sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
M = H._module
chi = DirichletCharacter(H, M([0,0,1,0]))
pari:[g,chi] = znchar(Mod(369,1840))
\(\chi_{1840}(369,\cdot)\)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\((1151,1381,737,1201)\) → \((1,1,-1,1)\)
\(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(27\) | \(29\) |
\( \chi_{ 1840 }(369, a) \) |
\(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
sage:chi.jacobi_sum(n)