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Show commands: Pari/GP / SageMath
sage: H = DirichletGroup(142252)
 
sage: chi = H[142251]
 
pari: [g,chi] = znchar(Mod(142251,142252))
 

Kronecker symbol representation

sage: kronecker_character(142252)
 
pari: znchartokronecker(g,chi)
 

\(\displaystyle\left(\frac{142252}{\bullet}\right)\)

Basic properties

Modulus: \(142252\)
Conductor: \(142252\)
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: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q\)

Values on generators

\((71127,103457,104677,111937)\) → \((-1,-1,-1,-1)\)

First values

\(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(13\)\(15\)\(17\)\(19\)\(21\)
\(1\)\(1\)\(1\)\(-1\)\(-1\)\(1\)\(-1\)\(-1\)\(1\)\(-1\)\(-1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 142252 }(142251,a) \;\) at \(\;a = \) e.g. 2