/* 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([16,4,-1/6*w^3 + 1/6*w^2 + 1/6*w + 1]) 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^10 - 28*x^8 + 283*x^6 - 1275*x^4 + 2478*x^2 - 1587 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 0, -3/2*e^8 + 65/2*e^6 - 218*e^4 + 1037/2*e^2 - 721/2, 5/6*e^8 - 109/6*e^6 + 123*e^4 - 591/2*e^2 + 411/2, 37/69*e^9 - 806/69*e^7 + 1819/23*e^5 - 4386/23*e^3 + 3054/23*e, -61/69*e^9 + 1340/69*e^7 - 3071/23*e^5 + 7617/23*e^3 - 5605/23*e, 25/69*e^9 - 539/69*e^7 + 1193/23*e^5 - 2782/23*e^3 + 1905/23*e, -7/3*e^8 + 152/3*e^6 - 341*e^4 + 815*e^2 - 571, 93/46*e^9 - 2029/46*e^7 + 6892/23*e^5 - 33567/46*e^3 + 24305/46*e, -107/138*e^9 + 2329/138*e^7 - 2628/23*e^5 + 12769/46*e^3 - 9377/46*e, 197/69*e^9 - 4297/69*e^7 + 9721/23*e^5 - 23580/23*e^3 + 16833/23*e, -74/69*e^9 + 1612/69*e^7 - 3638/23*e^5 + 8795/23*e^3 - 6269/23*e, 3/46*e^9 - 61/46*e^7 + 183/23*e^5 - 743/46*e^3 + 649/46*e, -427/138*e^9 + 9311/138*e^7 - 10530/23*e^5 + 51111/46*e^3 - 36613/46*e, e^8 - 22*e^6 + 151*e^4 - 370*e^2 + 264, -23/3*e^8 + 502/3*e^6 - 1137*e^4 + 2764*e^2 - 1972, -7/3*e^8 + 152/3*e^6 - 341*e^4 + 816*e^2 - 578, 13/3*e^8 - 284/3*e^6 + 644*e^4 - 1567*e^2 + 1128, 35/3*e^8 - 763/3*e^6 + 1725*e^4 - 4184*e^2 + 2999, -157/138*e^9 + 3407/138*e^7 - 3821/23*e^5 + 18333/46*e^3 - 13095/46*e, 77/46*e^9 - 1673/46*e^7 + 5640/23*e^5 - 27105/46*e^3 + 19295/46*e, -97/138*e^9 + 2141/138*e^7 - 2463/23*e^5 + 12153/46*e^3 - 8569/46*e, 1/6*e^8 - 23/6*e^6 + 29*e^4 - 173/2*e^2 + 163/2, -25/6*e^8 + 545/6*e^6 - 616*e^4 + 2991/2*e^2 - 2157/2, 25/46*e^9 - 539/46*e^7 + 1778/23*e^5 - 8001/46*e^3 + 4657/46*e, 49/6*e^8 - 1067/6*e^6 + 1204*e^4 - 5827/2*e^2 + 4171/2, 3*e^8 - 66*e^6 + 455*e^4 - 1134*e^2 + 838, 6*e^8 - 131*e^6 + 890*e^4 - 2157*e^2 + 1528, -79/46*e^9 + 1729/46*e^7 - 5900/23*e^5 + 28827/46*e^3 - 20479/46*e, 293/138*e^9 - 6433/138*e^7 + 7376/23*e^5 - 36849/46*e^3 + 27819/46*e, -457/69*e^9 + 9944/69*e^7 - 22395/23*e^5 + 53879/23*e^3 - 37933/23*e, -44/69*e^9 + 979/69*e^7 - 2303/23*e^5 + 6004/23*e^3 - 4650/23*e, -167/138*e^9 + 3595/138*e^7 - 3963/23*e^5 + 18213/46*e^3 - 11557/46*e, 111/23*e^9 - 2418/23*e^7 + 16371/23*e^5 - 39543/23*e^3 + 28061/23*e, 61/46*e^9 - 