/* 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([44, 14, -13, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([5,5,1/2*w^3 + 1/2*w^2 - 6*w - 9]) primes_array = [ [4, 2, w^2 - 2*w - 6],\ [4, 2, -w^2 + 7],\ [5, 5, -1/2*w^3 + 2*w^2 + 7/2*w - 14],\ [5, 5, 1/2*w^3 + 1/2*w^2 - 6*w - 9],\ [11, 11, 1/2*w^3 - 2*w^2 - 5/2*w + 11],\ [11, 11, 1/2*w^3 + 1/2*w^2 - 5*w - 7],\ [31, 31, 1/2*w^2 + 1/2*w - 4],\ [31, 31, -1/2*w^2 + 3/2*w + 3],\ [41, 41, 1/2*w^2 + 1/2*w - 6],\ [41, 41, 2*w^3 - 15/2*w^2 - 25/2*w + 50],\ [41, 41, 5/2*w^2 - 1/2*w - 17],\ [41, 41, 1/2*w^2 - 3/2*w - 5],\ [61, 61, -1/2*w^3 + w^2 + 7/2*w - 1],\ [61, 61, -1/2*w^3 + 1/2*w^2 + 4*w - 3],\ [71, 71, 1/2*w^3 + w^2 - 11/2*w - 13],\ [71, 71, -1/2*w^3 + 5/2*w^2 + 2*w - 17],\ [81, 3, -3],\ [89, 89, -w^3 + 3/2*w^2 + 13/2*w - 9],\ [89, 89, w^3 - 7/2*w^2 - 11/2*w + 20],\ [89, 89, -w^3 - 1/2*w^2 + 19/2*w + 12],\ [89, 89, 1/2*w^3 + 2*w^2 - 17/2*w - 19],\ [109, 109, 1/2*w^3 + 3/2*w^2 - 7*w - 15],\ [109, 109, -1/2*w^3 + 1/2*w^2 + 4*w - 5],\ [121, 11, -3/2*w^2 + 3/2*w + 10],\ [131, 131, 3/2*w^3 - 13/2*w^2 - 9*w + 43],\ [131, 131, -3/2*w^3 - 2*w^2 + 35/2*w + 29],\ [139, 139, -3/2*w^3 + 11/2*w^2 + 10*w - 39],\ [139, 139, 1/2*w^3 + w^2 - 11/2*w - 9],\ [139, 139, -1/2*w^3 + 5/2*w^2 + 2*w - 13],\ [139, 139, -3/2*w^3 - w^2 + 33/2*w + 25],\ [151, 151, -1/2*w^3 + 3/2*w^2 + 3*w - 5],\ [151, 151, -1/2*w^3 + 9/2*w + 1],\ [179, 179, 5/2*w^2 - 3/2*w - 20],\ [179, 179, -w^3 + 5/2*w^2 + 11/2*w - 5],\ [179, 179, -w^3 + 1/2*w^2 + 15/2*w - 2],\ [179, 179, w^3 + 1/2*w^2 - 19/2*w - 10],\ [181, 181, 1/2*w^2 - 3/2*w - 8],\ [181, 181, 3/2*w^2 - 1/2*w - 13],\ [181, 181, -3/2*w^2 + 5/2*w + 12],\ [181, 181, 1/2*w^2 + 1/2*w - 9],\ [191, 191, w^3 + 1/2*w^2 - 17/2*w - 9],\ [191, 191, 1/2*w^3 - w^2 - 5/2*w + 8],\ [199, 199, -1/2*w^3 + 7/2*w^2 + 3*w - 23],\ [199, 199, -1/2*w^3 - 2*w^2 + 17/2*w + 17],\ [211, 211, w^3 - 5/2*w^2 - 9/2*w + 3],\ [211, 211, -w^3 + 1/2*w^2 + 13/2*w - 3],\ [229, 229, 3/2*w^3 - 2*w^2 - 21/2*w - 6],\ [229, 229, -w^3 + 3*w^2 + 8*w - 23],\ [239, 239, -w^3 + 3*w^2 + 