sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3360, base_ring=CyclotomicField(8))
M = H._module
chi = DirichletCharacter(H, M([0,1,0,0,0]))
pari:[g,chi] = znchar(Mod(421,3360))
χ3360(421,⋅)
χ3360(1261,⋅)
χ3360(2101,⋅)
χ3360(2941,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1471,421,1121,2017,1921) → (1,e(81),1,1,1)
a |
−1 | 1 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 |
χ3360(421,a) |
1 | 1 | e(85) | e(87) | −1 | e(87) | −i | e(83) | 1 | e(81) | −i | e(85) |
sage:chi.jacobi_sum(n)