1317/46*e^7 + 4388/23*e^5 - 20689/46*e^3 + 14607/46*e, -86/69*e^9 + 1879/69*e^7 - 4264/23*e^5 + 10376/23*e^3 - 7349/23*e, 316/69*e^9 - 6893/69*e^7 + 15603/23*e^5 - 37930/23*e^3 + 27244/23*e, 305/69*e^9 - 6631/69*e^7 + 14918/23*e^5 - 35900/23*e^3 + 25518/23*e, -4*e^9 + 87*e^7 - 587*e^5 + 1406*e^3 - 976*e, -34/3*e^8 + 743/3*e^6 - 1687*e^4 + 4121*e^2 - 2967, 15*e^8 - 327*e^6 + 2217*e^4 - 5369*e^2 + 3830, 346/69*e^9 - 7526/69*e^7 + 16938/23*e^5 - 40721/23*e^3 + 28725/23*e, -27/2*e^8 + 589/2*e^6 - 1999*e^4 + 9699/2*e^2 - 6929/2, 115/6*e^8 - 2507/6*e^6 + 2834*e^4 - 13747/2*e^2 + 9861/2, -e^8 + 21*e^6 - 133*e^4 + 286*e^2 - 171, -35/3*e^8 + 763/3*e^6 - 1725*e^4 + 4182*e^2 - 2983, -7/6*e^8 + 155/6*e^6 - 181*e^4 + 933/2*e^2 - 721/2, -71/6*e^8 + 1549/6*e^6 - 1753*e^4 + 8515/2*e^2 - 6105/2, 109/6*e^8 - 2375/6*e^6 + 2682*e^4 - 12989/2*e^2 + 9305/2, -29/6*e^8 + 631/6*e^6 - 710*e^4 + 3409/2*e^2 - 2413/2, 11/23*e^9 - 239/23*e^7 + 1595/23*e^5 - 3629/23*e^3 + 2096/23*e, -6*e^9 + 131*e^7 - 891*e^5 + 2173*e^3 - 1577*e, 15/2*e^8 - 327/2*e^6 + 1108*e^4 - 5363/2*e^2 + 3861/2, 131/6*e^8 - 2857/6*e^6 + 3231*e^4 - 15679/2*e^2 + 11233/2, -8/3*e^8 + 175/3*e^6 - 398*e^4 + 975*e^2 - 712, -64/3*e^8 + 1397/3*e^6 - 3164*e^4 + 7685*e^2 - 5474, -71/3*e^8 + 1549/3*e^6 - 3506*e^4 + 8513*e^2 - 6085, -41/3*e^8 + 895/3*e^6 - 2028*e^4 + 4931*e^2 - 3517, 63/23*e^9 - 1373/23*e^7 + 9319/23*e^5 - 22733/23*e^3 + 16734/23*e, 19/2*e^8 - 413/2*e^6 + 1394*e^4 - 6723/2*e^2 + 4823/2, -85/23*e^9 + 1851/23*e^7 - 12509/23*e^5 + 29991/23*e^3 - 20742/23*e, 35/6*e^8 - 763/6*e^6 + 862*e^4 - 4175/2*e^2 + 3009/2, -2*e^8 + 44*e^6 - 302*e^4 + 738*e^2 - 504, 8*e^8 - 175*e^6 + 1193*e^4 - 2913*e^2 + 2109, 113/6*e^8 - 2467/6*e^6 + 2796*e^4 - 13613/2*e^2 + 9737/2, 37/3*e^8 - 806/3*e^6 + 1818*e^4 - 4381*e^2 + 3094, -43/3*e^8 + 938/3*e^6 - 2123*e^4 + 5160*e^2 - 3712, 31/3*e^8 - 677/3*e^6 + 1536*e^4 - 3749*e^2 + 2697, -19/3*e^8 + 413/3*e^6 - 929*e^4 + 2236*e^2 - 1593, -605/69*e^9 + 13168/69*e^7 - 29671/23*e^5 + 71446/23*e^3 - 50494/23*e, 22/23*e^9 - 478/23*e^7 + 3213/23*e^5 - 7672/23*e^3 + 5733/23*e, 67/69*e^9 - 1439/69*e^7 + 3154/23*e^5 - 7108/23*e^3 + 4006/23*e, -446/69*e^9 + 9751/69*e^7 - 22170/23*e^5 + 54402/23*e^3 - 