/* 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([9, 3, -7, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([41, 41, -1/3*w^3 + 4/3*w^2 + 7/3*w - 6]) primes_array = [ [5, 5, -1/3*w^3 - 2/3*w^2 + 7/3*w + 4],\ [5, 5, 1/3*w^3 - 4/3*w^2 - 1/3*w + 3],\ [9, 3, -w],\ [9, 3, 1/3*w^3 - 1/3*w^2 - 7/3*w + 1],\ [16, 2, 2],\ [19, 19, 2/3*w^3 - 2/3*w^2 - 11/3*w],\ [19, 19, -1/3*w^3 + 1/3*w^2 + 1/3*w + 1],\ [31, 31, 2/3*w^3 + 1/3*w^2 - 11/3*w - 2],\ [31, 31, 2/3*w^3 - 5/3*w^2 - 5/3*w + 5],\ [41, 41, -1/3*w^3 + 4/3*w^2 + 7/3*w - 6],\ [41, 41, -1/3*w^3 + 4/3*w^2 + 7/3*w - 3],\ [61, 61, 1/3*w^3 - 4/3*w^2 + 2/3*w + 4],\ [61, 61, 2/3*w^3 + 1/3*w^2 - 14/3*w - 2],\ [71, 71, -1/3*w^3 + 4/3*w^2 + 1/3*w - 7],\ [71, 71, 1/3*w^3 + 2/3*w^2 - 7/3*w],\ [89, 89, -1/3*w^3 + 1/3*w^2 + 10/3*w - 3],\ [89, 89, 1/3*w^3 - 1/3*w^2 - 10/3*w - 1],\ [101, 101, 1/3*w^3 - 1/3*w^2 - 7/3*w - 3],\ [101, 101, -2/3*w^3 + 5/3*w^2 + 11/3*w - 4],\ [101, 101, 2/3*w^3 - 5/3*w^2 - 8/3*w + 3],\ [101, 101, w - 4],\ [109, 109, 2/3*w^3 + 1/3*w^2 - 8/3*w - 4],\ [109, 109, -w^3 + 2*w^2 + 4*w - 4],\ [121, 11, w^3 - w^2 - 4*w + 1],\ [121, 11, -w^3 + w^2 + 4*w - 2],\ [131, 131, 4/3*w^3 - 1/3*w^2 - 22/3*w - 1],\ [131, 131, -w^3 + 7*w + 2],\ [139, 139, 2/3*w^3 - 2/3*w^2 - 14/3*w + 1],\ [139, 139, 2*w - 1],\ [139, 139, 1/3*w^3 + 5/3*w^2 - 7/3*w - 10],\ [139, 139, -2/3*w^3 + 8/3*w^2 + 5/3*w - 5],\ [149, 149, w^3 + w^2 - 7*w - 11],\ [149, 149, -w^3 - w^2 + 5*w + 4],\ [151, 151, -2/3*w^3 - 4/3*w^2 + 14/3*w + 5],\ [151, 151, 2/3*w^3 - 8/3*w^2 - 2/3*w + 9],\ [169, 13, -2/3*w^3 - 1/3*w^2 + 11/3*w],\ [169, 13, -2/3*w^3 + 5/3*w^2 + 5/3*w - 7],\ [179, 179, 4/3*w^3 - 7/3*w^2 - 13/3*w + 6],\ [179, 179, -4/3*w^3 + 1/3*w^2 + 19/3*w + 1],\ [181, 181, 5/3*w^3 - 8/3*w^2 - 20/3*w + 5],\ [181, 181, -1/3*w^3 + 1/3*w^2 + 10/3*w - 1],\ [181, 181, -4/3*w^3 + 1/3*w^2 + 16/3*w + 3],\ [191, 191, w^2 - 3*w - 1],\ [191, 191, -1/3*w^3 + 4/3*w^2 + 10/3*w - 3],\ [199, 199, -w^3 + 3*w^2 + w - 7],\ [199, 199, -4/3*w^3 + 1/3*w^2 + 19/3*w - 1],\ [211, 211, -1/3*w^3 - 