/* 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, 10, -7, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([16, 2, 2]) primes_array = [ [2, 2, -w + 1],\ [5, 5, w^3 + w^2 - 4*w + 1],\ [7, 7, -w^3 + 6*w - 2],\ [8, 2, w^3 - 7*w + 3],\ [11, 11, -w^3 + 6*w - 4],\ [17, 17, w^3 + w^2 - 6*w - 1],\ [17, 17, -w^2 - w + 3],\ [31, 31, 2*w^3 + w^2 - 13*w + 3],\ [37, 37, -3*w^3 - w^2 + 18*w - 3],\ [41, 41, w^2 + 2*w - 4],\ [47, 47, 2*w^3 + 2*w^2 - 11*w - 2],\ [47, 47, -3*w^3 - w^2 + 19*w - 6],\ [59, 59, -2*w^3 + 13*w - 6],\ [59, 59, -w^3 - w^2 + 5*w + 2],\ [59, 59, w^2 + w - 1],\ [59, 59, w^2 + 2*w - 6],\ [61, 61, -w^3 + w^2 + 8*w - 7],\ [67, 67, w^3 + 2*w^2 - 4*w - 4],\ [73, 73, -2*w^3 - w^2 + 12*w - 4],\ [81, 3, -3],\ [107, 107, 2*w^2 + 2*w - 11],\ [109, 109, 2*w^3 + w^2 - 11*w + 3],\ [113, 113, w^3 + w^2 - 7*w - 2],\ [113, 113, 2*w^3 - 12*w + 9],\ [125, 5, -4*w^3 - 3*w^2 + 24*w + 2],\ [131, 131, 5*w^3 + 3*w^2 - 31*w + 2],\ [151, 151, 4*w^3 + 2*w^2 - 26*w + 1],\ [151, 151, w^3 + 2*w^2 - 6*w - 10],\ [167, 167, w + 4],\ [167, 167, 4*w^3 + w^2 - 26*w + 10],\ [173, 173, -2*w^3 + w^2 + 13*w - 11],\ [179, 179, 4*w^3 + w^2 - 24*w + 4],\ [179, 179, 2*w^3 + 2*w^2 - 12*w - 3],\ [179, 179, -w^3 + 8*w - 4],\ [179, 179, w^3 + 2*w^2 - 4*w - 6],\ [181, 181, 6*w^3 + 3*w^2 - 39*w + 5],\ [197, 197, -w^3 + 4*w - 4],\ [199, 199, 2*w^3 - 12*w + 3],\ [199, 199, 3*w - 2],\ [223, 223, w^3 + w^2 - 7*w - 4],\ [223, 223, 2*w^3 + w^2 - 10*w + 4],\ [227, 227, 7*w^3 + 2*w^2 - 44*w + 12],\ [227, 227, -4*w^3 - w^2 + 25*w - 9],\ [229, 229, 8*w^3 + 4*w^2 - 51*w + 4],\ [229, 229, 3*w^3 + w^2 - 18*w + 5],\ [233, 233, -6*w^3 - 3*w^2 + 39*w - 7],\ [233, 233, -w^3 - 2*w^2 + 8*w + 2],\ [241, 241, 2*w^3 + w^2 - 10*w],\ [251, 251, w^3 + w^2 - 7*w - 6],\ [257, 257, -6*w^3 - w^2 + 39*w - 17],\ [263, 263, -2*w^3 + 13*w - 4],\ [263, 263, -w^3 + 6*w - 8],\ [269, 269, -8*w^3 - 4*w^2 + 50*w - 7],\ [269, 269, -w^3 + w^2 + 7*w - 6],\ [277, 277, 2*w^3 + 2*w^2 - 11*w + 4],\ [277, 277, w^3 + w^2 - 4*w - 3],\ [281, 281, -w^2 - 3*w + 5],\ [281, 281, 2*w^3 + 3*w^2 - 9*w - 3],\ [283, 283, -3*w^3 - 4*w^2 + 12*w + 2],\ [289, 17, -2*w^3 - w^2 + 13*w - 5],\ [293, 293, -w^3 - 2*w^2 + 6*w + 6],\ [293, 293, w^3 + w^2 - 8*w - 1],\ [307, 307, 2*w^3 - 11*w + 12],\ [317, 317, 2*w^3 - 14*w + 11],\ [317, 317, -2*w^3 - 