sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2299, base_ring=CyclotomicField(330))
M = H._module
chi = DirichletCharacter(H, M([36,55]))
pari:[g,chi] = znchar(Mod(103,2299))
Modulus: | 2299 | |
Conductor: | 2299 |
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)
|
χ2299(31,⋅)
χ2299(69,⋅)
χ2299(103,⋅)
χ2299(126,⋅)
χ2299(141,⋅)
χ2299(179,⋅)
χ2299(236,⋅)
χ2299(240,⋅)
χ2299(278,⋅)
χ2299(312,⋅)
χ2299(335,⋅)
χ2299(350,⋅)
χ2299(388,⋅)
χ2299(411,⋅)
χ2299(445,⋅)
χ2299(449,⋅)
χ2299(521,⋅)
χ2299(544,⋅)
χ2299(559,⋅)
χ2299(597,⋅)
χ2299(620,⋅)
χ2299(654,⋅)
χ2299(658,⋅)
χ2299(696,⋅)
χ2299(730,⋅)
χ2299(768,⋅)
χ2299(806,⋅)
χ2299(829,⋅)
χ2299(863,⋅)
χ2299(867,⋅)
...
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(970,1332) → (e(556),e(61))
a |
−1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 |
χ2299(103,a) |
−1 | 1 | e(33091) | e(3023) | e(16591) | e(165122) | e(1657) | e(5542) | e(11091) | e(158) | e(661) | e(227) |
sage:chi.jacobi_sum(n)