5/3*w^2 + 4/3*w + 8],\ [211, 211, w^3 - 3*w^2 - 4*w + 8],\ [229, 229, -4/3*w^3 + 4/3*w^2 + 13/3*w - 4],\ [229, 229, -5/3*w^3 + 5/3*w^2 + 23/3*w - 5],\ [229, 229, 1/3*w^3 - 7/3*w^2 + 2/3*w + 10],\ [229, 229, -2/3*w^3 + 2/3*w^2 + 2/3*w - 3],\ [239, 239, 4/3*w^3 - 1/3*w^2 - 19/3*w - 2],\ [239, 239, -2/3*w^3 + 2/3*w^2 + 11/3*w - 6],\ [251, 251, 2*w^2 - w - 8],\ [251, 251, -1/3*w^3 - 2/3*w^2 + 7/3*w - 2],\ [251, 251, 1/3*w^3 - 4/3*w^2 - 1/3*w + 9],\ [251, 251, -1/3*w^3 + 7/3*w^2 + 1/3*w - 7],\ [269, 269, -5/3*w^3 + 8/3*w^2 + 17/3*w - 8],\ [269, 269, -5/3*w^3 + 11/3*w^2 + 17/3*w - 12],\ [271, 271, 1/3*w^3 + 2/3*w^2 - 13/3*w - 3],\ [271, 271, 1/3*w^3 + 2/3*w^2 - 13/3*w - 2],\ [311, 311, -1/3*w^3 + 7/3*w^2 - 5/3*w - 8],\ [311, 311, -w^3 + 5*w - 1],\ [331, 331, -2/3*w^3 - 1/3*w^2 + 8/3*w + 6],\ [331, 331, -w^3 + 2*w^2 + 4*w - 2],\ [349, 349, -w^3 + 2*w^2 + w + 1],\ [349, 349, 1/3*w^3 - 1/3*w^2 - 7/3*w - 4],\ [349, 349, -4/3*w^3 + 13/3*w^2 + 10/3*w - 11],\ [349, 349, w - 5],\ [361, 19, -4/3*w^3 + 4/3*w^2 + 16/3*w - 3],\ [379, 379, 7/3*w^3 - 1/3*w^2 - 43/3*w - 9],\ [379, 379, 2*w^3 - 3*w^2 - 9*w + 8],\ [401, 401, 1/3*w^3 + 2/3*w^2 - 7/3*w - 8],\ [401, 401, -1/3*w^3 + 10/3*w^2 - 2/3*w - 15],\ [401, 401, -4/3*w^3 + 4/3*w^2 + 13/3*w - 3],\ [401, 401, -1/3*w^3 + 4/3*w^2 - 5/3*w + 3],\ [409, 409, -5/3*w^3 + 8/3*w^2 + 20/3*w - 7],\ [409, 409, 4/3*w^3 - 1/3*w^2 - 16/3*w - 1],\ [419, 419, 4/3*w^3 - 16/3*w^2 - 1/3*w + 10],\ [419, 419, 5/3*w^3 + 7/3*w^2 - 35/3*w - 17],\ [421, 421, -2*w^3 + 4*w^2 + 7*w - 10],\ [421, 421, -5/3*w^3 + 8/3*w^2 + 29/3*w - 7],\ [421, 421, 1/3*w^3 + 2/3*w^2 + 5/3*w - 4],\ [421, 421, -5/3*w^3 - 1/3*w^2 + 23/3*w + 5],\ [431, 431, -2/3*w^3 + 5/3*w^2 + 11/3*w - 1],\ [431, 431, -w^2 - w + 8],\ [439, 439, -2/3*w^3 + 11/3*w^2 - 1/3*w - 8],\ [439, 439, -2/3*w^3 + 11/3*w^2 + 8/3*w - 15],\ [479, 479, w^3 + 2*w^2 - 6*w - 10],\ [479, 479, -5/3*w^3 + 5/3*w^2 + 14/3*w],\ [479, 479, -5/3*w^3 + 5/3*w^2 + 23/3*w - 3],\ [479, 479, -4/3*w^3 + 4/3*w^2 + 13/3*w - 2],\ [521, 521, -w^3 + 2*w^2 + 5*w + 