sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(431, base_ring=CyclotomicField(86))
M = H._module
chi = DirichletCharacter(H, M([77]))
pari:[g,chi] = znchar(Mod(282,431))
Modulus: | 431 | |
Conductor: | 431 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 86 |
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)
|
χ431(47,⋅)
χ431(94,⋅)
χ431(101,⋅)
χ431(107,⋅)
χ431(133,⋅)
χ431(141,⋅)
χ431(143,⋅)
χ431(175,⋅)
χ431(188,⋅)
χ431(202,⋅)
χ431(211,⋅)
χ431(214,⋅)
χ431(215,⋅)
χ431(239,⋅)
χ431(266,⋅)
χ431(269,⋅)
χ431(282,⋅)
χ431(286,⋅)
χ431(287,⋅)
χ431(303,⋅)
χ431(321,⋅)
χ431(323,⋅)
χ431(335,⋅)
χ431(350,⋅)
χ431(359,⋅)
χ431(367,⋅)
χ431(376,⋅)
χ431(377,⋅)
χ431(383,⋅)
χ431(395,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
7 → e(8677)
a |
−1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
χ431(282,a) |
−1 | 1 | e(4342) | e(4330) | e(4341) | e(439) | e(4329) | e(8677) | e(4340) | e(4317) | e(438) | e(4311) |
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)