/* 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([9, -1, -7, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([16, 2, 2]) primes_array = [ [2, 2, -w^2 + w + 4],\ [3, 3, -w^2 + w + 3],\ [5, 5, w^2 - 4],\ [8, 2, w^3 - w^2 - 4*w + 5],\ [17, 17, -w^2 + w + 5],\ [27, 3, -w^3 + 4*w - 2],\ [29, 29, -w^2 + w + 1],\ [29, 29, -w^3 + 4*w + 2],\ [37, 37, -2*w^3 + 3*w^2 + 9*w - 13],\ [41, 41, w^3 - w^2 - 5*w + 2],\ [43, 43, -w^3 + w^2 + 3*w - 4],\ [61, 61, w^2 - 2*w - 2],\ [61, 61, 2*w^2 - w - 8],\ [67, 67, -4*w^3 + 5*w^2 + 18*w - 22],\ [73, 73, -w^2 - 2*w + 2],\ [79, 79, w^2 - 2*w - 4],\ [89, 89, w^2 + w - 5],\ [89, 89, 2*w^3 - 2*w^2 - 9*w + 8],\ [89, 89, w^3 - 5*w - 5],\ [89, 89, -w^3 + 2*w^2 + 4*w - 4],\ [97, 97, w^3 + w^2 - 5*w - 4],\ [101, 101, -2*w^3 + 2*w^2 + 8*w - 11],\ [103, 103, w^3 - 5*w + 1],\ [109, 109, 2*w - 1],\ [109, 109, -w^3 + 2*w^2 + 3*w - 7],\ [113, 113, 2*w^2 - 7],\ [125, 5, -w^3 + 3*w^2 + 3*w - 8],\ [127, 127, 2*w^3 - 4*w^2 - 11*w + 16],\ [131, 131, 3*w^2 + 2*w - 8],\ [131, 131, -2*w^3 + 4*w^2 + 8*w - 13],\ [137, 137, w^3 - 3*w^2 - 7*w + 10],\ [149, 149, -w^3 + 4*w - 4],\ [149, 149, w^2 - 2*w - 8],\ [157, 157, -w - 4],\ [163, 163, -w^3 + 2*w^2 + 6*w - 10],\ [167, 167, -w^3 + 2*w^2 + 5*w - 11],\ [167, 167, -3*w^2 - 2*w + 10],\ [167, 167, -w^2 - w + 7],\ [167, 167, 2*w^2 - 2*w - 5],\ [173, 173, -3*w^3 + 2*w^2 + 13*w - 11],\ [179, 179, w^3 - 3*w^2 - 5*w + 10],\ [191, 191, -2*w^3 - 3*w^2 + 10*w + 14],\ [191, 191, 3*w^2 + w - 7],\ [193, 193, w^2 - w + 1],\ [193, 193, -w^2 - w - 1],\ [227, 227, 4*w^3 - 4*w^2 - 17*w + 20],\ [227, 227, -3*w^3 + 4*w^2 + 13*w - 17],\ [229, 229, -w^3 + 6*w - 2],\ [233, 233, -3*w^3 + 3*w^2 + 13*w - 16],\ [241, 241, -w^2 + 2*w - 2],\ [263, 263, 2*w^3 - 5*w^2 - 12*w + 16],\ [263, 263, -3*w^3 + 4*w^2 + 13*w - 19],\ [269, 269, w^3 + 2*w^2 - 5*w - 7],\ [269, 269, -w^3 - 2*w^2 + w + 5],\ [281, 281, 2*w^3 - 2*w^2 - 8*w + 1],\ [281, 281, w^2 - 8],\ [289, 17, 2*w^3 - 10*w - 7],\ [307, 307, w^3 + 2*w^2 - 6*w - 8],\ [307, 307, -2*w^3 + 2*w^2 + 8*w - 7],\ [313, 313, 5*w^3 - 6*w^2 - 24*w + 28],\ [313, 313, 2*w^3 - 2*w^2 - 10*w + 5],\ [337, 337, w^3 - 2*w - 2],\ [347, 347, -w^3 + 4*w^2 + w - 13],\ [349, 349, -2*w^3 + w^2 + 9*w - 7],\ [353, 353, 2*w^3 + w^2 - 7*w + 1],\ [359, 359, -3*w^2 - 3*w + 5],\ [359, 359, 3*w^3 - 5*w^2 - 13*w + 16],\ [367, 367, 3*w^3 - 6*w^2 - 15*w + 23],\ [367, 367, -w^3 + 2*w^2 + 6*w - 4],\ [367, 367, -2*w^3 + 2*w^2 + 8*w - 5],\ [367, 367, 2*w^3 - 3*w^2 - 12*w + 16],\ [373, 373, -2*w^3 + 4*w^2 + 12*w - 17],\ [373, 373, 3*w^2 + 4*w - 8],\ [383, 383, -w^3 + 2*w^2 + 3*w - 13],\ [383, 383, 2*w^2 - 2*w - 11],\ [389, 389, 5*w^3 - 6*w^2 - 24*w + 26],\ [389, 389, -w^3 + 3*w - 5],\ [401, 401, w^3 + 2*w^2 - 4*w - 10],\ [401, 401, 2*w^3 - w^2 - 7*w + 5],\ [409, 409, -2*w^2 + 3*w + 10],\ [419, 419, w^2 - 3*w - 1],\ [419, 419, -w^3 + 5*w^2 + 9*w - 14],\ [421, 421, 2*w^3 - 8*w - 7],\ [431, 431, -3*w^2 + 16],\ [431, 431, -3*w^3 + 11*w - 7],\ [433, 433, 4*w^3 - 7*w^2 - 18*w + 26],\ [439, 439, 3*w - 2],\ [439, 439, -w^3 + w^2 + 5*w - 8],\ [443, 443, 2*w^3 - w^2 - 6*w + 4],\ [443, 443, w^2 + 3*w - 1],\ [449, 449, -2*w^3 + 5*w^2 + 7*w - 17],\ [457, 457, 4*w^3 - 6*w^2 - 19*w + 22],\ [479, 479, 3*w^2 - 3*w - 13],\ [479, 479, -4*w^3 + 8*w^2 + 22*w - 31],\ [479, 479, 3*w^3 - 7*w^2 - 17*w + 26],\ [479, 479, -6*w^3 + 7*w^2 + 28*w - 32],\ [487, 487, -2*w^3 + 4*w^2 + 7*w - 8],\ [491, 491, 3*w^2 - w - 11],\ [491, 491, 4*w^3 - 5*w^2 - 18*w + 20],\ [521, 521, -3*w^3 + 11*w - 5],\ [521, 521, 3*w^3 - 3*w^2 - 15*w + 14],\ [523, 523, -2*w^3 + 5*w^2 + 8*w - 14],\ [529, 23, -2*w^3 + 3*w^2 + 8*w - 14],\ [529, 23, 3*w^3 - 2*w^2 - 14*w + 4],\ [541, 541, -w^3 + 2*w^2 + 7*w - 11],\ [541, 541, -w^3 - w^2 + 5*w - 2],\ [547, 547, -3*w - 2],\ [547, 547, w^3 - 2*w^2 - 7*w + 7],\ [547, 547, w^3 - 4*w^2 - 8*w + 10],\ [547, 547, 2*w^3 - 3*w^2 - 7*w + 11],\ [563, 563, 2*w^3 - 4*w^2 - 12*w + 13],\ [563, 563, -w^3 + 4*w^2 + w - 7],\ [571, 571, -w^3 + 2*w^2 + 2*w - 8],\ [571, 571, 3*w^2 - 10],\ [577, 577, 2*w^3 + w^2 - 7*w - 5],\ [599, 599, 2*w^3 - 7*w + 2],\ [599, 599, -4*w^3 + 7*w^2 + 21*w - 29],\ [617, 617, -2*w^3 + w^2 + 11*w + 1],\ [631, 631, 3*w^2 + w - 13],\ [631, 631, 3*w^2 - 4*w - 10],\ [647, 647, 3*w^3 - 4*w^2 - 13*w + 11],\ [677, 677, -2*w^3 + 4*w^2 + 8*w - 17],\ [691, 691, -w^3 + 3*w^2 + 3*w - 14],\ [733, 733, -w^3 + 4*w^2 + 3*w - 11],\ [733, 733, 3*w^3 - w^2 - 15*w - 2],\ [733, 733, -w^3 + w^2 + 7*w - 2],\ [733, 733, 3*w^3 - 4*w^2 - 16*w + 16],\ [739, 739, -3*w^3 + w^2 + 11*w - 8],\ [743, 743, -3*w^3 + 2*w^2 + 12*w - 14],\ [751, 751, -2*w^3 + w^2 + 8*w - 2],\ [761, 761, -2*w^3 + 2*w^2 + 7*w - 10],\ [761, 761, 2*w^3 - 4*w^2 - 3*w + 8],\ [769, 769, -w^3 + w^2 + 7*w - 4],\ [769, 769, 2*w^3 + 2*w^2 - 8*w - 11],\ [787, 787, -2*w^3 + 3*w^2 + 6*w - 10],\ [787, 787, -2*w^2 - 3*w + 8],\ [797, 797, -2*w^3 + w^2 + 7*w - 1],\ [797, 797, -2*w^3 - 2*w^2 + 11*w + 10],\ [809, 809, -2*w^3 + 5*w^2 + 7*w - 19],\ [811, 811, 2*w^3 - 2*w^2 - 7*w - 2],\ [811, 811, 3*w^3 - 2*w^2 - 11*w - 1],\ [827, 827, 3*w^3 - 2*w^2 - 14*w + 10],\ [829, 829, 2*w^3 - 2*w^2 - 9*w + 2],\ [829, 829, 4*w^2 + 2*w - 11],\ [841, 29, 2*w^3 + w^2 - 6*w - 2],\ [863, 863, 2*w^3 - 8*w - 1],\ [883, 883, 3*w^3 - 4*w^2 - 15*w + 13],\ [887, 887, 3*w^3 - 2*w^2 - 12*w + 10],\ [907, 907, 2*w^3 - 3*w^2 - 9*w + 7],\ [911, 911, 2*w^3 + w^2 - 11*w - 5],\ [919, 919, -2*w^3 + 5*w - 8],\ [929, 929, -w^3 + 4*w^2 + 3*w - 13],\ [937, 937, w^3 - 5*w - 7],\ [937, 937, -2*w^3 + 3*w^2 + 10*w - 8],\ [971, 971, -2*w^3 + 4*w^2 + 11*w - 20],\ [971, 971, -4*w^3 + 4*w^2 + 19*w - 20],\ [977, 977, -4*w^3 + 6*w^2 + 19*w - 28],\ [983, 983, -4*w^2 - 4*w + 7],\ [991, 991, -5*w^3 + 8*w^2 + 26*w - 32],\ [991, 991, -6*w^3 + 6*w^2 + 26*w - 31],\ [997, 997, -3*w^3 + 8*w^2 + 18*w - 26]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^7 + x^6 - 18*x^5 - 17*x^4 + 78*x^3 + 72*x^2 - 20*x - 16 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1, e, 1/60*e^6 - 7/60*e^5 - 11/30*e^4 + 33/20*e^3 + 21/10*e^2 - 23/5*e - 23/15, -1, -17/60*e^6 - 1/60*e^5 + 157/30*e^4 - 1/20*e^3 - 237/10*e^2 + 1/5*e + 151/15, -4/15*e^6 - 2/15*e^5 + 73/15*e^4 + 13/5*e^3 - 108/5*e^2 - 62/5*e + 68/15, 1/4*e^6 + 1/4*e^5 - 9/2*e^4 - 17/4*e^3 + 39/2*e^2 + 18*e - 3, 1/4*e^6 + 1/4*e^5 - 9/2*e^4 - 17/4*e^3 + 39/2*e^2 + 16*e - 7, 17/60*e^6 + 1/60*e^5 - 157/30*e^4 - 19/20*e^3 + 237/10*e^2 + 44/5*e - 151/15, 3/20*e^6 - 1/20*e^5 - 23/10*e^4 + 17/20*e^3 + 69/10*e^2 - 17/5*e + 