/* 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([5, 5, -4, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([880,110,2*w^3 - 6*w^2 - 4*w + 10]) primes_array = [ [5, 5, w],\ [5, 5, w^3 - 2*w^2 - 2*w + 3],\ [11, 11, -w^2 + 4],\ [11, 11, w^2 - 2*w - 3],\ [16, 2, 2],\ [29, 29, w^3 - 4*w - 1],\ [29, 29, w^3 - 3*w^2 - w + 4],\ [41, 41, w^3 - 2*w^2 - w + 4],\ [41, 41, -w^3 + w^2 + 2*w + 2],\ [59, 59, -2*w^3 + 4*w^2 + 4*w - 7],\ [59, 59, -3*w^2 + 2*w + 7],\ [61, 61, -w^3 + 4*w^2 - 6],\ [61, 61, w^3 + w^2 - 5*w - 3],\ [71, 71, w^3 + w^2 - 4*w - 6],\ [71, 71, 3*w^2 - 2*w - 8],\ [71, 71, 3*w^2 - 4*w - 7],\ [71, 71, w^3 - 4*w^2 + w + 8],\ [79, 79, -2*w^3 + 3*w^2 + 5*w - 2],\ [79, 79, 2*w^2 - 3*w - 7],\ [79, 79, 2*w^2 - w - 8],\ [79, 79, -2*w^3 + 3*w^2 + 5*w - 4],\ [81, 3, -3],\ [89, 89, -w - 3],\ [89, 89, w - 4],\ [101, 101, w^3 - 6*w - 2],\ [101, 101, 2*w^3 - 3*w^2 - 5*w + 3],\ [101, 101, -w^3 + 3*w^2 + 3*w - 7],\ [109, 109, -3*w^2 + 5*w + 4],\ [109, 109, -2*w^3 + w^2 + 6*w + 4],\ [121, 11, 3*w^2 - 3*w - 8],\ [139, 139, -w^3 - w^2 + 6*w + 3],\ [139, 139, w^3 - 4*w^2 - w + 7],\ [149, 149, -2*w^3 + 6*w^2 + w - 11],\ [149, 149, 2*w^3 - 7*w - 6],\ [151, 151, -w^3 + 2*w^2 + 4*w - 4],\ [151, 151, w^3 - w^2 - 5*w + 1],\ [169, 13, -4*w^2 + 5*w + 11],\ [169, 13, 3*w^3 - 6*w^2 - 7*w + 8],\ [181, 181, w^3 + w^2 - 4*w - 7],\ [181, 181, -2*w^2 + 5*w + 1],\ [181, 181, 3*w^3 - 3*w^2 - 9*w + 2],\ [181, 181, -w^3 + 4*w^2 - w - 9],\ [191, 191, w^3 - 5*w + 1],\ [191, 191, -w^3 + 3*w^2 + 2*w - 3],\ [199, 199, -2*w^3 + 2*w^2 + 5*w + 4],\ [199, 199, -2*w^3 + 9*w + 4],\ [229, 229, 2*w^2 - 5*w - 4],\ [229, 229, -4*w^2 + 5*w + 8],\ [241, 241, -3*w^3 + 7*w^2 + 5*w - 12],\ [241, 241, -3*w^3 + 2*w^2 + 10*w + 3],\ [269, 269, -w^3 + 6*w^2 - 3*w - 13],\ [269, 269, w^3 + 3*w^2 - 6*w - 11],\ [271, 271, 2*w^3 - 2*w^2 - 7*w + 3],\ [271, 271, -2*w^3 + 4*w^2 + 5*w - 4],\ [289, 17, w^3 - 6*w^2 + 2*w + 11],\ [289, 17, w^3 + 3*w^2 - 7*w - 8],\ [311, 311, -2*w^3 + w^2 + 5*w + 4],\ [311, 311, 2*w^3 - 5*w^2 - w + 8],\ [331, 331, 3*w^3 - 3*w^2 - 11*w - 3],\ [331, 331, -3*w^3 + 6*w^2 + 8*w - 14],\ [349, 349, -3*w^3 + 6*w^2 + 6*w - 8],\ [349, 349, 3*w^3 - 3*w^2 - 9*w + 1],\ [359, 359, -2*w^3 - w^2 + 7*w + 8],\ [359, 359, -2*w^3 + 6*w^2 + w - 12],\ [359, 359, 2*w^3 - 7*w - 7],\ [359, 359, -2*w^3 + 7*w^2 - w - 12],\ [361, 19, 4*w^2 - 4*w - 11],\ [361, 19, -4*w^2 + 4*w + 9],\ [389, 389, -w^3 + 4*w^2 - w - 11],\ [389, 389, w^3 + w^2 - 4*w - 9],\ [401, 401, w^2 - 8],\ [401, 401, w^2 - 2*w - 7],\ [409, 409, -3*w^2 + 5*w + 9],\ [409, 409, -3*w^3 + w^2 + 12*w + 4],\ [409, 409, -w^3 + w^2 + 6*w + 1],\ [409, 409, 3*w^2 - w - 11],\ [419, 419, w^3 - 7*w - 3],\ [419, 419, -w^3 + 3*w^2 + 4*w - 9],\ [431, 431, -2*w^3 + 2*w^2 + 7*w - 4],\ [431, 431, w^3 + 2*w^2 - 7*w - 4],\ [439, 439, -2*w^3 + 5*w^2 + 2*w - 11],\ [439, 439, 2*w^3 - w^2 - 6*w - 6],\ [449, 449, w^3 + 3*w^2 - 7*w - 9],\ [449, 449, w^3 - 6*w^2 + 5*w + 11],\ [449, 449, 3*w^3 - 7*w^2 - 3*w + 8],\ [449, 449, -w^3 + 6*w^2 - 2*w - 12],\ [461, 461, -3*w^3 + 8*w^2 + 4*w - 18],\ [461, 461, 3*w^3 - 4*w^2 - 5*w - 1],\ [479, 479, -w^3 + 5*w^2 - 2*w - 16],\ [479, 479, 2*w^3 - 4*w^2 - w - 1],\ [491, 491, -w^3 + 7*w^2 - w - 18],\ [491, 491, w^3 + 2*w^2 - 5*w - 11],\ [491, 491, -w^3 + 5*w^2 - 2*w - 13],\ [491, 491, w^3 + 4*w^2 - 10*w - 13],\ [499, 499, 3*w^3 - 4*w^2 - 8*w + 3],\ [499, 499, -w^3 + 4*w^2 + 2*w - 6],\ [499, 499, -w^3 - w^2 + 7*w + 1],\ [499, 499, 3*w^3 - 5*w^2 - 7*w + 6],\ [529, 23, 4*w^3 - 3*w^2 - 13*w - 1],\ [529, 23, w^3 + 4*w^2 - 9*w - 8],\ [569, 569, -3*w^3 + 7*w^2 + 4*w - 14],\ [569, 569, 3*w^3 - 4*w^2 - 7*w + 1],\ [569, 569, 3*w^3 - 5*w^2 - 6*w + 7],\ [569, 569, w^3 - 4*w^2 + 4*w + 7],\ [571, 571, -w^3 + 7*w^2 - w - 17],\ [571, 571, w^3 + 4*w^2 - 10*w - 12],\ [599, 599, 3*w^3 - 6*w^2 - 5*w + 7],\ [599, 599, 3*w^3 - 3*w^2 - 8*w + 1],\ [619, 619, -w^3 + 3*w^2 + 4*w - 7],\ [619, 619, 2*w^3 - 6*w^2 - w + 13],\ [619, 619, -w^3 + 3*w^2 - 2*w - 6],\ [619, 619, w^3 - 7*w - 1],\ [641, 641, 3*w^3 - 3*w^2 - 7*w + 1],\ [641, 641, -3*w^3 + 6*w^2 + 4*w - 6],\ [659, 659, -2*w^3 + 5*w^2 + 6*w - 7],\ [659, 659, -2*w^3 + w^2 + 10*w - 2],\ [661, 661, 2*w^3 - 4*w^2 - w + 6],\ [661, 661, w^3 + 2*w^2 - 5*w - 12],\ [701, 701, -w^3 + 3*w^2 - w - 9],\ [701, 701, -2*w^3 + w^2 + 9*w - 1],\ [701, 701, 2*w^3 - 8*w - 1],\ [701, 701, w^3 - 2*w - 8],\ [709, 709, 2*w^3 - 2*w^2 - 9*w + 1],\ [709, 709, w^3 - w^2 + w - 2],\ [719, 719, -5*w^2 + 4*w + 14],\ [719, 719, -5*w^2 + 6*w + 13],\ [739, 739, 4*w^3 - 6*w^2 - 11*w + 7],\ [739, 739, -4*w^3 + 6*w^2 + 11*w - 6],\ [751, 751, -w^3 + 7*w^2 - 4*w - 16],\ [751, 751, -w^3 - 4*w^2 + 7*w + 14],\ [769, 769, w^3 - 3*w^2 - w + 11],\ [769, 769, -w^3 + 4*w + 8],\ [811, 811, -w^3 + 4*w^2 - 14],\ [811, 811, -w^3 - w^2 + 5*w + 11],\ [829, 829, -w^3 + 2*w^2 - w - 6],\ [829, 829, w^2 + 3*w - 1],\ [829, 829, 3*w^3 - 13*w - 6],\ [829, 829, w^3 - w^2 - 6],\ [841, 29, 5*w^2 - 5*w - 14],\ [859, 859, -w^3 + 6*w^2 - 11],\ [859, 859, -3*w^3 + 5*w^2 + 8*w - 2],\ [881, 881, -3*w^3 + w^2 + 11*w + 2],\ [881, 881, -3*w^3 + 8*w^2 + 4*w - 11],\ [911, 911, -2*w^2 - w + 11],\ [911, 911, 2*w^2 - 5*w - 8],\ [919, 919, w^3 - 5*w^2 - w + 8],\ [919, 919, -w^3 - 2*w^2 + 8*w + 3],\ [941, 941, 2*w^3 + 2*w^2 - 11*w - 7],\ [941, 941, -2*w^3 + 8*w^2 + w - 14],\ [961, 31, -2*w^2 + 2*w + 11],\ [961, 31, 5*w^2 - 5*w - 13],\ [971, 971, w^3 - 2*w^2 - 3*w - 3],\ [971, 971, -w^3 + w^2 + 4*w - 7],\ [991, 991, -w^3 + 4*w^2 + 2*w - 16],\ [991, 991, w^3 + 3*w^2 - 5*w - 13],\ [991, 991, -w^3 + 6*w^2 - 4*w - 14],\ [991, 991, 2*w^3 + 3*w^2 - 10*w - 12]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^9 - 7*x^8 - 10*x^7 + 163*x^6 - 185*x^5 - 975*x^4 + 2169*x^3 + 255*x^2 - 2949*x + 1194 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1, e, 1, 3071/51963*e^8 - 9178/51963*e^7 - 71204/51963*e^6 + 72346/17321*e^5 + 140742/17321*e^4 - 473960/17321*e^3 - 29393/17321*e^2 + 553581/17321*e - 188490/17321, 1, 1444/51963*e^8 - 11033/51963*e^7 - 23362/51963*e^6 + 90267/17321*e^5 - 8442/17321*e^4 - 627722/17321*e^3 + 434664/17321*e^2 + 911247/17321*e - 464502/17321, -1838/51963*e^8 + 12532/51963*e^7 + 33191/51963*e^6 - 101630/17321*e^5 - 5520/17321*e^4 + 685044/17321*e^3 - 517278/17321*e^2 - 854655/17321*e + 598296/17321, -8737/103926*e^8 + 15763/51963*e^7 + 101660/51963*e^6 - 260021/34642*e^5 - 191249/17321*e^4 + 1815723/34642*e^3 - 92625/17321*e^2 - 2539771/34642*e + 430869/17321, 26159/103926*e^8 - 55367/51963*e^7 - 278218/51963*e^6 + 899019/34642*e^5 + 395747/17321*e^4 - 6144753/34642*e^3 + 1206966/17321*e^2 + 8138323/34642*e - 1886496/17321, 4643/103926*e^8 - 2292/17321*e^7 - 51869/51963*e^6 + 310229/103926*e^5 + 92597/17321*e^4 - 627667/34642*e^3 + 52121/17321*e^2 + 561665/34642*e - 214321/17321, -19013/103926*e^8 + 13646/17321*e^7 + 204602/51963*e^6 - 2011697/103926*e^5 - 297092/17321*e^4 + 4638225/34642*e^3 - 879989/17321*e^2 - 6363657/34642*e + 1479619/17321, -24433/103926*e^8 + 51688/51963*e^7 + 261305/51963*e^6 - 842295/34642*e^5 - 379321/17321*e^4 + 5774593/34642*e^3 - 1088350/17321*e^2 - 7699375/34642*e + 1837780/17321, -3564/17321*e^8 + 42349/51963*e^7 + 235693/51963*e^6 - 1044124/51963*e^5 - 374931/17321*e^4 + 2403488/17321*e^3 - 739282/17321*e^2 - 3170648/17321*e + 1377023/17321, 3071/51963*e^8 - 9178/51963*e^7 - 