# Properties

 Modulus $1287$ Structure $$C_{60}\times C_{6}\times C_{2}$$ Order $720$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1287)

pari: g = idealstar(,1287,2)

## Character group

 sage: G.order()  pari: g.no Order = 720 sage: H.invariants()  pari: g.cyc Structure = $$C_{60}\times C_{6}\times C_{2}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1287}(1145,\cdot)$, $\chi_{1287}(937,\cdot)$, $\chi_{1287}(496,\cdot)$

## First 32 of 720 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$14$$ $$16$$ $$17$$ $$19$$
$$\chi_{1287}(1,\cdot)$$ 1287.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1287}(2,\cdot)$$ 1287.em 60 yes $$-1$$ $$1$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{43}{60}\right)$$
$$\chi_{1287}(4,\cdot)$$ 1287.dw 30 yes $$1$$ $$1$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$
$$\chi_{1287}(5,\cdot)$$ 1287.ea 60 yes $$1$$ $$1$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$-1$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{1287}(7,\cdot)$$ 1287.ee 60 yes $$1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{41}{60}\right)$$
$$\chi_{1287}(8,\cdot)$$ 1287.cx 20 no $$-1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{1287}(10,\cdot)$$ 1287.v 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1287}(14,\cdot)$$ 1287.df 30 no $$-1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1287}(16,\cdot)$$ 1287.cq 15 yes $$1$$ $$1$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{1287}(17,\cdot)$$ 1287.dc 30 no $$1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{1287}(19,\cdot)$$ 1287.ec 60 no $$1$$ $$1$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{59}{60}\right)$$
$$\chi_{1287}(20,\cdot)$$ 1287.eh 60 yes $$1$$ $$1$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{23}{60}\right)$$
$$\chi_{1287}(23,\cdot)$$ 1287.x 6 no $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1287}(25,\cdot)$$ 1287.de 30 yes $$1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{1287}(28,\cdot)$$ 1287.ec 60 no $$1$$ $$1$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{60}\right)$$
$$\chi_{1287}(29,\cdot)$$ 1287.cy 30 yes $$1$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$
$$\chi_{1287}(31,\cdot)$$ 1287.eb 60 yes $$-1$$ $$1$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$-1$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{1287}(32,\cdot)$$ 1287.cb 12 yes $$-1$$ $$1$$ $$-i$$ $$-1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{1287}(34,\cdot)$$ 1287.ce 12 no $$-1$$ $$1$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$-i$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$i$$
$$\chi_{1287}(35,\cdot)$$ 1287.du 30 no $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{1287}(37,\cdot)$$ 1287.eg 60 no $$-1$$ $$1$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{31}{60}\right)$$
$$\chi_{1287}(38,\cdot)$$ 1287.ds 30 yes $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{1287}(40,\cdot)$$ 1287.di 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$-1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{1287}(41,\cdot)$$ 1287.ed 60 yes $$-1$$ $$1$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$
$$\chi_{1287}(43,\cdot)$$ 1287.bc 6 yes $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1287}(46,\cdot)$$ 1287.ec 60 no $$1$$ $$1$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{53}{60}\right)$$
$$\chi_{1287}(47,\cdot)$$ 1287.ea 60 yes $$1$$ $$1$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$-1$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$
$$\chi_{1287}(49,\cdot)$$ 1287.dg 30 yes $$1$$ $$1$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{1287}(50,\cdot)$$ 1287.ed 60 yes $$-1$$ $$1$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$
$$\chi_{1287}(53,\cdot)$$ 1287.by 10 no $$-1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{1287}(56,\cdot)$$ 1287.x 6 no $$-1$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1287}(58,\cdot)$$ 1287.ep 60 yes $$-1$$ $$1$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{29}{60}\right)$$