/* 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, -2, -6, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([11, 11, -w^3 + 5*w + 1]) primes_array = [ [2, 2, w + 1],\ [3, 3, -w^3 + w^2 + 5*w - 2],\ [11, 11, -w^3 + 5*w + 1],\ [11, 11, -w + 2],\ [13, 13, -w^3 + w^2 + 4*w + 1],\ [17, 17, -w^3 + w^2 + 6*w - 1],\ [17, 17, -w^2 - w + 3],\ [23, 23, w^3 - 6*w],\ [27, 3, w^3 + w^2 - 5*w - 4],\ [41, 41, -w^3 + w^2 + 5*w],\ [41, 41, 2*w^3 - 11*w - 4],\ [53, 53, 2*w^3 - 2*w^2 - 11*w + 6],\ [59, 59, 2*w^3 - 11*w - 2],\ [67, 67, w^3 - 7*w - 1],\ [71, 71, 3*w^3 - 2*w^2 - 15*w + 1],\ [79, 79, -3*w^3 + w^2 + 16*w + 3],\ [89, 89, -4*w^3 + 2*w^2 + 22*w - 3],\ [101, 101, -2*w^3 + 13*w + 6],\ [101, 101, w^3 + w^2 - 6*w - 3],\ [101, 101, -3*w^3 + 2*w^2 + 17*w - 3],\ [101, 101, w^3 - w^2 - 8*w - 3],\ [107, 107, 2*w^3 - 3*w^2 - 6*w],\ [109, 109, -w^3 + w^2 + 4*w - 3],\ [113, 113, w^3 - 8*w - 4],\ [113, 113, 7*w^3 - 4*w^2 - 39*w + 7],\ [121, 11, w^3 - w^2 - 6*w - 1],\ [127, 127, -2*w^3 + w^2 + 9*w + 3],\ [127, 127, 2*w^3 - 13*w],\ [131, 131, 6*w^3 - 3*w^2 - 34*w + 6],\ [139, 139, w^2 - 2*w - 4],\ [149, 149, 3*w^3 - w^2 - 18*w - 3],\ [151, 151, -2*w^3 + 2*w^2 + 9*w - 4],\ [163, 163, 3*w^3 - 2*w^2 - 16*w + 2],\ [163, 163, 2*w^3 - 10*w + 1],\ [167, 167, 3*w^3 - 18*w - 4],\ [173, 173, -3*w^3 + w^2 + 18*w - 3],\ [193, 193, 4*w^3 - 3*w^2 - 23*w + 9],\ [197, 197, 3*w^3 - w^2 - 17*w + 2],\ [197, 197, -3*w^3 - 2*w^2 + 15*w + 9],\ [199, 199, 2*w^3 - w^2 - 8*w - 6],\ [223, 223, -6*w^3 + 3*w^2 + 35*w - 7],\ [227, 227, 2*w^3 - 12*w - 1],\ [227, 227, -w^3 + w^2 + 7*w - 8],\ [227, 227, 3*w^3 - w^2 - 18*w - 1],\ [227, 227, -4*w^3 - 2*w^2 + 21*w + 14],\ [229, 229, -w^3 + 2*w^2 + 3*w - 5],\ [233, 233, w^3 - 3*w - 3],\ [233, 233, -3*w^3 + 3*w^2 + 15*w - 8],\ [241, 241, 4*w^2 - 7*w - 8],\ [241, 241, w^3 + w^2 - 4*w - 5],\ [251, 251, 2*w^3 - w^2 - 13*w - 1],\ [251, 251, 2*w^3 - 9*w - 6],\ [257, 257, w^3 - 8*w],\ [263, 263, -w^3 + 2*w^2 + 5*w - 7],\ [269, 269, 3*w^3 - 3*w^2 - 12*w - 1],\ [271, 271, 2*w^3 - w^2 - 12*w - 2],\ [271, 271, 9*w^3 - 5*w^2 - 50*w + 9],\ [277, 277, w^3 - 2*w^2 - 6*w + 6],\ [277, 277, w^3 + w^2 - 7*w - 2],\ [281, 281, 4*w^3 - 2*w^2 - 24*w + 5],\ [281, 281, -7*w^3 + 4*w^2 + 40*w - 12],\ [289, 17, -5*w^3 + 5*w^2 + 26*w - 15],\ [293, 293, -w^3 + 2*w^2 + 