1],\ [521, 521, 1/3*w^3 + 2/3*w^2 - 1/3*w - 10],\ [541, 541, 1/3*w^3 + 5/3*w^2 + 2/3*w - 7],\ [541, 541, 5/3*w^3 - 5/3*w^2 - 26/3*w],\ [569, 569, -w - 5],\ [569, 569, 1/3*w^3 - 1/3*w^2 - 7/3*w + 6],\ [571, 571, w^3 - 4*w - 8],\ [571, 571, -1/3*w^3 + 7/3*w^2 + 7/3*w - 4],\ [599, 599, 5/3*w^3 - 5/3*w^2 - 14/3*w + 4],\ [599, 599, -4/3*w^3 + 13/3*w^2 + 13/3*w - 15],\ [599, 599, 2*w^3 - 3*w^2 - 8*w + 5],\ [599, 599, 7/3*w^3 - 7/3*w^2 - 34/3*w + 6],\ [601, 601, -4/3*w^3 + 13/3*w^2 + 13/3*w - 13],\ [601, 601, -w^3 + 8*w + 5],\ [619, 619, -5/3*w^3 + 11/3*w^2 + 17/3*w - 13],\ [619, 619, 4/3*w^3 + 2/3*w^2 - 19/3*w - 2],\ [631, 631, w^3 - w^2 - 7*w + 1],\ [631, 631, 3*w - 2],\ [641, 641, -2/3*w^3 + 5/3*w^2 + 2/3*w - 7],\ [641, 641, -1/3*w^3 + 7/3*w^2 - 5/3*w - 9],\ [661, 661, -5/3*w^3 + 11/3*w^2 + 20/3*w - 9],\ [661, 661, w^3 + w^2 - 4*w - 7],\ [691, 691, -5/3*w^3 + 8/3*w^2 + 17/3*w - 6],\ [691, 691, 2*w^2 - 3*w - 10],\ [691, 691, 5/3*w^3 - 2/3*w^2 - 23/3*w - 1],\ [691, 691, 1/3*w^3 + 5/3*w^2 - 13/3*w - 3],\ [701, 701, 2/3*w^3 + 4/3*w^2 - 20/3*w - 11],\ [701, 701, -2/3*w^3 - 1/3*w^2 + 17/3*w + 9],\ [709, 709, -2/3*w^3 - 7/3*w^2 + 17/3*w + 11],\ [709, 709, -1/3*w^3 + 10/3*w^2 - 2/3*w - 8],\ [709, 709, -2/3*w^3 + 11/3*w^2 - 1/3*w - 10],\ [709, 709, 3*w^2 - 2*w - 14],\ [719, 719, 7/3*w^3 + 8/3*w^2 - 46/3*w - 21],\ [719, 719, -2*w^3 + 7*w^2 + 2*w - 13],\ [719, 719, 2/3*w^3 + 7/3*w^2 - 14/3*w - 9],\ [719, 719, -w^3 + 4*w^2 + 2*w - 13],\ [761, 761, 1/3*w^3 + 5/3*w^2 - 1/3*w - 8],\ [761, 761, 5/3*w^3 - 2/3*w^2 - 14/3*w + 1],\ [761, 761, -8/3*w^3 + 11/3*w^2 + 38/3*w - 11],\ [761, 761, -4/3*w^3 + 10/3*w^2 + 19/3*w - 9],\ [809, 809, -2/3*w^3 + 11/3*w^2 + 5/3*w - 15],\ [809, 809, 3*w^2 - w - 8],\ [811, 811, 2/3*w^3 + 7/3*w^2 - 14/3*w - 11],\ [811, 811, 1/3*w^3 + 8/3*w^2 - 13/3*w - 10],\ [811, 811, 1/3*w^3 - 10/3*w^2 + 5/3*w + 11],\ [811, 811, -w^3 + 4*w^2 + 2*w - 11],\ [821, 821, 2*w^3 - w^2 - 12*w - 5],\ [821, 821, 1/3*w^3 + 5/3*w^2 - 7/3*w - 14],\ [829, 829, -2/3*w^3 + 11/3*w^2 + 5/3*w - 10],\ [829, 829, 