sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3267, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([10,6]))
pari:[g,chi] = znchar(Mod(928,3267))
χ3267(856,⋅)
χ3267(874,⋅)
χ3267(928,⋅)
χ3267(1576,⋅)
χ3267(1963,⋅)
χ3267(2017,⋅)
χ3267(2665,⋅)
χ3267(3034,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(3026,244) → (e(31),e(51))
a |
−1 | 1 | 2 | 4 | 5 | 7 | 8 | 10 | 13 | 14 | 16 | 17 |
χ3267(928,a) |
1 | 1 | e(158) | e(151) | e(157) | e(1511) | e(53) | 1 | e(1513) | e(154) | e(152) | e(54) |
sage:chi.jacobi_sum(n)