sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2675, base_ring=CyclotomicField(212))
M = H._module
chi = DirichletCharacter(H, M([159,66]))
pari:[g,chi] = znchar(Mod(593,2675))
χ2675(7,⋅)
χ2675(18,⋅)
χ2675(32,⋅)
χ2675(43,⋅)
χ2675(68,⋅)
χ2675(82,⋅)
χ2675(93,⋅)
χ2675(157,⋅)
χ2675(232,⋅)
χ2675(257,⋅)
χ2675(268,⋅)
χ2675(282,⋅)
χ2675(307,⋅)
χ2675(318,⋅)
χ2675(343,⋅)
χ2675(393,⋅)
χ2675(418,⋅)
χ2675(443,⋅)
χ2675(482,⋅)
χ2675(493,⋅)
χ2675(532,⋅)
χ2675(543,⋅)
χ2675(557,⋅)
χ2675(593,⋅)
χ2675(607,⋅)
χ2675(632,⋅)
χ2675(657,⋅)
χ2675(668,⋅)
χ2675(693,⋅)
χ2675(707,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1927,751) → (−i,e(10633))
a |
−1 | 1 | 2 | 3 | 4 | 6 | 7 | 8 | 9 | 11 | 12 | 13 |
χ2675(593,a) |
1 | 1 | e(21213) | e(2129) | e(10613) | e(10611) | e(21229) | e(21239) | e(1069) | e(5345) | e(21235) | e(212129) |
sage:chi.jacobi_sum(n)