sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3528, base_ring=CyclotomicField(42))
M = H._module
chi = DirichletCharacter(H, M([0,21,7,39]))
pari:[g,chi] = znchar(Mod(461,3528))
Modulus: | 3528 | |
Conductor: | 3528 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 42 |
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)
|
χ3528(461,⋅)
χ3528(797,⋅)
χ3528(965,⋅)
χ3528(1301,⋅)
χ3528(1805,⋅)
χ3528(1973,⋅)
χ3528(2309,⋅)
χ3528(2477,⋅)
χ3528(2813,⋅)
χ3528(2981,⋅)
χ3528(3317,⋅)
χ3528(3485,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(2647,1765,785,1081) → (1,−1,e(61),e(1413))
a |
−1 | 1 | 5 | 11 | 13 | 17 | 19 | 23 | 25 | 29 | 31 | 37 |
χ3528(461,a) |
1 | 1 | e(4211) | e(2117) | e(2110) | e(75) | 1 | e(425) | e(2111) | e(218) | e(65) | e(143) |
sage:chi.jacobi_sum(n)