/* 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, -1, -6, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([16, 4, 3*w^3 - 5*w^2 - 15*w + 6]) primes_array = [ [2, 2, w^3 - w^2 - 6*w - 2],\ [3, 3, -w^3 + 2*w^2 + 4*w - 2],\ [4, 2, w^3 - w^2 - 5*w - 2],\ [17, 17, -w^3 + w^2 + 6*w - 1],\ [17, 17, -w + 2],\ [29, 29, -w^3 + 2*w^2 + 4*w - 4],\ [29, 29, w^3 - 2*w^2 - 4*w],\ [31, 31, -w^2 + 2],\ [31, 31, -w^3 + 7*w + 5],\ [41, 41, -2*w^3 + 2*w^2 + 13*w - 2],\ [41, 41, 3*w^3 - 4*w^2 - 17*w + 5],\ [67, 67, 3*w^3 - 4*w^2 - 17*w + 1],\ [67, 67, -w^2 + 4*w + 2],\ [83, 83, 2*w^2 - 5*w - 2],\ [83, 83, -w^3 + 8*w + 6],\ [83, 83, w^3 - 2*w^2 - 2*w - 2],\ [83, 83, w^3 - 2*w^2 - 6*w],\ [97, 97, -3*w^3 + 2*w^2 + 17*w + 7],\ [97, 97, w^3 - 4*w^2 + 3*w + 1],\ [97, 97, -5*w^3 + 8*w^2 + 24*w - 8],\ [97, 97, 2*w^3 - 2*w^2 - 13*w - 4],\ [101, 101, -w^3 + 6*w + 6],\ [101, 101, -w^3 + 6*w + 2],\ [103, 103, -4*w^3 + 3*w^2 + 26*w + 12],\ [103, 103, -w^3 + 2*w^2 + 9*w + 3],\ [107, 107, 2*w^3 - 2*w^2 - 11*w],\ [107, 107, -w^3 + 2*w^2 + 3*w - 3],\ [107, 107, w^3 - w^2 - 4*w - 3],\ [107, 107, 2*w^3 - 3*w^2 - 10*w],\ [121, 11, -2*w^3 + 3*w^2 + 8*w + 2],\ [149, 149, -3*w^3 + 5*w^2 + 14*w - 3],\ [149, 149, -2*w^3 + 4*w^2 + 7*w - 4],\ [157, 157, 2*w^3 - 2*w^2 - 10*w - 1],\ [157, 157, 2*w^3 - 3*w^2 - 8*w + 2],\ [157, 157, 2*w^3 - 2*w^2 - 10*w - 3],\ [157, 157, -3*w^3 + 4*w^2 + 15*w + 1],\ [163, 163, -2*w^2 + 4*w + 5],\ [163, 163, 2*w^3 - 4*w^2 - 10*w + 5],\ [169, 13, 2*w^3 - 3*w^2 - 12*w + 2],\ [169, 13, -w^3 + 9*w + 3],\ [173, 173, 3*w^3 - 2*w^2 - 17*w - 9],\ [173, 173, -2*w^3 + 14*w + 7],\ [197, 197, 2*w^3 - 2*w^2 - 12*w + 1],\ [197, 197, 3*w^3 - 3*w^2 - 18*w - 1],\ [199, 199, 3*w^3 - 4*w^2 - 18*w + 8],\ [199, 199, 4*w^3 - 5*w^2 - 24*w + 6],\ [223, 223, w^3 - 2*w^2 - 3*w - 3],\ [223, 223, 2*w^3 - 3*w^2 - 10*w + 6],\ [227, 227, -w^3 + 2*w^2 + 6*w - 8],\ [227, 227, 3*w + 4],\ [227, 227, 3*w^3 - 3*w^2 - 18*w - 7],\ [227, 227, -2*w^3 + 3*w^2 + 12*w - 6],\ [229, 229, -w - 4],\ [229, 229, w^2 - 2*w + 2],\ [229, 229, -w^3 + w^2 + 6*w + 5],\ [229, 229, -w^3 + 2*w^2 + 5*w - 7],\ [233, 233, -2*w^3 + 3*w^2 + 8*w - 4],\ [233, 233, -3*w^3 + 4*w^2 + 15*w + 3],\ [281, 