![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(220669, base_ring=CyclotomicField(1480))
M = H._module
chi = DirichletCharacter(H, M([850,533]))
![Copy content]()
gp:[g,chi] = znchar(Mod(11362, 220669))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("220669.11362");
| Modulus: | \(220669\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(220669\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(1480\) |
![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);
|
\(\chi_{220669}(407,\cdot)\)
\(\chi_{220669}(932,\cdot)\)
\(\chi_{220669}(1487,\cdot)\)
\(\chi_{220669}(1879,\cdot)\)
\(\chi_{220669}(2258,\cdot)\)
\(\chi_{220669}(2661,\cdot)\)
\(\chi_{220669}(2844,\cdot)\)
\(\chi_{220669}(3058,\cdot)\)
\(\chi_{220669}(3562,\cdot)\)
\(\chi_{220669}(4251,\cdot)\)
\(\chi_{220669}(4827,\cdot)\)
\(\chi_{220669}(4991,\cdot)\)
\(\chi_{220669}(5285,\cdot)\)
\(\chi_{220669}(5869,\cdot)\)
\(\chi_{220669}(6095,\cdot)\)
\(\chi_{220669}(6716,\cdot)\)
\(\chi_{220669}(7366,\cdot)\)
\(\chi_{220669}(7376,\cdot)\)
\(\chi_{220669}(7525,\cdot)\)
\(\chi_{220669}(8008,\cdot)\)
\(\chi_{220669}(9628,\cdot)\)
\(\chi_{220669}(10173,\cdot)\)
\(\chi_{220669}(10690,\cdot)\)
\(\chi_{220669}(11258,\cdot)\)
\(\chi_{220669}(11362,\cdot)\)
\(\chi_{220669}(11985,\cdot)\)
\(\chi_{220669}(12456,\cdot)\)
\(\chi_{220669}(12513,\cdot)\)
\(\chi_{220669}(12774,\cdot)\)
\(\chi_{220669}(12776,\cdot)\)
...
![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 };
\((48874,122926)\) → \((e\left(\frac{85}{148}\right),e\left(\frac{533}{1480}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 220669 }(11362, a) \) |
\(1\) | \(1\) | \(e\left(\frac{167}{740}\right)\) | \(e\left(\frac{483}{1480}\right)\) | \(e\left(\frac{167}{370}\right)\) | \(e\left(\frac{267}{740}\right)\) | \(e\left(\frac{817}{1480}\right)\) | \(e\left(\frac{103}{370}\right)\) | \(e\left(\frac{501}{740}\right)\) | \(e\left(\frac{483}{740}\right)\) | \(e\left(\frac{217}{370}\right)\) | \(e\left(\frac{57}{296}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
