sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(330))
M = H._module
chi = DirichletCharacter(H, M([220,237]))
pari:[g,chi] = znchar(Mod(39,847))
Modulus: | 847 | |
Conductor: | 847 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 330 |
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)
|
χ847(2,⋅)
χ847(18,⋅)
χ847(30,⋅)
χ847(39,⋅)
χ847(46,⋅)
χ847(51,⋅)
χ847(72,⋅)
χ847(74,⋅)
χ847(79,⋅)
χ847(95,⋅)
χ847(107,⋅)
χ847(116,⋅)
χ847(123,⋅)
χ847(128,⋅)
χ847(149,⋅)
χ847(151,⋅)
χ847(156,⋅)
χ847(172,⋅)
χ847(184,⋅)
χ847(193,⋅)
χ847(200,⋅)
χ847(205,⋅)
χ847(226,⋅)
χ847(228,⋅)
χ847(249,⋅)
χ847(261,⋅)
χ847(270,⋅)
χ847(277,⋅)
χ847(303,⋅)
χ847(305,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(122,365) → (e(32),e(11079))
a |
−1 | 1 | 2 | 3 | 4 | 5 | 6 | 8 | 9 | 10 | 12 | 13 |
χ847(39,a) |
−1 | 1 | e(33017) | e(1513) | e(16517) | e(16579) | e(110101) | e(11017) | e(1511) | e(6635) | e(3332) | e(11059) |
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)