/* 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([16, 0, -13, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([16, 2, 2]) primes_array = [ [4, 2, 1/4*w^3 - 1/2*w^2 - 11/4*w + 5],\ [4, 2, 1/8*w^3 - 1/2*w^2 - 5/8*w + 3/2],\ [5, 5, -3/8*w^3 + 35/8*w - 1/2],\ [5, 5, 3/8*w^3 - 35/8*w - 1/2],\ [9, 3, -1/8*w^3 + 17/8*w + 3/2],\ [41, 41, 1/8*w^3 - 1/8*w + 3/2],\ [41, 41, 3/8*w^3 - 35/8*w + 3/2],\ [41, 41, 3/8*w^3 - 35/8*w - 3/2],\ [41, 41, -1/8*w^3 + 1/8*w + 3/2],\ [49, 7, 1/8*w^3 - 17/8*w + 7/2],\ [59, 59, 5/8*w^3 - 53/8*w - 5/2],\ [59, 59, -7/8*w^3 + 3/2*w^2 + 83/8*w - 35/2],\ [59, 59, -3/4*w^3 + 3/2*w^2 + 33/4*w - 16],\ [59, 59, 5/8*w^3 - 53/8*w + 5/2],\ [79, 79, 3/8*w^3 - w^2 - 35/8*w + 21/2],\ [79, 79, -1/2*w^3 + 3/2*w^2 + 3*w - 5],\ [79, 79, 7/8*w^3 - 79/8*w - 1/2],\ [79, 79, -3/8*w^3 - w^2 + 35/8*w + 21/2],\ [89, 89, 1/8*w^3 - 1/8*w - 5/2],\ [89, 89, 3/8*w^3 - 35/8*w + 5/2],\ [89, 89, 3/8*w^3 - 35/8*w - 5/2],\ [89, 89, -1/8*w^3 + 1/8*w - 5/2],\ [101, 101, -3/8*w^3 + 1/2*w^2 + 31/8*w - 5/2],\ [101, 101, 1/4*w^3 + 1/2*w^2 - 7/4*w - 4],\ [101, 101, -1/4*w^3 + 1/2*w^2 + 7/4*w - 4],\ [101, 101, 3/8*w^3 + 1/2*w^2 - 31/8*w - 5/2],\ [109, 109, 1/8*w^3 - w^2 + 15/8*w - 3/2],\ [109, 109, 1/8*w^3 + 1/2*w^2 - 13/8*w - 15/2],\ [109, 109, -1/8*w^3 + 1/2*w^2 + 13/8*w - 15/2],\ [109, 109, -1/2*w^2 + 1/2*w - 1],\ [121, 11, -1/8*w^3 + 9/8*w - 7/2],\ [121, 11, 3/8*w^3 - 27/8*w + 1/2],\ [131, 131, 1/2*w^3 - 13/2*w + 3],\ [131, 131, 2*w - 3],\ [131, 131, -1/8*w^3 - 1/2*w^2 + 21/8*w - 3/2],\ [131, 131, 1/2*w^3 - 13/2*w - 3],\ [151, 151, 1/8*w^3 - 25/8*w - 5/2],\ [151, 151, 3/8*w^3 - 43/8*w + 5/2],\ [151, 151, -3/8*w^3 + 43/8*w + 5/2],\ [151, 151, -1/8*w^3 + 25/8*w - 5/2],\ [169, 13, -5/8*w^3 + w^2 + 61/8*w - 27/2],\ [169, 13, 1/8*w^3 - w^2 + 7/8*w - 1/2],\ [211, 211, 13/8*w^3 - w^2 - 149/8*w + 23/2],\ [211, 211, -3/4*w^3 + 1/2*w^2 + 37/4*w - 6],\ [211, 211, -5/8*w^3 + 1/2*w^2 + 65/8*w - 7/2],\ [211, 211, -13/8*w^3 - w^2 + 149/8*w + 23/2],\ [251, 251, 1/2*w^3 + 1/2*w^2 - 6*w - 3],\ [251, 251, 1/8*w^3 + 1/2*w^2 + 3/8*w - 7/2],\ [251, 251, -1/8*w^3 + 1/2*w^2 - 3/8*w - 7/2],\ [251, 251, -1/2*w^3 + 1/2*w^2 + 6*w - 3],\ [269, 269, w^2 - w - 9],\ [269, 269, 3/8*w^3 - 2*w^2 + 13/8*w + 3/2],\ [269, 269, -1/4*w^3 + w^2 + 13/4*w - 4],\ [269, 269, 13/8*w^3 - 2*w^2 - 157/8*w + 49/2],\ [289, 17, 1/4*w^3 - 17/4*w - 2],\ [289, 17, -1/4*w^3 + 17/4*w - 2],\ [311, 311, -1/8*w^3 - w^2 + 17/8*w + 21/2],\ [311, 311, 3/2*w^3 - 35/2*w - 1],\ [311, 311, 3/2*w^3 - 35/2*w + 1],\ [311, 311, 1/8*w^3 - w^2 - 17/8*w + 21/2],\ [331, 331, -3/8*w^3 + w^2 - 5/8*w - 3/2],\ [331, 331, 1/4*w^3 - 3/2*w^2 - 11/4*w + 16],\ [331, 331, 7/8*w^3 - 2*w^2 - 31/8*w + 11/2],\ [331, 331, 1/4*w^3 - w^2 + 11/4*w - 2],\ [361, 19, -1/8*w^3 + 9/8*w - 9/2],\ [361, 19, -1/2*w^3 + 9/2*w - 1],\ [379, 379, 3/8*w^3 - 43/8*w + 1/2],\ [379, 379, 1/8*w^3 - 25/8*w - 1/2],\ [379, 379, -1/8*w^3 + 25/8*w - 1/2],\ [379, 379, 3/8*w^3 - 43/8*w - 1/2],\ [419, 419, 5/8*w^3 + w^2 - 45/8*w - 9/2],\ [419, 419, -5/8*w^3 + w^2 + 53/8*w - 13/2],\ [419, 419, 5/8*w^3 - w^2 - 45/8*w + 17/2],\ [419, 419, 3/8*w^3 + w^2 - 19/8*w - 13/2],\ [421, 421, 1/8*w^3 + w^2 - 9/8*w - 17/2],\ [421, 421, -1/8*w^3 + w^2 + 9/8*w - 9/2],\ [421, 421, 1/8*w^3 + w^2 - 9/8*w - 9/2],\ [421, 421, -1/8*w^3 + w^2 + 9/8*w - 17/2],\ [461, 461, -3/4*w^3 - 1/2*w^2 + 29/4*w],\ [461, 461, -5/8*w^3 + 3/2*w^2 + 33/8*w - 9/2],\ [461, 461, -5/8*w^3 + 1/2*w^2 + 41/8*w - 13/2],\ [461, 461, 1/8*w^3 - 1/2*w^2 - 21/8*w + 17/2],\ [479, 479, 5/8*w^3 - 3/2*w^2 - 9/8*w + 7/2],\ [479, 479, -7/4*w^3 + 3/2*w^2 + 81/4*w - 16],\ [479, 479, -13/8*w^3 + w^2 + 157/8*w - 29/2],\ [479, 479, -3/8*w^3 + w^2 - 13/8*w + 3/2],\ [499, 499, 7/8*w^3 - 71/8*w - 7/2],\ [499, 499, 1/2*w^3 - 1/2*w^2 - 3*w + 1],\ [499, 499, -1/2*w^3 - 1/2*w^2 + 3*w + 1],\ [499, 499, 7/8*w^3 + 1/2*w^2 - 75/8*w - 11/2],\ [509, 509, 3/8*w^3 - 11/8*w - 5/2],\ [509, 509, -1/8*w^3 + w^2 + 17/8*w - 23/2],\ [509, 509, 7/8*w^3 - 79/8*w + 5/2],\ [509, 509, -3/8*w^3 + 11/8*w - 5/2],\ [521, 521, -9/8*w^3 + 1/2*w^2 + 109/8*w - 17/2],\ [521, 521, 1/4*w^3 - 1/2*w^2 + 5/4*w - 2],\ [521, 521, -1/8*w^3 - w^2 + 25/8*w - 3/2],\ [521, 521, 3/2*w^3 - 3/2*w^2 - 17*w + 15],\ [529, 23, 9/8*w^3 - w^2 - 97/8*w + 19/2],\ [529, 23, -5/8*w^3 + w^2 + 29/8*w - 7/2],\ [541, 541, -3/8*w^3 - 1/2*w^2 + 39/8*w + 19/2],\ [541, 541, -5/8*w^3 - 1/2*w^2 + 41/8*w + 9/2],\ [541, 541, -5/8*w^3 + 1/2*w^2 + 41/8*w - 9/2],\ [541, 541, -3/8*w^3 + 1/2*w^2 + 39/8*w - 19/2],\ [571, 571, -1/8*w^3 + w^2 + 9/8*w - 15/2],\ [571, 571, -1/8*w^3 + w^2 + 9/8*w - 11/2],\ [571, 571, 1/8*w^3 + w^2 - 9/8*w - 11/2],\ [571, 571, 1/8*w^3 + w^2 - 9/8*w - 15/2],\ [631, 631, 5/8*w^3 - w^2 - 21/8*w + 3/2],\ [631, 631, -3/2*w^3 + 3/2*w^2 + 16*w - 13],\ [631, 631, -11/8*w^3 + w^2 + 123/8*w - 23/2],\ [631, 631, -7/4*w^3 - w^2 + 83/4*w + 12],\ [709, 709, -1/2*w^3 - 3/2*w^2 + 6*w + 15],\ [709, 709, 15/8*w^3 + 1/2*w^2 - 171/8*w - 13/2],\ [709, 709, 15/8*w^3 - 1/2*w^2 - 171/8*w + 13/2],\ [709, 709, 3/8*w^3 + 3/2*w^2 - 39/8*w - 29/2],\ [719, 719, 7/8*w^3 - w^2 - 95/8*w + 33/2],\ [719, 719, 1/8*w^3 + w^2 - 41/8*w + 7/2],\ [719, 719, 3/8*w^3 - w^2 - 27/8*w + 5/2],\ [719, 719, 3/8*w^3 - w^2 - 27/8*w + 21/2],\ [739, 739, w^3 - 1/2*w^2 - 21/2*w + 3],\ [739, 739, -w^2 + 3*w - 3],\ [739, 739, 5/8*w^3 - 1/2*w^2 - 33/8*w + 7/2],\ [739, 739, 3/8*w^3 - 1/2*w^2 - 23/8*w + 23/2],\ [751, 751, -13/8*w^3 + w^2 + 157/8*w - 27/2],\ [751, 751, -3/4*w^3 + 3/2*w^2 + 37/4*w - 20],\ [751, 751, 11/8*w^3 - 2*w^2 - 131/8*w + 51/2],\ [751, 751, -15/8*w^3 + 3/2*w^2 + 179/8*w - 37/2],\ [761, 761, 13/8*w^3 - 1/2*w^2 - 153/8*w + 15/2],\ [761, 761, 1/8*w^3 + 3/2*w^2 - 5/8*w - 31/2],\ [761, 761, 5/8*w^3 - 5/2*w^2 - 17/8*w + 7/2],\ [761, 761, -9/8*w^3 + 2*w^2 + 113/8*w - 53/2],\ [839, 839, 3/8*w^3 + 1/2*w^2 - 15/8*w - 9/2],\ [839, 839, -3/4*w^3 - 1/2*w^2 + 33/4*w + 2],\ [839, 839, -3/4*w^3 + 1/2*w^2 + 33/4*w - 2],\ [839, 839, -3/8*w^3 + 1/2*w^2 + 15/8*w - 9/2],\ [841, 29, -1/8*w^3 + 9/8*w - 11/2],\ [841, 29, -5/8*w^3 + 45/8*w - 3/2],\ [881, 881, -1/2*w^3 + 1/2*w^2 + 5*w + 1],\ [881, 881, -3/8*w^3 + 1/2*w^2 + 23/8*w - 15/2],\ [881, 881, 3/8*w^3 + 1/2*w^2 - 23/8*w - 15/2],\ [881, 881, 1/2*w^3 + 1/2*w^2 - 5*w + 1],\ [919, 919, 5/8*w^3 + 1/2*w^2 - 41/8*w - 5/2],\ [919, 919, 3/4*w^3 + 1/2*w^2 - 29/4*w - 4],\ [919, 919, -3/4*w^3 + 1/2*w^2 + 29/4*w - 4],\ [919, 919, -5/8*w^3 + 1/2*w^2 + 41/8*w - 5/2],\ [929, 929, -5/8*w^3 + w^2 + 45/8*w - 19/2],\ [929, 929, 5/8*w^3 - w^2 - 45/8*w + 7/2],\ [929, 929, -5/8*w^3 - w^2 + 45/8*w + 7/2],\ [929, 929, 5/8*w^3 + w^2 - 45/8*w - 19/2],\ [941, 941, -5/8*w^3 + 61/8*w + 11/2],\ [941, 941, 5/8*w^3 - w^2 - 53/8*w + 11/2],\ [941, 941, -5/8*w^3 - w^2 + 53/8*w + 11/2],\ [941, 941, 1/4*w^3 + w^2 - 21/4*w - 2],\ [961, 31, 5/8*w^3 - 45/8*w + 1/2],\ [961, 31, -1/4*w^3 + 9/4*w - 6],\ [971, 971, -5/8*w^3 + 1/2*w^2 + 33/8*w - 11/2],\ [971, 971, -w^3 - 1/2*w^2 + 21/2*w + 1],\ [971, 971, -3/8*w^3 + w^2 + 43/8*w - 27/2],\ [971, 971, -3/4*w^3 + 2*w^2 + 19/4*w - 6],\ [991, 991, -1/2*w^2 + 1/2*w - 3],\ [991, 991, -1/8*w^3 + 1/2*w^2 + 13/8*w - 19/2],\ [991, 991, 1/8*w^3 + 1/2*w^2 - 13/8*w - 19/2],\ [991, 991, -1/2*w^2 - 1/2*w - 3],\ [1009, 1009, 11/8*w^3 - 123/8*w + 1/2],\ [1009, 1009, 3/2*w^3 - 