/* 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([-2, 1, 8, -1, -6, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([17, 17, -w^5 + w^4 + 5*w^3 - 3*w^2 - 5*w + 1]) primes_array = [ [2, 2, -w],\ [13, 13, -w^2 + 3],\ [17, 17, -w^5 + w^4 + 5*w^3 - 3*w^2 - 5*w + 1],\ [23, 23, w^4 - w^3 - 4*w^2 + 2*w + 1],\ [31, 31, w^5 - w^4 - 6*w^3 + 5*w^2 + 7*w - 5],\ [32, 2, w^5 - 6*w^3 - w^2 + 8*w + 1],\ [43, 43, w^4 - 5*w^2 + 3],\ [47, 47, -w^4 + w^3 + 5*w^2 - 2*w - 5],\ [49, 7, -w^5 + w^4 + 5*w^3 - 3*w^2 - 4*w - 1],\ [53, 53, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 5*w - 7],\ [59, 59, w^5 - w^4 - 6*w^3 + 4*w^2 + 7*w - 3],\ [71, 71, w^5 - w^4 - 5*w^3 + 4*w^2 + 4*w - 5],\ [79, 79, w^3 - w^2 - 4*w + 1],\ [83, 83, w^5 - 6*w^3 - w^2 + 7*w - 1],\ [83, 83, 2*w^5 - w^4 - 11*w^3 + 2*w^2 + 12*w + 1],\ [89, 89, -w^5 + w^4 + 4*w^3 - 2*w^2 - w - 1],\ [89, 89, -w^5 + w^4 + 5*w^3 - 3*w^2 - 4*w + 3],\ [89, 89, w^5 + w^4 - 6*w^3 - 6*w^2 + 6*w + 3],\ [89, 89, 2*w^4 - w^3 - 9*w^2 + w + 5],\ [101, 101, w^5 - 5*w^3 - w^2 + 5*w - 1],\ [107, 107, w^4 - w^3 - 3*w^2 + 2*w - 1],\ [107, 107, -w^5 + w^4 + 6*w^3 - 3*w^2 - 7*w + 1],\ [107, 107, -w^5 + 4*w^3 + 2*w^2 + 1],\ [113, 113, 2*w^5 - w^4 - 10*w^3 + 2*w^2 + 8*w - 3],\ [121, 11, 2*w^5 - w^4 - 10*w^3 + 2*w^2 + 8*w - 1],\ [125, 5, -w^3 + 4*w - 1],\ [125, 5, -2*w^5 + w^4 + 10*w^3 - 3*w^2 - 9*w + 3],\ [131, 131, w^5 + 2*w^4 - 7*w^3 - 10*w^2 + 9*w + 5],\ [137, 137, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 6*w - 7],\ [137, 137, w^4 - 3*w^2 - 2*w + 1],\ [139, 139, -w^5 + w^4 + 5*w^3 - 4*w^2 - 5*w + 1],\ [139, 139, w^5 - w^4 - 5*w^3 + 4*w^2 + 3*w - 3],\ [149, 149, -w^5 + 2*w^4 + 4*w^3 - 9*w^2 - w + 7],\ [151, 151, w^4 - 6*w^2 - w + 5],\ [163, 163, -w^5 + w^4 + 4*w^3 - 3*w^2 - w + 3],\ [167, 167, -w^5 + w^4 + 5*w^3 - 2*w^2 - 6*w + 1],\ [169, 13, -2*w^5 + 12*w^3 + w^2 - 13*w + 1],\ [179, 179, -w^5 + 6*w^3 + 2*w^2 - 9*w - 3],\ [179, 179, -w^3 + 5*w - 1],\ [191, 191, w^4 - 3*w^2 - 1],\ [193, 193, -w^5 - 3*w^4 + 6*w^3 + 17*w^2 - 5*w - 15],\ [197, 197, 2*w^5 - 11*w^3 - 2*w^2 + 10*w + 1],\ [197, 197, w^5 - 5*w^3 - 2*w^2 + 3*w - 1],\ [227, 227, w^5 - w^4 - 5*w^3 + 5*w^2 + 4*w - 5],\ [229, 229, -2*w^4 + w^3 + 10*w^2 - w - 9],\ [241, 241, 3*w^5 - 2*w^4 - 16*w^3 + 6*w^2 + 17*w - 3],\ [263, 263, -2*w^5 + 11*w^3 + w^2 - 11*w - 1],\ [269, 269, -w^5 + w^4 + 5*w^3 - 4*w^2 - 7*w + 3],\ [277, 277, 2*w^5 - w^4 - 10*w^3 + w^2 + 7*w + 1],\ [277, 277, 2*w^5 - 2*w^4 - 10*w^3 + 7*w^2 + 11*w - 5],\ [283, 283, -w^4 + w^3 + 4*w^2 - 3],\ [289, 17, -w^5 - w^4 + 7*w^3 + 4*w^2 - 10*w - 1],\ [293, 293, -3*w^5 + 16*w^3 + 3*w^2 - 15*w - 1],\ [293, 293, -2*w^5 - w^4 + 10*w^3 + 7*w^2 - 6*w - 5],\ [307, 307, -2*w^5 + w^4 + 9*w^3 - w^2 - 4*w - 1],\ [311, 311, w^4 - w^3 - 5*w^2 + 4*w + 1],\ [311, 311, -3*w^5 + 17*w^3 + 4*w^2 - 18*w - 7],\ [311, 311, -w^5 - w^4 + 5*w^3 + 6*w^2 - 2*w - 5],\ [311, 311, 2*w^4 - w^3 - 10*w^2 + w + 5],\ [313, 313, w^5 - 5*w^3 - 3*w^2 + 3*w + 3],\ [313, 313, -w^5 - w^4 + 5*w^3 + 7*w^2 - 3*w - 3],\ [317, 317, -w^5 + 2*w^4 + 3*w^3 - 8*w^2 + w + 5],\ [337, 337, 3*w^5 + w^4 - 16*w^3 - 10*w^2 + 14*w + 11],\ [337, 337, -w^5 - 2*w^4 + 6*w^3 + 10*w^2 - 6*w - 7],\ [337, 337, 2*w^5 + w^4 - 11*w^3 - 7*w^2 + 10*w + 3],\ [337, 337, w^4 - w^3 - 6*w^2 + 4*w + 7],\ [347, 347, -2*w^5 + 2*w^4 + 9*w^3 - 7*w^2 - 7*w + 3],\ [347, 347, -w^5 - w^4 + 5*w^3 + 7*w^2 - 2*w - 7],\ [347, 347, -w^5 - w^4 + 6*w^3 + 7*w^2 - 5*w - 7],\ [349, 349, 3*w^5 - w^4 - 17*w^3 + 3*w^2 + 19*w - 3],\ [349, 349, w^4 + w^3 - 6*w^2 - 4*w + 7],\ [359, 359, -2*w^5 + w^4 + 11*w^3 - 3*w^2 - 13*w + 1],\ [373, 373, -2*w^5 + 10*w^3 + 2*w^2 - 9*w - 1],\ [379, 379, -w^5 + 2*w^4 + 4*w^3 - 9*w^2 - w + 9],\ [389, 389, -2*w^5 + w^4 + 11*w^3 - 2*w^2 - 13*w - 1],\ [397, 397, w^5 - 3*w^4 - 5*w^3 + 14*w^2 + 7*w - 11],\ [419, 419, w^5 - 6*w^3 + w^2 + 7*w - 1],\ [419, 419, -w^5 + w^4 + 3*w^3 - 2*w^2 + w - 1],\ [433, 433, -w^5 + w^4 + 4*w^3 - 4*w^2 - w + 5],\ [433, 433, w^5 + w^4 - 7*w^3 - 4*w^2 + 9*w - 1],\ [439, 439, w^4 - 2*w^3 - 4*w^2 + 7*w + 3],\ [443, 443, -w^3 + w^2 + 3*w - 5],\ [443, 443, w^5 - w^4 - 5*w^3 + 2*w^2 + 5*w + 3],\ [449, 449, 2*w^5 - 2*w^4 - 11*w^3 + 8*w^2 + 12*w - 5],\ [457, 457, -2*w^5 - 2*w^4 + 11*w^3 + 13*w^2 - 10*w - 11],\ [461, 461, w^5 + 2*w^4 - 6*w^3 - 10*w^2 + 5*w + 7],\ [479, 479, -2*w^5 + 10*w^3 + w^2 - 6*w + 1],\ [479, 479, w^5 - w^4 - 6*w^3 + 3*w^2 + 9*w - 1],\ [491, 491, w^5 - w^4 - 4*w^3 + w^2 + w + 3],\ [499, 499, -w^3 + 5*w - 3],\ [499, 499, w^5 - 2*w^4 - 5*w^3 + 7*w^2 + 6*w - 1],\ [509, 509, -2*w^5 + 2*w^4 + 10*w^3 - 9*w^2 - 9*w + 11],\ [521, 521, -w^5 + 4*w^3 + 2*w^2 - w - 3],\ [521, 521, 2*w^5 + 2*w^4 - 11*w^3 - 13*w^2 + 9*w + 13],\ [521, 521, -w^4 + 2*w^3 + 4*w^2 - 5*w - 3],\ [523, 523, -w^5 + w^4 + 6*w^3 - 5*w^2 - 8*w + 3],\ [523, 523, w^5 + w^4 - 5*w^3 - 8*w^2 + 3*w + 7],\ [541, 541, w^5 + 3*w^4 - 7*w^3 - 16*w^2 + 8*w + 13],\ [547, 547, w^5 - 2*w^4 - 5*w^3 + 7*w^2 + 7*w - 3],\ [557, 557, 3*w^5 - w^4 - 15*w^3 + w^2 + 11*w - 1],\ [557, 557, 2*w^5 - w^4 - 11*w^3 + 2*w^2 + 11*w + 1],\ [563, 563, w^5 - 3*w^4 - 4*w^3 + 13*w^2 + 3*w - 9],\ [569, 569, -w^5 - w^4 + 5*w^3 + 6*w^2 - 4*w - 1],\ [571, 571, -3*w^5 + 2*w^4 + 15*w^3 - 7*w^2 - 10*w + 3],\ [577, 577, 2*w^5 - 11*w^3 - 2*w^2 + 9*w + 3],\ [587, 587, w^4 - 6*w^2 - 2*w + 7],\ [599, 599, -2*w^5 + 2*w^4 + 10*w^3 - 7*w^2 - 10*w + 3],\ [599, 599, w^5 - 2*w^4 - 4*w^3 + 9*w^2 + 3*w - 7],\ [601, 601, 2*w^2 - 5],\ [607, 607, -w^5 - w^4 + 4*w^3 + 7*w^2 - 5],\ [613, 613, -w^5 + 5*w^3 + w^2 - 3*w + 3],\ [617, 617, -2*w^4 + 11*w^2 + 2*w - 9],\ [619, 619, -2*w^5 + 10*w^3 + w^2 - 7*w + 1],\ [619, 619, -2*w^5 + 4*w^4 + 8*w^3 - 15*w^2 - 5*w + 7],\ [643, 643, -2*w^5 - w^4 + 12*w^3 + 6*w^2 - 12*w - 3],\ [647, 647, 3*w^5 - w^4 - 18*w^3 + w^2 + 23*w + 3],\ [647, 647, 2*w^5 + w^4 - 10*w^3 - 9*w^2 + 9*w + 9],\ [653, 653, -w^4 + 7*w^2 + w - 7],\ [673, 673, -2*w^4 + w^3 + 8*w^2 - w - 5],\ [673, 673, -2*w^5 + 11*w^3 + w^2 - 9*w + 1],\ [677, 677, 4*w^5 - w^4 - 20*w^3 + w^2 + 15*w - 3],\ [683, 683, 3*w^5 - 2*w^4 - 14*w^3 + 6*w^2 + 11*w - 5],\ [683, 683, 2*w^5 - w^4 - 11*w^3 + 3*w^2 + 10*w - 3],\ [683, 683, -w^5 + 5*w^3 + w^2 - 4*w + 3],\ [691, 691, w^5 + w^4 - 6*w^3 - 6*w^2 + 8*w + 3],\ [709, 709, -2*w^5 + 2*w^4 + 11*w^3 - 7*w^2 - 13*w + 3],\ [719, 719, 2*w^5 - 2*w^4 - 10*w^3 + 8*w^2 + 9*w - 9],\ [719, 719, -2*w^5 + w^4 + 11*w^3 - 4*w^2 - 12*w + 3],\ [727, 727, w^5 - w^4 - 6*w^3 + 4*w^2 + 7*w - 1],\ [729, 3, -3],\ [739, 739, 2*w^4 - w^3 - 9*w^2 + 5],\ [739, 739, -w^5 + w^4 + 4*w^3 - 3*w^2 - 3*w - 1],\ [751, 751, -2*w^4 + w^3 + 9*w^2 - 3*w - 3],\ [761, 761, -w^5 - 2*w^4 + 7*w^3 + 12*w^2 - 9*w - 13],\ [773, 773, -w^5 + 5*w^3 + 2*w^2 - 2*w - 3],\ [787, 787, 2*w^5 - 12*w^3 - 2*w^2 + 13*w + 3],\ [787, 787, -2*w^5 + w^4 + 10*w^3 - 3*w^2 - 10*w + 1],\ [797, 797, -w^5 + 2*w^4 + 5*w^3 - 8*w^2 - 7*w + 3],\ [811, 811, -2*w^5 + 12*w^3 + w^2 - 15*w - 1],\ [821, 821, 4*w^5 + w^4 - 22*w^3 - 8*w^2 + 21*w + 3],\ [821, 821, w^5 - 2*w^4 - 3*w^3 + 8*w^2 - 3*w - 3],\ [821, 821, -w^5 + 7*w^3 - 9*w - 1],\ [827, 827, w^5 - 7*w^3 - w^2 + 10*w + 1],\ [829, 829, -2*w^4 + 10*w^2 + w - 7],\ [839, 839, -w^5 + 2*w^4 + 6*w^3 - 10*w^2 - 8*w + 9],\ [853, 853, -w^5 + w^4 + 3*w^3 - 3*w^2 + 2*w + 1],\ [859, 859, -w^5 + 6*w^3 - 9*w + 1],\ [859, 859, -2*w^5 + 3*w^4 + 8*w^3 - 10*w^2 - 6*w + 5],\ [859, 859, w^5 - 2*w^4 - 4*w^3 + 8*w^2 + 2*w - 7],\ [859, 859, 2*w^5 - 2*w^4 - 10*w^3 + 6*w^2 + 10*w - 3],\ [863, 863, 3*w^5 - 4*w^4 - 14*w^3 + 14*w^2 + 13*w - 7],\ [877, 877, w^3 + w^2 - 4*w - 1],\ [881, 881, -w^5 + w^4 + 4*w^3 - 4*w^2 - 2*w + 5],\ [881, 881, -2*w^5 + 10*w^3 + 4*w^2 - 7*w - 5],\ [907, 907, -w^4 + w^3 + 4*w^2 - w + 1],\ [937, 937, w^5 - 7*w^3 + w^2 + 11*w - 3],\ [941, 941, -2*w^5 + w^4 + 11*w^3 - w^2 - 12*w - 1],\ [947, 947, -w^5 + 5*w^3 + 3*w^2 - 5*w - 7],\ [953, 953, 2*w^5 - w^4 - 11*w^3 + 4*w^2 + 10*w - 7],\ [971, 971, w^5 - w^4 - 5*w^3 + 3*w^2 + 7*w + 1],\ [983, 983, -2*w^5 + 9*w^3 + 3*w^2 - 5*w - 3],\ [997, 997, 3*w^5 - 18*w^3 - 2*w^2 + 22*w + 1]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^20 - 32*x^18 + 431*x^16 - 3184*x^14 + 14092*x^12 - 38285*x^10 + 62634*x^8 - 57251*x^6 + 23878*x^4 - 1920*x^2 + 36 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, -8/45*e^19 + 241/45*e^17 - 5993/90*e^15 + 19862/45*e^13 - 75554/45*e^11 + 164623/45*e^9 - 21176/5*e^7 + 36703/18*e^5 - 1778/45*e^3 - 221/15*e, -1, -1/6*e^17 + 5*e^15 - 371/6*e^13 + 407*e^11 - 4604/3*e^9 + 6621/2*e^7 - 3802*e^5 + 11105/6*e^3 - 90*e, -29/180*e^19 + 877/180*e^17 - 2743/45*e^15 + 36739/90*e^13 - 71141/45*e^11 + 641377/180*e^9 - 17751/4*e^7 + 236963/90*e^5 - 43771/90*e^3 + 397/15*e, -1/60*e^19 + 29/60*e^17 - 169/30*e^15 + 199/6*e^13 - 1471/15*e^11 + 1141/12*e^9 + 4051/20*e^7 - 8893/15*e^5 + 2633/6*e^3 - 146/5*e, 37/180*e^19 - 1139/180*e^17 + 3644/45*e^15 - 25132/45*e^13 + 101239/45*e^11 - 964457/180*e^9 + 145129/20*e^7 - 90083/18*e^5 + 60568/45*e^3 - 1214/15*e, -1/5*e^19 + 181/30*e^17 - 751/10*e^15 + 7468/15*e^13 - 1889*e^11 + 61127/15*e^9 - 45667/10*e^7 + 19117/10*e^5 + 3563/15*e^3 - 253/5*e, -4/9*e^19 + 616/45*e^17 - 1577/9*e^15 + 54353/45*e^13 - 218423/45*e^11 + 516592/45*e^9 - 76318/5*e^7 + 450409/45*e^5 - 102437/45*e^3 + 1219/15*e, 1/5*e^19 - 31/5*e^17 + 801/10*e^15 - 5597/10*e^13 + 2296*e^11 - 28049/5*e^9 + 39391/5*e^7 - 57257/10*e^5 + 16543/10*e^3 - 387/5*e, -1/15*e^16 + 2*e^14 - 368/15*e^12 + 791/5*e^10 - 8602/15*e^8 + 5779/5*e^6 - 5938/5*e^4 + 7232/15*e^2 - 79/5, -17/60*e^18 + 523/60*e^16 - 1669/15*e^14 + 2287/3*e^12 - 45362/15*e^10 + 83477/12*e^8 - 173723/20*e^6 + 145013/30*e^4 - 1618/3*e^2 + 133/5, 11/90*e^19 - 158/45*e^17 + 1814/45*e^15 - 20741/90*e^13 + 5663/9*e^11 - 29149/90*e^9 - 11863/5*e^7 + 243142/45*e^5 - 328471/90*e^3 + 2743/15*e, -1/5*e^19 + 31/5*e^17 - 801/10*e^15 + 5597/10*e^13 - 2296*e^11 + 28049/5*e^9 - 39391/5*e^7 + 57257/10*e^5 - 16543/10*e^3 + 377/5*e, 1/2*e^18 - 151/10*e^16 + 377/2*e^14 - 6289/5*e^12 + 24204/5*e^10 - 107847/10*e^8 + 131107/10*e^6 - 73049/10*e^4 + 5061/5*e^2 - 171/5, -11/30*e^18 + 111/10*e^16 - 2084/15*e^14 + 4647/5*e^12 - 53728/15*e^10 + 79601/10*e^8 - 19079/2*e^6 + 75332/15*e^4 - 2263/5*e^2 + 66/5, 9/20*e^18 - 273/20*e^16 + 1711/10*e^14 - 5724/5*e^12 + 22003/5*e^10 - 193869/20*e^8 + 226627/20*e^6 - 5485*e^4 + 551/5*e^2 + 66/5, 1/5*e^19 - 31/5*e^17 + 801/10*e^15 - 5597/10*e^13 + 2296*e^11 - 28049/5*e^9 + 39391/5*e^7 - 57277/10*e^5 + 16723/10*e^3 - 547/5*e, 8/15*e^18 - 49/3*e^16 + 3109/15*e^14 - 21139/15*e^12 + 83036/15*e^10 - 188606/15*e^8 + 77179/5*e^6 - 125041/15*e^4 + 11611/15*e^2 - 16, 1/5*e^18 - 181/30*e^16 + 751/10*e^14 - 7468/15*e^12 + 1889*e^10 - 61127/15*e^8 + 45667/10*e^6 - 19137/10*e^4 - 3293/15*e^2 + 103/5, 2/5*e^19 - 37/3*e^17 + 791/5*e^15 - 16423/15*e^13 + 