/* 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([25, 5, -11, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([16, 2, 2]) primes_array = [ [5, 5, 1/5*w^3 + 4/5*w^2 - 11/5*w - 7],\ [5, 5, 1/5*w^3 - 6/5*w^2 - 1/5*w + 4],\ [11, 11, w + 1],\ [11, 11, 1/5*w^3 - 1/5*w^2 - 11/5*w + 2],\ [16, 2, 2],\ [19, 19, -1/5*w^3 + 1/5*w^2 + 1/5*w + 1],\ [19, 19, 1/5*w^3 - 1/5*w^2 - 11/5*w],\ [19, 19, -2/5*w^3 + 2/5*w^2 + 17/5*w],\ [19, 19, w - 1],\ [29, 29, w^2 - w - 8],\ [29, 29, 2/5*w^3 - 2/5*w^2 - 7/5*w + 2],\ [31, 31, 1/5*w^3 - 1/5*w^2 - 1/5*w + 2],\ [31, 31, 2/5*w^3 - 2/5*w^2 - 17/5*w + 3],\ [61, 61, -2/5*w^3 - 3/5*w^2 + 12/5*w + 5],\ [61, 61, -4/5*w^3 - 6/5*w^2 + 39/5*w + 15],\ [61, 61, 3/5*w^3 + 2/5*w^2 - 18/5*w - 3],\ [61, 61, 7/5*w^3 + 3/5*w^2 - 62/5*w - 13],\ [71, 71, 1/5*w^3 - 6/5*w^2 - 6/5*w + 4],\ [71, 71, w^2 - 8],\ [79, 79, 3/5*w^3 + 12/5*w^2 - 33/5*w - 22],\ [79, 79, 1/5*w^3 + 4/5*w^2 - 11/5*w - 9],\ [81, 3, -3],\ [101, 101, 3/5*w^3 + 7/5*w^2 - 28/5*w - 15],\ [101, 101, 1/5*w^3 + 9/5*w^2 - 16/5*w - 16],\ [121, 11, 3/5*w^3 - 3/5*w^2 - 18/5*w + 1],\ [131, 131, 1/5*w^3 + 4/5*w^2 - 16/5*w - 8],\ [131, 131, w^2 - 2*w - 2],\ [149, 149, 4/5*w^3 + 1/5*w^2 - 29/5*w - 5],\ [149, 149, 4/5*w^3 - 9/5*w^2 - 19/5*w + 6],\ [151, 151, 2/5*w^3 + 3/5*w^2 - 17/5*w - 3],\ [151, 151, -2/5*w^3 + 7/5*w^2 + 7/5*w - 8],\ [151, 151, 4/5*w^3 + 1/5*w^2 - 29/5*w - 2],\ [151, 151, -4/5*w^3 + 9/5*w^2 + 19/5*w - 9],\ [179, 179, -3/5*w^3 + 8/5*w^2 + 18/5*w - 6],\ [179, 179, 2/5*w^3 + 3/5*w^2 - 12/5*w - 6],\ [211, 211, 1/5*w^3 + 4/5*w^2 - 6/5*w - 10],\ [211, 211, 2/5*w^3 - 7/5*w^2 - 12/5*w + 2],\ [229, 229, 6/5*w^3 - 11/5*w^2 - 41/5*w + 11],\ [229, 229, 2*w^2 - 2*w - 9],\ [229, 229, -4/5*w^3 - 1/5*w^2 + 19/5*w + 2],\ [229, 229, -3/5*w^3 + 3/5*w^2 + 28/5*w - 3],\ [239, 239, 11/5*w^3 + 4/5*w^2 - 96/5*w - 19],\ [239, 239, -6/5*w^3 + 1/5*w^2 + 51/5*w + 3],\ [241, 241, 1/5*w^3 + 4/5*w^2 - 1/5*w - 6],\ [241, 241, 4/5*w^3 - 4/5*w^2 - 29/5*w - 1],\ [251, 251, -1/5*w^3 + 6/5*w^2 + 11/5*w - 12],\ [251, 251, -1/5*w^3 + 11/5*w^2 + 1/5*w - 15],\ [269, 269, 2/5*w^3 + 3/5*w^2 - 17/5*w - 2],\ [269, 269, -2/5*w^3 + 7/5*w^2 + 7/5*w - 9],\ [271, 271, 1/5*w^3 - 1/5*w^2 + 4/5*w],\ [271, 271, 3/5*w^3 - 3/5*w^2 - 28/5*w + 2],\ [281, 281, w^3 - 3*w^2 - 4*w + 13],\ [281, 281, -3/5*w^3 + 3/5*w^2 + 28/5*w - 6],\ [281, 281, -6/5*w^3 + 26/5*w^2 + 11/5*w - 16],\ [281, 281, w^3 + w^2 - 8*w - 9],\ [289, 17, 2/5*w^3 + 3/5*w^2 - 7/5*w - 5],\ [289, 17, 4/5*w^3 - 9/5*w^2 - 29/5*w + 8],\ [311, 311, -w^2 + 2*w + 11],\ [311, 311, -1/5*w^3 + 6/5*w^2 + 1/5*w - 1],\ [311, 311, 1/5*w^3 + 4/5*w^2 - 16/5*w + 1],\ [311, 311, -1/5*w^3 - 4/5*w^2 + 11/5*w + 10],\ [349, 349, -1/5*w^3 - 9/5*w^2 + 11/5*w + 16],\ [349, 349, 2/5*w^3 - 12/5*w^2 - 7/5*w + 7],\ [359, 359, -4/5*w^3 + 4/5*w^2 + 19/5*w - 1],\ [359, 359, -w^3 + 3*w^2 + 5*w - 12],\ [359, 359, w^3 - w^2 - 7*w + 2],\ [359, 359, 4/5*w^3 + 6/5*w^2 - 29/5*w - 11],\ [379, 379, 4/5*w^3 + 6/5*w^2 - 34/5*w - 9],\ [379, 379, 3/5*w^3 - 3/5*w^2 - 28/5*w + 7],\ [389, 389, w^2 - 3*w - 8],\ [389, 389, -4/5*w^3 + 14/5*w^2 + 19/5*w - 16],\ [401, 401, -3*w^2 + 2*w + 23],\ [401, 401, 1/5*w^3 - 16/5*w^2 + 4/5*w + 11],\ [409, 409, -w^3 + 2*w^2 + 3*w - 7],\ [409, 409, 7/5*w^3 - 2/5*w^2 - 57/5*w - 2],\ [419, 419, -1/5*w^3 + 1/5*w^2 + 16/5*w - 2],\ [419, 419, 1/5*w^3 - 1/5*w^2 - 16/5*w],\ [421, 421, 2/5*w^3 + 3/5*w^2 - 27/5*w - 3],\ [421, 421, 1/5*w^3 + 4/5*w^2 + 4/5*w - 3],\ [439, 439, -w^3 + 3*w^2 + 5*w - 16],\ [439, 439, -4/5*w^3 - 6/5*w^2 + 29/5*w + 7],\ [439, 439, -3/5*w^3 + 13/5*w^2 + 3/5*w - 11],\ [439, 439, 4/5*w^3 + 6/5*w^2 - 39/5*w - 10],\ [449, 449, 2/5*w^3 - 12/5*w^2 - 2/5*w + 5],\ [449, 449, 4/5*w^3 - 24/5*w^2 - 4/5*w + 15],\ [461, 461, -1/5*w^3 - 4/5*w^2 - 4/5*w + 4],\ [461, 461, 2*w^2 - 2*w - 11],\ [461, 461, 3/5*w^3 + 2/5*w^2 - 33/5*w - 4],\ [479, 479, -w^3 + 3*w^2 + 6*w - 14],\ [479, 479, -3/5*w^3 + 3/5*w^2 + 28/5*w + 3],\ [499, 499, 2/5*w^3 + 8/5*w^2 - 17/5*w - 6],\ [499, 499, -3/5*w^3 + 13/5*w^2 + 13/5*w - 17],\ [509, 509, -w^3 + 2*w^2 + 4*w - 6],\ [509, 509, 6/5*w^3 - 1/5*w^2 - 46/5*w - 4],\ [521, 521, -2/5*w^3 + 2/5*w^2 + 7/5*w - 7],\ [521, 521, -3/5*w^3 + 3/5*w^2 + 23/5*w - 8],\ [529, 23, -7/5*w^3 + 17/5*w^2 + 42/5*w - 15],\ [529, 23, 2/5*w^3 + 13/5*w^2 - 27/5*w - 21],\ [541, 541, 1/5*w^3 - 11/5*w^2 - 1/5*w + 10],\ [541, 541, 3/5*w^3 - 8/5*w^2 - 13/5*w + 13],\ [541, 541, -2*w^2 + w + 13],\ [541, 541, 3/5*w^3 + 2/5*w^2 - 23/5*w + 2],\ [569, 569, w^3 - 2*w^2 - 5*w + 7],\ [569, 569, -1/5*w^3 + 1/5*w^2 + 1/5*w - 6],\ [571, 571, w^2 + w - 9],\ [571, 571, -2/5*w^3 + 12/5*w^2 + 7/5*w - 12],\ [571, 571, 1/5*w^3 + 9/5*w^2 - 11/5*w - 11],\ [571, 571, -2/5*w^3 + 7/5*w^2 + 17/5*w - 4],\ [601, 601, -3/5*w^3 + 13/5*w^2 + 18/5*w - 11],\ [601, 601, -4/5*w^3 + 4/5*w^2 + 34/5*w + 1],\ [631, 631, 2/5*w^3 + 18/5*w^2 - 27/5*w - 30],\ [631, 631, 3/5*w^3 - 23/5*w^2 - 3/5*w + 15],\ [661, 661, -2*w^3 + 17*w + 12],\ [661, 661, -9/5*w^3 + 4/5*w^2 + 74/5*w + 1],\ [691, 691, -7/5*w^3 - 18/5*w^2 + 72/5*w + 35],\ [691, 691, 