Properties

Modulus $927$
Structure \(C_{102}\times C_{6}\)
Order $612$

Learn more

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(927)
 
pari: g = idealstar(,927,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 612
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{102}\times C_{6}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{927}(722,\cdot)$, $\chi_{927}(829,\cdot)$

First 32 of 612 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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(13\) \(14\) \(16\)
\(\chi_{927}(1,\cdot)\) 927.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{927}(2,\cdot)\) 927.bn 102 yes \(-1\) \(1\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{49}{102}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{10}{17}\right)\)
\(\chi_{927}(4,\cdot)\) 927.y 51 yes \(1\) \(1\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{3}{17}\right)\)
\(\chi_{927}(5,\cdot)\) 927.bm 102 yes \(1\) \(1\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{65}{102}\right)\) \(e\left(\frac{1}{17}\right)\)
\(\chi_{927}(7,\cdot)\) 927.z 51 yes \(1\) \(1\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{29}{51}\right)\)
\(\chi_{927}(8,\cdot)\) 927.x 34 no \(-1\) \(1\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{13}{17}\right)\)
\(\chi_{927}(10,\cdot)\) 927.v 34 no \(-1\) \(1\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{14}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{11}{17}\right)\)
\(\chi_{927}(11,\cdot)\) 927.bg 102 yes \(1\) \(1\) \(e\left(\frac{49}{102}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{22}{51}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{47}{51}\right)\)
\(\chi_{927}(13,\cdot)\) 927.bb 51 yes \(1\) \(1\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{29}{51}\right)\)
\(\chi_{927}(14,\cdot)\) 927.bf 102 yes \(-1\) \(1\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{65}{102}\right)\) \(e\left(\frac{11}{51}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{77}{102}\right)\) \(e\left(\frac{8}{51}\right)\)
\(\chi_{927}(16,\cdot)\) 927.y 51 yes \(1\) \(1\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{6}{17}\right)\)
\(\chi_{927}(17,\cdot)\) 927.be 102 no \(-1\) \(1\) \(e\left(\frac{71}{102}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{19}{102}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{37}{102}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{15}{34}\right)\) \(e\left(\frac{40}{51}\right)\)
\(\chi_{927}(19,\cdot)\) 927.ba 51 no \(1\) \(1\) \(e\left(\frac{26}{51}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{2}{51}\right)\)
\(\chi_{927}(20,\cdot)\) 927.bm 102 yes \(1\) \(1\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{20}{51}\right)\) \(e\left(\frac{8}{51}\right)\) \(e\left(\frac{73}{102}\right)\) \(e\left(\frac{4}{17}\right)\)
\(\chi_{927}(22,\cdot)\) 927.bl 102 yes \(-1\) \(1\) \(e\left(\frac{32}{51}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{71}{102}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{13}{102}\right)\) \(e\left(\frac{40}{51}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{26}{51}\right)\)
\(\chi_{927}(23,\cdot)\) 927.bf 102 yes \(-1\) \(1\) \(e\left(\frac{19}{102}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{41}{102}\right)\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{19}{34}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{19}{102}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{47}{102}\right)\) \(e\left(\frac{38}{51}\right)\)
\(\chi_{927}(25,\cdot)\) 927.y 51 yes \(1\) \(1\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{38}{51}\right)\) \(e\left(\frac{14}{51}\right)\) \(e\left(\frac{2}{17}\right)\)
\(\chi_{927}(26,\cdot)\) 927.be 102 no \(-1\) \(1\) \(e\left(\frac{55}{102}\right)\) \(e\left(\frac{4}{51}\right)\) \(e\left(\frac{65}{102}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{89}{102}\right)\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{8}{51}\right)\)
