/* 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([14,14,1/3*w^3 - 3*w + 2]) 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^6 + 4*x^5 - 14*x^4 - 60*x^3 - 19*x^2 + 72*x + 44 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1, 1, e, 1/10*e^5 + 7/20*e^4 - 29/20*e^3 - 103/20*e^2 - 19/20*e + 53/10, 1/5*e^5 + 9/20*e^4 - 73/20*e^3 - 121/20*e^2 + 147/20*e + 61/10, -1/5*e^5 - 9/20*e^4 + 73/20*e^3 + 121/20*e^2 - 147/20*e - 81/10, 1/20*e^5 + 1/20*e^4 - 17/20*e^3 + 1/20*e^2 - 21/10*e - 28/5, 3/20*e^5 + 2/5*e^4 - 14/5*e^3 - 61/10*e^2 + 149/20*e + 87/10, 1/10*e^5 + 7/20*e^4 - 39/20*e^3 - 103/20*e^2 + 131/20*e + 53/10, 3/20*e^5 + 2/5*e^4 - 14/5*e^3 - 61/10*e^2 + 149/20*e + 87/10, -1/5*e^5 - 7/10*e^4 + 17/5*e^3 + 103/10*e^2 - 33/5*e - 58/5, 9/20*e^5 + 6/5*e^4 - 79/10*e^3 - 163/10*e^2 + 257/20*e + 151/10, 3/20*e^5 + 3/20*e^4 - 51/20*e^3 + 3/20*e^2 + 27/10*e - 54/5, -13/20*e^5 - 33/20*e^4 + 231/20*e^3 + 447/20*e^2 - 106/5*e - 141/5, 2/5*e^5 + 7/5*e^4 - 34/5*e^3 - 103/5*e^2 + 46/5*e + 76/5, -7/10*e^5 - 39/20*e^4 + 233/20*e^3 + 531/20*e^2 - 217/20*e - 221/10, -3/5*e^5 - 21/10*e^4 + 97/10*e^3 + 309/10*e^2 - 83/10*e - 179/5, -19/20*e^5 - 59/20*e^4 + 313/20*e^3 + 821/20*e^2 - 88/5*e - 183/5, -11/10*e^5 - 67/20*e^4 + 369/20*e^3 + 963/20*e^2 - 461/20*e - 523/10, -9/20*e^5 - 29/20*e^4 + 143/20*e^3 + 411/20*e^2 - 28/5*e - 93/5, -1/20*e^5 - 1/20*e^4 + 17/20*e^3 + 19/20*e^2 + 21/10*e - 12/5, 13/20*e^5 + 43/20*e^4 - 211/20*e^3 - 617/20*e^2 + 61/5*e + 161/5, 3/10*e^5 + 21/20*e^4 - 97/20*e^3 - 309/20*e^2 + 53/20*e + 159/10, -2/5*e^5 - 9/10*e^4 + 39/5*e^3 + 121/10*e^2 - 111/5*e - 76/5, -2/5*e^5 - 9/10*e^4 + 34/5*e^3 + 111/10*e^2 - 31/5*e - 26/5, 11/20*e^5 + 13/10*e^4 - 101/10*e^3 - 91/5*e^2 + 403/20*e + 209/10, 11/10*e^5 + 18/5*e^4 - 91/5*e^3 - 267/5*e^2 + 203/10*e + 289/5, -e^5 - 3*e^4 + 16*e^3 + 42*e^2 - 10*e - 46, -3/5*e^5 - 11/10*e^4 + 56/5*e^3 + 139/10*e^2 - 119/5*e - 64/5, 9/20*e^5 + 29/20*e^4 - 143/20*e^3 - 411/20*e^2 + 3/5*e + 93/5, 19/20*e^5 + 27/10*e^4 - 82/5*e^3 - 194/5*e^2 + 457/20*e + 431/10, 9/20*e^5 + 19/20*e^4 - 163/20*e^3 - 241/20*e^2 + 83/5*e + 33/5, 7/5*e^5 + 39/10*e^4 - 119/5*e^3 - 541/10*e^2 + 146/5*e + 286/5, -29/20*e^5 - 89/20*e^4 + 503/20*e^3 + 1291/20*e^2 - 213/5*e - 393/5, 6/5*e^5 + 69/20*e^4 - 413/20*e^3 - 1001/20*e^2 + 527/20*e + 631/10, 1/10*e^5 + 3/5*e^4 - 17/10*e^3 - 52/5*e^2 + 34/5*e + 114/5, 3/10*e^5 + 11/20*e^4 - 127/20*e^3 - 139/20*e^2 + 443/20*e + 109/10, 13/20*e^5 + 7/5*e^4 - 113/10*e^3 - 161/10*e^2 + 309/20*e + 17/10, -6/5*e^5 - 37/10*e^4 + 97/5*e^3 + 513/10*e^2 - 88/5*e - 218/5, 1/4*e^5 + 1/2*e^4 - 11/2*e^3 - 8*e^2 + 81/4*e + 37/2, -11/20*e^5 - 23/10*e^4 + 81/10*e^3 + 176/5*e^2 + 57/20*e - 359/10, 1/20*e^5 + 1/20*e^4 - 17/20*e^3 + 21/20*e^2 + 19/10*e - 58/5, 9/20*e^5 + 17/10*e^4 - 37/5*e^3 - 134/5*e^2 + 207/20*e + 381/10, -11/20*e^5 - 41/20*e^4 + 167/20*e^3 + 619/20*e^2 - 9/10*e - 202/5, 2/5*e^5 + 7/5*e^4 - 63/10*e^3 - 103/5*e^2 + 37/10*e + 101/5, -7/10*e^5 - 39/20*e^4 + 233/20*e^3 + 531/20*e^2 - 217/20*e - 241/10, -3/10*e^5 - 21/20*e^4 + 107/20*e^3 + 349/20*e^2 - 203/20*e - 319/10, 2/5*e^5 + 9/10*e^4 - 39/5*e^3 - 121/10*e^2 + 126/5*e + 36/5, -19/20*e^5 - 59/20*e^4 + 323/20*e^3 + 821/20*e^2 - 221/10*e - 178/5, -1/5*e^5 + 3/10*e^4 + 49/10*e^3 - 67/10*e^2 - 201/10*e + 17/5, 3/20*e^5 + 3/20*e^4 - 61/20*e^3 - 17/20*e^2 + 41/5*e + 1/5, -9/10*e^5 - 63/20*e^4 + 291/20*e^3 + 947/20*e^2 - 299/20*e - 567/10, 4/5*e^5 + 61/20*e^4 - 247/20*e^3 - 889/20*e^2 + 93/20*e + 479/10, -1/4*e^5 - e^4 + 9/2*e^3 + 31/2*e^2 - 45/4*e - 55/2, -7/5*e^5 - 73/20*e^4 + 481/20*e^3 + 997/20*e^2 - 639/20*e - 467/10, 11/20*e^5 + 41/20*e^4 - 177/20*e^3 - 619/20*e^2 + 32/5*e + 187/5, -17/20*e^5 - 57/20*e^4 + 289/20*e^3 + 843/20*e^2 - 203/10*e - 184/5, 8/5*e^5 + 23/5*e^4 - 267/10*e^3 - 327/5*e^2 + 263/10*e + 339/5, -17/20*e^5 - 57/20*e^4 + 279/20*e^3 + 823/20*e^2 - 89/5*e - 209/5, 8/5*e^5 + 23/5*e^4 - 136/5*e^3 - 327/5*e^2 + 189/5*e + 364/5, 17/20*e^5 + 21/10*e^4 - 76/5*e^3 - 147/5*e^2 + 611/20*e + 363/10, -11/20*e^5 - 13/10*e^4 + 53/5*e^3 + 96/5*e^2 - 533/20*e - 289/10, -e^5 - 11/4*e^4 + 71/4*e^3 + 159/4*e^2 - 109/4*e - 103/2, -33/20*e^5 - 93/20*e^4 + 561/20*e^3 + 1287/20*e^2 - 327/10*e - 306/5, -23/20*e^5 - 17/5*e^4 + 99/5*e^3 + 491/10*e^2 - 689/20*e - 607/10, -19/20*e^5 - 49/20*e^4 + 323/20*e^3 + 631/20*e^2 - 231/10*e - 98/5, -1/10*e^5 - 7/20*e^4 + 29/20*e^3 + 103/20*e^2 - 21/20*e - 83/10, -29/20*e^5 - 79/20*e^4 + 503/20*e^3 + 1101/20*e^2 - 188/5*e - 293/5, 49/20*e^5 + 149/20*e^4 - 813/20*e^3 - 2091/20*e^2 + 431/10*e + 518/5, -21/20*e^5 - 14/5*e^4 + 191/10*e^3 + 387/10*e^2 - 773/20*e - 429/10, -41/20*e^5 - 121/20*e^4 + 697/20*e^3 + 1699/20*e^2 - 459/10*e - 392/5, -13/20*e^5 - 19/10*e^4 + 54/5*e^3 + 133/5*e^2 - 299/20*e - 447/10, 11/4*e^5 + 31/4*e^4 - 189/4*e^3 - 437/4*e^2 + 67*e + 