2*w^2 + 8*w + 1],\ [337, 337, 2*w^2 + 4*w - 11],\ [343, 7, -5*w^3 - w^2 + 31*w - 10],\ [349, 349, 2*w^3 - 11*w + 8],\ [349, 349, w^2 + w - 9],\ [353, 353, 4*w^3 + 4*w^2 - 23*w - 8],\ [373, 373, -2*w - 3],\ [373, 373, -4*w^3 + 26*w - 13],\ [389, 389, 6*w^3 + 3*w^2 - 37*w + 1],\ [389, 389, -2*w^3 - w^2 + 14*w - 6],\ [401, 401, 2*w^3 - 12*w + 13],\ [421, 421, 2*w^2 + 2*w - 15],\ [421, 421, 3*w^3 + 2*w^2 - 20*w + 4],\ [431, 431, w^3 + 3*w^2 - 2*w - 9],\ [433, 433, 2*w^3 + 2*w^2 - 12*w + 3],\ [433, 433, -7*w^3 - 2*w^2 + 44*w - 16],\ [433, 433, -3*w^3 + 18*w - 14],\ [433, 433, -w^3 + w^2 + 9*w - 10],\ [439, 439, 5*w^3 + 3*w^2 - 31*w - 2],\ [443, 443, -w^3 - w^2 + 3*w - 4],\ [443, 443, -4*w^3 + 27*w - 14],\ [449, 449, w^3 + w^2 - 4*w - 5],\ [449, 449, w^3 + 3*w^2 - 3*w - 8],\ [449, 449, 2*w^3 - 11*w + 6],\ [449, 449, -3*w^3 - 2*w^2 + 18*w - 4],\ [461, 461, -3*w^3 + w^2 + 20*w - 15],\ [463, 463, 2*w^3 - 10*w + 7],\ [479, 479, -2*w^3 - 3*w^2 + 11*w + 9],\ [491, 491, w^3 + w^2 - 4*w + 5],\ [499, 499, -2*w^3 - 2*w^2 + 14*w - 3],\ [499, 499, -6*w^3 - 2*w^2 + 39*w - 10],\ [499, 499, 4*w^3 + w^2 - 24*w + 14],\ [499, 499, -5*w^3 - 3*w^2 + 30*w - 5],\ [503, 503, -2*w^3 + w^2 + 14*w - 18],\ [509, 509, 4*w^3 + 3*w^2 - 24*w],\ [509, 509, 4*w^3 + 2*w^2 - 23*w + 4],\ [547, 547, w^3 + 2*w^2 - 2*w - 6],\ [547, 547, 6*w^3 + 2*w^2 - 38*w + 7],\ [563, 563, -5*w^3 - w^2 + 33*w - 12],\ [569, 569, 2*w^3 - w^2 - 15*w + 13],\ [569, 569, -4*w^3 - 2*w^2 + 24*w - 7],\ [577, 577, -w^2 - 2],\ [577, 577, 3*w^3 - 20*w + 8],\ [587, 587, 6*w^3 + 4*w^2 - 36*w - 1],\ [587, 587, -w^3 + w^2 + 9*w - 8],\ [593, 593, 6*w^3 + 3*w^2 - 36*w + 2],\ [593, 593, -3*w^3 - w^2 + 21*w - 4],\ [599, 599, -2*w^3 - w^2 + 12*w - 10],\ [599, 599, -4*w^3 - 2*w^2 + 25*w - 6],\ [601, 601, -2*w^3 + 2*w^2 + 15*w - 16],\ [607, 607, w^3 - w^2 - 7*w + 4],\ [607, 607, -2*w^3 - 2*w^2 + 10*w + 3],\ [631, 631, 2*w^2 + 4*w - 7],\ [641, 641, -3*w^3 - 2*w^2 + 16*w],\ [643, 643, w^3 + w^2 - 3*w - 4],\ [643, 643, w^3 + 3*w^2 - 6*w - 13],\ [653, 653, -w^3 + 6*w + 2],\ [653, 653, -3*w^2 - 5*w + 11],\ [659, 659, -2*w^3 + 10*w - 5],\ [661, 661, w^3 - w^2 - 8*w + 3],\ [673, 673, 3*w^3 + 4*w^2 - 14*w - 2],\ [677, 677, 4*w^3 + 2*w^2 - 23*w + 6],\ [677, 677, 2*w^3 - 13*w + 14],\ [683, 683, 2*w^3 + w^2 - 13*w + 7],\ [701, 701, 8*w^3 + 4*w^2 - 51*w + 8],\ [701, 701, -4*w^3 - w^2 + 24*w - 12],\ [709, 709, -4*w^3 - w^2 + 27*w - 7],\ [709, 709, 3*w^3 + 3*w^2 - 18*w - 5],\ [709, 709, -3*w^3 + w^2 + 21*w - 14],\ [709, 709, w^2 - w - 7],\ [719, 719, -9*w^3 - 4*w^2 + 58*w - 8],\ [719, 719, 11*w^3 + 5*w^2 - 68*w + 9],\ [727, 727, -w^3 + 4*w - 6],\ [733, 733, 2*w^3 + w^2 - 13*w + 9],\ [739, 739, -2*w^2 - 3*w + 4],\ [743, 743, 3*w^3 + 3*w^2 - 19*w - 4],\ [751, 751, 2*w^3 + 3*w^2 - 10*w - 2],\ [761, 761, -12*w^3 - 5*w^2 + 75*w - 9],\ [761, 761, -3*w^3 - 3*w^2 + 17*w],\ [769, 769, -6*w^3 - 4*w^2 + 37*w],\ [769, 769, -8*w^3 - 3*w^2 + 51*w - 7],\ [773, 773, -w^2 - 2*w - 2],\ [787, 787, -5*w^3 - 5*w^2 + 28*w + 7],\ [811, 811, 7*w^3 + 2*w^2 - 42*w + 6],\ [811, 811, -2*w^3 - w^2 + 9*w - 7],\ [823, 823, -3*w^3 - 2*w^2 + 14*w - 10],\ [829, 829, 4*w^3 + 3*w^2 - 20*w + 6],\ [829, 829, -7*w^3 - 2*w^2 + 44*w - 14],\ [841, 29, w^3 + 4*w^2 - 2*w - 14],\ [841, 29, -w^2 + 10],\ [857, 857, -3*w^3 - w^2 + 20*w - 9],\ [859, 859, -w^3 + 2*w^2 + 10*w - 18],\ [863, 863, 11*w^3 + 5*w^2 - 69*w + 6],\ [863, 863, w^3 - 2*w^2 - 10*w + 12],\ [877, 877, 3*w^3 - 18*w + 10],\ [883, 883, 4*w^3 + 3*w^2 - 22*w],\ [887, 887, 3*w^3 + 3*w^2 - 15*w - 2],\ [887, 887, w^2 + 4*w - 10],\ [887, 887, w^3 + w^2 - 3*w - 8],\ [887, 887, w - 6],\ [907, 907, 6*w^3 + w^2 - 38*w + 16],\ [919, 919, -2*w^3 - 3*w^2 + 11*w + 1],\ [919, 919, 5*w^3 - w^2 - 34*w + 27],\ [937, 937, -w^3 - w^2 + 8*w + 3],\ [941, 941, -4*w^3 + 25*w - 20],\ [947, 947, -2*w^3 + w^2 + 8*w - 6],\ [967, 967, -7*w^3 - w^2 + 44*w - 23],\ [971, 971, 2*w^2 + 2*w - 3]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^9 - 4*x^8 - 23*x^7 + 84*x^6 + 188*x^5 - 580*x^4 - 636*x^3 + 1522*x^2 + 764*x - 1176 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1, e, -149/6304*e^8 + 609/6304*e^7 + 1285/3152*e^6 - 4847/3152*e^5 - 6031/3152*e^4 + 20001/3152*e^3 + 557/3152*e^2 - 9809/1576*e + 5671/788, -1, 383/12608*e^8 - 275/12608*e^7 - 5831/6304*e^6 + 253/6304*e^5 + 57917/6304*e^4 + 22861/6304*e^3 - 197575/6304*e^2 - 47589/3152*e + 41355/1576, 247/12608*e^8 - 523/12608*e^7 - 3135/6304*e^6 + 3381/6304*e^5 + 28677/6304*e^4 - 7115/6304*e^3 - 100095/6304*e^2 - 1837/3152*e + 23547/1576, -247/12608*e^8 + 523/12608*e^7 + 3135/6304*e^6 - 3381/6304*e^5 - 28677/6304*e^4 + 7115/6304*e^3 + 100095/6304*e^2 + 1837/3152*e - 23547/1576, 585/12608*e^8 - 741/12608*e^7 - 9001/6304*e^6 + 5851/6304*e^5 + 90315/6304*e^4 - 17349/6304*e^3 - 306577/6304*e^2 - 5595/3152*e + 57677/1576, -149/6304*e^8 + 609/6304*e^7 + 1285/3152*e^6 - 4847/3152*e^5 - 6031/3152*e^4 + 20001/3152*e^3 - 2595/3152*e^2 - 9809/1576*e + 10399/788, -111/12608*e^8 + 771/12608*e^7 + 439/6304*e^6 - 6509/6304*e^5 + 563/6304*e^4 + 37091/6304*e^3 + 2615/6304*e^2 - 40763/3152*e - 5739/1576, -883/12608*e^8 + 1959/12608*e^7 + 11571/6304*e^6 - 15545/6304*e^5 - 102377/6304*e^4 + 57351/6304*e^3 + 313995/6304*e^2 - 17175/3152*e - 55791/1576, 209/6304*e^8 - 685/6304*e^7 - 2289/3152*e^6 + 5043/3152*e^5 + 18931/3152*e^4 - 14749/3152*e^3 - 67481/3152*e^2 - 3979/1576*e + 19197/788, 159/3152*e^8 - 359/3152*e^7 - 2109/1576*e^6 + 3041/1576*e^5 + 18425/1576*e^4 - 12559/1576*e^3 - 53475/1576*e^2 + 5541/788*e + 8061/394, -193/3152*e^8 + 297/3152*e^7 + 2783/1576*e^6 - 2259/1576*e^5 - 25735/1576*e^4 + 5065/1576*e^3 + 76269/1576*e^2 + 5897/788*e - 10149/394, 383/12608*e^8 - 275/12608*e^7 - 5831/6304*e^6 + 253/6304*e^5 + 57917/6304*e^4 + 22861/6304*e^3 - 210183/6304*e^2 - 41285/3152*e + 60267/1576, 639/12608*e^8 - 179/12608*e^7 - 10535/6304*e^6 - 2483/6304*e^5 + 112957/6304*e^4 + 57037/6304*e^3 - 409991/6304*e^2 - 98853/3152*e + 86835/1576, -37/394*e^8 + 30/197*e^7 + 1015/394*e^6 - 331/197*e^5 - 4803/197*e^4 - 310/197*e^3 + 16172/197*e^2 + 4870/197*e - 13562/197, 1383/12608*e^8 - 3643/12608*e^7 - 17311/6304*e^6 + 30837/6304*e^5 + 146837/6304*e^4 - 131259/6304*e^3 - 430415/6304*e^2 + 47267/3152*e + 73379/1576, -1545/12608*e^8 + 5109/12608*e^7 + 17185/6304*e^6 - 43659/6304*e^5 - 129659/6304*e^4 + 201237/6304*e^3 + 340353/6304*e^2 - 112637/3152*e - 50533/1576, 117/12608*e^8 - 1409/12608*e^7 + 91/6304*e^6 + 15039/6304*e^5 - 13457/6304*e^4 - 96769/6304*e^3 + 68547/6304*e^2 + 87137/3152*e - 11159/1576, 237/6304*e^8 + 15/6304*e^7 - 4281/3152*e^6 - 329/3152*e^5 + 45439/3152*e^4 + 9871/3152*e^3 - 158285/3152*e^2 - 21603/1576*e + 33849/788, -763/12608*e^8 + 1807/12608*e^7 + 9563/6304*e^6 - 15153/6304*e^5 - 76577/6304*e^4 + 61551/6304*e^3 + 192755/6304*e^2 - 19535/3152*e - 15511/1576, 5/3152*e^8 - 269/3152*e^7 + 573/1576*e^6 + 1855/1576*e^5 - 9957/1576*e^4 - 5341/1576*e^3 + 48007/1576*e^2 + 427/788*e - 14607/394, 1757/12608*e^8 - 4537/12608*e^7 - 21573/6304*e^6 + 37207/6304*e^5 + 178391/6304*e^4 - 155993/6304*e^3 - 503061/6304*e^2 + 71169/3152*e + 70737/1576, -1019/6304*e^8 + 1711/6304*e^7 + 14267/3152*e^6 - 12417/3152*e^5 - 131617/3152*e^4 + 27375/3152*e^3 + 408323/3152*e^2 + 28577/1576*e - 68871/788, 375/12608*e^8 - 3627/12608*e^7 + 817/6304*e^6 + 31957/6304*e^5 - 50971/6304*e^4 - 166539/6304*e^3 + 272801/6304*e^2 + 123827/3152*e - 74277/1576, -99/1576*e^8 + 283/1576*e^7 + 1105/788*e^6 - 2057/788*e^5 - 8677/788*e^4 + 6779/788*e^3 + 23587/788*e^2 - 1205/394*e - 923/197, -17/788*e^8 - 31/788*e^7 + 337/394*e^6 + 391/394*e^5 - 3655/394*e^4 - 3353/394*e^3 + 11397/394*e^2 + 3552/197*e - 1694/197, 465/3152*e^8 - 589/3152*e^7 - 6993/1576*e^6 + 3883/1576*e^5 + 69243/1576*e^4 - 2637/1576*e^3 - 235769/1576*e^2 - 17419/788*e + 48129/394, -643/6304*e^8 + 1655/6304*e^7 + 7555/3152*e^6 - 11609/3152*e^5 - 60233/3152*e^4 + 24775/3152*e^3 + 166075/3152*e^2 + 23809/1576*e - 24087/788, 99/1576*e^8 - 283/1576*e^7 - 1105/788*e^6 + 2057/788*e^5 + 8677/788*e^4 - 6779/788*e^3 - 24375/788*e^2 + 1205/394*e + 3681/197, -57/3152*e^8 + 545/3152*e^7 + 87/1576*e^6 - 5387/1576*e^5 + 3505/1576*e^4 + 31889/1576*e^3 - 11755/1576*e^2 - 24095/788*e - 1797/394, -135/1576*e^8 + 565/1576*e^7 + 637/394*e^6 - 4775/788*e^5 - 8143/788*e^4 + 21673/788*e^3 + 20165/788*e^2 - 5075/197*e - 3354/197, -921/6304*e^8 + 1797/6304*e^7 + 12417/3152*e^6 - 13883/3152*e^5 - 112123/3152*e^4 + 43413/3152*e^3 + 359217/3152*e^2 + 12203/1576*e - 79053/788, 23/3152*e^8 - 607/3152*e^7 + 587/1576*e^6 + 6169/1576*e^5 - 10815/1576*e^4 - 40959/1576*e^3 + 44005/1576*e^2 + 39473/788*e - 12111/394, -133/3152*e^8 + 1009/3152*e^7 + 597/1576*e^6 - 9943/1576*e^5 + 3713/1576*e^4 + 58385/1576*e^3 - 35571/1576*e^2 - 46897/788*e + 13931/394, 1743/12608*e^8 - 947/12608*e^7 - 28063/6304*e^6 + 493/6304*e^5 + 290429/6304*e^4 + 92525/6304*e^3 - 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125383/1576, 153/12608*e^8 - 2085/12608*e^7 + 1695/6304*e^6 + 18939/6304*e^5 - 43541/6304*e^4 - 111269/6304*e^3 + 214991/6304*e^2 + 108493/3152*e - 57387/1576, -1791/12608*e^8 + 2899/12608*e^7 + 25399/6304*e^6 - 21453/6304*e^5 - 234557/6304*e^4 + 53939/6304*e^3 + 697639/6304*e^2 + 39557/3152*e - 95283/1576, -333/12608*e^8 + 2313/12608*e^7 + 1317/6304*e^6 - 