4*w - 4],\ [293, 293, -9*w^3 + 5*w^2 + 51*w - 12],\ [307, 307, -2*w^3 + 2*w^2 + 12*w - 7],\ [311, 311, -4*w^3 + 24*w + 11],\ [313, 313, 2*w^3 - 9*w - 4],\ [317, 317, 2*w^3 - 4*w^2 - 2*w - 3],\ [317, 317, 2*w^3 - 14*w - 7],\ [331, 331, -3*w^3 + 19*w + 3],\ [349, 349, -w^3 - 2*w^2 + 8*w + 8],\ [349, 349, w^3 + w^2 - 5*w - 8],\ [361, 19, -w^3 + w^2 + 7*w - 6],\ [361, 19, w^3 + w^2 - 3*w - 4],\ [373, 373, 2*w^3 - w^2 - 11*w - 3],\ [379, 379, -4*w^3 + 25*w + 14],\ [383, 383, -3*w^3 + w^2 + 15*w - 2],\ [383, 383, 3*w^3 - 4*w^2 - 10*w],\ [401, 401, 4*w^3 - w^2 - 24*w - 4],\ [409, 409, w^2 + 5*w + 5],\ [419, 419, w^2 - 2*w - 6],\ [419, 419, -6*w^3 + 3*w^2 + 34*w - 8],\ [433, 433, 3*w^3 - 16*w - 6],\ [433, 433, 3*w^3 - w^2 - 16*w - 5],\ [443, 443, -w^3 + 2*w^2 + w + 3],\ [449, 449, 2*w^2 - 2*w - 5],\ [457, 457, -4*w^3 + 4*w^2 + 20*w - 9],\ [457, 457, w^2 + w - 7],\ [463, 463, w^3 - 7*w - 7],\ [463, 463, w^3 + 2*w^2 - 5*w - 9],\ [487, 487, w^3 + 2*w^2 - 5*w - 5],\ [487, 487, -w^3 + w^2 + 6*w - 7],\ [509, 509, -2*w^3 - 2*w^2 + 13*w + 10],\ [509, 509, 3*w^3 - 17*w - 3],\ [509, 509, -5*w^3 + 3*w^2 + 30*w - 11],\ [509, 509, -w^3 - 2*w^2 + 4*w + 6],\ [521, 521, -2*w^3 - w^2 + 9*w + 7],\ [541, 541, -2*w^3 - 2*w^2 + 12*w + 9],\ [541, 541, -2*w^3 + 12*w + 9],\ [547, 547, 2*w^3 + w^2 - 7*w - 3],\ [547, 547, 5*w^3 - 3*w^2 - 30*w + 3],\ [557, 557, w^3 + 2*w^2 - 5*w - 11],\ [557, 557, -w^3 + w^2 + 3*w - 4],\ [563, 563, 3*w^3 - w^2 - 15*w - 4],\ [569, 569, 2*w^2 - w - 8],\ [577, 577, 4*w^3 - 22*w - 7],\ [593, 593, -3*w^3 + w^2 + 17*w + 4],\ [607, 607, -w^3 - 3*w^2 + w + 4],\ [613, 613, 3*w^3 - 2*w^2 - 14*w],\ [613, 613, w^2 - 3*w - 5],\ [619, 619, -w^3 + 2*w^2 + 4*w - 10],\ [625, 5, -5],\ [641, 641, -3*w^3 - 3*w^2 + 12*w + 7],\ [643, 643, 2*w^3 + 2*w^2 - 14*w - 13],\ [643, 643, 3*w^3 - 19*w - 7],\ [647, 647, w^3 - 5*w - 7],\ [653, 653, -3*w^3 + 2*w^2 + 14*w - 2],\ [659, 659, -6*w^3 + 2*w^2 + 34*w - 1],\ [659, 659, -2*w^3 + w^2 + 17*w + 9],\ [683, 683, w^3 + 2*w^2 - 7*w - 7],\ [691, 691, 3*w^3 - 15*w - 7],\ [701, 701, w^3 + 2*w^2 - 6*w - 10],\ [701, 701, -w^3 + 3*w^2 + 6*w - 13],\ [701, 701, 5*w^3 - 2*w^2 - 30*w + 4],\ [701, 701, 4*w^3 - 2*w^2 - 21*w + 2],\ [727, 727, -2*w^3 - 3*w^2 + 9*w + 7],\ [743, 743, 3*w - 4],\ [751, 751, w^3 - 9*w - 3],\ [757, 757, w^3 - 