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Show commands: PariGP / SageMath
H = DirichletGroup(374790)
 
chi = H[124931]
 
pari: [g,chi] = znchar(Mod(124931,374790))
 

Basic properties

Modulus: \(374790\)
Conductor: \(3\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(2\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: no, induced from \(\chi_{3}(2,\cdot)\)
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

\((124931,149917,86491,26911)\) → \((-1,1,1,1)\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(17\)\(19\)\(23\)\(29\)\(37\)\(41\)\(43\)
\( \chi_{ 374790 }(124931, a) \) \(-1\)\(1\)\(1\)\(-1\)\(-1\)\(1\)\(-1\)\(-1\)\(1\)\(-1\)\(1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 374790 }(124931,a) \;\) at \(\;a = \) e.g. 2