121, -5/4*e^5 - 7/2*e^4 + 43/2*e^3 + 48*e^2 - 117/4*e - 89/2, 33/20*e^5 + 27/5*e^4 - 139/5*e^3 - 801/10*e^2 + 699/20*e + 817/10, -3/20*e^5 - 9/10*e^4 + 23/10*e^3 + 78/5*e^2 + 21/20*e - 227/10, 3/5*e^5 + 37/20*e^4 - 209/20*e^3 - 533/20*e^2 + 331/20*e + 263/10, -9/10*e^5 - 7/5*e^4 + 173/10*e^3 + 78/5*e^2 - 236/5*e - 56/5, 23/20*e^5 + 39/10*e^4 - 193/10*e^3 - 288/5*e^2 + 579/20*e + 657/10, -11/20*e^5 - 13/10*e^4 + 91/10*e^3 + 76/5*e^2 - 103/20*e + 61/10, -9/10*e^5 - 29/10*e^4 + 74/5*e^3 + 411/10*e^2 - 207/10*e - 231/5, 19/20*e^5 + 16/5*e^4 - 77/5*e^3 - 443/10*e^2 + 257/20*e + 281/10, -6/5*e^5 - 27/10*e^4 + 209/10*e^3 + 313/10*e^2 - 291/10*e - 23/5, 4/5*e^5 + 51/20*e^4 - 257/20*e^3 - 759/20*e^2 + 143/20*e + 409/10, 1/4*e^4 + 5/4*e^3 - 9/4*e^2 - 67/4*e - 9/2, -9/20*e^5 - 39/20*e^4 + 113/20*e^3 + 581/20*e^2 + 169/10*e - 188/5, 33/20*e^5 + 22/5*e^4 - 293/10*e^3 - 601/10*e^2 + 1009/20*e + 627/10, 1/4*e^5 - 1/4*e^4 - 25/4*e^3 + 27/4*e^2 + 59/2*e - 6, 3/5*e^5 + 11/10*e^4 - 107/10*e^3 - 109/10*e^2 + 223/10*e - 1/5, -41/20*e^5 - 53/10*e^4 + 361/10*e^3 + 371/5*e^2 - 1253/20*e - 889/10, 3/5*e^5 + 11/10*e^4 - 56/5*e^3 - 119/10*e^2 + 84/5*e - 6/5, -3/5*e^5 - 21/10*e^4 + 51/5*e^3 + 329/10*e^2 - 49/5*e - 244/5, 7/4*e^5 + 21/4*e^4 - 117/4*e^3 - 303/4*e^2 + 37*e + 91, 1/5*e^5 + 9/20*e^4 - 83/20*e^3 - 141/20*e^2 + 177/20*e + 31/10, -7/4*e^5 - 21/4*e^4 + 119/4*e^3 + 311/4*e^2 - 83/2*e - 96, 7/10*e^5 + 11/5*e^4 - 119/10*e^3 - 154/5*e^2 + 93/5*e + 8/5, 7/5*e^5 + 83/20*e^4 - 481/20*e^3 - 1227/20*e^2 + 679/20*e + 747/10, 3/20*e^5 + 33/20*e^4 - 11/20*e^3 - 507/20*e^2 - 183/10*e + 86/5, -3/20*e^5 - 23/20*e^4 + 41/20*e^3 + 377/20*e^2 - 6/5*e - 191/5, -21/10*e^5 - 28/5*e^4 + 377/10*e^3 + 402/5*e^2 - 349/5*e - 514/5, 9/5*e^5 + 91/20*e^4 - 617/20*e^3 - 1199/20*e^2 + 783/20*e + 479/10, -13/10*e^5 - 14/5*e^4 + 231/10*e^3 + 181/5*e^2 - 187/5*e - 152/5, 31/20*e^5 + 101/20*e^4 - 497/20*e^3 - 1399/20*e^2 + 107/5*e + 247/5, 43/20*e^5 + 123/20*e^4 - 741/20*e^3 - 1717/20*e^2 + 251/5*e + 431/5, 13/10*e^5 + 81/20*e^4 - 407/20*e^3 - 1109/20*e^2 + 123/20*e + 659/10, 1/4*e^5 + e^4 - 9/2*e^3 - 35/2*e^2 + 57/4*e + 63/2, 3/5*e^5 + 13/5*e^4 - 77/10*e^3 - 197/5*e^2 - 147/10*e + 249/5, 5/4*e^5 + 7/2*e^4 - 20*e^3 - 48*e^2 + 47/4*e + 91/2, -7/4*e^5 - 11/2*e^4 + 59/2*e^3 + 80*e^2 - 163/4*e - 205/2, 13/10*e^5 + 19/5*e^4 - 221/10*e^3 - 276/5*e^2 + 127/5*e + 362/5, 31/10*e^5 + 91/10*e^4 - 517/10*e^3 - 