11/5, -4/15*e^6 - 2/15*e^5 + 73/15*e^4 + 8/5*e^3 - 108/5*e^2 - 12/5*e + 128/15, -1/4*e^6 - 1/4*e^5 + 9/2*e^4 + 17/4*e^3 - 39/2*e^2 - 16*e + 3, 23/60*e^6 + 19/60*e^5 - 193/30*e^4 - 101/20*e^3 + 253/10*e^2 + 96/5*e - 109/15, 4/15*e^6 + 2/15*e^5 - 73/15*e^4 - 13/5*e^3 + 103/5*e^2 + 77/5*e - 8/15, 1/4*e^6 + 1/4*e^5 - 9/2*e^4 - 17/4*e^3 + 37/2*e^2 + 16*e + 5, 2/3*e^6 + 1/3*e^5 - 38/3*e^4 - 5*e^3 + 59*e^2 + 19*e - 52/3, -1/60*e^6 + 7/60*e^5 + 11/30*e^4 - 33/20*e^3 - 31/10*e^2 + 33/5*e + 143/15, -11/20*e^6 - 3/20*e^5 + 101/10*e^4 + 51/20*e^3 - 453/10*e^2 - 56/5*e + 93/5, -11/12*e^6 - 7/12*e^5 + 97/6*e^4 + 33/4*e^3 - 135/2*e^2 - 28*e + 49/3, -13/20*e^6 - 9/20*e^5 + 113/10*e^4 + 133/20*e^3 - 449/10*e^2 - 118/5*e + 19/5, 1/4*e^6 + 1/4*e^5 - 9/2*e^4 - 17/4*e^3 + 37/2*e^2 + 20*e + 1, -2/15*e^6 - 1/15*e^5 + 44/15*e^4 + 9/5*e^3 - 79/5*e^2 - 51/5*e + 34/15, 4/15*e^6 + 2/15*e^5 - 73/15*e^4 - 13/5*e^3 + 108/5*e^2 + 57/5*e - 8/15, -3/20*e^6 + 1/20*e^5 + 33/10*e^4 + 3/20*e^3 - 179/10*e^2 - 28/5*e + 29/5, -4/5*e^6 - 2/5*e^5 + 73/5*e^4 + 29/5*e^3 - 324/5*e^2 - 81/5*e + 118/5, -3/20*e^6 + 1/20*e^5 + 23/10*e^4 - 17/20*e^3 - 79/10*e^2 + 2/5*e + 9/5, 49/60*e^6 + 17/60*e^5 - 449/30*e^4 - 83/20*e^3 + 669/10*e^2 + 88/5*e - 347/15, -2/15*e^6 - 1/15*e^5 + 29/15*e^4 + 4/5*e^3 - 19/5*e^2 - 6/5*e - 176/15, -2/5*e^6 - 1/5*e^5 + 34/5*e^4 + 17/5*e^3 - 137/5*e^2 - 78/5*e + 44/5, 4/15*e^6 + 2/15*e^5 - 73/15*e^4 - 3/5*e^3 + 118/5*e^2 - 28/5*e - 248/15, 3/20*e^6 - 1/20*e^5 - 23/10*e^4 - 3/20*e^3 + 59/10*e^2 + 28/5*e + 51/5, -2/15*e^6 - 1/15*e^5 + 29/15*e^4 + 4/5*e^3 - 29/5*e^2 + 4/5*e - 26/15, -1/4*e^6 - 1/4*e^5 + 9/2*e^4 + 17/4*e^3 - 35/2*e^2 - 16*e - 1, 11/12*e^6 + 7/12*e^5 - 97/6*e^4 - 33/4*e^3 + 137/2*e^2 + 26*e - 49/3, -4/15*e^6 - 2/15*e^5 + 73/15*e^4 + 8/5*e^3 - 118/5*e^2 - 32/5*e + 308/15, 4/15*e^6 + 2/15*e^5 - 73/15*e^4 - 3/5*e^3 + 108/5*e^2 - 23/5*e - 188/15, -2/15*e^6 - 1/15*e^5 + 44/15*e^4 + 9/5*e^3 - 89/5*e^2 - 61/5*e + 184/15, -8/15*e^6 - 4/15*e^5 + 146/15*e^4 + 16/5*e^3 - 216/5*e^2 - 34/5*e + 316/15, -2/5*e^6 - 1/5*e^5 + 39/5*e^4 + 22/5*e^3 - 187/5*e^2 - 118/5*e + 64/5, 2/15*e^6 + 1/15*e^5 - 29/15*e^4 - 4/5*e^3 + 