281, -2*w^3 + 3*w^2 + 10*w + 2],\ [281, 281, -w^3 + 2*w^2 + 3*w - 5],\ [289, 17, -2*w^3 + 2*w^2 + 14*w + 5],\ [293, 293, w^2 - 6],\ [293, 293, w^3 - 7*w - 1],\ [331, 331, -6*w^3 + 10*w^2 + 27*w - 6],\ [331, 331, 2*w^3 - 2*w^2 - 12*w - 7],\ [347, 347, 3*w^3 - 2*w^2 - 18*w - 6],\ [347, 347, -4*w^3 + 2*w^2 + 23*w + 10],\ [347, 347, 2*w^3 - 6*w^2 - w + 4],\ [347, 347, -4*w^3 + 3*w^2 + 24*w + 8],\ [359, 359, -3*w^3 + 4*w^2 + 17*w + 1],\ [359, 359, w^2 - 4*w - 4],\ [359, 359, w^3 - 8*w],\ [359, 359, -w^3 + 2*w^2 + 6*w - 6],\ [367, 367, 2*w^2 - 3*w - 4],\ [367, 367, -w^3 + 3*w^2 + 4*w - 7],\ [379, 379, 3*w^3 - 3*w^2 - 16*w - 3],\ [379, 379, 2*w^3 - 2*w^2 - 9*w - 2],\ [461, 461, -2*w^3 + 5*w^2 + 2*w + 2],\ [461, 461, 4*w^3 - 4*w^2 - 26*w - 11],\ [463, 463, -2*w^3 + 13*w + 8],\ [463, 463, -w^3 - w^2 + 6*w + 7],\ [487, 487, 2*w^3 - 17*w - 8],\ [487, 487, -w^3 + 10*w + 4],\ [491, 491, -5*w^3 + 3*w^2 + 30*w + 13],\ [491, 491, -5*w^3 + 4*w^2 + 28*w + 14],\ [491, 491, 3*w^3 - 8*w^2 - 4*w + 4],\ [491, 491, 7*w^3 - 12*w^2 - 33*w + 15],\ [499, 499, -2*w^3 + 2*w^2 + 12*w - 5],\ [499, 499, 2*w^2 - 7*w],\ [529, 23, -w^3 + 3*w^2 + 4*w - 5],\ [529, 23, 2*w^2 - 3*w - 6],\ [557, 557, -2*w^3 + 3*w^2 + 12*w + 4],\ [557, 557, w^3 - 9*w - 9],\ [569, 569, 4*w^3 - 5*w^2 - 22*w + 4],\ [569, 569, -3*w^3 + 2*w^2 + 20*w + 4],\ [577, 577, 3*w^3 - 3*w^2 - 20*w + 3],\ [577, 577, -4*w^3 + 8*w^2 + 16*w - 9],\ [577, 577, 7*w^3 - 11*w^2 - 34*w + 9],\ [577, 577, -4*w^3 + 6*w^2 + 22*w - 11],\ [593, 593, -6*w^3 + 10*w^2 + 29*w - 14],\ [593, 593, -w^3 + 4*w^2 - w - 7],\ [619, 619, -3*w^3 + 5*w^2 + 12*w - 1],\ [619, 619, -4*w^3 + 8*w^2 + 18*w - 15],\ [625, 5, -5],\ [631, 631, -3*w^3 + 8*w^2 + 6*w - 4],\ [631, 631, -2*w^3 + 8*w^2 - 3*w - 8],\ [643, 643, 3*w^3 - 4*w^2 - 14*w + 2],\ [643, 643, -3*w^3 + 4*w^2 + 14*w + 2],\ [661, 661, w^3 - 8*w - 10],\ [661, 661, -3*w^3 + 2*w^2 + 21*w + 3],\ [661, 661, w^3 - 2*w^2 - 6*w - 4],\ [661, 661, 2*w^3 - 3*w^2 - 14*w + 4],\ [677, 677, -9*w^3 + 12*w^2 + 50*w - 10],\ [677, 677, 3*w^3 - 4*w^2 - 17*w - 7],\ [691, 691, 3*w^3 - 2*w^2 - 21*w - 9],\ [691, 691, 2*w^3 - 3*w^2 - 14*w - 2],\ [701, 701, -9*w^3 + 13*w^2 + 48*w - 15],\ [701, 701, 