sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(518400, base_ring=CyclotomicField(2))
M = H._module
chi = DirichletCharacter(H, M([0,0,0,0]))
pari:[g,chi] = znchar(Mod(1,518400))
\(\chi_{518400}(1,\cdot)\)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\((157951,202501,6401,331777)\) → \((1,1,1,1)\)
\(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 518400 }(1, a) \) |
\(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(1\) |
sage:chi.jacobi_sum(n)