sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([0,22,51]))
pari:[g,chi] = znchar(Mod(751,966))
χ966(37,⋅)
χ966(67,⋅)
χ966(79,⋅)
χ966(109,⋅)
χ966(205,⋅)
χ966(235,⋅)
χ966(247,⋅)
χ966(319,⋅)
χ966(373,⋅)
χ966(457,⋅)
χ966(571,⋅)
χ966(613,⋅)
χ966(655,⋅)
χ966(697,⋅)
χ966(709,⋅)
χ966(751,⋅)
χ966(793,⋅)
χ966(835,⋅)
χ966(865,⋅)
χ966(907,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(323,829,925) → (1,e(31),e(2217))
a |
−1 | 1 | 5 | 11 | 13 | 17 | 19 | 25 | 29 | 31 | 37 | 41 |
χ966(751,a) |
−1 | 1 | e(6629) | e(6619) | e(119) | e(6649) | e(6617) | e(3329) | e(1110) | e(3332) | e(6659) | e(113) |
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)