sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(93, base_ring=CyclotomicField(30))
M = H._module
chi = DirichletCharacter(H, M([15,4]))
pari:[g,chi] = znchar(Mod(50,93))
Modulus: | 93 | |
Conductor: | 93 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 30 |
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)
|
χ93(14,⋅)
χ93(20,⋅)
χ93(38,⋅)
χ93(41,⋅)
χ93(50,⋅)
χ93(59,⋅)
χ93(71,⋅)
χ93(80,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(32,34) → (−1,e(152))
a |
−1 | 1 | 2 | 4 | 5 | 7 | 8 | 10 | 11 | 13 | 14 | 16 |
χ93(50,a) |
−1 | 1 | e(107) | e(52) | e(61) | e(1511) | e(101) | e(1513) | e(3017) | e(157) | e(3013) | e(54) |
sage:chi.jacobi_sum(n)
sage:chi.gauss_sum(a)
pari:znchargauss(g,chi,a)
sage:chi.jacobi_sum(n)
sage:chi.kloosterman_sum(a,b)