# Properties

 Modulus $7$ Structure $$C_{6}$$ Order $6$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(7)

pari: g = idealstar(,7,2)

## 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 = $\chi_{7}(3,\cdot)$

## 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$
$$\chi_{7}(1,\cdot)$$ 7.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{7}(2,\cdot)$$ 7.c 3 yes $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{7}(3,\cdot)$$ 7.d 6 yes $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{7}(4,\cdot)$$ 7.c 3 yes $$1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{7}(5,\cdot)$$ 7.d 6 yes $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{7}(6,\cdot)$$ 7.b 2 yes $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$