# 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(20736)

sage: chi = H[1]

pari: [g,chi] = znchar(Mod(1,20736))

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Conductor = 1 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 1 Real = yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = no sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = even

## Galois orbit

sage: chi.sage_character().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

$$(2309,18305,12799)$$ → $$(1,1,1)$$

## First values

 1 5 7 11 13 17 19 23 25 29 31 35 37 41 43 47 49 53 55 59 61 65 67 71 73 77 79 83 85 89 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 $$\Q$$