/* 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([-3, -7, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([11, 11, -w^2 + 5]) primes_array = [ [3, 3, w],\ [3, 3, w + 1],\ [3, 3, w + 2],\ [8, 2, 2],\ [11, 11, -w^2 + 5],\ [13, 13, w^2 - w - 7],\ [17, 17, -w^2 + w + 4],\ [19, 19, -w^2 - w + 4],\ [29, 29, 2*w^2 - 2*w - 11],\ [31, 31, w^2 - 2*w - 4],\ [37, 37, -2*w^2 + 3*w + 7],\ [41, 41, w^2 - 2],\ [59, 59, 2*w^2 - 13],\ [61, 61, w^2 + w - 10],\ [67, 67, 2*w^2 - w - 11],\ [73, 73, -w^2 - 1],\ [83, 83, w^2 - w - 10],\ [89, 89, -w^2 + 4*w - 2],\ [97, 97, w^2 - 2*w - 7],\ [97, 97, -w^2 - 4*w - 5],\ [97, 97, 2*w^2 + w - 8],\ [101, 101, -4*w^2 + 2*w + 25],\ [103, 103, w^2 + w - 7],\ [107, 107, -3*w - 4],\ [109, 109, 5*w^2 - 3*w - 31],\ [121, 11, 2*w^2 - 3*w - 4],\ [125, 5, -5],\ [137, 137, -5*w^2 + 3*w + 34],\ [139, 139, w^2 + 2*w - 4],\ [151, 151, 3*w^2 - 23],\ [151, 151, w^2 - 3*w - 5],\ [151, 151, 3*w^2 - 3*w - 17],\ [157, 157, 4*w^2 - 9*w - 8],\ [157, 157, w^2 + 3*w - 2],\ [157, 157, 2*w^2 - w - 2],\ [167, 167, 2*w^2 + w - 11],\ [167, 167, -w^2 + 11],\ [167, 167, -3*w^2 + 19],\ [169, 13, w^2 - 4*w - 4],\ [173, 173, 2*w^2 - 3*w - 10],\ [179, 179, -3*w + 7],\ [191, 191, -w^2 + 5*w - 5],\ [193, 193, -w^2 + w - 2],\ [199, 199, 3*w - 2],\ [211, 211, w^2 - 3*w - 11],\ [223, 223, 3*w^2 - 20],\ [223, 223, w^2 - 5*w - 4],\ [223, 223, 2*w^2 - w - 8],\ [229, 229, 4*w^2 - 3*w - 26],\ [229, 229, 2*w^2 + w - 20],\ [229, 229, 2*w^2 - 2*w - 5],\ [239, 239, -6*w^2 + 3*w + 38],\ [241, 241, -w^2 + 4*w - 5],\ [257, 257, -2*w^2 + 5*w - 1],\ [263, 263, -2*w^2 - w + 17],\ [269, 269, -w^2 - w + 13],\ [269, 269, 3*w - 4],\ [269, 269, -4*w^2 + w + 31],\ [271, 271, 2*w^2 - 7],\ [271, 271, 3*w - 5],\ [271, 271, w^2 - 3*w - 8],\ [289, 17, 2*w^2 + w - 5],\ [307, 307, 2*w^2 - w - 5],\ [311, 311, 3*w^2 - 3*w - 19],\ [311, 311, -7*w^2 + 13*w + 19],\ [311, 311, w^2 - 2*w - 13],\ [313, 313, w^2 + 2*w - 7],\ [317, 317, -5*w^2 + w + 35],\ [331, 331, -w^2 + 3*w - 4],\ [337, 337, 3*w^2 - 3*w - 13],\ [343, 7, -7],\ [347, 347, 2*w^2 - 3*w - 13],\ [349, 349, 3*w^2 - 3*w - 20],\ [359, 359, -w^2 + 5*w - 2],\ [361, 19, -2*w^2 + 7*w - 1],\ [389, 389, -2*w^2 + w - 1],\ [397, 397, w^2 - 6*w + 10],\ [401, 401, 6*w^2 - 3*w - 44],\ [419, 419, -3*w^2 + 6*w + 10],\ [419, 419, 4*w^2 - 2*w - 31],\ [419, 419, -4*w^2 + 4*w + 19],\ [421, 421, 6*w^2 - 12*w - 13],\ [431, 431, 4*w^2 - 7*w - 10],\ [433, 433, w^2 - 4*w - 7],\ [443, 443, 2*w^2 + 4*w - 5],\ [443, 443, 5*w^2 - 11*w - 11],\ [443, 443, 3*w^2 - 14],\ [449, 449, -2*w^2 + 2*w - 1],\ [457, 457, w^2 - 6*w - 5],\ [457, 457, w^2 + 3*w - 5],\ [457, 457, 6*w^2 - 3*w - 37],\ [463, 463, w^2 + 5*w - 1],\ [467, 467, w^2 - w - 13],\ [479, 479, 5*w^2 - 9*w - 16],\ [487, 487, -6*w - 5],\ [499, 499, 3*w^2 - 3*w - 4],\ [499, 499, 3*w^2 + 3*w - 1],\ [499, 499, w^2 - 5*w + 8],\ [503, 503, 4*w^2 - 5*w - 16],\ [509, 509, 2*w^2 - 5*w - 8],\ [521, 521, 4*w^2 - w - 22],\ [523, 523, w^2 - 5*w - 16],\ [547, 547, 5*w^2 - 2*w - 38],\ [547, 547, 8*w^2 - 3*w - 58],\ [547, 547, 4*w^2 - 29],\ [557, 557, 7*w^2 - 4*w - 43],\ [557, 557, 3*w - 11],\ [557, 557, 2*w^2 - 4*w - 11],\ [569, 569, 5*w^2 - 4*w - 32],\ [569, 569, 3*w^2 - 3*w - 11],\ [569, 569, w^2 + 2*w - 16],\ [571, 571, w^2 - 4*w - 10],\ [593, 593, 2*w^2 - 6*w - 7],\ [601, 601, -w^2 - 3*w + 14],\ [607, 607, 3*w^2 + 3*w - 7],\ [619, 619, 3*w^2 - 6*w - 11],\ [631, 631, -w^2 - w - 5],\ [641, 641, 3*w^2 - 3*w - 5],\ [647, 647, -w^2 + 6*w - 1],\ [653, 653, -5*w^2 + 4*w + 35],\ [661, 661, 3*w^2 - 3*w - 10],\ [673, 673, w^2 + 4*w - 4],\ [677, 677, 5*w^2 - 6*w - 25],\ [677, 677, w^2 - 14],\ [677, 677, 4*w^2 - 3*w - 20],\ [691, 691, 5*w^2 - 2*w - 29],\ [701, 701, 5*w^2 - 10*w - 14],\ [719, 719, -3*w - 11],\ [727, 727, -2*w^2 + 9*w - 8],\ [733, 733, -w^2 - 4*w - 8],\ [739, 739, w^2 + 3*w - 8],\ [743, 743, 2*w^2 - 4*w - 17],\ [757, 757, -w^2 + w - 5],\ [769, 769, 3*w^2 - 3*w - 7],\ [769, 769, -w^2 - 3*w - 7],\ [769, 769, 5*w^2 - 3*w - 28],\ [773, 773, 7*w^2 - 6*w - 38],\ [787, 787, 2*w^2 - w - 20],\ [797, 797, -5*w^2 + 14*w - 1],\ [821, 821, -w^2 + 6*w - 4],\ [823, 823, 7*w^2 - 6*w - 41],\ [839, 839, 4*w^2 - 6*w - 11],\ [841, 29, 5*w^2 - 4*w - 26],\ [857, 857, 3*w^2 - 11],\ [863, 863, 2*w^2 + 2*w - 17],\ [881, 881, 5*w^2 - 5*w - 29],\ [883, 883, -4*w^2 + 8*w + 13],\ [907, 907, 4*w^2 - 9*w - 11],\ [911, 911, 2*w^2 + 