1289/10*e^2 + 254/5*e + 624/5, 4/5*e^5 + 41/20*e^4 - 277/20*e^3 - 549/20*e^2 + 403/20*e + 459/10, -7/10*e^5 - 27/10*e^4 + 109/10*e^3 + 393/10*e^2 - 18/5*e - 198/5, 3/20*e^5 + 13/20*e^4 - 61/20*e^3 - 127/20*e^2 + 86/5*e - 99/5, -e^5 - 3*e^4 + 31/2*e^3 + 40*e^2 - 11/2*e - 23, -57/20*e^5 - 157/20*e^4 + 979/20*e^3 + 2143/20*e^2 - 324/5*e - 499/5, -4/5*e^5 - 14/5*e^4 + 68/5*e^3 + 201/5*e^2 - 112/5*e - 122/5, -7/4*e^5 - 19/4*e^4 + 121/4*e^3 + 273/4*e^2 - 41*e - 89, -23/10*e^5 - 63/10*e^4 + 381/10*e^3 + 857/10*e^2 - 177/5*e - 342/5, 11/20*e^5 + 23/10*e^4 - 91/10*e^3 - 181/5*e^2 + 383/20*e + 559/10, -23/10*e^5 - 131/20*e^4 + 797/20*e^3 + 1879/20*e^2 - 1193/20*e - 989/10, 41/20*e^5 + 141/20*e^4 - 657/20*e^3 - 2099/20*e^2 + 269/10*e + 522/5, 13/20*e^5 + 33/20*e^4 - 251/20*e^3 - 487/20*e^2 + 206/5*e + 161/5, e^5 + 7/4*e^4 - 73/4*e^3 - 75/4*e^2 + 111/4*e - 29/2, -11/20*e^5 - 1/20*e^4 + 237/20*e^3 - 81/20*e^2 - 207/5*e + 13/5, 13/20*e^5 + 53/20*e^4 - 171/20*e^3 - 767/20*e^2 - 64/5*e + 111/5, 29/20*e^5 + 37/10*e^4 - 122/5*e^3 - 239/5*e^2 + 407/20*e + 151/10, 29/20*e^5 + 21/5*e^4 - 127/5*e^3 - 583/10*e^2 + 967/20*e + 651/10, 33/20*e^5 + 83/20*e^4 - 571/20*e^3 - 1097/20*e^2 + 176/5*e + 121/5, 1/4*e^5 + e^4 - 7/2*e^3 - 23/2*e^2 + 21/4*e - 31/2, 3/20*e^5 + 3/20*e^4 - 61/20*e^3 - 17/20*e^2 - 4/5*e - 59/5, 3*e^5 + 9*e^4 - 103/2*e^3 - 129*e^2 + 149/2*e + 151, -13/10*e^5 - 81/20*e^4 + 427/20*e^3 + 1189/20*e^2 - 363/20*e - 469/10, -1/5*e^5 - 7/10*e^4 + 12/5*e^3 + 113/10*e^2 + 32/5*e - 88/5, 3/2*e^5 + 21/4*e^4 - 93/4*e^3 - 301/4*e^2 + 13/4*e + 123/2, 41/20*e^5 + 63/10*e^4 - 168/5*e^3 - 441/5*e^2 + 563/20*e + 889/10, -2/5*e^5 + 1/10*e^4 + 73/10*e^3 - 69/10*e^2 - 57/10*e + 189/5, -11/20*e^5 - 31/20*e^4 + 157/20*e^3 + 469/20*e^2 + 53/5*e - 227/5, 1/2*e^5 + 2*e^4 - 8*e^3 - 28*e^2 + 31/2*e + 15, 23/20*e^5 + 39/10*e^4 - 84/5*e^3 - 278/5*e^2 - 291/20*e + 527/10, 7/10*e^5 + 29/20*e^4 - 273/20*e^3 - 381/20*e^2 + 717/20*e + 91/10, -7/20*e^5 - 8/5*e^4 + 47/10*e^3 + 259/10*e^2 + 89/20*e - 503/10, 9/10*e^5 + 29/10*e^4 - 74/5*e^3 - 391/10*e^2 + 207/10*e + 71/5, 9/10*e^5 + 17/5*e^4 - 69/5*e^3 - 258/5*e^2 + 67/10*e + 211/5, -21/10*e^5 - 117/20*e^4 + 729/20*e^3 + 1633/20*e^2 - 1061/20*e - 723/10, 9/20*e^5 + 6/5*e^4 - 32/5*e^3 - 133/10*e^2 - 73/20*e - 169/10, 11/10*e^5 + 57/20*e^4 - 369/20*e^3 - 813/20*e^2 + 281/20*e + 563/10, -1/20*e^5 - 3/10*e^4 + 1/10*e^3 + 41/5*e^2 + 187/20*e - 