*e, 2*e^7 - 23*e^5 + 83*e^3 - 92*e, 1/2*e^7 - 2*e^5 - 13*e^3 + 97/2*e, -3*e^7 + 34*e^5 - 118*e^3 + 121*e, -e^4 + 8*e^2 - 11, e^6 - 9*e^4 + 17*e^2 + 15, -2*e^6 + 19*e^4 - 45*e^2 + 6, 1/2*e^6 - 4*e^4 + 3*e^2 + 31/2, 1/2*e^6 - 6*e^4 + 13*e^2 + 21/2, -2*e^6 + 15*e^4 - 21*e^2 - 8, 2*e^6 - 18*e^4 + 41*e^2 - 7, 3/2*e^6 - 13*e^4 + 28*e^2 - 3/2, 2*e^7 - 27*e^5 + 113*e^3 - 144*e, 2*e^7 - 24*e^5 + 96*e^3 - 132*e, e^7 - 14*e^5 + 61*e^3 - 80*e, e^7 - 8*e^5 + 9*e^3 + 26*e, 2*e^6 - 17*e^4 + 34*e^2 + 3, -e^4 + 8*e^2 - 3, 2*e^4 - 10*e^2 + 4, 3/2*e^6 - 13*e^4 + 25*e^2 + 21/2, -1/2*e^7 + 25*e^3 - 111/2*e, -5/2*e^7 + 25*e^5 - 71*e^3 + 103/2*e, 3*e^7 - 37*e^5 + 142*e^3 - 172*e, 3/2*e^7 - 20*e^5 + 82*e^3 - 191/2*e, 2*e^6 - 20*e^4 + 47*e^2 - 5, -3/2*e^6 + 12*e^4 - 17*e^2 - 29/2, 1/2*e^6 - 7*e^4 + 26*e^2 - 41/2, 3*e^6 - 28*e^4 + 65*e^2 - 20, -3/2*e^6 + 11*e^4 - 19*e^2 + 19/2, 3*e^6 - 25*e^4 + 44*e^2 + 24, -2*e^6 + 17*e^4 - 37*e^2 + 8, 1/2*e^6 - 18*e^2 + 47/2, 5*e^5 - 50*e^3 + 113*e, -3*e^7 + 29*e^5 - 76*e^3 + 40*e, 2*e^7 - 28*e^5 + 125*e^3 - 173*e, 3/2*e^7 - 16*e^5 + 46*e^3 - 55/2*e, 3/2*e^7 - 20*e^5 + 84*e^3 - 211/2*e, -1/2*e^7 + 4*e^5 - 7*e^3 + 17/2*e, -5/2*e^7 + 35*e^5 - 161*e^3 + 469/2*e, 2*e^7 - 21*e^5 + 75*e^3 - 106*e, e^6 - 7*e^4 + 4*e^2 + 22, -2*e^4 + 13*e^2 - 11, -3*e^6 + 23*e^4 - 31*e^2 - 27, -5/2*e^6 + 27*e^4 - 73*e^2 + 53/2, 1/2*e^7 - 8*e^5 + 40*e^3 - 147/2*e, -3/2*e^7 + 15*e^5 - 37*e^3 + 13/2*e, 4*e^7 - 50*e^5 + 194*e^3 - 224*e, -5*e^7 + 58*e^5 - 207*e^3 + 224*e, -7/2*e^6 + 31*e^4 - 63*e^2 - 23/2, 3*e^6 - 25*e^4 + 46*e^2 - 6, -e^6 + 9*e^4 - 22*e^2 + 24, 7/2*e^6 - 32*e^4 + 79*e^2 - 67/2, -e^6 + 9*e^4 - 13*e^2 - 17, -1/2*e^6 + 11*e^2 + 7/2, -1/2*e^7 + 8*e^5 - 37*e^3 + 97/2*e, 2*e^7 - 24*e^5 + 88*e^3 - 106*e, 5/2*e^7 - 37*e^5 + 164*e^3 - 397/2*e, -3*e^7 + 34*e^5 - 120*e^3 + 133*e, -5/2*e^7 + 28*e^5 - 97*e^3 + 213/2*e, -11/2*e^7 + 66*e^5 - 259*e^3 + 673/2*e, -3/2*e^7 + 15*e^5 - 35*e^3 + 13/2*e, 4*e^7 - 51*e^5 + 203*e^3 - 250*e, 5/2*e^6 - 21*e^4 + 42*e^2 - 5/2, -3/2*e^6 + 12*e^4 - 13*e^2 - 23/2, 3*e^6 - 27*e^4 + 53*e^2 + 7, -3/2*e^6 + 11*e^4 - 17*e^2 - 13/2, 5/2*e^6 - 13*e^4 - 6*e^2 + 55/2, 3*e^4 - 20*e^2 + 19, -3/2*e^6 + 8*e^4 + 3*e^2 - 13/2, 2*e^6 - 19*e^4 + 53*e^2 - 20, -2*e^7 + 21*e^5 - 56*e^3 + 17*e, -11/2*e^7 + 62*e^5 - 213*e^3 + 441/2*e, 5*e^7 - 65*e^5 + 267*e^3 - 331*e, -9/2*e^7 + 58*e^5 - 236*e^3 + 575/2*e, 2*e^6 - 20*e^4 + 42*e^2 + 24, e^6 - 11*e^4 + 33*e^2 - 27, -9/2*e^6 + 38*e^4 - 77*e^2 + 9/2, 5*e^6 - 42*e^4 + 79*e^2 + 16, 4*e^7 - 46*e^5 + 170*e^3 - 210*e, 6*e^7 - 69*e^5 + 240*e^3 - 239*e, -3/2*e^7 + 13*e^5 - 17*e^3 - 79/2*e, 2*e^7 - 26*e^5 + 100*e^3 - 106*e, -3/2*e^6 + 14*e^4 - 35*e^2 - 27/2, 2*e^6 - 12*e^4 + 3*e^2 + 17, 5*e^7 - 57*e^5 + 198*e^3 - 196*e, 13/2*e^7 - 71*e^5 + 241*e^3 - 521/2*e, 2*e^7 - 27*e^5 + 118*e^3 - 173*e, -4*e^7 + 44*e^5 - 151*e^3 + 171*e, -9/2*e^6 + 35*e^4 - 58*e^2 - 29/2, -1/2*e^6 + 11*e^4 - 47*e^2 + 45/2, 2*e^6 - 19*e^4 + 42*e^2 + 25, 2*e^6 - 17*e^4 + 33*e^2 + 16, 5*e^7 - 65*e^5 + 269*e^3 - 347*e, 5/2*e^7 - 33*e^5 + 129*e^3 - 277/2*e, -3/2*e^7 + 18*e^5 - 58*e^3 + 65/2*e, -3*e^7 + 35*e^5 - 114*e^3 + 86*e, 4*e^6 - 38*e^4 + 86*e^2 - 16, -e^6 + 11*e^4 - 30*e^2 + 20, 4*e^6 - 27*e^4 + 21*e^2 + 44, 7*e^6 - 60*e^4 + 118*e^2 + 9, 11/2*e^6 - 47*e^4 + 90*e^2 + 3/2, -e^6 + 5*e^4 + 3*e^2 - 13, 6*e^6 - 50*e^4 + 100*e^2 - 30, e^6 - 13*e^4 + 39*e^2 + 7, -5*e^6 + 51*e^4 - 136*e^2 + 50, 2*e^7 - 31*e^5 + 151*e^3 - 216*e, -5*e^7 + 59*e^5 - 217*e^3 + 237*e, -7/2*e^7 + 50*e^5 - 234*e^3 + 699/2*e, 13/2*e^7 - 75*e^5 + 276*e^3 - 673/2*e, 3/2*e^6 - 15*e^4 + 32*e^2 - 19/2, 5*e^6 - 47*e^4 + 100*e^2 + 20, -2*e^6 + 16*e^4 - 30*e^2 + 16, 5/2*e^6 - 28*e^4 + 83*e^2 - 71/2, 4*e^7 - 49*e^5 + 181*e^3 - 194*e, 5/2*e^7 - 27*e^5 + 83*e^3 - 91/2*e, 3*e^7 - 51*e^5 + 260*e^3 - 390*e, 