![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29792, base_ring=CyclotomicField(504))
M = H._module
chi = DirichletCharacter(H, M([0,315,180,364]))
![Copy content]()
gp:[g,chi] = znchar(Mod(3765, 29792))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29792.3765");
| Modulus: | \(29792\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(29792\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(504\) |
![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);
|
\(\chi_{29792}(13,\cdot)\)
\(\chi_{29792}(181,\cdot)\)
\(\chi_{29792}(573,\cdot)\)
\(\chi_{29792}(629,\cdot)\)
\(\chi_{29792}(965,\cdot)\)
\(\chi_{29792}(1021,\cdot)\)
\(\chi_{29792}(1245,\cdot)\)
\(\chi_{29792}(1637,\cdot)\)
\(\chi_{29792}(1693,\cdot)\)
\(\chi_{29792}(2029,\cdot)\)
\(\chi_{29792}(2085,\cdot)\)
\(\chi_{29792}(2141,\cdot)\)
\(\chi_{29792}(2309,\cdot)\)
\(\chi_{29792}(2701,\cdot)\)
\(\chi_{29792}(2757,\cdot)\)
\(\chi_{29792}(3093,\cdot)\)
\(\chi_{29792}(3149,\cdot)\)
\(\chi_{29792}(3205,\cdot)\)
\(\chi_{29792}(3373,\cdot)\)
\(\chi_{29792}(3765,\cdot)\)
\(\chi_{29792}(4157,\cdot)\)
\(\chi_{29792}(4269,\cdot)\)
\(\chi_{29792}(4437,\cdot)\)
\(\chi_{29792}(4829,\cdot)\)
\(\chi_{29792}(4885,\cdot)\)
\(\chi_{29792}(5221,\cdot)\)
\(\chi_{29792}(5277,\cdot)\)
\(\chi_{29792}(5333,\cdot)\)
\(\chi_{29792}(5501,\cdot)\)
\(\chi_{29792}(5893,\cdot)\)
...
![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 };
\((9311,11173,3041,3137)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{5}{14}\right),e\left(\frac{13}{18}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
| \( \chi_{ 29792 }(3765, a) \) |
\(1\) | \(1\) | \(e\left(\frac{313}{504}\right)\) | \(e\left(\frac{271}{504}\right)\) | \(e\left(\frac{61}{252}\right)\) | \(e\left(\frac{13}{168}\right)\) | \(e\left(\frac{389}{504}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{41}{63}\right)\) | \(e\left(\frac{193}{252}\right)\) | \(e\left(\frac{19}{252}\right)\) | \(e\left(\frac{145}{168}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
