# Related objects

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(24882)

sage: chi = H[1]

pari: [g,chi] = znchar(Mod(1,24882))

## Basic properties

 Modulus: $$24882$$ 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 $$\chi_{1}(1,\cdot)$$ 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)

## Galois orbit 24882.None

sage: chi.galois_orbit()

pari: order = charorder(g,chi)

pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

## Values on generators

sage: chi(k) for k in H.gens()

pari: [ chareval(g,chi,x) | x <- g.gen ] \\ value in Q/Z

$$(5077,4135,17863,16589)$$ → $$(1,1,1,1)$$

## First values

 $$1$$ $$5$$ $$7$$ $$17$$ $$19$$ $$23$$ $$25$$ $$31$$ $$35$$ $$37$$ $$41$$ $$43$$ $$47$$ $$49$$ $$53$$ $$59$$ $$61$$ $$67$$ $$71$$ $$73$$ $$79$$ $$83$$ $$85$$ $$89$$ $$95$$ $$97$$ $$101$$ $$103$$ $$107$$ $$109$$ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 value at e.g. 2

## Related number fields

 Field of values: $$\Q$$