![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63580, base_ring=CyclotomicField(680))
M = H._module
chi = DirichletCharacter(H, M([340,340,544,135]))
![Copy content]()
gp:[g,chi] = znchar(Mod(2599, 63580))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63580.2599");
| Modulus: | \(63580\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(63580\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(680\) |
![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);
|
\(\chi_{63580}(59,\cdot)\)
\(\chi_{63580}(559,\cdot)\)
\(\chi_{63580}(1039,\cdot)\)
\(\chi_{63580}(1379,\cdot)\)
\(\chi_{63580}(1719,\cdot)\)
\(\chi_{63580}(1879,\cdot)\)
\(\chi_{63580}(1919,\cdot)\)
\(\chi_{63580}(2099,\cdot)\)
\(\chi_{63580}(2259,\cdot)\)
\(\chi_{63580}(2599,\cdot)\)
\(\chi_{63580}(3239,\cdot)\)
\(\chi_{63580}(3419,\cdot)\)
\(\chi_{63580}(3459,\cdot)\)
\(\chi_{63580}(3579,\cdot)\)
\(\chi_{63580}(3799,\cdot)\)
\(\chi_{63580}(3919,\cdot)\)
\(\chi_{63580}(4139,\cdot)\)
\(\chi_{63580}(4299,\cdot)\)
\(\chi_{63580}(5119,\cdot)\)
\(\chi_{63580}(5459,\cdot)\)
\(\chi_{63580}(5619,\cdot)\)
\(\chi_{63580}(5659,\cdot)\)
\(\chi_{63580}(5839,\cdot)\)
\(\chi_{63580}(5999,\cdot)\)
\(\chi_{63580}(6339,\cdot)\)
\(\chi_{63580}(6979,\cdot)\)
\(\chi_{63580}(7159,\cdot)\)
\(\chi_{63580}(7199,\cdot)\)
\(\chi_{63580}(7319,\cdot)\)
\(\chi_{63580}(7539,\cdot)\)
...
![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 };
\((31791,12717,52021,29481)\) → \((-1,-1,e\left(\frac{4}{5}\right),e\left(\frac{27}{136}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(13\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) | \(31\) |
| \( \chi_{ 63580 }(2599, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{407}{680}\right)\) | \(e\left(\frac{253}{680}\right)\) | \(e\left(\frac{67}{340}\right)\) | \(e\left(\frac{18}{85}\right)\) | \(e\left(\frac{231}{340}\right)\) | \(e\left(\frac{33}{34}\right)\) | \(e\left(\frac{37}{136}\right)\) | \(e\left(\frac{541}{680}\right)\) | \(e\left(\frac{283}{680}\right)\) | \(e\left(\frac{59}{680}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
