Properties

Label 2665.2664
Modulus $2665$
Conductor $2665$
Order $2$
Real yes
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2665, base_ring=CyclotomicField(2))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([1,1,1]))
 
pari: [g,chi] = znchar(Mod(2664,2665))
 

Kronecker symbol representation

sage: kronecker_character(2665)
 
pari: znchartokronecker(g,chi)
 

\(\displaystyle\left(\frac{2665}{\bullet}\right)\)

Basic properties

Modulus: \(2665\)
Conductor: \(2665\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(2\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2665.h

\(\chi_{2665}(2664,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q\)
Fixed field: \(\Q(\sqrt{2665}) \)

Values on generators

\((1067,821,1236)\) → \((-1,-1,-1)\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(14\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(-1\)\(1\)\(1\)\(1\)\(1\)\(-1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2665 }(2664,a) \;\) at \(\;a = \) e.g. 2