sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2128, base_ring=CyclotomicField(6))
M = H._module
chi = DirichletCharacter(H, M([0,3,3,5]))
pari:[g,chi] = znchar(Mod(601,2128))
χ2128(601,⋅)
χ2128(825,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(799,533,913,1009) → (1,−1,−1,e(65))
a |
−1 | 1 | 3 | 5 | 9 | 11 | 13 | 15 | 17 | 23 | 25 | 27 |
χ2128(601,a) |
1 | 1 | e(65) | e(31) | e(32) | −1 | e(61) | e(61) | e(65) | e(32) | e(32) | −1 |
sage:chi.jacobi_sum(n)