/* 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([36, 6, -13, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([36, 6, -w]) primes_array = [ [4, 2, 1/3*w^3 - 4/3*w^2 - 4/3*w + 6],\ [4, 2, -1/3*w^3 - 2/3*w^2 + 10/3*w + 7],\ [9, 3, -1/2*w^3 + 3/2*w^2 + 7/2*w - 9],\ [9, 3, 1/3*w^3 + 2/3*w^2 - 7/3*w - 5],\ [11, 11, -1/6*w^3 + 1/6*w^2 + 1/6*w],\ [19, 19, w + 1],\ [19, 19, 1/6*w^3 - 1/6*w^2 - 13/6*w + 2],\ [25, 5, -1/3*w^3 + 1/3*w^2 + 7/3*w - 1],\ [29, 29, -1/6*w^3 + 1/6*w^2 + 13/6*w],\ [29, 29, w - 1],\ [31, 31, 1/3*w^3 - 1/3*w^2 - 10/3*w + 3],\ [31, 31, 1/6*w^3 - 1/6*w^2 - 1/6*w + 2],\ [41, 41, -1/2*w^3 - 1/2*w^2 + 9/2*w + 5],\ [41, 41, -1/2*w^3 + 3/2*w^2 + 5/2*w - 8],\ [59, 59, 1/3*w^3 - 1/3*w^2 - 10/3*w - 1],\ [59, 59, -1/3*w^3 + 4/3*w^2 + 7/3*w - 7],\ [59, 59, 1/2*w^3 - 1/2*w^2 - 5/2*w + 2],\ [79, 79, w^2 - 11],\ [79, 79, 1/6*w^3 - 7/6*w^2 - 7/6*w + 3],\ [89, 89, -1/6*w^3 + 1/6*w^2 + 19/6*w - 5],\ [89, 89, 1/6*w^3 - 1/6*w^2 - 19/6*w - 3],\ [109, 109, -1/6*w^3 + 7/6*w^2 + 1/6*w - 9],\ [109, 109, -7/6*w^3 + 19/6*w^2 + 49/6*w - 20],\ [109, 109, -5/6*w^3 + 17/6*w^2 + 23/6*w - 12],\ [109, 109, 1/6*w^3 + 5/6*w^2 - 13/6*w - 4],\ [121, 11, 1/6*w^3 - 1/6*w^2 - 7/6*w - 3],\ [139, 139, 1/3*w^3 - 4/3*w^2 + 5/3*w - 1],\ [139, 139, -5/3*w^3 - 7/3*w^2 + 50/3*w + 29],\ [169, 13, w^3 + w^2 - 10*w - 13],\ [169, 13, -5/6*w^3 + 17/6*w^2 + 17/6*w - 12],\ [179, 179, -1/3*w^3 + 4/3*w^2 + 1/3*w - 7],\ [179, 179, -2/3*w^3 + 2/3*w^2 + 17/3*w - 5],\ [181, 181, -w^3 + 3*w^2 + 4*w - 13],\ [181, 181, -1/6*w^3 + 7/6*w^2 + 1/6*w - 11],\ [181, 181, 7/6*w^3 + 11/6*w^2 - 79/6*w - 25],\ [181, 181, 1/6*w^3 + 5/6*w^2 - 13/6*w - 2],\ [191, 191, -5/6*w^3 - 1/6*w^2 + 53/6*w + 7],\ [191, 191, 1/6*w^3 + 11/6*w^2 - 19/6*w - 16],\ [211, 211, -1/6*w^3 + 1/6*w^2 - 5/6*w - 2],\ [211, 211, -1/2*w^3 + 1/2*w^2 + 9/2*w + 2],\ [211, 211, 1/3*w^3 - 1/3*w^2 - 4/3*w - 3],\ [211, 211, -1/2*w^3 + 1/2*w^2 + 11/2*w - 4],\ [229, 229, 5/6*w^3 + 1/6*w^2 - 53/6*w - 9],\ [229, 229, 1/2*w^3 - 3/2*w^2 - 1/2*w + 2],\ [239, 239, 5/6*w^3 + 7/6*w^2 - 59/6*w - 19],\ [239, 239, 1/2*w^3 - 5/2*w^2 + 1/2*w + 5],\ [241, 241, 1/6*w^3 - 1/6*w^2 - 13/6*w - 4],\ [241, 241, w - 5],\ [269, 269, -1/6*w^3 + 7/6*w^2 + 1/6*w - 2],\ [269, 269, 1/3*w^3 - 7/3*w^2 - 1/3*w + 7],\ [271, 271, 5/3*w^3 + 7/3*w^2 - 47/3*w - 25],\ [271, 271, -5/3*w^3 + 17/3*w^2 + 23/3*w - 27],\ [281, 281, 1/6*w^3 + 5/6*w^2 - 1/6*w - 7],\ [281, 281, -1/2*w^3 + 3/2*w^2 + 9/2*w - 8],\ [311, 311, 11/6*w^3 + 7/6*w^2 - 113/6*w - 23],\ [311, 311, -4/3*w^3 + 13/3*w^2 + 10/3*w - 13],\ [311, 311, -2/3*w^3 + 5/3*w^2 + 20/3*w - 17],\ [311, 311, 1/6*w^3 + 5/6*w^2 + 5/6*w + 1],\ [349, 349, -1/2*w^3 + 1/2*w^2 + 11/2*w - 1],\ [349, 349, -5/6*w^3 + 17/6*w^2 + 29/6*w - 14],\ [349, 349, 1/6*w^3 - 1/6*w^2 + 5/6*w - 1],\ [349, 349, -2/3*w^3 - 4/3*w^2 + 17/3*w + 13],\ [359, 359, -1/6*w^3 + 13/6*w^2 + 7/6*w - 18],\ [359, 359, -1/6*w^3 - 11/6*w^2 + 13/6*w + 18],\ [361, 19, 2/3*w^3 - 2/3*w^2 - 14/3*w + 1],\ [379, 379, 1/2*w^3 + 1/2*w^2 - 7/2*w - 7],\ [379, 379, -5/6*w^3 + 11/6*w^2 + 23/6*w - 7],\ [379, 379, w^3 - 9*w - 5],\ [379, 379, -2/3*w^3 + 5/3*w^2 + 14/3*w - 7],\ [401, 401, -1/3*w^3 + 7/3*w^2 + 4/3*w - 17],\ [401, 401, -4/3*w^3 - 8/3*w^2 + 43/3*w + 31],\ [419, 419, 1/6*w^3 - 1/6*w^2 + 5/6*w],\ [419, 419, 1/2*w^3 - 1/2*w^2 - 11/2*w + 2],\ [421, 421, -5/6*w^3 - 7/6*w^2 + 47/6*w + 11],\ [421, 421, 1/3*w^3 - 1/3*w^2 - 19/3*w - 7],\ [431, 431, 5/6*w^3 + 1/6*w^2 - 41/6*w - 6],\ [431, 431, 2/3*w^3 - 8/3*w^2 - 8/3*w + 15],\ [431, 431, 5/6*w^3 - 11/6*w^2 - 29/6*w + 7],\ [431, 431, 1/2*w^3 - 5/2*w^2 + 5/2*w + 2],\ [439, 439, 5/6*w^3 + 1/6*w^2 - 41/6*w - 4],\ [439, 439, 1/2*w^3 - 1/2*w^2 - 9/2*w + 8],\ [449, 449, 5/6*w^3 - 17/6*w^2 - 29/6*w + 18],\ [449, 449, 11/6*w^3 - 41/6*w^2 - 41/6*w + 29],\ [449, 449, -7/6*w^3 + 31/6*w^2 + 7/6*w - 16],\ [449, 449, 5/3*w^3 + 7/3*w^2 - 56/3*w - 33],\ [461, 461, -1/6*w^3 + 1/6*w^2 + 19/6*w - 3],\ [461, 461, 1/6*w^3 - 1/6*w^2 - 19/6*w - 1],\ [479, 479, -2*w - 1],\ [479, 479, 1/3*w^3 - 1/3*w^2 - 13/3*w + 3],\ [491, 491, 2/3*w^3 + 1/3*w^2 - 14/3*w - 7],\ [491, 491, 5/6*w^3 - 11/6*w^2 - 35/6*w + 7],\ [509, 509, 5/6*w^3 - 11/6*w^2 - 29/6*w + 8],\ [509, 509, 5/6*w^3 + 1/6*w^2 - 41/6*w - 5],\ [521, 521, -1/6*w^3 + 7/6*w^2 - 17/6*w + 1],\ [521, 521, -1/6*w^3 + 7/6*w^2 - 11/6*w - 3],\ [521, 521, -1/6*w^3 + 7/6*w^2 + 19/6*w - 5],\ [521, 521, 2/3*w^3 + 1/3*w^2 - 26/3*w - 11],\ [541, 541, 1/6*w^3 + 5/6*w^2 - 31/6*w - 17],\ [541, 541, 5/6*w^3 - 17/6*w^2 - 47/6*w + 23],\ [541, 541, 3*w^3 + 3*w^2 - 32*w - 47],\ [541, 541, 2/3*w^3 + 4/3*w^2 - 14/3*w - 11],\ [571, 571, -1/3*w^3 + 1/3*w^2 + 13/3*w - 1],\ [571, 571, 2*w - 1],\ [571, 571, -1/3*w^3 + 4/3*w^2 + 7/3*w - 1],\ [571, 571, 1/6*w^3 + 5/6*w^2 - 7/6*w - 13],\ [599, 599, 1/2*w^3 + 1/2*w^2 - 9/2*w - 2],\ [599, 599, -1/6*w^3 + 1/6*w^2 + 19/6*w - 2],\ [599, 599, 1/6*w^3 - 1/6*w^2 - 19/6*w],\ [599, 599, 1/2*w^3 - 3/2*w^2 - 5/2*w + 11],\ [601, 601, 1/6*w^3 + 11/6*w^2 - 7/6*w - 15],\ [601, 601, -1/3*w^3 + 7/3*w^2 - 5/3*w - 5],\ [601, 601, 2/3*w^3 + 4/3*w^2 - 26/3*w - 19],\ [601, 601, 1/2*w^3 - 5/2*w^2 - 7/2*w + 13],\ [659, 659, w^2 - 13],\ [659, 659, -5/6*w^3 + 11/6*w^2 + 29/6*w - 12],\ [659, 659, -1/6*w^3 + 7/6*w^2 + 7/6*w - 1],\ [659, 659, 5/6*w^3 + 1/6*w^2 - 41/6*w - 1],\ [691, 691, 1/2*w^3 - 1/2*w^2 - 11/2*w + 10],\ [691, 691, -1/6*w^3 + 1/6*w^2 - 5/6*w - 8],\ [701, 701, -2*w^2 + w + 11],\ [701, 701, -1/6*w^3 + 13/6*w^2 + 7/6*w - 9],\ [701, 701, -1/6*w^3 + 13/6*w^2 + 1/6*w - 16],\ [701, 701, -w^3 + w^2 + 9*w - 1],\ [709, 709, -2/3*w^3 + 11/3*w^2 + 14/3*w - 21],\ [709, 709, 1/3*w^3 + 5/3*w^2 + 2/3*w - 5],\ [709, 709, 7/6*w^3 - 25/6*w^2 - 43/6*w + 25],\ [709, 709, 2/3*w^3 - 2/3*w^2 - 23/3*w - 1],\ [719, 719, 2*w^2 - 2*w - 19],\ [719, 719, -2*w^2 + 2*w + 7],\ [739, 739, 5/6*w^3 - 5/6*w^2 - 29/6*w + 4],\ [739, 739, -5/6*w^3 + 11/6*w^2 + 53/6*w - 17],\ [739, 739, -1/6*w^3 - 5/6*w^2 - 11/6*w],\ [739, 739, -w^3 + w^2 + 8*w - 5],\ [751, 751, -1/6*w^3 + 1/6*w^2 + 25/6*w + 8],\ [751, 751, -1/3*w^3 + 1/3*w^2 + 16/3*w - 11],\ [761, 761, -2/3*w^3 + 5/3*w^2 + 8/3*w - 9],\ [761, 761, 5/6*w^3 + 1/6*w^2 - 47/6*w - 3],\ [769, 769, 1/3*w^3 - 7/3*w^2 - 7/3*w + 11],\ [769, 769, -4/3*w^3 - 8/3*w^2 + 46/3*w + 33],\ [769, 769, -1/2*w^3 + 5/2*w^2 + 5/2*w - 20],\ [769, 769, 2*w^2 - 17],\ [809, 809, 1/6*w^3 + 11/6*w^2 - 31/6*w - 15],\ [809, 809, -5/6*w^3 - 1/6*w^2 + 35/6*w + 3],\ [809, 809, 1/6*w^3 + 11/6*w^2 - 31/6*w - 9],\ [809, 809, w^3 - 2*w^2 - 7*w + 11],\ [811, 811, -1/6*w^3 - 5/6*w^2 + 25/6*w + 7],\ [811, 811, 1/6*w^3 + 5/6*w^2 - 25/6*w - 15],\ [811, 811, -1/6*w^3 - 5/6*w^2 + 25/6*w - 4],\ [811, 811, 1/6*w^3 + 5/6*w^2 - 25/6*w - 4],\ [821, 821, -1/2*w^3 - 5/2*w^2 + 13/2*w + 16],\ [821, 821, 1/6*w^3 - 13/6*w^2 - 7/6*w + 21],\ [821, 821, 3/2*w^3 + 1/2*w^2 - 35/2*w - 20],\ [821, 821, -1/6*w^3 + 13/6*w^2 + 7/6*w - 7],\ [829, 829, -1/6*w^3 + 19/6*w^2 - 11/6*w - 23],\ [829, 829, 5/6*w^3 - 17/6*w^2 - 5/6*w + 8],\ [829, 829, -4/3*w^3 - 2/3*w^2 + 43/3*w + 15],\ [829, 829, -1/6*w^3 - 17/6*w^2 + 25/6*w + 16],\ [839, 839, 1/3*w^3 - 7/3*w^2 + 2/3*w + 5],\ [839, 839, 1/2*w^3 + 3/2*w^2 - 13/2*w - 20],\ [841, 29, -5/6*w^3 + 5/6*w^2 + 35/6*w - 4],\ [859, 859, 1/6*w^3 + 5/6*w^2 - 37/6*w + 7],\ [859, 859, 13/6*w^3 + 17/6*w^2 - 127/6*w - 33],\ [881, 881, -2/3*w^3 + 2/3*w^2 + 20/3*w + 5],\ [881, 881, 17/6*w^3 + 19/6*w^2 - 167/6*w - 42],\ [911, 911, -1/6*w^3 + 13/6*w^2 - 11/6*w - 6],\ [911, 911, 3/2*w^3 + 1/2*w^2 - 33/2*w - 17],\ [911, 911, 5/6*w^3 - 17/6*w^2 + 1/6*w + 5],\ [911, 911, 7/6*w^3 - 1/6*w^2 - 61/6*w - 1],\ [929, 929, -7/6*w^3 - 11/6*w^2 + 67/6*w + 22],\ [929, 929, -1/6*w^3 + 1/6*w^2 - 11/6*w + 6],\ [941, 941, 11/6*w^3 + 19/6*w^2 - 107/6*w - 34],\ [941, 941, 4/3*w^3 - 10/3*w^2 - 25/3*w + 19],\ [941, 941, -11/6*w^3 + 41/6*w^2 + 47/6*w - 31],\ [941, 941, 1/2*w^3 + 1/2*w^2 - 13/2*w - 13],\ [961, 31, -1/3*w^3 + 1/3*w^2 + 7/3*w + 5],\ [991, 991, -1/6*w^3 - 5/6*w^2 + 25/6*w + 6],\ [991, 991, 1/6*w^3 + 5/6*w^2 - 25/6*w - 5]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^11 - 4*x^10 - 16*x^9 + 80*x^8 + 7*x^7 - 334*x^6 + 215*x^5 + 362*x^4 - 283*x^3 - 81*x^2 + 81*x - 10 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1, e, -1, 13862/78891*e^10 - 13794/26297*e^9 - 261848/78891*e^8 + 857771/78891*e^7 + 885817/78891*e^6 - 3993691/78891*e^5 - 24437/26297*e^4 + 5707762/78891*e^3 - 1292608/78891*e^2 - 2204131/78891*e + 608015/78891, 10372/78891*e^10 - 12590/26297*e^9 - 168082/78891*e^8 + 747907/78891*e^7 + 128567/78891*e^6 - 2995244/78891*e^5 + 612225/26297*e^4 + 2883101/78891*e^3 - 1865534/78891*e^2 - 574004/78891*e + 230272/78891, 7454/26297*e^10 - 30440/26297*e^9 - 123320/26297*e^8 + 616310/26297*e^7 + 133262/26297*e^6 - 2694502/26297*e^5 + 1237753/26297*e^4 + 3348313/26297*e^3 - 1624790/26297*e^2 - 1175850/26297*e + 432860/26297, 23777/78891*e^10 - 31757/26297*e^9 - 394640/78891*e^8 + 1913366/78891*e^7 + 481438/78891*e^6 - 8119522/78891*e^5 + 1090386/26297*e^4 + 9189085/78891*e^3 - 3163948/78891*e^2 - 2144656/78891*e + 655025/78891, 15600/26297*e^10 - 56382/26297*e^9 - 263077/26297*e^8 + 1128540/26297*e^7 + 388190/26297*e^6 - 4710797/26297*e^5 + 2079884/26297*e^4 + 5186126/26297*e^3 - 2633368/26297*e^2 - 1486193/26297*e + 529527/26297, 9097/78891*e^10 - 2204/26297*e^9 - 214978/78891*e^8 + 153499/78891*e^7 + 1451894/78891*e^6 - 863120/78891*e^5 - 1220666/26297*e^4 + 1684232/78891*e^3 + 2987068/78891*e^2 - 1034231/78891*e - 248045/78891, -44555/78891*e^10 + 39332/26297*e^9 + 847364/78891*e^8 - 2372099/78891*e^7 - 3037405/78891*e^6 + 9877300/78891*e^5 + 653780/26297*e^4 - 10524130/78891*e^3 - 358727/78891*e^2 + 2222200/78891*e + 132880/78891, 60263/78891*e^10 - 57892/26297*e^9 - 1131095/78891*e^8 + 