# Properties

 Modulus $183$ Structure $$C_{60}\times C_{2}$$ Order $120$

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(183)

pari: g = idealstar(,183,2)

## Character group

 sage: G.order()  pari: g.no Order = 120 sage: H.invariants()  pari: g.cyc Structure = $$C_{60}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{183}(62,\cdot)$, $\chi_{183}(124,\cdot)$

## First 32 of 120 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$11$$ $$13$$ $$14$$ $$16$$
$$\chi_{183}(1,\cdot)$$ 183.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{183}(2,\cdot)$$ 183.x 60 yes $$1$$ $$1$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{183}(4,\cdot)$$ 183.u 30 no $$1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{183}(5,\cdot)$$ 183.v 30 yes $$-1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{183}(7,\cdot)$$ 183.w 60 no $$-1$$ $$1$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{183}(8,\cdot)$$ 183.r 20 yes $$1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$i$$ $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{183}(10,\cdot)$$ 183.w 60 no $$-1$$ $$1$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{183}(11,\cdot)$$ 183.g 4 yes $$1$$ $$1$$ $$-i$$ $$-1$$ $$1$$ $$i$$ $$i$$ $$-i$$ $$i$$ $$1$$ $$1$$ $$1$$
$$\chi_{183}(13,\cdot)$$ 183.e 3 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{183}(14,\cdot)$$ 183.i 6 yes $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{183}(16,\cdot)$$ 183.q 15 no $$1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{183}(17,\cdot)$$ 183.x 60 yes $$1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{183}(19,\cdot)$$ 183.u 30 no $$1$$ $$1$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{183}(20,\cdot)$$ 183.n 10 yes $$-1$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$-1$$ $$1$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{183}(22,\cdot)$$ 183.q 15 no $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$
$$\chi_{183}(23,\cdot)$$ 183.r 20 yes $$1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$-i$$ $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{183}(25,\cdot)$$ 183.q 15 no $$1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{183}(26,\cdot)$$ 183.x 60 yes $$1$$ $$1$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{183}(28,\cdot)$$ 183.s 20 no $$-1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$-i$$ $$1$$ $$-1$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{183}(29,\cdot)$$ 183.o 12 yes $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{183}(31,\cdot)$$ 183.w 60 no $$-1$$ $$1$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{183}(32,\cdot)$$ 183.o 12 yes $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{183}(34,\cdot)$$ 183.h 5 no $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$1$$ $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{183}(35,\cdot)$$ 183.x 60 yes $$1$$ $$1$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{183}(37,\cdot)$$ 183.s 20 no $$-1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$-i$$ $$1$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{183}(38,\cdot)$$ 183.r 20 yes $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$i$$ $$1$$ $$1$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{183}(40,\cdot)$$ 183.p 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{183}(41,\cdot)$$ 183.l 10 yes $$-1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$1$$ $$1$$ $$-1$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{183}(43,\cdot)$$ 183.w 60 no $$-1$$ $$1$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{183}(44,\cdot)$$ 183.x 60 yes $$1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{15}\right)$$
$$\chi_{183}(46,\cdot)$$ 183.u 30 no $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{183}(47,\cdot)$$ 183.k 6 yes $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$