![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(24648, base_ring=CyclotomicField(2))
M = H._module
chi = DirichletCharacter(H, M([0,1,1,1,1]))
![Copy content]()
pari:[g,chi] = znchar(Mod(18485,24648))
![Copy content]()
sage:kronecker_character(24648)
![Copy content]()
pari:znchartokronecker(g,chi)
\(\displaystyle\left(\frac{24648}{\bullet}\right)\)
| Modulus: | \(24648\) | |
| Conductor: | \(24648\) |
![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: | even |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
pari:zncharisodd(g,chi)
|
\(\chi_{24648}(18485,\cdot)\)
![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 ]
\((18487,12325,16433,11377,12169)\) → \((1,-1,-1,-1,-1)\)
| \(a\) |
\(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 24648 }(18485, a) \) |
\(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
![Copy content]()
sage:chi.jacobi_sum(n)