419/10, 51/20*e^5 + 141/20*e^4 - 847/20*e^3 - 1899/20*e^2 + 429/10*e + 412/5, 14/5*e^5 + 171/20*e^4 - 957/20*e^3 - 2499/20*e^2 + 1423/20*e + 1479/10, -12/5*e^5 - 143/20*e^4 + 831/20*e^3 + 2087/20*e^2 - 1229/20*e - 1327/10, 23/10*e^5 + 29/5*e^4 - 401/10*e^3 - 406/5*e^2 + 297/5*e + 432/5, -13/20*e^5 - 17/5*e^4 + 83/10*e^3 + 511/10*e^2 + 251/20*e - 467/10, -51/20*e^5 - 73/10*e^4 + 451/10*e^3 + 536/5*e^2 - 1763/20*e - 1459/10, 3/20*e^5 + 19/10*e^4 + 7/10*e^3 - 158/5*e^2 - 701/20*e + 367/10, 8/5*e^5 + 87/20*e^4 - 539/20*e^3 - 1223/20*e^2 + 541/20*e + 503/10, -11/20*e^5 - 31/20*e^4 + 177/20*e^3 + 409/20*e^2 + 3/5*e - 77/5, 11/20*e^5 + 51/20*e^4 - 167/20*e^3 - 769/20*e^2 + 9/10*e + 152/5, e^5 + 9/4*e^4 - 79/4*e^3 - 121/4*e^2 + 209/4*e + 43/2, 3/4*e^5 + 3*e^4 - 11*e^3 - 87/2*e^2 + 1/4*e + 103/2, 37/20*e^5 + 97/20*e^4 - 679/20*e^3 - 1363/20*e^2 + 424/5*e + 419/5, -9/10*e^5 - 33/20*e^4 + 351/20*e^3 + 437/20*e^2 - 799/20*e - 487/10, -7/5*e^5 - 73/20*e^4 + 461/20*e^3 + 957/20*e^2 - 239/20*e - 327/10, 27/20*e^5 + 87/20*e^4 - 439/20*e^3 - 1233/20*e^2 + 153/10*e + 234/5, 43/20*e^5 + 123/20*e^4 - 761/20*e^3 - 1777/20*e^2 + 376/5*e + 491/5, 13/10*e^5 + 43/10*e^4 - 108/5*e^3 - 617/10*e^2 + 359/10*e + 257/5, 3/5*e^5 + 11/10*e^4 - 56/5*e^3 - 129/10*e^2 + 149/5*e + 4/5, -1/5*e^5 - 6/5*e^4 + 17/5*e^3 + 119/5*e^2 - 83/5*e - 338/5, 23/10*e^5 + 141/20*e^4 - 777/20*e^3 - 1969/20*e^2 + 933/20*e + 769/10, -39/10*e^5 - 52/5*e^4 + 663/10*e^3 + 703/5*e^2 - 426/5*e - 636/5, -3/5*e^5 - 13/5*e^4 + 56/5*e^3 + 207/5*e^2 - 179/5*e - 394/5, 3/10*e^5 + 13/10*e^4 - 41/10*e^3 - 187/10*e^2 - 48/5*e + 12/5, 11/20*e^5 + 1/20*e^4 - 237/20*e^3 + 21/20*e^2 + 207/5*e + 147/5, 63/20*e^5 + 42/5*e^4 - 553/10*e^3 - 1191/10*e^2 + 1979/20*e + 1507/10, 1/20*e^5 - 6/5*e^4 - 41/10*e^3 + 193/10*e^2 + 673/20*e - 181/10, 8/5*e^5 + 23/5*e^4 - 257/10*e^3 - 332/5*e^2 + 103/10*e + 309/5, 91/20*e^5 + 64/5*e^4 - 781/10*e^3 - 1817/10*e^2 + 2103/20*e + 1949/10, 1/2*e^5 + 3*e^4 - 9/2*e^3 - 45*e^2 - 33*e + 32, 3/4*e^5 + 13/4*e^4 - 43/4*e^3 - 191/4*e^2 - 1/2*e + 64, -1/2*e^5 - 3/4*e^4 + 41/4*e^3 + 43/4*e^2 - 117/4*e - 75/2, 17/20*e^5 + 11/10*e^4 - 167/10*e^3 - 52/5*e^2 + 641/20*e - 187/10, 1/4*e^4 - 5/4*e^3 - 37/4*e^2 + 71/4*e + 53/2, -79/20*e^5 - 56/5*e^4 + 337/5*e^3 + 1573/10*e^2 - 1797/20*e - 1631/10, 71/20*e^5 + 201/20*e^4 - 1207/20*e^3 - 2799/20*e^2 + 689/10*e + 572/5, 17/5*e^5 + 99/10*e^4 - 294/5*e^3 - 