Properties

 Modulus $1183$ Structure $$C_{156}\times C_{6}$$ Order $936$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1183)

pari: g = idealstar(,1183,2)

Character group

 sage: G.order()  pari: g.no Order = 936 sage: H.invariants()  pari: g.cyc Structure = $$C_{156}\times C_{6}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1183}(339,\cdot)$, $\chi_{1183}(1016,\cdot)$

First 32 of 936 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 $$-1$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$8$$ $$9$$ $$10$$ $$11$$ $$12$$
$$\chi_{1183}(1,\cdot)$$ 1183.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1183}(2,\cdot)$$ 1183.cg 156 yes $$-1$$ $$1$$ $$e\left(\frac{35}{52}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{113}{156}\right)$$ $$e\left(\frac{125}{156}\right)$$ $$e\left(\frac{1}{52}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{155}{156}\right)$$ $$e\left(\frac{37}{78}\right)$$
$$\chi_{1183}(3,\cdot)$$ 1183.bx 78 yes $$-1$$ $$1$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{77}{78}\right)$$
$$\chi_{1183}(4,\cdot)$$ 1183.bz 78 yes $$1$$ $$1$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{47}{78}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{37}{39}\right)$$
$$\chi_{1183}(5,\cdot)$$ 1183.cc 156 yes $$1$$ $$1$$ $$e\left(\frac{113}{156}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{107}{156}\right)$$ $$e\left(\frac{37}{52}\right)$$ $$e\left(\frac{9}{52}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{43}{156}\right)$$ $$e\left(\frac{17}{39}\right)$$
$$\chi_{1183}(6,\cdot)$$ 1183.cb 156 yes $$1$$ $$1$$ $$e\left(\frac{125}{156}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{47}{78}\right)$$ $$e\left(\frac{37}{52}\right)$$ $$e\left(\frac{103}{156}\right)$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{83}{156}\right)$$ $$e\left(\frac{6}{13}\right)$$
$$\chi_{1183}(8,\cdot)$$ 1183.bm 52 no $$-1$$ $$1$$ $$e\left(\frac{1}{52}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{1}{26}\right)$$ $$e\left(\frac{9}{52}\right)$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{3}{52}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{11}{26}\right)$$
$$\chi_{1183}(9,\cdot)$$ 1183.bj 39 yes $$1$$ $$1$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{38}{39}\right)$$
$$\chi_{1183}(10,\cdot)$$ 1183.bu 78 yes $$-1$$ $$1$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{71}{78}\right)$$
$$\chi_{1183}(11,\cdot)$$ 1183.ca 156 yes $$-1$$ $$1$$ $$e\left(\frac{155}{156}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{43}{156}\right)$$ $$e\left(\frac{83}{156}\right)$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{35}{52}\right)$$ $$e\left(\frac{41}{78}\right)$$
$$\chi_{1183}(12,\cdot)$$ 1183.br 78 yes $$-1$$ $$1$$ $$e\left(\frac{37}{78}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{71}{78}\right)$$ $$e\left(\frac{41}{78}\right)$$ $$e\left(\frac{73}{78}\right)$$
$$\chi_{1183}(15,\cdot)$$ 1183.cf 156 no $$-1$$ $$1$$ $$e\left(\frac{133}{156}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{55}{78}\right)$$ $$e\left(\frac{35}{52}\right)$$ $$e\left(\frac{89}{156}\right)$$ $$e\left(\frac{29}{52}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{41}{78}\right)$$ $$e\left(\frac{127}{156}\right)$$ $$e\left(\frac{11}{26}\right)$$
$$\chi_{1183}(16,\cdot)$$ 1183.bi 39 yes $$1$$ $$1$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{35}{39}\right)$$
$$\chi_{1183}(17,\cdot)$$ 1183.by 78 yes $$-1$$ $$1$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{17}{78}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{41}{78}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{59}{78}\right)$$
$$\chi_{1183}(18,\cdot)$$ 1183.ce 156 yes $$-1$$ $$1$$ $$e\left(\frac{145}{156}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{109}{156}\right)$$ $$e\left(\frac{27}{52}\right)$$ $$e\left(\frac{41}{52}\right)$$ $$e\left(\frac{7}{39}\right)$$ $$e\left(\frac{49}{78}\right)$$ $$e\left(\frac{11}{156}\right)$$ $$e\left(\frac{35}{78}\right)$$
$$\chi_{1183}(19,\cdot)$$ 1183.w 12 no $$1$$ $$1$$ $$e\left(\frac{1}{12}\right)$$ $$-1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$i$$ $$1$$ $$1$$ $$i$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1183}(20,\cdot)$$ 1183.cb 156 yes $$1$$ $$1$$ $$e\left(\frac{11}{156}\right)$$ $$e\left(\frac{19}{78}\right)$$ $$e\left(\frac{11}{78}\right)$$ $$e\left(\frac{7}{52}\right)$$ $$e\left(\frac{49}{156}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{41}{156}\right)$$ $$e\left(\frac{5}{13}\right)$$