4*w - 9],\ [239, 239, w^3 - 9*w - 7],\ [239, 239, 1/2*w^3 - 3/2*w^2 - 2*w + 13],\ [239, 239, -w^3 + 7*w + 3],\ [241, 241, 1/2*w^3 + 2*w^2 - 15/2*w - 16],\ [241, 241, -1/2*w^3 + 7/2*w^2 + 2*w - 21],\ [251, 251, w^3 - 5/2*w^2 - 9/2*w + 10],\ [251, 251, w^3 - 9*w - 9],\ [269, 269, w^3 - 1/2*w^2 - 17/2*w - 10],\ [269, 269, w^3 - 5/2*w^2 - 13/2*w + 18],\ [281, 281, -1/2*w^3 + 3*w^2 + 3/2*w - 19],\ [281, 281, 1/2*w^3 + 3/2*w^2 - 6*w - 15],\ [289, 17, w^3 - 3/2*w^2 - 15/2*w - 1],\ [289, 17, -w^3 + 3/2*w^2 + 15/2*w - 9],\ [331, 331, 3/2*w^2 - 1/2*w - 14],\ [331, 331, -3/2*w^2 + 5/2*w + 13],\ [349, 349, -w^3 + 3/2*w^2 + 11/2*w - 1],\ [349, 349, w^3 - 5/2*w^2 - 13/2*w + 14],\ [359, 359, -w^3 + 5/2*w^2 + 11/2*w - 14],\ [359, 359, w^3 - 1/2*w^2 - 15/2*w - 7],\ [361, 19, 2*w^2 - 2*w - 15],\ [361, 19, -2*w^2 + 2*w + 13],\ [379, 379, 5/2*w^2 - 3/2*w - 16],\ [379, 379, 5/2*w^2 - 7/2*w - 15],\ [389, 389, 7/2*w^2 - 1/2*w - 26],\ [389, 389, 1/2*w^3 - 3/2*w^2 - 5*w + 5],\ [389, 389, 1/2*w^3 + 2*w^2 - 11/2*w - 18],\ [389, 389, 3/2*w^3 - 1/2*w^2 - 13*w - 15],\ [409, 409, -w^3 + 7/2*w^2 + 9/2*w - 19],\ [409, 409, w^3 + 1/2*w^2 - 17/2*w - 12],\ [439, 439, -1/2*w^3 + 5/2*w^2 + w - 15],\ [439, 439, 1/2*w^3 + w^2 - 9/2*w - 12],\ [461, 461, 1/2*w^3 + 2*w^2 - 15/2*w - 18],\ [461, 461, -1/2*w^3 + 7/2*w^2 + 2*w - 23],\ [479, 479, -1/2*w^3 + 2*w^2 + 7/2*w - 10],\ [479, 479, 1/2*w^3 - 2*w^2 - 5/2*w + 7],\ [491, 491, -2*w^3 + 1/2*w^2 + 29/2*w - 1],\ [491, 491, 2*w^3 - 11/2*w^2 - 19/2*w + 12],\ [499, 499, -w^3 + 5/2*w^2 + 13/2*w - 13],\ [499, 499, w^3 - 1/2*w^2 - 17/2*w - 5],\ [509, 509, -w^3 + 3/2*w^2 + 15/2*w - 2],\ [509, 509, w^3 - 3/2*w^2 - 15/2*w + 6],\ [521, 521, -1/2*w^3 + 2*w^2 + 9/2*w - 15],\ [521, 521, 1/2*w^3 + 1/2*w^2 - 7*w - 9],\ [529, 23, -w^3 + 2*w^2 + 5*w - 9],\ [529, 23, -3/2*w^2 + 7/2*w + 12],\ [541, 541, 3/2*w^3 + 1/2*w^2 - 14*w - 17],\ [541, 541, -3/2*w^3 + 5*w^2 + 17/2*w - 29],\ [569, 569, -2*w^3 + 1/2*w^2 + 35/2*w + 18],\ [569, 569, -w^3 - 5/2*w^2 + 27/2*w + 27],\ [571, 571, -w^3 + w^2 + 8*w + 7],\ [571, 571, -1/2*w^3 + 2*w^2 + 3/2*w - 4],\ [571, 571, 1/2*w^3 + 1/2*w^2 - 4*w - 1],\ [571, 571, -4*w^3 - 7/2*w^2 + 91/2*w + 68],\ [599, 599, -1/2*w^3 - 5/2*w^2 + 10*w + 21],\ [599, 599, 2*w^3 + 5/2*w^2 - 47/2*w - 37],\ [599, 599, 2*w^3 - 17/2*w^2 - 25/2*w + 56],\ [599, 599, -1/2*w^3 + 4*w^2 + 7/2*w - 28],\ [601, 601, -w^3 - 3/2*w^2 + 23/2*w + 18],\ [601, 601, 1/2*w^3 + 7/2*w^2 - 5*w - 27],\ [601, 601, 1/2*w^3 - 5*w^2 + 7/2*w + 28],\ [601, 601, 2*w^3 - 3*w^2 - 13*w + 21],\ [619, 619, -w^3 + 5/2*w^2 + 9/2*w - 8],\ [619, 619, w^3 - 1/2*w^2 - 13/2*w - 2],\ [631, 631, -5/2*w^3 + 1/2*w^2 + 18*w - 1],\ [631, 631, -5/2*w^3 + 7*w^2 + 23/2*w - 15],\ [641, 641, 5/2*w^2 - 1/2*w - 20],\ [641, 641, -5/2*w^2 + 9/2*w + 18],\ [659, 659, w^3 - 7/2*w^2 - 15/2*w + 28],\ [659, 659, w^3 + 2*w^2 - 11*w - 21],\ [661, 661, -w^3 + 15/2*w^2 + 11/2*w - 52],\ [661, 661, -3/2*w^3 + 1/2*w^2 + 13*w + 5],\ [661, 661, 3/2*w^3 - 4*w^2 - 19/2*w + 17],\ [661, 661, -w^3 - 9/2*w^2 + 35/2*w + 40],\ [691, 691, 2*w^3 - 9/2*w^2 - 21/2*w + 5],\ [691, 691, -5/2*w^3 - w^2 + 55/2*w + 37],\ [701, 701, w^3 - 2*w^2 - 7*w + 3],\ [701, 701, w^3 - w^2 - 8*w + 5],\ [709, 709, -11/2*w^2 + 3/2*w + 40],\ [709, 709, -3/2*w^3 - 3/2*w^2 + 16*w + 23],\ [739, 739, 1/2*w^3 - 9/2*w^2 + 3*w + 25],\ [739, 739, 1/2*w^3 + 3*w^2 - 9/2*w - 24],\ [751, 751, -7/2*w^3 + 12*w^2 + 47/2*w - 83],\ [751, 751, -3/2*w^3 + 23/2*w + 3],\ [751, 751, -3/2*w^3 + 9/2*w^2 + 7*w - 13],\ [751, 751, 7/2*w^3 + 3/2*w^2 - 37*w - 51],\ [761, 761, -3/2*w^3 - 1/2*w^2 + 14*w + 19],\ [761, 761, -w^3 + 3/2*w^2 + 15/2*w - 4],\ [761, 761, -3/2*w^3 + 5*w^2 + 17/2*w - 31],\ [769, 769, -3*w^3 - 5/2*w^2 + 69/2*w + 51],\ [769, 769, -1/2*w^3 - 4*w^2 + 9/2*w + 27],\ [769, 769, -w^3 - 5/2*w^2 + 29/2*w + 25],\ [769, 769, 3*w^3 - 23/2*w^2 - 41/2*w + 80],\ [809, 809, 1/2*w^3 + 2*w^2 - 13/2*w - 17],\ [809, 809, 1/2*w^3 - 7/2*w^2 - w + 21],\ [821, 821, 1/2*w^3 - 1/2*w^2 - 6*w + 3],\ [821, 821, -1/2*w^3 + w^2 + 11/2*w - 3],\ [829, 829, -3/2*w^3 + 3*w^2 + 23/2*w - 10],\ [829, 829, -w^3 + 2*w^2 + 5*w + 1],\ [829, 829, 7/2*w^2 - 3/2*w - 28],\ [829, 