sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4050, base_ring=CyclotomicField(540))
M = H._module
chi = DirichletCharacter(H, M([530,189]))
pari:[g,chi] = znchar(Mod(203,4050))
χ4050(23,⋅)
χ4050(47,⋅)
χ4050(77,⋅)
χ4050(83,⋅)
χ4050(113,⋅)
χ4050(137,⋅)
χ4050(167,⋅)
χ4050(173,⋅)
χ4050(203,⋅)
χ4050(227,⋅)
χ4050(263,⋅)
χ4050(317,⋅)
χ4050(347,⋅)
χ4050(353,⋅)
χ4050(383,⋅)
χ4050(437,⋅)
χ4050(473,⋅)
χ4050(497,⋅)
χ4050(527,⋅)
χ4050(533,⋅)
χ4050(563,⋅)
χ4050(587,⋅)
χ4050(617,⋅)
χ4050(623,⋅)
χ4050(653,⋅)
χ4050(677,⋅)
χ4050(713,⋅)
χ4050(767,⋅)
χ4050(797,⋅)
χ4050(803,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(2351,3727) → (e(5453),e(207))
a |
−1 | 1 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 |
χ4050(203,a) |
1 | 1 | e(10849) | e(27097) | e(540271) | e(180169) | e(9037) | e(540349) | e(1352) | e(13558) | e(18067) | e(270113) |
sage:chi.jacobi_sum(n)