![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5203, base_ring=CyclotomicField(2310))
M = H._module
chi = DirichletCharacter(H, M([1932,1375]))
![Copy content]()
gp:[g,chi] = znchar(Mod(48, 5203))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5203.48");
| Modulus: | \(5203\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(5203\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(2310\) |
![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);
|
\(\chi_{5203}(5,\cdot)\)
\(\chi_{5203}(20,\cdot)\)
\(\chi_{5203}(26,\cdot)\)
\(\chi_{5203}(48,\cdot)\)
\(\chi_{5203}(69,\cdot)\)
\(\chi_{5203}(71,\cdot)\)
\(\chi_{5203}(91,\cdot)\)
\(\chi_{5203}(104,\cdot)\)
\(\chi_{5203}(114,\cdot)\)
\(\chi_{5203}(115,\cdot)\)
\(\chi_{5203}(119,\cdot)\)
\(\chi_{5203}(141,\cdot)\)
\(\chi_{5203}(147,\cdot)\)
\(\chi_{5203}(157,\cdot)\)
\(\chi_{5203}(158,\cdot)\)
\(\chi_{5203}(159,\cdot)\)
\(\chi_{5203}(163,\cdot)\)
\(\chi_{5203}(190,\cdot)\)
\(\chi_{5203}(191,\cdot)\)
\(\chi_{5203}(192,\cdot)\)
\(\chi_{5203}(201,\cdot)\)
\(\chi_{5203}(218,\cdot)\)
\(\chi_{5203}(234,\cdot)\)
\(\chi_{5203}(235,\cdot)\)
\(\chi_{5203}(278,\cdot)\)
\(\chi_{5203}(284,\cdot)\)
\(\chi_{5203}(291,\cdot)\)
\(\chi_{5203}(306,\cdot)\)
\(\chi_{5203}(313,\cdot)\)
\(\chi_{5203}(334,\cdot)\)
...
![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 };
\((3269,3873)\) → \((e\left(\frac{46}{55}\right),e\left(\frac{25}{42}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 5203 }(48, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{699}{770}\right)\) | \(e\left(\frac{41}{210}\right)\) | \(e\left(\frac{314}{385}\right)\) | \(e\left(\frac{1783}{2310}\right)\) | \(e\left(\frac{17}{165}\right)\) | \(e\left(\frac{227}{330}\right)\) | \(e\left(\frac{557}{770}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{157}{231}\right)\) | \(e\left(\frac{5}{462}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
