# Related objects

Show commands: Pari/GP / SageMath
sage: H = DirichletGroup(140659)

sage: chi = H[140658]

pari: [g,chi] = znchar(Mod(140658,140659))

## Kronecker symbol representation

sage: kronecker_character(-140659)

pari: znchartokronecker(g,chi)

$$\displaystyle\left(\frac{-140659}{\bullet}\right)$$

## Basic properties

 Modulus: $$140659$$ Conductor: $$140659$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$2$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: yes Primitive: yes 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

$$3$$ → $$-1$$

## First values

 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$7$$ $$8$$ $$9$$ $$10$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 140659 }(140658,a) \;$$ at $$\;a =$$ e.g. 2