sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4284, base_ring=CyclotomicField(48))
M = H._module
chi = DirichletCharacter(H, M([24,40,32,9]))
pari:[g,chi] = znchar(Mod(95,4284))
Modulus: | 4284 | |
Conductor: | 4284 |
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)
|
χ4284(95,⋅)
χ4284(347,⋅)
χ4284(947,⋅)
χ4284(1355,⋅)
χ4284(1451,⋅)
χ4284(1703,⋅)
χ4284(1859,⋅)
χ4284(2111,⋅)
χ4284(2207,⋅)
χ4284(2459,⋅)
χ4284(2615,⋅)
χ4284(2867,⋅)
χ4284(2963,⋅)
χ4284(3371,⋅)
χ4284(3971,⋅)
χ4284(4223,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(2143,3809,1837,1261) → (−1,e(65),e(32),e(163))
a |
−1 | 1 | 5 | 11 | 13 | 19 | 23 | 25 | 29 | 31 | 37 | 41 |
χ4284(95,a) |
−1 | 1 | e(167) | e(165) | e(125) | e(2411) | e(1613) | e(87) | e(4813) | e(4825) | e(4825) | e(4811) |
sage:chi.jacobi_sum(n)