22169/5*e^11 - 159692/15*e^9 + 73003/5*e^7 - 51329/5*e^5 + 42697/15*e^3 - 175*e, 1/15*e^16 - 2*e^14 + 368/15*e^12 - 791/5*e^10 + 8602/15*e^8 - 5784/5*e^6 + 5993/5*e^4 - 7682/15*e^2 + 139/5, -2/15*e^18 + 61/15*e^16 - 1547/30*e^14 + 5294/15*e^12 - 21257/15*e^10 + 50971/15*e^8 - 4727*e^6 + 104111/30*e^4 - 15596/15*e^2 + 184/5, 3/10*e^19 - 277/30*e^17 + 592/5*e^15 - 24653/30*e^13 + 16794/5*e^11 - 247327/30*e^9 + 23709/2*e^7 - 45976/5*e^5 + 92957/30*e^3 - 834/5*e, -11/45*e^19 + 659/90*e^17 - 8111/90*e^15 + 26384/45*e^13 - 96788/45*e^11 + 195091/45*e^9 - 40749/10*e^7 + 8665/18*e^5 + 55294/45*e^3 - 1262/15*e, 11/30*e^18 - 331/30*e^16 + 2054/15*e^14 - 13573/15*e^12 + 10271/3*e^10 - 221599/30*e^8 + 83827/10*e^6 - 57353/15*e^4 - 863/15*e^2 + 73/5, 1/4*e^18 - 461/60*e^16 + 98*e^14 - 10072/15*e^12 + 13349/5*e^10 - 371507/60*e^8 + 158409/20*e^6 - 47609/10*e^4 + 12388/15*e^2 - 176/5, -1/5*e^19 + 179/30*e^17 - 731/10*e^15 + 1420/3*e^13 - 8654/5*e^11 + 10505/3*e^9 - 34109/10*e^7 + 7241/10*e^5 + 2147/3*e^3 - 252/5*e, -7/30*e^18 + 106/15*e^16 - 2651/30*e^14 + 8831/15*e^12 - 6730/3*e^10 + 145193/30*e^8 - 26667/5*e^6 + 59867/30*e^4 + 7351/15*e^2 - 176/5, -1/15*e^18 + 61/30*e^16 - 383/15*e^14 + 2542/15*e^12 - 9451/15*e^10 + 18758/15*e^8 - 1993/2*e^6 - 5371/15*e^4 + 11237/15*e^2 - 148/5, -31/90*e^19 + 481/45*e^17 - 6229/45*e^15 + 43742/45*e^13 - 181244/45*e^11 + 903521/90*e^9 - 73366/5*e^7 + 104102/9*e^5 - 178118/45*e^3 + 3379/15*e, -7/10*e^18 + 641/30*e^16 - 2701/10*e^14 + 27428/15*e^12 - 7149*e^10 + 484889/30*e^8 - 197727/10*e^6 + 106917/10*e^4 - 15677/15*e^2 + 122/5, -2/5*e^19 + 37/3*e^17 - 791/5*e^15 + 16423/15*e^13 - 22169/5*e^11 + 159692/15*e^9 - 73003/5*e^7 + 51329/5*e^5 - 42697/15*e^3 + 177*e, 1/5*e^18 - 181/30*e^16 + 751/10*e^14 - 7468/15*e^12 + 1889*e^10 - 61127/15*e^8 + 45677/10*e^6 - 19247/10*e^4 - 2813/15*e^2 + 23/5, -37/60*e^18 + 1127/60*e^16 - 3554/15*e^14 + 24013/15*e^12 - 18755/3*e^10 + 849113/60*e^8 - 349199/20*e^6 + 293491/30*e^4 - 19177/15*e^2 + 252/5, 31/60*e^18 - 311/20*e^16 + 2897/15*e^14 - 6391/5*e^12 + 72724/15*e^10 - 209861/20*e^8 + 47697/4*e^6 - 160687/30*e^4 - 1026/5*e^2 + 117/5, -7/90*e^19 + 37/18*e^17 - 913/45*e^15 + 3608/45*e^13 + 1783/45*e^11 - 132391/90*e^9 + 51913/10*e^7 - 349868/45*e^5 + 202828/45*e^3 - 694/3*e, 8/15*e^19 - 159/10*e^17 + 2914/15*e^15 - 12483/10*e^13 + 67094/15*e^11 - 42721/5*e^9 + 66751/10*e^7 + 5431/3*e^5 - 41773/10*e^3 + 906/5*e, -1/5*e^18 + 179/30*e^16 - 731/10*e^14 + 1420/3*e^12 - 8654/5*e^10 + 10505/3*e^8 - 34109/10*e^6 + 7261/10*e^4 + 2099/3*e^2 - 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17416/45*e^15 + 113714/45*e^13 - 419042/45*e^11 + 849181/45*e^9 - 