sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2898, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([11,33,3]))
pari:[g,chi] = znchar(Mod(2351,2898))
χ2898(83,⋅)
χ2898(293,⋅)
χ2898(419,⋅)
χ2898(797,⋅)
χ2898(839,⋅)
χ2898(1049,⋅)
χ2898(1091,⋅)
χ2898(1217,⋅)
χ2898(1469,⋅)
χ2898(1721,⋅)
χ2898(1805,⋅)
χ2898(1847,⋅)
χ2898(2057,⋅)
χ2898(2183,⋅)
χ2898(2225,⋅)
χ2898(2351,⋅)
χ2898(2435,⋅)
χ2898(2687,⋅)
χ2898(2729,⋅)
χ2898(2813,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1289,829,1891) → (e(61),−1,e(221))
a |
−1 | 1 | 5 | 11 | 13 | 17 | 19 | 25 | 29 | 31 | 37 | 41 |
χ2898(2351,a) |
−1 | 1 | e(6625) | e(3319) | e(6631) | e(227) | e(112) | e(3325) | e(6665) | e(667) | e(2221) | e(3329) |
sage:chi.jacobi_sum(n)