sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4729, base_ring=CyclotomicField(394))
M = H._module
chi = DirichletCharacter(H, M([387]))
pari:[g,chi] = znchar(Mod(1079,4729))
Modulus: | 4729 | |
Conductor: | 4729 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 394 |
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)
|
χ4729(4,⋅)
χ4729(6,⋅)
χ4729(9,⋅)
χ4729(64,⋅)
χ4729(96,⋅)
χ4729(144,⋅)
χ4729(197,⋅)
χ4729(216,⋅)
χ4729(242,⋅)
χ4729(254,⋅)
χ4729(324,⋅)
χ4729(350,⋅)
χ4729(355,⋅)
χ4729(363,⋅)
χ4729(381,⋅)
χ4729(413,⋅)
χ4729(422,⋅)
χ4729(451,⋅)
χ4729(454,⋅)
χ4729(455,⋅)
χ4729(458,⋅)
χ4729(475,⋅)
χ4729(486,⋅)
χ4729(525,⋅)
χ4729(607,⋅)
χ4729(613,⋅)
χ4729(633,⋅)
χ4729(634,⋅)
χ4729(643,⋅)
χ4729(670,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
17 → e(394387)
a |
−1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
χ4729(1079,a) |
1 | 1 | e(19769) | e(197193) | e(197138) | e(19774) | e(19765) | e(1972) | e(19710) | e(197189) | e(197143) | e(394219) |
sage:chi.jacobi_sum(n)