829, 3/2*w^3 - 3/2*w^2 - 13*w + 3],\ [839, 839, -w^3 - 7/2*w^2 + 17/2*w + 27],\ [839, 839, 2*w^3 + 1/2*w^2 - 43/2*w - 27],\ [839, 839, 2*w^3 - 13/2*w^2 - 29/2*w + 46],\ [839, 839, -w^3 - 3/2*w^2 + 19/2*w + 14],\ [841, 29, 5/2*w^2 - 5/2*w - 19],\ [841, 29, 5/2*w^2 - 5/2*w - 16],\ [859, 859, 1/2*w^3 + w^2 - 5/2*w - 12],\ [859, 859, w^3 + 3/2*w^2 - 19/2*w - 19],\ [859, 859, -w^3 + 9/2*w^2 + 7/2*w - 26],\ [859, 859, 1/2*w^3 - 5/2*w^2 + w + 13],\ [881, 881, -1/2*w^3 + 1/2*w^2 + 6*w + 1],\ [881, 881, 1/2*w^3 - w^2 - 11/2*w + 7],\ [911, 911, -1/2*w^3 + 5/2*w^2 + 3*w - 13],\ [911, 911, 1/2*w^3 + w^2 - 13/2*w - 8],\ [941, 941, -2*w^3 + 7/2*w^2 + 27/2*w - 21],\ [941, 941, 3/2*w^3 - 7*w^2 - 21/2*w + 51],\ [941, 941, 3/2*w^3 + 5/2*w^2 - 20*w - 35],\ [941, 941, -2*w^3 + 13/2*w^2 + 29/2*w - 48],\ [961, 31, -w^2 + w + 13],\ [1009, 1009, -5/2*w^2 - 1/2*w + 18],\ [1009, 1009, 3/2*w^3 - 3/2*w^2 - 12*w - 5],\ [1021, 1021, w^3 + w^2 - 10*w - 19],\ [1021, 1021, w^3 - 5/2*w^2 - 9/2*w + 12],\ [1031, 1031, -1/2*w^3 + 3/2*w^2 + 5*w - 9],\ [1031, 1031, -w^3 + 3/2*w^2 + 13/2*w - 2],\ [1049, 1049, -3/2*w^3 - 1/2*w^2 + 16*w + 23],\ [1049, 1049, -2*w^3 + 9/2*w^2 + 23/2*w - 6],\ [1049, 1049, -2*w^3 + 3/2*w^2 + 29/2*w - 8],\ [1049, 1049, 3/2*w^3 - 5*w^2 - 21/2*w + 37],\ [1051, 1051, -2*w^3 + 11/2*w^2 + 17/2*w - 10],\ [1051, 1051, -3*w^3 - 1/2*w^2 + 59/2*w + 36],\ [1051, 1051, -3*w^3 + 19/2*w^2 + 39/2*w - 62],\ [1051, 1051, 2*w^3 - 1/2*w^2 - 27/2*w + 2],\ [1061, 1061, 11/2*w^2 - 3/2*w - 38],\ [1061, 1061, 11/2*w^2 - 19/2*w - 34],\ [1069, 1069, 1/2*w^3 - 4*w^2 - 5/2*w + 25],\ [1069, 1069, 2*w^3 - 20*w - 25],\ [1069, 1069, -2*w^3 + 6*w^2 + 14*w - 43],\ [1069, 1069, 1/2*w^3 + 5/2*w^2 - 9*w - 19],\ [1109, 1109, -5/2*w^3 + 13/2*w^2 + 12*w - 13],\ [1109, 1109, -5/2*w^3 + w^2 + 35/2*w - 3],\ [1151, 1151, 13/2*w^2 - 3/2*w - 46],\ [1151, 1151, 1/2*w^3 + 3/2*w^2 - 5*w - 17],\ [1151, 1151, 1/2*w^3 - 3*w^2 - 1/2*w + 20],\ [1151, 1151, 13/2*w^2 - 23/2*w - 41],\ [1171, 1171, w^3 - 3/2*w^2 - 13/2*w + 12],\ [1171, 1171, 1/2*w^3 - 1/2*w^2 - 6*w + 1],\ [1171, 