Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: H = DirichletGroup(20627)
 
sage: chi = H[20626]
 
pari: [g,chi] = znchar(Mod(20626,20627))
 

Kronecker symbol representation

sage: kronecker_character(-20627)
 
pari: znchartokronecker(g,chi)
 

\(\displaystyle\left(\frac{-20627}{\bullet}\right)\)

Basic properties

Modulus: \(20627\)
Conductor: \(20627\)
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 \\ if not primitive returns [cond,factorization]
 
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q\)

Values on generators

\(2\) → \(-1\)

First values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)
\(-1\)\(1\)\(-1\)\(1\)\(1\)\(-1\)\(-1\)\(1\)\(-1\)\(1\)\(1\)
value at e.g. 2