Properties

Modulus $1323$
Structure \(C_{126}\times C_{6}\)
Order $756$

Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(1323)
 
pari: g = idealstar(,1323,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 756
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{126}\times C_{6}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1323}(785,\cdot)$, $\chi_{1323}(1081,\cdot)$

First 32 of 756 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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(11\) \(13\) \(16\) \(17\) \(19\)
\(\chi_{1323}(1,\cdot)\) 1323.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1323}(2,\cdot)\) 1323.cg 126 yes \(-1\) \(1\) \(e\left(\frac{19}{126}\right)\) \(e\left(\frac{19}{63}\right)\) \(e\left(\frac{29}{126}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{61}{126}\right)\) \(e\left(\frac{55}{63}\right)\) \(e\left(\frac{38}{63}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1323}(4,\cdot)\) 1323.cc 63 yes \(1\) \(1\) \(e\left(\frac{19}{63}\right)\) \(e\left(\frac{38}{63}\right)\) \(e\left(\frac{29}{63}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{61}{63}\right)\) \(e\left(\frac{47}{63}\right)\) \(e\left(\frac{13}{63}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1323}(5,\cdot)\) 1323.ci 126 yes \(1\) \(1\) \(e\left(\frac{29}{126}\right)\) \(e\left(\frac{29}{63}\right)\) \(e\left(\frac{26}{63}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{29}{126}\right)\) \(e\left(\frac{1}{126}\right)\) \(e\left(\frac{58}{63}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\)
\(\chi_{1323}(8,\cdot)\) 1323.bq 42 no \(-1\) \(1\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(1\)
\(\chi_{1323}(10,\cdot)\) 1323.bx 42 no \(-1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(11,\cdot)\) 1323.cd 126 yes \(-1\) \(1\) \(e\left(\frac{61}{126}\right)\) \(e\left(\frac{61}{63}\right)\) \(e\left(\frac{29}{126}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{61}{126}\right)\) \(e\left(\frac{13}{63}\right)\) \(e\left(\frac{59}{63}\right)\) \(e\left(\frac{9}{14}\right)\) \(1\)
\(\chi_{1323}(13,\cdot)\) 1323.ck 126 yes \(-1\) \(1\) \(e\left(\frac{55}{63}\right)\) \(e\left(\frac{47}{63}\right)\) \(e\left(\frac{1}{126}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{13}{63}\right)\) \(e\left(\frac{61}{126}\right)\) \(e\left(\frac{31}{63}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(16,\cdot)\) 1323.cc 63 yes \(1\) \(1\) \(e\left(\frac{38}{63}\right)\) \(e\left(\frac{13}{63}\right)\) \(e\left(\frac{58}{63}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{59}{63}\right)\) \(e\left(\frac{31}{63}\right)\) \(e\left(\frac{26}{63}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1323}(17,\cdot)\) 1323.bp 42 no \(1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(19,\cdot)\) 1323.k 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(20,\cdot)\) 1323.ce 126 yes \(1\) \(1\) \(e\left(\frac{67}{126}\right)\) \(e\left(\frac{4}{63}\right)\) \(e\left(\frac{55}{63}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{25}{126}\right)\) \(e\left(\frac{95}{126}\right)\) \(e\left(\frac{8}{63}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(22,\cdot)\) 1323.cb 63 yes \(1\) \(1\) \(e\left(\frac{40}{63}\right)\) \(e\left(\frac{17}{63}\right)\) \(e\left(\frac{29}{63}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{61}{63}\right)\) \(e\left(\frac{5}{63}\right)\) \(e\left(\frac{34}{63}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1323}(23,\cdot)\) 1323.cd 126 yes \(-1\) \(1\) \(e\left(\frac{17}{126}\right)\) \(e\left(\frac{17}{63}\right)\) \(e\left(\frac{37}{126}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{17}{126}\right)\) \(e\left(\frac{47}{63}\right)\) \(e\left(\frac{34}{63}\right)\) \(e\left(\frac{11}{14}\right)\) \(1\)
