sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(832, base_ring=CyclotomicField(12))
M = H._module
chi = DirichletCharacter(H, M([6,0,11]))
pari:[g,chi] = znchar(Mod(319,832))
χ832(63,⋅)
χ832(319,⋅)
χ832(383,⋅)
χ832(639,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(703,261,769) → (−1,1,e(1211))
a |
−1 | 1 | 3 | 5 | 7 | 9 | 11 | 15 | 17 | 19 | 21 | 23 |
χ832(319,a) |
1 | 1 | e(61) | i | e(127) | e(31) | e(1211) | e(125) | e(65) | e(121) | −i | e(32) |
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)