sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([30,30,30,51,25]))
pari:[g,chi] = znchar(Mod(3347,7800))
Modulus: | 7800 | |
Conductor: | 7800 |
sage:chi.conductor()
pari:znconreyconductor(g,chi)
|
Order: | 60 |
sage:chi.multiplicative_order()
pari:charorder(g,chi)
|
Real: | no |
Primitive: | yes |
sage:chi.is_primitive()
pari:#znconreyconductor(g,chi)==1
|
Minimal: | yes |
Parity: | even |
sage:chi.is_odd()
pari:zncharisodd(g,chi)
|
χ7800(227,⋅)
χ7800(323,⋅)
χ7800(587,⋅)
χ7800(683,⋅)
χ7800(1787,⋅)
χ7800(1883,⋅)
χ7800(2147,⋅)
χ7800(3347,⋅)
χ7800(3803,⋅)
χ7800(5003,⋅)
χ7800(5267,⋅)
χ7800(5363,⋅)
χ7800(6467,⋅)
χ7800(6563,⋅)
χ7800(6827,⋅)
χ7800(6923,⋅)
sage:chi.galois_orbit()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
(1951,3901,5201,7177,4201) → (−1,−1,−1,e(2017),e(125))
a |
−1 | 1 | 7 | 11 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 |
χ7800(3347,a) |
1 | 1 | e(31) | e(601) | e(6023) | e(6023) | e(6031) | e(3011) | e(201) | e(151) | e(6019) | e(127) |
sage:chi.jacobi_sum(n)