sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4400, base_ring=CyclotomicField(20))
M = H._module
chi = DirichletCharacter(H, M([10,15,8,10]))
pari:[g,chi] = znchar(Mod(131,4400))
Modulus: | 4400 | |
Conductor: | 4400 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 20 |
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)
|
χ4400(131,⋅)
χ4400(571,⋅)
χ4400(1011,⋅)
χ4400(1891,⋅)
χ4400(2331,⋅)
χ4400(2771,⋅)
χ4400(3211,⋅)
χ4400(4091,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(2751,3301,177,1201) → (−1,−i,e(52),−1)
a |
−1 | 1 | 3 | 7 | 9 | 13 | 17 | 19 | 21 | 23 | 27 | 29 |
χ4400(131,a) |
1 | 1 | e(2011) | −1 | e(101) | e(207) | e(107) | e(209) | e(201) | e(52) | e(2013) | e(2011) |
sage:chi.jacobi_sum(n)