\(\chi_{1323}(25,\cdot)\) 1323.ca 63 yes \(1\) \(1\) \(e\left(\frac{29}{63}\right)\) \(e\left(\frac{58}{63}\right)\) \(e\left(\frac{52}{63}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{29}{63}\right)\) \(e\left(\frac{1}{63}\right)\) \(e\left(\frac{53}{63}\right)\) \(e\left(\frac{6}{7}\right)\) \(1\)
\(\chi_{1323}(26,\cdot)\) 1323.bs 42 no \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(29,\cdot)\) 1323.ch 126 yes \(-1\) \(1\) \(e\left(\frac{25}{126}\right)\) \(e\left(\frac{25}{63}\right)\) \(e\left(\frac{89}{126}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{109}{126}\right)\) \(e\left(\frac{37}{63}\right)\) \(e\left(\frac{50}{63}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1323}(31,\cdot)\) 1323.bd 18 no \(-1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(32,\cdot)\) 1323.cg 126 yes \(-1\) \(1\) \(e\left(\frac{95}{126}\right)\) \(e\left(\frac{32}{63}\right)\) \(e\left(\frac{19}{126}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{53}{126}\right)\) \(e\left(\frac{23}{63}\right)\) \(e\left(\frac{1}{63}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1323}(34,\cdot)\) 1323.ck 126 yes \(-1\) \(1\) \(e\left(\frac{29}{63}\right)\) \(e\left(\frac{58}{63}\right)\) \(e\left(\frac{83}{126}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{8}{63}\right)\) \(e\left(\frac{23}{126}\right)\) \(e\left(\frac{53}{63}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1323}(37,\cdot)\) 1323.bk 21 no \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1323}(38,\cdot)\) 1323.ci 126 yes \(1\) \(1\) \(e\left(\frac{61}{126}\right)\) \(e\left(\frac{61}{63}\right)\) \(e\left(\frac{46}{63}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{61}{126}\right)\) \(e\left(\frac{89}{126}\right)\) \(e\left(\frac{59}{63}\right)\) \(e\left(\frac{1}{7}\right)\) \(-1\)
\(\chi_{1323}(40,\cdot)\) 1323.cl 126 yes \(-1\) \(1\) \(e\left(\frac{43}{63}\right)\) \(e\left(\frac{23}{63}\right)\) \(e\left(\frac{13}{126}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{43}{63}\right)\) \(e\left(\frac{79}{126}\right)\) \(e\left(\frac{46}{63}\right)\) \(e\left(\frac{5}{14}\right)\) \(-1\)
\(\chi_{1323}(41,\cdot)\) 1323.ce 126 yes \(1\) \(1\) \(e\left(\frac{29}{126}\right)\) \(e\left(\frac{29}{63}\right)\) \(e\left(\frac{5}{63}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{71}{126}\right)\) \(e\left(\frac{43}{126}\right)\) \(e\left(\frac{58}{63}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(43,\cdot)\) 1323.cb 63 yes \(1\) \(1\) \(e\left(\frac{59}{63}\right)\) \(e\left(\frac{55}{63}\right)\) \(e\left(\frac{16}{63}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{38}{63}\right)\) \(e\left(\frac{31}{63}\right)\) \(e\left(\frac{47}{63}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1323}(44,\cdot)\) 1323.by 42 no \(-1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1323}(46,\cdot)\) 1323.bk 21 no \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1323}(47,\cdot)\) 1323.cf 126 yes \(1\) \(1\) \(e\left(\frac{61}{126}\right)\) \(e\left(\frac{61}{63}\right)\) \(e\left(\frac{25}{63}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{103}{126}\right)\) \(e\left(\frac{5}{126}\right)\) \(e\left(\frac{59}{63}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1323}(50,\cdot)\) 1323.bf 18 no \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1323}(52,\cdot)\) 1323.cl 126 yes \(-1\) \(1\) \(e\left(\frac{11}{63}\right)\) \(e\left(\frac{22}{63}\right)\) \(e\left(\frac{59}{126}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{11}{63}\right)\) \(e\left(\frac{29}{126}\right)\) \(e\left(\frac{44}{63}\right)\) \(e\left(\frac{13}{14}\right)\) \(-1\)
\(\chi_{1323}(53,\cdot)\) 1323.br 42 no \(-1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1323}(55,\cdot)\) 1323.y 14 no \(-1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(-1\)