sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2058, base_ring=CyclotomicField(294))
M = H._module
chi = DirichletCharacter(H, M([147,149]))
pari:[g,chi] = znchar(Mod(677,2058))
χ2058(5,⋅)
χ2058(17,⋅)
χ2058(47,⋅)
χ2058(59,⋅)
χ2058(89,⋅)
χ2058(101,⋅)
χ2058(131,⋅)
χ2058(143,⋅)
χ2058(173,⋅)
χ2058(185,⋅)
χ2058(257,⋅)
χ2058(269,⋅)
χ2058(299,⋅)
χ2058(311,⋅)
χ2058(341,⋅)
χ2058(353,⋅)
χ2058(383,⋅)
χ2058(395,⋅)
χ2058(425,⋅)
χ2058(437,⋅)
χ2058(467,⋅)
χ2058(479,⋅)
χ2058(551,⋅)
χ2058(563,⋅)
χ2058(593,⋅)
χ2058(605,⋅)
χ2058(635,⋅)
χ2058(647,⋅)
χ2058(677,⋅)
χ2058(689,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1373,1375) → (−1,e(294149))
a |
−1 | 1 | 5 | 11 | 13 | 17 | 19 | 23 | 25 | 29 | 31 | 37 |
χ2058(677,a) |
1 | 1 | e(14729) | e(294269) | e(9843) | e(14725) | e(61) | e(294181) | e(14758) | e(985) | e(4217) | e(14774) |
sage:chi.jacobi_sum(n)