sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4140, base_ring=CyclotomicField(66))
M = H._module
chi = DirichletCharacter(H, M([33,11,0,51]))
pari:[g,chi] = znchar(Mod(3971,4140))
χ4140(11,⋅)
χ4140(191,⋅)
χ4140(911,⋅)
χ4140(1031,⋅)
χ4140(1091,⋅)
χ4140(1211,⋅)
χ4140(1391,⋅)
χ4140(1571,⋅)
χ4140(1631,⋅)
χ4140(1811,⋅)
χ4140(2291,⋅)
χ4140(2351,⋅)
χ4140(2471,⋅)
χ4140(2711,⋅)
χ4140(3011,⋅)
χ4140(3191,⋅)
χ4140(3731,⋅)
χ4140(3791,⋅)
χ4140(3971,⋅)
χ4140(4091,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(2071,461,1657,3961) → (−1,e(61),1,e(2217))
a |
−1 | 1 | 7 | 11 | 13 | 17 | 19 | 29 | 31 | 37 | 41 | 43 |
χ4140(3971,a) |
−1 | 1 | e(3328) | e(6641) | e(335) | e(1110) | e(111) | e(665) | e(6631) | e(225) | e(667) | e(331) |
sage:chi.jacobi_sum(n)