3*w^2 - w - 13],\ [839, 839, 4/3*w^3 - 1/3*w^2 - 25/3*w + 1],\ [839, 839, -2/3*w^3 + 5/3*w^2 - 1/3*w - 6],\ [841, 29, 5/3*w^3 - 5/3*w^2 - 20/3*w + 1],\ [841, 29, -5/3*w^3 + 5/3*w^2 + 20/3*w - 4],\ [859, 859, -1/3*w^3 - 8/3*w^2 + 13/3*w + 11],\ [859, 859, -1/3*w^3 + 10/3*w^2 - 5/3*w - 10],\ [859, 859, 2/3*w^3 - 8/3*w^2 + 1/3*w + 9],\ [859, 859, -2/3*w^3 + 5/3*w^2 + 2/3*w - 8],\ [881, 881, -4/3*w^3 + 16/3*w^2 + 4/3*w - 11],\ [881, 881, 1/3*w^3 - 13/3*w^2 - 4/3*w + 18],\ [911, 911, -1/3*w^3 + 10/3*w^2 + 1/3*w - 14],\ [911, 911, -1/3*w^3 + 10/3*w^2 + 1/3*w - 9],\ [929, 929, 4/3*w^3 - 7/3*w^2 - 22/3*w + 4],\ [929, 929, 1/3*w^3 + 2/3*w^2 + 2/3*w - 6],\ [961, 31, 5/3*w^3 - 5/3*w^2 - 20/3*w + 2],\ [971, 971, -2/3*w^3 + 11/3*w^2 + 2/3*w - 13],\ [971, 971, 1/3*w^3 + 8/3*w^2 - 10/3*w - 9],\ [991, 991, -4/3*w^3 + 10/3*w^2 + 16/3*w - 17],\ [991, 991, -2*w^3 + 4*w^2 + 11*w - 11]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^4 + 2*x^3 - 15*x^2 - 28*x - 5 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 1/6*e^3 - 3*e - 13/6, -1/3*e^3 - 1/2*e^2 + 11/2*e + 29/6, -e - 1, -1/3*e^3 + 4*e - 5/3, 1/3*e^3 - 5*e - 10/3, 1/2*e^3 + 1/2*e^2 - 15/2*e - 7, -2/3*e^3 - 1/2*e^2 + 19/2*e + 31/6, 1/6*e^3 + 1/2*e^2 - 5/2*e - 17/3, 1, 1/2*e^2 + 1/2*e - 9/2, 1/6*e^3 + 1/2*e^2 - 3/2*e - 29/3, 1/6*e^3 - e + 47/6, -1/2*e^3 - 1/2*e^2 + 13/2*e + 2, -1/6*e^3 - e^2 + 2*e + 13/6, -3/2*e^3 - e^2 + 23*e + 37/2, 2/3*e^3 + e^2 - 9*e - 44/3, -1/6*e^3 + 1/2*e^2 + 5/2*e - 1/3, -1/2*e^3 - e^2 + 5*e + 9/2, 1/2*e^2 + 3/2*e - 23/2, 5/6*e^3 + e^2 - 10*e - 53/6, 1/2*e^3 + e^2 - 8*e - 33/2, 1/2*e^3 - 6*e - 21/2, -1/2*e^2 + 1/2*e + 17/2, 2/3*e^3 - 11*e - 5/3, -5/6*e^3 - 1/2*e^2 + 25/2*e + 37/3, 1/6*e^3 - 1/2*e^2 - 1/2*e + 40/3, -5/6*e^3 + 1/2*e^2 + 25/2*e - 20/3, -2/3*e^3 - 1/2*e^2 + 21/2*e - 17/6, 5/6*e^3 + 1/2*e^2 - 31/2*e - 37/3, -e^3 - 3/2*e^2 + 25/2*e + 23/2, 5/6*e^3 - 12*e - 5/6, -2*e^3 - 5/2*e^2 + 55/2*e + 47/2, 1/6*e^3 - 4*e - 85/6, e^2 - e - 10, -4/3*e^3 - 2*e^2 + 21*e + 70/3, -e^3 - 3/2*e^2 + 29/2*e + 35/2, e^3 + e^2 - 