5*w^2 + 4*w + 7],\ [757, 757, 4*w^3 - 5*w^2 - 11*w - 5],\ [761, 761, 4*w^3 - 5*w^2 - 20*w + 16],\ [769, 769, -3*w^3 + 16*w + 12],\ [773, 773, 2*w^3 + 2*w^2 - 11*w - 10],\ [773, 773, w^3 - 3*w - 5],\ [773, 773, -w^3 + 2*w^2 + 9*w + 3],\ [773, 773, 5*w^3 - w^2 - 27*w],\ [787, 787, -4*w^3 + 3*w^2 + 22*w - 4],\ [787, 787, -2*w^3 + w^2 + 14*w - 6],\ [797, 797, 2*w^3 - w^2 - 14*w + 2],\ [797, 797, -3*w^3 + 2*w^2 + 19*w - 7],\ [811, 811, 2*w^3 + w^2 - 14*w - 12],\ [811, 811, 2*w^3 + 2*w^2 - 8*w - 3],\ [829, 829, -2*w^3 + 14*w + 11],\ [857, 857, -3*w^3 + 3*w^2 + 14*w - 7],\ [859, 859, 3*w^3 - w^2 - 15*w],\ [859, 859, -11*w^3 + 7*w^2 + 60*w - 15],\ [863, 863, 2*w^2 - 2*w - 13],\ [863, 863, 2*w^3 + w^2 - 12*w - 4],\ [877, 877, -6*w^3 - 2*w^2 + 32*w + 19],\ [887, 887, 3*w^3 + w^2 - 14*w - 7],\ [887, 887, 2*w^3 - w^2 - 15*w - 5],\ [911, 911, 3*w^3 - 18*w - 2],\ [919, 919, w^3 - w^2 - 6*w - 5],\ [919, 919, -4*w^3 + w^2 + 24*w - 2],\ [941, 941, 3*w^3 - 3*w^2 - 13*w],\ [947, 947, 2*w^3 - 2*w^2 - 10*w - 1],\ [947, 947, -3*w^3 + 2*w^2 + 14*w + 6],\ [953, 953, -4*w^3 + 3*w^2 + 21*w - 3],\ [953, 953, 4*w^3 - w^2 - 23*w + 1],\ [961, 31, -2*w^3 + 3*w^2 + 12*w - 8],\ [961, 31, 3*w^2 - 4*w - 6],\ [967, 967, -5*w^3 - 3*w^2 + 23*w + 14],\ [971, 971, 5*w^3 - w^2 - 27*w - 8],\ [971, 971, -9*w^3 + 6*w^2 + 50*w - 12],\ [983, 983, -w^3 + w^2 + 10*w + 3],\ [997, 997, 2*w^3 + w^2 - 11*w - 3],\ [997, 997, w^3 + 2*w^2 - 6*w - 8],\ [997, 997, -5*w^3 + 4*w^2 + 29*w - 15]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^11 - 5*x^10 - 4*x^9 + 48*x^8 - 19*x^7 - 152*x^6 + 90*x^5 + 203*x^4 - 100*x^3 - 107*x^2 + 27*x + 9 K. = NumberField(heckePol) hecke_eigenvalues_array = [e, 2/9*e^10 - 8/9*e^9 - 13/9*e^8 + 71/9*e^7 + 2*e^6 - 193/9*e^5 - 22/9*e^4 + 22*e^3 + 55/9*e^2 - 20/3*e - 2, -1, -5/9*e^10 + 23/9*e^9 + 16/9*e^8 - 188/9*e^7 + 37/3*e^6 + 424/9*e^5 - 401/9*e^4 - 98/3*e^3 + 317/9*e^2 + 16/3*e - 3, 2/9*e^10 + 1/9*e^9 - 40/9*e^8 - 1/9*e^7 + 26*e^6 - 22/9*e^5 - 472/9*e^4 + 2*e^3 + 289/9*e^2 + 10/3*e, -1/3*e^10 + e^9 + 4*e^8 - 35/3*e^7 - 52/3*e^6 + 134/3*e^5 + 100/3*e^4 - 181/3*e^3 - 77/3*e^2 + 58/3*e + 4, -2/9*e^10 - 1/9*e^9 + 49/9*e^8 - 26/9*e^7 - 34*e^6 + 238/9*e^5 + 643/9*e^4 - 53*e^3 - 442/9*e^2 + 77/3*e + 3, e^10 - 14/3*e^9 - 10/3*e^8 + 118/3*e^7 - 65/3*e^6 - 96*e^5 + 244/3*e^4 + 247/3*e^3 - 66*e^2 - 67/3*e + 7, -8/9*e^10 + 26/9*e^9 + 58/9*e^8 - 209/9*e^7 - 32/3*e^6 + 430/9*e^5 + 19/9*e^4 - 56/3*e^3 - 40/9*e^2 - 23/3*e + 8, e^10 - 13/3*e^9 - 14/3*e^8 + 110/3*e^7 - 25/3*e^6 - 91*e^5 + 125/3*e^4 + 248/3*e^3 - 33*e^2 - 80/3*e + 6, -13/9*e^10 + 52/9*e^9 + 71/9*e^8 - 439/9*e^7 + 4*e^6 + 1079/9*e^5 - 433/9*e^4 - 107*e^3 + 385/9*e^2 + 100/3*e - 2, -7/9*e^10 + 10/9*e^9 + 104/9*e^8 - 127/9*e^7 - 57*e^6 + 536/9*e^5 + 923/9*e^4 - 98*e^3 - 467/9*e^2 + 154/3*e - 1, 1/9*e^10 - 4/9*e^9 - 11/9*e^8 + 49/9*e^7 + 5*e^6 - 200/9*e^5 - 83/9*e^4 + 29*e^3 + 32/9*e^2 + 2/3*e + 5, -1/9*e^10 + 13/9*e^9 - 25/9*e^8 - 112/9*e^7 + 33*e^6 + 290/9*e^5 - 916/9*e^4 - 32*e^3 + 913/9*e^2 + 37/3*e - 16, 2/3*e^10 - 3*e^9 - 3*e^8 + 82/3*e^7 - 31/3*e^6 - 229/3*e^5 + 166/3*e^4 + 227/3*e^3 - 170/3*e^2 - 59/3*e + 12, -1/9*e^10 + 7/9*e^9 - 1/9*e^8 - 64/9*e^7 + 16/3*e^6 + 191/9*e^5 - 85/9*e^4 - 80/3*e^3 - 23/9*e^2 + 10*e + 4, 1/9*e^10 - 16/9*e^9 + 46/9*e^8 + 82/9*e^7 - 136/3*e^6 + 70/9*e^5 + 868/9*e^4 - 163/3*e^3 - 454/9*e^2 + 36*e - 7, 1/9*e^10 + 26/9*e^9 - 131/9*e^8 - 119/9*e^7 + 352/3*e^6 - 227/9*e^5 - 2501/9*e^4 + 337/3*e^3 + 1832/9*e^2 - 182/3*e - 13, -11/9*e^10 + 65/9*e^9 - 26/9*e^8 - 473/9*e^7 + 247/3*e^6 + 733/9*e^5 - 2000/9*e^4 + 64/3*e^3 + 1484/9*e^2 - 164/3*e - 16, -19/9*e^10 + 82/9*e^9 + 104/9*e^8 - 736/9*e^7 + 17/3*e^6 + 2000/9*e^5 - 595/9*e^4 - 625/3*e^3 + 445/9*e^2 + 128/3*e - 4, 8/9*e^10 - 17/9*e^9 - 112/9*e^8 + 218/9*e^7 + 176/3*e^6 - 916/9*e^5 - 955/9*e^4 + 467/3*e^3 + 625/9*e^2 - 214/3*e - 5, 1/9*e^10 - 28/9*e^9 + 85/9*e^8 + 178/9*e^7 - 254/3*e^6 - 110/9*e^5 + 1819/9*e^4 - 179/3*e^3 - 1300/9*e^2 + 160/3*e + 19, -1/9*e^10 - 2/9*e^9 + 17/9*e^8 + 35/9*e^7 - 35/3*e^6 - 160/9*e^5 + 248/9*e^4 + 49/3*e^3 - 185/9*e^2 + 8*e + 10, -4/3*e^10 + 7*e^9 + e^8 - 164/3*e^7 + 167/3*e^6 + 320/3*e^5 - 476/3*e^4 - 91/3*e^3 + 289/3*e^2 - 98/3*e + 1, 10/9*e^10 - 73/9*e^9 + 58/9*e^8 + 583/9*e^7 - 329/3*e^6 - 1289/9*e^5 + 2647/9*e^4 + 325/3*e^3 - 1993/9*e^2 - 101/3*e + 19, -1/9*e^10 + 1/9*e^9 + 5/9*e^8 + 11/9*e^7 + 11/3*e^6 - 151/9*e^5 - 253/9*e^4 + 125/3*e^3 + 418/9*e^2 - 55/3*e - 15, -2/9*e^10 + 50/9*e^9 - 146/9*e^8 - 335/9*e^7 + 443/3*e^6 + 391/9*e^5 - 3239/9*e^4 + 107/3*e^3 + 2456/9*e^2 - 33*e - 30, e^10 - 7*e^9 + 5*e^8 + 54*e^7 - 90*e^6 - 103*e^5 + 234*e^4 + 26*e^3 - 167*e^2 + 34*e + 24, -8/9*e^10 + 29/9*e^9 + 46/9*e^8 - 224/9*e^7 - 4/3*e^6 + 439/9*e^5 - 95/9*e^4 - 67/3*e^3 - 112/9*e^2 - 8*e + 14, 4/9*e^10 + 8/9*e^9 - 104/9*e^8 - 23/9*e^7 + 215/3*e^6 - 170/9*e^5 - 1262/9*e^4 + 182/3*e^3 + 776/9*e^2 - 41*e - 15, 1/9*e^10 - 10/9*e^9 + 4/9*e^8 + 97/9*e^7 - 17/3*e^6 - 317/9*e^5 - 17/9*e^4 + 136/3*e^3 + 221/9*e^2 - 50/3*e, 7/3*e^10 - 25/3*e^9 - 44/3*e^8 + 202/3*e^7 + 10*e^6 - 437/3*e^5 + 109/3*e^4 + 84*e^3 - 91/3*e^2 + 9*e + 9, 13/9*e^10 - 73/9*e^9 + 4/9*e^8 + 562/9*e^7 - 211/3*e^6 - 1061/9*e^5 + 1699/9*e^4 + 80/3*e^3 - 1222/9*e^2 + 43*e + 25, -20/9*e^10 + 53/9*e^9 + 211/9*e^8 - 503/9*e^7 - 89*e^6 + 1471/9*e^5 + 1399/9*e^4 - 166*e^3 - 1045/9*e^2 + 116/3*e + 15, -e^10 + 3*e^9 + 11*e^8 - 32*e^7 - 44*e^6 + 110*e^5 + 84*e^4 - 131*e^3 - 77*e^2 + 34*e + 18, 1/9*e^10 - 4/9*e^9 - 2/9*e^8 + 31/9*e^7 - 6*e^6 - 56/9*e^5 + 250/9*e^4 + 4*e^3 - 220/9*e^2 - 40/3*e - 12, 4*e^10 - 15*e^9 - 25*e^8 + 126*e^7 + 17*e^6 - 298*e^5 + 54*e^4 + 215*e^3 - 32*e^2 - 16*e - 1, -11/9*e^10 + 38/9*e^9 + 82/9*e^8 - 347/9*e^7 - 41/3*e^6 + 1003/9*e^5 - 155/9*e^4 - 395/3*e^3 + 359/9*e^2 + 169/3*e - 7, e^10 - 3*e^9 - 9*e^8 + 27*e^7 + 26*e^6 - 73*e^5 - 28*e^4 + 71*e^3 - 7*e^2 - 25*e + 21, -16/9*e^10 + 76/9*e^9 + 65/9*e^8 - 664/9*e^7 + 67/3*e^6 + 1751/9*e^5 - 739/9*e^4 - 569/3*e^3 + 469/9*e^2 + 57*e - 13, -2/9*e^10 + 14/9*e^9 + 7/9*e^8 - 155/9*e^7 + 14/3*e^6 + 553/9*e^5 - 134/9*e^4 - 205/3*e^3 + 17/9*e^2 + 8*e + 3, -e^10 + 8/3*e^9 + 34/3*e^8 - 85/3*e^7 - 127/3*e^6 + 93*e^5 + 161/3*e^4 - 280/3*e^3 - 7*e^2 + 34/3*e - 10, -7/3*e^9 + 28/3*e^8 + 35/3*e^7 - 226/3*e^6 + 14*e^5 + 497/3*e^4 - 265/3*e^3 - 111*e^2 + 178/3*e + 17, 5/3*e^10 - 9*e^9 + 208/3*e^7 - 238/3*e^6 - 409/3*e^5 + 673/3*e^4 + 200/3*e^3 - 509/3*e^2 + 10/3*e + 30, 2/9*e^10 - 2/9*e^9 - 37/9*e^8 + 68/9*e^7 + 47/3*e^6 - 445/9*e^5 + 65/9*e^4 + 305/3*e^3 - 467/9*e^2 - 214/3*e + 13, -4/9*e^10 + 55/9*e^9 - 112/9*e^8 - 427/9*e^7 + 391/3*e^6 + 881/9*e^5 - 3076/9*e^4 - 182/3*e^3 + 2563/9*e^2 + 13*e - 35, -5/9*e^10 + 29/9*e^9 - 8/9*e^8 - 218/9*e^7 + 34*e^6 + 388/9*e^5 - 863/9*e^4 - 3*e^3 + 776/9*e^2 - 94/3*e - 26, 26/9*e^10 - 113/9*e^9 - 115/9*e^8 + 950/9*e^7 - 33*e^6 - 2284/9*e^5 + 1370/9*e^4 + 197*e^3 - 1085/9*e^2 - 71/3*e + 17, -16/9*e^10 + 82/9*e^9 + 23/9*e^8 - 658/9*e^7 + 65*e^6 + 