3529085/78891*e^7 + 3777628/78891*e^6 - 15358867/78891*e^5 - 318773/26297*e^4 + 18755710/78891*e^3 - 2383981/78891*e^2 - 5943388/78891*e + 1354712/78891, 13862/78891*e^10 - 13794/26297*e^9 - 261848/78891*e^8 + 857771/78891*e^7 + 885817/78891*e^6 - 3993691/78891*e^5 - 24437/26297*e^4 + 5707762/78891*e^3 - 1213717/78891*e^2 - 2204131/78891*e + 371342/78891, 36568/78891*e^10 - 34723/26297*e^9 - 692725/78891*e^8 + 2107741/78891*e^7 + 2440982/78891*e^6 - 9041039/78891*e^5 - 512599/26297*e^4 + 10620554/78891*e^3 + 607345/78891*e^2 - 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259656/26297*e^6 - 1804881/26297*e^5 + 1023912/26297*e^4 + 4420797/26297*e^3 - 2008032/26297*e^2 - 2338242/26297*e + 802434/26297, -81430/26297*e^10 + 259615/26297*e^9 + 1464880/26297*e^8 - 5228352/26297*e^7 - 3846695/26297*e^6 + 22137342/26297*e^5 - 3619726/26297*e^4 - 24725861/26297*e^3 + 7262082/26297*e^2 + 5718590/26297*e - 1984711/26297, -34018/26297*e^10 + 147041/26297*e^9 + 549844/26297*e^8 - 2970091/26297*e^7 - 406770/26297*e^6 + 12902564/26297*e^5 - 5583490/26297*e^4 - 15612273/26297*e^3 + 4781929/26297*e^2 + 4145332/26297*e - 1409860/26297, 99378/26297*e^10 - 300735/26297*e^9 - 1815650/26297*e^8 + 6057856/26297*e^7 + 5266369/26297*e^6 - 25611284/26297*e^5 + 1980021/26297*e^4 + 28666712/26297*e^3 - 6239856/26297*e^2 - 7141884/26297*e + 1879085/26297, 30707/78891*e^10 - 16742/26297*e^9 - 703121/78891*e^8 + 1082654/78891*e^7 + 4508923/78891*e^6 - 5421547/78891*e^5 - 3972490/26297*e^4 + 7790203/78891*e^3 + 12689693/78891*e^2 - 533263/78891*e - 1705105/78891, -38905/78891*e^10 + 42808/26297*e^9 + 708676/78891*e^8 - 2640007/78891*e^7 - 1971527/78891*e^6 + 12029135/78891*e^5 - 556854/26297*e^4 - 16319657/78891*e^3 + 4312382/78891*e^2 + 5067563/78891*e - 287500/78891, -75659/78891*e^10 + 103425/26297*e^9 + 1194455/78891*e^8 - 6146651/78891*e^7 - 286789/78891*e^6 + 24849076/78891*e^5 - 5344516/26297*e^4 - 24705124/78891*e^3 + 17719723/78891*e^2 + 5305840/78891*e - 2826980/78891, -40139/78891*e^10 - 3694/26297*e^9 + 920318/78891*e^8 + 325018/78891*e^7 - 5888155/78891*e^6 - 3622262/78891*e^5 + 4659082/26297*e^4 + 11843099/78891*e^3 - 10880750/78891*e^2 - 7281248/78891*e + 2710435/78891, -26053/78891*e^10 + 18060/26297*e^9 + 591283/78891*e^8 - 1148317/78891*e^7 - 3732620/78891*e^6 + 5614973/78891*e^5 + 3370135/26297*e^4 - 8236409/78891*e^3 - 12038797/78891*e^2 + 2940959/78891*e + 2091470/78891, 