![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(36667, base_ring=CyclotomicField(660))
M = H._module
chi = DirichletCharacter(H, M([385,628]))
![Copy content]()
gp:[g,chi] = znchar(Mod(29, 36667))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("36667.29");
| Modulus: | \(36667\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(36667\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(660\) |
![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: | odd |
![Copy content]()
sage:chi.is_odd()
![Copy content]()
gp:zncharisodd(g,chi)
![Copy content]()
magma:IsOdd(chi);
|
\(\chi_{36667}(29,\cdot)\)
\(\chi_{36667}(125,\cdot)\)
\(\chi_{36667}(378,\cdot)\)
\(\chi_{36667}(865,\cdot)\)
\(\chi_{36667}(1096,\cdot)\)
\(\chi_{36667}(1102,\cdot)\)
\(\chi_{36667}(1420,\cdot)\)
\(\chi_{36667}(1614,\cdot)\)
\(\chi_{36667}(1642,\cdot)\)
\(\chi_{36667}(2360,\cdot)\)
\(\chi_{36667}(2382,\cdot)\)
\(\chi_{36667}(2428,\cdot)\)
\(\chi_{36667}(2493,\cdot)\)
\(\chi_{36667}(2567,\cdot)\)
\(\chi_{36667}(2598,\cdot)\)
\(\chi_{36667}(2863,\cdot)\)
\(\chi_{36667}(3227,\cdot)\)
\(\chi_{36667}(3264,\cdot)\)
\(\chi_{36667}(3612,\cdot)\)
\(\chi_{36667}(3671,\cdot)\)
\(\chi_{36667}(4559,\cdot)\)
\(\chi_{36667}(4580,\cdot)\)
\(\chi_{36667}(4670,\cdot)\)
\(\chi_{36667}(4750,\cdot)\)
\(\chi_{36667}(4981,\cdot)\)
\(\chi_{36667}(5209,\cdot)\)
\(\chi_{36667}(5246,\cdot)\)
\(\chi_{36667}(5453,\cdot)\)
\(\chi_{36667}(5653,\cdot)\)
\(\chi_{36667}(5943,\cdot)\)
...
![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 };
\((22794,32709)\) → \((e\left(\frac{7}{12}\right),e\left(\frac{157}{165}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 36667 }(29, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{101}{660}\right)\) | \(e\left(\frac{181}{330}\right)\) | \(e\left(\frac{101}{330}\right)\) | \(e\left(\frac{169}{220}\right)\) | \(e\left(\frac{463}{660}\right)\) | \(e\left(\frac{13}{165}\right)\) | \(e\left(\frac{101}{220}\right)\) | \(e\left(\frac{16}{165}\right)\) | \(e\left(\frac{152}{165}\right)\) | \(e\left(\frac{269}{330}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
