sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(90))
M = H._module
chi = DirichletCharacter(H, M([72,10]))
pari:[g,chi] = znchar(Mod(61,950))
χ950(61,⋅)
χ950(81,⋅)
χ950(111,⋅)
χ950(131,⋅)
χ950(161,⋅)
χ950(271,⋅)
χ950(291,⋅)
χ950(321,⋅)
χ950(441,⋅)
χ950(461,⋅)
χ950(481,⋅)
χ950(491,⋅)
χ950(511,⋅)
χ950(541,⋅)
χ950(631,⋅)
χ950(671,⋅)
χ950(681,⋅)
χ950(731,⋅)
χ950(821,⋅)
χ950(841,⋅)
χ950(861,⋅)
χ950(871,⋅)
χ950(891,⋅)
χ950(921,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(77,401) → (e(54),e(91))
a |
−1 | 1 | 3 | 7 | 9 | 11 | 13 | 17 | 21 | 23 | 27 | 29 |
χ950(61,a) |
1 | 1 | e(452) | e(32) | e(454) | e(152) | e(4534) | e(4523) | e(4532) | e(451) | e(152) | e(4522) |
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)