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Show commands: PariGP / SageMath
H = DirichletGroup(334620)
 
chi = H[174241]
 
pari: [g,chi] = znchar(Mod(174241,334620))
 

Basic properties

Modulus: \(334620\)
Conductor: \(169\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(156\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{169}(2,\cdot)\)
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: $\Q(\zeta_{156})$

Values on generators

\((167311,37181,267697,273781,174241)\) → \((1,1,1,1,e\left(\frac{1}{156}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 334620 }(174241, a) \) \(-1\)\(1\)\(e\left(\frac{107}{156}\right)\)\(e\left(\frac{73}{78}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{10}{39}\right)\)\(e\left(\frac{7}{52}\right)\)\(e\left(\frac{151}{156}\right)\)\(e\left(\frac{85}{156}\right)\)\(e\left(\frac{61}{78}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 334620 }(174241,a) \;\) at \(\;a = \) e.g. 2