3*w - 10],\ [947, 947, 2*w^2 + 5*w - 5],\ [953, 953, 2*w^2 - 5*w - 11],\ [961, 31, w^2 - 5*w - 13],\ [967, 967, 2*w^2 - 3*w - 22],\ [967, 967, 5*w^2 - 9*w - 10],\ [967, 967, 3*w^2 - 10],\ [977, 977, 5*w^2 - 37],\ [983, 983, 7*w^2 - 5*w - 40],\ [997, 997, -7*w^2 + 5*w + 49]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^6 + 3*x^5 - 9*x^4 - 28*x^3 + 15*x^2 + 63*x + 26 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 1/3*e^4 + 1/3*e^3 - 7/3*e^2 - 4/3*e + 1/3, -1/3*e^5 - 2/3*e^4 + 3*e^3 + 14/3*e^2 - 6*e - 19/3, 1/3*e^4 + 4/3*e^3 - 1/3*e^2 - 19/3*e - 23/3, -1, -1/3*e^5 - e^4 + 5/3*e^3 + 6*e^2 - 2/3*e - 20/3, 2/3*e^4 + 5/3*e^3 - 11/3*e^2 - 26/3*e - 1/3, 1/3*e^5 + 4/3*e^4 - 7/3*e^3 - 28/3*e^2 + 10/3*e + 11, 1/3*e^5 + e^4 - 5/3*e^3 - 6*e^2 - 1/3*e + 5/3, -e^2 + 4, -1/3*e^5 - 2/3*e^4 + 4*e^3 + 17/3*e^2 - 12*e - 34/3, -e^4 - 2*e^3 + 5*e^2 + 8*e, 1/3*e^5 + 2/3*e^4 - 3*e^3 - 17/3*e^2 + 6*e + 40/3, e^5 + 5/3*e^4 - 31/3*e^3 - 41/3*e^2 + 82/3*e + 86/3, 1/3*e^5 + e^4 - 2/3*e^3 - 4*e^2 - 22/3*e + 2/3, -e^5 - 7/3*e^4 + 23/3*e^3 + 37/3*e^2 - 41/3*e - 19/3, -2/3*e^5 - 2*e^4 + 16/3*e^3 + 12*e^2 - 31/3*e - 25/3, e^5 + 1/3*e^4 - 38/3*e^3 - 13/3*e^2 + 110/3*e + 52/3, 5/3*e^4 + 11/3*e^3 - 29/3*e^2 - 50/3*e - 4/3, -e^5 - 4/3*e^4 + 35/3*e^3 + 31/3*e^2 - 110/3*e - 76/3, 4/3*e^5 + 4/3*e^4 - 40/3*e^3 - 25/3*e^2 + 85/3*e + 7, -1/3*e^5 - e^4 - 1/3*e^3 + 5*e^2 + 43/3*e - 17/3, e^5 + 4/3*e^4 - 26/3*e^3 - 16/3*e^2 + 50/3*e + 16/3, -e^5 - 4/3*e^4 + 23/3*e^3 + 13/3*e^2 - 38/3*e + 29/3, -e^5 - 4/3*e^4 + 44/3*e^3 + 46/3*e^2 - 152/3*e - 133/3, 2*e^5 + 4*e^4 - 17*e^3 - 26*e^2 + 37*e + 32, e^5 + 4/3*e^4 - 38/3*e^3 - 40/3*e^2 + 104/3*e + 73/3, 1/3*e^5 + 2/3*e^4 - 4*e^3 - 23/3*e^2 + 14*e + 43/3, 2/3*e^5 + 5/3*e^4 - 23/3*e^3 - 47/3*e^2 + 65/3*e + 32, -7/3*e^5 - 8/3*e^4 + 26*e^3 + 71/3*e^2 - 71*e - 169/3, -1/3*e^5 - 4/3*e^4 - 5/3*e^3 + 7/3*e^2 + 59/3*e + 8, 1/3*e^5 + 4/3*e^4 - 7/3*e^3 - 13/3*e^2 + 22/3*e - 12, 1/3*e^5 - e^4 - 14/3*e^3 + 6*e^2 + 23/3*e - 19/3, -1/3*e^5 + 5/3*e^3 - e^2 + 25/3*e + 16/3, -2/3*e^5 - 8/3*e^4 + 5/3*e^3 + 53/3*e^2 + 31/3*e - 15, -2/3*e^5 - 4/3*e^4 + 7*e^3 + 31/3*e^2 - 17*e - 35/3, -1/3*e^5 - 5/3*e^4 + 6*e^3 + 44/3*e^2 - 31*e - 