↑

Properties

Label 5887.1104
Modulus $5887$
Conductor $5887$
Order $2436$
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(5887, base_ring=CyclotomicField(2436)) M = H._module chi = DirichletCharacter(H, M([2030,1599]))
 
Copy content gp:[g,chi] = znchar(Mod(1104, 5887))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5887.1104");
 

Basic properties

Modulus: \(5887\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(5887\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(2436\)
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 5887.bu

\(\chi_{5887}(3,\cdot)\) \(\chi_{5887}(10,\cdot)\) \(\chi_{5887}(19,\cdot)\) \(\chi_{5887}(26,\cdot)\) \(\chi_{5887}(31,\cdot)\) \(\chi_{5887}(40,\cdot)\) \(\chi_{5887}(47,\cdot)\) \(\chi_{5887}(61,\cdot)\) \(\chi_{5887}(66,\cdot)\) \(\chi_{5887}(68,\cdot)\) \(\chi_{5887}(73,\cdot)\) \(\chi_{5887}(89,\cdot)\) \(\chi_{5887}(101,\cdot)\) \(\chi_{5887}(108,\cdot)\) \(\chi_{5887}(124,\cdot)\) \(\chi_{5887}(131,\cdot)\) \(\chi_{5887}(143,\cdot)\) \(\chi_{5887}(159,\cdot)\) \(\chi_{5887}(164,\cdot)\) \(\chi_{5887}(166,\cdot)\) \(\chi_{5887}(171,\cdot)\) \(\chi_{5887}(185,\cdot)\) \(\chi_{5887}(192,\cdot)\) \(\chi_{5887}(201,\cdot)\) \(\chi_{5887}(206,\cdot)\) \(\chi_{5887}(213,\cdot)\) \(\chi_{5887}(222,\cdot)\) \(\chi_{5887}(229,\cdot)\) \(\chi_{5887}(234,\cdot)\) \(\chi_{5887}(243,\cdot)\) ...

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: $\Q(\zeta_{2436})$
Fixed field: Number field defined by a degree 2436 polynomial (not computed)

Values on generators

\((1683,5048)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{533}{812}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(8\)\(9\)\(10\)\(11\)\(12\)
\( \chi_{ 5887 }(1104, a) \) \(1\)\(1\)\(e\left(\frac{787}{2436}\right)\)\(e\left(\frac{785}{2436}\right)\)\(e\left(\frac{787}{1218}\right)\)\(e\left(\frac{244}{609}\right)\)\(e\left(\frac{131}{203}\right)\)\(e\left(\frac{787}{812}\right)\)\(e\left(\frac{785}{1218}\right)\)\(e\left(\frac{1763}{2436}\right)\)\(e\left(\frac{1223}{2436}\right)\)\(e\left(\frac{337}{348}\right)\)
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)
 
\( \chi_{ 5887 }(1104,a) \;\) at \(\;a = \) e.g. 2