19/5*e^2 - 4/5*e + 146/15, -4/15*e^6 - 2/15*e^5 + 73/15*e^4 + 8/5*e^3 - 108/5*e^2 - 12/5*e + 188/15, -2*e^3 + 18*e + 8, 7/15*e^6 - 4/15*e^5 - 139/15*e^4 + 21/5*e^3 + 239/5*e^2 - 74/5*e - 404/15, -41/60*e^6 - 13/60*e^5 + 361/30*e^4 + 67/20*e^3 - 491/10*e^2 - 82/5*e + 163/15, -e^2 + 18, 7/15*e^6 - 4/15*e^5 - 124/15*e^4 + 31/5*e^3 + 179/5*e^2 - 154/5*e - 344/15, -2/5*e^6 - 1/5*e^5 + 34/5*e^4 + 7/5*e^3 - 132/5*e^2 + 27/5*e + 4/5, 5/12*e^6 + 1/12*e^5 - 43/6*e^4 - 7/4*e^3 + 55/2*e^2 + 14*e + 17/3, 14/15*e^6 + 7/15*e^5 - 248/15*e^4 - 43/5*e^3 + 353/5*e^2 + 212/5*e - 358/15, 16/15*e^6 + 8/15*e^5 - 277/15*e^4 - 32/5*e^3 + 382/5*e^2 + 78/5*e - 362/15, 2/5*e^6 + 1/5*e^5 - 34/5*e^4 - 7/5*e^3 + 147/5*e^2 - 27/5*e - 124/5, 26/15*e^6 + 13/15*e^5 - 452/15*e^4 - 67/5*e^3 + 617/5*e^2 + 253/5*e - 412/15, -11/15*e^6 + 2/15*e^5 + 197/15*e^4 - 3/5*e^3 - 287/5*e^2 - 48/5*e + 322/15, -11/60*e^6 + 17/60*e^5 + 121/30*e^4 - 103/20*e^3 - 221/10*e^2 + 88/5*e + 193/15, 1/12*e^6 - 7/12*e^5 - 5/6*e^4 + 37/4*e^3 + 1/2*e^2 - 30*e - 23/3, -4/5*e^6 - 2/5*e^5 + 73/5*e^4 + 24/5*e^3 - 324/5*e^2 - 76/5*e + 78/5, -11/60*e^6 + 17/60*e^5 + 91/30*e^4 - 123/20*e^3 - 101/10*e^2 + 148/5*e + 73/15, -2/5*e^6 - 1/5*e^5 + 39/5*e^4 + 12/5*e^3 - 197/5*e^2 - 33/5*e + 144/5, -1/3*e^6 - 2/3*e^5 + 19/3*e^4 + 11*e^3 - 28*e^2 - 40*e + 8/3, 4/5*e^6 + 2/5*e^5 - 68/5*e^4 - 24/5*e^3 + 279/5*e^2 + 46/5*e - 58/5, 23/60*e^6 + 19/60*e^5 - 223/30*e^4 - 81/20*e^3 + 363/10*e^2 + 31/5*e - 349/15, -41/60*e^6 - 13/60*e^5 + 331/30*e^4 + 67/20*e^3 - 421/10*e^2 - 72/5*e + 403/15, 2/5*e^6 + 1/5*e^5 - 34/5*e^4 - 7/5*e^3 + 137/5*e^2 - 17/5*e - 124/5, 4/15*e^6 + 2/15*e^5 - 88/15*e^4 - 8/5*e^3 + 168/5*e^2 + 32/5*e - 338/15, 27/20*e^6 + 11/20*e^5 - 237/10*e^4 - 167/20*e^3 + 971/10*e^2 + 187/5*e - 101/5, 8/5*e^6 + 4/5*e^5 - 146/5*e^4 - 58/5*e^3 + 648/5*e^2 + 232/5*e - 196/5, 3/5*e^6 - 1/5*e^5 - 51/5*e^4 + 22/5*e^3 + 208/5*e^2 - 113/5*e - 116/5, -7/15*e^6 + 4/15*e^5 + 124/15*e^4 - 26/5*e^3 - 169/5*e^2 + 99/5*e + 44/15, -8/15*e^6 - 4/15*e^5 + 146/15*e^4 + 16/5*e^3 - 226/5*e^2 - 24/5*e + 616/15, 1/3*e^6 - 1/3*e^5 - 19/3*e^4 + 6*e^3 + 30*e^2 - 23*e - 32/3, -e^4 - e^3 + 10*e^2 + 