Properties

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

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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 \(-1\) \(1\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{29}{78}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{67}{78}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{47}{78}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{67}{78}\right)\)