![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64829, base_ring=CyclotomicField(1072))
M = H._module
chi = DirichletCharacter(H, M([737,104]))
![Copy content]()
gp:[g,chi] = znchar(Mod(1972, 64829))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64829.1972");
| Modulus: | \(64829\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(64829\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(1072\) |
![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);
|
\(\chi_{64829}(126,\cdot)\)
\(\chi_{64829}(558,\cdot)\)
\(\chi_{64829}(593,\cdot)\)
\(\chi_{64829}(1040,\cdot)\)
\(\chi_{64829}(1320,\cdot)\)
\(\chi_{64829}(1331,\cdot)\)
\(\chi_{64829}(1557,\cdot)\)
\(\chi_{64829}(1561,\cdot)\)
\(\chi_{64829}(1576,\cdot)\)
\(\chi_{64829}(1763,\cdot)\)
\(\chi_{64829}(1802,\cdot)\)
\(\chi_{64829}(1813,\cdot)\)
\(\chi_{64829}(1817,\cdot)\)
\(\chi_{64829}(1972,\cdot)\)
\(\chi_{64829}(2334,\cdot)\)
\(\chi_{64829}(2486,\cdot)\)
\(\chi_{64829}(2521,\cdot)\)
\(\chi_{64829}(2575,\cdot)\)
\(\chi_{64829}(2816,\cdot)\)
\(\chi_{64829}(2936,\cdot)\)
\(\chi_{64829}(2968,\cdot)\)
\(\chi_{64829}(3248,\cdot)\)
\(\chi_{64829}(3450,\cdot)\)
\(\chi_{64829}(3730,\cdot)\)
\(\chi_{64829}(3741,\cdot)\)
\(\chi_{64829}(3745,\cdot)\)
\(\chi_{64829}(3982,\cdot)\)
\(\chi_{64829}(4021,\cdot)\)
\(\chi_{64829}(4173,\cdot)\)
\(\chi_{64829}(4223,\cdot)\)
...
![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 };
\((60257,11569)\) → \((e\left(\frac{11}{16}\right),e\left(\frac{13}{134}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 64829 }(1972, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{387}{536}\right)\) | \(e\left(\frac{375}{536}\right)\) | \(e\left(\frac{119}{268}\right)\) | \(e\left(\frac{29}{536}\right)\) | \(e\left(\frac{113}{268}\right)\) | \(e\left(\frac{569}{1072}\right)\) | \(e\left(\frac{89}{536}\right)\) | \(e\left(\frac{107}{268}\right)\) | \(e\left(\frac{52}{67}\right)\) | \(e\left(\frac{537}{1072}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
