![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2652, base_ring=CyclotomicField(4))
M = H._module
chi = DirichletCharacter(H, M([2,2,2,3]))
![Copy content]()
pari:[g,chi] = znchar(Mod(2027,2652))
| Modulus: | \(2652\) | |
| Conductor: | \(2652\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
pari:znconreyconductor(g,chi)
|
| Order: | \(4\) |
![Copy content]()
sage:chi.multiplicative_order()
![Copy content]()
pari:charorder(g,chi)
|
| Real: | no |
| Primitive: | yes |
![Copy content]()
sage:chi.is_primitive()
![Copy content]()
pari:#znconreyconductor(g,chi)==1
|
| Minimal: | yes |
| Parity: | even |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
pari:zncharisodd(g,chi)
|
\(\chi_{2652}(2027,\cdot)\)
\(\chi_{2652}(2495,\cdot)\)
![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 ]
\((1327,1769,613,1873)\) → \((-1,-1,-1,-i)\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) | \(37\) |
| \( \chi_{ 2652 }(2027, a) \) |
\(1\) | \(1\) | \(-i\) | \(i\) | \(-i\) | \(-1\) | \(i\) | \(-1\) | \(i\) | \(-i\) | \(1\) | \(i\) |
![Copy content]()
sage:chi.jacobi_sum(n)
