sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1260, base_ring=CyclotomicField(6))
M = H._module
chi = DirichletCharacter(H, M([0,2,3,4]))
pari:[g,chi] = znchar(Mod(949,1260))
χ1260(709,⋅)
χ1260(949,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(631,281,757,1081) → (1,e(31),−1,e(32))
a |
−1 | 1 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 |
χ1260(949,a) |
1 | 1 | 1 | e(61) | e(61) | e(31) | −1 | e(31) | e(31) | e(65) | e(32) | e(65) |
sage:chi.jacobi_sum(n)