sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4050, base_ring=CyclotomicField(108))
M = H._module
chi = DirichletCharacter(H, M([22,27]))
pari:[g,chi] = znchar(Mod(1157,4050))
χ4050(257,⋅)
χ4050(293,⋅)
χ4050(407,⋅)
χ4050(443,⋅)
χ4050(707,⋅)
χ4050(743,⋅)
χ4050(857,⋅)
χ4050(893,⋅)
χ4050(1157,⋅)
χ4050(1193,⋅)
χ4050(1307,⋅)
χ4050(1343,⋅)
χ4050(1607,⋅)
χ4050(1643,⋅)
χ4050(1757,⋅)
χ4050(1793,⋅)
χ4050(2057,⋅)
χ4050(2093,⋅)
χ4050(2207,⋅)
χ4050(2243,⋅)
χ4050(2507,⋅)
χ4050(2543,⋅)
χ4050(2657,⋅)
χ4050(2693,⋅)
χ4050(2957,⋅)
χ4050(2993,⋅)
χ4050(3107,⋅)
χ4050(3143,⋅)
χ4050(3407,⋅)
χ4050(3443,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(2351,3727) → (e(5411),i)
a |
−1 | 1 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 |
χ4050(1157,a) |
1 | 1 | e(10855) | e(5435) | e(10841) | e(3635) | e(185) | e(108107) | e(271) | e(272) | e(3629) | e(5443) |
sage:chi.jacobi_sum(n)