1171, -1/2*w^3 + w^2 + 11/2*w - 5],\ [1171, 1171, -1/2*w^3 + 5*w^2 - 7/2*w - 26],\ [1201, 1201, 1/2*w^3 + 1/2*w^2 - 6*w - 3],\ [1201, 1201, -1/2*w^3 + 2*w^2 + 7/2*w - 8],\ [1229, 1229, 1/2*w^3 + 5/2*w^2 - 8*w - 21],\ [1229, 1229, -1/2*w^3 + 4*w^2 + 3/2*w - 26],\ [1249, 1249, -w^3 + 7/2*w^2 + 9/2*w - 12],\ [1249, 1249, w^3 + 1/2*w^2 - 17/2*w - 5],\ [1279, 1279, 1/2*w^3 + 3/2*w^2 - 3*w - 15],\ [1279, 1279, -1/2*w^3 + 3*w^2 - 3/2*w - 16],\ [1289, 1289, 5/2*w^2 - 9/2*w - 19],\ [1289, 1289, w^3 - 9/2*w^2 - 15/2*w + 32],\ [1289, 1289, -w^3 - 3/2*w^2 + 27/2*w + 21],\ [1289, 1289, 5/2*w^2 - 1/2*w - 21],\ [1291, 1291, -1/2*w^3 + 5*w^2 - 9/2*w - 23],\ [1291, 1291, 1/2*w^3 + 7/2*w^2 - 4*w - 23],\ [1301, 1301, -3/2*w^3 + 2*w^2 + 21/2*w - 10],\ [1301, 1301, -3/2*w^3 + 5/2*w^2 + 10*w - 1],\ [1319, 1319, 4*w^3 - 29/2*w^2 - 49/2*w + 93],\ [1319, 1319, -4*w^3 - 5/2*w^2 + 83/2*w + 58],\ [1321, 1321, -17/2*w^2 + 31/2*w + 52],\ [1321, 1321, 17/2*w^2 - 3/2*w - 59],\ [1361, 1361, -3*w^3 - 7/2*w^2 + 71/2*w + 58],\ [1361, 1361, -3/2*w^3 - 3*w^2 + 39/2*w + 34],\ [1369, 37, 3/2*w^3 - 1/2*w^2 - 13*w - 17],\ [1369, 37, 3/2*w^3 + 1/2*w^2 - 11*w - 3],\ [1381, 1381, w^3 - 5*w^2 - 2*w + 27],\ [1381, 1381, w^3 + 2*w^2 - 9*w - 21],\ [1399, 1399, w^3 + 5/2*w^2 - 19/2*w - 25],\ [1399, 1399, w^3 - 11/2*w^2 - 3/2*w + 31],\ [1439, 1439, -2*w^3 + 13/2*w^2 + 23/2*w - 40],\ [1439, 1439, 4*w^3 + 3*w^2 - 43*w - 65],\ [1451, 1451, 1/2*w^3 + 9/2*w^2 - 5*w - 35],\ [1451, 1451, -1/2*w^3 + 6*w^2 - 11/2*w - 35],\ [1459, 1459, -3/2*w^3 + 9/2*w^2 + 9*w - 25],\ [1459, 1459, -3/2*w^3 + 1/2*w^2 + 10*w + 7],\ [1471, 1471, 3/2*w^3 - 11/2*w^2 - 7*w + 31],\ [1471, 1471, -3/2*w^3 - w^2 + 27/2*w + 20],\ [1489, 1489, -3*w^3 - 3*w^2 + 34*w + 51],\ [1489, 1489, 1/2*w^3 + 5/2*w^2 - 6*w - 25],\ [1489, 1489, -1/2*w^3 + 4*w^2 - 1/2*w - 28],\ [1489, 1489, 3*w^3 - 12*w^2 - 19*w + 79],\ [1499, 1499, 1/2*w^3 - 7/2*w^2 + 2*w + 19],\ [1499, 1499, 1/2*w^3 + 5/2*w^2 - 6*w - 21],\ [1499, 1499, -1/2*w^3 + 4*w^2 - 1/2*w - 24],\ [1499, 1499, -w^3 + 5/2*w^2 + 11/2*w - 17],\ [1511, 1511, -2*w^3 + 15/2*w^2 + 17/2*w - 37],\ [1511, 1511, -2*w^3 - 3/2*w^2 + 35/2*w + 23],\ [1531, 1531, 1/2*w^3 - 3*w^2 - 9/2*w + 16],\ [1531, 1531, -2*w^3 + 9/2*w^2 + 23/2*w - 8],\ [1531, 1531, -2*w^3 + 3/2*w^2 + 29/2*w - 6],\ [1531, 1531, w^3 + 5/2*w^2 - 21/2*w - 25],\ [1549, 1549, -1/2*w^3 + 1/2*w^2 + 3*w - 7],\ [1549, 1549, 1/2*w^3 - w^2 - 5/2*w - 4],\ [1579, 1579, w^3 + 3/2*w^2 - 19/2*w - 13],\ [1579, 1579, -w^3 + 9/2*w^2 + 7/2*w - 20],\ [1609, 1609, -11/2*w^2 + 1/2*w + 37],\ [1609, 1609, 11/2*w^2 - 21/2*w - 32],\ [1619, 1619, 1/2*w^3 - 3/2*w^2 - w + 15],\ [1619, 1619, w^3 - 3/2*w^2 - 21/2*w + 1],\ [1621, 1621, -2*w^3 + 15/2*w^2 + 23/2*w - 49],\ [1621, 1621, 1/2*w^3 + 3/2*w^2 - 9*w - 19],\ [1669, 1669, 1/2*w^3 + 5/2*w^2 - 7*w - 23],\ [1669, 1669, 1/2*w^3 - 4*w^2 - 1/2*w + 27],\ [1699, 1699, -w^3 + 1/2*w^2 + 17/2*w - 2],\ [1699, 1699, -w^3 + 5/2*w^2 + 13/2*w - 6],\ [1709, 1709, 1/2*w^3 + 3/2*w^2 - 2*w - 15],\ [1709, 1709, -1/2*w^3 + 3*w^2 - 5/2*w - 15],\ [1721, 1721, 5/2*w^3 - w^2 - 45/2*w - 20],\ [1721, 1721, -5/2*w^3 + 13/2*w^2 + 17*w - 41],\ [1741, 1741, -w^3 + 5/2*w^2 + 13/2*w - 3],\ [1741, 1741, -5/2*w^3 - 3*w^2 + 61/2*w + 48],\ [1741, 1741, -5*w^3 + 35/2*w^2 + 65/2*w - 116],\ [1741, 1741, -w^3 + 5*w^2 + 6*w - 31],\ [1759, 1759, 4*w^3 - 16*w^2 - 26*w + 111],\ [1759, 1759, 3*w^3 + 3/2*w^2 - 61/2*w - 43],\ [1789, 1789, w^3 + 1/2*w^2 - 17/2*w - 14],\ [1789, 1789, -w^3 + 7/2*w^2 + 9/2*w - 21],\ [1801, 1801, w^3 + 5/2*w^2 - 23/2*w - 24],\ [1801, 1801, w^3 + 11/2*w^2 - 15/2*w - 38],\ [1831, 1831, 13/2*w^2 - 1/2*w - 46],\ [1831, 1831, -3/2*w^3 + 8*w^2 + 19/2*w - 53],\ [1831, 1831, 9/2*w^3 - 33/2*w^2 - 28*w + 109],\ [1831, 1831, -13/2*w^2 + 25/2*w + 40],\ [1861, 1861, 5/2*w^2 - 9/2*w - 8],\ [1861, 1861, 5/2*w^2 - 1/2*w - 10],\ [1871, 1871, -1/2*w^3 - 1/2*w^2 + 7*w + 15],\ [1871, 1871, -1/2*w^3 - 4*w^2 + 7/2*w + 26],\ [1879, 1879, 1/2*w^3 - 9/2*w^2 - w + 25],\ [1879, 1879, -w^3 - 5/2*w^2 + 23/2*w + 27],\ [1879, 1879, w^3 - 11/2*w^2 - 7/2*w + 35],\ [1879, 1879, 1/2*w^3 + 3*w^2 - 17/2*w - 20],\ [1889, 1889, w^3 + 5/2*w^2 - 25/2*w - 27],\ [1889, 1889, -w^3 + 11/2*w^2 + 9/2*w - 36],\ [1901, 1901, -3*w^3 - w^2 + 32*w + 41],\ [1901, 1901, 3*w^3 - 10*w^2 - 21*w + 69],\ [1931, 1931, 2*w^3 - 15/2*w^2 - 13/2*w + 26],\ [1931, 1931, -w^3 + 11/2*w^2 + 5/2*w - 31],\ [1951, 1951, -w^3 + 1/2*w^2 + 13/2*w + 7],\ [1951, 1951, 2*w^2 - 19],\ [1979, 1979, -1/2*w^3 + 4*w^2 + 1/2*w - 25],\ [1979, 1979, 7/2*w^3 + w^2 - 73/2*w - 47],\ [1979, 1979, 7/2*w^3 - 23/2*w^2 - 24*w + 79],\ [1979, 1979, 1/2*w^3 + 5/2*w^2 - 7*w - 21],\ [1999, 1999, -w^3 + 15/2*w^2 + 11/2*w - 54],\ [1999, 1999, -w^3 + 15/2*w^2 - 9/2*w - 37]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, -3, -2, -1, 0, 4, -8, 0, -2, 10, -10, -2, 6, 14, 8, 12, -14, 6, -6, 6, -10, 18, 18, -10, 4, -20, 8, 8, 0, -12, 8, -8, 16, 0, -12, -16, 10, 14, 14, 2, 0, 0, 8, -16, 4, -24, 6, -6, 4, -16, -12, 20, -26, -10, -20, 12, 6, 2, 18, -6, 14, -2, 16, -4, 6, -14, 16, 0, 34, -26, 20, -20, 34, 6, 22, 26, 14, -6, -20, 20, 30, -2, -32, -12, -12, 12, -4, 4, 2, -30, 30, 22, -10, -30, 18, 26, 10, 46, -16, -28, 12, 44, -48, 32, -24, 0, -42, 46, -2, -14, -24, 20, -36, 8, 18, 26, 36, 20, 18, 26, 22, -10, -20, 8, 50, 30, -10, 2, -20, 4, 16, -20, 16, 40, 34, -10, -22, 14, -18, 26, -26, 46, 10, 10, -2, 2, 6, -22, -34, 0, -16, -16, -16, -22, 34, 36, -44, -20, 8, 14, 30, 12, 48, -30, 34, 18, 42, -42, 38, 10, 34, 50, 24, 48, 6, 38, -54, -42, -4, 12, -48, -12, 58, -22, 10, 30, -34, -14, -10, -10, 36, 32, -8, 48, -28, 12, 36, -28, -14, 30, 18, -26, 26, 14, 24, 20, -42, 22, -30, 50, -4, -12, -42, 2, 16, -48, -34, -38, 18, 42, 18, -58, -38, 22, 32, -16, -56, 64, -64, -36, -28, 4, 32, 12, 18, 14, 34, -18, -60, -4, -8, 12, 8, -16, -20, 20, 40, 56, -74, 62, 68, 28, -62, 26, 36, 0, 10, -14, 10, 26, -4, -20, 54, 58, -34, 30, 22, -50, 14, 46, 16, 24, 34, -46, 26, -26, -24, 40, -36, 64, -78, 50, 72, -24, -4, -56, 60, -44, -58, -38, -18, -38, 60, 28, 64, -44, -60, 44, -12, -20, -20, -32] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([5,5,1/2*w^3 + 1/2*w^2 - 6*w - 9])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]