sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1197, base_ring=CyclotomicField(18))
M = H._module
chi = DirichletCharacter(H, M([9,0,10]))
pari:[g,chi] = znchar(Mod(701,1197))
χ1197(386,⋅)
χ1197(575,⋅)
χ1197(701,⋅)
χ1197(764,⋅)
χ1197(890,⋅)
χ1197(1016,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(533,514,1009) → (−1,1,e(95))
a |
−1 | 1 | 2 | 4 | 5 | 8 | 10 | 11 | 13 | 16 | 17 | 20 |
χ1197(701,a) |
−1 | 1 | e(181) | e(91) | e(187) | e(61) | e(94) | e(61) | e(97) | e(92) | e(181) | −1 |
sage:chi.jacobi_sum(n)