# 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(10055)

sage: chi = H[10054]

pari: [g,chi] = znchar(Mod(10054,10055))

## Kronecker symbol representation

sage: kronecker_character(-10055)

pari: znchartokronecker(g,chi)

$$\displaystyle\left(\frac{-10055}{\bullet}\right)$$

## Basic properties

 sage: chi.conductor()  pari: znconreyconductor(g,chi) Modulus = 10055 Conductor = 10055 sage: chi.multiplicative_order()  pari: charorder(g,chi) Order = 2 Real = yes sage: chi.is_primitive()  pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization] Primitive = yes sage: chi.is_odd()  pari: zncharisodd(g,chi) Parity = odd

## Galois orbit

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

$$(3,4021)$$ → $$(1,-1)$$

## First values

 1 2 3 4 6 7 8 9 11 12 13 14 16 17 18 19 21 22 23 24 26 27 28 29 31 32 33 34 36 37 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 $$\Q$$