# Properties

 Modulus 96 Structure $$C_{8}\times C_{2}\times C_{2}$$ Order 32

Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
sage: H = DirichletGroup_conrey(96)
pari: g = idealstar(,96,2)

## Character group

 sage: G.order() pari: g.no Order = 32 sage: H.invariants() pari: g.cyc Structure = $$C_{8}\times C_{2}\times C_{2}$$ sage: H.gens() pari: g.gen Generators = $\chi_{96}(37,\cdot)$, $\chi_{96}(65,\cdot)$, $\chi_{96}(31,\cdot)$

## First 32 of 32 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 5 7 11 13 17 19 23 25 29 31
$$\chi_{96}(1,\cdot)$$ 96.a 1 No $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{96}(5,\cdot)$$ 96.p 8 Yes $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$1$$
$$\chi_{96}(7,\cdot)$$ 96.l 4 No $$-1$$ $$1$$ $$i$$ $$1$$ $$-i$$ $$-i$$ $$1$$ $$i$$ $$1$$ $$-1$$ $$-i$$ $$-1$$
$$\chi_{96}(11,\cdot)$$ 96.o 8 Yes $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$
$$\chi_{96}(13,\cdot)$$ 96.n 8 No $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$1$$
$$\chi_{96}(17,\cdot)$$ 96.h 2 No $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$1$$
$$\chi_{96}(19,\cdot)$$ 96.m 8 No $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$
$$\chi_{96}(23,\cdot)$$ 96.k 4 No $$1$$ $$1$$ $$i$$ $$1$$ $$-i$$ $$i$$ $$-1$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$-1$$
$$\chi_{96}(25,\cdot)$$ 96.j 4 No $$1$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$-i$$ $$1$$ $$-i$$ $$-1$$ $$-1$$ $$-i$$ $$1$$
$$\chi_{96}(29,\cdot)$$ 96.p 8 Yes $$-1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$1$$
$$\chi_{96}(31,\cdot)$$ 96.g 2 No $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$
$$\chi_{96}(35,\cdot)$$ 96.o 8 Yes $$1$$ $$1$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$
$$\chi_{96}(37,\cdot)$$ 96.n 8 No $$1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$1$$
$$\chi_{96}(41,\cdot)$$ 96.i 4 No $$-1$$ $$1$$ $$i$$ $$-1$$ $$i$$ $$i$$ $$-1$$ $$i$$ $$1$$ $$-1$$ $$-i$$ $$1$$
$$\chi_{96}(43,\cdot)$$ 96.m 8 No $$-1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{7}{8}\right)$$ $$i$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$
$$\chi_{96}(47,\cdot)$$ 96.f 2 No $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$-1$$
$$\chi_{96}(49,\cdot)$$ 96.d 2 No $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$
$$\chi_{96}(53,\cdot)$$ 96.p 8 Yes $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$1$$
$$\chi_{96}(55,\cdot)$$ 96.l 4 No $$-1$$ $$1$$ $$-i$$ $$1$$ $$i$$ $$i$$ $$1$$ $$-i$$ $$1$$ $$-1$$ $$i$$ $$-1$$
$$\chi_{96}(59,\cdot)$$ 96.o 8 Yes $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$-i$$ $$e\left(\frac{5}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$
$$\chi_{96}(61,\cdot)$$ 96.n 8 No $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$1$$
$$\chi_{96}(65,\cdot)$$ 96.e 2 No $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$
$$\chi_{96}(67,\cdot)$$ 96.m 8 No $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{5}{8}\right)$$ $$-1$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$
$$\chi_{96}(71,\cdot)$$ 96.k 4 No $$1$$ $$1$$ $$-i$$ $$1$$ $$i$$ $$-i$$ $$-1$$ $$i$$ $$-1$$ $$-1$$ $$i$$ $$-1$$
$$\chi_{96}(73,\cdot)$$ 96.j 4 No $$1$$ $$1$$ $$-i$$ $$-1$$ $$-i$$ $$i$$ $$1$$ $$i$$ $$-1$$ $$-1$$ $$i$$ $$1$$
$$\chi_{96}(77,\cdot)$$ 96.p 8 Yes $$-1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$e\left(\frac{7}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$1$$
$$\chi_{96}(79,\cdot)$$ 96.b 2 No $$-1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$
$$\chi_{96}(83,\cdot)$$ 96.o 8 Yes $$1$$ $$1$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$e\left(\frac{1}{8}\right)$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$-1$$
$$\chi_{96}(85,\cdot)$$ 96.n 8 No $$1$$ $$1$$ $$e\left(\frac{5}{8}\right)$$ $$i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$-i$$ $$i$$ $$e\left(\frac{7}{8}\right)$$ $$1$$
$$\chi_{96}(89,\cdot)$$ 96.i 4 No $$-1$$ $$1$$ $$-i$$ $$-1$$ $$-i$$ $$-i$$ $$-1$$ $$-i$$ $$1$$ $$-1$$ $$i$$ $$1$$
$$\chi_{96}(91,\cdot)$$ 96.m 8 No $$-1$$ $$1$$ $$e\left(\frac{1}{8}\right)$$ $$-i$$ $$e\left(\frac{1}{8}\right)$$ $$e\left(\frac{7}{8}\right)$$ $$-1$$ $$e\left(\frac{3}{8}\right)$$ $$i$$ $$i$$ $$e\left(\frac{3}{8}\right)$$ $$-1$$
$$\chi_{96}(95,\cdot)$$ 96.c 2 No $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$