Properties

 Modulus $30$ Structure $$C_{2}\times C_{4}$$ Order $8$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(30)

pari: g = idealstar(,30,2)

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 = $\chi_{30}(11,\cdot)$, $\chi_{30}(7,\cdot)$

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 $$-1$$ $$1$$ $$7$$ $$11$$ $$13$$ $$17$$ $$19$$ $$23$$
$$\chi_{30}(1,\cdot)$$ 30.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{30}(7,\cdot)$$ 30.f 4 no $$-1$$ $$1$$ $$i$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$-i$$
$$\chi_{30}(11,\cdot)$$ 30.d 2 no $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$
$$\chi_{30}(13,\cdot)$$ 30.f 4 no $$-1$$ $$1$$ $$-i$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$i$$
$$\chi_{30}(17,\cdot)$$ 30.e 4 no $$1$$ $$1$$ $$i$$ $$-1$$ $$-i$$ $$-i$$ $$-1$$ $$i$$
$$\chi_{30}(19,\cdot)$$ 30.c 2 no $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$
$$\chi_{30}(23,\cdot)$$ 30.e 4 no $$1$$ $$1$$ $$-i$$ $$-1$$ $$i$$ $$i$$ $$-1$$ $$-i$$
$$\chi_{30}(29,\cdot)$$ 30.b 2 no $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$1$$