sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6384, base_ring=CyclotomicField(12))
M = H._module
chi = DirichletCharacter(H, M([0,9,6,4,6]))
pari:[g,chi] = znchar(Mod(5357,6384))
Modulus: | 6384 | |
Conductor: | 6384 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 12 |
sage:chi.multiplicative_order()
pari:charorder(g,chi)
|
Real: | no |
Primitive: | yes |
sage:chi.is_primitive()
pari:#znconreyconductor(g,chi)==1
|
Minimal: | yes |
Parity: | even |
sage:chi.is_odd()
pari:zncharisodd(g,chi)
|
χ6384(2165,⋅)
χ6384(3077,⋅)
χ6384(5357,⋅)
χ6384(6269,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(799,4789,2129,913,1009) → (1,−i,−1,e(31),−1)
a |
−1 | 1 | 5 | 11 | 13 | 17 | 23 | 25 | 29 | 31 | 37 | 41 |
χ6384(5357,a) |
1 | 1 | e(1211) | e(127) | −i | e(65) | e(32) | e(65) | i | e(65) | e(1211) | −1 |
sage:chi.jacobi_sum(n)