sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, base_ring=CyclotomicField(980))
M = H._module
chi = DirichletCharacter(H, M([882,435]))
pari:[g,chi] = znchar(Mod(149,4334))
χ4334(13,⋅)
χ4334(17,⋅)
χ4334(35,⋅)
χ4334(57,⋅)
χ4334(73,⋅)
χ4334(79,⋅)
χ4334(95,⋅)
χ4334(117,⋅)
χ4334(123,⋅)
χ4334(139,⋅)
χ4334(145,⋅)
χ4334(149,⋅)
χ4334(151,⋅)
χ4334(167,⋅)
χ4334(189,⋅)
χ4334(195,⋅)
χ4334(205,⋅)
χ4334(215,⋅)
χ4334(227,⋅)
χ4334(249,⋅)
χ4334(255,⋅)
χ4334(271,⋅)
χ4334(277,⋅)
χ4334(283,⋅)
χ4334(299,⋅)
χ4334(303,⋅)
χ4334(305,⋅)
χ4334(315,⋅)
χ4334(321,⋅)
χ4334(327,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1971,199) → (e(109),e(19687))
a |
−1 | 1 | 3 | 5 | 7 | 9 | 13 | 15 | 17 | 19 | 21 | 23 |
χ4334(149,a) |
1 | 1 | e(980531) | e(980103) | e(24526) | e(49041) | e(980977) | e(490317) | e(980663) | e(352) | e(196127) | e(4913) |
sage:chi.jacobi_sum(n)