Properties

Label 3233.3232
Modulus $3233$
Conductor $3233$
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(3233, base_ring=CyclotomicField(2))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([1,1]))
 
pari: [g,chi] = znchar(Mod(3232,3233))
 

Kronecker symbol representation

sage: kronecker_character(3233)
 
pari: znchartokronecker(g,chi)
 

\(\displaystyle\left(\frac{3233}{\bullet}\right)\)

Basic properties

Modulus: \(3233\)
Conductor: \(3233\)
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 3233.d

\(\chi_{3233}(3232,\cdot)\)

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: \(\Q(\sqrt{3233}) \)

Values on generators

\((1221,2015)\) → \((-1,-1)\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(1\)\(-1\)\(1\)\(-1\)\(-1\)\(-1\)\(1\)\(1\)\(-1\)\(-1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 3233 }(3232,a) \;\) at \(\;a = \) e.g. 2