71204/51963*e^6 + 72346/17321*e^5 + 140742/17321*e^4 - 473960/17321*e^3 - 29393/17321*e^2 + 605544/17321*e - 240453/17321, 1730/51963*e^8 - 8780/51963*e^7 - 13536/17321*e^6 + 213337/51963*e^5 + 78890/17321*e^4 - 480383/17321*e^3 + 18349/17321*e^2 + 620200/17321*e - 97999/17321, -3617/103926*e^8 + 2125/17321*e^7 + 39467/51963*e^6 - 332507/103926*e^5 - 51382/17321*e^4 + 787889/34642*e^3 - 258707/17321*e^2 - 906511/34642*e + 414409/17321, -4594/51963*e^8 + 7438/17321*e^7 + 98603/51963*e^6 - 547912/51963*e^5 - 132198/17321*e^4 + 1247699/17321*e^3 - 572801/17321*e^2 - 1580355/17321*e + 971638/17321, -8134/51963*e^8 + 11224/17321*e^7 + 176891/51963*e^6 - 815947/51963*e^5 - 275404/17321*e^4 + 1849417/17321*e^3 - 596731/17321*e^2 - 2444644/17321*e + 1196297/17321, -15718/51963*e^8 + 62350/51963*e^7 + 113090/17321*e^6 - 1525223/51963*e^5 - 508106/17321*e^4 + 3482534/17321*e^3 - 1281242/17321*e^2 - 4545637/17321*e + 2202045/17321, -215/34642*e^8 - 756/17321*e^7 + 4726/17321*e^6 + 31207/34642*e^5 - 61413/17321*e^4 - 201409/34642*e^3 + 276644/17321*e^2 + 530593/34642*e - 341843/17321, -364/17321*e^8 + 7144/51963*e^7 + 15460/51963*e^6 - 178975/51963*e^5 + 23993/17321*e^4 + 420006/17321*e^3 - 418095/17321*e^2 - 584613/17321*e + 379964/17321, 26093/103926*e^8 - 17432/17321*e^7 - 282890/51963*e^6 + 2547767/103926*e^5 + 440298/17321*e^4 - 5807019/34642*e^3 + 886598/17321*e^2 + 7745815/34642*e - 1652315/17321, -6164/51963*e^8 + 26177/51963*e^7 + 42582/17321*e^6 - 645502/51963*e^5 - 153631/17321*e^4 + 1493523/17321*e^3 - 824538/17321*e^2 - 2017443/17321*e + 1220167/17321, -634/51963*e^8 + 214/51963*e^7 + 6122/17321*e^6 + 8803/51963*e^5 - 56845/17321*e^4 - 67167/17321*e^3 + 180863/17321*e^2 + 266912/17321*e - 178606/17321, 601/103926*e^8 - 7232/51963*e^7 + 1934/17321*e^6 + 349577/103926*e^5 - 70549/17321*e^4 - 820547/34642*e^3 + 433564/17321*e^2 + 1424823/34642*e - 304576/17321, -2497/34642*e^8 + 10799/51963*e^7 + 93284/51963*e^6 - 524107/103926*e^5 - 217706/17321*e^4 + 1196585/34642*e^3 + 306789/17321*e^2 - 1610899/34642*e - 16852/17321, 18901/51963*e^8 - 76702/51963*e^7 - 136613/17321*e^6 + 1876979/51963*e^5 + 621516/17321*e^4 - 4288699/17321*e^3 + 1531895/17321*e^2 + 5618851/17321*e - 2839436/17321, 2489/17321*e^8 - 10129/17321*e^7 - 54399/17321*e^6 + 250035/17321*e^5 + 245789/17321*e^4 - 1747717/17321*e^3 + 665078/17321*e^2 + 2463339/17321*e - 1192685/17321, 22615/103926*e^8 - 