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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] # Trace form for 3997.1.cz.a, downloaded from the LMFDB on 20 January 2019. f3997_1_cz_a = [0, 144, 1, 0, 5, 0, 0, 2, 21, -1, 0, 6, 0, 0, 1, 0, 6, 0, -9, 0, 0, 0, 21, 3, 0, -1, 0, 0, -10, -4, 0, 0, -5, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -9, -20, 0, -34, 0, 0, 2, -2, 0, 0, 6, 0, 0, -8, 0, -1, 0, 0, 0, 0, -1, 11, 0, 0, 20, 0, 0, 0, 3, 23, 0, -31, 0, 0, 1, 0, 6, 0, -1, 0, 0, 0, 0, 7, 0, -9, 0, 0, 0, 9, 0, 0, 0, 0, 0, 6, -2, -10, 0, 0, 0, 0, 0, 2, -2, 0, -2, 0, 0, -32, 1, 0, 0, 10, 0, 0, 0, 0, 5, 0, 0, 0, 0, -32, -2, -4, 0, 0, 0, 0, 0, -6, 0, 0, -9, 0, 0, 0, 0, 1, 0, 6, 0, 0, 0, 5, -2, 0, 1, 0, 0, 7, 0, 0, 0, 7, 0, 0, -2, -2, -6, 0, 0, 0, 0, 0, -1, 0, 0, 5, 0, 0, 4, 31, 0, 0, -2, 0, 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1, 0, 0, 27, 0, 0, 0, 5, 0, 0, 1, 0, 0, 0, 0, 5, 0, 0, 0, 0, -9, -39, 1, 0, -2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, -9, 13, 0, 15, 0, 0, 1, -3, 0, 0, 1, 0, 0, 5, 0, 7, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 20, -16, 0, 0, 2, 0, 0, 0, 0, -31, 0, 0, 0, 0, 0, 0, -8, 0, 5, 0, 0, 0, 0, -1, 0, 1, 0, 0, 1, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 9, 0, 0, 6, 0, 0, 0, 5, -2, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, 27, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 2, 11, 0, 0, 1, 0, 0, -18, -2, -25, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, -2, 0, 0, 4, 0, 0, 0, -5, 0, 0, -6, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 7, -34, 0, 1, 0, 0, 15, 0, 0, 0, 48, 0, 0, -2, 0, -8, 0, 0, 0, 0, 0, 9, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 12, 0, -19, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, 4, 0, 0, -43, 0, 0, 0, -27, 0, 0, 0, 0, 0, -1, 0, -23, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 0, 1, 0, 0, 6, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 6, 5, 0, -11, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 6, -19, 0, 0, 0, 0, 0, 6, 0, 0, -9, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 5, 0, -1, 0, 0, 0, 0, -1, -66, 6, 0, -2, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 20, 0, -2, 0, 0, -5, -31, 0, 0, 9, 0, 0, 0, -8, -9, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -73, -6, 0, 0, 4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, -10, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -10, 7, 0, 19, 0, 0, 0, -42, 0, 0, 22, 0, 0, 0, 1, -7, 0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, -5, -34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, -18, 0, 0, 0, 0, -2, 0, 8, 0, 0, 0, 0, -1, 0, -38, 0, 0, 0, -4, 1, 0, 0, 0, 0, 4, 0, 0, 0, 1, 0, 0, -9, 2, 0, 0, 0, 0, 0, 0, 1, 2, 0, -30, 0, 0, -6, 0, 0, 0, -1, 0, 0, 0, 0, -14, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -4, -8, 0, 14, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, -37, 0, 0, 8, 0, 0, 0, 2, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 10, 1, 0, 1, 0] fs = [f23_2_a_a, f163_3_b_a, f124_1_i_a, f8_14_b_a, f983_2_c_a, f3600_1_e_a,f3997_1_cz_a] PS.<q> = PowerSeriesRing(CDF) fqs = map(PS, fs[:100]) fqs = zip(['23.2.a.a', '163.3.b.a', '124.1.i.a', '8.14.b.a', '983.2.c.a', '3600.1.e.a', '3997.1.cz.a'], fqs) fqs = [('j', PS(j_invariant_qexp(101).list())/q)] + fqs
In [3]:
DtoH = lambda x: (-CDF.0 *x + 1)/(x - CDF.0) Htoq = lambda x: exp(2*CDF.pi()*CDF.0*x) Dtoq = lambda x: Htoq(DtoH(CDF(x))) normalize3 = lambda x: Htoq(x.abs()+3/5) #on H for name, f in fqs: print name #complex_plot( f(Htoq(x)),(-1.5,1.2), (0.0001,2), plot_points=300, aspect_ratio = 1, axes = False).show() #complex_plot(lambda x: +Infinity if abs(x) >= 0.99 else 10*f(Dtoq(x)), (-1,1),(-1,1), plot_points=600, aspect_ratio=1,axes=false).show() complex_plot(lambda x: +Infinity if abs(x) >= 0.99 else 10*normalize3(f(Dtoq(x))), (-1,1),(-1,1), plot_points=1200, aspect_ratio=1,axes=false).show()
j