sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1013, base_ring=CyclotomicField(506))
M = H._module
chi = DirichletCharacter(H, M([113]))
pari:[g,chi] = znchar(Mod(123,1013))
Modulus: | 1013 | |
Conductor: | 1013 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 506 |
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)
|
χ1013(9,⋅)
χ1013(13,⋅)
χ1013(15,⋅)
χ1013(21,⋅)
χ1013(24,⋅)
χ1013(25,⋅)
χ1013(35,⋅)
χ1013(40,⋅)
χ1013(43,⋅)
χ1013(49,⋅)
χ1013(51,⋅)
χ1013(53,⋅)
χ1013(54,⋅)
χ1013(56,⋅)
χ1013(66,⋅)
χ1013(71,⋅)
χ1013(73,⋅)
χ1013(74,⋅)
χ1013(76,⋅)
χ1013(78,⋅)
χ1013(79,⋅)
χ1013(85,⋅)
χ1013(87,⋅)
χ1013(93,⋅)
χ1013(110,⋅)
χ1013(119,⋅)
χ1013(123,⋅)
χ1013(126,⋅)
χ1013(130,⋅)
χ1013(136,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
3 → e(506113)
a |
−1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
χ1013(123,a) |
1 | 1 | e(463) | e(506113) | e(233) | e(50627) | e(25373) | e(506175) | e(469) | e(253113) | e(25330) | e(2315) |
sage:chi.jacobi_sum(n)