sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(485, base_ring=CyclotomicField(96))
M = H._module
chi = DirichletCharacter(H, M([72,77]))
pari:[g,chi] = znchar(Mod(23,485))
Modulus: | 485 | |
Conductor: | 485 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 96 |
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)
|
χ485(7,⋅)
χ485(13,⋅)
χ485(23,⋅)
χ485(37,⋅)
χ485(57,⋅)
χ485(68,⋅)
χ485(82,⋅)
χ485(83,⋅)
χ485(87,⋅)
χ485(107,⋅)
χ485(112,⋅)
χ485(118,⋅)
χ485(137,⋅)
χ485(138,⋅)
χ485(153,⋅)
χ485(157,⋅)
χ485(173,⋅)
χ485(187,⋅)
χ485(208,⋅)
χ485(223,⋅)
χ485(232,⋅)
χ485(252,⋅)
χ485(268,⋅)
χ485(278,⋅)
χ485(308,⋅)
χ485(317,⋅)
χ485(362,⋅)
χ485(383,⋅)
χ485(393,⋅)
χ485(427,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(292,296) → (−i,e(9677))
a |
−1 | 1 | 2 | 3 | 4 | 6 | 7 | 8 | 9 | 11 | 12 | 13 |
χ485(23,a) |
1 | 1 | e(481) | e(4819) | e(241) | e(125) | e(9659) | e(161) | e(2419) | e(4847) | e(167) | e(9629) |
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)