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Show commands: PariGP / SageMath
H = DirichletGroup(1871424)
 
chi = H[1]
 
pari: [g,chi] = znchar(Mod(1,1871424))
 

Basic properties

Modulus: \(1871424\)
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

\((1345087,1052677,1478657,129601)\) → \((1,1,1,1)\)

First values

\(a\) \(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(23\)\(25\)\(29\)\(31\)
\( \chi_{ 1871424 }(1, a) \) \(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)\(1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1871424 }(1,a) \;\) at \(\;a = \) e.g. 2