/* 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([16, 2, 2]) 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^2 - x - 14 K. = NumberField(heckePol) hecke_eigenvalues_array = [1, 1, e, -e + 1, e + 1, -e + 2, 7, 7, 0, 4, 4, 0, e - 10, -e - 9, -e - 5, e - 6, -1, -e + 9, -2*e - 8, 2*e - 10, e + 8, -3*e + 7, 3*e + 4, -6, 3*e - 9, -3*e - 6, -8, 5*e - 3, -5*e + 2, -8, -2, -2, -e - 2, 5*e + 2, -5*e + 7, e - 3, -e + 8, e - 6, -e - 5, e + 7, 2*e + 11, -2*e + 13, -22, -22, 3*e + 1, -3*e + 4, -2*e, 2*e - 2, 5*e + 5, -4*e - 12, 4*e - 16, -5*e + 10, 4*e + 6, -4*e + 10, 2*e, -2*e + 2, -3*e + 9, 3*e + 6, -2*e + 24, 2*e + 22, -6*e - 4, 6*e - 10, -3*e - 1, 3*e - 4, 4*e - 2, -4*e + 2, e + 6, -e + 7, -20, -20, 4*e + 4, -4*e + 8, -3*e - 25, 4*e + 2, -4*e + 6, 3*e - 28, -e - 12, e - 13, 4*e + 12, -4*e + 16, 5*e - 2, -5*e + 3, -2*e + 13, 2*e + 11, -9*e + 9, 9*e, -3*e - 28, 3*e - 31, 22, 22, -2*e + 13, 2*e + 11, e + 3, -e + 4, 9*e - 11, -9*e - 2, 2*e - 10, -2*e - 8, -5*e - 2, -5*e + 14, 5*e + 9, 5*e - 7, -24, -32, -32, -24, 2*e - 14, -3*e + 7, 3*e + 4, -2*e - 12, -5*e + 3, 5*e - 2, 6*e + 19, -6*e + 25, -6*e - 13, 6*e - 19, -5*e + 8, 5*e + 3, 5*e + 13, -e + 46, e + 45, -5*e + 18, -4*e - 24, 4*e - 28, -2*e + 28, 2*e + 26, -e + 3, e + 2, e - 9, -e - 8, 8*e - 4, 8*e + 7, -8*e + 15, -8*e + 4, 3*e + 17, -8, -3*e + 20, 10*e - 16, -7*e + 11, 7*e + 4, -10*e - 6, 2*e + 38, -2*e + 40, 11*e, -11*e + 11, 7*e + 14, -5*e - 31, 5*e - 36, -7*e + 21, 12, 2*e - 41, -2*e - 39, 12, -24, 22, -20, -5*e - 28, 5*e - 33, -20, -4*e + 29, 4*e + 25, -e - 45, e - 46, -9*e + 29, -3*e + 38, 3*e + 35, 9*e + 20, -23, -3*e + 4, 3*e + 1, -e - 38, e - 39, 6*e - 37, -6*e - 31, 0, 6, 6, 0, 12*e - 20, 7*e - 10, -7*e - 3, -12*e - 8, 11*e - 10, -11*e + 1, 7*e - 8, 3*e + 38, -3*e + 41, -7*e - 1, e + 32, -e + 33, -11, 10*e, -10*e + 10, -11, e - 51, -5*e - 2, 5*e - 7, -e - 50, 3*e + 8, -3*e + 11, 2*e - 16, -2*e - 14, e - 16, -e - 15, 10*e + 17, -10*e + 27, -e + 16, 4*e - 6, -4*e - 2, e + 15, 11*e - 18, -11*e - 7, 2*e + 44, -2*e + 46, 2*e - 28, -2*e - 26, 2*e + 12, -2*e + 14, -4, -4, -5*e + 9, 5*e + 4, -5*e + 24, 5*e + 19, -6*e + 4, 6*e - 2, -8*e - 25, 8*e - 33, 19*e - 6, -19*e + 13, -4*e + 52, 4*e + 48, -10, -10, 6*e - 25, -6*e - 42, 6*e - 48, -6*e - 19, 3*e - 28, -4*e - 36, 4*e - 40, -3*e - 25, 2*e - 28, -2*e - 26, -5*e - 48, 4*e - 8, -4*e - 4, 5*e - 53, 11*e - 35, -11*e - 24, 6*e + 10, -6*e + 16, -12*e - 25, 12*e - 37, 5*e + 6, -5*e + 11, -5*e + 21, 5*e + 16, -11*e + 38, 11*e + 27, 3*e - 31, -3*e - 28, -5*e - 5, 5*e - 10, e, -e + 1, -4*e + 42, -9*e - 15, 9*e - 24, 4*e + 38, 5*e - 22, -5*e - 17, -6*e + 14, 6*e + 8, 7*e + 9, -7*e + 16, 8*e + 37, -2*e + 38, 2*e + 36, -8*e + 45, 16*e - 2, -16*e + 14, -14*e - 22, 14*e - 36, -6*e - 4, 4*e - 38, -4*e - 34, 6*e - 10, 16*e - 21, -16*e - 5, 3*e - 57, -3*e - 54, -11*e - 2, 11*e - 13, -12*e - 14, 12*e - 26, -11*e - 10, 17*e + 6, -17*e + 23, 11*e - 21, -8*e + 52, 8*e + 44] 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, w^2 - 2*w - 6])] = -1 AL_eigenvalues[ZF.ideal([4, 2, -w^2 + 7])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]