# Properties

 Modulus $18$ Structure $$C_{6}$$ Order $6$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(18)

pari: g = idealstar(,18,2)

## Character group

 sage: G.order()  pari: g.no Order = 6 sage: H.invariants()  pari: g.cyc Structure = $$C_{6}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{18}(11,\cdot)$

## Characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive $$-1$$ $$1$$ $$5$$ $$7$$ $$11$$ $$13$$
$$\chi_{18}(1,\cdot)$$ 18.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{18}(5,\cdot)$$ 18.d 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{18}(7,\cdot)$$ 18.c 3 no $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{18}(11,\cdot)$$ 18.d 6 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{18}(13,\cdot)$$ 18.c 3 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{18}(17,\cdot)$$ 18.b 2 no $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$