![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(46475, base_ring=CyclotomicField(780))
M = H._module
chi = DirichletCharacter(H, M([663,78,110]))
![Copy content]()
gp:[g,chi] = znchar(Mod(6822, 46475))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("46475.6822");
| Modulus: | \(46475\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(46475\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(780\) |
![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);
|
\(\chi_{46475}(17,\cdot)\)
\(\chi_{46475}(62,\cdot)\)
\(\chi_{46475}(173,\cdot)\)
\(\chi_{46475}(238,\cdot)\)
\(\chi_{46475}(602,\cdot)\)
\(\chi_{46475}(842,\cdot)\)
\(\chi_{46475}(998,\cdot)\)
\(\chi_{46475}(1063,\cdot)\)
\(\chi_{46475}(1278,\cdot)\)
\(\chi_{46475}(1427,\cdot)\)
\(\chi_{46475}(1733,\cdot)\)
\(\chi_{46475}(2103,\cdot)\)
\(\chi_{46475}(2422,\cdot)\)
\(\chi_{46475}(2812,\cdot)\)
\(\chi_{46475}(3247,\cdot)\)
\(\chi_{46475}(3592,\cdot)\)
\(\chi_{46475}(3637,\cdot)\)
\(\chi_{46475}(3748,\cdot)\)
\(\chi_{46475}(3813,\cdot)\)
\(\chi_{46475}(4177,\cdot)\)
\(\chi_{46475}(4573,\cdot)\)
\(\chi_{46475}(4638,\cdot)\)
\(\chi_{46475}(4853,\cdot)\)
\(\chi_{46475}(5002,\cdot)\)
\(\chi_{46475}(5308,\cdot)\)
\(\chi_{46475}(5678,\cdot)\)
\(\chi_{46475}(5997,\cdot)\)
\(\chi_{46475}(6133,\cdot)\)
\(\chi_{46475}(6387,\cdot)\)
\(\chi_{46475}(6822,\cdot)\)
...
![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 };
\((26027,4226,16226)\) → \((e\left(\frac{17}{20}\right),e\left(\frac{1}{10}\right),e\left(\frac{11}{78}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(14\) | \(16\) |
| \( \chi_{ 46475 }(6822, a) \) |
\(1\) | \(1\) | \(e\left(\frac{71}{780}\right)\) | \(e\left(\frac{37}{156}\right)\) | \(e\left(\frac{71}{390}\right)\) | \(e\left(\frac{64}{195}\right)\) | \(e\left(\frac{31}{780}\right)\) | \(e\left(\frac{71}{260}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{109}{260}\right)\) | \(e\left(\frac{17}{130}\right)\) | \(e\left(\frac{71}{195}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
