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Show commands for: Pari/GP / SageMath
sage: H = DirichletGroup(221067)
 
sage: chi = H[1]
 
pari: [g,chi] = znchar(Mod(1,221067))
 

Basic properties

Modulus: \(221067\)
Conductor: \(1\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(1\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: no, induced from \(\chi_{1}(0,\cdot)\)
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

\((122816,126325,202798,53362)\) → \((1,1,1,1)\)

First values

\(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(13\)\(16\)\(17\)\(19\)
\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
value at e.g. 2