2*w^3 - 6*w^2 + w - 2],\ [709, 709, 2*w^2 - 2*w - 5],\ [709, 709, 2*w^2 - 2*w - 7],\ [709, 709, 4*w^3 - 5*w^2 - 20*w - 4],\ [709, 709, -3*w^3 + 6*w^2 + 14*w - 10],\ [727, 727, 7*w^3 - 10*w^2 - 36*w + 8],\ [727, 727, 3*w^2 - 6*w - 8],\ [743, 743, 9*w^3 - 12*w^2 - 51*w + 13],\ [743, 743, w^3 - 2*w^2 - w - 5],\ [743, 743, -4*w^3 + 4*w^2 + 27*w - 8],\ [743, 743, -3*w^3 + 4*w^2 + 21*w + 9],\ [751, 751, -w^3 + 10*w + 2],\ [751, 751, 3*w^3 - 4*w^2 - 18*w + 2],\ [761, 761, 4*w^3 - 4*w^2 - 23*w - 2],\ [761, 761, -3*w^3 + 2*w^2 + 19*w + 5],\ [809, 809, -3*w^3 + 5*w^2 + 10*w + 5],\ [809, 809, -w^3 - w^2 + 10*w + 3],\ [821, 821, -w^3 + 3*w^2 + 2*w - 9],\ [821, 821, 2*w^2 - 4*w - 9],\ [823, 823, w^3 - 6*w^2 + 9*w + 1],\ [823, 823, -3*w^3 + 2*w^2 + 15*w + 5],\ [827, 827, 3*w^3 - 3*w^2 - 18*w + 1],\ [827, 827, 2*w^3 - 16*w - 11],\ [827, 827, 3*w^3 - 24*w - 14],\ [827, 827, 3*w - 4],\ [829, 829, w^2 - 6*w - 2],\ [829, 829, 2*w^3 - 2*w^2 - 10*w - 9],\ [829, 829, 5*w^3 - 6*w^2 - 29*w - 1],\ [829, 829, w^3 + 2*w^2 - 14*w - 6],\ [841, 29, -2*w^3 + 2*w^2 + 14*w + 3],\ [857, 857, -3*w^3 + 6*w^2 + 11*w - 7],\ [857, 857, -4*w^3 + 7*w^2 + 18*w - 4],\ [859, 859, -w^3 + w^2 + 6*w - 5],\ [859, 859, w - 6],\ [883, 883, 5*w^3 - 5*w^2 - 26*w - 11],\ [883, 883, -3*w^3 + 3*w^2 + 14*w + 5],\ [887, 887, 5*w^3 - 2*w^2 - 34*w - 16],\ [887, 887, -w^3 + 4*w^2 - 10],\ [887, 887, 4*w^3 - 2*w^2 - 26*w - 11],\ [887, 887, 2*w^3 - 8*w^2 + 4*w + 7],\ [907, 907, 6*w^3 - 8*w^2 - 34*w + 7],\ [907, 907, -w^3 + w^2 + 8*w - 7],\ [941, 941, 2*w^3 - 2*w^2 - 8*w - 5],\ [941, 941, -3*w^3 + 23*w + 11],\ [953, 953, 2*w^3 - 10*w - 3],\ [953, 953, -4*w^3 + 2*w^2 + 24*w + 15],\ [961, 31, -2*w^3 + 2*w^2 + 14*w - 7],\ [991, 991, -3*w^3 + 4*w^2 + 13*w + 3],\ [991, 991, 4*w^3 - 5*w^2 - 20*w + 2]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^8 - 112*x^6 + 3824*x^4 - 41600*x^2 + 40000 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1/112000*e^7 - 11/14000*e^5 + 1697/14000*e^3 - 167/70*e, 1/2800*e^6 - 87/2800*e^4 + 114/175*e^2 - 15/14, 0, -1/56000*e^7 - 11/7000*e^5 + 1697/7000*e^3 - 202/35*e, e, -41/112000*e^7 + 1023/28000*e^5 - 13723/14000*e^3 + 957/140*e, 1/16000*e^7 - 7/1000*e^5 + 603/2000*e^3 - 28/5*e, -1/11200*e^6 - 11/1400*e^4 + 997/1400*e^2 - 34/7, -1/1600*e^6 + 7/100*e^4 - 403/200*e^2 + 9, 27/112000*e^7 - 403/14000*e^5 + 15081/14000*e^3 - 179/14*e, -3/16000*e^7 + 59/4000*e^5 - 409/2000*e^3 - 7/20*e, 3/1400*e^6 - 261/1400*e^4 + 1193/350*e^2 + 32/7, -1/1400*e^6 + 87/1400*e^4 - 281/350*e^2 - 48/7, -1/4480*e^7 + 17/560*e^5 - 739/560*e^3 + 1299/70*e, -79/112000*e^7 + 1937/28000*e^5 - 26237/14000*e^3 + 383/28*e, 3/16000*e^7 - 59/4000*e^5 + 409/2000*e^3 - 13/20*e, 69/112000*e^7 - 51/875*e^5 + 20807/14000*e^3 - 353/35*e, 33/11200*e^6 - 337/1400*e^4 + 5599/1400*e^2 + 44/7, 1/1600*e^6 - 7/100*e^4 + 503/200*e^2 - 19, -3/1400*e^6 + 261/1400*e^4 - 684/175*e^2 + 136/7, -3/1400*e^6 + 261/1400*e^4 - 684/175*e^2 + 136/7, 3/112000*e^7 - 109/28000*e^5 + 1209/14000*e^3 + 281/140*e, 51/112000*e^7 - 83/1750*e^5 + 19153/14000*e^3 - 73/7*e, -3/2800*e^6 + 261/2800*e^4 - 509/350*e^2 - 109/14, 1/560*e^6 - 87/560*e^4 + 193/70*e^2 + 51/14, 61/56000*e^7 - 729/7000*e^5 + 18283/7000*e^3 - 516/35*e, 11/112000*e^7 - 229/14000*e^5 + 10033/14000*e^3 - 103/14*e, -19/28000*e^7 + 457/7000*e^5 - 6257/3500*e^3 + 514/35*e, 61/112000*e^7 - 1633/28000*e^5 + 24583/14000*e^3 - 1823/140*e, 1/1400*e^6 - 87/1400*e^4 + 228/175*e^2 - 29/7, -1/1120*e^7 + 47/560*e^5 - 291/140*e^3 + 793/70*e, 1/1120*e^7 - 47/560*e^5 + 291/140*e^3 - 793/70*e, 17/11200*e^6 - 163/1400*e^4 + 1951/1400*e^2 + 88/7, 27/11200*e^6 - 631/2800*e^4 + 7381/1400*e^2 - 271/14, -9/11200*e^6 + 19/350*e^4 - 127/1400*e^2 - 89/7, 3/1600*e^6 - 59/400*e^4 + 509/200*e^2 - 11/2, 9/5600*e^6 - 479/2800*e^4 + 3627/700*e^2 - 365/14, 19/5600*e^6 - 739/2800*e^4 + 2757/700*e^2 + 183/14, 1/2800*e^6 - 87/2800*e^4 + 403/350*e^2 - 197/14, 9/2800*e^6 - 783/2800*e^4 + 1877/350*e^2 - 37/14, -3/8000*e^7 + 21/500*e^5 - 1309/1000*e^3 + 43/5*e, -1/2800*e^7 + 61/1400*e^5 - 543/350*e^3 + 538/35*e, 61/56000*e^7 - 1633/14000*e^5 + 24583/7000*e^3 - 1823/70*e, 11/56000*e^7 - 229/7000*e^5 + 10033/7000*e^3 - 103/7*e, -1/2800*e^6 + 87/2800*e^4 - 403/350*e^2 + 337/14, -9/2800*e^6 + 783/2800*e^4 - 1877/350*e^2 + 177/14, -3/11200*e^6 + 109/2800*e^4 - 1209/1400*e^2 - 43/14, 1/320*e^6 - 23/80*e^4 + 243/40*e^2 - 11/2, 