17834*e^7 + 94918/45*e^5 + 240709/45*e^3 - 3476/15*e, 9/10*e^18 - 137/5*e^16 + 1726/5*e^14 - 11632/5*e^12 + 9038*e^10 - 202371/10*e^8 + 121637/5*e^6 - 62827/5*e^4 + 3973/5*e^2 - 39/5, 1/5*e^17 - 13/2*e^15 + 881/10*e^13 - 3218/5*e^11 + 13637/5*e^9 - 33407/5*e^7 + 87573/10*e^5 - 48619/10*e^3 + 1482/5*e, 2/3*e^18 - 304/15*e^16 + 766/3*e^14 - 25907/15*e^12 + 101902/15*e^10 - 235798/15*e^8 + 102781/5*e^6 - 202361/15*e^4 + 48413/15*e^2 - 616/5, -5/18*e^19 + 743/90*e^17 - 1807/18*e^15 + 28817/45*e^13 - 102077/45*e^11 + 382391/90*e^9 - 31639/10*e^7 - 97213/90*e^5 + 95197/45*e^3 - 1904/15*e, -31/90*e^19 + 466/45*e^17 - 5779/45*e^15 + 38177/45*e^13 - 144614/45*e^11 + 627281/90*e^9 - 40256/5*e^7 + 35540/9*e^5 - 8978/45*e^3 - 161/15*e, 8/5*e^18 - 1453/30*e^16 + 3029/5*e^14 - 60679/15*e^12 + 15530*e^10 - 513416/15*e^8 + 402141/10*e^6 - 99253/5*e^4 + 10561/15*e^2 + 209/5, 1/5*e^18 - 92/15*e^16 + 388/5*e^14 - 1565/3*e^12 + 9959/5*e^10 - 12691/3*e^8 + 21682/5*e^6 - 4758/5*e^4 - 3013/3*e^2 + 217/5, -4/15*e^16 + 15/2*e^14 - 1277/15*e^12 + 2494/5*e^10 - 23983/15*e^8 + 13651/5*e^6 - 22149/10*e^4 + 9323/15*e^2 - 111/5, -43/30*e^18 + 433/10*e^16 - 8107/15*e^14 + 18011/5*e^12 - 207209/15*e^10 + 304833/10*e^8 - 72215/2*e^6 + 276856/15*e^4 - 6119/5*e^2 + 13/5, -19/90*e^19 + 283/45*e^17 - 6917/90*e^15 + 4459/9*e^13 - 80843/45*e^11 + 64291/18*e^9 - 16611/5*e^7 + 40637/90*e^5 + 8525/9*e^3 - 2633/15*e, 4/3*e^18 - 203/5*e^16 + 1535/3*e^14 - 17249/5*e^12 + 201122/15*e^10 - 150116/5*e^8 + 180226/5*e^6 - 277726/15*e^4 + 5341/5*e^2 + 144/5, 7/10*e^19 - 65/3*e^17 + 2791/10*e^15 - 29099/15*e^13 + 39422/5*e^11 - 568637/30*e^9 + 129364/5*e^7 - 178519/10*e^5 + 69836/15*e^3 - 240*e, -e^8 + 16*e^6 - 80*e^4 + 119*e^2 - 6, 31/45*e^19 - 977/45*e^17 + 12908/45*e^15 - 93049/45*e^13 + 399118/45*e^11 - 1041596/45*e^9 + 179757/5*e^7 - 275866/9*e^5 + 514801/45*e^3 - 7583/15*e, 43/45*e^19 - 1319/45*e^17 + 33613/90*e^15 - 230567/90*e^13 + 461068/45*e^11 - 1086569/45*e^9 + 32103*e^7 - 1910809/90*e^5 + 446033/90*e^3 - 1511/15*e, -11/6*e^18 + 1667/30*e^16 - 4177/6*e^14 + 69878/15*e^12 - 268988/15*e^10 + 1189769/30*e^8 - 468163/10*e^6 + 699683/30*e^4 - 14312/15*e^2 - 101/5, -1/15*e^18 + 32/15*e^16 - 428/15*e^14 + 3109/15*e^12 - 13348/15*e^10 + 34541/15*e^8 - 17506/5*e^6 + 8632/3*e^4 - 15541/15*e^2 + 308/5, -3/20*e^19 + 257/60*e^17 - 246/5*e^15 + 8609/30*e^13 - 4297/5*e^11 + 59837/60*e^9 + 3767/4*e^7 - 35529/10*e^5 + 80299/30*e^3 - 1093/5*e, -28/15*e^18 + 283/5*e^16 - 10649/15*e^14 + 23817/5*e^12 - 276658/15*e^10 + 206598/5*e^8 - 50303*e^6 + 413027/15*e^4 - 15863/5*e^2 + 396/5, -19/10*e^18 + 115/2*e^16 - 3596/5*e^14 + 24026/5*e^12 - 92409/5*e^10 + 409383/10*e^8 - 487711/10*e^6 + 126464/5*e^4 - 10004/5*e^2 + 53, -1/2*e^18 + 153/10*e^16 - 194*e^14 + 6592/5*e^12 - 25907/5*e^10 + 118101/10*e^8 - 146831/10*e^6 + 41561/5*e^4 - 5528/5*e^2 + 133/5, -1/10*e^18 + 89/30*e^16 - 363/10*e^14 + 3548/15*e^12 - 4408/5*e^10 + 55769/30*e^8 - 3959/2*e^6 + 6279/10*e^4 + 4408/15*e^2 + 43/5, -89/60*e^19 + 2723/60*e^17 - 8638/15*e^15 + 58849/15*e^13 - 232673/15*e^11 + 2149469/60*e^9 - 917019/20*e^7 + 167647/6*e^5 - 77941/15*e^3 + 1188/5*e, -31/60*e^18 + 61/4*e^16 - 5539/30*e^14 + 5909/5*e^12 - 64408/15*e^10 + 176309/20*e^8 - 189423/20*e^6 + 62393/15*e^4 - 321/5*e^2 + 17, 1/15*e^18 - 19/10*e^16 + 661/30*e^14 - 667/5*e^12 + 1343/3*e^10 - 3993/5*e^8 + 5799/10*e^6 + 5393/30*e^4 - 1902/5*e^2 + 161/5, 3/5*e^18 - 269/15*e^16 + 1104/5*e^14 - 21679/15*e^12 + 5406*e^10 - 172466/15*e^8 + 63963/5*e^6 - 28068/5*e^4 - 2954/15*e^2 + 194/5, -6/5*e^18 + 367/10*e^16 - 4651/10*e^14 + 15796/5*e^12 - 12410*e^10 + 141344/5*e^8 - 350907/10*e^6 + 197497/10*e^4 - 12759/5*e^2 + 472/5, 53/30*e^18 - 537/10*e^16 + 10127/15*e^14 - 22687/5*e^12 + 263452/15*e^10 - 391371/10*e^8 + 467443/10*e^6 - 71704/3*e^4 + 7033/5*e^2 - 32/5, -5/6*e^19 + 751/30*e^17 - 929/3*e^15 + 30499/15*e^13 - 113909/15*e^11 + 477517/30*e^9 - 167069/10*e^7 + 79252/15*e^5 + 34184/15*e^3 - 1193/5*e, 1/30*e^18 - 31/30*e^16 + 199/15*e^14 - 1363/15*e^12 + 1066/3*e^10 - 23509/30*e^8 + 8937/10*e^6 - 6463/15*e^4 + 1057/15*e^2 - 122/5, 1/5*e^18 - 181/30*e^16 + 751/10*e^14 - 7468/15*e^12 + 1889*e^10 - 61142/15*e^8 + 45807/10*e^6 - 19717/10*e^4 - 2318/15*e^2 + 143/5, -1/90*e^19 + 43/45*e^17 - 2003/90*e^15 + 10943/45*e^13 - 13114/9*e^11 + 451349/90*e^9 - 48847/5*e^7 + 894791/90*e^5 - 189707/45*e^3 + 3562/15*e, 2/15*e^19 - 41/10*e^17 + 1577/30*e^15 - 1826/5*e^13 + 22451/15*e^11 - 18479/5*e^9 + 53929/10*e^7 - 26227/6*e^5 + 8579/5*e^3 - 1146/5*e, -62/45*e^19 + 1903/45*e^17 - 48527/90*e^15 + 66617/18*e^13 - 666503/45*e^11 + 314390/9*e^9 - 232646/5*e^7 + 2789447/90*e^5 - 135401/18*e^3 + 4342/15*e, 1/5*e^18 - 86/15*e^16 + 333/5*e^14 - 6007/15*e^12 + 6558/5*e^10 - 32993/15*e^8 + 6658/5*e^6 + 667*e^4 - 12437/15*e^2 + 136/5, 49/30*e^18 - 1489/30*e^16 + 9361/15*e^14 - 62962/15*e^12 + 48841/3*e^10 - 1093081/30*e^8 + 439413/10*e^6 - 346762/15*e^4 + 28528/15*e^2 - 293/5, 2/5*e^18 - 176/15*e^16 + 706/5*e^14 - 13486/15*e^12 + 3256*e^10 - 100394/15*e^8 + 36432/5*e^6 - 17072/5*e^4 + 3784/15*e^2 - 14/5, 13/30*e^18 - 197/15*e^16 + 4949/30*e^14 - 16693/15*e^12 + 65534/15*e^10 - 303199/30*e^8 + 13258*e^6 - 264377/30*e^4 + 33307/15*e^2 - 368/5, 1/45*e^19 - 2/45*e^17 - 472/45*e^15 + 8036/45*e^13 - 60272/45*e^11 + 245029/45*e^9 - 62028/5*e^7 + 134780/9*e^5 - 348404/45*e^3 + 7222/15*e, -1/2*e^19 + 481/30*e^17 - 216*e^15 + 23854/15*e^13 - 34838/5*e^11 + 555697/30*e^9 - 290989/10*e^7 + 124079/5*e^5 - 138406/15*e^3 + 2617/5*e, -4/3*e^18 + 1201/30*e^16 - 1487/3*e^14 + 49009/15*e^12 - 184979/15*e^10 + 398201/15*e^8 - 300509/10*e^6 + 203827/15*e^4 + 5084/15*e^2 - 138/5, -43/90*e^19 + 1307/90*e^17 - 16469/90*e^15 + 22295/18*e^13 - 219581/45*e^11 + 203923/18*e^9 - 149349/10*e^7 + 905279/90*e^5 - 48653/18*e^3 + 3034/15*e, -31/30*e^18 + 94/3*e^16 - 11783/30*e^14 + 39454/15*e^12 - 152081/15*e^10 + 674617/30*e^8 - 133629/5*e^6 + 407087/30*e^4 - 10666/15*e^2 - 45, 3/5*e^18 - 177/10*e^16 + 2143/10*e^14 - 6862/5*e^12 + 24934/5*e^10 - 50973/5*e^8 + 106973/10*e^6 - 8285/2*e^4 - 2217/5*e^2 + 298/5, 11/15*e^18 - 22*e^16 + 4078/15*e^14 - 8926/5*e^12 + 100337/15*e^10 - 70999/5*e^8 + 78058/5*e^6 - 97162/15*e^4 - 2816/5*e^2 + 41, 23/30*e^19 - 117/5*e^17 + 8869/30*e^15 - 1998*e^13 + 116686/15*e^11 - 34825/2*e^9 + 103756/5*e^7 - 306589/30*e^5 + e^3 + 1276/5*e, 1/3*e^18 - 10*e^16 + 371/3*e^14 - 814*e^12 + 9208/3*e^10 - 6621*e^8 + 7603*e^6 - 11072/3*e^4 + 150*e^2 + 14, 11/15*e^19 - 653/30*e^17 + 7931/30*e^15 - 10109/6*e^13 + 89489/15*e^11 - 33527/3*e^9 + 82793/10*e^7 + 93049/30*e^5 - 35527/6*e^3 + 1824/5*e, 19/30*e^18 - 293/15*e^16 + 3751/15*e^14 - 5159/3*e^12 + 102893/15*e^10 - 95627/6*e^8 + 101753/5*e^6 - 181186/15*e^4 + 5843/3*e^2 - 302/5, -1/10*e^18 + 41/15*e^16 - 293/10*e^14 + 452/3*e^12 - 1642/5*e^10 - 829/6*e^8 + 9984/5*e^6 - 33447/10*e^4 + 5551/3*e^2 - 516/5, 71/90*e^19 - 2083/90*e^17 + 12449/45*e^15 - 77491/45*e^13 + 263803/45*e^11 - 908443/90*e^9 + 10289/2*e^7 + 321148/45*e^5 - 354371/45*e^3 + 5419/15*e, -4/15*e^18 + 79/10*e^16 - 2899/30*e^14 + 633*e^12 - 36226/15*e^10 + 5493*e^8 - 73607/10*e^6 + 164689/30*e^4 - 1881*e^2 + 354/5, -9/5*e^18 + 821/15*e^16 - 3442/5*e^14 + 69409/15*e^12 - 89479/5*e^10 + 595811/15*e^8 - 46827*e^6 + 114076/5*e^4 - 5971/15*e^2 - 151/5, -26/15*e^18 + 158/3*e^16 - 9928/15*e^14 + 66698/15*e^12 - 258137/15*e^10 + 575602/15*e^8 - 229968/5*e^6 + 358402/15*e^4 - 26522/15*e^2 + 41, 4/15*e^19 - 139/15*e^17 + 4099/30*e^15 - 16694/15*e^13 + 16376/3*e^11 - 246811/15*e^9 + 148528/5*e^7 - 883513/30*e^5 + 189296/15*e^3 - 2581/5*e, -41/30*e^19 + 1249/30*e^17 - 15763/30*e^15 + 21331/6*e^13 - 208972/15*e^11 + 190763/6*e^9 - 400109/10*e^7 + 711613/30*e^5 - 24673/6*e^3 + 1078/5*e, 49/45*e^19 - 593/18*e^17 + 18542/45*e^15 - 247889/90*e^13 + 477553/45*e^11 - 1063103/45*e^9 + 285513/10*e^7 - 701513/45*e^5 + 183041/90*e^3 - 736/3*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([17, 17, -w^5 + w^4 + 5*w^3 - 3*w^2 - 5*w + 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]