1/2*w^2 - 18*w + 5],\ [1009, 1009, -3/2*w^3 - 1/2*w^2 + 18*w + 5],\ [1009, 1009, -11/8*w^3 + 123/8*w + 1/2],\ [1049, 1049, -3/8*w^3 + 1/2*w^2 + 7/8*w - 7/2],\ [1049, 1049, 3/8*w^3 + w^2 - 27/8*w - 27/2],\ [1049, 1049, 3/8*w^3 - w^2 - 27/8*w + 27/2],\ [1049, 1049, 17/8*w^3 + 1/2*w^2 - 197/8*w - 9/2],\ [1051, 1051, -w^3 - w^2 + 10*w + 9],\ [1051, 1051, -3/8*w^3 + 43/8*w - 15/2],\ [1051, 1051, -3/4*w^3 - w^2 + 23/4*w + 4],\ [1051, 1051, -w^3 + w^2 + 10*w - 9],\ [1091, 1091, 1/2*w^3 - 3/2*w^2 + w - 1],\ [1091, 1091, -5/4*w^3 + 2*w^2 + 61/4*w - 24],\ [1091, 1091, 7/8*w^3 - 2*w^2 - 71/8*w + 39/2],\ [1091, 1091, -5/8*w^3 + w^2 + 21/8*w - 9/2],\ [1109, 1109, 15/8*w^3 - 175/8*w + 3/2],\ [1109, 1109, -9/8*w^3 + 105/8*w + 5/2],\ [1109, 1109, -9/8*w^3 + 105/8*w - 5/2],\ [1109, 1109, 15/8*w^3 - 175/8*w - 3/2],\ [1129, 1129, -5/8*w^3 + 2*w^2 + 29/8*w - 15/2],\ [1129, 1129, -1/2*w^3 + 3/2*w^2 + 5*w - 13],\ [1129, 1129, 1/2*w^3 + 3/2*w^2 - 5*w - 13],\ [1129, 1129, -3/8*w^3 + 3/2*w^2 + 23/8*w - 13/2],\ [1151, 1151, 7/8*w^3 + w^2 - 71/8*w - 11/2],\ [1151, 1151, 5/8*w^3 + w^2 - 37/8*w - 15/2],\ [1151, 1151, 5/8*w^3 - w^2 - 37/8*w + 15/2],\ [1151, 1151, -7/8*w^3 + w^2 + 71/8*w - 11/2],\ [1171, 1171, 5/8*w^3 - 69/8*w - 5/2],\ [1171, 1171, 3/8*w^3 + 3/2*w^2 - 39/8*w - 17/2],\ [1171, 1171, -3/8*w^3 + 3/2*w^2 + 39/8*w - 17/2],\ [1171, 1171, 3/2*w^2 - 3/2*w - 11],\ [1181, 1181, -w^3 + w^2 + 10*w - 5],\ [1181, 1181, -3/4*w^3 + w^2 + 23/4*w - 8],\ [1181, 1181, -1/4*w^3 + 1/2*w^2 + 23/4*w - 8],\ [1181, 1181, -5/8*w^3 - 1/2*w^2 + 73/8*w - 3/2],\ [1201, 1201, 1/8*w^3 - w^2 - 9/8*w - 3/2],\ [1201, 1201, -1/8*w^3 + w^2 + 9/8*w - 29/2],\ [1201, 1201, 1/8*w^3 + w^2 - 9/8*w - 29/2],\ [1201, 1201, -1/8*w^3 - w^2 + 9/8*w - 3/2],\ [1259, 1259, -1/4*w^3 + 2*w^2 + 9/4*w - 22],\ [1259, 1259, -1/4*w^3 + 2*w^2 + 9/4*w - 4],\ [1259, 1259, -1/4*w^3 - 2*w^2 + 9/4*w + 4],\ [1259, 1259, -25/8*w^3 + 4*w^2 + 297/8*w - 97/2],\ [1301, 1301, w^2 - w - 13],\ [1301, 1301, -w^3 - 3*w^2 + 12*w + 35],\ [1301, 1301, w^3 - 3*w^2 - 12*w + 35],\ [1301, 1301, -w^2 - w + 13],\ [1319, 1319, -3/4*w^3 - 3/2*w^2 + 25/4*w + 6],\ [1319, 1319, -7/8*w^3 + 3/2*w^2 + 67/8*w - 27/2],\ [1319, 1319, 1/4*w^3 - 1/2*w^2 - 19/4*w + 10],\ [1319, 1319, 3/4*w^3 - 3/2*w^2 - 25/4*w + 6],\ [1361, 1361, -5/8*w^3 - 2*w^2 + 53/8*w + 49/2],\ [1361, 1361, -7/8*w^3 + 2*w^2 + 87/8*w - 45/2],\ [1361, 1361, -7/8*w^3 - 2*w^2 + 87/8*w + 45/2],\ [1361, 1361, 5/8*w^3 - 2*w^2 - 53/8*w + 49/2],\ [1369, 37, -7/8*w^3 + 1/2*w^2 + 67/8*w - 13/2],\ [1369, 37, -3/4*w^3 - 1/2*w^2 + 25/4*w],\ [1381, 1381, -5/8*w^3 + 3*w^2 + 5/8*w - 5/2],\ [1381, 1381, -11/8*w^3 + 5/2*w^2 + 135/8*w - 65/2],\ [1381, 1381, 15/8*w^3 - 3*w^2 - 175/8*w + 73/2],\ [1381, 1381, 1/4*w^3 - 5/2*w^2 + 9/4*w],\ [1429, 1429, 5/8*w^3 - 77/8*w - 13/2],\ [1429, 1429, -5/8*w^3 + 2*w^2 + 29/8*w - 17/2],\ [1429, 1429, -3/8*w^3 + 59/8*w + 13/2],\ [1429, 1429, -5/8*w^3 + 77/8*w - 13/2],\ [1471, 1471, -3/4*w^3 - 1/2*w^2 + 41/4*w + 2],\ [1471, 1471, -1/2*w^3 + 5/2*w^2 - 3*w - 1],\ [1471, 1471, -1/8*w^3 + 1/2*w^2 + 37/8*w - 9/2],\ [1471, 1471, -19/8*w^3 + 5/2*w^2 + 231/8*w - 63/2],\ [1511, 1511, -1/2*w^3 + 1/2*w^2 + 4*w - 9],\ [1511, 1511, 3/8*w^3 + w^2 - 43/8*w - 7/2],\ [1511, 1511, 5/8*w^3 - 1/2*w^2 - 49/8*w - 5/2],\ [1511, 1511, -1/8*w^3 + w^2 + 25/8*w - 19/2],\ [1549, 1549, 21/8*w^3 + 1/2*w^2 - 241/8*w - 11/2],\ [1549, 1549, -1/4*w^3 - 3/2*w^2 + 11/4*w + 14],\ [1549, 1549, -1/4*w^3 + 3/2*w^2 + 11/4*w - 14],\ [1549, 1549, -21/8*w^3 + 1/2*w^2 + 241/8*w - 11/2],\ [1559, 1559, -1/8*w^3 + 1/2*w^2 + 29/8*w - 15/2],\ [1559, 1559, -1/2*w^3 - 1/2*w^2 + 7*w - 1],\ [1559, 