19527/6304*e^5 + 7993/6304*e^4 + 92361/6304*e^3 - 67803/6304*e^2 - 59249/3152*e + 33215/1576, -289/12608*e^8 + 1837/12608*e^7 + 1001/6304*e^6 - 15811/6304*e^5 + 14301/6304*e^4 + 81293/6304*e^3 - 117511/6304*e^2 - 69045/3152*e + 39579/1576, -1123/6304*e^8 + 3839/6304*e^7 + 11647/3152*e^6 - 30513/3152*e^5 - 83057/3152*e^4 + 123023/3152*e^3 + 223939/3152*e^2 - 44763/1576*e - 42579/788, 21/394*e^8 - 33/197*e^7 - 427/394*e^6 + 502/197*e^5 + 1363/197*e^4 - 1826/197*e^3 - 2502/197*e^2 + 1341/197*e + 222/197, -581/3152*e^8 + 841/3152*e^7 + 8041/1576*e^6 - 4367/1576*e^5 - 75271/1576*e^4 - 9303/1576*e^3 + 249477/1576*e^2 + 42815/788*e - 53445/394, 99/1576*e^8 - 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5757/1576*e^2 + 17053/788*e + 15161/394, -925/6304*e^8 + 3273/6304*e^7 + 9437/3152*e^6 - 27975/3152*e^5 - 59399/3152*e^4 + 131529/3152*e^3 + 99541/3152*e^2 - 78601/1576*e + 8911/788, 4023/12608*e^8 - 3835/12608*e^7 - 59911/6304*e^6 + 14245/6304*e^5 + 578901/6304*e^4 + 159717/6304*e^3 - 1896783/6304*e^2 - 415989/3152*e + 370115/1576, -317/3152*e^8 + 1137/3152*e^7 + 2993/1576*e^6 - 8863/1576*e^5 - 16935/1576*e^4 + 34609/1576*e^3 + 17421/1576*e^2 - 10445/788*e + 13895/394, 25/788*e^8 - 163/788*e^7 - 45/197*e^6 + 1395/394*e^5 - 1323/394*e^4 - 6611/394*e^3 + 11909/394*e^2 + 4893/197*e - 7776/197, 2217/12608*e^8 - 4069/12608*e^7 - 31897/6304*e^6 + 37659/6304*e^5 + 289899/6304*e^4 - 174565/6304*e^3 - 827025/6304*e^2 + 100997/3152*e + 107469/1576, -4465/12608*e^8 + 7757/12608*e^7 + 62369/6304*e^6 - 58451/6304*e^5 - 577795/6304*e^4 + 177837/6304*e^3 + 1797529/6304*e^2 + 2051/3152*e - 290485/1576, 581/12608*e^8 - 2417/12608*e^7 - 4101/6304*e^6 + 16975/6304*e^5 + 10655/6304*e^4 - 55313/6304*e^3 + 20019/6304*e^2 + 4465/3152*e + 6953/1576, 1539/6304*e^8 - 2895/6304*e^7 - 20079/3152*e^6 + 16217/3152*e^5 + 185105/3152*e^4 + 8161/3152*e^3 - 624275/3152*e^2 - 101581/1576*e + 139927/788, -889/12608*e^8 - 555/12608*e^7 + 15769/6304*e^6 + 13749/6304*e^5 - 174587/6304*e^4 - 182411/6304*e^3 + 643137/6304*e^2 + 284747/3152*e - 108237/1576, -883/12608*e^8 + 1959/12608*e^7 + 11571/6304*e^6 - 15545/6304*e^5 - 102377/6304*e^4 + 57351/6304*e^3 + 313995/6304*e^2 - 23479/3152*e - 52639/1576, 1879/6304*e^8 - 5427/6304*e^7 - 22091/3152*e^6 + 43069/3152*e^5 + 182557/3152*e^4 - 162755/3152*e^3 - 555927/3152*e^2 + 42503/1576*e + 102495/788, 3155/12608*e^8 - 11351/12608*e^7 - 32043/6304*e^6 + 92521/6304*e^5 + 222073/6304*e^4 - 403351/6304*e^3 - 555419/6304*e^2 + 195759/3152*e + 59319/1576, -1093/6304*e^8 + 3801/6304*e^7 + 11145/3152*e^6 - 30415/3152*e^5 - 75031/3152*e^4 + 120921/3152*e^3 + 179445/3152*e^2 - 46141/1576*e - 26993/788, -799/3152*e^8 + 907/3152*e^7 + 11899/1576*e^6 - 4869/1576*e^5 - 115837/1576*e^4 - 15357/1576*e^3 + 394607/1576*e^2 + 64701/788*e - 91423/394, 635/6304*e^8 + 1297/6304*e^7 - 13515/3152*e^6 - 13423/3152*e^5 + 156225/3152*e^4 + 97873/3152*e^3 - 584563/3152*e^2 - 102977/1576*e + 140127/788, 1837/6304*e^8 - 4113/6304*e^7 - 24225/3152*e^6 + 33791/3152*e^5 + 219231/3152*e^4 - 145313/3152*e^3 - 704189/3152*e^2 + 75637/1576*e + 129373/788, -903/6304*e^8 + 1459/6304*e^7 + 13219/3152*e^6 - 11933/3152*e^5 - 127165/3152*e^4 + 36163/3152*e^3 + 426135/3152*e^2 + 19729/1576*e - 97439/788, 5/197*e^8 - 91/788*e^7 - 341/788*e^6 + 919/394*e^5 + 557/394*e^4 - 5801/394*e^3 + 1529/394*e^2 + 9523/394*e + 2329/197, -1745/6304*e^8 + 6413/6304*e^7 + 17905/3152*e^6 - 54819/3152*e^5 - 119075/3152*e^4 + 247821/3152*e^3 + 254537/3152*e^2 - 128141/1576*e - 11549/788, -535/3152*e^8 + 1203/3152*e^7 + 6851/1576*e^6 - 9365/1576*e^5 - 59077/1576*e^4 + 34859/1576*e^3 + 165703/1576*e^2 - 11411/788*e - 13051/394, 1743/12608*e^8 - 947/12608*e^7 - 28063/6304*e^6 + 493/6304*e^5 + 290429/6304*e^4 + 92525/6304*e^3 - 1036839/6304*e^2 - 191485/3152*e + 250955/1576, 327/12608*e^8 - 4827/12608*e^7 + 2881/6304*e^6 + 48821/6304*e^5 - 86507/6304*e^4 - 313211/6304*e^3 + 472593/6304*e^2 + 310739/3152*e - 107725/1576, 3681/12608*e^8 - 5293/12608*e^7 - 52297/6304*e^6 + 32355/6304*e^5 + 488035/6304*e^4 + 12211/6304*e^3 - 1527609/6304*e^2 - 222507/3152*e + 264773/1576, 299/12608*e^8 + 5505/12608*e^7 - 14827/6304*e^6 - 56127/6304*e^5 + 216369/6304*e^4 + 350881/6304*e^3 - 919619/6304*e^2 - 288641/3152*e + 243255/1576, -57/1576*e^8 + 151/1576*e^7 + 339/394*e^6 - 1447/788*e^5 - 4769/788*e^4 + 9431/788*e^3 + 5187/788*e^2 - 4660/197*e + 4507/197, -661/1576*e^8 + 1993/1576*e^7 + 7541/788*e^6 - 16711/788*e^5 - 57011/788*e^4 + 73001/788*e^3 + 143285/788*e^2 - 34937/394*e - 15945/197, 939/12608*e^8 - 3711/12608*e^7 - 10827/6304*e^6 + 36321/6304*e^5 + 89201/6304*e^4 - 206687/6304*e^3 - 259203/6304*e^2 + 147407/3152*e + 28359/1576, -721/3152*e^8 + 493/3152*e^7 + 11697/1576*e^6 - 2723/1576*e^5 - 119555/1576*e^4 - 11051/1576*e^3 + 404057/1576*e^2 + 31647/788*e - 76273/394, 2589/6304*e^8 - 7377/6304*e^7 - 29769/3152*e^6 + 57471/3152*e^5 + 232767/3152*e^4 - 210401/3152*e^3 - 630781/3152*e^2 + 42461/1576*e + 86557/788, 601/12608*e^8 - 6645/12608*e^7 + 2919/6304*e^6 + 55915/6304*e^5 - 101669/6304*e^4 - 268949/6304*e^3 + 543007/6304*e^2 + 162197/3152*e - 196467/1576, 1267/6304*e^8 - 1815/6304*e^7 - 17051/3152*e^6 + 6713/3152*e^5 + 159721/3152*e^4 + 53801/3152*e^3 - 541211/3152*e^2 - 140097/1576*e + 112191/788, -2657/12608*e^8 + 8829/12608*e^7 + 28753/6304*e^6 - 74819/6304*e^5 - 201683/6304*e^4 + 341981/6304*e^3 + 422633/6304*e^2 - 189005/3152*e - 13509/1576, -77/12608*e^8 - 743/12608*e^7 + 4493/6304*e^6 - 199/6304*e^5 - 59895/6304*e^4 + 60345/6304*e^3 + 189429/6304*e^2 - 137305/3152*e - 23745/1576, -1517/12608*e^8 + 7385/12608*e^7 + 12829/6304*e^6 - 67943/6304*e^5 - 60599/6304*e^4 + 369273/6304*e^3 + 49397/6304*e^2 - 298105/3152*e + 25583/1576, -2965/12608*e^8 + 5857/12608*e^7 + 40421/6304*e^6 - 44095/6304*e^5 - 378223/6304*e^4 + 129473/6304*e^3 + 1268605/6304*e^2 + 18255/3152*e - 256633/1576, -2687/12608*e^8 + 2563/12608*e^7 + 40287/6304*e^6 - 10301/6304*e^5 - 386221/6304*e^4 - 100349/6304*e^3 + 1210999/6304*e^2 + 252077/3152*e - 196939/1576, 2251/12608*e^8 - 5583/12608*e^7 - 27843/6304*e^6 + 43969/6304*e^5 + 229441/6304*e^4 - 157615/6304*e^3 - 614995/6304*e^2 + 54887/3152*e + 73703/1576, -3193/12608*e^8 + 4885/12608*e^7 + 45497/6304*e^6 - 34123/6304*e^5 - 430395/6304*e^4 + 64757/6304*e^3 + 1407553/6304*e^2 + 109419/3152*e - 266973/1576, 335/6304*e^8 - 3051/6304*e^7 + 173/3152*e^6 + 28149/3152*e^5 - 35931/3152*e^4 - 160059/3152*e^3 + 199217/3152*e^2 + 130655/1576*e - 54345/788, -681/6304*e^8 + 1493/6304*e^7 + 8401/3152*e^6 - 9947/3152*e^5 - 69979/3152*e^4 + 23445/3152*e^3 + 192385/3152*e^2 - 13005/1576*e - 22133/788, -211/6304*e^8 - 1729/6304*e^7 + 7103/3152*e^6 + 16279/3152*e^5 - 91857/3152*e^4 - 103521/3152*e^3 + 333219/3152*e^2 + 116965/1576*e - 54015/788] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([2, 2, -w + 1])] = 1 AL_eigenvalues[ZF.ideal([8, 2, w^3 - 7*w + 3])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]