$$\chi_{1183}(22,\cdot)$$ 1183.f 3 no $$1$$ $$1$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$
$$\chi_{1183}(23,\cdot)$$ 1183.k 6 no $$1$$ $$1$$ $$-1$$ $$e\left(\frac{2}{3}\right)$$ $$1$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-1$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{2}{3}\right)$$
$$\chi_{1183}(24,\cdot)$$ 1183.ch 156 yes $$1$$ $$1$$ $$e\left(\frac{23}{156}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{23}{78}\right)$$ $$e\left(\frac{25}{156}\right)$$ $$e\left(\frac{41}{156}\right)$$ $$e\left(\frac{23}{52}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{27}{52}\right)$$ $$e\left(\frac{16}{39}\right)$$
$$\chi_{1183}(25,\cdot)$$ 1183.bs 78 yes $$1$$ $$1$$ $$e\left(\frac{35}{78}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{29}{78}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{34}{39}\right)$$
$$\chi_{1183}(27,\cdot)$$ 1183.bf 26 yes $$-1$$ $$1$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{5}{26}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{25}{26}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{25}{26}\right)$$
$$\chi_{1183}(29,\cdot)$$ 1183.bk 39 no $$1$$ $$1$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{31}{39}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{4}{13}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{23}{39}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{16}{39}\right)$$ $$e\left(\frac{4}{13}\right)$$
$$\chi_{1183}(30,\cdot)$$ 1183.bp 78 yes $$1$$ $$1$$ $$e\left(\frac{41}{78}\right)$$ $$e\left(\frac{11}{13}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{29}{78}\right)$$ $$e\left(\frac{15}{26}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{35}{39}\right)$$
$$\chi_{1183}(31,\cdot)$$ 1183.cc 156 yes $$1$$ $$1$$ $$e\left(\frac{73}{156}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{73}{78}\right)$$ $$e\left(\frac{7}{156}\right)$$ $$e\left(\frac{17}{52}\right)$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{83}{156}\right)$$ $$e\left(\frac{31}{39}\right)$$
$$\chi_{1183}(32,\cdot)$$ 1183.cg 156 yes $$-1$$ $$1$$ $$e\left(\frac{19}{52}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{97}{156}\right)$$ $$e\left(\frac{1}{156}\right)$$ $$e\left(\frac{5}{52}\right)$$ $$e\left(\frac{11}{39}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{151}{156}\right)$$ $$e\left(\frac{29}{78}\right)$$
$$\chi_{1183}(33,\cdot)$$ 1183.ch 156 yes $$1$$ $$1$$ $$e\left(\frac{19}{156}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{19}{78}\right)$$ $$e\left(\frac{41}{156}\right)$$ $$e\left(\frac{61}{156}\right)$$ $$e\left(\frac{19}{52}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{11}{52}\right)$$ $$e\left(\frac{20}{39}\right)$$
$$\chi_{1183}(34,\cdot)$$ 1183.bn 52 yes $$1$$ $$1$$ $$e\left(\frac{49}{52}\right)$$ $$e\left(\frac{9}{26}\right)$$ $$e\left(\frac{23}{26}\right)$$ $$e\left(\frac{51}{52}\right)$$ $$e\left(\frac{15}{52}\right)$$ $$e\left(\frac{43}{52}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{12}{13}\right)$$ $$e\left(\frac{3}{52}\right)$$ $$e\left(\frac{3}{13}\right)$$
$$\chi_{1183}(36,\cdot)$$ 1183.bt 78 no $$1$$ $$1$$ $$e\left(\frac{47}{78}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{8}{39}\right)$$ $$e\left(\frac{11}{26}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{21}{26}\right)$$ $$e\left(\frac{17}{39}\right)$$ $$e\left(\frac{1}{39}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{12}{13}\right)$$
$$\chi_{1183}(37,\cdot)$$ 1183.cg 156 yes $$-1$$ $$1$$ $$e\left(\frac{33}{52}\right)$$ $$e\left(\frac{14}{39}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{59}{156}\right)$$ $$e\left(\frac{155}{156}\right)$$ $$e\left(\frac{47}{52}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{5}{156}\right)$$ $$e\left(\frac{49}{78}\right)$$
$$\chi_{1183}(38,\cdot)$$ 1183.br 78 yes $$-1$$ $$1$$ $$e\left(\frac{59}{78}\right)$$ $$e\left(\frac{49}{78}\right)$$ $$e\left(\frac{20}{39}\right)$$ $$e\left(\frac{25}{39}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{7}{26}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{31}{78}\right)$$ $$e\left(\frac{19}{78}\right)$$ $$e\left(\frac{11}{78}\right)$$
$$\chi_{1183}(40,\cdot)$$ 1183.bv 78 yes $$-1$$ $$1$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{29}{78}\right)$$ $$e\left(\frac{19}{39}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{3}{26}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{47}{78}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{67}{78}\right)$$