![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6169, base_ring=CyclotomicField(198))
M = H._module
chi = DirichletCharacter(H, M([165,79]))
![Copy content]()
gp:[g,chi] = znchar(Mod(1866, 6169))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6169.1866");
| Modulus: | \(6169\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(6169\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(198\) |
![Copy content]()
sage:chi.multiplicative_order()
![Copy content]()
gp:charorder(g,chi)
![Copy content]()
magma:Order(chi);
|
| Real: | no |
![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);
|
\(\chi_{6169}(150,\cdot)\)
\(\chi_{6169}(192,\cdot)\)
\(\chi_{6169}(243,\cdot)\)
\(\chi_{6169}(347,\cdot)\)
\(\chi_{6169}(367,\cdot)\)
\(\chi_{6169}(471,\cdot)\)
\(\chi_{6169}(564,\cdot)\)
\(\chi_{6169}(595,\cdot)\)
\(\chi_{6169}(739,\cdot)\)
\(\chi_{6169}(770,\cdot)\)
\(\chi_{6169}(925,\cdot)\)
\(\chi_{6169}(998,\cdot)\)
\(\chi_{6169}(1029,\cdot)\)
\(\chi_{6169}(1184,\cdot)\)
\(\chi_{6169}(1235,\cdot)\)
\(\chi_{6169}(1370,\cdot)\)
\(\chi_{6169}(1556,\cdot)\)
\(\chi_{6169}(1700,\cdot)\)
\(\chi_{6169}(1711,\cdot)\)
\(\chi_{6169}(1866,\cdot)\)
\(\chi_{6169}(2103,\cdot)\)
\(\chi_{6169}(2176,\cdot)\)
\(\chi_{6169}(2227,\cdot)\)
\(\chi_{6169}(2258,\cdot)\)
\(\chi_{6169}(2475,\cdot)\)
\(\chi_{6169}(2641,\cdot)\)
\(\chi_{6169}(2692,\cdot)\)
\(\chi_{6169}(2754,\cdot)\)
\(\chi_{6169}(2816,\cdot)\)
\(\chi_{6169}(2920,\cdot)\)
...
![Copy content]()
sage:chi.galois_orbit()
![Copy content]()
gp:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
![Copy content]()
magma:order := Order(chi);
{ chi^k : k in [1..order-1] | GCD(k,order) eq 1 };
\((4777,1396)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{79}{198}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6169 }(1866, a) \) |
\(1\) | \(1\) | \(e\left(\frac{29}{99}\right)\) | \(e\left(\frac{23}{99}\right)\) | \(e\left(\frac{58}{99}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{52}{99}\right)\) | \(e\left(\frac{98}{99}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{46}{99}\right)\) | \(e\left(\frac{2}{99}\right)\) | \(e\left(\frac{19}{33}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
