sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1254, base_ring=CyclotomicField(90))
M = H._module
chi = DirichletCharacter(H, M([45,81,80]))
pari:[g,chi] = znchar(Mod(347,1254))
χ1254(17,⋅)
χ1254(35,⋅)
χ1254(101,⋅)
χ1254(149,⋅)
χ1254(161,⋅)
χ1254(215,⋅)
χ1254(233,⋅)
χ1254(347,⋅)
χ1254(359,⋅)
χ1254(365,⋅)
χ1254(479,⋅)
χ1254(491,⋅)
χ1254(503,⋅)
χ1254(557,⋅)
χ1254(689,⋅)
χ1254(701,⋅)
χ1254(821,⋅)
χ1254(833,⋅)
χ1254(899,⋅)
χ1254(959,⋅)
χ1254(1031,⋅)
χ1254(1073,⋅)
χ1254(1157,⋅)
χ1254(1163,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(419,343,1123) → (−1,e(109),e(98))
a |
−1 | 1 | 5 | 7 | 13 | 17 | 23 | 25 | 29 | 31 | 35 | 37 |
χ1254(347,a) |
1 | 1 | e(9029) | e(3019) | e(9031) | e(4522) | e(185) | e(4529) | e(4541) | e(1511) | e(4543) | e(54) |
sage:chi.jacobi_sum(n)