11*e - 8, -11/12*e^6 - 7/12*e^5 + 97/6*e^4 + 41/4*e^3 - 133/2*e^2 - 44*e + 49/3, 1/12*e^6 + 5/12*e^5 - 5/6*e^4 - 23/4*e^3 - 5/2*e^2 + 17*e + 73/3, -2/5*e^6 - 6/5*e^5 + 34/5*e^4 + 92/5*e^3 - 142/5*e^2 - 288/5*e + 24/5, 1/5*e^6 - 2/5*e^5 - 17/5*e^4 + 29/5*e^3 + 61/5*e^2 - 96/5*e - 12/5, -19/12*e^6 - 11/12*e^5 + 173/6*e^4 + 53/4*e^3 - 255/2*e^2 - 49*e + 125/3, -7/20*e^6 - 11/20*e^5 + 57/10*e^4 + 207/20*e^3 - 211/10*e^2 - 232/5*e + 21/5, -37/60*e^6 + 19/60*e^5 + 347/30*e^4 - 101/20*e^3 - 517/10*e^2 + 66/5*e + 311/15, 7/60*e^6 + 11/60*e^5 - 47/30*e^4 - 89/20*e^3 + 37/10*e^2 + 164/5*e + 139/15, 29/60*e^6 - 23/60*e^5 - 259/30*e^4 + 117/20*e^3 + 399/10*e^2 - 77/5*e - 367/15, 1/5*e^6 - 2/5*e^5 - 17/5*e^4 + 39/5*e^3 + 71/5*e^2 - 181/5*e - 52/5, -1/5*e^6 - 3/5*e^5 + 17/5*e^4 + 56/5*e^3 - 81/5*e^2 - 249/5*e + 12/5, 67/60*e^6 + 11/60*e^5 - 617/30*e^4 - 69/20*e^3 + 887/10*e^2 + 119/5*e - 221/15, 13/15*e^6 - 1/15*e^5 - 256/15*e^4 + 9/5*e^3 + 426/5*e^2 - 16/5*e - 716/15, -1/3*e^6 + 1/3*e^5 + 16/3*e^4 - 7*e^3 - 20*e^2 + 30*e + 20/3, -13/15*e^6 - 14/15*e^5 + 241/15*e^4 + 71/5*e^3 - 376/5*e^2 - 234/5*e + 506/15, -4/3*e^6 - 2/3*e^5 + 73/3*e^4 + 11*e^3 - 106*e^2 - 49*e + 92/3, -8/15*e^6 - 4/15*e^5 + 131/15*e^4 + 11/5*e^3 - 176/5*e^2 + 11/5*e + 256/15, -6/5*e^6 - 3/5*e^5 + 112/5*e^4 + 51/5*e^3 - 511/5*e^2 - 224/5*e + 152/5, 3/5*e^6 + 4/5*e^5 - 56/5*e^4 - 58/5*e^3 + 263/5*e^2 + 152/5*e - 116/5, -1/15*e^6 + 7/15*e^5 + 22/15*e^4 - 33/5*e^3 - 22/5*e^2 + 57/5*e - 178/15, 1/5*e^6 - 2/5*e^5 - 17/5*e^4 + 39/5*e^3 + 61/5*e^2 - 171/5*e + 18/5, 2/5*e^6 + 1/5*e^5 - 39/5*e^4 - 12/5*e^3 + 207/5*e^2 - 2/5*e - 184/5, 11/15*e^6 - 2/15*e^5 - 197/15*e^4 + 13/5*e^3 + 277/5*e^2 - 52/5*e - 292/15, 2/5*e^6 + 1/5*e^5 - 29/5*e^4 - 12/5*e^3 + 67/5*e^2 + 38/5*e + 56/5, 17/15*e^6 + 1/15*e^5 - 314/15*e^4 + 1/5*e^3 + 484/5*e^2 - 24/5*e - 844/15, -2/15*e^6 - 1/15*e^5 + 44/15*e^4 + 9/5*e^3 - 59/5*e^2 - 31/5*e - 416/15, 1/5*e^6 - 2/5*e^5 - 22/5*e^4 + 34/5*e^3 + 121/5*e^2 - 146/5*e - 52/5, -2/5*e^6 - 1/5*e^5 + 44/5*e^4 + 17/5*e^3 - 247/5*e^2 - 78/5*e + 144/5, 13/20*e^6 + 9/20*e^5 - 113/10*e^4 - 193/20*e^3 + 469/10*e^2 + 258/5*e - 139/5, 7/4*e^6 + 3/4*e^5 - 63/2*e^4 - 35/4*e^3 + 279/2*e^2 + 14*e - 61, e^4 + 2*e^3 - 8*e^2 - 20*e, 17/60*e^6 + 1/60*e^5 - 157/30*e^4 + 21/20*e^3 + 217/10*e^2 - 21/5*e + 89/15, -1/12*e^6 - 5/12*e^5 + 5/6*e^4 + 27/4*e^3 + 1/2*e^2 - 24*e - 1/3, -1/4*e^6 + 3/4*e^5 + 9/2*e^4 - 51/4*e^3 - 37/2*e^2 + 37*e + 7, 1/5*e^6 + 3/5*e^5 - 22/5*e^4 - 41/5*e^3 + 136/5*e^2 + 124/5*e - 122/5, 8, 6/5*e^6 + 3/5*e^5 - 107/5*e^4 - 56/5*e^3 + 446/5*e^2 + 264/5*e - 12/5, 8/15*e^6 + 4/15*e^5 - 131/15*e^4 - 26/5*e^3 + 146/5*e^2 + 134/5*e + 224/15, -2/15*e^6 - 16/15*e^5 + 29/15*e^4 + 79/5*e^3 - 34/5*e^2 - 216/5*e + 64/15, -e^4 - 2*e^3 + 8*e^2 + 18*e + 4, -e^6 + 19*e^4 + e^3 - 92*e^2 - 10*e + 56, 4/5*e^6 - 3/5*e^5 - 73/5*e^4 + 46/5*e^3 + 324/5*e^2 - 124/5*e - 128/5, -e^6 + 19*e^4 - e^3 - 92*e^2 - 2*e + 64, -4/15*e^6 - 2/15*e^5 + 73/15*e^4 + 18/5*e^3 - 98/5*e^2 - 92/5*e - 142/15, 4/5*e^6 + 7/5*e^5 - 73/5*e^4 - 114/5*e^3 + 329/5*e^2 + 426/5*e - 108/5, -1/15*e^6 - 8/15*e^5 + 37/15*e^4 + 47/5*e^3 - 87/5*e^2 - 218/5*e - 28/15, -16/15*e^6 - 8/15*e^5 + 307/15*e^4 + 42/5*e^3 - 472/5*e^2 - 148/5*e + 362/15, 22/15*e^6 + 11/15*e^5 - 394/15*e^4 - 59/5*e^3 + 569/5*e^2 + 231/5*e - 644/15, 1/3*e^6 - 1/3*e^5 - 16/3*e^4 + 3*e^3 + 16*e^2 + 4*e + 52/3, -7/15*e^6 - 11/15*e^5 + 124/15*e^4 + 59/5*e^3 - 154/5*e^2 - 206/5*e - 76/15, -7/20*e^6 - 11/20*e^5 + 57/10*e^4 + 167/20*e^3 - 171/10*e^2 - 152/5*e - 99/5, -e^6 + 17*e^4 - e^3 - 68*e^2 + 2*e + 20, 1/20*e^6 - 7/20*e^5 - 21/10*e^4 + 39/20*e^3 + 143/10*e^2 + 76/5*e + 17/5, -5/4*e^6 - 1/4*e^5 + 43/2*e^4 + 13/4*e^3 - 181/2*e^2 - 12*e + 55, -29/60*e^6 + 23/60*e^5 + 259/30*e^4 - 97/20*e^3 - 399/10*e^2 - 8/5*e + 487/15, 53/60*e^6 + 49/60*e^5 - 463/30*e^4 - 271/20*e^3 + 683/10*e^2 + 276/5*e - 439/15, -1/5*e^6 + 2/5*e^5 + 27/5*e^4 - 19/5*e^3 - 181/5*e^2 + 16/5*e + 112/5, 1/15*e^6 + 8/15*e^5 - 7/15*e^4 - 27/5*e^3 + 7/5*e^2 + 18/5*e - 392/15, 3/5*e^6 + 4/5*e^5 - 51/5*e^4 - 63/5*e^3 + 193/5*e^2 + 192/5*e + 44/5, -1/3*e^6 - 2/3*e^5 + 16/3*e^4 + 8*e^3 - 21*e^2 - 6*e - 10/3, -7/20*e^6 + 9/20*e^5 + 67/10*e^4 - 153/20*e^3 - 361/10*e^2 + 163/5*e + 201/5, -26/15*e^6 - 13/15*e^5 + 467/15*e^4 + 72/5*e^3 - 677/5*e^2 - 283/5*e + 