sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, base_ring=CyclotomicField(10))
M = H._module
chi = DirichletCharacter(H, M([0,0,0,8,5]))
pari:[g,chi] = znchar(Mod(961,7800))
χ7800(961,⋅)
χ7800(2521,⋅)
χ7800(4081,⋅)
χ7800(5641,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1951,3901,5201,7177,4201) → (1,1,1,e(54),−1)
a |
−1 | 1 | 7 | 11 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 |
χ7800(961,a) |
1 | 1 | −1 | e(103) | e(52) | e(109) | e(54) | e(53) | e(109) | e(107) | e(107) | 1 |
sage:chi.jacobi_sum(n)