# Properties

 Modulus 60 Structure $$C_{4}\times C_{2}\times C_{2}$$ Order 16

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(60)
pari: g = idealstar(,60,2)

## Character group

 sage: G.order() pari: g.no Order = 16 sage: H.invariants() pari: g.cyc Structure = $$C_{4}\times C_{2}\times C_{2}$$ sage: H.gens() pari: g.gen Generators = $\chi_{60}(37,\cdot)$, $\chi_{60}(41,\cdot)$, $\chi_{60}(31,\cdot)$

## 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 7 11 13 17 19 23 29 31 37 41
$$\chi_{60}(1,\cdot)$$ 60.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{60}(7,\cdot)$$ 60.j 4 No $$1$$ $$1$$ $$-i$$ $$-1$$ $$-i$$ $$i$$ $$1$$ $$i$$ $$-1$$ $$-1$$ $$i$$ $$1$$
$$\chi_{60}(11,\cdot)$$ 60.e 2 No $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$
$$\chi_{60}(13,\cdot)$$ 60.k 4 No $$-1$$ $$1$$ $$-i$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$i$$ $$-1$$ $$1$$ $$-i$$ $$1$$
$$\chi_{60}(17,\cdot)$$ 60.i 4 No $$1$$ $$1$$ $$i$$ $$-1$$ $$-i$$ $$-i$$ $$-1$$ $$i$$ $$1$$ $$1$$ $$i$$ $$-1$$
$$\chi_{60}(19,\cdot)$$ 60.f 2 No $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$
$$\chi_{60}(23,\cdot)$$ 60.l 4 Yes $$-1$$ $$1$$ $$i$$ $$1$$ $$i$$ $$i$$ $$1$$ $$i$$ $$1$$ $$-1$$ $$-i$$ $$-1$$
$$\chi_{60}(29,\cdot)$$ 60.b 2 No $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$
$$\chi_{60}(31,\cdot)$$ 60.c 2 No $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$
$$\chi_{60}(37,\cdot)$$ 60.k 4 No $$-1$$ $$1$$ $$i$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$-i$$ $$-1$$ $$1$$ $$i$$ $$1$$
$$\chi_{60}(41,\cdot)$$ 60.g 2 No $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$
$$\chi_{60}(43,\cdot)$$ 60.j 4 No $$1$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$-i$$ $$1$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$1$$
$$\chi_{60}(47,\cdot)$$ 60.l 4 Yes $$-1$$ $$1$$ $$-i$$ $$1$$ $$-i$$ $$-i$$ $$1$$ $$-i$$ $$1$$ $$-1$$ $$i$$ $$-1$$
$$\chi_{60}(49,\cdot)$$ 60.d 2 No $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$
$$\chi_{60}(53,\cdot)$$ 60.i 4 No $$1$$ $$1$$ $$-i$$ $$-1$$ $$i$$ $$i$$ $$-1$$ $$-i$$ $$1$$ $$1$$ $$-i$$ $$-1$$
$$\chi_{60}(59,\cdot)$$ 60.h 2 Yes $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$