682/15, 3/20*e^6 - 1/20*e^5 - 23/10*e^4 + 57/20*e^3 + 59/10*e^2 - 52/5*e + 51/5, e^6 + e^5 - 19*e^4 - 14*e^3 + 88*e^2 + 48*e - 4, 3/5*e^6 - 1/5*e^5 - 51/5*e^4 + 7/5*e^3 + 168/5*e^2 + 52/5*e + 144/5, -17/12*e^6 - 1/12*e^5 + 163/6*e^4 + 15/4*e^3 - 257/2*e^2 - 33*e + 151/3, -2*e^2 - 4*e + 18, -19/20*e^6 - 7/20*e^5 + 169/10*e^4 + 79/20*e^3 - 727/10*e^2 - 59/5*e + 177/5, 17/15*e^6 + 1/15*e^5 - 299/15*e^4 - 4/5*e^3 + 414/5*e^2 + 11/5*e - 304/15, 2/5*e^6 + 1/5*e^5 - 34/5*e^4 - 12/5*e^3 + 137/5*e^2 + 58/5*e + 56/5, e^6 + e^5 - 19*e^4 - 14*e^3 + 90*e^2 + 44*e - 16, 79/60*e^6 + 47/60*e^5 - 689/30*e^4 - 313/20*e^3 + 939/10*e^2 + 383/5*e - 497/15, 4/3*e^6 + 2/3*e^5 - 76/3*e^4 - 10*e^3 + 120*e^2 + 34*e - 194/3, -3/5*e^6 + 1/5*e^5 + 61/5*e^4 - 7/5*e^3 - 298/5*e^2 - 42/5*e + 106/5, 3/5*e^6 - 1/5*e^5 - 56/5*e^4 + 27/5*e^3 + 248/5*e^2 - 108/5*e - 56/5, 7/15*e^6 + 11/15*e^5 - 109/15*e^4 - 54/5*e^3 + 114/5*e^2 + 176/5*e + 196/15, 1/15*e^6 - 7/15*e^5 + 8/15*e^4 + 33/5*e^3 - 78/5*e^2 - 62/5*e + 508/15, -2/5*e^6 - 6/5*e^5 + 29/5*e^4 + 92/5*e^3 - 82/5*e^2 - 288/5*e - 36/5, -2*e^6 + 36*e^4 - 160*e^2 - 14*e + 80, -19/15*e^6 - 17/15*e^5 + 343/15*e^4 + 78/5*e^3 - 478/5*e^2 - 217/5*e + 8/15, 1/12*e^6 - 7/12*e^5 - 5/6*e^4 + 29/4*e^3 + 5/2*e^2 - 17*e - 143/3, 23/60*e^6 + 79/60*e^5 - 223/30*e^4 - 421/20*e^3 + 353/10*e^2 + 366/5*e + 71/15, 7/15*e^6 + 11/15*e^5 - 124/15*e^4 - 44/5*e^3 + 174/5*e^2 + 61/5*e - 14/15, 3/5*e^6 - 1/5*e^5 - 61/5*e^4 + 22/5*e^3 + 308/5*e^2 - 88/5*e - 156/5, -26/15*e^6 + 2/15*e^5 + 467/15*e^4 - 8/5*e^3 - 662/5*e^2 - 38/5*e + 772/15, -127/60*e^6 - 71/60*e^5 + 1127/30*e^4 + 349/20*e^3 - 1597/10*e^2 - 344/5*e + 521/15, -6/5*e^6 + 2/5*e^5 + 112/5*e^4 - 34/5*e^3 - 536/5*e^2 + 106/5*e + 272/5, 7/15*e^6 + 26/15*e^5 - 139/15*e^4 - 129/5*e^3 + 229/5*e^2 + 406/5*e - 284/15, 22/15*e^6 + 11/15*e^5 - 379/15*e^4 - 64/5*e^3 + 509/5*e^2 + 336/5*e - 104/15, -31/60*e^6 - 23/60*e^5 + 281/30*e^4 + 137/20*e^3 - 391/10*e^2 - 167/5*e - 307/15] 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, -w^2 + w + 4])] = 1 AL_eigenvalues[ZF.ideal([8, 2, w^3 - w^2 - 4*w + 5])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]