sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2835, base_ring=CyclotomicField(54))
M = H._module
chi = DirichletCharacter(H, M([25,27,18]))
pari:[g,chi] = znchar(Mod(2774,2835))
Modulus: | 2835 | |
Conductor: | 2835 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 54 |
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)
|
χ2835(254,⋅)
χ2835(284,⋅)
χ2835(569,⋅)
χ2835(599,⋅)
χ2835(884,⋅)
χ2835(914,⋅)
χ2835(1199,⋅)
χ2835(1229,⋅)
χ2835(1514,⋅)
χ2835(1544,⋅)
χ2835(1829,⋅)
χ2835(1859,⋅)
χ2835(2144,⋅)
χ2835(2174,⋅)
χ2835(2459,⋅)
χ2835(2489,⋅)
χ2835(2774,⋅)
χ2835(2804,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1541,1702,2026) → (e(5425),−1,e(31))
a |
−1 | 1 | 2 | 4 | 8 | 11 | 13 | 16 | 17 | 19 | 22 | 23 |
χ2835(2774,a) |
−1 | 1 | e(2717) | e(277) | e(98) | e(5419) | e(5411) | e(2714) | e(91) | e(98) | e(5453) | e(277) |
sage:chi.jacobi_sum(n)