1431/10*e^2 + 436/5*e + 876/5, -17/20*e^5 - 31/10*e^4 + 117/10*e^3 + 237/5*e^2 + 499/20*e - 503/10, -57/20*e^5 - 157/20*e^4 + 959/20*e^3 + 2163/20*e^2 - 324/5*e - 579/5, 9/5*e^5 + 43/10*e^4 - 163/5*e^3 - 567/10*e^2 + 317/5*e + 232/5, 1/20*e^5 + 1/20*e^4 - 7/20*e^3 - 39/20*e^2 - 68/5*e - 43/5, 8/5*e^5 + 31/10*e^4 - 146/5*e^3 - 379/10*e^2 + 309/5*e + 194/5, -3/20*e^5 - 3/20*e^4 + 51/20*e^3 - 23/20*e^2 - 17/10*e + 174/5, 1/20*e^5 + 11/20*e^4 - 27/20*e^3 - 269/20*e^2 + 2/5*e + 267/5, -31/20*e^5 - 24/5*e^4 + 128/5*e^3 + 677/10*e^2 - 453/20*e - 889/10, -19/20*e^5 - 11/5*e^4 + 87/5*e^3 + 303/10*e^2 - 837/20*e - 171/10, 3/2*e^5 + 19/4*e^4 - 97/4*e^3 - 263/4*e^2 + 61/4*e + 77/2, -71/20*e^5 - 201/20*e^4 + 1237/20*e^3 + 2879/20*e^2 - 507/5*e - 827/5, 9/4*e^5 + 6*e^4 - 79/2*e^3 - 171/2*e^2 + 293/4*e + 241/2, 9/10*e^5 + 7/5*e^4 - 173/10*e^3 - 63/5*e^2 + 211/5*e - 124/5, 59/20*e^5 + 41/5*e^4 - 499/10*e^3 - 1153/10*e^2 + 1227/20*e + 1171/10, -23/10*e^5 - 39/5*e^4 + 381/10*e^3 + 586/5*e^2 - 267/5*e - 732/5, 11/4*e^5 + 31/4*e^4 - 189/4*e^3 - 441/4*e^2 + 70*e + 129, -31/10*e^5 - 101/10*e^4 + 517/10*e^3 + 1459/10*e^2 - 324/5*e - 704/5, -1/2*e^5 - 5/4*e^4 + 31/4*e^3 + 61/4*e^2 + 29/4*e + 3/2, e^5 + 5/2*e^4 - 18*e^3 - 61/2*e^2 + 40*e - 6, 9/4*e^5 + 13/2*e^4 - 39*e^3 - 97*e^2 + 251/4*e + 289/2, 21/10*e^5 + 117/20*e^4 - 709/20*e^3 - 1673/20*e^2 + 941/20*e + 1283/10, -6/5*e^5 - 89/20*e^4 + 393/20*e^3 + 1341/20*e^2 - 387/20*e - 671/10, -39/20*e^5 - 89/20*e^4 + 693/20*e^3 + 1151/20*e^2 - 273/5*e - 283/5, 9/10*e^5 + 73/20*e^4 - 261/20*e^3 - 1037/20*e^2 - 31/20*e + 577/10, 3/2*e^5 + 19/4*e^4 - 97/4*e^3 - 259/4*e^2 + 117/4*e + 93/2, -1/20*e^5 - 13/10*e^4 - 2/5*e^3 + 131/5*e^2 + 237/20*e - 619/10, -14/5*e^5 - 39/5*e^4 + 248/5*e^3 + 561/5*e^2 - 412/5*e - 722/5, -29/20*e^5 - 69/20*e^4 + 503/20*e^3 + 911/20*e^2 - 198/5*e - 223/5, -29/20*e^5 - 47/10*e^4 + 112/5*e^3 + 329/5*e^2 - 67/20*e - 701/10, 1/5*e^5 + 17/10*e^4 - 9/10*e^3 - 293/10*e^2 - 219/10*e + 153/5, 83/20*e^5 + 253/20*e^4 - 1391/20*e^3 - 3607/20*e^2 + 867/10*e + 866/5, -3/2*e^5 - 17/4*e^4 + 105/4*e^3 + 253/4*e^2 - 193/4*e - 177/2, 9/10*e^5 + 63/20*e^4 - 331/20*e^3 - 927/20*e^2 + 839/20*e + 397/10, 1/5*e^5 + 19/20*e^4 - 23/20*e^3 - 251/20*e^2 - 363/20*e - 189/10, 4/5*e^5 + 41/20*e^4 - 247/20*e^3 - 449/20*e^2 + 33/20*e - 31/10, -1/2*e^5 - 3/2*e^4 + 7*e^3 + 43/2*e^2 + 37/2*e - 37, 1/10*e^5 + 37/20*e^4 + 41/20*e^3 - 