1559, -1/2*w^3 + 1/2*w^2 + 7*w + 1],\ [1559, 1559, 1/8*w^3 + 1/2*w^2 - 29/8*w - 15/2],\ [1571, 1571, 1/8*w^3 + 15/8*w - 9/2],\ [1571, 1571, -1/8*w^3 + 3/2*w^2 - 3/8*w - 25/2],\ [1571, 1571, 1/8*w^3 + 3/2*w^2 + 3/8*w - 25/2],\ [1571, 1571, 1/2*w^3 + 3/2*w^2 - 6*w - 7],\ [1579, 1579, -5/8*w^3 - w^2 + 53/8*w + 31/2],\ [1579, 1579, -3/8*w^3 - 3*w^2 + 35/8*w + 67/2],\ [1579, 1579, 3/8*w^3 - 3*w^2 - 35/8*w + 67/2],\ [1579, 1579, -5/8*w^3 + w^2 + 53/8*w - 31/2],\ [1601, 1601, -1/8*w^3 + w^2 + 1/8*w - 21/2],\ [1601, 1601, 3/8*w^3 + w^2 - 35/8*w - 5/2],\ [1601, 1601, -3/8*w^3 + w^2 + 35/8*w - 5/2],\ [1601, 1601, 1/8*w^3 + w^2 - 1/8*w - 21/2],\ [1621, 1621, 19/8*w^3 - 2*w^2 - 211/8*w + 39/2],\ [1621, 1621, 1/4*w^3 - 2*w^2 - 9/4*w + 20],\ [1621, 1621, 23/8*w^3 - 4*w^2 - 263/8*w + 87/2],\ [1621, 1621, 5/2*w^3 - 2*w^2 - 57/2*w + 23],\ [1721, 1721, 7/4*w^3 - 3*w^2 - 75/4*w + 30],\ [1721, 1721, 17/8*w^3 - 3/2*w^2 - 197/8*w + 31/2],\ [1721, 1721, w^3 - 3*w^2 - 6*w + 9],\ [1721, 1721, 7/8*w^3 - 2*w^2 - 87/8*w + 47/2],\ [1759, 1759, -5/8*w^3 + 69/8*w - 1/2],\ [1759, 1759, -1/8*w^3 + 33/8*w - 1/2],\ [1759, 1759, 1/8*w^3 - 33/8*w - 1/2],\ [1759, 1759, 5/8*w^3 - 69/8*w - 1/2],\ [1789, 1789, -3/4*w^3 + 1/2*w^2 + 25/4*w - 4],\ [1789, 1789, 7/8*w^3 + 1/2*w^2 - 67/8*w - 5/2],\ [1789, 1789, -7/8*w^3 + 1/2*w^2 + 67/8*w - 5/2],\ [1789, 1789, 3/4*w^3 + 1/2*w^2 - 25/4*w - 4],\ [1801, 1801, -9/8*w^3 + w^2 + 81/8*w - 21/2],\ [1801, 1801, 9/8*w^3 + w^2 - 81/8*w - 5/2],\ [1801, 1801, 1/4*w^3 - 1/4*w + 10],\ [1801, 1801, -1/8*w^3 + w^2 - 15/8*w + 7/2],\ [1811, 1811, 19/8*w^3 - 3/2*w^2 - 223/8*w + 39/2],\ [1811, 1811, -3/2*w^3 + 1/2*w^2 + 18*w - 9],\ [1811, 1811, 19/8*w^3 - 5/2*w^2 - 215/8*w + 51/2],\ [1811, 1811, -11/4*w^3 + 5/2*w^2 + 125/4*w - 26],\ [1831, 1831, -1/2*w^3 - 1/2*w^2 + 8*w + 7],\ [1831, 1831, -1/2*w^3 + 3/2*w^2 + 5*w - 11],\ [1831, 1831, 1/2*w^3 + 3/2*w^2 - 5*w - 11],\ [1831, 1831, 1/2*w^3 - 1/2*w^2 - 8*w + 7],\ [1849, 43, -3/8*w^3 + 51/8*w - 19/2],\ [1849, 43, 7/8*w^3 - w^2 - 55/8*w + 5/2],\ [1889, 1889, -9/4*w^3 + 3*w^2 + 101/4*w - 34],\ [1889, 1889, w^3 - 3*w^2 - 4*w + 5],\ [1889, 1889, -3/8*w^3 - w^2 + 43/8*w - 7/2],\ [1889, 1889, 13/8*w^3 - 3/2*w^2 - 145/8*w + 27/2],\ [1931, 1931, -3/2*w^2 + 9/2*w - 1],\ [1931, 1931, 9/8*w^3 - 3/2*w^2 - 117/8*w + 41/2],\ [1931, 1931, -1/2*w^3 + 3/2*w^2 + 4*w - 13],\ [1931, 1931, 5/8*w^3 - 3/2*w^2 - 49/8*w + 13/2],\ [1949, 1949, -1/8*w^3 + 1/2*w^2 - 3/8*w - 19/2],\ [1949, 1949, -1/2*w^3 - 1/2*w^2 + 6*w - 3],\ [1949, 1949, 1/2*w^3 - 1/2*w^2 - 6*w - 3],\ [1949, 1949, 1/8*w^3 + 1/2*w^2 + 3/8*w - 19/2],\ [1979, 1979, 15/8*w^3 + w^2 - 175/8*w - 19/2],\ [1979, 1979, -1/2*w^3 - 2*w^2 + 13/2*w + 23],\ [1979, 1979, -1/2*w^3 + 2*w^2 + 13/2*w - 23],\ [1979, 1979, 1/4*w^3 + 2*w^2 - 9/4*w - 24],\ [1999, 1999, -1/8*w^3 + 3/2*w^2 + 13/8*w - 13/2],\ [1999, 1999, 3/2*w^2 - 1/2*w - 13],\ [1999, 1999, 3/2*w^2 + 1/2*w - 13],\ [1999, 1999, 1/8*w^3 + 3/2*w^2 - 13/8*w - 13/2],\ [2011, 2011, -3/4*w^3 - 1/2*w^2 + 25/4*w + 2],\ [2011, 2011, 7/8*w^3 + 1/2*w^2 - 67/8*w - 9/2],\ [2011, 2011, -7/8*w^3 + 1/2*w^2 + 67/8*w - 9/2],\ [2011, 2011, -3/8*w^3 + 35/8*w - 15/2],\ [2099, 2099, -3/8*w^3 + w^2 + 35/8*w - 3/2],\ [2099, 2099, 1/8*w^3 + w^2 - 1/8*w - 23/2],\ [2099, 2099, -1/8*w^3 + w^2 + 1/8*w - 23/2],\ [2099, 2099, 3/8*w^3 + w^2 - 35/8*w - 3/2],\ [2141, 2141, -1/4*w^3 + w^2 + 5/4*w - 10],\ [2141, 2141, -1/2*w^3 + w^2 + 11/2*w - 3],\ [2141, 2141, 1/2*w^3 + w^2 - 11/2*w - 3],\ [2141, 2141, 1/4*w^3 + w^2 - 5/4*w - 10],\ [2179, 2179, -3/8*w^3 + 3/2*w^2 - 17/8*w - 3/2],\ [2179, 2179, 9/8*w^3 + 1/2*w^2 - 117/8*w - 3/2],\ [2179, 