# Properties

 Modulus $1131$ Structure $$C_{2}\times C_{4}\times C_{84}$$ Order $672$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1131)

pari: g = idealstar(,1131,2)

## Character group

 sage: G.order()  pari: g.no Order = 672 sage: H.invariants()  pari: g.cyc Structure = $$C_{2}\times C_{4}\times C_{84}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1131}(755,\cdot)$, $\chi_{1131}(262,\cdot)$, $\chi_{1131}(118,\cdot)$

## First 32 of 672 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 $$-1$$ $$1$$ $$2$$ $$4$$ $$5$$ $$7$$ $$8$$ $$10$$ $$11$$ $$14$$ $$16$$ $$17$$
$$\chi_{1131}(1,\cdot)$$ 1131.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1131}(2,\cdot)$$ 1131.da 84 yes $$-1$$ $$1$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{1131}(4,\cdot)$$ 1131.co 42 no $$1$$ $$1$$ $$e\left(\frac{5}{21}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1131}(5,\cdot)$$ 1131.cb 28 yes $$1$$ $$1$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$-1$$
$$\chi_{1131}(7,\cdot)$$ 1131.cu 84 no $$-1$$ $$1$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1131}(8,\cdot)$$ 1131.by 28 yes $$-1$$ $$1$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$i$$
$$\chi_{1131}(10,\cdot)$$ 1131.cs 84 no $$-1$$ $$1$$ $$e\left(\frac{55}{84}\right)$$ $$e\left(\frac{13}{42}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{19}{84}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{1131}(11,\cdot)$$ 1131.cr 84 yes $$-1$$ $$1$$ $$e\left(\frac{41}{42}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{11}{84}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{1131}(14,\cdot)$$ 1131.bz 28 no $$1$$ $$1$$ $$e\left(\frac{27}{28}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$i$$
$$\chi_{1131}(16,\cdot)$$ 1131.bw 21 no $$1$$ $$1$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{13}{21}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1131}(17,\cdot)$$ 1131.bg 12 yes $$1$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$-1$$ $$e\left(\frac{5}{6}\right)$$ $$i$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{1131}(19,\cdot)$$ 1131.cq 84 no $$1$$ $$1$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{37}{84}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{47}{84}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{20}{21}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{1131}(20,\cdot)$$ 1131.cv 84 yes $$1$$ $$1$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{23}{42}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{31}{84}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1131}(22,\cdot)$$ 1131.ck 42 no $$1$$ $$1$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{10}{21}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{1}{42}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{5}{6}\right)$$
$$\chi_{1131}(23,\cdot)$$ 1131.cn 42 yes $$-1$$ $$1$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{31}{42}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1131}(25,\cdot)$$ 1131.bv 14 no $$1$$ $$1$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$1$$
$$\chi_{1131}(28,\cdot)$$ 1131.bh 12 no $$-1$$ $$1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1131}(31,\cdot)$$ 1131.ci 28 no $$1$$ $$1$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$i$$
$$\chi_{1131}(32,\cdot)$$ 1131.da 84 yes $$-1$$ $$1$$ $$e\left(\frac{2}{21}\right)$$ $$e\left(\frac{4}{21}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{61}{84}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{23}{84}\right)$$ $$e\left(\frac{37}{42}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{1131}(34,\cdot)$$ 1131.cc 28 no $$-1$$ $$1$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{5}{28}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$1$$
$$\chi_{1131}(35,\cdot)$$ 1131.cp 42 yes $$-1$$ $$1$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{19}{21}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{25}{42}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{1}{3}\right)$$
$$\chi_{1131}(37,\cdot)$$ 1131.cq 84 no $$1$$ $$1$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{25}{84}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{1131}(38,\cdot)$$ 1131.bt 14 yes $$-1$$ $$1$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{13}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$1$$
$$\chi_{1131}(40,\cdot)$$ 1131.cf 28 no $$-1$$ $$1$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{9}{28}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$-i$$
$$\chi_{1131}(41,\cdot)$$ 1131.bn 12 yes $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-i$$ $$e\left(\frac{11}{12}\right)$$ $$-1$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{11}{12}\right)$$
$$\chi_{1131}(43,\cdot)$$ 1131.cs 84 no $$-1$$ $$1$$ $$e\left(\frac{53}{84}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{5}{7}\right)$$ $$e\left(\frac{17}{42}\right)$$ $$e\left(\frac{25}{28}\right)$$ $$e\left(\frac{29}{84}\right)$$ $$e\left(\frac{65}{84}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{11}{21}\right)$$ $$e\left(\frac{1}{12}\right)$$
$$\chi_{1131}(44,\cdot)$$ 1131.ch 28 yes $$-1$$ $$1$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{23}{28}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{19}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$e\left(\frac{1}{28}\right)$$ $$e\left(\frac{6}{7}\right)$$ $$i$$
$$\chi_{1131}(46,\cdot)$$ 1131.bd 12 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$-i$$ $$e\left(\frac{1}{12}\right)$$ $$1$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{1131}(47,\cdot)$$ 1131.by 28 yes $$-1$$ $$1$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{2}{7}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{13}{28}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{15}{28}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{17}{28}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$i$$
$$\chi_{1131}(49,\cdot)$$ 1131.cl 42 no $$1$$ $$1$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{19}{42}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{1}{21}\right)$$ $$e\left(\frac{11}{42}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1131}(50,\cdot)$$ 1131.cr 84 yes $$-1$$ $$1$$ $$e\left(\frac{29}{42}\right)$$ $$e\left(\frac{8}{21}\right)$$ $$e\left(\frac{3}{28}\right)$$ $$e\left(\frac{59}{84}\right)$$ $$e\left(\frac{1}{14}\right)$$ $$e\left(\frac{67}{84}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{11}{28}\right)$$ $$e\left(\frac{16}{21}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{1131}(53,\cdot)$$ 1131.bu 14 no $$-1$$ $$1$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{11}{14}\right)$$ $$e\left(\frac{3}{7}\right)$$ $$e\left(\frac{5}{14}\right)$$ $$e\left(\frac{4}{7}\right)$$ $$e\left(\frac{9}{14}\right)$$ $$e\left(\frac{3}{14}\right)$$ $$e\left(\frac{1}{7}\right)$$ $$-1$$