# Properties

 Modulus $184$ Structure $$C_{22}\times C_{2}\times C_{2}$$ Order $88$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(184)

pari: g = idealstar(,184,2)

## Character group

 sage: G.order()  pari: g.no Order = 88 sage: H.invariants()  pari: g.cyc Structure = $$C_{22}\times C_{2}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{184}(47,\cdot)$, $\chi_{184}(93,\cdot)$, $\chi_{184}(97,\cdot)$

## First 32 of 88 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$21$$
$$\chi_{184}(1,\cdot)$$ 184.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{184}(3,\cdot)$$ 184.k 22 yes $$-1$$ $$1$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{184}(5,\cdot)$$ 184.m 22 yes $$-1$$ $$1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{184}(7,\cdot)$$ 184.o 22 no $$1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{184}(9,\cdot)$$ 184.i 11 no $$1$$ $$1$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{184}(11,\cdot)$$ 184.j 22 yes $$1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{184}(13,\cdot)$$ 184.p 22 yes $$1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{184}(15,\cdot)$$ 184.o 22 no $$1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{184}(17,\cdot)$$ 184.l 22 no $$-1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{184}(19,\cdot)$$ 184.j 22 yes $$1$$ $$1$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{184}(21,\cdot)$$ 184.m 22 yes $$-1$$ $$1$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{184}(25,\cdot)$$ 184.i 11 no $$1$$ $$1$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{184}(27,\cdot)$$ 184.k 22 yes $$-1$$ $$1$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{184}(29,\cdot)$$ 184.p 22 yes $$1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{184}(31,\cdot)$$ 184.n 22 no $$-1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{184}(33,\cdot)$$ 184.l 22 no $$-1$$ $$1$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{184}(35,\cdot)$$ 184.k 22 yes $$-1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{184}(37,\cdot)$$ 184.m 22 yes $$-1$$ $$1$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{184}(39,\cdot)$$ 184.n 22 no $$-1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{184}(41,\cdot)$$ 184.i 11 no $$1$$ $$1$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{184}(43,\cdot)$$ 184.j 22 yes $$1$$ $$1$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{184}(45,\cdot)$$ 184.e 2 yes $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$
$$\chi_{184}(47,\cdot)$$ 184.d 2 no $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$
$$\chi_{184}(49,\cdot)$$ 184.i 11 no $$1$$ $$1$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{184}(51,\cdot)$$ 184.j 22 yes $$1$$ $$1$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{184}(53,\cdot)$$ 184.m 22 yes $$-1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{184}(55,\cdot)$$ 184.n 22 no $$-1$$ $$1$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{184}(57,\cdot)$$ 184.l 22 no $$-1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{184}(59,\cdot)$$ 184.k 22 yes $$-1$$ $$1$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{184}(61,\cdot)$$ 184.m 22 yes $$-1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{184}(63,\cdot)$$ 184.o 22 no $$1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{184}(65,\cdot)$$ 184.l 22 no $$-1$$ $$1$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$