sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8512, base_ring=CyclotomicField(48))
M = H._module
chi = DirichletCharacter(H, M([24,15,40,24]))
pari:[g,chi] = znchar(Mod(75,8512))
Modulus: | 8512 | |
Conductor: | 8512 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 48 |
sage:chi.multiplicative_order()
pari:charorder(g,chi)
|
Real: | no |
Primitive: | yes |
sage:chi.is_primitive()
pari:#znconreyconductor(g,chi)==1
|
Minimal: | yes |
Parity: | odd |
sage:chi.is_odd()
pari:zncharisodd(g,chi)
|
χ8512(75,⋅)
χ8512(227,⋅)
χ8512(1139,⋅)
χ8512(1291,⋅)
χ8512(2203,⋅)
χ8512(2355,⋅)
χ8512(3267,⋅)
χ8512(3419,⋅)
χ8512(4331,⋅)
χ8512(4483,⋅)
χ8512(5395,⋅)
χ8512(5547,⋅)
χ8512(6459,⋅)
χ8512(6611,⋅)
χ8512(7523,⋅)
χ8512(7675,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(5055,6917,7297,3137) → (−1,e(165),e(65),−1)
a |
−1 | 1 | 3 | 5 | 9 | 11 | 13 | 15 | 17 | 23 | 25 | 27 |
χ8512(75,a) |
−1 | 1 | e(4837) | e(4823) | e(2413) | e(4819) | e(1611) | i | e(127) | e(2413) | e(2423) | e(165) |
sage:chi.jacobi_sum(n)