6/5*w^3 - 31/5*w^2 - 6/5*w + 19],\ [701, 701, -1/5*w^3 + 6/5*w^2 + 16/5*w - 6],\ [701, 701, 2/5*w^3 - 7/5*w^2 - 22/5*w + 8],\ [709, 709, -3/5*w^3 + 13/5*w^2 + 13/5*w - 18],\ [709, 709, 1/5*w^3 + 14/5*w^2 - 11/5*w - 20],\ [709, 709, -2/5*w^3 - 8/5*w^2 + 17/5*w + 5],\ [709, 709, 1/5*w^3 + 4/5*w^2 - 21/5*w - 10],\ [719, 719, -3/5*w^3 + 8/5*w^2 + 13/5*w - 12],\ [719, 719, 3/5*w^3 + 2/5*w^2 - 23/5*w + 1],\ [719, 719, -7/5*w^3 + 17/5*w^2 + 32/5*w - 14],\ [719, 719, 7/5*w^3 + 3/5*w^2 - 52/5*w - 8],\ [739, 739, 1/5*w^3 - 1/5*w^2 - 11/5*w - 5],\ [739, 739, w - 6],\ [761, 761, -4/5*w^3 + 9/5*w^2 + 19/5*w - 11],\ [761, 761, 4/5*w^3 + 1/5*w^2 - 29/5*w],\ [769, 769, 3/5*w^3 - 13/5*w^2 - 13/5*w + 8],\ [769, 769, -2/5*w^3 - 8/5*w^2 + 17/5*w + 15],\ [769, 769, 7/5*w^3 - 17/5*w^2 - 37/5*w + 18],\ [769, 769, -6/5*w^3 - 4/5*w^2 + 41/5*w + 5],\ [809, 809, -1/5*w^3 + 6/5*w^2 - 4/5*w - 14],\ [809, 809, -2/5*w^3 - 3/5*w^2 + 22/5*w - 4],\ [809, 809, -6/5*w^3 + 6/5*w^2 + 41/5*w - 5],\ [809, 809, w^3 - w^2 - 5*w + 4],\ [821, 821, -3/5*w^3 - 17/5*w^2 + 33/5*w + 30],\ [821, 821, -4/5*w^3 + 24/5*w^2 + 9/5*w - 15],\ [829, 829, 7/5*w^3 - 12/5*w^2 - 52/5*w + 10],\ [829, 829, -1/5*w^3 + 11/5*w^2 - 4/5*w - 19],\ [829, 829, -13/5*w^3 + 3/5*w^2 + 108/5*w + 10],\ [829, 829, -w^3 + 4*w^2 + 5*w - 23],\ [839, 839, 4/5*w^3 - 9/5*w^2 - 24/5*w + 4],\ [839, 839, 3/5*w^3 + 2/5*w^2 - 18/5*w - 8],\ [841, 29, -w^3 + w^2 + 6*w - 4],\ [859, 859, 6/5*w^3 - 11/5*w^2 - 36/5*w + 9],\ [859, 859, w^3 - 6*w - 3],\ [881, 881, 4/5*w^3 - 4/5*w^2 - 9/5*w - 1],\ [881, 881, 9/5*w^3 - 24/5*w^2 - 19/5*w + 14],\ [881, 881, -w^3 + 6*w + 2],\ [881, 881, 1/5*w^3 - 1/5*w^2 - 1/5*w - 6],\ [911, 911, w^3 - w^2 - 5*w + 1],\ [911, 911, 6/5*w^3 - 6/5*w^2 - 41/5*w + 2],\ [919, 919, -7/5*w^3 + 12/5*w^2 + 42/5*w - 7],\ [919, 919, -6/5*w^3 + 1/5*w^2 + 36/5*w + 5],\ [929, 929, -2/5*w^3 - 8/5*w^2 + 17/5*w + 16],\ [929, 929, -3/5*w^3 + 13/5*w^2 + 13/5*w - 7],\ [961, 31, w^3 - w^2 - 6*w + 2],\ [971, 971, 8/5*w^3 - 13/5*w^2 - 48/5*w + 6],\ [971, 971, -2/5*w^3 - 3/5*w^2 + 22/5*w],\ [971, 971, 7/5*w^3 - 7/5*w^2 - 57/5*w + 7],\ [971, 971, -1/5*w^3 + 6/5*w^2 - 4/5*w - 10],\ [991, 991, 2/5*w^3 + 8/5*w^2 - 22/5*w - 7],\ [991, 991, -2/5*w^3 + 12/5*w^2 + 2/5*w - 15]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^11 - 3*x^10 - 28*x^9 + 77*x^8 + 246*x^7 - 587*x^6 - 764*x^5 + 1151*x^4 + 1359*x^3 - 364*x^2 - 736*x - 192 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, e, 17540/49759*e^10 - 264347/199036*e^9 - 