# Properties

 Modulus 15 Structure $$C_{4}\times C_{2}$$ Order 8

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed

sage: H = DirichletGroup_conrey(15)

pari: g = idealstar(,15,2)

## Character group

 sage: G.order()  pari: g.no Order = 8 sage: H.invariants()  pari: g.cyc Structure = $$C_{4}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{15}(7,\cdot)$, $\chi_{15}(11,\cdot)$

## 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.

orbit label order primitive -1 1 2 4 7 8 11 13
$$\chi_{15}(1,\cdot)$$ 15.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{15}(2,\cdot)$$ 15.e 4 Yes $$1$$ $$1$$ $$-i$$ $$-1$$ $$i$$ $$i$$ $$-1$$ $$-i$$
$$\chi_{15}(4,\cdot)$$ 15.b 2 No $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$
$$\chi_{15}(7,\cdot)$$ 15.f 4 No $$-1$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$-i$$ $$1$$ $$-i$$
$$\chi_{15}(8,\cdot)$$ 15.e 4 Yes $$1$$ $$1$$ $$i$$ $$-1$$ $$-i$$ $$-i$$ $$-1$$ $$i$$
$$\chi_{15}(11,\cdot)$$ 15.c 2 No $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$
$$\chi_{15}(13,\cdot)$$ 15.f 4 No $$-1$$ $$1$$ $$-i$$ $$-1$$ $$-i$$ $$i$$ $$1$$ $$i$$
$$\chi_{15}(14,\cdot)$$ 15.d 2 Yes $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$