# Properties

 Modulus $232$ Structure $$C_{28}\times C_{2}\times C_{2}$$ Order $112$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(232)

pari: g = idealstar(,232,2)

## Character group

 sage: G.order()  pari: g.no Order = 112 sage: H.invariants()  pari: g.cyc Structure = $$C_{28}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{232}(175,\cdot)$, $\chi_{232}(117,\cdot)$, $\chi_{232}(89,\cdot)$

## First 32 of 112 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$21$$
$$\chi_{232}(1,\cdot)$$ 232.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{232}(3,\cdot)$$ 232.v 28 yes $$1$$ $$1$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$-i$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{15}{28}\right)$$
$$\chi_{232}(5,\cdot)$$ 232.o 14 yes $$1$$ $$1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$-1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$
$$\chi_{232}(7,\cdot)$$ 232.r 14 no $$-1$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$1$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$
$$\chi_{232}(9,\cdot)$$ 232.q 14 no $$1$$ $$1$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$-1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$
$$\chi_{232}(11,\cdot)$$ 232.v 28 yes $$1$$ $$1$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$-i$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$
$$\chi_{232}(13,\cdot)$$ 232.o 14 yes $$1$$ $$1$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$-1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$
$$\chi_{232}(15,\cdot)$$ 232.x 28 no $$1$$ $$1$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$i$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$
$$\chi_{232}(17,\cdot)$$ 232.j 4 no $$-1$$ $$1$$ $$-i$$ $$-1$$ $$1$$ $$-1$$ $$-i$$ $$-1$$ $$i$$ $$-i$$ $$-i$$ $$-i$$
$$\chi_{232}(19,\cdot)$$ 232.v 28 yes $$1$$ $$1$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$-i$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$
$$\chi_{232}(21,\cdot)$$ 232.u 28 yes $$-1$$ $$1$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$-i$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{23}{28}\right)$$
$$\chi_{232}(23,\cdot)$$ 232.r 14 no $$-1$$ $$1$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$
$$\chi_{232}(25,\cdot)$$ 232.m 7 no $$1$$ $$1$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$
$$\chi_{232}(27,\cdot)$$ 232.v 28 yes $$1$$ $$1$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$i$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{17}{28}\right)$$
$$\chi_{232}(31,\cdot)$$ 232.x 28 no $$1$$ $$1$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$-i$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{17}{28}\right)$$
$$\chi_{232}(33,\cdot)$$ 232.q 14 no $$1$$ $$1$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$-1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$
$$\chi_{232}(35,\cdot)$$ 232.t 14 yes $$-1$$ $$1$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$-1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$
$$\chi_{232}(37,\cdot)$$ 232.u 28 yes $$-1$$ $$1$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$i$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$
$$\chi_{232}(39,\cdot)$$ 232.x 28 no $$1$$ $$1$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$i$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{27}{28}\right)$$
$$\chi_{232}(41,\cdot)$$ 232.j 4 no $$-1$$ $$1$$ $$i$$ $$-1$$ $$1$$ $$-1$$ $$i$$ $$-1$$ $$-i$$ $$i$$ $$i$$ $$i$$
$$\chi_{232}(43,\cdot)$$ 232.v 28 yes $$1$$ $$1$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$-i$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{11}{28}\right)$$
$$\chi_{232}(45,\cdot)$$ 232.s 14 yes $$1$$ $$1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$1$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$
$$\chi_{232}(47,\cdot)$$ 232.x 28 no $$1$$ $$1$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$i$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$
$$\chi_{232}(49,\cdot)$$ 232.m 7 no $$1$$ $$1$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$1$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$
$$\chi_{232}(51,\cdot)$$ 232.t 14 yes $$-1$$ $$1$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$-1$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{2}{7}\right)$$
$$\chi_{232}(53,\cdot)$$ 232.s 14 yes $$1$$ $$1$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$1$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$
$$\chi_{232}(55,\cdot)$$ 232.x 28 no $$1$$ $$1$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$i$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{15}{28}\right)$$
$$\chi_{232}(57,\cdot)$$ 232.e 2 no $$1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$
$$\chi_{232}(59,\cdot)$$ 232.f 2 no $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$-1$$
$$\chi_{232}(61,\cdot)$$ 232.u 28 yes $$-1$$ $$1$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$-i$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{15}{28}\right)$$
$$\chi_{232}(63,\cdot)$$ 232.n 14 no $$-1$$ $$1$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$-1$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$
$$\chi_{232}(65,\cdot)$$ 232.m 7 no $$1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$1$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$