/* 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([-1, -6, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([11, 11, -w^2 + 2*w + 2]) primes_array = [ [3, 3, w + 1],\ [7, 7, w - 1],\ [8, 2, 2],\ [9, 3, -w^2 + 2*w + 4],\ [11, 11, -w^2 + 2*w + 2],\ [13, 13, -w^2 + w + 4],\ [19, 19, w + 3],\ [19, 19, -w^2 + 2*w + 5],\ [19, 19, -w^2 + 3*w + 2],\ [23, 23, w^2 - w - 3],\ [23, 23, -w^2 + 2],\ [23, 23, -w + 4],\ [31, 31, w^2 - 5],\ [43, 43, w^2 - 3*w - 3],\ [49, 7, w^2 - 6],\ [53, 53, 2*w - 5],\ [61, 61, 2*w^2 - 2*w - 9],\ [71, 71, 2*w - 3],\ [73, 73, 2*w^2 - 5*w - 5],\ [83, 83, w^2 - w - 9],\ [97, 97, 2*w^2 - 3*w - 7],\ [103, 103, w^2 - 3*w - 6],\ [109, 109, w^2 - 4*w - 3],\ [121, 11, 2*w^2 - w - 7],\ [125, 5, -5],\ [127, 127, w^2 + w - 5],\ [131, 131, w^2 - 11],\ [137, 137, 3*w^2 - 7*w - 8],\ [137, 137, 2*w^2 - 5*w - 6],\ [137, 137, -w^2 + w - 2],\ [139, 139, 3*w^2 - 2*w - 16],\ [139, 139, 3*w - 2],\ [139, 139, -w^2 + 3*w - 3],\ [151, 151, w^2 + w - 11],\ [157, 157, 2*w^2 - 3*w - 3],\ [163, 163, w^2 - w - 10],\ [169, 13, 2*w^2 - 3*w - 4],\ [173, 173, -3*w^2 + 6*w + 8],\ [191, 191, -4*w^2 + 7*w + 15],\ [193, 193, 2*w^2 - 3],\ [197, 197, w^2 - 3*w - 11],\ [199, 199, 3*w^2 - 5*w - 16],\ [211, 211, w^2 - 4*w - 9],\ [223, 223, 2*w^2 - w - 4],\ [227, 227, 3*w - 4],\ [229, 229, w^2 + w - 8],\ [241, 241, w^2 - 4*w - 6],\ [251, 251, w - 7],\ [257, 257, w^2 - 4*w - 7],\ [263, 263, 3*w^2 - 5*w - 10],\ [263, 263, 2*w^2 - 5*w - 15],\ [263, 263, -w^2 + 6*w - 1],\ [269, 269, -w^2 - w + 14],\ [277, 277, 2*w^2 - 5*w - 8],\ [277, 277, w^2 + 3*w - 3],\ [277, 277, 3*w^2 - 4*w - 12],\ [281, 281, -2*w - 7],\ [293, 293, 3*w^2 - 2*w - 12],\ [307, 307, 2*w^2 + w - 8],\ [313, 313, w^2 + 4*w - 2],\ [317, 317, 3*w^2 - 6*w - 5],\ [331, 331, 4*w^2 - 4*w - 19],\ [337, 337, -5*w^2 + 8*w + 21],\ [347, 347, 3*w^2 - 6*w - 13],\ [347, 347, 3*w^2 - 5*w - 22],\ [347, 347, 3*w^2 - 5*w - 9],\ [349, 349, w^2 - 5*w - 11],\ [353, 353, -w^2 + 6*w - 7],\ [359, 359, -4*w^2 + 8*w + 11],\ [367, 367, 3*w^2 - 4*w - 11],\ [373, 373, w^2 + 2*w - 6],\ [379, 379, 5*w^2 - 9*w - 18],\ [409, 409, -w^2 - 4],\ [439, 439, 3*w^2 - 6*w - 14],\ [443, 443, -w^2 - 2*w + 13],\ [443, 443, 2*w^2 - 15],\ [443, 443, 3*w^2 - 13],\ [449, 449, w^2 + 2*w - 7],\ [449, 449, 2*w^2 - 6*w - 7],\ [449, 449, 3*w^2 - 3*w - 11],\ [461, 461, -w^2 - 2*w - 5],\ [467, 467, 3*w^2 - 5*w - 7],\ [479, 479, -w^2 + 6*w - 4],\ [491, 491, 3*w^2 - 5*w - 6],\ [499, 499, w^2 - 5*w - 8],\ [509, 509, 3*w^2 - 6*w - 19],\ [521, 521, 3*w^2 - 2*w - 10],\ [523, 523, 4*w - 9],\ [541, 541, 3*w^2 - 3*w - 10],\ [547, 547, 2*w^2 + w - 20],\ [547, 547, w^2 - 6*w - 5],\ [547, 547, 6*w^2 - 11*w - 24],\ [557, 557, -5*w^2 + 11*w + 11],\ [563, 563, 3*w^2 - 6*w - 16],\ [569, 569, 4*w^2 - 5*w - 17],\ [587, 587, 5*w^2 - 8*w - 20],\ [593, 593, 5*w - 3],\ [593, 593, 3*w^2 - w - 17],\ [593, 593, w - 9],\ [613, 613, 2*w^2 - w - 19],\ [613, 613, 3*w^2 - 4*w - 5],\ [613, 613, 3*w^2 - w - 8],\ [617, 617, 3*w^2 - 2*w - 9],\ [617, 617, -w^2 + w - 5],\ [617, 617, 4*w^2 - 6*w - 15],\ [619, 619, -w^2 + 3*w - 6],\ [631, 631, 4*w^2 - 7*w - 21],\ [641, 641, -w^2 - 3*w + 20],\ [643, 643, 3*w^2 - 14],\ [643, 643, w^2 - w - 13],\ [643, 643, 2*w^2 - 9*w + 2],\ [647, 647, 2*w^2 - 6*w - 9],\ [653, 653, 3*w^2 - 5],\ [659, 659, 6*w^2 - 11*w - 21],\ [661, 661, w^2 - 6*w - 6],\ [661, 661, w^2 + 3*w - 6],\ [661, 661, 5*w^2 - 7*w - 22],\ [673, 673, w^2 - 6*w - 12],\ [677, 677, 4*w^2 - 7*w - 22],\ [677, 677, 3*w^2 - 7*w - 12],\ [677, 677, -2*w^2 - 3],\ [683, 683, -2*w - 9],\ [683, 683, 4*w^2 - 7*w - 12],\ [683, 683, 3*w^2 - 3*w - 8],\ [691, 691, 2*w^2 + w - 11],\ [701, 701, 3*w^2 - 3*w - 5],\ [709, 709, -w^2 - 2*w - 6],\ [727, 727, 3*w^2 - w - 6],\ [727, 727, 3*w^2 - w - 27],\ [727, 727, 3*w^2 - w - 5],\ [733, 733, -2*w^2 + 9*w - 5],\ [739, 739, 3*w^2 - 4*w - 23],\ [743, 743, 2*w^2 - 7*w - 7],\ [743, 743, 3*w^2 - w - 20],\ [743, 743, 3*w^2 - 2*w - 7],\ [757, 757, -w - 9],\ [757, 757, 4*w^2 - 2*w - 29],\ [757, 757, 2*w^2 - 3*w - 18],\ [761, 761, 3*w^2 - 2*w - 6],\ [761, 761, 3*w^2 - 2*w - 25],\ [773, 773, -5*w - 12],\ [787, 787, -3*w - 10],\ [809, 809, 4*w^2 - w - 19],\ [821, 821, 5*w^2 - 10*w - 19],\ [823, 823, -4*w - 11],\ [827, 827, -7*w - 5],\ [827, 827, 2*w^2 - 6*w - 13],\ [827, 827, -w^2 - 2*w + 18],\ [839, 839, 6*w^2 - 9*w - 26],\ [839, 839, 5*w^2 - 12*w - 13],\ [839, 839, w - 10],\ [857, 857, -w^2 + 4*w - 8],\ [859, 859, 3*w^2 - 8*w - 10],\ [859, 859, 4*w^2 - 9*w - 14],\ [859, 859, 3*w^2 - 26],\ [863, 863, 2*w^2 + 3*w - 7],\ [877, 877, -5*w^2 + 11*w + 9],\ [877, 877, -5*w^2 + 10*w + 13],\ [877, 877, -w^2 + w - 6],\ [881, 881, w^2 - 3*w - 14],\ [883, 883, -w^2 + 3*w - 7],\ [887, 887, -3*w^2 + 6*w - 2],\ [907, 907, w^2 + 3*w - 8],\ [911, 911, 4*w^2 - 6*w - 29],\ [937, 937, -6*w^2 + 11*w + 25],\ [953, 953, 6*w^2 - 6*w - 29],\ [961, 31, -w^2 + 7*w - 5],\ [967, 967, 2*w^2 + w - 14],\ [971, 971, 5*w^2 - 3*w - 27],\ [971, 971, 4*w - 15],\ [971, 971, w^2 - 2*w - 14],\ [977, 977, 3*w^2 - 5*w - 24],\ [983, 983, w^2 - 4*w - 15],\ [991, 991, 6*w^2 - 10*w - 23],\ [991, 991, 5*w^2 - 6*w - 22],\ [991, 991, 3*w^2 + w - 13]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^5 - 2*x^4 - 7*x^3 + 8*x^2 + 8*x + 1 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, e^4 - 2*e^3 - 7*e^2 + 9*e + 6, -4/3*e^4 + 10/3*e^3 + 23/3*e^2 - 14*e - 14/3, -e^4 + 2*e^3 + 6*e^2 - 8*e - 1, 1, e^4 - 2*e^3 - 6*e^2 + 7*e + 4, 1/3*e^4 - 4/3*e^3 - 5/3*e^2 + 5*e + 5/3, -e^2 + 2*e + 3, 4/3*e^4 - 7/3*e^3 - 26/3*e^2 + 8*e + 29/3, 5/3*e^4 - 11/3*e^3 - 31/3*e^2 + 16*e + 25/3, -2*e^4 + 4*e^3 + 13*e^2 - 18*e - 6, 1/3*e^4 - 4/3*e^3 + 1/3*e^2 + 6*e - 16/3, 4/3*e^4 - 13/3*e^3 - 23/3*e^2 + 21*e + 20/3, -e^4 + 3*e^3 + 4*e^2 - 14*e, -7/3*e^4 + 16/3*e^3 + 41/3*e^2 - 19*e - 35/3, -10/3*e^4 + 25/3*e^3 + 59/3*e^2 - 38*e - 41/3, -2*e^4 + 4*e^3 + 13*e^2 - 13*e - 13, 4/3*e^4 - 7/3*e^3 - 32/3*e^2 + 11*e + 20/3, 5*e^4 - 13*e^3 - 29*e^2 + 54*e + 24, -1/3*e^4 - 2/3*e^3 + 8/3*e^2 + 5*e - 2/3, -e^4 + e^3 + 9*e^2 - 5*e - 9, -4*e^4 + 9*e^3 + 26*e^2 - 43*e - 17, 2*e^3 - 4*e^2 - 11*e + 15, -e^4 + 2*e^3 + 10*e^2 - 11*e - 16, 4/3*e^4 - 7/3*e^3 - 32/3*e^2 + 4*e + 41/3, 2*e^4 - 6*e^3 - 9*e^2 + 29*e + 3, -11/3*e^4 + 29/3*e^3 + 58/3*e^2 - 37*e - 28/3, -11/3*e^4 + 26/3*e^3 + 70/3*e^2 - 35*e - 34/3, 2/3*e^4 - 11/3*e^3 - 7/3*e^2 + 21*e + 16/3, -5/3*e^4 + 11/3*e^3 + 37/3*e^2 - 20*e - 37/3, 20/3*e^4 - 47/3*e^3 - 121/3*e^2 + 64*e + 76/3, e^4 - 7*e^2 - 9*e + 7, 4/3*e^4 - 4/3*e^3 - 26/3*e^2 + 5*e + 8/3, -2*e^4 + 5*e^3 + 14*e^2 - 28*e - 18, -10/3*e^4 + 25/3*e^3 + 59/3*e^2 - 32*e - 26/3, 2*e^4 - 6*e^3 - 9*e^2 + 20*e, 10/3*e^4 - 16/3*e^3 - 74/3*e^2 + 21*e + 56/3, -22/3*e^4 + 55/3*e^3 + 134/3*e^2 - 81*e - 113/3, -11/3*e^4 + 23/3*e^3 + 79/3*e^2 - 33*e - 73/3, 5/3*e^4 - 11/3*e^3 - 43/3*e^2 + 15*e + 64/3, 3*e^4 - 7*e^3 - 15*e^2 + 29*e + 2, 17/3*e^4 - 47/3*e^3 - 94/3*e^2 + 70*e + 70/3, 13/3*e^4 - 37/3*e^3 - 62/3*e^2 + 53*e + 32/3, 5*e^4 - 13*e^3 - 32*e^2 + 63*e + 36, 1/3*e^4 + 5/3*e^3 - 17/3*e^2 - 10*e + 50/3, -7/3*e^4 + 13/3*e^3 + 41/3*e^2 - 13*e - 50/3, -7/3*e^4 + 13/3*e^3 + 44/3*e^2 - 10*e - 23/3, -14/3*e^4 + 35/3*e^3 + 94/3*e^2 - 58*e - 58/3, 1/3*e^4 + 2/3*e^3 - 11/3*e^2 - 9*e - 1/3, e^4 - 4*e^3 - 2*e^2 + 21*e - 13, 4*e^4 - 11*e^3 - 19*e^2 + 42*e + 5, -11/3*e^4 + 23/3*e^3 + 79/3*e^2 - 33*e - 82/3, 8/3*e^4 - 17/3*e^3 - 64/3*e^2 + 28*e + 88/3, 14/3*e^4 - 32/3*e^3 - 79/3*e^2 + 41*e + 70/3, 5*e^4 - 12*e^3 - 27*e^2 + 41*e + 9, 4*e^4 - 9*e^3 - 22*e^2 + 38*e + 5, -3*e^4 + 6*e^3 + 18*e^2 - 18*e, -14/3*e^4 + 41/3*e^3 + 76/3*e^2 - 56*e - 52/3, 3*e^4 - 10*e^3 - 16*e^2 + 49*e + 15, 2*e^4 - 4*e^3 - 9*e^2 + 8*e - 5, 2/3*e^4 + 4/3*e^3 - 34/3*e^2 - 4*e + 103/3, e^4 - 4*e^3 + 8*e - 25, 8/3*e^4 - 20/3*e^3 - 49/3*e^2 + 22*e + 16/3, -23/3*e^4 + 59/3*e^3 + 139/3*e^2 - 85*e - 73/3, -7/3*e^4 + 1/3*e^3 + 65/3*e^2 - e - 56/3, 10/3*e^4 - 22/3*e^3 - 80/3*e^2 + 34*e + 89/3, 26/3*e^4 - 53/3*e^3 - 160/3*e^2 + 73*e + 70/3, 28/3*e^4 - 58/3*e^3 - 179/3*e^2 + 84*e + 137/3, -19/3*e^4 + 49/3*e^3 + 110/3*e^2 - 76*e - 65/3, -25/3*e^4 + 55/3*e^3 + 152/3*e^2 - 68*e - 107/3, 13/3*e^4 - 28/3*e^3 - 83/3*e^2 + 32*e + 80/3, 5/3*e^4 - 20/3*e^3 - 34/3*e^2 + 43*e + 43/3, -8/3*e^4 + 14/3*e^3 + 67/3*e^2 - 23*e - 64/3, 26/3*e^4 - 74/3*e^3 - 145/3*e^2 + 110*e + 100/3, 19/3*e^4 - 37/3*e^3 - 134/3*e^2 + 51*e + 143/3, 1/3*e^4 - 1/3*e^3 - 23/3*e^2 + 7*e + 74/3, -e^4 + e^3 + 9*e^2 - 2*e - 25, -17/3*e^4 + 50/3*e^3 + 118/3*e^2 - 89*e - 118/3, 8/3*e^4 - 32/3*e^3 - 40/3*e^2 + 48*e + 64/3, 1/3*e^4 + 2/3*e^3 - 17/3*e^2 - 8*e - 16/3, 8/3*e^4 - 20/3*e^3 - 46/3*e^2 + 23*e - 47/3, 