76/3, e^5 + 8/3*e^4 - 19/3*e^3 - 47/3*e^2 + 19/3*e + 26/3, -e^4 + e^3 + 11*e^2 - 10*e - 19, 1/3*e^5 - 4/3*e^4 - 10*e^3 + 13/3*e^2 + 43*e + 34/3, e^4 + 4*e^3 - 2*e^2 - 22*e - 12, -e^5 - 8/3*e^4 + 19/3*e^3 + 47/3*e^2 - 25/3*e - 32/3, 1/3*e^5 + 8/3*e^4 - e^3 - 62/3*e^2 + 5*e + 94/3, e^5 + 2*e^4 - 12*e^3 - 21*e^2 + 39*e + 42, e^5 - 2/3*e^4 - 53/3*e^3 - 25/3*e^2 + 182/3*e + 178/3, 4/3*e^4 + 16/3*e^3 - 7/3*e^2 - 67/3*e - 56/3, 2/3*e^5 - 49/3*e^3 - 14*e^2 + 193/3*e + 181/3, 2/3*e^5 + 4/3*e^4 - 7*e^3 - 22/3*e^2 + 23*e + 26/3, 1/3*e^5 + e^4 - 2/3*e^3 - 2*e^2 - 31/3*e - 64/3, 2/3*e^5 + 2/3*e^4 - 35/3*e^3 - 44/3*e^2 + 137/3*e + 52, 2*e^5 + 5*e^4 - 15*e^3 - 31*e^2 + 23*e + 36, -1/3*e^5 - 5/3*e^4 - e^3 + 35/3*e^2 + 14*e - 67/3, -2/3*e^5 - 8/3*e^4 + 23/3*e^3 + 65/3*e^2 - 74/3*e - 28, 8/3*e^5 + 4*e^4 - 82/3*e^3 - 30*e^2 + 181/3*e + 124/3, 1/3*e^5 - e^4 - 14/3*e^3 + 7*e^2 + 29/3*e + 20/3, -3*e^5 - 5*e^4 + 27*e^3 + 32*e^2 - 61*e - 49, 4/3*e^5 + 11/3*e^4 - 15*e^3 - 104/3*e^2 + 43*e + 166/3, -8/3*e^5 - 5*e^4 + 55/3*e^3 + 24*e^2 - 64/3*e - 34/3, 2/3*e^5 - 4/3*e^4 - 26/3*e^3 + 28/3*e^2 + 50/3*e - 8, 4/3*e^5 + 8/3*e^4 - 10*e^3 - 41/3*e^2 + 14*e + 25/3, -2/3*e^5 + 2*e^4 + 43/3*e^3 - 11*e^2 - 151/3*e - 4/3, 2*e^4 + 3*e^3 - 6*e^2 - 7*e - 20, 1/3*e^5 + 7/3*e^4 + 5/3*e^3 - 37/3*e^2 - 35/3*e - 1, -1/3*e^5 - 2*e^4 - 13/3*e^3 + 5*e^2 + 106/3*e + 67/3, e^5 + 4/3*e^4 - 20/3*e^3 + 5/3*e^2 + 26/3*e - 86/3, 1/3*e^5 - 2/3*e^4 - 25/3*e^3 - 1/3*e^2 + 118/3*e + 11, -11/3*e^4 - 32/3*e^3 + 59/3*e^2 + 143/3*e - 20/3, -5/3*e^5 - 11/3*e^4 + 50/3*e^3 + 86/3*e^2 - 119/3*e - 45, 5/3*e^5 + 14/3*e^4 - 53/3*e^3 - 116/3*e^2 + 140/3*e + 65, -5/3*e^5 - 7/3*e^4 + 18*e^3 + 67/3*e^2 - 47*e - 146/3, -2/3*e^5 - 16/3*e^4 + 3*e^3 + 118/3*e^2 - 5*e - 143/3, e^5 + 11/3*e^4 - 22/3*e^3 - 71/3*e^2 + 55/3*e + 32/3, -5/3*e^5 - 10/3*e^4 + 18*e^3 + 82/3*e^2 - 52*e - 194/3, 14/3*e^5 + 26/3*e^4 - 122/3*e^3 - 176/3*e^2 + 239/3*e + 82, -2/3*e^5 - 5/3*e^4 + 23/3*e^3 + 47/3*e^2 - 59/3*e - 48, 2/3*e^5 + 14/3*e^4 + 13/3*e^3 - 62/3*e^2 - 103/3*e - 10, -2/3*e^5 + 1/3*e^4 + 29/3*e^3 + 17/3*e^2 - 83/3*e - 35, -7/3*e^5 - 6*e^4 + 50/3*e^3 + 37*e^2 - 83/3*e - 92/3, 2*e^5 + 11/3*e^4 - 46/3*e^3 - 62/3*e^2 + 