# Properties

 Modulus $92$ Structure $$C_{2}\times C_{22}$$ Order $44$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(92)

pari: g = idealstar(,92,2)

## Character group

 sage: G.order()  pari: g.no Order = 44 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{22}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{92}(47,\cdot)$, $\chi_{92}(5,\cdot)$

## First 32 of 44 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 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$13$$ $$15$$ $$17$$ $$19$$ $$21$$
$$\chi_{92}(1,\cdot)$$ 92.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{92}(3,\cdot)$$ 92.g 22 yes $$-1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{92}(5,\cdot)$$ 92.f 22 no $$-1$$ $$1$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{92}(7,\cdot)$$ 92.h 22 yes $$1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{92}(9,\cdot)$$ 92.e 11 no $$1$$ $$1$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{92}(11,\cdot)$$ 92.h 22 yes $$1$$ $$1$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{92}(13,\cdot)$$ 92.e 11 no $$1$$ $$1$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{92}(15,\cdot)$$ 92.h 22 yes $$1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{92}(17,\cdot)$$ 92.f 22 no $$-1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{92}(19,\cdot)$$ 92.h 22 yes $$1$$ $$1$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$
$$\chi_{92}(21,\cdot)$$ 92.f 22 no $$-1$$ $$1$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$
$$\chi_{92}(25,\cdot)$$ 92.e 11 no $$1$$ $$1$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$
$$\chi_{92}(27,\cdot)$$ 92.g 22 yes $$-1$$ $$1$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$
$$\chi_{92}(29,\cdot)$$ 92.e 11 no $$1$$ $$1$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$
$$\chi_{92}(31,\cdot)$$ 92.g 22 yes $$-1$$ $$1$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$
$$\chi_{92}(33,\cdot)$$ 92.f 22 no $$-1$$ $$1$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$
$$\chi_{92}(35,\cdot)$$ 92.g 22 yes $$-1$$ $$1$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$
$$\chi_{92}(37,\cdot)$$ 92.f 22 no $$-1$$ $$1$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$
$$\chi_{92}(39,\cdot)$$ 92.g 22 yes $$-1$$ $$1$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$
$$\chi_{92}(41,\cdot)$$ 92.e 11 no $$1$$ $$1$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$
$$\chi_{92}(43,\cdot)$$ 92.h 22 yes $$1$$ $$1$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$
$$\chi_{92}(45,\cdot)$$ 92.d 2 no $$-1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$
$$\chi_{92}(47,\cdot)$$ 92.c 2 no $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$ $$-1$$ $$1$$
$$\chi_{92}(49,\cdot)$$ 92.e 11 no $$1$$ $$1$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$
$$\chi_{92}(51,\cdot)$$ 92.h 22 yes $$1$$ $$1$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$
$$\chi_{92}(53,\cdot)$$ 92.f 22 no $$-1$$ $$1$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$
$$\chi_{92}(55,\cdot)$$ 92.g 22 yes $$-1$$ $$1$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$
$$\chi_{92}(57,\cdot)$$ 92.f 22 no $$-1$$ $$1$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{1}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$
$$\chi_{92}(59,\cdot)$$ 92.g 22 yes $$-1$$ $$1$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{7}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{1}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$
$$\chi_{92}(61,\cdot)$$ 92.f 22 no $$-1$$ $$1$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{8}{11}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{9}{22}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{1}{22}\right)$$
$$\chi_{92}(63,\cdot)$$ 92.h 22 yes $$1$$ $$1$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{7}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{2}{11}\right)$$ $$e\left(\frac{4}{11}\right)$$ $$e\left(\frac{5}{11}\right)$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{3}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$
$$\chi_{92}(65,\cdot)$$ 92.f 22 no $$-1$$ $$1$$ $$e\left(\frac{10}{11}\right)$$ $$e\left(\frac{15}{22}\right)$$ $$e\left(\frac{21}{22}\right)$$ $$e\left(\frac{9}{11}\right)$$ $$e\left(\frac{3}{22}\right)$$ $$e\left(\frac{6}{11}\right)$$ $$e\left(\frac{13}{22}\right)$$ $$e\left(\frac{17}{22}\right)$$ $$e\left(\frac{5}{22}\right)$$ $$e\left(\frac{19}{22}\right)$$