# 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(10003)

sage: chi = H[7809]

pari: [g,chi] = znchar(Mod(7809,10003))

## Basic properties

 Modulus: $$10003$$ Conductor: $$10003$$ sage: chi.conductor()  pari: znconreyconductor(g,chi) Order: $$3$$ sage: chi.multiplicative_order()  pari: charorder(g,chi) Real: no Primitive: yes 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 10003.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

$$(2864,2859)$$ → $$(e\left(\frac{1}{3}\right),e\left(\frac{2}{3}\right))$$

## First values

 $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$8$$ $$9$$ $$10$$ $$11$$ $$12$$ $$13$$ $$15$$ $$16$$ $$17$$ $$18$$ $$19$$ $$20$$ $$22$$ $$23$$ $$24$$ $$25$$ $$26$$ $$27$$ $$29$$ $$30$$ $$31$$ $$32$$ $$33$$ $$34$$ 1 1 $$e\left(\frac{1}{3}\right)$$ 1 $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ 1 $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ 1 1 $$e\left(\frac{2}{3}\right)$$ 1 $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ 1 $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ 1 $$e\left(\frac{2}{3}\right)$$ 1
 value at e.g. 2