sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(696, base_ring=CyclotomicField(4))
M = H._module
chi = DirichletCharacter(H, M([2,2,0,1]))
pari:[g,chi] = znchar(Mod(331,696))
χ696(307,⋅)
χ696(331,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(175,349,233,553) → (−1,−1,1,i)
a |
−1 | 1 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 25 | 31 | 35 |
χ696(331,a) |
1 | 1 | 1 | −1 | i | 1 | i | i | −1 | 1 | −i | −1 |
sage:chi.jacobi_sum(n)
sage:chi.gauss_sum(a)
pari:znchargauss(g,chi,a)
sage:chi.jacobi_sum(n)
sage:chi.kloosterman_sum(a,b)