sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3520, base_ring=CyclotomicField(40))
M = H._module
chi = DirichletCharacter(H, M([0,15,30,28]))
pari:[g,chi] = znchar(Mod(73,3520))
χ3520(57,⋅)
χ3520(73,⋅)
χ3520(217,⋅)
χ3520(233,⋅)
χ3520(393,⋅)
χ3520(1337,⋅)
χ3520(1513,⋅)
χ3520(1657,⋅)
χ3520(1817,⋅)
χ3520(1833,⋅)
χ3520(1977,⋅)
χ3520(1993,⋅)
χ3520(2153,⋅)
χ3520(3097,⋅)
χ3520(3273,⋅)
χ3520(3417,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(2751,1541,2817,321) → (1,e(83),−i,e(107))
a |
−1 | 1 | 3 | 7 | 9 | 13 | 17 | 19 | 21 | 23 | 27 | 29 |
χ3520(73,a) |
1 | 1 | e(4039) | e(52) | e(2019) | e(4023) | e(2011) | e(409) | e(83) | −1 | e(4037) | e(4021) |
sage:chi.jacobi_sum(n)