9/2*e^7 - 54*e^5 + 204*e^3 - 471/2*e, -13/2*e^6 + 61*e^4 - 148*e^2 + 69/2, -4*e^6 + 32*e^4 - 44*e^2 - 42, 1/2*e^6 - e^4 - 16*e^2 + 47/2, 5*e^6 - 40*e^4 + 67*e^2 - 2, -6*e^7 + 80*e^5 - 336*e^3 + 416*e, -e^7 + 14*e^5 - 56*e^3 + 49*e, -e^7 + 14*e^5 - 56*e^3 + 49*e, -9/2*e^7 + 43*e^5 - 108*e^3 + 91/2*e, -4*e^6 + 35*e^4 - 72*e^2 - 11, 1/2*e^6 - 7*e^4 + 24*e^2 + 35/2, -1/2*e^6 + 2*e^4 + 16*e^2 - 57/2, 7/2*e^6 - 28*e^4 + 44*e^2 + 57/2, -7/2*e^7 + 38*e^5 - 124*e^3 + 249/2*e, -5/2*e^7 + 23*e^5 - 64*e^3 + 129/2*e, 3/2*e^7 - 33*e^5 + 197*e^3 - 685/2*e, 5*e^7 - 53*e^5 + 167*e^3 - 157*e, -1/2*e^7 + 10*e^5 - 72*e^3 + 319/2*e, 3/2*e^7 - 27*e^5 + 141*e^3 - 447/2*e, 2*e^7 - 19*e^5 + 48*e^3 - 9*e, -9/2*e^7 + 62*e^5 - 286*e^3 + 857/2*e, -17/2*e^7 + 105*e^5 - 401*e^3 + 899/2*e, 5/2*e^7 - 43*e^5 + 227*e^3 - 731/2*e, 1/2*e^7 - 7*e^5 + 23*e^3 + 3/2*e, e^7 - 17*e^5 + 92*e^3 - 158*e, -5/2*e^6 + 12*e^4 + 19*e^2 - 91/2, -e^6 + 7*e^4 - 7*e^2 - 35, -2*e^4 + 8*e^2 + 46, -9/2*e^6 + 40*e^4 - 78*e^2 - 37/2, 1/2*e^7 - 9*e^5 + 42*e^3 - 91/2*e, 3/2*e^7 - 26*e^5 + 136*e^3 - 459/2*e, 6*e^7 - 73*e^5 + 277*e^3 - 324*e, -9/2*e^7 + 61*e^5 - 262*e^3 + 719/2*e, 2*e^6 - 21*e^4 + 55*e^2 - 12, -3*e^6 + 31*e^4 - 77*e^2 - 17, 17/2*e^6 - 74*e^4 + 156*e^2 - 77/2, -6*e^6 + 60*e^4 - 147*e^2 + 35, 2*e^6 - 22*e^4 + 61*e^2 - 3, e^6 - 13*e^4 + 31*e^2 + 13, -10*e^2 + 26, -6*e^6 + 49*e^4 - 87*e^2 - 12, 2*e^6 - 18*e^4 + 38*e^2 + 20, -4*e^6 + 33*e^4 - 72*e^2 + 25, 13/2*e^7 - 80*e^5 + 309*e^3 - 739/2*e, 4*e^7 - 43*e^5 + 143*e^3 - 158*e, 1/2*e^7 - 3*e^5 + 4*e^3 - 23/2*e, 3/2*e^7 - 12*e^5 + 9*e^3 + 125/2*e, 5/2*e^6 - 27*e^4 + 72*e^2 - 29/2, -7/2*e^6 + 30*e^4 - 46*e^2 - 55/2, e^6 - 8*e^4 + 6*e^2 + 25, -3*e^6 + 36*e^4 - 105*e^2 + 20, 4*e^7 - 55*e^5 + 229*e^3 - 280*e, 4*e^7 - 53*e^5 + 220*e^3 - 289*e, 3/2*e^7 - 27*e^5 + 161*e^3 - 599/2*e, 13/2*e^7 - 75*e^5 + 287*e^3 - 763/2*e, 3*e^7 - 33*e^5 + 112*e^3 - 122*e, -3*e^7 + 35*e^5 - 123*e^3 + 123*e, -3*e^7 + 46*e^5 - 220*e^3 + 309*e, 9/2*e^7 - 69*e^5 + 339*e^3 - 1045/2*e, 7/2*e^7 - 55*e^5 + 284*e^3 - 943/2*e, 6*e^7 - 70*e^5 + 261*e^3 - 329*e, -3*e^7 + 39*e^5 - 156*e^3 + 186*e, 4*e^7 - 45*e^5 + 150*e^3 - 125*e, 3/2*e^6 - 18*e^4 + 65*e^2 - 131/2, 6*e^6 - 51*e^4 + 96*e^2 + 15, -7/2*e^6 + 30*e^4 - 62*e^2 + 23/2, -7/2*e^6 + 29*e^4 - 53*e^2 - 9/2, e^7 - 14*e^5 + 66*e^3 - 99*e, -4*e^7 + 66*e^5 - 343*e^3 + 563*e, -7/2*e^7 + 38*e^5 - 132*e^3 + 289/2*e, 2*e^7 - 13*e^5 + 4*e^3 + 35*e, 1/2*e^6 - 9*e^4 + 37*e^2 - 9/2, e^6 - 9*e^4 + 10*e^2 + 52, -9/2*e^6 + 38*e^4 - 68*e^2 - 101/2, -3*e^6 + 26*e^4 - 41*e^2 - 30, -7/2*e^6 + 28*e^4 - 53*e^2 + 69/2, 8*e^6 - 74*e^4 + 171*e^2 - 61, 19/2*e^6 - 86*e^4 + 183*e^2 + 27/2, 7/2*e^6 - 22*e^4 + 13*e^2 + 77/2, 6*e^7 - 79*e^5 + 331*e^3 - 448*e, 9*e^7 - 103*e^5 + 376*e^3 - 452*e, -17/2*e^7 + 98*e^5 - 333*e^3 + 629/2*e, -9/2*e^7 + 54*e^5 - 200*e^3 + 429/2*e, 9/2*e^6 - 40*e^4 + 93*e^2 - 119/2, -e^6 + 10*e^4 - 38*e^2 + 57, -11*e^4 + 57*e^2 - 22, 9/2*e^6 - 33*e^4 + 52*e^2 - 19/2, 7*e^6 - 65*e^4 + 157*e^2 - 51, 1/2*e^6 - 5*e^4 + 5*e^2 + 31/2, 7/2*e^6 - 39*e^4 + 116*e^2 - 107/2, 1/2*e^6 - 6*e^4 + e^2 + 127/2, -4*e^6 + 46*e^4 - 132*e^2 + 62, 9*e^6 - 79*e^4 + 170*e^2 - 42, 3/2*e^6 - 9*e^4 + 65/2, 7/2*e^6 - 37*e^4 + 102*e^2 - 25/2, e^7 - 16*e^5 + 77*e^3 - 102*e, -7*e^7 + 93*e^5 - 388*e^3 + 470*e, -5*e^7 + 59*e^5 - 218*e^3 + 270*e, -10*e^7 + 112*e^5 - 394*e^3 + 450*e, -4*e^7 + 41*e^5 - 117*e^3 + 90*e, -e^7 + 3*e^5 + 29*e^3 - 91*e, -1/2*e^7 + 26*e^5 - 195*e^3 + 767/2*e, e^7 - 10*e^5 + 48*e^3 - 109*e, -5/2*e^6 + 28*e^4 - 81*e^2 + 71/2, 11/2*e^6 - 52*e^4 + 127*e^2 - 105/2, -5*e^6 + 44*e^4 - 90*e^2 + 9, 5*e^6 - 33*e^4 + 33*e^2 + 15, -2*e^7 + 14*e^5 - 23*e^3 + 33*e, -7/2*e^7 + 41*e^5 - 164*e^3 + 457/2*e, 2*e^7 - 23*e^5 + 79*e^3 - 96*e, -5*e^7 + 54*e^5 - 172*e^3 + 149*e, -15/2*e^7 + 93*e^5 - 353*e^3 + 775/2*e, -7*e^7 + 95*e^5 - 412*e^3 + 578*e, 5*e^7 - 64*e^5 + 276*e^3 - 397*e, 9/2*e^7 - 63*e^5 + 291*e^3 - 905/2*e, 4*e^6 - 34*e^4 + 54*e^2 + 48, -4*e^6 + 40*e^4 - 99*e^2 + 45, -4*e^6 + 31*e^4 - 41*e^2 - 42, 3/2*e^6 - 14*e^4 + 22*e^2 + 43/2, -e^6 + 3*e^4 + 5*e^2 + 45, -e^6 + 9*e^4 - 4*e^2 - 64, 21/2*e^6 - 93*e^4 + 201*e^2 - 79/2, -8*e^6 + 70*e^4 - 155*e^2 + 49, 5/2*e^7 - 45*e^5 + 241*e^3 - 799/2*e, 7*e^5 - 59*e^3 + 100*e, 7*e^7 - 93*e^5 + 385*e^3 - 497*e, -15/2*e^7 + 85*e^5 - 297*e^3 + 645/2*e, -e^7 + 14*e^5 - 71*e^3 + 126*e, -4*e^7 + 47*e^5 - 194*e^3 + 289*e, 9/2*e^7 - 57*e^5 + 224*e^3 - 559/2*e, e^7 - 6*e^5 - e^3 + 22*e, 3*e^6 - 18*e^4 + 4*e^2 + 11, e^6 - 6*e^4 - 5*e^2 + 18, -13/2*e^6 + 50*e^4 - 73*e^2 - 73/2, -2*e^6 + 22*e^4 - 42*e^2 - 38, 8*e^6 - 72*e^4 + 168*e^2 - 52, 9*e^6 - 75*e^4 + 149*e^2 - 33, 9/2*e^6 - 32*e^4 + 51*e^2 - 21/2, e^4 - 8*e^2 + 27, -9/2*e^7 + 56*e^5 - 236*e^3 + 673/2*e, -1/2*e^7 + 19*e^5 - 131*e^3 + 445/2*e, -11/2*e^7 + 84*e^5 - 387*e^3 + 1039/2*e, -5/2*e^7 + 31*e^5 - 118*e^3 + 249/2*e, e^6 - 10*e^4 + 2*e^2 + 59, -11*e^6 + 100*e^4 - 211*e^2 - 10, -11/2*e^6 + 49*e^4 - 97*e^2 - 29/2, e^6 - 14*e^4 + 47*e^2 - 46, 6*e^7 - 71*e^5 + 252*e^3 - 253*e, 23*e^5 - 201*e^3 + 402*e, -5*e^7 + 70*e^5 - 306*e^3 + 399*e, -21/2*e^7 + 119*e^5 - 406*e^3 + 789/2*e, -11/2*e^6 + 53*e^4 - 132*e^2 + 61/2, e^6 - 10*e^4 + 15*e^2 + 14, 13/2*e^6 - 45*e^4 + 45*e^2 + 99/2, e^6 - 10*e^4 + 30*e^2 + 3, -11/2*e^6 + 44*e^4 - 66*e^2 - 73/2, 11/2*e^6 - 52*e^4 + 109*e^2 + 111/2, -15/2*e^6 + 78*e^4 - 205*e^2 + 121/2, 13/2*e^6 - 68*e^4 + 186*e^2 - 133/2, -15/2*e^7 + 97*e^5 - 396*e^3 + 963/2*e, 3*e^7 - 17*e^5 - 6*e^3 + 58*e, -7*e^7 + 99*e^5 - 440*e^3 + 618*e, -1/2*e^7 + 9*e^5 - 67*e^3 + 341/2*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([7,7,-1/3*w^3 + 1/3*w^2 + 3*w - 3])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]