58/3*e + 44/3, 5/3*e^5 + 3*e^4 - 52/3*e^3 - 24*e^2 + 133/3*e + 154/3, 3*e^5 + 7/3*e^4 - 113/3*e^3 - 88/3*e^2 + 329/3*e + 256/3, -3*e^5 - 5*e^4 + 34*e^3 + 46*e^2 - 97*e - 94, -4/3*e^5 - 8/3*e^4 + 16*e^3 + 89/3*e^2 - 48*e - 172/3, -e^5 + 2*e^4 + 26*e^3 + 4*e^2 - 100*e - 65, 2/3*e^5 + 2/3*e^4 - 5/3*e^3 - 2/3*e^2 - 37/3*e - 1, -5/3*e^5 - 5*e^4 + 16/3*e^3 + 19*e^2 + 62/3*e + 44/3, 1/3*e^5 + 1/3*e^4 - 13/3*e^3 + 11/3*e^2 + 55/3*e - 17, -4/3*e^5 - 4/3*e^4 + 37/3*e^3 + 34/3*e^2 - 70/3*e - 29, 2*e^5 + 2*e^4 - 21*e^3 - 16*e^2 + 48*e + 30, -5/3*e^4 - 32/3*e^3 - 1/3*e^2 + 170/3*e + 133/3, 7/3*e^5 + 13/3*e^4 - 52/3*e^3 - 79/3*e^2 + 79/3*e + 42, 13/3*e^4 + 52/3*e^3 - 37/3*e^2 - 259/3*e - 116/3, -4/3*e^5 - e^4 + 59/3*e^3 + 20*e^2 - 185/3*e - 173/3, 1/3*e^5 + 8/3*e^4 + 10*e^3 - 8/3*e^2 - 55*e - 134/3, -5*e^4 - 16*e^3 + 15*e^2 + 79*e + 40, -7/3*e^5 - 6*e^4 + 62/3*e^3 + 43*e^2 - 164/3*e - 170/3, 10/3*e^5 + 17/3*e^4 - 31*e^3 - 119/3*e^2 + 64*e + 196/3, -4/3*e^5 + 4/3*e^4 + 19*e^3 - 25/3*e^2 - 62*e - 22/3, 2*e^5 + 4/3*e^4 - 59/3*e^3 - 10/3*e^2 + 128/3*e + 19/3, -2/3*e^5 - 7/3*e^4 + 11*e^3 + 88/3*e^2 - 47*e - 206/3, -2/3*e^5 - e^4 - 11/3*e^3 - 8*e^2 + 119/3*e + 152/3, 5/3*e^5 - 2/3*e^4 - 24*e^3 - 4/3*e^2 + 73*e + 56/3, 11/3*e^5 + 4*e^4 - 115/3*e^3 - 26*e^2 + 283/3*e + 124/3, -2*e^5 - 23/3*e^4 + 49/3*e^3 + 170/3*e^2 - 142/3*e - 227/3, -1/3*e^5 + 2/3*e^4 + 19/3*e^3 - 2/3*e^2 - 88/3*e - 22, e^5 - 1/3*e^4 - 55/3*e^3 - 41/3*e^2 + 193/3*e + 194/3, 1/3*e^5 + 7/3*e^3 + 5*e^2 - 94/3*e - 37/3, 2*e^5 + 19/3*e^4 - 41/3*e^3 - 124/3*e^2 + 89/3*e + 115/3, 10/3*e^5 + 10/3*e^4 - 94/3*e^3 - 43/3*e^2 + 205/3*e + 8, -2*e^5 - 7/3*e^4 + 92/3*e^3 + 103/3*e^2 - 311/3*e - 316/3, 5/3*e^5 + 17/3*e^4 - 23/3*e^3 - 77/3*e^2 + 11/3*e - 24, 5/3*e^5 + 10/3*e^4 - 24*e^3 - 121/3*e^2 + 85*e + 278/3, -e^5 - 1/3*e^4 + 35/3*e^3 - 8/3*e^2 - 89/3*e + 50/3, -5/3*e^5 - 10/3*e^4 + 14*e^3 + 58/3*e^2 - 22*e - 11/3, -1/3*e^5 + 2*e^4 + 29/3*e^3 - 9*e^2 - 116/3*e - 41/3, -16/3*e^4 - 19/3*e^3 + 106/3*e^2 + 67/3*e - 82/3, -11/3*e^5 - 5*e^4 + 112/3*e^3 + 34*e^2 - 286/3*e - 211/3, 2/3*e^5 + 5/3*e^4 - 17/3*e^3 - 41/3*e^2 + 38/3*e + 56, -e^4 - 2*e^3 + 6*e^2 + 9*e + 20, 7/3*e^4 + 19/3*e^3 - 25/3*e^2 - 61/3*e - 26/3, 7/3*e^5 + 7/3*e^4 - 76/3*e^3 - 64/3*e^2 + 226/3*e + 66, 4*e^5 + 5/3*e^4 - 166/3*e^3 - 92/3*e^2 + 508/3*e + 383/3, 4/3*e^5 + 13/3*e^4 - 7/3*e^3 - 64/3*e^2 - 89/3*e + 20, 2*e^3 + 6*e^2 - 9*e - 15, -10/3*e^5 - 8/3*e^4 + 37*e^3 + 77/3*e^2 - 86*e - 190/3, -3*e^5 - 5*e^4 + 29*e^3 + 35*e^2 - 58*e - 59, 8/3*e^4 + 32/3*e^3 - 44/3*e^2 - 179/3*e + 8/3, -1/3*e^4 - 10/3*e^3 + 13/3*e^2 + 58/3*e - 4/3, 2/3*e^5 + 4/3*e^4 - 2*e^3 - 28/3*e^2 - 2*e + 128/3, -3*e^5 - 5*e^4 + 27*e^3 + 24*e^2 - 62*e - 8, 10/3*e^5 + 10*e^4 - 44/3*e^3 - 46*e^2 - 31/3*e - 37/3, 2*e^5 + 10/3*e^4 - 92/3*e^3 - 127/3*e^2 + 344/3*e + 343/3, 5/3*e^5 + 14/3*e^4 - 20/3*e^3 - 47/3*e^2 - 34/3*e - 14, 2/3*e^5 + 2*e^4 - 7/3*e^3 - 16*e^2 - 17/3*e + 130/3, 4/3*e^5 - 1/3*e^4 - 11*e^3 + 31/3*e^2 + 12*e - 143/3, 7/3*e^5 + 2*e^4 - 77/3*e^3 - 18*e^2 + 215/3*e + 173/3, 5/3*e^5 + 3*e^4 - 49/3*e^3 - 25*e^2 + 97/3*e + 172/3, 5/3*e^5 - 25/3*e^3 + 16*e^2 - 53/3*e - 182/3, 1/3*e^5 + e^4 - 20/3*e^3 - 13*e^2 + 74/3*e + 35/3, -1/3*e^5 + 20/3*e^4 + 82/3*e^3 - 74/3*e^2 - 373/3*e - 39, -2/3*e^5 - 5/3*e^4 + 26/3*e^3 + 41/3*e^2 - 98/3*e - 24, e^5 - 10/3*e^4 - 67/3*e^3 + 46/3*e^2 + 250/3*e + 35/3, -1/3*e^4 - 37/3*e^3 - 44/3*e^2 + 226/3*e + 218/3, -4/3*e^5 - 11/3*e^4 + 12*e^3 + 65/3*e^2 - 31*e - 34/3, 5/3*e^5 + 7*e^4 - 19/3*e^3 - 47*e^2 - 26/3*e + 187/3, 13/3*e^5 + 7/3*e^4 - 145/3*e^3 - 40/3*e^2 + 397/3*e + 49, 7/3*e^5 + 32/3*e^4 - 12*e^3 - 200/3*e^2 + 16*e + 160/3, 1/3*e^5 - 7/3*e^4 + 88/3*e^2 - 12*e - 215/3, 3*e^5 + 11/3*e^4 - 94/3*e^3 - 92/3*e^2 + 223/3*e + 170/3, -11/3*e^5 - 17/3*e^4 + 101/3*e^3 + 89/3*e^2 - 230/3*e - 41, -1/3*e^4 - 22/3*e^3 - 47/3*e^2 + 106/3*e + 170/3, 5/3*e^5 + 4/3*e^4 - 11*e^3 - 7/3*e^2 - 2*e - 37/3, -5*e^5 - 26/3*e^4 + 130/3*e^3 + 161/3*e^2 - 250/3*e - 206/3, -13/3*e^5 - 9*e^4 + 125/3*e^3 + 70*e^2 - 284/3*e - 374/3, -5/3*e^5 + 2*e^4 + 58/3*e^3 - 17*e^2 - 118/3*e + 56/3, -11/3*e^5 - 9*e^4 + 121/3*e^3 + 76*e^2 - 316/3*e - 343/3, 4*e^5 + 25/3*e^4 - 125/3*e^3 - 187/3*e^2 + 305/3*e + 232/3, -e^5 - 22/3*e^4 - 10/3*e^3 + 127/3*e^2 + 112/3*e - 70/3] 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 + 5])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]