sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7488, base_ring=CyclotomicField(16))
M = H._module
chi = DirichletCharacter(H, M([8,9,8,8]))
pari:[g,chi] = znchar(Mod(5147,7488))
χ7488(467,⋅)
χ7488(1403,⋅)
χ7488(2339,⋅)
χ7488(3275,⋅)
χ7488(4211,⋅)
χ7488(5147,⋅)
χ7488(6083,⋅)
χ7488(7019,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(703,6085,5825,5761) → (−1,e(169),−1,−1)
a |
−1 | 1 | 5 | 7 | 11 | 17 | 19 | 23 | 25 | 29 | 31 | 35 |
χ7488(5147,a) |
1 | 1 | e(169) | e(85) | e(165) | i | e(1615) | e(87) | e(81) | e(1611) | −1 | e(163) |
sage:chi.jacobi_sum(n)