39887/23*e, -563/138*e^9 + 12337/138*e^7 - 14085/23*e^5 + 69581/46*e^3 - 51015/46*e, -985/138*e^9 + 21485/138*e^7 - 24291/23*e^5 + 117417/46*e^3 - 82141/46*e, -17*e^8 + 371*e^6 - 2520*e^4 + 6120*e^2 - 4368, -85/69*e^9 + 1874/69*e^7 - 4323/23*e^5 + 10917/23*e^3 - 8639/23*e, -43/3*e^8 + 938/3*e^6 - 2123*e^4 + 5155*e^2 - 3671, -146/69*e^9 + 3145/69*e^7 - 6957/23*e^5 + 16234/23*e^3 - 10840/23*e, 35/3*e^8 - 763/3*e^6 + 1725*e^4 - 4185*e^2 + 2990, -20/3*e^8 + 436/3*e^6 - 986*e^4 + 2398*e^2 - 1746, -133/138*e^9 + 2873/138*e^7 - 3195/23*e^5 + 15125/46*e^3 - 10981/46*e, 375/46*e^9 - 8177/46*e^7 + 27751/23*e^5 - 135011/46*e^3 + 98329/46*e, -173/23*e^9 + 3786/23*e^7 - 25844/23*e^5 + 63255/23*e^3 - 45514/23*e, -34/69*e^9 + 722/69*e^7 - 1559/23*e^5 + 3479/23*e^3 - 2094/23*e, -25/138*e^9 + 539/138*e^7 - 585/23*e^5 + 2391/46*e^3 - 433/46*e, -1303/138*e^9 + 28319/138*e^7 - 31815/23*e^5 + 152379/46*e^3 - 106483/46*e, -42/23*e^9 + 900/23*e^7 - 5906/23*e^5 + 13461/23*e^3 - 8833/23*e, 257/69*e^9 - 5563/69*e^7 + 12414/23*e^5 - 29392/23*e^3 + 20232/23*e, 38/3*e^8 - 826/3*e^6 + 1856*e^4 - 4443*e^2 + 3109, 26/3*e^8 - 565/3*e^6 + 1271*e^4 - 3060*e^2 + 2176, -23/6*e^8 + 499/6*e^6 - 557*e^4 + 2619/2*e^2 - 1759/2, -17/2*e^8 + 373/2*e^6 - 1281*e^4 + 6367/2*e^2 - 4707/2, 539/138*e^9 - 11803/138*e^7 + 13459/23*e^5 - 66373/46*e^3 + 48441/46*e, 71/23*e^9 - 1551/23*e^7 + 10571/23*e^5 - 25941/23*e^3 + 19124/23*e, 56/69*e^9 - 1246/69*e^7 + 2906/23*e^5 - 7332/23*e^3 + 5454/23*e, -1367/138*e^9 + 29743/138*e^7 - 33492/23*e^5 + 161225/46*e^3 - 113807/46*e, -377/138*e^9 + 8371/138*e^7 - 9774/23*e^5 + 50009/46*e^3 - 38461/46*e, -95/6*e^8 + 2077/6*e^6 - 2360*e^4 + 11553/2*e^2 - 8373/2, -1355/138*e^9 + 29545/138*e^7 - 33409/23*e^5 + 162243/46*e^3 - 116821/46*e, -59/6*e^8 + 1285/6*e^6 - 1450*e^4 + 7017/2*e^2 - 5013/2, -29/69*e^9 + 628/69*e^7 - 1394/23*e^5 + 3263/23*e^3 - 2472/23*e, 103/69*e^9 - 2240/69*e^7 + 5055/23*e^5 - 12403/23*e^3 + 9753/23*e, 14/3*e^8 - 304/3*e^6 + 684*e^4 - 1658*e^2 + 1220, 115/3*e^8 - 2510/3*e^6 + 5686*e^4 - 13828*e^2 + 9903, 461/69*e^9 - 10102/69*e^7 + 23056/23*e^5 - 56867/23*e^3 + 41720/23*e, 152/23*e^9 - 3313/23*e^7 + 22477/23*e^5 - 54673/23*e^3 + 39591/23*e, -65/23*e^9 + 1429/23*e^7 - 9839/23*e^5 + 24501/23*e^3 - 18240/23*e, -134/23*e^9 + 2924/23*e^7 - 19867/23*e^5 + 48375/23*e^3 - 35168/23*e, 73/6*e^8 - 1595/6*e^6 + 1811*e^4 - 8853/2*e^2 + 6367/2, -398/69*e^9 + 8683/69*e^7 - 19643/23*e^5 + 47572/23*e^3 - 33750/23*e, -557/69*e^9 + 12100/69*e^7 - 27167/23*e^5 + 64961/23*e^3 - 45369/23*e, -125/6*e^8 + 2725/6*e^6 - 3078*e^4 + 14883/2*e^2 - 10553/2, -25/3*e^8 + 542/3*e^6 - 1211*e^4 + 2866*e^2 - 1964, -269/69*e^9 + 5899/69*e^7 - 13500/23*e^5 + 33618/23*e^3 - 25452/23*e, 25/3*e^8 - 548/3*e^6 + 1251*e^4 - 3088*e^2 + 2276, 917/69*e^9 - 19972/69*e^7 + 45073/23*e^5 - 108987/23*e^3 + 77999/23*e, 28/3*e^8 - 611/3*e^6 + 1385*e^4 - 3383*e^2 + 2445, 36*e^8 - 785*e^6 + 5325*e^4 - 12901*e^2 + 9175, -43/46*e^9 + 951/46*e^7 - 3336/23*e^5 + 17565/46*e^3 - 15267/46*e, -4/3*e^8 + 86/3*e^6 - 189*e^4 + 428*e^2 - 263, 349/138*e^9 - 7541/138*e^7 + 8369/23*e^5 - 39029/46*e^3 + 26189/46*e, -29/3*e^8 + 631/3*e^6 - 1422*e^4 + 3429*e^2 - 2419, 305/46*e^9 - 6677/46*e^7 + 22814/23*e^5 - 112001/46*e^3 + 81039/46*e, 301/46*e^9 - 6565/46*e^7 + 22271/23*e^5 - 107821/46*e^3 + 75957/46*e, 751/138*e^9 - 16313/138*e^7 + 18314/23*e^5 - 87795/46*e^3 + 61955/46*e, 1399/138*e^9 - 30593/138*e^7 + 34779/23*e^5 - 170455/46*e^3 + 123725/46*e, -80/23*e^9 + 1757/23*e^7 - 12083/23*e^5 + 30102/23*e^3 - 22842/23*e, 1/69*e^9 - 5/69*e^7 - 36/23*e^5 + 104/23*e^3 + 458/23*e, 5*e^8 - 108*e^6 + 721*e^4 - 1704*e^2 + 1190, -154/23*e^9 + 3369/23*e^7 - 22974/23*e^5 + 56073/23*e^3 - 40062/23*e, 41/3*e^9 - 895/3*e^7 + 2028*e^5 - 4933*e^3 + 3523*e, 106/3*e^8 - 2309/3*e^6 + 5210*e^4 - 12577*e^2 + 8920, 58/3*e^8 - 1265/3*e^6 + 2861*e^4 - 6929*e^2 + 4915, -32/3*e^8 + 700/3*e^6 - 1592*e^4 + 3892*e^2 - 2786, 47/23*e^9 - 1040/23*e^7 + 7252/23*e^5 - 18456/23*e^3 + 13863/23*e, -313/23*e^9 + 6809/23*e^7 - 45983/23*e^5 + 110517/23*e^3 - 77748/23*e, -253/6*e^8 + 5519/6*e^6 - 6244*e^4 + 30301/2*e^2 - 21613/2, -745/138*e^9 + 16283/138*e^7 - 18514/23*e^5 + 91041/46*e^3 - 67441/46*e, -869/138*e^9 + 18835/138*e^7 - 21066/23*e^5 + 100225/46*e^3 - 69861/46*e, -5/2*e^8 + 107/2*e^6 - 349*e^4 + 1563/2*e^2 - 953/2, 17/69*e^9 - 361/69*e^7 + 768/23*e^5 - 1636/23*e^3 + 1346/23*e, 43/2*e^8 - 935/2*e^6 + 3155*e^4 - 15167/2*e^2 + 10731/2, 421/69*e^9 - 9143/69*e^7 + 20494/23*e^5 - 48722/23*e^3 + 33336/23*e, 53/6*e^8 - 1147/6*e^6 + 1278*e^4 - 6025/2*e^2 + 4117/2, 842/69*e^9 - 18355/69*e^7 + 41494/23*e^5 - 100664/23*e^3 + 72307/23*e, -55/3*e^8 + 1199/3*e^6 - 2711*e^4 + 6580*e^2 - 4731, -80/3*e^8 + 1744/3*e^6 - 3942*e^4 + 9551*e^2 - 6815, 43/23*e^9 - 928/23*e^7 + 6166/23*e^5 - 14253/23*e^3 + 8850/23*e, -5/69*e^9 + 94/69*e^7 - 165/23*e^5 + 285/23*e^3 - 289/23*e, 7*e^8 - 152*e^6 + 1025*e^4 - 2470*e^2 + 1764, 140/69*e^9 - 3046/69*e^7 + 6828/23*e^5 - 16007/23*e^3 + 10231/23*e, -29/3*e^8 + 634/3*e^6 - 1441*e^4 + 3526*e^2 - 2554, -68/23*e^9 + 1467/23*e^7 - 9768/23*e^5 + 22944/23*e^3 - 15485/23*e, -367/46*e^9 + 8045/46*e^7 - 27562/23*e^5 + 136127/46*e^3 - 99987/46*e, -19/2*e^9 + 415/2*e^7 - 1412*e^5 + 6885/2*e^3 - 4971/2*e, -371/69*e^9 + 8065/69*e^7 - 18131/23*e^5 + 43434/23*e^3 - 30147/23*e, -23/3*e^8 + 505/3*e^6 - 1155*e^4 + 2850*e^2 - 2083, -5*e^8 + 108*e^6 - 720*e^4 + 1699*e^2 - 1176, -9*e^8 + 195*e^6 - 1309*e^4 + 3125*e^2 - 2200, 45/23*e^9 - 984/23*e^7 + 6709/23*e^5 - 16389/23*e^3 + 11667/23*e, -62/23*e^9 + 1345/23*e^7 - 9036/23*e^5 + 21504/23*e^3 - 15015/23*e, -83/6*e^8 + 1807/6*e^6 - 2038*e^4 + 9869/2*e^2 - 7147/2, 59/2*e^8 - 1287/2*e^6 + 4367*e^4 - 21183/2*e^2 + 15123/2, 16/3*e^9 - 350/3*e^7 + 796*e^5 - 1949*e^3 + 1403*e, -23/3*e^9 + 502/3*e^7 - 1137*e^5 + 2763*e^3 - 1979*e, 37/3*e^9 - 809/3*e^7 + 1838*e^5 - 4490*e^3 + 3232*e, -979/69*e^9 + 21317/69*e^7 - 48062/23*e^5 + 115764/23*e^3 - 81440/23*e, -37/3*e^8 + 803/3*e^6 - 1802*e^4 + 4323*e^2 - 3077, 76/3*e^8 - 1655/3*e^6 + 3734*e^4 - 9017*e^2 + 6398, -59/46*e^9 + 1261/46*e^7 - 4151/23*e^5 + 19611/46*e^3 - 15125/46*e, -161/6*e^8 + 3505/6*e^6 - 3952*e^4 + 19083/2*e^2 - 13585/2, 225/46*e^9 - 4897/46*e^7 + 16554/23*e^5 - 79691/46*e^3 + 55897/46*e, -43/2*e^8 + 939/2*e^6 - 3192*e^4 + 15523/2*e^2 - 11121/2, 64/3*e^8 - 1397/3*e^6 + 3164*e^4 - 7686*e^2 + 5503, -178/23*e^9 + 3880/23*e^7 - 26293/23*e^5 + 63627/23*e^3 - 45668/23*e, 1102/69*e^9 - 24002/69*e^7 + 54145/23*e^5 - 130595/23*e^3 + 92142/23*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([4,2,1/3*w^3 + 2/3*w^2 - 10/3*w - 7])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]