sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2156, base_ring=CyclotomicField(70))
M = H._module
chi = DirichletCharacter(H, M([35,5,21]))
pari:[g,chi] = znchar(Mod(811,2156))
Modulus: | 2156 | |
Conductor: | 2156 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 70 |
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)
|
χ2156(83,⋅)
χ2156(139,⋅)
χ2156(167,⋅)
χ2156(447,⋅)
χ2156(475,⋅)
χ2156(503,⋅)
χ2156(699,⋅)
χ2156(755,⋅)
χ2156(811,⋅)
χ2156(1007,⋅)
χ2156(1063,⋅)
χ2156(1091,⋅)
χ2156(1119,⋅)
χ2156(1315,⋅)
χ2156(1399,⋅)
χ2156(1427,⋅)
χ2156(1623,⋅)
χ2156(1679,⋅)
χ2156(1707,⋅)
χ2156(1735,⋅)
χ2156(1931,⋅)
χ2156(1987,⋅)
χ2156(2015,⋅)
χ2156(2043,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1079,1277,981) → (−1,e(141),e(103))
a |
−1 | 1 | 3 | 5 | 9 | 13 | 15 | 17 | 19 | 23 | 25 | 27 |
χ2156(811,a) |
−1 | 1 | e(3534) | e(7019) | e(3533) | e(3523) | e(7017) | e(3517) | e(109) | e(143) | e(3519) | e(3532) |
sage:chi.jacobi_sum(n)