sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(644, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([0,55,3]))
pari:[g,chi] = znchar(Mod(5,644))
χ644(5,⋅)
χ644(17,⋅)
χ644(33,⋅)
χ644(61,⋅)
χ644(89,⋅)
χ644(129,⋅)
χ644(145,⋅)
χ644(157,⋅)
χ644(201,⋅)
χ644(241,⋅)
χ644(297,⋅)
χ644(313,⋅)
χ644(341,⋅)
χ644(425,⋅)
χ644(465,⋅)
χ644(481,⋅)
χ644(493,⋅)
χ644(521,⋅)
χ644(549,⋅)
χ644(605,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(323,185,281) → (1,e(65),e(221))
a |
−1 | 1 | 3 | 5 | 9 | 11 | 13 | 15 | 17 | 19 | 25 | 27 |
χ644(5,a) |
1 | 1 | e(6637) | e(337) | e(334) | e(6649) | e(223) | e(2217) | e(335) | e(3328) | e(3314) | e(2215) |
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)