# Properties

 Modulus $20$ Structure $$C_{2}\times C_{4}$$ Order $8$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(20)

pari: g = idealstar(,20,2)

## 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 = $\chi_{20}(11,\cdot)$, $\chi_{20}(17,\cdot)$

## 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 $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$
$$\chi_{20}(1,\cdot)$$ 20.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{20}(3,\cdot)$$ 20.e 4 yes $$1$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$-1$$ $$i$$ $$-i$$
$$\chi_{20}(7,\cdot)$$ 20.e 4 yes $$1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$i$$
$$\chi_{20}(9,\cdot)$$ 20.c 2 no $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$
$$\chi_{20}(11,\cdot)$$ 20.b 2 no $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$
$$\chi_{20}(13,\cdot)$$ 20.f 4 no $$-1$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$1$$ $$i$$ $$-i$$
$$\chi_{20}(17,\cdot)$$ 20.f 4 no $$-1$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$1$$ $$-i$$ $$i$$
$$\chi_{20}(19,\cdot)$$ 20.d 2 yes $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$