22/3*e^4 - 49/3*e^3 - 143/3*e^2 + 74*e + 83/3, -22/3*e^4 + 46/3*e^3 + 131/3*e^2 - 49*e - 80/3, 4*e^4 - 10*e^3 - 26*e^2 + 52*e + 16, 4/3*e^4 - 10/3*e^3 - 29/3*e^2 + 17*e - 49/3, 32/3*e^4 - 68/3*e^3 - 211/3*e^2 + 98*e + 115/3, -6*e^4 + 17*e^3 + 35*e^2 - 80*e - 20, -22/3*e^4 + 58/3*e^3 + 143/3*e^2 - 98*e - 95/3, -13*e^4 + 29*e^3 + 79*e^2 - 118*e - 53, -6*e^4 + 10*e^3 + 46*e^2 - 40*e - 32, 16/3*e^4 - 40/3*e^3 - 104/3*e^2 + 60*e + 152/3, -5*e^4 + 11*e^3 + 39*e^2 - 53*e - 38, -5/3*e^4 - 10/3*e^3 + 76/3*e^2 + 19*e - 100/3, 4*e^4 - 10*e^3 - 32*e^2 + 52*e + 34, -11*e^4 + 26*e^3 + 71*e^2 - 122*e - 51, 10*e^4 - 19*e^3 - 65*e^2 + 76*e + 55, e^4 - 4*e^3 - 5*e^2 + 20*e - 6, -19/3*e^4 + 46/3*e^3 + 116/3*e^2 - 60*e - 134/3, 5/3*e^4 + 4/3*e^3 - 67/3*e^2 - 12*e + 112/3, 3*e^4 - 9*e^3 - 17*e^2 + 43*e - 3, -11/3*e^4 + 26/3*e^3 + 76/3*e^2 - 34*e - 64/3, -31/3*e^4 + 79/3*e^3 + 182/3*e^2 - 121*e - 113/3, 8/3*e^4 + 1/3*e^3 - 64/3*e^2 - 15*e + 46/3, 8/3*e^4 - 11/3*e^3 - 67/3*e^2 + 13*e + 76/3, -40/3*e^4 + 103/3*e^3 + 248/3*e^2 - 156*e - 194/3, 16/3*e^4 - 40/3*e^3 - 119/3*e^2 + 61*e + 146/3, 10*e^4 - 25*e^3 - 57*e^2 + 103*e + 22, 25/3*e^4 - 61/3*e^3 - 131/3*e^2 + 86*e + 44/3, -13/3*e^4 + 40/3*e^3 + 80/3*e^2 - 67*e - 101/3, 5/3*e^4 - 5/3*e^3 - 64/3*e^2 + 19*e + 118/3, -6*e^4 + 18*e^3 + 34*e^2 - 83*e - 9, -1/3*e^4 - 2/3*e^3 - 1/3*e^2 + 3*e + 58/3, -23/3*e^4 + 47/3*e^3 + 148/3*e^2 - 67*e - 97/3, e^4 + 3*e^3 - 8*e^2 - 26*e - 6, 11*e^4 - 23*e^3 - 70*e^2 + 90*e + 53, -7*e^4 + 13*e^3 + 51*e^2 - 58*e - 37, -11/3*e^4 + 17/3*e^3 + 85/3*e^2 - 26*e - 34/3, 17/3*e^4 - 35/3*e^3 - 100/3*e^2 + 45*e - 5/3, -35/3*e^4 + 83/3*e^3 + 190/3*e^2 - 110*e - 88/3, 1/3*e^4 + 5/3*e^3 - 17/3*e^2 - 13*e + 86/3, e^3 - 9*e^2 - 6*e + 32, -37/3*e^4 + 82/3*e^3 + 236/3*e^2 - 116*e - 158/3, -13/3*e^4 + 22/3*e^3 + 95/3*e^2 - 34*e - 65/3, -8/3*e^4 + 5/3*e^3 + 70/3*e^2 + 4*e - 88/3, 7/3*e^4 - 16/3*e^3 - 47/3*e^2 + 21*e + 8/3, 7*e^4 - 11*e^3 - 49*e^2 + 33*e + 41, 5*e^3 - 5*e^2 - 20*e, 5/3*e^4 - 14/3*e^3 + 11/3*e^2 + 8*e - 122/3, -10/3*e^4 + 16/3*e^3 + 74/3*e^2 - 9*e - 131/3, -10*e^4 + 24*e^3 + 67*e^2 - 116*e - 56, 17/3*e^4 - 32/3*e^3 - 97/3*e^2 + 47*e - 14/3, 16/3*e^4 - 31/3*e^3 - 95/3*e^2 + 39*e + 35/3, 4*e^4 - 3*e^3 - 38*e^2 + 6*e + 46, 6*e^4 - 17*e^3 - 31*e^2 + 81*e + 18, -29/3*e^4 + 65/3*e^3 + 196/3*e^2 - 87*e - 196/3, 25/3*e^4 - 58/3*e^3 - 170/3*e^2 + 83*e + 110/3, 4/3*e^4 - 10/3*e^3 - 20/3*e^2 + 26*e + 23/3, 2*e^4 - 22*e^2 - 7*e + 26, 31/3*e^4 - 67/3*e^3 - 185/3*e^2 + 90*e + 68/3, 8/3*e^4 - 17/3*e^3 - 64/3*e^2 + 22*e + 61/3, -6*e^4 + 14*e^3 + 36*e^2 - 64*e - 31, 12*e^4 - 30*e^3 - 80*e^2 + 136*e + 72, -32/3*e^4 + 59/3*e^3 + 220/3*e^2 - 87*e - 130/3, -56/3*e^4 + 140/3*e^3 + 331/3*e^2 - 199*e - 241/3, -13*e^4 + 27*e^3 + 81*e^2 - 102*e - 39, 10/3*e^4 - 16/3*e^3 - 89/3*e^2 + 32*e + 188/3, -16/3*e^4 + 28/3*e^3 + 128/3*e^2 - 44*e - 107/3, 46/3*e^4 - 106/3*e^3 - 278/3*e^2 + 145*e + 200/3, 22/3*e^4 - 52/3*e^3 - 137/3*e^2 + 78*e + 122/3, 14/3*e^4 - 41/3*e^3 - 82/3*e^2 + 61*e + 115/3, -3*e^4 + 4*e^3 + 21*e^2 + 2*e - 42, -8/3*e^4 + 14/3*e^3 + 61/3*e^2 - 32*e - 16/3, 10*e^4 - 23*e^3 - 64*e^2 + 108*e + 39, 8/3*e^4 - 20/3*e^3 - 67/3*e^2 + 26*e + 97/3, -31/3*e^4 + 79/3*e^3 + 188/3*e^2 - 109*e - 140/3, -8/3*e^4 + 17/3*e^3 + 46/3*e^2 - 22*e - 70/3, 2/3*e^4 - 8/3*e^3 - 4/3*e^2 + 17*e - 56/3, 29/3*e^4 - 77/3*e^3 - 154/3*e^2 + 112*e + 133/3, -19*e^4 + 41*e^3 + 117*e^2 - 161*e - 85, -11*e^4 + 22*e^3 + 70*e^2 - 67*e - 62, -22/3*e^4 + 52/3*e^3 + 134/3*e^2 - 85*e - 68/3, -17/3*e^4 + 44/3*e^3 + 127/3*e^2 - 68*e - 166/3, -3*e^4 + 4*e^3 + 19*e^2 - e - 5, 10/3*e^4 - 1/3*e^3 - 86/3*e^2 - 5*e + 101/3, -10*e^4 + 26*e^3 + 52*e^2 - 105*e - 28, -44/3*e^4 + 95/3*e^3 + 274/3*e^2 - 129*e - 190/3, 17*e^4 - 36*e^3 - 100*e^2 + 137*e + 41, -14*e^4 + 35*e^3 + 87*e^2 - 163*e - 78, 31/3*e^4 - 70/3*e^3 - 194/3*e^2 + 95*e + 74/3, 26/3*e^4 - 59/3*e^3 - 145/3*e^2 + 61*e + 49/3, 8/3*e^4 - 32/3*e^3 - 28/3*e^2 + 59*e - 44/3, 11/3*e^4 - 26/3*e^3 - 25/3*e^2 + 22*e - 107/3, 25/3*e^4 - 61/3*e^3 - 143/3*e^2 + 94*e + 41/3, 4/3*e^4 - 19/3*e^3 - 17/3*e^2 + 21*e + 38/3, -1/3*e^4 - 5/3*e^3 + 23/3*e^2 + 24*e - 104/3, 2*e^4 - 10*e^3 - 9*e^2 + 44*e + 13] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([11, 11, -w^2 + 2*w + 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]