633/20*e^2 - 1049/20*e + 223/10, -7/20*e^5 - 21/10*e^4 + 47/10*e^3 + 172/5*e^2 + 189/20*e - 543/10, -41/20*e^5 - 131/20*e^4 + 677/20*e^3 + 1909/20*e^2 - 409/10*e - 482/5, -1/5*e^5 - 1/5*e^4 + 49/10*e^3 + 19/5*e^2 - 261/10*e - 23/5, 9/10*e^5 + 12/5*e^4 - 163/10*e^3 - 158/5*e^2 + 196/5*e + 86/5, 3/20*e^5 + 3/20*e^4 - 41/20*e^3 + 23/20*e^2 - 74/5*e - 219/5, 57/20*e^5 + 157/20*e^4 - 999/20*e^3 - 2263/20*e^2 + 374/5*e + 779/5, -e^5 - 2*e^4 + 37/2*e^3 + 25*e^2 - 83/2*e - 49, 31/20*e^5 + 61/20*e^4 - 577/20*e^3 - 779/20*e^2 + 282/5*e + 107/5, 63/20*e^5 + 42/5*e^4 - 543/10*e^3 - 1151/10*e^2 + 1539/20*e + 1177/10, -1/4*e^5 - 3/4*e^4 + 13/4*e^3 + 37/4*e^2 + 33/2*e - 10, 47/20*e^5 + 137/20*e^4 - 849/20*e^3 - 2023/20*e^2 + 444/5*e + 709/5, 8/5*e^5 + 18/5*e^4 - 141/5*e^3 - 212/5*e^2 + 179/5*e - 46/5, -41/10*e^5 - 131/10*e^4 + 687/10*e^3 + 1929/10*e^2 - 454/5*e - 1074/5, -11/20*e^5 - 14/5*e^4 + 48/5*e^3 + 497/10*e^2 - 493/20*e - 1079/10, -13/10*e^5 - 71/20*e^4 + 467/20*e^3 + 1039/20*e^2 - 923/20*e - 579/10, 3/20*e^5 - 7/20*e^4 - 81/20*e^3 + 33/20*e^2 + 96/5*e + 241/5, 37/20*e^5 + 127/20*e^4 - 659/20*e^3 - 1913/20*e^2 + 369/5*e + 749/5, -7/5*e^5 - 43/20*e^4 + 541/20*e^3 + 447/20*e^2 - 1539/20*e - 307/10, 23/10*e^5 + 34/5*e^4 - 371/10*e^3 - 461/5*e^2 + 172/5*e + 222/5, -1/20*e^5 + 7/10*e^4 + 18/5*e^3 - 59/5*e^2 - 843/20*e + 291/10, -3/4*e^5 - 11/4*e^4 + 45/4*e^3 + 149/4*e^2 + 4*e - 31, 13/20*e^5 + 53/20*e^4 - 201/20*e^3 - 767/20*e^2 - 3/10*e + 36/5, -19/20*e^5 - 16/5*e^4 + 139/10*e^3 + 473/10*e^2 + 113/20*e - 641/10, -63/20*e^5 - 42/5*e^4 + 279/5*e^3 + 1201/10*e^2 - 1829/20*e - 1637/10, 11/4*e^5 + 31/4*e^4 - 189/4*e^3 - 437/4*e^2 + 73*e + 97, -81/20*e^5 - 251/20*e^4 + 1337/20*e^3 + 3529/20*e^2 - 739/10*e - 922/5, 3/5*e^5 + 13/5*e^4 - 41/5*e^3 - 187/5*e^2 - 66/5*e + 54/5, 13/10*e^5 + 19/5*e^4 - 113/5*e^3 - 266/5*e^2 + 489/10*e + 287/5, -69/20*e^5 - 97/10*e^4 + 589/10*e^3 + 679/5*e^2 - 1617/20*e - 1581/10, -5/2*e^5 - 15/2*e^4 + 42*e^3 + 215/2*e^2 - 105/2*e - 139, -9/5*e^5 - 34/5*e^4 + 143/5*e^3 + 506/5*e^2 - 132/5*e - 492/5, -37/20*e^5 - 28/5*e^4 + 161/5*e^3 + 789/10*e^2 - 1071/20*e - 663/10, 33/10*e^5 + 103/10*e^4 - 561/10*e^3 - 1497/10*e^2 + 417/5*e + 822/5, 33/10*e^5 + 44/5*e^4 - 561/10*e^3 - 616/5*e^2 + 307/5*e + 582/5, 33/20*e^5 + 49/10*e^4 - 283/10*e^3 - 358/5*e^2 + 1089/20*e + 957/10, -1/4*e^5 + 1/4*e^4 + 27/4*e^3 - 39/4*e^2 - 34*e + 39, -3/20*e^5 + 