1400/9*e^5 - 1759/9*e^4 - 81*e^3 + 1117/9*e^2 - 23/3*e + 9, 22/9*e^10 - 82/9*e^9 - 140/9*e^8 + 697/9*e^7 + 35/3*e^6 - 1700/9*e^5 + 313/9*e^4 + 443/3*e^3 - 223/9*e^2 - 6*e - 6, 1/3*e^10 - 4/3*e^9 + 7/3*e^8 - 2/3*e^7 - 34*e^6 + 190/3*e^5 + 259/3*e^4 - 144*e^3 - 208/3*e^2 + 66*e + 12, 2/9*e^10 + 1/9*e^9 - 67/9*e^8 + 62/9*e^7 + 54*e^6 - 499/9*e^5 - 1219/9*e^4 + 96*e^3 + 1018/9*e^2 - 71/3*e - 11, 17/9*e^10 - 104/9*e^9 + 20/9*e^8 + 860/9*e^7 - 112*e^6 - 1996/9*e^5 + 2855/9*e^4 + 160*e^3 - 2147/9*e^2 - 83/3*e + 25, -16/9*e^10 + 43/9*e^9 + 143/9*e^8 - 355/9*e^7 - 127/3*e^6 + 770/9*e^5 + 254/9*e^4 - 121/3*e^3 + 235/9*e^2 - 43/3*e - 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74/3*e^3 + 1054/3*e^2 - 205/3*e - 54, -20/9*e^10 + 62/9*e^9 + 121/9*e^8 - 395/9*e^7 - 7*e^6 + 184/9*e^5 - 320/9*e^4 + 157*e^3 + 305/9*e^2 - 373/3*e - 3, 7/3*e^10 - 8/3*e^9 - 100/3*e^8 + 27*e^7 + 479/3*e^6 - 239/3*e^5 - 282*e^4 + 191/3*e^3 + 464/3*e^2 + 94/3*e - 3, 5/9*e^10 + 13/9*e^9 - 133/9*e^8 - 73/9*e^7 + 284/3*e^6 - 55/9*e^5 - 1750/9*e^4 + 242/3*e^3 + 1060/9*e^2 - 277/3*e - 12, -4/3*e^10 - 5/3*e^9 + 89/3*e^8 + 20/3*e^7 - 177*e^6 + 50/3*e^5 + 1049/3*e^4 - 62*e^3 - 668/3*e^2 + 25*e + 33, 8/9*e^10 + 25/9*e^9 - 262/9*e^8 - 73/9*e^7 + 601/3*e^6 - 511/9*e^5 - 3991/9*e^4 + 496/3*e^3 + 2659/9*e^2 - 85*e + 2, 19/9*e^10 - 103/9*e^9 - 2/9*e^8 + 796/9*e^7 - 97*e^6 - 1550/9*e^5 + 2338/9*e^4 + 69*e^3 - 1228/9*e^2 + 44/3*e - 25, 32/9*e^10 - 155/9*e^9 - 55/9*e^8 + 1208/9*e^7 - 126*e^6 - 2368/9*e^5 + 3653/9*e^4 + 98*e^3 - 2729/9*e^2 + 133/3*e + 17, 28/9*e^10 - 175/9*e^9 + 43/9*e^8 + 1417/9*e^7 - 182*e^6 - 3161/9*e^5 + 4111/9*e^4 + 233*e^3 - 2236/9*e^2 - 31/3*e - 18, 5/9*e^10 + 1/9*e^9 - 148/9*e^8 + 185/9*e^7 + 307/3*e^6 - 1495/9*e^5 - 1717/9*e^4 + 1036/3*e^3 + 853/9*e^2 - 192*e + 1, -31/9*e^10 + 196/9*e^9 - 109/9*e^8 - 1429/9*e^7 + 259*e^6 + 2258/9*e^5 - 5932/9*e^4 + 50*e^3 + 4120/9*e^2 - 518/3*e - 46, 4/3*e^10 - 25*e^8 + 23/3*e^7 + 424/3*e^6 - 179/3*e^5 - 859/3*e^4 + 415/3*e^3 + 632/3*e^2 - 316/3*e - 21, -11/9*e^10 + 11/9*e^9 + 154/9*e^8 - 68/9*e^7 - 266/3*e^6 - 5/9*e^5 + 1789/9*e^4 + 121/3*e^3 - 1594/9*e^2 - 101/3*e + 30, -5/3*e^10 + 32/3*e^9 - 5/3*e^8 - 278/3*e^7 + 96*e^6 + 718/3*e^5 - 818/3*e^4 - 214*e^3 + 644/3*e^2 + 59*e - 31, 7/3*e^10 - 16/3*e^9 - 74/3*e^8 + 130/3*e^7 + 102*e^6 - 293/3*e^5 - 668/3*e^4 + 77*e^3 + 674/3*e^2 + 3*e - 52, -11/9*e^10 - 10/9*e^9 + 274/9*e^8 - 44/9*e^7 - 202*e^6 + 724/9*e^5 + 4315/9*e^4 - 165*e^3 - 3565/9*e^2 + 230/3*e + 43, -22/9*e^10 + 124/9*e^9 - 55/9*e^8 - 835/9*e^7 + 167*e^6 + 827/9*e^5 - 4006/9*e^4 + 189*e^3 + 2833/9*e^2 - 623/3*e - 21, 8/3*e^10 - 13*e^9 - 6*e^8 + 316/3*e^7 - 235/3*e^6 - 721/3*e^5 + 757/3*e^4 + 599/3*e^3 - 569/3*e^2 - 209/3*e + 11, -23/9*e^10 + 146/9*e^9 - 44/9*e^8 - 1208/9*e^7 + 167*e^6 + 2836/9*e^5 - 4211/9*e^4 - 239*e^3 + 3242/9*e^2 + 134/3*e - 31, -31/9*e^10 + 88/9*e^9 + 287/9*e^8 - 799/9*e^7 - 93*e^6 + 2222/9*e^5 + 854/9*e^4 - 264*e^3 - 182/9*e^2 + 340/3*e + 6, -16/9*e^10 + 34/9*e^9 + 179/9*e^8 - 274/9*e^7 - 253/3*e^6 + 527/9*e^5 + 1523/9*e^4 - 22/3*e^3 - 1169/9*e^2 - 37/3*e + 4, -16/9*e^10 + 103/9*e^9 - 61/9*e^8 - 727/9*e^7 + 385/3*e^6 + 1040/9*e^5 - 2503/9*e^4 + 127/3*e^3 + 1081/9*e^2 - 99*e + 4, 16/3*e^10 - 55/3*e^9 - 119/3*e^8 + 475/3*e^7 + 75*e^6 - 1190/3*e^5 - 158/3*e^4 + 321*e^3 + 233/3*e^2 - 26*e - 48, -37/9*e^10 + 235/9*e^9 - 94/9*e^8 - 1861/9*e^7 + 860/3*e^6 + 3872/9*e^5 - 6994/9*e^4 - 649/3*e^3 + 5152/9*e^2 - 85/3*e - 59, -2/9*e^10 + 41/9*e^9 - 101/9*e^8 - 272/9*e^7 + 296/3*e^6 + 184/9*e^5 - 1835/9*e^4 + 359/3*e^3 + 854/9*e^2 - 132*e + 5, -5/9*e^10 + 8/9*e^9 + 85/9*e^8 - 149/9*e^7 - 133/3*e^6 + 757/9*e^5 + 484/9*e^4 - 391/3*e^3 + 83/9*e^2 + 49*e - 32, 20/9*e^10 - 68/9*e^9 - 142/9*e^8 + 596/9*e^7 + 46/3*e^6 - 1561/9*e^5 + 629/9*e^4 + 502/3*e^3 - 1178/9*e^2 - 51*e + 40, -10/3*e^9 + 40/3*e^8 + 62/3*e^7 - 355/3*e^6 - 12*e^5 + 935/3*e^4 - 139/3*e^3 - 267*e^2 + 28/3*e + 28, 5/9*e^10 - 14/9*e^9 - 25/9*e^8 + 80/9*e^7 - 37/3*e^6 + 80/9*e^5 + 788/9*e^4 - 229/3*e^3 - 1145/9*e^2 + 146/3*e + 33, 7/3*e^10 - 20/3*e^9 - 76/3*e^8 + 71*e^7 + 281/3*e^6 - 743/3*e^5 - 138*e^4 + 983/3*e^3 + 182/3*e^2 - 401/3*e + 25, 2*e^10 - e^9 - 29*e^8 + e^7 + 145*e^6 + 49*e^5 - 278*e^4 - 151*e^3 + 177*e^2 + 97*e, 2/3*e^10 + 16/3*e^9 - 100/3*e^8 - 91/3*e^7 + 253*e^6 + 8/3*e^5 - 1828/3*e^4 + 105*e^3 + 1441/3*e^2 - 64*e - 66, 25/9*e^10 - 52/9*e^9 - 314/9*e^8 + 535/9*e^7 + 478/3*e^6 - 1850/9*e^5 - 2720/9*e^4 + 916/3*e^3 + 1592/9*e^2 - 509/3*e + 3, 4/3*e^10 - 34/3*e^9 + 34/3*e^8 + 286/3*e^7 - 166*e^6 - 707/3*e^5 + 1360/3*e^4 + 210*e^3 - 1093/3*e^2 - 56*e + 42, -10/9*e^10 - 20/9*e^9 + 