sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(90))
M = H._module
chi = DirichletCharacter(H, M([20,18]))
pari:[g,chi] = znchar(Mod(16,675))
Modulus: | 675 | |
Conductor: | 675 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 45 |
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)
|
χ675(16,⋅)
χ675(31,⋅)
χ675(61,⋅)
χ675(106,⋅)
χ675(121,⋅)
χ675(166,⋅)
χ675(196,⋅)
χ675(211,⋅)
χ675(241,⋅)
χ675(256,⋅)
χ675(286,⋅)
χ675(331,⋅)
χ675(346,⋅)
χ675(391,⋅)
χ675(421,⋅)
χ675(436,⋅)
χ675(466,⋅)
χ675(481,⋅)
χ675(511,⋅)
χ675(556,⋅)
χ675(571,⋅)
χ675(616,⋅)
χ675(646,⋅)
χ675(661,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(326,352) → (e(92),e(51))
a |
−1 | 1 | 2 | 4 | 7 | 8 | 11 | 13 | 14 | 16 | 17 | 19 |
χ675(16,a) |
1 | 1 | e(4519) | e(4538) | e(95) | e(154) | e(454) | e(4526) | e(4544) | e(4531) | e(1514) | e(154) |
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)