127574/78891*e^10 - 188170/26297*e^9 - 1972823/78891*e^8 + 11278343/78891*e^7 - 375176/78891*e^6 - 47206489/78891*e^5 + 10217937/26297*e^4 + 52443358/78891*e^3 - 33056911/78891*e^2 - 16161742/78891*e + 5149235/78891, 52489/26297*e^10 - 197910/26297*e^9 - 893010/26297*e^8 + 3973871/26297*e^7 + 1477352/26297*e^6 - 16798044/26297*e^5 + 5915064/26297*e^4 + 18706409/26297*e^3 - 6815652/26297*e^2 - 4551085/26297*e + 1630314/26297, -7057/26297*e^10 + 72466/26297*e^9 + 32301/26297*e^8 - 1448210/26297*e^7 + 1521882/26297*e^6 + 6213882/26297*e^5 - 7141909/26297*e^4 - 7581510/26297*e^3 + 5437202/26297*e^2 + 2727805/26297*e - 1106186/26297, -87003/26297*e^10 + 262836/26297*e^9 + 1601017/26297*e^8 - 5336079/26297*e^7 - 4793315/26297*e^6 + 23184273/26297*e^5 - 1622206/26297*e^4 - 28016589/26297*e^3 + 7105253/26297*e^2 + 8743967/26297*e - 2659966/26297, 26006/78891*e^10 - 40076/26297*e^9 - 495125/78891*e^8 + 2574968/78891*e^7 + 1684819/78891*e^6 - 13387300/78891*e^5 - 41448/26297*e^4 + 22151158/78891*e^3 - 2951608/78891*e^2 - 7826953/78891*e + 2430317/78891, 66184/78891*e^10 - 23149/26297*e^9 - 1433128/78891*e^8 + 1396804/78891*e^7 + 7924352/78891*e^6 - 5220794/78891*e^5 - 5044427/26297*e^4 + 3473417/78891*e^3 + 7629610/78891*e^2 - 459419/78891*e + 471262/78891, -35505/26297*e^10 + 71633/26297*e^9 + 728544/26297*e^8 - 1475671/26297*e^7 - 3449233/26297*e^6 + 6553847/26297*e^5 + 5182357/26297*e^4 - 8178837/26297*e^3 - 2290313/26297*e^2 + 2166206/26297*e + 93914/26297, -115076/78891*e^10 + 110061/26297*e^9 + 2191943/78891*e^8 - 6794378/78891*e^7 - 7718851/78891*e^6 + 30900712/78891*e^5 + 678032/26297*e^4 - 42546766/78891*e^3 + 10285342/78891*e^2 + 17336053/78891*e - 4547528/78891, 80566/78891*e^10 - 44582/26297*e^9 - 1667806/78891*e^8 + 2686648/78891*e^7 + 8235809/78891*e^6 - 10738079/78891*e^5 - 4929463/26297*e^4 + 10407683/78891*e^3 + 12388696/78891*e^2 - 3090890/78891*e - 4023098/78891, 2815/78891*e^10 - 15815/26297*e^9 + 48470/78891*e^8 + 839323/78891*e^7 - 1725649/78891*e^6 - 1953326/78891*e^5 + 1955454/26297*e^4 - 3337045/78891*e^3 - 742271/78891*e^2 + 5560540/78891*e - 1211990/78891, -31661/26297*e^10 + 96619/26297*e^9 + 587532/26297*e^8 - 1965055/26297*e^7 - 1881419/26297*e^6 + 8609795/26297*e^5 + 589252/26297*e^4 - 10717615/26297*e^3 - 451209/26297*e^2 + 3099395/26297*e - 117810/26297, 142906/78891*e^10 - 172482/26297*e^9 - 2433982/78891*e^8 + 10358176/78891*e^7 + 4099844/78891*e^6 - 43233644/78891*e^5 + 5257882/26297*e^4 + 46871804/78891*e^3 - 18373628/78891*e^2 - 10531808/78891*e + 4706770/78891, -44957/26297*e^10 + 115383/26297*e^9 + 865805/26297*e^8 - 2355262/26297*e^7 - 3244737/26297*e^6 + 10332797/26297*e^5 + 2200287/26297*e^4 - 12907319/26297*e^3 + 568357/26297*e^2 + 4520796/26297*e + 94930/26297, -327962/78891*e^10 + 385124/26297*e^9 + 5702930/78891*e^8 - 23289200/78891*e^7 - 11605669/78891*e^6 + 99534073/78891*e^5 - 9733333/26297*e^4 - 115714504/78891*e^3 + 40296136/78891*e^2 + 34208047/78891*e - 9754220/78891, 97513/78891*e^10 - 73606/26297*e^9 - 1906522/78891*e^8 + 4375966/78891*e^7 + 7710674/78891*e^6 - 17060498/78891*e^5 - 2925559/26297*e^4 + 14343725/78891*e^3 + 6083323/78891*e^2 - 969815/78891*e - 2981375/78891, -103123/78891*e^10 + 140342/26297*e^9 + 1731736/78891*e^8 - 8553403/78891*e^7 - 2503385/78891*e^6 + 37833704/78891*e^5 - 4029428/26297*e^4 - 48208847/78891*e^3 + 9761534/78891*e^2 + 15022802/78891*e - 716818/78891, -41086/26297*e^10 + 179990/26297*e^9 + 680184/26297*e^8 - 3665890/26297*e^7 - 780282/26297*e^6 + 16390424/26297*e^5 - 5902639/26297*e^4 - 21140647/26297*e^3 + 5877627/26297*e^2 + 6124621/26297*e - 1303890/26297, 65499/26297*e^10 - 244830/26297*e^9 - 1120484/26297*e^8 + 4940330/26297*e^7 + 1973203/26297*e^6 - 21262091/26297*e^5 + 6794442/26297*e^4 + 25207447/26297*e^3 - 8031677/26297*e^2 - 6947111/26297*e + 2429110/26297, 167051/78891*e^10 - 194676/26297*e^9 - 2888285/78891*e^8 + 11687669/78891*e^7 + 5540233/78891*e^6 - 48651916/78891*e^5 + 5687140/26297*e^4 + 52330138/78891*e^3 - 24748270/78891*e^2 - 13889170/78891*e + 5701502/78891, -98689/78891*e^10 + 123652/26297*e^9 + 1608403/78891*e^8 - 7403068/78891*e^7 - 1320233/78891*e^6 + 30630914/78891*e^5 - 6043033/26297*e^4 - 33231908/78891*e^3 + 21985724/78891*e^2 + 9691853/78891*e - 3436213/78891, -118750/78891*e^10 + 145929/26297*e^9 + 2118313/78891*e^8 - 8939590/78891*e^7 - 5287145/78891*e^6 + 40094345/78891*e^5 - 1747055/26297*e^4 - 52775744/78891*e^3 + 6347630/78891*e^2 + 18783623/78891*e - 1032238/78891, -55198/26297*e^10 + 193450/26297*e^9 + 968415/26297*e^8 - 3911630/26297*e^7 - 2144486/26297*e^6 + 16904035/26297*e^5 - 3819922/26297*e^4 - 20250902/26297*e^3 + 4763444/26297*e^2 + 5574780/26297*e - 1264736/26297, 11887/26297*e^10 - 41071/26297*e^9 - 213834/26297*e^8 + 862057/26297*e^7 + 548837/26297*e^6 - 4216334/26297*e^5 + 