![Copy content]()
sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10255, base_ring=CyclotomicField(146))
M = H._module
chi = DirichletCharacter(H, M([73,73,118]))
![Copy content]()
gp:[g,chi] = znchar(Mod(419, 10255))
![Copy content]()
magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10255.419");
| Modulus: | \(10255\) |
![Copy content]()
sage:chi.modulus()
![Copy content]()
gp:g[1][1]
![Copy content]()
magma:Modulus(chi);
|
| Conductor: | \(10255\) |
![Copy content]()
sage:chi.conductor()
![Copy content]()
gp:znconreyconductor(g,chi)
![Copy content]()
magma:Conductor(chi);
|
| Order: | \(146\) |
![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);
|
\(\chi_{10255}(69,\cdot)\)
\(\chi_{10255}(244,\cdot)\)
\(\chi_{10255}(279,\cdot)\)
\(\chi_{10255}(349,\cdot)\)
\(\chi_{10255}(384,\cdot)\)
\(\chi_{10255}(419,\cdot)\)
\(\chi_{10255}(454,\cdot)\)
\(\chi_{10255}(489,\cdot)\)
\(\chi_{10255}(734,\cdot)\)
\(\chi_{10255}(944,\cdot)\)
\(\chi_{10255}(979,\cdot)\)
\(\chi_{10255}(1014,\cdot)\)
\(\chi_{10255}(1084,\cdot)\)
\(\chi_{10255}(1189,\cdot)\)
\(\chi_{10255}(1434,\cdot)\)
\(\chi_{10255}(1504,\cdot)\)
\(\chi_{10255}(1574,\cdot)\)
\(\chi_{10255}(1749,\cdot)\)
\(\chi_{10255}(1784,\cdot)\)
\(\chi_{10255}(2309,\cdot)\)
\(\chi_{10255}(2484,\cdot)\)
\(\chi_{10255}(2554,\cdot)\)
\(\chi_{10255}(2659,\cdot)\)
\(\chi_{10255}(2694,\cdot)\)
\(\chi_{10255}(2834,\cdot)\)
\(\chi_{10255}(2869,\cdot)\)
\(\chi_{10255}(3079,\cdot)\)
\(\chi_{10255}(3219,\cdot)\)
\(\chi_{10255}(3429,\cdot)\)
\(\chi_{10255}(3569,\cdot)\)
...
![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 };
\((2052,1466,2346)\) → \((-1,-1,e\left(\frac{59}{73}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 10255 }(419, a) \) |
\(-1\) | \(1\) | \(e\left(\frac{45}{146}\right)\) | \(e\left(\frac{65}{73}\right)\) | \(e\left(\frac{45}{73}\right)\) | \(e\left(\frac{29}{146}\right)\) | \(e\left(\frac{135}{146}\right)\) | \(e\left(\frac{57}{73}\right)\) | \(e\left(\frac{69}{73}\right)\) | \(e\left(\frac{37}{73}\right)\) | \(e\left(\frac{29}{73}\right)\) | \(e\left(\frac{17}{73}\right)\) |
![Copy content]()
sage:chi(x)
![Copy content]()
gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
![Copy content]()
magma:chi(x)
