sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2156, base_ring=CyclotomicField(42))
M = H._module
chi = DirichletCharacter(H, M([21,25,0]))
pari:[g,chi] = znchar(Mod(507,2156))
χ2156(199,⋅)
χ2156(243,⋅)
χ2156(507,⋅)
χ2156(551,⋅)
χ2156(859,⋅)
χ2156(1123,⋅)
χ2156(1167,⋅)
χ2156(1431,⋅)
χ2156(1475,⋅)
χ2156(1739,⋅)
χ2156(2047,⋅)
χ2156(2091,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1079,1277,981) → (−1,e(4225),1)
a |
−1 | 1 | 3 | 5 | 9 | 13 | 15 | 17 | 19 | 23 | 25 | 27 |
χ2156(507,a) |
1 | 1 | e(212) | e(4211) | e(214) | e(149) | e(145) | e(4237) | e(31) | e(425) | e(2111) | e(72) |
sage:chi.jacobi_sum(n)