48977/51963*e^7 - 78561/17321*e^6 + 2385857/103926*e^5 + 301125/17321*e^4 - 5415491/34642*e^3 + 1313103/17321*e^2 + 7075461/34642*e - 1947093/17321, 6470/17321*e^8 - 75781/51963*e^7 - 415459/51963*e^6 + 1822675/51963*e^5 + 616693/17321*e^4 - 4081044/17321*e^3 + 1561513/17321*e^2 + 5178571/17321*e - 2777349/17321, -6249/17321*e^8 + 73918/51963*e^7 + 408547/51963*e^6 - 1799998/51963*e^5 - 633116/17321*e^4 + 4089567/17321*e^3 - 1376335/17321*e^2 - 5326555/17321*e + 2531810/17321, 12319/51963*e^8 - 13498/17321*e^7 - 283535/51963*e^6 + 990361/51963*e^5 + 524115/17321*e^4 - 2249726/17321*e^3 + 275225/17321*e^2 + 2812982/17321*e - 979764/17321, -7223/103926*e^8 + 15125/51963*e^7 + 73939/51963*e^6 - 232623/34642*e^5 - 95755/17321*e^4 + 1484847/34642*e^3 - 365867/17321*e^2 - 1799567/34642*e + 596370/17321, -10697/103926*e^8 + 5911/17321*e^7 + 117755/51963*e^6 - 868577/103926*e^5 - 194588/17321*e^4 + 1956683/34642*e^3 - 265316/17321*e^2 - 2219385/34642*e + 552463/17321, -5770/51963*e^8 + 8226/17321*e^7 + 117917/51963*e^6 - 611413/51963*e^5 - 139669/17321*e^4 + 1436201/17321*e^3 - 724603/17321*e^2 - 2108677/17321*e + 1121015/17321, 1775/34642*e^8 - 15515/51963*e^7 - 49781/51963*e^6 + 767443/103926*e^5 + 24846/17321*e^4 - 1796571/34642*e^3 + 648967/17321*e^2 + 2642987/34642*e - 977149/17321, 6997/34642*e^8 - 37447/51963*e^7 - 227296/51963*e^6 + 1835447/103926*e^5 + 343393/17321*e^4 - 4209947/34642*e^3 + 867641/17321*e^2 + 5473225/34642*e - 1728066/17321, 9019/103926*e^8 - 22586/51963*e^7 - 29857/17321*e^6 + 1112459/103926*e^5 + 90649/17321*e^4 - 2597421/34642*e^3 + 652107/17321*e^2 + 3782251/34642*e - 697680/17321, 15733/103926*e^8 - 9837/17321*e^7 - 178021/51963*e^6 + 1431607/103926*e^5 + 318723/17321*e^4 - 3250663/34642*e^3 + 206399/17321*e^2 + 4445887/34642*e - 571630/17321, 7421/51963*e^8 - 31355/51963*e^7 - 51496/17321*e^6 + 764677/51963*e^5 + 201340/17321*e^4 - 1735925/17321*e^3 + 765953/17321*e^2 + 2232288/17321*e - 883047/17321, 32543/103926*e^8 - 64258/51963*e^7 - 118462/17321*e^6 + 3135805/103926*e^5 + 569440/17321*e^4 - 7187845/34642*e^3 + 995444/17321*e^2 + 9783989/34642*e - 2009863/17321, -17327/103926*e^8 + 44369/51963*e^7 + 169636/51963*e^6 - 723083/34642*e^5 - 164436/17321*e^4 + 4989233/34642*e^3 - 1312453/17321*e^2 - 6975105/34642*e + 1762837/17321, 7291/51963*e^8 - 37103/51963*e^7 - 141925/51963*e^6 + 298241/17321*e^5 + 125427/17321*e^4 - 2007600/17321*e^3 + 1237047/17321*e^2 + 2577158/17321*e - 1566120/17321, -703/17321*e^8 + 13607/51963*e^7 + 33665/51963*e^6 - 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2369647/51963*e^5 - 563519/17321*e^4 + 5478237/17321*e^3 - 2301711/17321*e^2 - 7498241/17321*e + 2957042/17321, 25139/103926*e^8 - 47272/51963*e^7 - 87414/17321*e^6 + 2273113/103926*e^5 + 345758/17321*e^4 - 5075969/34642*e^3 + 1271041/17321*e^2 + 6364749/34642*e - 1563049/17321, 14161/103926*e^8 - 44545/51963*e^7 - 127112/51963*e^6 + 752143/34642*e^5 - 15281/17321*e^4 - 5331365/34642*e^3 + 2417293/17321*e^2 + 7313089/34642*e - 2755247/17321, -22172/51963*e^8 + 105017/51963*e^7 + 152134/17321*e^6 - 2589451/51963*e^5 - 569934/17321*e^4 + 6047485/17321*e^3 - 2561805/17321*e^2 - 8808941/17321*e + 3575906/17321, -8002/51963*e^8 + 21388/51963*e^7 + 65193/17321*e^6 - 517367/51963*e^5 - 453608/17321*e^4 + 1156628/17321*e^3 + 736704/17321*e^2 - 1399813/17321*e - 554514/17321, -19369/51963*e^8 + 69866/51963*e^7 + 406567/51963*e^6 - 553900/17321*e^5 - 569168/17321*e^4 + 3657089/17321*e^3 - 1713553/17321*e^2 - 4377319/17321*e + 2767207/17321, 8233/17321*e^8 - 111334/51963*e^7 - 523267/51963*e^6 + 2790547/51963*e^5 + 702389/17321*e^4 - 6583066/17321*e^3 + 2768195/17321*e^2 + 9360033/17321*e - 4449408/17321, 32657/103926*e^8 - 58540/51963*e^7 - 124695/17321*e^6 + 2937025/103926*e^5 + 662549/17321*e^4 - 6908303/34642*e^3 + 747317/17321*e^2 + 9476235/34642*e - 2212804/17321, 82003/103926*e^8 - 177952/51963*e^7 - 870590/51963*e^6 + 2923687/34642*e^5 + 1221580/17321*e^4 - 20287031/34642*e^3 + 3924973/17321*e^2 + 27745335/34642*e - 6043631/17321, 59879/103926*e^8 - 125315/51963*e^7 - 648439/51963*e^6 + 2054213/34642*e^5 + 1004989/17321*e^4 - 14263147/34642*e^3 + 2101557/17321*e^2 + 20020195/34642*e - 3929981/17321, -22033/103926*e^8 + 23471/51963*e^7 + 95968/17321*e^6 - 1119779/103926*e^5 - 719178/17321*e^4 + 2412097/34642*e^3 + 1162391/17321*e^2 - 2354545/34642*e + 39506/17321, -19627/34642*e^8 + 37490/17321*e^7 + 214151/17321*e^6 - 1821711/34642*e^5 - 1038302/17321*e^4 + 12440891/34642*e^3 - 1689281/17321*e^2 - 16610715/34642*e + 3984825/17321, 15011/103926*e^8 - 13762/51963*e^7 - 66054/17321*e^6 + 750595/103926*e^5 + 485383/17321*e^4 - 1880221/34642*e^3 - 629749/17321*e^2 + 2526639/34642*e - 360239/17321, 17983/34642*e^8 - 101857/51963*e^7 - 601069/51963*e^6 + 5054417/103926*e^5 + 993031/17321*e^4 - 11726337/34642*e^3 + 1535511/17321*e^2 + 15632565/34642*e - 2968411/17321, 45883/103926*e^8 - 79787/51963*e^7 - 175656/17321*e^6 + 3898373/103926*e^5 + 969516/17321*e^4 - 8979351/34642*e^3 + 537147/17321*e^2 + 12666437/34642*e - 2045983/17321, -5195/51963*e^8 + 19457/51963*e^7 + 40547/17321*e^6 - 464464/51963*e^5 - 216273/17321*e^4 + 959702/17321*e^3 - 314064/17321*e^2 - 632201/17321*e + 974555/17321, 3818/51963*e^8 - 2087/17321*e^7 - 81970/51963*e^6 + 124241/51963*e^5 + 155783/17321*e^4 - 233933/17321*e^3 - 110508/17321*e^2 + 262701/17321*e - 290047/17321, 14210/51963*e^8 - 21069/17321*e^7 - 294001/51963*e^6 + 1533758/51963*e^5 + 386175/17321*e^4 - 3446900/17321*e^3 + 1386815/17321*e^2 + 4285163/17321*e - 1589903/17321, -16065/34642*e^8 + 92362/51963*e^7 + 529693/51963*e^6 - 4459775/103926*e^5 - 868044/17321*e^4 + 10055509/34642*e^3 - 1315697/17321*e^2 - 13019105/34642*e + 2885365/17321, 11725/51963*e^8 - 12393/17321*e^7 - 263705/51963*e^6 + 893863/51963*e^5 + 442662/17321*e^4 - 1964159/17321*e^3 + 657556/17321*e^2 + 1965165/17321*e - 1233324/17321, -3193/17321*e^8 + 36400/51963*e^7 + 193288/51963*e^6 - 868036/51963*e^5 - 217848/17321*e^4 + 1902790/17321*e^3 - 1301443/17321*e^2 - 2136771/17321*e + 2115617/17321, 30723/34642*e^8 - 192235/51963*e^7 - 992866/51963*e^6 + 9326627/103926*e^5 + 1482506/17321*e^4 - 21057037/34642*e^3 + 3751139/17321*e^2 + 26896569/34642*e - 6326791/17321, 300/17321*e^8 - 2724/17321*e^7 - 6341/17321*e^6 + 67632/17321*e^5 + 52555/17321*e^4 - 516133/17321*e^3 - 195603/17321*e^2 + 1203215/17321*e - 23649/17321, -36584/51963*e^8 + 56917/17321*e^7 + 763795/51963*e^6 - 4129256/51963*e^5 - 1029298/17321*e^4 + 9388019/17321*e^3 - 3694672/17321*e^2 - 12980595/17321*e + 5757375/17321, -17884/51963*e^8 + 87560/51963*e^7 + 356992/51963*e^6 - 715979/17321*e^5 - 356875/17321*e^4 + 4943747/17321*e^3 - 2885893/17321*e^2 - 6665971/17321*e + 4284478/17321, -15121/51963*e^8 + 66629/51963*e^7 + 323014/51963*e^6 - 550612/17321*e^5 - 418106/17321*e^4 + 3776828/17321*e^3 - 1927331/17321*e^2 - 4566499/17321*e + 2528794/17321, -31700/51963*e^8 + 32435/17321*e^7 + 745090/51963*e^6 - 2400494/51963*e^5 - 1473891/17321*e^4 + 5544644/17321*e^3 + 122835/17321*e^2 - 7491563/17321*e + 2103177/17321] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([5,5,-w^3 + w^2 + 3*w])] = 1 AL_eigenvalues[ZF.ideal([11,11,w^2 - 4])] = -1 AL_eigenvalues[ZF.ideal([16,2,2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]