2179, -15/8*w^3 + 3*w^2 + 167/8*w - 61/2],\ [2179, 2179, -1/2*w^2 + 11/2*w - 5],\ [2209, 47, -1/8*w^3 + 3/2*w^2 + 21/8*w - 19/2],\ [2209, 47, -1/4*w^3 + 3/2*w^2 + 15/4*w - 10],\ [2221, 2221, 17/8*w^3 - 193/8*w + 1/2],\ [2221, 2221, -3/8*w^3 - 2*w^2 + 35/8*w + 41/2],\ [2221, 2221, 3/8*w^3 - 2*w^2 - 35/8*w + 41/2],\ [2221, 2221, -w^3 + 5/2*w^2 + 23/2*w - 31],\ [2251, 2251, -11/8*w^3 + w^2 + 139/8*w - 29/2],\ [2251, 2251, 5/8*w^3 - 2*w^2 - 53/8*w + 21/2],\ [2251, 2251, -5/8*w^3 + 2*w^2 + 45/8*w - 19/2],\ [2251, 2251, -3/8*w^3 + 2*w^2 + 19/8*w - 31/2],\ [2269, 2269, -1/8*w^3 - 23/8*w - 3/2],\ [2269, 2269, 9/8*w^3 - 113/8*w - 3/2],\ [2269, 2269, -9/8*w^3 + 113/8*w - 3/2],\ [2269, 2269, 1/8*w^3 + 23/8*w - 3/2],\ [2309, 2309, -11/4*w^3 + 5/2*w^2 + 129/4*w - 32],\ [2309, 2309, -13/8*w^3 + 3*w^2 + 157/8*w - 73/2],\ [2309, 2309, -2*w^3 + 7/2*w^2 + 45/2*w - 39],\ [2309, 2309, -13/8*w^3 + w^2 + 141/8*w - 13/2],\ [2311, 2311, -3/8*w^3 + w^2 + 43/8*w - 33/2],\ [2311, 2311, -1/8*w^3 - w^2 + 25/8*w - 7/2],\ [2311, 2311, 3/8*w^3 - 2*w^2 + 13/8*w - 3/2],\ [2311, 2311, 13/8*w^3 - 3/2*w^2 - 137/8*w + 25/2],\ [2351, 2351, -5/8*w^3 + 2*w^2 + 29/8*w - 7/2],\ [2351, 2351, 9/8*w^3 - 2*w^2 - 97/8*w + 45/2],\ [2351, 2351, w^3 - 3/2*w^2 - 27/2*w + 23],\ [2351, 2351, 1/8*w^3 + 3/2*w^2 - 45/8*w + 7/2],\ [2389, 2389, -3/8*w^3 + 3/2*w^2 + 31/8*w - 23/2],\ [2389, 2389, 1/4*w^3 + 3/2*w^2 - 7/4*w - 8],\ [2389, 2389, -1/4*w^3 + 3/2*w^2 + 7/4*w - 8],\ [2389, 2389, 3/8*w^3 + 3/2*w^2 - 31/8*w - 23/2],\ [2399, 2399, 9/8*w^3 - 2*w^2 - 41/8*w + 15/2],\ [2399, 2399, 21/8*w^3 - 2*w^2 - 245/8*w + 51/2],\ [2399, 2399, -19/8*w^3 + 2*w^2 + 211/8*w - 37/2],\ [2399, 2399, -7/8*w^3 + 2*w^2 + 7/8*w - 1/2],\ [2411, 2411, 1/4*w^3 + 3/2*w^2 - 3/4*w - 12],\ [2411, 2411, 5/8*w^3 - 3/2*w^2 - 57/8*w + 15/2],\ [2411, 2411, 5/8*w^3 + 3/2*w^2 - 57/8*w - 15/2],\ [2411, 2411, -1/4*w^3 + 3/2*w^2 + 3/4*w - 12],\ [2441, 2441, -3/8*w^3 + w^2 + 35/8*w - 1/2],\ [2441, 2441, 1/8*w^3 + w^2 - 1/8*w - 25/2],\ [2441, 2441, -1/8*w^3 + w^2 + 1/8*w - 25/2],\ [2441, 2441, -3/8*w^3 - w^2 + 35/8*w + 1/2],\ [2521, 2521, -2*w^3 + 1/2*w^2 + 45/2*w - 7],\ [2521, 2521, -7/8*w^3 - 5/2*w^2 + 83/8*w + 53/2],\ [2521, 2521, 7/8*w^3 - 5/2*w^2 - 83/8*w + 53/2],\ [2521, 2521, 2*w^3 + 1/2*w^2 - 45/2*w - 7],\ [2579, 2579, 1/4*w^3 - 5/2*w^2 + 21/4*w - 2],\ [2579, 2579, -1/4*w^3 + 3/2*w^2 + 7/4*w - 16],\ [2579, 2579, -9/8*w^3 + w^2 + 113/8*w - 13/2],\ [2579, 2579, 3/8*w^3 - 3/2*w^2 - 31/8*w + 7/2],\ [2609, 2609, -3/4*w^3 + w^2 + 31/4*w - 4],\ [2609, 2609, 1/2*w^3 + w^2 - 7/2*w - 9],\ [2609, 2609, -1/2*w^3 + w^2 + 7/2*w - 9],\ [2609, 2609, 3/4*w^3 + w^2 - 31/4*w - 4],\ [2621, 2621, 5/8*w^3 - w^2 - 61/8*w + 9/2],\ [2621, 2621, 1/8*w^3 + w^2 + 7/8*w - 17/2],\ [2621, 2621, -5/8*w^3 - 1/2*w^2 + 57/8*w - 3/2],\ [2621, 2621, -1/4*w^3 + 1/2*w^2 + 3/4*w - 8],\ [2671, 2671, 3/2*w^3 - w^2 - 37/2*w + 13],\ [2671, 2671, 1/8*w^3 + w^2 - 49/8*w - 15/2],\ [2671, 2671, 1/8*w^3 - w^2 - 49/8*w + 15/2],\ [2671, 2671, 3/8*w^3 + 2*w^2 - 27/8*w - 37/2],\ [2689, 2689, 23/8*w^3 - 271/8*w - 1/2],\ [2689, 2689, -3/8*w^3 - w^2 + 35/8*w + 31/2],\ [2689, 2689, 3/8*w^3 - w^2 - 35/8*w + 31/2],\ [2689, 2689, 23/8*w^3 - 271/8*w + 1/2],\ [2729, 2729, -9/8*w^3 + 1/2*w^2 + 101/8*w - 3/2],\ [2729, 2729, -1/2*w^3 + 1/2*w^2 + 2*w - 5],\ [2729, 2729, 1/2*w^3 + 1/2*w^2 - 2*w - 5],\ [2729, 2729, -9/8*w^3 - 1/2*w^2 + 101/8*w + 3/2],\ [2731, 2731, 1/2*w^3 - 7/2*w^2 - 6*w + 39],\ [2731, 2731, 11/8*w^3 - 1/2*w^2 - 119/8*w + 13/2],\ [2731, 2731, -1/8*w^3 + w^2 + 9/8*w - 31/2],\ [2731, 2731, 1/2*w^3 + 7/2*w^2 - 6*w - 39],\ [2789, 2789, 17/8*w^3 - 201/8*w - 5/2],\ [2789, 2789, 15/8*w^3 - w^2 - 175/8*w + 29/2],\ [2789, 2789, -19/8*w^3 + 5/2*w^2 + 207/8*w - 45/2],\ [2789, 2789, 5/8*w^3 - w^2 - 5/8*w - 3/2],\ [2809, 53, -7/8*w^3 + 2*w^2 + 71/8*w - 33/2],\ [2809, 53, -5/8*w^3 + 2*w^2 + 37/8*w - 19/2],\ [2819, 2819, -5/8*w^3 + w^2 + 45/8*w - 1/2],\ [2819, 2819, 5/8*w^3 + w^2 - 45/8*w - 25/2],\ [2819, 2819, -5/8*w^3 + w^2 + 45/8*w - 25/2],\ [2819, 2819, 5/8*w^3 + w^2 - 45/8*w - 1/2],\ [2851, 2851, -3/8*w^3 - 1/2*w^2 + 31/8*w - 11/2],\ [2851, 2851, -1/4*w^3 - 1/2*w^2 + 7/4*w + 12],\ [2851, 2851, -1/4*w^3 + 1/2*w^2 + 7/4*w - 12],\ [2851, 2851, -3/4*w^3 - 1/2*w^2 + 21/4*w + 2],\ [2861, 2861, 5/8*w^3 - 2*w^2 + 11/8*w - 3/2],\ [2861, 2861, -3/8*w^3 + w^2 + 19/8*w - 35/2],\ [2861, 2861, 3/8*w^3 + w^2 - 19/8*w - 35/2],\ [2861, 2861, 3/4*w^3 - w^2 - 15/4*w + 6],\ [2939, 2939, -7/8*w^3 - 1/2*w^2 + 75/8*w - 1/2],\ [2939, 2939, 1/2*w^3 + 1/2*w^2 - 3*w - 7],\ [2939, 2939, -1/2*w^3 + 1/2*w^2 + 3*w - 7],\ [2939, 2939, 7/8*w^3 - 1/2*w^2 - 75/8*w - 1/2],\ [2999, 2999, 3/4*w^3 - 3/2*w^2 - 17/4*w + 8],\ [2999, 2999, -11/8*w^3 + 3/2*w^2 + 119/8*w - 23/2],\ [2999, 2999, 11/8*w^3 + 3/2*w^2 - 119/8*w - 23/2],\ [2999, 2999, 1/8*w^3 - 1/2*w^2 + 27/8*w - 11/2],\ [3019, 3019, 5/8*w^3 - 5/2*w^2 - 57/8*w + 53/2],\ [3019, 3019, -2*w^3 + 1/2*w^2 + 45/2*w - 5],\ [3019, 3019, 2*w^3 + 1/2*w^2 - 45/2*w - 5],\ [3019, 3019, -5/8*w^3 - 5/2*w^2 + 57/8*w + 53/2],\ [3041, 3041, -w^3 + 3*w^2 - 1],\ [3041, 3041, 9/8*w^3 - 3*w^2 - 17/8*w + 13/2],\ [3041, 3041, -1/2*w^3 + w^2 - 5/2*w + 3],\ [3041, 3041, -25/8*w^3 + 3*w^2 + 289/8*w - 65/2],\ [3049, 3049, -5/8*w^3 - 3*w^2 + 61/8*w + 65/2],\ [3049, 3049, -15/8*w^3 - w^2 + 167/8*w + 25/2],\ [3049, 3049, -15/8*w^3 + w^2 + 167/8*w - 25/2],\ [3049, 3049, 5/8*w^3 - 3*w^2 - 61/8*w + 65/2],\ [3061, 3061, 1/8*w^3 + 3/2*w^2 - 13/8*w - 17/2],\ [3061, 3061, -5/8*w^3 - 1/2*w^2 + 73/8*w + 9/2],\ [3061, 3061, -5/8*w^3 + 1/2*w^2 + 73/8*w - 9/2],\ [3061, 3061, -1/8*w^3 + 3/2*w^2 + 13/8*w - 17/2],\ [3109, 3109, 7/4*w^3 - 3/2*w^2 - 89/4*w + 22],\ [3109, 3109, 1/8*w^3 - 41/8*w + 7/2],\ [3109, 3109, 1/8*w^3 - 3/2*w^2 + 43/8*w - 5/2],\ [3109, 3109, 2*w^2 - 2*w - 15],\ [3191, 3191, -w^3 + 5/2*w^2 + 1/2*w - 1],\ [3191, 3191, 25/8*w^3 - 5/2*w^2 - 293/8*w + 63/2],\ [3191, 3191, -21/8*w^3 + 2*w^2 + 237/8*w - 39/2],\ [3191, 3191, 23/8*w^3 - 3*w^2 - 263/8*w + 63/2],\ [3209, 3209, -1/4*w^3 + 1/2*w^2 - 1/4*w - 6],\ [3209, 3209, -7/8*w^3 + 1/2*w^2 + 83/8*w - 1/2],\ [3209, 3209, -7/8*w^3 - 1/2*w^2 + 83/8*w + 1/2],\ [3209, 3209, 1/4*w^3 + 1/2*w^2 + 1/4*w - 6],\ [3229, 3229, -15/8*w^3 - w^2 + 167/8*w + 21/2],\ [3229, 3229, -7/8*w^3 + 3*w^2 + 79/8*w - 65/2],\ [3229, 3229, -7/8*w^3 - 3*w^2 + 79/8*w + 65/2],\ [3229, 3229, -15/8*w^3 + w^2 + 167/8*w - 21/2],\ [3251, 3251, 7/8*w^3 - 87/8*w + 19/2],\ [3251, 3251, 9/8*w^3 - 3/2*w^2 - 93/8*w + 19/2],\ [3251, 3251, -7/8*w^3 + 95/8*w - 17/2],\ [3251, 3251, -7/8*w^3 + 87/8*w + 19/2],\ [3259, 3259, 1/2*w^3 - 1/2*w^2 - 8*w + 3],\ [3259, 3259, 3/2*w^2 + 1/2*w - 9],\ [3259, 3259, 3/2*w^2 - 1/2*w - 9],\ [3259, 3259, -1/8*w^3 + 3/2*w^2 + 13/8*w - 21/2],\ [3271, 3271, 11/8*w^3 - 139/8*w + 7/2],\ [3271, 3271, -3/4*w^3 + 3*w^2 - 9/4*w - 2],\ [3271, 3271, -1/2*w^3 + 5/2*w^2 + 2*w - 7],\ [3271, 3271, -3*w^3 + 3*w^2 + 36*w - 37],\ [3301, 3301, 3/4*w^3 - 2*w^2 - 27/4*w + 14],\ [3301, 3301, -5/8*w^3 + 2*w^2 + 37/8*w - 21/2],\ [3301, 3301, 5/8*w^3 + 2*w^2 - 37/8*w - 21/2],\ [3301, 3301, -7/8*w^3 + 2*w^2 + 71/8*w - 31/2],\ [3319, 3319, -11/8*w^3 - w^2 + 115/8*w + 17/2],\ [3319, 3319, -9/8*w^3 + 2*w^2 + 57/8*w - 15/2],\ [3319, 3319, 7/8*w^3 - w^2 - 47/8*w + 9/2],\ [3319, 3319, -11/8*w^3 + w^2 + 115/8*w - 17/2],\ [3359, 3359, -3/8*w^3 + 2*w^2 + 43/8*w - 51/2],\ [3359, 3359, -13/8*w^3 + 3*w^2 + 157/8*w - 71/2],\ [3359, 3359, -15/8*w^3 + 7/2*w^2 + 163/8*w - 73/2],\ [3359, 3359, 19/8*w^3 + 2*w^2 - 219/8*w - 41/2],\ [3361, 3361, -1/4*w^3 + 1/2*w^2 + 15/4*w - 12],\ [3361, 3361, -1/8*w^3 - 1/2*w^2 + 21/8*w - 11/2],\ [3361, 3361, 1/8*w^3 - 1/2*w^2 - 21/8*w - 11/2],\ [3361, 3361, 1/4*w^3 + 1/2*w^2 - 15/4*w - 12],\ [3449, 3449, -23/8*w^3 + 2*w^2 + 263/8*w - 41/2],\ [3449, 3449, -17/8*w^3 + 2*w^2 + 193/8*w - 39/2],\ [3449, 3449, -9/8*w^3 + 3*w^2 + 1/8*w - 3/2],\ [3449, 3449, 29/8*w^3 - 3*w^2 - 341/8*w + 75/2],\ [3461, 3461, 1/8*w^3 - w^2 + 47/8*w - 13/2],\ [3461, 3461, -7/4*w^3 + 3/2*w^2 + 81/4*w - 14],\ [3461, 3461, 15/8*w^3 - w^2 - 191/8*w + 39/2],\ [3461, 3461, -5/8*w^3 + 3/2*w^2 + 9/8*w - 11/2],\ [3469, 3469, -3/4*w^3 + 2*w^2 + 35/4*w - 26],\ [3469, 3469, -9/8*w^3 - 3*w^2 + 105/8*w + 65/2],\ [3469, 3469, -9/8*w^3 + 3*w^2 + 105/8*w - 65/2],\ [3469, 3469, 15/8*w^3 - 167/8*w + 3/2],\ [3491, 3491, 1/8*w^3 + w^2 - 33/8*w - 19/2],\ [3491, 3491, -3/8*w^3 + w^2 + 19/8*w - 21/2],\ [3491, 3491, -5/8*w^3 + w^2 + 69/8*w - 7/2],\ [3491, 3491, -1/8*w^3 + w^2 + 33/8*w - 19/2],\ [3511, 3511, 15/8*w^3 - w^2 - 167/8*w + 23/2],\ [3511, 3511, 1/8*w^3 - 3*w^2 - 9/8*w + 65/2],\ [3511, 3511, -1/8*w^3 - 3*w^2 + 9/8*w + 65/2],\ [3511, 3511, -15/8*w^3 - w^2 + 167/8*w + 23/2],\ [3529, 3529, 15/8*w^3 - 1/2*w^2 - 187/8*w + 21/2],\ [3529, 3529, -7/8*w^3 + 3*w^2 - 9/8*w - 7/2],\ [3529, 3529, -1/4*w^3 + 1/2*w^2 - 17/4*w + 4],\ [3529, 3529, 25/8*w^3 - 3*w^2 - 297/8*w + 71/2],\ [3571, 3571, -23/8*w^3 + w^2 + 263/8*w - 23/2],\ [3571, 3571, 1/8*w^3 + 2*w^2 - 9/8*w - 39/2],\ [3571, 3571, -1/8*w^3 + 2*w^2 + 9/8*w - 39/2],\ [3571, 3571, -23/8*w^3 - w^2 + 263/8*w + 23/2],\ [3659, 3659, 7/8*w^3 - 87/8*w + 15/2],\ [3659, 3659, 7/8*w^3 - 3/2*w^2 - 75/8*w + 17/2],\ [3659, 3659, -7/8*w^3 - 3/2*w^2 + 75/8*w + 17/2],\ [3659, 3659, 7/8*w^3 - 87/8*w - 15/2],\ [3671, 3671, 11/8*w^3 - 123/8*w + 9/2],\ [3671, 3671, 7/2*w^2 + 1/2*w - 41],\ [3671, 3671, -7/2*w^2 + 1/2*w + 41],\ [3671, 3671, 11/8*w^3 - 123/8*w - 9/2],\ [3691, 3691, -5/4*w^3 + 1/2*w^2 + 51/4*w - 2],\ [3691, 3691, 7/8*w^3 - 1/2*w^2 - 51/8*w + 9/2],\ [3691, 3691, -11/8*w^3 + 3*w^2 + 59/8*w - 17/2],\ [3691, 3691, 5/8*w^3 + w^2 - 61/8*w - 33/2],\ [3701, 3701, 3/4*w^3 - 3/2*w^2 - 25/4*w + 4],\ [3701, 3701, 1/8*w^3 + 2*w^2 + 15/8*w - 27/2],\ [3701, 3701, -7/8*w^3 + 3/2*w^2 + 67/8*w - 31/2],\ [3701, 3701, 7/8*w^3 + 2*w^2 - 87/8*w - 25/2],\ [3721, 61, 3/8*w^3 - 27/8*w - 17/2],\ [3721, 61, -3/8*w^3 + 27/8*w - 17/2],\ [3739, 3739, -7/8*w^3 - 1/2*w^2 + 59/8*w + 3/2],\ [3739, 3739, w^3 + 1/2*w^2 - 19/2*w - 5],\ [3739, 3739, w^3 - 1/2*w^2 - 19/2*w + 5],\ [3739, 3739, -3/8*w^3 + 35/8*w - 17/2],\ [3779, 3779, 1/2*w^2 - 5/2*w - 9],\ [3779, 3779, -5/8*w^3 - 1/2*w^2 + 65/8*w - 5/2],\ [3779, 3779, 5/8*w^3 - 1/2*w^2 - 65/8*w - 5/2],\ [3779, 3779, 1/2*w^2 + 5/2*w - 9],\ [3821, 3821, -3/8*w^3 - 7/2*w^2 + 39/8*w + 81/2],\ [3821, 3821, 11/8*w^3 + w^2 - 131/8*w - 15/2],\ [3821, 3821, 11/8*w^3 - w^2 - 131/8*w + 15/2],\ [3821, 3821, -3/8*w^3 + 7/2*w^2 + 39/8*w - 81/2],\ [3881, 3881, 1/8*w^3 - w^2 - 25/8*w + 29/2],\ [3881, 3881, -5/4*w^3 + 3*w^2 + 33/4*w - 10],\ [3881, 3881, 3/8*w^3 + w^2 - 43/8*w + 3/2],\ [3881, 3881, -2*w^3 + 3*w^2 + 21*w - 29],\ [3889, 3889, 5/8*w^3 + 2*w^2 - 61/8*w - 37/2],\ [3889, 3889, -1/8*w^3 + 2*w^2 + 25/8*w - 17/2],\ [3889, 3889, 1/8*w^3 + 2*w^2 - 25/8*w - 17/2],\ [3889, 3889, -3/8*w^3 - 2*w^2 + 43/8*w + 35/2],\ [3911, 3911, 1/8*w^3 + w^2 - 25/8*w - 27/2],\ [3911, 3911, -3/8*w^3 - w^2 + 43/8*w - 