\(\chi_{927}(28,\cdot)\) 927.ba 51 no \(1\) \(1\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{19}{51}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{10}{17}\right)\) \(e\left(\frac{1}{51}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{38}{51}\right)\)
\(\chi_{927}(29,\cdot)\) 927.bn 102 yes \(-1\) \(1\) \(e\left(\frac{9}{34}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{27}{34}\right)\) \(e\left(\frac{16}{17}\right)\) \(e\left(\frac{61}{102}\right)\) \(e\left(\frac{2}{51}\right)\) \(e\left(\frac{31}{102}\right)\) \(e\left(\frac{1}{17}\right)\)
\(\chi_{927}(31,\cdot)\) 927.bl 102 yes \(-1\) \(1\) \(e\left(\frac{47}{51}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{23}{102}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{5}{34}\right)\) \(e\left(\frac{43}{102}\right)\) \(e\left(\frac{46}{51}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{35}{51}\right)\)
\(\chi_{927}(32,\cdot)\) 927.bn 102 yes \(-1\) \(1\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{8}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{41}{102}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{71}{102}\right)\) \(e\left(\frac{16}{17}\right)\)
\(\chi_{927}(34,\cdot)\) 927.bb 51 yes \(1\) \(1\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{23}{51}\right)\) \(e\left(\frac{7}{51}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{50}{51}\right)\) \(e\left(\frac{19}{51}\right)\)
\(\chi_{927}(35,\cdot)\) 927.bh 102 no \(1\) \(1\) \(e\left(\frac{67}{102}\right)\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{10}{51}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{25}{51}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{29}{34}\right)\) \(e\left(\frac{32}{51}\right)\)
\(\chi_{927}(37,\cdot)\) 927.v 34 no \(-1\) \(1\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{4}{17}\right)\) \(e\left(\frac{31}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{6}{17}\right)\) \(e\left(\frac{1}{34}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{8}{17}\right)\)
\(\chi_{927}(38,\cdot)\) 927.bd 102 yes \(-1\) \(1\) \(e\left(\frac{67}{102}\right)\) \(e\left(\frac{16}{51}\right)\) \(e\left(\frac{5}{102}\right)\) \(e\left(\frac{9}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{44}{51}\right)\) \(e\left(\frac{19}{102}\right)\) \(e\left(\frac{32}{51}\right)\)
\(\chi_{927}(40,\cdot)\) 927.bc 102 yes \(-1\) \(1\) \(e\left(\frac{12}{17}\right)\) \(e\left(\frac{7}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{2}{17}\right)\) \(e\left(\frac{23}{34}\right)\) \(e\left(\frac{89}{102}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{13}{51}\right)\) \(e\left(\frac{14}{17}\right)\)
\(\chi_{927}(41,\cdot)\) 927.bd 102 yes \(-1\) \(1\) \(e\left(\frac{41}{102}\right)\) \(e\left(\frac{41}{51}\right)\) \(e\left(\frac{67}{102}\right)\) \(e\left(\frac{5}{17}\right)\) \(e\left(\frac{7}{34}\right)\) \(e\left(\frac{1}{17}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{71}{102}\right)\) \(e\left(\frac{31}{51}\right)\)
\(\chi_{927}(43,\cdot)\) 927.bc 102 yes \(-1\) \(1\) \(e\left(\frac{15}{17}\right)\) \(e\left(\frac{13}{17}\right)\) \(e\left(\frac{3}{34}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{11}{17}\right)\) \(e\left(\frac{33}{34}\right)\) \(e\left(\frac{73}{102}\right)\) \(e\left(\frac{35}{51}\right)\) \(e\left(\frac{29}{51}\right)\) \(e\left(\frac{9}{17}\right)\)
\(\chi_{927}(44,\cdot)\) 927.bh 102 no \(1\) \(1\) \(e\left(\frac{79}{102}\right)\) \(e\left(\frac{28}{51}\right)\) \(e\left(\frac{49}{51}\right)\) \(e\left(\frac{43}{51}\right)\) \(e\left(\frac{11}{34}\right)\) \(e\left(\frac{25}{34}\right)\) \(e\left(\frac{31}{51}\right)\) \(e\left(\frac{3}{17}\right)\) \(e\left(\frac{21}{34}\right)\) \(e\left(\frac{5}{51}\right)\)
\(\chi_{927}(46,\cdot)\) 927.f 3 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{927}(47,\cdot)\) 927.p 6 yes \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)