![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3391, base_ring=CyclotomicField(2))
M = H._module
chi = DirichletCharacter(H, M([1]))
![Copy content]()
pari:[g,chi] = znchar(Mod(3390,3391))
![Copy content]()
sage:kronecker_character(-3391)
![Copy content]()
pari:znchartokronecker(g,chi)
\(\displaystyle\left(\frac{-3391}{\bullet}\right)\)
| Modulus: | \(3391\) | |
| Conductor: | \(3391\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(2\) |
![Copy content]()
sage:chi.multiplicative_order()
![Copy content]()
pari:charorder(g,chi)
|
| Real: | yes |
| Primitive: | yes |
![Copy content]()
sage:chi.is_primitive()
![Copy content]()
pari:#znconreyconductor(g,chi)==1
|
| Minimal: | yes |
| Parity: | odd |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
pari:zncharisodd(g,chi)
|
\(\chi_{3391}(3390,\cdot)\)
![Copy content]()
sage:chi.galois_orbit()
![Copy content]()
pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\(3\) → \(-1\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 3391 }(3390, a) \) |
\(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
![Copy content]()
sage:chi.jacobi_sum(n)
