Properties

Modulus $3920$
Structure \(C_{84}\times C_{4}\times C_{2}\times C_{2}\)
Order $1344$

Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(3920)
 
pari: g = idealstar(,3920,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1344
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{84}\times C_{4}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{3920}(1471,\cdot)$, $\chi_{3920}(981,\cdot)$, $\chi_{3920}(3137,\cdot)$, $\chi_{3920}(3041,\cdot)$

First 32 of 1344 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 \(-1\) \(1\) \(3\) \(9\) \(11\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{3920}(1,\cdot)\) 3920.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{3920}(3,\cdot)\) 3920.fg 84 yes \(-1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(9,\cdot)\) 3920.fa 42 no \(1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(11,\cdot)\) 3920.fv 84 no \(-1\) \(1\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(13,\cdot)\) 3920.dt 28 yes \(1\) \(1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(i\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{25}{28}\right)\) \(-1\)
\(\chi_{3920}(17,\cdot)\) 3920.fx 84 no \(1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(19,\cdot)\) 3920.cp 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(23,\cdot)\) 3920.fy 84 no \(1\) \(1\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(27,\cdot)\) 3920.eo 28 yes \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(i\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(1\)
\(\chi_{3920}(29,\cdot)\) 3920.eg 28 yes \(1\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(i\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(1\)
\(\chi_{3920}(31,\cdot)\) 3920.bs 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(33,\cdot)\) 3920.fx 84 no \(1\) \(1\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(37,\cdot)\) 3920.fi 84 yes \(-1\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(39,\cdot)\) 3920.ev 42 no \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(41,\cdot)\) 3920.dh 14 no \(-1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{13}{14}\right)\) \(-1\)
\(\chi_{3920}(43,\cdot)\) 3920.en 28 yes \(1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{9}{28}\right)\) \(-i\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{23}{28}\right)\) \(-1\)
\(\chi_{3920}(47,\cdot)\) 3920.fn 84 no \(-1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(51,\cdot)\) 3920.fv 84 no \(-1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(53,\cdot)\) 3920.ga 84 yes \(-1\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(57,\cdot)\) 3920.el 28 no \(-1\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(1\)
\(\chi_{3920}(59,\cdot)\) 3920.ft 84 yes \(1\) \(1\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(61,\cdot)\) 3920.fo 84 no \(-1\) \(1\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(67,\cdot)\) 3920.dc 12 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(-i\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(69,\cdot)\) 3920.ec 28 yes \(-1\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(i\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(-1\)
\(\chi_{3920}(71,\cdot)\) 3920.df 14 no \(-1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(-1\)
\(\chi_{3920}(73,\cdot)\) 3920.fm 84 no \(1\) \(1\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(79,\cdot)\) 3920.bt 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(81,\cdot)\) 3920.ds 21 no \(1\) \(1\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(83,\cdot)\) 3920.eo 28 yes \(-1\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{3}{28}\right)\) \(-i\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(1\)
\(\chi_{3920}(87,\cdot)\) 3920.fw 84 no \(-1\) \(1\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(89,\cdot)\) 3920.et 42 no \(-1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(93,\cdot)\) 3920.fi 84 yes \(-1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{1}{3}\right)\)