753853/26297*e^4 + 6946002/26297*e^3 - 1827355/26297*e^2 - 3622410/26297*e + 427064/26297, 8728/78891*e^10 - 16152/26297*e^9 - 96199/78891*e^8 + 937258/78891*e^7 - 853168/78891*e^6 - 3484673/78891*e^5 + 2107974/26297*e^4 + 2503367/78891*e^3 - 9332039/78891*e^2 - 618716/78891*e + 2783272/78891, -173531/78891*e^10 + 259527/26297*e^9 + 2786378/78891*e^8 - 15761159/78891*e^7 - 1574875/78891*e^6 + 69100759/78891*e^5 - 10697256/26297*e^4 - 85401151/78891*e^3 + 32965381/78891*e^2 + 23735545/78891*e - 7803920/78891, 12356/26297*e^10 - 24874/26297*e^9 - 248497/26297*e^8 + 496170/26297*e^7 + 1141351/26297*e^6 - 1964648/26297*e^5 - 2167767/26297*e^4 + 1789078/26297*e^3 + 3165654/26297*e^2 - 422343/26297*e - 764620/26297, 67309/78891*e^10 - 86454/26297*e^9 - 1196842/78891*e^8 + 5308954/78891*e^7 + 2937458/78891*e^6 - 24035801/78891*e^5 + 961335/26297*e^4 + 32045639/78891*e^3 - 3195410/78891*e^2 - 10708262/78891*e + 1148542/78891, 5873/26297*e^10 - 53865/26297*e^9 - 67868/26297*e^8 + 1124670/26297*e^7 - 456850/26297*e^6 - 5522548/26297*e^5 + 2628270/26297*e^4 + 8422291/26297*e^3 - 915350/26297*e^2 - 2723728/26297*e + 14359/26297, -60723/26297*e^10 + 170686/26297*e^9 + 1159654/26297*e^8 - 3489540/26297*e^7 - 4246575/26297*e^6 + 15466657/26297*e^5 + 3435549/26297*e^4 - 19502879/26297*e^3 - 2530483/26297*e^2 + 5500144/26297*e + 633404/26297, -70852/78891*e^10 + 65629/26297*e^9 + 1425898/78891*e^8 - 4133998/78891*e^7 - 6403421/78891*e^6 + 19949051/78891*e^5 + 3414965/26297*e^4 - 29747237/78891*e^3 - 10483072/78891*e^2 + 9611657/78891*e + 816602/78891, -19838/26297*e^10 + 107726/26297*e^9 + 265166/26297*e^8 - 2116219/26297*e^7 + 847937/26297*e^6 + 8363298/26297*e^5 - 7254082/26297*e^4 - 7456075/26297*e^3 + 5309120/26297*e^2 + 1182246/26297*e - 185441/26297, 39679/78891*e^10 - 41131/26297*e^9 - 707680/78891*e^8 + 2475712/78891*e^7 + 1790222/78891*e^6 - 10286249/78891*e^5 + 558927/26297*e^4 + 10551092/78891*e^3 - 2580239/78891*e^2 - 867017/78891*e + 2249242/78891, -75464/26297*e^10 + 272097/26297*e^9 + 1316406/26297*e^8 - 5521139/26297*e^7 - 2737419/26297*e^6 + 24165966/26297*e^5 - 6597168/26297*e^4 - 29767555/26297*e^3 + 9726704/26297*e^2 + 8787722/26297*e - 2436096/26297] 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, 1/3*w^3 - 4/3*w^2 - 4/3*w + 6])] = 1 AL_eigenvalues[ZF.ideal([9, 3, -1/2*w^3 + 3/2*w^2 + 7/2*w - 9])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]