11*e - 6, 1/2*e^3 + 2*e^2 - 7*e - 33/2, 1/3*e^3 + e^2 - 9*e - 46/3, e^3 + 1/2*e^2 - 35/2*e - 43/2, 5/3*e^3 + e^2 - 30*e - 56/3, 7/3*e^3 + 2*e^2 - 37*e - 82/3, -1/2*e^3 + 1/2*e^2 + 21/2*e - 3, 2/3*e^3 - 3/2*e^2 - 15/2*e + 77/6, 1/3*e^3 + 1/2*e^2 - 7/2*e + 31/6, -5/6*e^3 - e^2 + 14*e - 13/6, -1/3*e^3 + 1/2*e^2 + 13/2*e - 79/6, 5/3*e^3 + 7/2*e^2 - 55/2*e - 193/6, -e^2 + 11, -1/2*e^2 - 5/2*e + 17/2, 2/3*e^3 + 2*e^2 - 13*e - 71/3, 4/3*e^3 + 3/2*e^2 - 49/2*e - 155/6, 7/6*e^3 + e^2 - 21*e - 85/6, 7/6*e^3 + 3/2*e^2 - 35/2*e - 47/3, -11/6*e^3 - 7/2*e^2 + 51/2*e + 85/3, -1/3*e^3 - 3/2*e^2 + 3/2*e + 83/6, -3/2*e^3 - 5/2*e^2 + 39/2*e + 22, -1/2*e^3 + e^2 + 5*e - 23/2, 5/6*e^3 - 1/2*e^2 - 29/2*e + 2/3, 7/6*e^3 + 1/2*e^2 - 39/2*e - 32/3, -11/6*e^3 - 5/2*e^2 + 49/2*e + 100/3, -1/2*e^3 - e^2 + 11*e + 25/2, 2/3*e^3 - 2*e^2 - 10*e + 19/3, -1/3*e^3 + 9*e - 53/3, -e^3 - 2*e^2 + 18*e + 26, 2/3*e^3 + e^2 - 11*e - 68/3, -7/6*e^3 - 3/2*e^2 + 31/2*e + 71/3, -4/3*e^3 - 7/2*e^2 + 53/2*e + 245/6, 5/6*e^3 - 1/2*e^2 - 23/2*e - 28/3, -5/2*e^3 - 4*e^2 + 41*e + 81/2, 4/3*e^3 + 3*e^2 - 21*e - 76/3, 3/2*e^2 + 3/2*e - 13/2, -4/3*e^3 - e^2 + 28*e + 49/3, -5/3*e^3 - 4*e^2 + 26*e + 104/3, 2/3*e^3 + 7/2*e^2 - 23/2*e - 157/6, 1/3*e^3 - 3*e^2 - e + 116/3, 7/6*e^3 + 1/2*e^2 - 33/2*e - 14/3, -11/6*e^3 + 1/2*e^2 + 45/2*e - 23/3, -7/6*e^3 - 1/2*e^2 + 29/2*e + 23/3, 1/2*e^3 + 1/2*e^2 - 5/2*e - 5, 3/2*e^3 + 3*e^2 - 20*e - 43/2, 1/3*e^3 + 2*e^2 - e - 46/3, -e^3 - 3*e^2 + 17*e + 25, 1/6*e^3 - e^2 - 9*e + 59/6, -4/3*e^3 - 9/2*e^2 + 39/2*e + 215/6, 8/3*e^3 + 5*e^2 - 39*e - 140/3, -2/3*e^3 + 11*e - 28/3, -7/3*e^3 - e^2 + 36*e + 91/3, -e^3 + e^2 + 17*e - 8, 5/3*e^3 + 3*e^2 - 17*e - 125/3, -7/6*e^3 + 17*e + 49/6, -5/3*e^3 - 3*e^2 + 21*e + 95/3, 5/2*e^3 + 2*e^2 - 35*e - 83/2, -11/6*e^3 - e^2 + 31*e + 83/6, -e^3 - e^2 + 13*e - 4, 7/3*e^3 + 3*e^2 - 35*e - 142/3, 7/3*e^3 + 3/2*e^2 - 65/2*e - 23/6, -2/3*e^3 + 2*e^2 + 11*e - 64/3, -7/3*e^3 - e^2 + 39*e + 70/3, e^3 + 7/2*e^2 - 25/2*e - 49/2, 7/6*e^3 + 3/2*e^2 - 39/2*e - 2/3, -7/3*e^3 - 2*e^2 + 38*e + 37/3, -4/3*e^3 - 2*e^2 + 21*e + 55/3, -e^3 + e^2 + 26*e - 11, e^3 + e^2 - 14*e + 7, 2/3*e^3 + e^2 - 14*e - 47/3, -11/6*e^3 - 3/2*e^2 + 51/2*e + 49/3, 11/6*e^3 + 5/2*e^2 - 43/2*e - 100/3, -7/2*e^2 - 9/2*e + 63/2, -7/6*e^3 + 2*e^2 + 16*e - 83/6, 7/2*e^3 + 9/2*e^2 - 93/2*e - 41, -1/3*e^3 + 3/2*e^2 + 23/2*e - 205/6, 1/2*e^3 + 7/2*e^2 - 29/2*e - 35, 4*e^3 + 2*e^2 - 57*e - 41, 14/3*e^3 + 9/2*e^2 - 121/2*e - 307/6, -5/2*e^3 - 3*e^2 + 48*e + 87/2, -5/6*e^3 + e^2 + 11*e + 5/6, -19/6*e^3 - 2*e^2 + 45*e + 127/6, 1/6*e^3 - 3*e^2 - 7*e + 233/6, -1/2*e^3 + 2*e^2 + 6*e - 1/2, -3/2*e^3 - e^2 + 23*e + 87/2, e^3 - 1/2*e^2 - 29/2*e - 37/2, -11/6*e^3 - 5/2*e^2 + 65/2*e + 79/3, 9/2*e^3 + 9/2*e^2 - 125/2*e - 59, 3/2*e^3 - 30*e - 23/2, 13/6*e^3 + 5*e^2 - 33*e - 307/6, -1/3*e^3 - 7/2*e^2 + 17/2*e + 311/6, 7/6*e^3 + e^2 - 28*e - 115/6, -e^3 + 3/2*e^2 + 37/2*e - 19/2, -7/6*e^3 - 2*e^2 + 28*e + 205/6, 19/6*e^3 + 11/2*e^2 - 101/2*e - 173/3, 1/3*e^3 - 16*e - 19/3, 5/2*e^3 + e^2 - 33*e - 33/2, 3/2*e^3 - 16*e + 9/2, 3/2*e^3 - 2*e^2 - 14*e + 49/2, 7/3*e^3 + 3/2*e^2 - 77/2*e - 95/6, -3/2*e^3 - 2*e^2 + 19*e + 1/2, -13/6*e^3 - 4*e^2 + 30*e + 199/6, 5/2*e^3 + 1/2*e^2 - 61/2*e - 8, 17/6*e^3 - e^2 - 37*e + 19/6, 1/3*e^3 - 2*e^2 - 9*e - 13/3, -7/6*e^3 - 3*e^2 + 19*e + 91/6, 3*e^3 + 11/2*e^2 - 83/2*e - 117/2, 1/2*e^3 - 5/2*e^2 - 25/2*e + 16, -5/6*e^3 - 1/2*e^2 + 21/2*e + 13/3, 7/6*e^3 - e^2 - 16*e + 95/6, -5*e - 5, e^3 + 7/2*e^2 - 37/2*e - 57/2, -1/2*e^3 - 4*e^2 + 9*e + 53/2, -1/3*e^3 + e^2 + 2*e - 71/3, 4/3*e^3 - 25*e + 20/3, -17/6*e^3 - 1/2*e^2 + 87/2*e + 133/3, -10/3*e^3 - 9/2*e^2 + 109/2*e + 401/6, 4/3*e^3 - 5/2*e^2 - 31/2*e + 175/6, -1/2*e^3 - 2*e^2 + 6*e + 95/2, -3/2*e^3 - 4*e^2 + 23*e + 43/2, 17/6*e^3 + 5/2*e^2 - 83/2*e - 181/3, -7/3*e^3 - 9/2*e^2 + 73/2*e + 305/6, 4/3*e^3 - 5/2*e^2 - 33/2*e + 43/6, 11/2*e^3 + 7/2*e^2 - 173/2*e - 73, 17/6*e^3 + 2*e^2 - 47*e - 275/6] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([41, 41, -1/3*w^3 + 4/3*w^2 + 7/3*w - 6])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]