1/2],\ [3911, 3911, -3/8*w^3 + w^2 + 43/8*w + 1/2],\ [3911, 3911, -1/8*w^3 + w^2 + 25/8*w - 27/2],\ [3931, 3931, -13/8*w^3 + 141/8*w + 5/2],\ [3931, 3931, 21/8*w^3 - 1/2*w^2 - 249/8*w + 13/2],\ [3931, 3931, -21/8*w^3 - 1/2*w^2 + 249/8*w + 13/2],\ [3931, 3931, -13/8*w^3 + 141/8*w - 5/2],\ [3989, 3989, -3/8*w^3 + w^2 + 59/8*w - 23/2],\ [3989, 3989, -5/8*w^3 + w^2 + 77/8*w - 3/2],\ [3989, 3989, -5/8*w^3 + 3/2*w^2 + 41/8*w - 27/2],\ [3989, 3989, 3/8*w^3 + w^2 - 59/8*w - 23/2]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^2 - 18 K. = NumberField(heckePol) hecke_eigenvalues_array = [1, 1, e, -e, 4, 2*e, -2*e, 2*e, -2*e, 14, e, e, -e, -e, -10, -10, -10, -10, 0, 0, 0, 0, 3*e, -3*e, 3*e, -3*e, 2, 2, 2, 2, -22, -22, 3*e, 3*e, -3*e, -3*e, 8, 8, 8, 8, 8, 8, -4, -4, -4, -4, -5*e, -5*e, 5*e, 5*e, e, -e, e, -e, 2, 2, 4*e, -4*e, 4*e, -4*e, -28, -28, -28, -28, 20, 20, -16, -16, -16, -16, e, e, -e, -e, -10, -10, -10, -10, -7*e, -7*e, 7*e, 7*e, -2*e, -2*e, 2*e, 2*e, -40, -40, -40, -40, -7*e, 7*e, -7*e, 7*e, -2*e, -2*e, 2*e, 2*e, -10, -10, 2, 2, 2, 2, 32, 32, 32, 32, 38, 38, 38, 38, 26, 26, 26, 26, 10*e, 10*e, -10*e, -10*e, -52, -52, -52, -52, 32, 32, 32, 32, -10*e, 10*e, -10*e, 10*e, 2*e, 2*e, -2*e, -2*e, -22, -22, 12*e, 12*e, -12*e, -12*e, 2, 2, 2, 2, 10*e, 10*e, -10*e, -10*e, -7*e, 7*e, -7*e, 7*e, -10, -10, -7*e, 7*e, -7*e, 7*e, 2, 2, 2, 2, -16, -16, -16, -16, 8*e, 8*e, -8*e, -8*e, 8, 8, 8, 8, 5*e, -5*e, 5*e, -5*e, -5*e, 5*e, -5*e, 5*e, -22, -22, -22, -22, 2*e, 2*e, -2*e, -2*e, 20, 20, 20, 20, e, e, -e, -e, -4, -4, -4, -4, e, e, -e, -e, -3*e, -3*e, 3*e, 3*e, 4*e, -4*e, 4*e, -4*e, -6*e, -6*e, 6*e, 6*e, 38, 38, 50, 50, 50, 50, 26, 26, 26, 26, -22, -22, -22, -22, -4*e, 4*e, -4*e, 4*e, 2, 2, 2, 2, 2*e, 2*e, -2*e, -2*e, -7*e, -7*e, 7*e, 7*e, 32, 32, 32, 32, 0, 0, 0, 0, 38, 38, 38, 38, -12*e, 12*e, -12*e, 12*e, 32, 32, 32, 32, 62, 62, 62, 62, 20, 20, 20, 20, -e, -e, e, e, 50, 50, 50, 50, -58, -58, 8*e, 8*e, -8*e, -8*e, -7*e, -7*e, 7*e, 7*e, -7*e, 7*e, -7*e, 7*e, 17*e, 17*e, -17*e, -17*e, 38, 38, 38, 38, -40, -40, -40, -40, -7*e, 7*e, -7*e, 7*e, -19*e, -19*e, 19*e, 19*e, 20, 20, 20, 20, 86, 86, -46, -46, -46, -46, -16, -16, -16, -16, -34, -34, -34, -34, -7*e, 7*e, -7*e, 7*e, 26, 26, 26, 26, 8*e, 8*e, -8*e, -8*e, -58, -58, -58, -58, -6*e, 6*e, -6*e, 6*e, -13*e, 13*e, -13*e, 13*e, -4*e, 4*e, -4*e, 4*e, -16, -16, -16, -16, 9*e, -9*e, 9*e, -9*e, 6*e, -6*e, 6*e, -6*e, -7*e, 7*e, -7*e, 7*e, -82, -82, -82, -82, -100, -100, -100, -100, -22*e, -22*e, 22*e, 22*e, 68, 68, 68, 68, 9*e, -9*e, 9*e, -9*e, -70, -70, -9*e, 9*e, -9*e, 9*e, 8, 8, 8, 8, 9*e, 9*e, -9*e, -9*e, -13*e, -13*e, 13*e, 13*e, -18*e, -18*e, 18*e, 18*e, -76, -76, -76, -76, 18*e, -18*e, 18*e, -18*e, 44, 44, 44, 44, -34, -34, -34, -34, -22, -22, -22, -22, 24*e, 24*e, -24*e, -24*e, -18*e, -18*e, 18*e, 18*e, -10, -10, -10, -10, 13*e, 13*e, -13*e, -13*e, 56, 56, 56, 56, 32, 32, 32, 32, -10, -10, -10, -10, -64, -64, -64, -64, -4*e, -4*e, 4*e, 4*e, -4, -4, -4, -4, 4*e, 4*e, -4*e, -4*e, -13*e, 13*e, -13*e, 13*e, -58, -58, -58, -58, 23*e, -23*e, 23*e, -23*e, 56, 56, 56, 56, -34, -34, -34, -34, 80, 80, 80, 80, 19*e, 19*e, -19*e, -19*e, -16*e, 16*e, -16*e, 16*e, -52, -52, -52, -52, -15*e, 15*e, -15*e, 15*e, 104, 104, 68, 68, 68, 68, 9*e, -9*e, 9*e, -9*e, -13*e, -13*e, 13*e, 13*e, 6*e, -6*e, 6*e, -6*e, -16, -16, -16, -16, 16*e, -16*e, 16*e, -16*e, -100, -100, -100, -100, -11*e, 11*e, -11*e, 11*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([4,2,1/4*w^3-1/2*w^2-11/4*w+5])] = -1 AL_eigenvalues[ZF.ideal([4,2,1/8*w^3-1/2*w^2-5/8*w+3/2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]