11/10*e^4 + 24/5*e^3 - 107/5*e^2 - 329/20*e + 453/10, -37/20*e^5 - 87/20*e^4 + 699/20*e^3 + 1173/20*e^2 - 404/5*e - 359/5, -63/20*e^5 - 183/20*e^4 + 1111/20*e^3 + 2637/20*e^2 - 927/10*e - 756/5, 3/2*e^4 + e^3 - 55/2*e^2 + 94, 57/20*e^5 + 38/5*e^4 - 241/5*e^3 - 1029/10*e^2 + 991/20*e + 853/10, -63/20*e^5 - 193/20*e^4 + 1081/20*e^3 + 2767/20*e^2 - 456/5*e - 881/5, 51/10*e^5 + 68/5*e^4 - 897/10*e^3 - 957/5*e^2 + 769/5*e + 1194/5, 2*e^5 + 4*e^4 - 75/2*e^3 - 49*e^2 + 193/2*e + 47, 13/10*e^5 + 101/20*e^4 - 417/20*e^3 - 1609/20*e^2 + 373/20*e + 999/10, -1/2*e^5 + 17/2*e^3 - 8*e^2 - 5*e + 60, -3/10*e^5 - 3/10*e^4 + 51/10*e^3 + 37/10*e^2 - 17/5*e - 112/5, -1/4*e^5 + 7*e^3 - 11/2*e^2 - 179/4*e + 53/2, -61/20*e^5 - 44/5*e^4 + 263/5*e^3 + 1217/10*e^2 - 1683/20*e - 1199/10, -3/20*e^5 - 9/10*e^4 - 7/10*e^3 + 48/5*e^2 + 661/20*e + 303/10, -53/20*e^5 - 42/5*e^4 + 443/10*e^3 + 1181/10*e^2 - 1349/20*e - 947/10, -12/5*e^5 - 32/5*e^4 + 219/5*e^3 + 458/5*e^2 - 501/5*e - 666/5, -19/5*e^5 - 231/20*e^4 + 1267/20*e^3 + 3299/20*e^2 - 1713/20*e - 2009/10, -19/10*e^5 - 39/10*e^4 + 353/10*e^3 + 481/10*e^2 - 326/5*e - 226/5, 7/20*e^5 + 57/20*e^4 - 69/20*e^3 - 963/20*e^2 - 91/5*e + 249/5, 6/5*e^5 + 49/20*e^4 - 413/20*e^3 - 601/20*e^2 + 447/20*e - 99/10, 17/20*e^5 + 27/20*e^4 - 349/20*e^3 - 453/20*e^2 + 503/10*e + 364/5, 3/20*e^5 + 33/20*e^4 - 1/20*e^3 - 447/20*e^2 - 79/5*e - 29/5, 77/20*e^5 + 207/20*e^4 - 1329/20*e^3 - 2893/20*e^2 + 1033/10*e + 804/5, 67/20*e^5 + 217/20*e^4 - 1159/20*e^3 - 3303/20*e^2 + 973/10*e + 1064/5, -7/4*e^5 - 4*e^4 + 67/2*e^3 + 99/2*e^2 - 387/4*e - 89/2, -49/10*e^5 - 149/10*e^4 + 414/5*e^3 + 2151/10*e^2 - 997/10*e - 1091/5, 29/20*e^5 + 47/10*e^4 - 219/10*e^3 - 339/5*e^2 - 163/20*e + 671/10, -27/10*e^5 - 189/20*e^4 + 863/20*e^3 + 2841/20*e^2 - 587/20*e - 1391/10, -23/10*e^5 - 141/20*e^4 + 767/20*e^3 + 2049/20*e^2 - 843/20*e - 1119/10, -31/20*e^5 - 53/10*e^4 + 118/5*e^3 + 381/5*e^2 + 67/20*e - 659/10, -21/20*e^5 - 13/10*e^4 + 221/10*e^3 + 76/5*e^2 - 1633/20*e - 339/10, 19/10*e^5 + 113/20*e^4 - 671/20*e^3 - 1757/20*e^2 + 1219/20*e + 1347/10, -21/10*e^5 - 33/5*e^4 + 347/10*e^3 + 472/5*e^2 - 139/5*e - 564/5, 8/5*e^5 + 38/5*e^4 - 106/5*e^3 - 582/5*e^2 - 116/5*e + 594/5, 11/10*e^5 + 47/20*e^4 - 379/20*e^3 - 583/20*e^2 + 691/20*e + 393/10] 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^2 + w])] = 1 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]