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Show commands: PariGP / SageMath
H = DirichletGroup(374790)
 
chi = H[26911]
 
pari: [g,chi] = znchar(Mod(26911,374790))
 

Basic properties

Modulus: \(374790\)
Conductor: \(961\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(930\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{961}(3,\cdot)\)
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: $\Q(\zeta_{465})$

Values on generators

\((124931,149917,86491,26911)\) → \((1,1,1,e\left(\frac{1}{930}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(17\)\(19\)\(23\)\(29\)\(37\)\(41\)\(43\)
\( \chi_{ 374790 }(26911, a) \) \(-1\)\(1\)\(e\left(\frac{329}{465}\right)\)\(e\left(\frac{323}{930}\right)\)\(e\left(\frac{727}{930}\right)\)\(e\left(\frac{107}{465}\right)\)\(e\left(\frac{29}{310}\right)\)\(e\left(\frac{153}{310}\right)\)\(e\left(\frac{167}{186}\right)\)\(e\left(\frac{37}{465}\right)\)\(e\left(\frac{889}{930}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 374790 }(26911,a) \;\) at \(\;a = \) e.g. 2