sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1254, base_ring=CyclotomicField(90))
M = H._module
chi = DirichletCharacter(H, M([45,27,65]))
pari:[g,chi] = znchar(Mod(41,1254))
χ1254(29,⋅)
χ1254(41,⋅)
χ1254(167,⋅)
χ1254(173,⋅)
χ1254(281,⋅)
χ1254(299,⋅)
χ1254(371,⋅)
χ1254(413,⋅)
χ1254(431,⋅)
χ1254(497,⋅)
χ1254(545,⋅)
χ1254(611,⋅)
χ1254(623,⋅)
χ1254(629,⋅)
χ1254(743,⋅)
χ1254(755,⋅)
χ1254(827,⋅)
χ1254(887,⋅)
χ1254(941,⋅)
χ1254(953,⋅)
χ1254(965,⋅)
χ1254(1085,⋅)
χ1254(1097,⋅)
χ1254(1229,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(419,343,1123) → (−1,e(103),e(1813))
a |
−1 | 1 | 5 | 7 | 13 | 17 | 23 | 25 | 29 | 31 | 35 | 37 |
χ1254(41,a) |
−1 | 1 | e(9023) | e(3013) | e(4541) | e(4519) | e(1817) | e(4523) | e(9079) | e(3019) | e(4531) | e(101) |
sage:chi.jacobi_sum(n)