1757827/199036*e^8 + 99176/2927*e^7 + 11980401/199036*e^6 - 25091513/99518*e^5 - 14313187/199036*e^4 + 22592735/49759*e^3 + 24903875/199036*e^2 - 43289233/199036*e - 4450014/49759, 17540/49759*e^10 - 264347/199036*e^9 - 1757827/199036*e^8 + 99176/2927*e^7 + 11980401/199036*e^6 - 25091513/99518*e^5 - 14313187/199036*e^4 + 22592735/49759*e^3 + 24903875/199036*e^2 - 43289233/199036*e - 4450014/49759, -1, 184289/796144*e^10 - 720943/796144*e^9 - 561245/99518*e^8 + 1075661/46832*e^7 + 14137797/398072*e^6 - 134196867/796144*e^5 - 1798733/99518*e^4 + 228517839/796144*e^3 + 25186459/796144*e^2 - 6301777/49759*e - 1709944/49759, -329479/796144*e^10 + 1202149/796144*e^9 + 2110725/199036*e^8 - 1814923/46832*e^7 - 30453349/398072*e^6 + 233006461/796144*e^5 + 24728329/199036*e^4 - 443681033/796144*e^3 - 153596745/796144*e^2 + 55610965/199036*e + 5858451/49759, 184289/796144*e^10 - 720943/796144*e^9 - 561245/99518*e^8 + 1075661/46832*e^7 + 14137797/398072*e^6 - 134196867/796144*e^5 - 1798733/99518*e^4 + 228517839/796144*e^3 + 25186459/796144*e^2 - 6301777/49759*e - 1709944/49759, -329479/796144*e^10 + 1202149/796144*e^9 + 2110725/199036*e^8 - 1814923/46832*e^7 - 30453349/398072*e^6 + 233006461/796144*e^5 + 24728329/199036*e^4 - 443681033/796144*e^3 - 153596745/796144*e^2 + 55610965/199036*e + 5858451/49759, -1544/49759*e^10 + 6937/99518*e^9 + 100699/99518*e^8 - 5908/2927*e^7 - 1112245/99518*e^6 + 963422/49759*e^5 + 4789715/99518*e^4 - 3229066/49759*e^3 - 7269745/99518*e^2 + 4365399/99518*e + 1772992/49759, -1544/49759*e^10 + 6937/99518*e^9 + 100699/99518*e^8 - 5908/2927*e^7 - 1112245/99518*e^6 + 963422/49759*e^5 + 4789715/99518*e^4 - 3229066/49759*e^3 - 7269745/99518*e^2 + 4365399/99518*e + 1772992/49759, 156215/398072*e^10 - 555877/398072*e^9 - 1018475/99518*e^8 + 841467/23416*e^7 + 15377953/199036*e^6 - 108901565/398072*e^5 - 15308425/99518*e^4 + 213945889/398072*e^3 + 98081137/398072*e^2 - 27013701/99518*e - 6831340/49759, 156215/398072*e^10 - 555877/398072*e^9 - 1018475/99518*e^8 + 841467/23416*e^7 + 15377953/199036*e^6 - 108901565/398072*e^5 - 15308425/99518*e^4 + 213945889/398072*e^3 + 98081137/398072*e^2 - 27013701/99518*e - 6831340/49759, -193791/99518*e^10 + 354370/49759*e^9 + 4953897/99518*e^8 - 1068509/5854*e^7 - 35554085/99518*e^6 + 136824409/99518*e^5 + 56647373/99518*e^4 - 258494795/99518*e^3 - 45168291/49759*e^2 + 128854165/99518*e + 28442946/49759, -193791/99518*e^10 + 354370/49759*e^9 + 4953897/99518*e^8 - 1068509/5854*e^7 - 35554085/99518*e^6 + 136824409/99518*e^5 + 56647373/99518*e^4 - 258494795/99518*e^3 - 45168291/49759*e^2 + 128854165/99518*e + 28442946/49759, 189133/199036*e^10 - 722221/199036*e^9 - 2361119/99518*e^8 + 1086037/11708*e^7 + 7975583/49759*e^6 - 137883815/199036*e^5 - 17820211/99518*e^4 + 251246199/199036*e^3 + 60408677/199036*e^2 - 60446167/99518*e - 11253562/49759, 189133/199036*e^10 - 722221/199036*e^9 - 2361119/99518*e^8 + 1086037/11708*e^7 + 7975583/49759*e^6 - 137883815/199036*e^5 - 17820211/99518*e^4 + 251246199/199036*e^3 + 60408677/199036*e^2 - 60446167/99518*e - 11253562/49759, 164341/199036*e^10 - 594467/199036*e^9 - 1056402/49759*e^8 + 896477/11708*e^7 + 15395191/99518*e^6 - 114984335/199036*e^5 - 13218598/49759*e^4 + 218919647/199036*e^3 + 85135535/199036*e^2 - 27534071/49759*e - 12955276/49759, 164341/199036*e^10 - 594467/199036*e^9 - 1056402/49759*e^8 + 896477/11708*e^7 + 15395191/99518*e^6 - 114984335/199036*e^5 - 13218598/49759*e^4 + 218919647/199036*e^3 + 85135535/199036*e^2 - 27534071/49759*e - 12955276/49759, 138245/99518*e^10 - 508773/99518*e^9 - 1760661/49759*e^8 + 766473/5854*e^7 + 12526165/49759*e^6 - 97945597/99518*e^5 - 19125945/49759*e^4 + 183421477/99518*e^3 + 61339227/99518*e^2 - 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10140917/23416*e^7 - 172099955/199036*e^6 + 1301032275/398072*e^5 + 144192839/99518*e^4 - 2473140711/398072*e^3 - 922364719/398072*e^2 + 307148059/99518*e + 69555164/49759, 2237/23416*e^10 - 14175/23416*e^9 - 8561/5854*e^8 + 353825/23416*e^7 - 85269/11708*e^6 - 2419375/23416*e^5 + 889151/5854*e^4 + 2627195/23416*e^3 - 5623829/23416*e^2 - 91497/5854*e + 294802/2927, 284867/398072*e^10 - 899221/398072*e^9 - 982096/49759*e^8 + 1372599/23416*e^7 + 33376755/199036*e^6 - 182167233/398072*e^5 - 23424686/49759*e^4 + 391450325/398072*e^3 + 290304297/398072*e^2 - 25886884/49759*e - 17349868/49759, 284867/398072*e^10 - 899221/398072*e^9 - 982096/49759*e^8 + 1372599/23416*e^7 + 33376755/199036*e^6 - 182167233/398072*e^5 - 23424686/49759*e^4 + 391450325/398072*e^3 + 290304297/398072*e^2 - 25886884/49759*e - 17349868/49759, 2237/23416*e^10 - 14175/23416*e^9 - 8561/5854*e^8 + 353825/23416*e^7 - 85269/11708*e^6 - 2419375/23416*e^5 + 889151/5854*e^4 + 2627195/23416*e^3 - 5623829/23416*e^2 - 91497/5854*e + 294802/2927, -1096795/199036*e^10 + 4043585/199036*e^9 + 6989072/49759*e^8 - 6097875/11708*e^7 - 99678351/99518*e^6 + 780930109/199036*e^5 + 77237830/49759*e^4 - 1474507833/199036*e^3 - 500442293/199036*e^2 + 183128245/49759*e + 79232566/49759, -1096795/199036*e^10 + 4043585/199036*e^9 + 6989072/49759*e^8 - 6097875/11708*e^7 - 99678351/99518*e^6 + 780930109/199036*e^5 + 77237830/49759*e^4 - 1474507833/199036*e^3 - 500442293/199036*e^2 + 183128245/49759*e + 79232566/49759, -175665/99518*e^10 + 1261597/199036*e^9 + 9079287/199036*e^8 - 953305/5854*e^7 - 66900249/199036*e^6 + 61422945/49759*e^5 + 119854835/199036*e^4 - 237626095/99518*e^3 - 187863525/199036*e^2 + 241316373/199036*e + 30009934/49759, -297709/199036*e^10 + 284266/49759*e^9 + 7419037/199036*e^8 - 1710601/11708*e^7 - 49699557/199036*e^6 + 217283673/199036*e^5 + 50639173/199036*e^4 - 396418431/199036*e^3 - 19595399/49759*e^2 + 195024091/199036*e + 15949462/49759, -297709/199036*e^10 + 284266/49759*e^9 + 7419037/199036*e^8 - 1710601/11708*e^7 - 49699557/199036*e^6 + 217283673/199036*e^5 + 50639173/199036*e^4 - 396418431/199036*e^3 - 19595399/49759*e^2 + 195024091/199036*e + 15949462/49759, -4597237/796144*e^10 + 16838311/796144*e^9 + 29352757/199036*e^8 - 25378129/46832*e^7 - 420590843/398072*e^6 + 3248207399/796144*e^5 + 332911009/199036*e^4 - 6128086267/796144*e^3 - 2130333459/796144*e^2 + 760672113/199036*e + 82771497/49759, -4597237/796144*e^10 + 16838311/796144*e^9 + 29352757/199036*e^8 - 25378129/46832*e^7 - 420590843/398072*e^6 + 3248207399/796144*e^5 + 332911009/199036*e^4 - 6128086267/796144*e^3 - 2130333459/796144*e^2 + 760672113/199036*e + 82771497/49759, 1189171/796144*e^10 - 4632029/796144*e^9 - 3639705/99518*e^8 + 6928279/46832*e^7 + 92712151/398072*e^6 - 867433497/796144*e^5 - 13571433/99518*e^4 + 1491205789/796144*e^3 + 176220033/796144*e^2 - 41754620/49759*e - 11207922/49759, 1189171/796144*e^10 - 4632029/796144*e^9 - 3639705/99518*e^8 + 6928279/46832*e^7 + 92712151/398072*e^6 - 867433497/796144*e^5 - 13571433/99518*e^4 + 1491205789/796144*e^3 + 176220033/796144*e^2 - 41754620/49759*e - 11207922/49759, 122137/49759*e^10 - 878013/99518*e^9 - 6306755/99518*e^8 + 662949/2927*e^7 + 46356611/99518*e^6 - 85217113/49759*e^5 - 82329575/99518*e^4 + 163049088/49759*e^3 + 130686035/99518*e^2 - 162575445/99518*e - 37719346/49759, 122137/49759*e^10 - 878013/99518*e^9 - 6306755/99518*e^8 + 662949/2927*e^7 + 46356611/99518*e^6 - 85217113/49759*e^5 - 82329575/99518*e^4 + 163049088/49759*e^3 + 130686035/99518*e^2 - 162575445/99518*e - 37719346/49759, 1098177/398072*e^10 - 4054263/398072*e^9 - 3497853/49759*e^8 + 6114037/23416*e^7 + 99754225/199036*e^6 - 783322987/398072*e^5 - 38725118/49759*e^4 + 1484196647/398072*e^3 + 508034971/398072*e^2 - 94052987/49759*e - 41270040/49759, 1098177/398072*e^10 - 4054263/398072*e^9 - 3497853/49759*e^8 + 6114037/23416*e^7 + 99754225/199036*e^6 - 783322987/398072*e^5 - 38725118/49759*e^4 + 1484196647/398072*e^3 + 508034971/398072*e^2 - 94052987/49759*e - 41270040/49759, -301509/99518*e^10 + 2131869/199036*e^9 + 15753143/199036*e^8 - 1615341/5854*e^7 - 119105097/199036*e^6 + 104738699/49759*e^5 + 236744175/199036*e^4 - 414179739/99518*e^3 - 373341965/199036*e^2 + 431390473/199036*e + 53217562/49759, -301509/99518*e^10 + 2131869/199036*e^9 + 15753143/199036*e^8 - 1615341/5854*e^7 - 119105097/199036*e^6 + 104738699/49759*e^5 + 236744175/199036*e^4 - 414179739/99518*e^3 - 373341965/199036*e^2 + 431390473/199036*e + 53217562/49759, 941929/796144*e^10 - 3384211/796144*e^9 - 6065285/199036*e^8 + 5096437/46832*e^7 + 88715951/398072*e^6 - 652009603/796144*e^5 - 77248713/199036*e^4 + 1231425863/796144*e^3 + 492872079/796144*e^2 - 153583409/199036*e - 15789053/49759, -981411/796144*e^10 + 3724697/796144*e^9 + 6162205/199036*e^8 - 5605895/46832*e^7 - 84751481/398072*e^6 + 714046609/796144*e^5 + 53433113/199036*e^4 - 1319797629/796144*e^3 - 341249293/796144*e^2 + 157330429/199036*e + 13994551/49759, 20911/49759*e^10 - 312363/199036*e^9 - 2099115/199036*e^8 + 117254/2927*e^7 + 14384157/199036*e^6 - 29850749/99518*e^5 - 17496191/199036*e^4 + 27796677/49759*e^3 + 26085655/199036*e^2 - 55805405/199036*e - 5346774/49759, -981411/796144*e^10 + 3724697/796144*e^9 + 6162205/199036*e^8 - 5605895/46832*e^7 - 84751481/398072*e^6 + 714046609/796144*e^5 + 53433113/199036*e^4 - 1319797629/796144*e^3 - 341249293/796144*e^2 + 157330429/199036*e + 13994551/49759, 20911/49759*e^10 - 312363/199036*e^9 - 2099115/199036*e^8 + 117254/2927*e^7 + 14384157/199036*e^6 - 29850749/99518*e^5 - 17496191/199036*e^4 + 27796677/49759*e^3 + 26085655/199036*e^2 - 55805405/199036*e - 5346774/49759, 92471/398072*e^10 - 326053/398072*e^9 - 596261/99518*e^8 + 487027/23416*e^7 + 8800881/199036*e^6 - 61136397/398072*e^5 - 8407849/99518*e^4 + 106494225/398072*e^3 + 67583561/398072*e^2 - 11345051/99518*e - 5050056/49759, 92471/398072*e^10 - 326053/398072*e^9 - 596261/99518*e^8 + 487027/23416*e^7 + 8800881/199036*e^6 - 61136397/398072*e^5 - 8407849/99518*e^4 + 106494225/398072*e^3 + 67583561/398072*e^2 - 11345051/99518*e - 5050056/49759] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([16, 2, 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]