![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
M = H._module
chi = DirichletCharacter(H, M([1]))
chi.galois_orbit()
![Copy content]()
gp:[g,chi] = znchar(Mod(196, 197))
order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.196");
order := Order(chi);
{ chi^k : k in [1..order-1] | GCD(k,order) eq 1 };
![Copy content]()
sage:kronecker_character(197)
![Copy content]()
gp:znchartokronecker(g,chi)
![Copy content]()
magma:KroneckerCharacter(197);
\(\displaystyle\left(\frac{197}{\bullet}\right)\)
| Modulus: | \(197\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(197\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(2\) |
![Copy content]()
sage:chi.multiplicative_order()
![Copy content]()
gp:charorder(g,chi)
![Copy content]()
magma:Order(chi);
|
| Real: | yes |
![Copy content]()
sage:chi.multiplicative_order() <= 2
![Copy content]()
gp:charorder(g,chi) <= 2
![Copy content]()
magma:Order(chi) le 2;
|
| Primitive: | yes |
![Copy content]()
sage:chi.is_primitive()
![Copy content]()
gp:#znconreyconductor(g,chi)==1
![Copy content]()
magma:IsPrimitive(chi);
|
| Minimal: | yes |
| Parity: | even |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
gp:zncharisodd(g,chi)
![Copy content]()
magma:IsOdd(chi);
|
| Character | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
|
\(\chi_{197}(196,\cdot)\)
|
\(1\) | \(1\) | \(-1\) | \(-1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
