↑

Properties

Label 2863.933
Modulus $2863$
Conductor $2863$
Order $204$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the Dirichlet character
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2863, base_ring=CyclotomicField(204)) M = H._module chi = DirichletCharacter(H, M([68,101]))
 
Copy content gp:[g,chi] = znchar(Mod(933, 2863))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2863.933");
 

Basic properties

Modulus: \(2863\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(2863\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(204\)
Copy content comment:Order
 
Copy content sage:chi.multiplicative_order()
 
Copy content gp:charorder(g,chi)
 
Copy content magma:Order(chi);
 
Real: no
Copy content comment:Whether the character is real
 
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 comment:If the character is primitive
 
Copy content sage:chi.is_primitive()
 
Copy content gp:#znconreyconductor(g,chi)==1
 
Copy content magma:IsPrimitive(chi);
 
Minimal: yes
Parity: even
Copy content comment:Parity
 
Copy content sage:chi.is_odd()
 
Copy content gp:zncharisodd(g,chi)
 
Copy content magma:IsOdd(chi);
 

Galois orbit 2863.ct

\(\chi_{2863}(2,\cdot)\) \(\chi_{2863}(18,\cdot)\) \(\chi_{2863}(23,\cdot)\) \(\chi_{2863}(32,\cdot)\) \(\chi_{2863}(72,\cdot)\) \(\chi_{2863}(128,\cdot)\) \(\chi_{2863}(207,\cdot)\) \(\chi_{2863}(249,\cdot)\) \(\chi_{2863}(319,\cdot)\) \(\chi_{2863}(359,\cdot)\) \(\chi_{2863}(368,\cdot)\) \(\chi_{2863}(375,\cdot)\) \(\chi_{2863}(424,\cdot)\) \(\chi_{2863}(613,\cdot)\) \(\chi_{2863}(648,\cdot)\) \(\chi_{2863}(655,\cdot)\) \(\chi_{2863}(676,\cdot)\) \(\chi_{2863}(709,\cdot)\) \(\chi_{2863}(758,\cdot)\) \(\chi_{2863}(828,\cdot)\) \(\chi_{2863}(893,\cdot)\) \(\chi_{2863}(933,\cdot)\) \(\chi_{2863}(949,\cdot)\) \(\chi_{2863}(954,\cdot)\) \(\chi_{2863}(982,\cdot)\) \(\chi_{2863}(996,\cdot)\) \(\chi_{2863}(1096,\cdot)\) \(\chi_{2863}(1152,\cdot)\) \(\chi_{2863}(1369,\cdot)\) \(\chi_{2863}(1390,\cdot)\) ...

Copy content comment:Galois orbit
 
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 };
 

Related number fields

Field of values: $\Q(\zeta_{204})$
Fixed field: Number field defined by a degree 204 polynomial (not computed)

Values on generators

\((1228,2066)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{101}{204}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(8\)\(9\)\(10\)\(11\)\(12\)
\( \chi_{ 2863 }(933, a) \) \(1\)\(1\)\(e\left(\frac{9}{34}\right)\)\(e\left(\frac{31}{34}\right)\)\(e\left(\frac{9}{17}\right)\)\(e\left(\frac{28}{51}\right)\)\(e\left(\frac{3}{17}\right)\)\(e\left(\frac{27}{34}\right)\)\(e\left(\frac{14}{17}\right)\)\(e\left(\frac{83}{102}\right)\)\(e\left(\frac{185}{204}\right)\)\(e\left(\frac{15}{34}\right)\)
Copy content comment:Value of chi at x
 
Copy content sage:chi(x)
 
Copy content gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
 
Copy content magma:chi(x)
 
\( \chi_{ 2863 }(933,a) \;\) at \(\;a = \) e.g. 2