# Related objects

Show commands: Pari/GP / SageMath
sage: H = DirichletGroup(310464)

sage: chi = H[1]

pari: [g,chi] = znchar(Mod(1,310464))

## Basic properties

 Modulus: $$310464$$ 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

$$(48511,213445,275969,145729,141121)$$ → $$(1,1,1,1,1)$$

## First values

 $$a$$ $$-1$$ $$1$$ $$5$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$37$$ $$\chi_{ 310464 }(1, a)$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
sage: chi.jacobi_sum(n)

$$\chi_{ 310464 }(1,a) \;$$ at $$\;a =$$ e.g. 2