# Properties

 Modulus $1584$ Structure $$C_{2}\times C_{2}\times C_{2}\times C_{60}$$ Order $480$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1584)

pari: g = idealstar(,1584,2)

## Character group

 sage: G.order()  pari: g.no Order = 480 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{2}\times C_{2}\times C_{60}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1584}(991,\cdot)$, $\chi_{1584}(1189,\cdot)$, $\chi_{1584}(353,\cdot)$, $\chi_{1584}(145,\cdot)$

## First 32 of 480 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 $$-1$$ $$1$$ $$5$$ $$7$$ $$13$$ $$17$$ $$19$$ $$23$$ $$25$$ $$29$$ $$31$$ $$35$$
$$\chi_{1584}(1,\cdot)$$ 1584.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1584}(5,\cdot)$$ 1584.dn 60 yes $$-1$$ $$1$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{13}{20}\right)$$
$$\chi_{1584}(7,\cdot)$$ 1584.dc 30 no $$1$$ $$1$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{1584}(13,\cdot)$$ 1584.dr 60 yes $$-1$$ $$1$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{1}{60}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{1584}(17,\cdot)$$ 1584.cd 10 no $$1$$ $$1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$-1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1584}(19,\cdot)$$ 1584.cu 20 no $$1$$ $$1$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{1584}(23,\cdot)$$ 1584.bg 6 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$
$$\chi_{1584}(25,\cdot)$$ 1584.da 30 no $$1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{1584}(29,\cdot)$$ 1584.dp 60 yes $$1$$ $$1$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{9}{20}\right)$$
$$\chi_{1584}(31,\cdot)$$ 1584.dg 30 no $$-1$$ $$1$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{1}{10}\right)$$
$$\chi_{1584}(35,\cdot)$$ 1584.cs 20 no $$-1$$ $$1$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$-1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{1584}(37,\cdot)$$ 1584.cr 20 no $$1$$ $$1$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$-1$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{1584}(41,\cdot)$$ 1584.df 30 no $$1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$
$$\chi_{1584}(43,\cdot)$$ 1584.cj 12 yes $$1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$-1$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-i$$
$$\chi_{1584}(47,\cdot)$$ 1584.cy 30 no $$1$$ $$1$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{1584}(49,\cdot)$$ 1584.cm 15 no $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{2}{15}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$
$$\chi_{1584}(53,\cdot)$$ 1584.ct 20 no $$-1$$ $$1$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{1584}(59,\cdot)$$ 1584.dq 60 yes $$1$$ $$1$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{1584}(61,\cdot)$$ 1584.dr 60 yes $$-1$$ $$1$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{1584}(65,\cdot)$$ 1584.bn 6 no $$1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$1$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$
$$\chi_{1584}(67,\cdot)$$ 1584.ch 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$1$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$
$$\chi_{1584}(71,\cdot)$$ 1584.bu 10 no $$1$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$1$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{1584}(73,\cdot)$$ 1584.ca 10 no $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{1}{5}\right)$$
$$\chi_{1584}(79,\cdot)$$ 1584.dh 30 no $$1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{13}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{1584}(83,\cdot)$$ 1584.dk 60 yes $$-1$$ $$1$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{3}{20}\right)$$
$$\chi_{1584}(85,\cdot)$$ 1584.dr 60 yes $$-1$$ $$1$$ $$e\left(\frac{7}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{1584}(89,\cdot)$$ 1584.n 2 no $$-1$$ $$1$$ $$1$$ $$1$$ $$-1$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1584}(91,\cdot)$$ 1584.co 20 no $$-1$$ $$1$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$1$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{1584}(95,\cdot)$$ 1584.cz 30 no $$-1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{10}\right)$$
$$\chi_{1584}(97,\cdot)$$ 1584.cm 15 no $$1$$ $$1$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{1584}(101,\cdot)$$ 1584.dp 60 yes $$1$$ $$1$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{11}{60}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{20}\right)$$
$$\chi_{1584}(103,\cdot)$$ 1584.cv 30 no $$-1$$ $$1$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$