3/56000*e^7 - 109/14000*e^5 + 1209/7000*e^3 + 281/70*e, 17/16000*e^7 - 451/4000*e^5 + 6851/2000*e^3 - 521/20*e, -33/112000*e^7 + 81/7000*e^5 + 7701/14000*e^3 - 554/35*e, 51/56000*e^7 - 83/875*e^5 + 19153/7000*e^3 - 146/7*e, -3/2240*e^6 + 39/560*e^4 + 51/280*e^2 - 61/14, -11/2800*e^6 + 957/2800*e^4 - 2333/350*e^2 + 221/14, -33/11200*e^6 + 849/2800*e^4 - 11199/1400*e^2 + 521/14, -3/2800*e^6 + 261/2800*e^4 - 859/350*e^2 + 381/14, 9/28000*e^7 - 479/14000*e^5 + 3977/3500*e^3 - 1163/70*e, -27/56000*e^7 + 403/7000*e^5 - 15081/7000*e^3 + 200/7*e, -31/56000*e^7 + 359/7000*e^5 - 8293/7000*e^3 + 262/35*e, 1/3500*e^7 - 523/14000*e^5 + 2837/1750*e^3 - 1691/70*e, -3/1400*e^6 + 261/1400*e^4 - 684/175*e^2 + 31/7, -23/56000*e^7 + 34/875*e^5 - 5769/7000*e^3 - 33/35*e, -11/28000*e^7 + 283/7000*e^5 - 3733/3500*e^3 + 204/35*e, 51/11200*e^6 - 1153/2800*e^4 + 12153/1400*e^2 - 333/14, 13/11200*e^6 - 239/2800*e^4 + 2439/1400*e^2 - 299/14, 1/1750*e^7 - 87/1750*e^5 + 1649/1750*e^3 - 5/7*e, 3/16000*e^7 + 1/250*e^5 - 2791/2000*e^3 + 144/5*e, -29/112000*e^7 + 1287/28000*e^5 - 34087/14000*e^3 + 965/28*e, -17/56000*e^7 + 501/14000*e^5 - 9651/7000*e^3 + 1217/70*e, -137/112000*e^7 + 3461/28000*e^5 - 49611/14000*e^3 + 3879/140*e, 111/112000*e^7 - 1229/14000*e^5 + 26533/14000*e^3 - 517/70*e, -41/28000*e^7 + 1871/14000*e^5 - 10573/3500*e^3 + 983/70*e, 13/11200*e^7 - 43/350*e^5 + 5519/1400*e^3 - 1409/35*e, -13/5600*e^6 + 653/2800*e^4 - 4189/700*e^2 + 521/14, -1/800*e^6 + 31/400*e^4 - 53/100*e^2 + 19/2, 11/11200*e^6 - 27/700*e^4 - 1167/1400*e^2 + 115/7, 29/11200*e^6 - 381/1400*e^4 + 10287/1400*e^2 - 176/7, -193/112000*e^7 + 563/3500*e^5 - 53979/14000*e^3 + 667/35*e, 31/22400*e^7 - 753/5600*e^5 + 10253/2800*e^3 - 3831/140*e, -13/5600*e^6 + 239/1400*e^4 - 1389/700*e^2 - 72/7, -3/5600*e^6 + 109/1400*e^4 - 2259/700*e^2 + 202/7, -23/11200*e^6 + 369/2800*e^4 - 869/1400*e^2 - 143/14, -9/11200*e^6 + 327/2800*e^4 - 6427/1400*e^2 + 599/14, 53/112000*e^7 - 467/14000*e^5 + 3159/14000*e^3 + 65/14*e, -1/22400*e^7 + 153/5600*e^5 - 6003/2800*e^3 + 1031/28*e, -13/16000*e^7 + 389/4000*e^5 - 7239/2000*e^3 + 839/20*e, 9/22400*e^7 - 41/2800*e^5 - 3093/2800*e^3 + 2181/70*e, -3/700*e^6 + 261/700*e^4 - 1193/175*e^2 - 78/7, 1/700*e^6 - 87/700*e^4 + 281/175*e^2 + 82/7, -11/11200*e^6 + 283/2800*e^4 - 2333/1400*e^2 - 265/14, 59/11200*e^6 - 1327/2800*e^4 + 13277/1400*e^2 - 139/14, 53/112000*e^7 - 1109/28000*e^5 + 12959/14000*e^3 - 1611/140*e, -27/16000*e^7 + 353/2000*e^5 - 10481/2000*e^3 + 439/10*e, -11/16000*e^7 + 233/4000*e^5 - 2433/2000*e^3 + 143/20*e, 169/112000*e^7 - 1083/7000*e^5 + 62507/14000*e^3 - 243/7*e, -13/5600*e^6 + 653/2800*e^4 - 4539/700*e^2 + 521/14, -27/5600*e^6 + 1087/2800*e^4 - 4581/700*e^2 - 165/14, -17/5600*e^6 + 827/2800*e^4 - 5451/700*e^2 + 383/14, -23/5600*e^6 + 913/2800*e^4 - 3669/700*e^2 - 27/14, -3/7000*e^7 + 261/7000*e^5 - 509/875*e^3 - 40/7*e, -23/56000*e^7 + 34/875*e^5 - 5769/7000*e^3 + 37/35*e, -23/11200*e^6 + 34/175*e^4 - 6469/1400*e^2 - 5/7, -17/11200*e^6 + 163/1400*e^4 - 2651/1400*e^2 - 102/7, -3/1400*e^6 + 261/1400*e^4 - 684/175*e^2 - 32/7, -1/224*e^6 + 5/14*e^4 - 165/28*e^2 - 55/7, -3/1120*e^6 + 37/140*e^4 - 999/140*e^2 + 219/7, 37/11200*e^6 - 761/2800*e^4 + 6511/1400*e^2 - 81/14, 11/11200*e^6 - 283/2800*e^4 + 4433/1400*e^2 - 435/14, 9/2240*e^6 - 187/560*e^4 + 1527/280*e^2 + 253/14, -17/11200*e^6 + 163/1400*e^4 - 3351/1400*e^2 + 52/7, -13/11200*e^6 + 239/2800*e^4 - 339/1400*e^2 - 261/14, -11/2240*e^6 + 31/70*e^4 - 2613/280*e^2 + 69/7, -29/56000*e^7 + 381/7000*e^5 - 11687/7000*e^3 + 491/35*e, 3/8000*e^7 - 59/2000*e^5 + 409/1000*e^3 + 27/10*e, 1/560*e^6 - 87/560*e^4 + 79/35*e^2 + 429/14, -11/2800*e^6 + 957/2800*e^4 - 1079/175*e^2 + 109/14, 143/112000*e^7 - 1927/14000*e^5 + 61829/14000*e^3 - 2719/70*e, -109/112000*e^7 + 1977/28000*e^5 - 7527/14000*e^3 - 2421/140*e, 17/2800*e^6 - 1479/2800*e^4 + 3351/350*e^2 + 305/14, -1/400*e^6 + 87/400*e^4 - 153/50*e^2 - 25/2, -31/11200*e^6 + 359/1400*e^4 - 8993/1400*e^2 + 318/7, -57/11200*e^6 + 299/700*e^4 - 11071/1400*e^2 + 141/7, 31/11200*e^6 - 359/1400*e^4 + 8293/1400*e^2 - 178/7, 1/448*e^6 - 5/28*e^4 + 179/56*e^2 - 81/7, 11/112000*e^7 + 767/28000*e^5 - 37567/14000*e^3 + 6817/140*e, -153/112000*e^7 + 821/7000*e^5 - 32259/14000*e^3 + 234/35*e, -21/16000*e^7 + 147/1000*e^5 - 9663/2000*e^3 + 193/5*e, 191/112000*e^7 - 5073/28000*e^5 + 79773/14000*e^3 - 7459/140*e, -81/11200*e^6 + 859/1400*e^4 - 15843/1400*e^2 + 4/7, -23/11200*e^6 + 34/175*e^4 - 7869/1400*e^2 + 261/7, -3/11200*e^7 + 109/2800*e^5 - 2609/1400*e^3 + 363/14*e, 1/1600*e^7 - 9/200*e^5 + 43/200*e^3 + 73/5*e, -3/112000*e^7 + 109/28000*e^5 - 1209/14000*e^3 - 701/140*e, -9/22400*e^7 + 73/1400*e^5 - 5867/2800*e^3 + 971/35*e, 361/112000*e^7 - 8683/28000*e^5 + 111883/14000*e^3 - 7141/140*e, -281/112000*e^7 + 423/1750*e^5 - 90843/14000*e^3 + 348/7*e, -13/5600*e^6 + 239/1400*e^4 - 1389/700*e^2 - 86/7, -3/5600*e^6 + 109/1400*e^4 - 2259/700*e^2 + 188/7, -19/11200*e^7 + 527/2800*e^5 - 8777/1400*e^3 + 4257/70*e, -143/112000*e^7 + 1927/14000*e^5 - 61829/14000*e^3 + 2859/70*e, 3/3200*e^7 - 59/800*e^5 + 409/400*e^3 + 23/4*e, 53/56000*e^7 - 467/7000*e^5 + 3159/7000*e^3 + 93/7*e, -1/320*e^6 + 23/80*e^4 - 263/40*e^2 + 15/2, 11/5600*e^6 - 283/1400*e^4 + 3033/700*e^2 - 22/7, -29/11200*e^6 + 587/2800*e^4 - 5387/1400*e^2 - 89/14, -27/5600*e^6 + 631/1400*e^4 - 6681/700*e^2 + 12/7, -1/280*e^6 + 87/280*e^4 - 228/35*e^2 + 33/7, -159/112000*e^7 + 1751/14000*e^5 - 34677/14000*e^3 + 47/70*e, 93/112000*e^7 - 2329/28000*e^5 + 34679/14000*e^3 - 2923/140*e, -1/560*e^6 + 61/280*e^4 - 254/35*e^2 + 160/7, -1/400*e^6 + 31/200*e^4 - 14/25*e^2 - 44, 3/560*e^6 - 113/280*e^4 + 369/70*e^2 + 101/7, 1/560*e^6 - 61/280*e^4 + 543/70*e^2 - 447/7, 7/16000*e^7 - 73/2000*e^5 + 1421/2000*e^3 - 29/10*e, -1/896*e^7 + 107/1120*e^5 - 1007/560*e^3 + 201/140*e, -99/112000*e^7 + 2547/28000*e^5 - 37097/14000*e^3 + 2921/140*e, 123/112000*e^7 - 811/7000*e^5 + 50969/14000*e^3 - 1178/35*e, -1/350*e^6 + 521/2800*e^4 - 212/175*e^2 - 209/14, -3/1400*e^6 + 697/2800*e^4 - 1384/175*e^2 + 727/14, 1/400*e^7 - 97/400*e^5 + 159/25*e^3 - 381/10*e, -111/56000*e^7 + 1229/7000*e^5 - 26533/7000*e^3 + 412/35*e, -17/56000*e^7 + 501/14000*e^5 - 9651/7000*e^3 + 1497/70*e, 1/2000*e^7 - 7/125*e^5 + 239/125*e^3 - 119/5*e, -1/175*e^6 + 87/175*e^4 - 1824/175*e^2 + 183/7, -3/400*e^6 + 143/200*e^4 - 809/50*e^2 + 59, 1/2800*e^6 - 131/1400*e^4 + 1103/350*e^2 + 185/7] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([4, 2, w^3 - w^2 - 5*w - 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]