314/9*e^8 - 28/9*e^7 - 743/3*e^6 + 1100/9*e^5 + 5405/9*e^4 - 887/3*e^3 - 4316/9*e^2 + 145*e + 52, -19/9*e^10 + 136/9*e^9 - 40/9*e^8 - 1231/9*e^7 + 413/3*e^6 + 3503/9*e^5 - 3277/9*e^4 - 1276/3*e^3 + 2335/9*e^2 + 413/3*e - 25, -e^10 + 7/3*e^9 + 44/3*e^8 - 86/3*e^7 - 251/3*e^6 + 124*e^5 + 652/3*e^4 - 662/3*e^3 - 219*e^2 + 371/3*e + 40, -28/9*e^10 + 124/9*e^9 + 134/9*e^8 - 1081/9*e^7 + 76/3*e^6 + 2783/9*e^5 - 1192/9*e^4 - 797/3*e^3 + 778/9*e^2 + 34*e - 12, -5/3*e^10 + 5*e^9 + 13*e^8 - 109/3*e^7 - 110/3*e^6 + 157/3*e^5 + 266/3*e^4 + 103/3*e^3 - 394/3*e^2 - 202/3*e + 17, 5/3*e^10 - 10/3*e^9 - 74/3*e^8 + 43*e^7 + 382/3*e^6 - 532/3*e^5 - 273*e^4 + 748/3*e^3 + 700/3*e^2 - 265/3*e - 24, 8/3*e^10 - 14*e^9 - 4*e^8 + 349/3*e^7 - 295/3*e^6 - 805/3*e^5 + 910/3*e^4 + 530/3*e^3 - 638/3*e^2 - 35/3*e + 20, 4/9*e^10 - 22/9*e^9 + 7/9*e^8 + 154/9*e^7 - 86/3*e^6 - 224/9*e^5 + 778/9*e^4 + 25/3*e^3 - 781/9*e^2 - 125/3*e + 24, -e^10 + 10/3*e^9 + 35/3*e^8 - 113/3*e^7 - 155/3*e^6 + 135*e^5 + 310/3*e^4 - 422/3*e^3 - 56*e^2 - 64/3*e - 18, 7/3*e^10 - 32/3*e^9 - 25/3*e^8 + 92*e^7 - 169/3*e^6 - 674/3*e^5 + 251*e^4 + 455/3*e^3 - 763/3*e^2 + 49/3*e + 49, -13/3*e^10 + 58/3*e^9 + 62/3*e^8 - 499/3*e^7 + 25*e^6 + 1262/3*e^5 - 316/3*e^4 - 364*e^3 - 17/3*e^2 + 82*e + 44, 4/3*e^10 - 4*e^9 - 8*e^8 + 80/3*e^7 - 14/3*e^6 - 65/3*e^5 + 278/3*e^4 - 218/3*e^3 - 505/3*e^2 + 248/3*e + 46, 25/9*e^10 - 58/9*e^9 - 281/9*e^8 + 556/9*e^7 + 377/3*e^6 - 1697/9*e^5 - 1988/9*e^4 + 695/3*e^3 + 1358/9*e^2 - 95*e - 6, 16/9*e^10 - 145/9*e^9 + 121/9*e^8 + 1297/9*e^7 - 198*e^6 - 3569/9*e^5 + 4468/9*e^4 + 395*e^3 - 3097/9*e^2 - 352/3*e + 51, 5/3*e^10 - 7*e^9 - 8*e^8 + 175/3*e^7 - 46/3*e^6 - 391/3*e^5 + 265/3*e^4 + 155/3*e^3 - 254/3*e^2 + 151/3*e + 4, -25/9*e^10 + 127/9*e^9 + 77/9*e^8 - 1135/9*e^7 + 66*e^6 + 3119/9*e^5 - 2164/9*e^4 - 354*e^3 + 1837/9*e^2 + 340/3*e - 17, 4/3*e^10 - 16/3*e^9 - 35/3*e^8 + 169/3*e^7 + 35*e^6 - 593/3*e^5 - 188/3*e^4 + 265*e^3 + 185/3*e^2 - 109*e - 13, 7/3*e^10 - 22/3*e^9 - 53/3*e^8 + 181/3*e^7 + 32*e^6 - 410/3*e^5 - 2/3*e^4 + 90*e^3 - 34/3*e^2 + 11*e - 18, 1/3*e^10 - 22/3*e^9 + 40/3*e^8 + 196/3*e^7 - 119*e^6 - 536/3*e^5 + 703/3*e^4 + 165*e^3 - 241/3*e^2 - 40*e - 18] 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^3 + 5*w + 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]