![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(19169, base_ring=CyclotomicField(462))
M = H._module
chi = DirichletCharacter(H, M([330,287]))
![Copy content]()
gp:[g,chi] = znchar(Mod(922, 19169))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("19169.922");
| Modulus: | \(19169\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(19169\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(462\) |
![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);
|
\(\chi_{19169}(227,\cdot)\)
\(\chi_{19169}(431,\cdot)\)
\(\chi_{19169}(574,\cdot)\)
\(\chi_{19169}(690,\cdot)\)
\(\chi_{19169}(721,\cdot)\)
\(\chi_{19169}(894,\cdot)\)
\(\chi_{19169}(922,\cdot)\)
\(\chi_{19169}(980,\cdot)\)
\(\chi_{19169}(1963,\cdot)\)
\(\chi_{19169}(2414,\cdot)\)
\(\chi_{19169}(2606,\cdot)\)
\(\chi_{19169}(2633,\cdot)\)
\(\chi_{19169}(2704,\cdot)\)
\(\chi_{19169}(3007,\cdot)\)
\(\chi_{19169}(3010,\cdot)\)
\(\chi_{19169}(3184,\cdot)\)
\(\chi_{19169}(3206,\cdot)\)
\(\chi_{19169}(3529,\cdot)\)
\(\chi_{19169}(3532,\cdot)\)
\(\chi_{19169}(3736,\cdot)\)
\(\chi_{19169}(3786,\cdot)\)
\(\chi_{19169}(3844,\cdot)\)
\(\chi_{19169}(4026,\cdot)\)
\(\chi_{19169}(4080,\cdot)\)
\(\chi_{19169}(4199,\cdot)\)
\(\chi_{19169}(4540,\cdot)\)
\(\chi_{19169}(4589,\cdot)\)
\(\chi_{19169}(4607,\cdot)\)
\(\chi_{19169}(4656,\cdot)\)
\(\chi_{19169}(4660,\cdot)\)
...
![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 };
\((15865,3307)\) → \((e\left(\frac{5}{7}\right),e\left(\frac{41}{66}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 19169 }(922, a) \) |
\(1\) | \(1\) | \(e\left(\frac{155}{462}\right)\) | \(e\left(\frac{51}{77}\right)\) | \(e\left(\frac{155}{231}\right)\) | \(e\left(\frac{74}{231}\right)\) | \(e\left(\frac{461}{462}\right)\) | \(e\left(\frac{67}{154}\right)\) | \(e\left(\frac{1}{154}\right)\) | \(e\left(\frac{25}{77}\right)\) | \(e\left(\frac{101}{154}\right)\) | \(e\left(\frac{212}{231}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
