# Properties

 Modulus $16$ Structure $$C_{2}\times C_{4}$$ Order $8$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(16)

pari: g = idealstar(,16,2)

## Character group

 sage: G.order()  pari: g.no Order = 8 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{4}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{16}(15,\cdot)$, $\chi_{16}(5,\cdot)$

## 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$
$$\chi_{16}(1,\cdot)$$ 16.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{16}(3,\cdot)$$ 16.f 4 yes $$-1$$ $$1$$ $$-i$$ $$-i$$ $$1$$ $$-1$$ $$i$$ $$i$$
$$\chi_{16}(5,\cdot)$$ 16.e 4 yes $$1$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$-1$$ $$i$$ $$-i$$
$$\chi_{16}(7,\cdot)$$ 16.d 2 no $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$
$$\chi_{16}(9,\cdot)$$ 16.b 2 no $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$
$$\chi_{16}(11,\cdot)$$ 16.f 4 yes $$-1$$ $$1$$ $$i$$ $$i$$ $$1$$ $$-1$$ $$-i$$ $$-i$$
$$\chi_{16}(13,\cdot)$$ 16.e 4 yes $$1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$i$$
$$\chi_{16}(15,\cdot)$$ 16.c 2 no $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$