![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10153, base_ring=CyclotomicField(210))
M = H._module
chi = DirichletCharacter(H, M([126,70,198]))
![Copy content]()
gp:[g,chi] = znchar(Mod(2616, 10153))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10153.2616");
| Modulus: | \(10153\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(10153\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(105\) |
![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);
|
\(\chi_{10153}(16,\cdot)\)
\(\chi_{10153}(191,\cdot)\)
\(\chi_{10153}(256,\cdot)\)
\(\chi_{10153}(334,\cdot)\)
\(\chi_{10153}(555,\cdot)\)
\(\chi_{10153}(718,\cdot)\)
\(\chi_{10153}(1160,\cdot)\)
\(\chi_{10153}(1290,\cdot)\)
\(\chi_{10153}(1439,\cdot)\)
\(\chi_{10153}(2148,\cdot)\)
\(\chi_{10153}(2616,\cdot)\)
\(\chi_{10153}(2876,\cdot)\)
\(\chi_{10153}(3188,\cdot)\)
\(\chi_{10153}(3435,\cdot)\)
\(\chi_{10153}(3721,\cdot)\)
\(\chi_{10153}(3844,\cdot)\)
\(\chi_{10153}(3909,\cdot)\)
\(\chi_{10153}(4085,\cdot)\)
\(\chi_{10153}(4195,\cdot)\)
\(\chi_{10153}(4442,\cdot)\)
\(\chi_{10153}(4475,\cdot)\)
\(\chi_{10153}(4559,\cdot)\)
\(\chi_{10153}(4618,\cdot)\)
\(\chi_{10153}(4624,\cdot)\)
\(\chi_{10153}(4702,\cdot)\)
\(\chi_{10153}(5404,\cdot)\)
\(\chi_{10153}(5658,\cdot)\)
\(\chi_{10153}(5723,\cdot)\)
\(\chi_{10153}(5801,\cdot)\)
\(\chi_{10153}(5846,\cdot)\)
...
![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 };
\((9231,782,859)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{1}{3}\right),e\left(\frac{33}{35}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 10153 }(2616, a) \) |
\(1\) | \(1\) | \(e\left(\frac{62}{105}\right)\) | \(e\left(\frac{68}{105}\right)\) | \(e\left(\frac{19}{105}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{31}{105}\right)\) | \(e\left(\frac{41}{105}\right)\) | \(e\left(\frac{29}{35}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
