![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11271, base_ring=CyclotomicField(68))
M = H._module
chi = DirichletCharacter(H, M([34,17,29]))
![Copy content]()
gp:[g,chi] = znchar(Mod(6014, 11271))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("11271.6014");
| Modulus: | \(11271\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(11271\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(68\) |
![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);
|
\(\chi_{11271}(47,\cdot)\)
\(\chi_{11271}(395,\cdot)\)
\(\chi_{11271}(710,\cdot)\)
\(\chi_{11271}(1058,\cdot)\)
\(\chi_{11271}(1373,\cdot)\)
\(\chi_{11271}(1721,\cdot)\)
\(\chi_{11271}(2036,\cdot)\)
\(\chi_{11271}(2384,\cdot)\)
\(\chi_{11271}(2699,\cdot)\)
\(\chi_{11271}(3047,\cdot)\)
\(\chi_{11271}(3362,\cdot)\)
\(\chi_{11271}(3710,\cdot)\)
\(\chi_{11271}(4025,\cdot)\)
\(\chi_{11271}(4688,\cdot)\)
\(\chi_{11271}(5036,\cdot)\)
\(\chi_{11271}(5351,\cdot)\)
\(\chi_{11271}(5699,\cdot)\)
\(\chi_{11271}(6014,\cdot)\)
\(\chi_{11271}(6362,\cdot)\)
\(\chi_{11271}(6677,\cdot)\)
\(\chi_{11271}(7025,\cdot)\)
\(\chi_{11271}(7340,\cdot)\)
\(\chi_{11271}(7688,\cdot)\)
\(\chi_{11271}(8003,\cdot)\)
\(\chi_{11271}(8351,\cdot)\)
\(\chi_{11271}(8666,\cdot)\)
\(\chi_{11271}(9014,\cdot)\)
\(\chi_{11271}(9329,\cdot)\)
\(\chi_{11271}(9677,\cdot)\)
\(\chi_{11271}(9992,\cdot)\)
...
![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 };
\((3758,2602,9829)\) → \((-1,i,e\left(\frac{29}{68}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(19\) |
| \( \chi_{ 11271 }(6014, a) \) |
\(1\) | \(1\) | \(e\left(\frac{53}{68}\right)\) | \(e\left(\frac{19}{34}\right)\) | \(e\left(\frac{7}{17}\right)\) | \(e\left(\frac{29}{34}\right)\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{13}{68}\right)\) | \(e\left(\frac{1}{17}\right)\) | \(e\left(\frac{43}{68}\right)\) | \(e\left(\frac{2}{17}\right)\) | \(e\left(\frac{15}{68}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
