sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6664, base_ring=CyclotomicField(168))
M = H._module
chi = DirichletCharacter(H, M([84,0,124,21]))
pari:[g,chi] = znchar(Mod(927,6664))
χ6664(87,⋅)
χ6664(383,⋅)
χ6664(495,⋅)
χ6664(535,⋅)
χ6664(831,⋅)
χ6664(927,⋅)
χ6664(943,⋅)
χ6664(1039,⋅)
χ6664(1335,⋅)
χ6664(1375,⋅)
χ6664(1447,⋅)
χ6664(1487,⋅)
χ6664(1879,⋅)
χ6664(1895,⋅)
χ6664(2287,⋅)
χ6664(2327,⋅)
χ6664(2399,⋅)
χ6664(2439,⋅)
χ6664(2735,⋅)
χ6664(2831,⋅)
χ6664(2847,⋅)
χ6664(2943,⋅)
χ6664(3239,⋅)
χ6664(3279,⋅)
χ6664(3391,⋅)
χ6664(3687,⋅)
χ6664(3783,⋅)
χ6664(3799,⋅)
χ6664(3895,⋅)
χ6664(4191,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(4999,3333,4217,785) → (−1,1,e(4231),e(81))
a |
−1 | 1 | 3 | 5 | 9 | 11 | 13 | 15 | 19 | 23 | 25 | 27 |
χ6664(927,a) |
1 | 1 | e(16861) | e(1685) | e(8461) | e(168151) | e(76) | e(2811) | e(121) | e(16871) | e(845) | e(565) |
sage:chi.jacobi_sum(n)