Properties

Modulus $8820$
Structure \(C_{84}\times C_{6}\times C_{2}\times C_{2}\)
Order $2016$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(8820)
 
pari: g = idealstar(,8820,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 2016
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{84}\times C_{6}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{8820}(4411,\cdot)$, $\chi_{8820}(7841,\cdot)$, $\chi_{8820}(7057,\cdot)$, $\chi_{8820}(1081,\cdot)$

First 32 of 2016 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 \(-1\) \(1\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{8820}(1,\cdot)\) 8820.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{8820}(11,\cdot)\) 8820.hk 42 no \(1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(-1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{37}{42}\right)\)
\(\chi_{8820}(13,\cdot)\) 8820.ja 84 no \(1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{11}{28}\right)\) \(1\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{25}{84}\right)\)
\(\chi_{8820}(17,\cdot)\) 8820.ig 84 no \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{8820}(19,\cdot)\) 8820.cz 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\)
\(\chi_{8820}(23,\cdot)\) 8820.iu 84 yes \(-1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{13}{21}\right)\) \(-1\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{43}{84}\right)\)
\(\chi_{8820}(29,\cdot)\) 8820.ge 42 no \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{31}{42}\right)\)
\(\chi_{8820}(31,\cdot)\) 8820.bi 6 no \(1\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{8820}(37,\cdot)\) 8820.iz 84 no \(-1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{8820}(41,\cdot)\) 8820.gd 42 no \(1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{10}{21}\right)\)
\(\chi_{8820}(43,\cdot)\) 8820.io 84 yes \(1\) \(1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{9}{28}\right)\) \(1\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{23}{84}\right)\)
\(\chi_{8820}(47,\cdot)\) 8820.id 84 yes \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{53}{84}\right)\)
\(\chi_{8820}(53,\cdot)\) 8820.ik 84 no \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{19}{28}\right)\)
\(\chi_{8820}(59,\cdot)\) 8820.fw 42 yes \(-1\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{4}{21}\right)\)
\(\chi_{8820}(61,\cdot)\) 8820.ft 42 no \(-1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{8820}(67,\cdot)\) 8820.dm 12 no \(1\) \(1\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{8820}(71,\cdot)\) 8820.es 14 no \(1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(-1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(-1\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{8820}(73,\cdot)\) 8820.iv 84 no \(1\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{8820}(79,\cdot)\) 8820.bj 6 no \(-1\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{8820}(83,\cdot)\) 8820.ir 84 yes \(1\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{17}{28}\right)\) \(-1\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{59}{84}\right)\)
\(\chi_{8820}(89,\cdot)\) 8820.ga 42 no \(1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{14}\right)\)
\(\chi_{8820}(97,\cdot)\) 8820.ea 12 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{8820}(101,\cdot)\) 8820.gi 42 no \(1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(-1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{8820}(103,\cdot)\) 8820.il 84 yes \(-1\) \(1\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(1\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{19}{84}\right)\)
\(\chi_{8820}(107,\cdot)\) 8820.is 84 no \(-1\) \(1\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{8820}(109,\cdot)\) 8820.ho 42 no \(1\) \(1\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{8820}(113,\cdot)\) 8820.if 84 no \(1\) \(1\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{3}{28}\right)\) \(-1\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{73}{84}\right)\)
\(\chi_{8820}(121,\cdot)\) 8820.fj 21 no \(1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{16}{21}\right)\)
\(\chi_{8820}(127,\cdot)\) 8820.fr 28 no \(1\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{27}{28}\right)\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(-1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{23}{28}\right)\)
\(\chi_{8820}(131,\cdot)\) 8820.he 42 no \(-1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{17}{42}\right)\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{29}{42}\right)\)
\(\chi_{8820}(137,\cdot)\) 8820.im 84 no \(1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{5}{21}\right)\) \(1\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{23}{84}\right)\)
\(\chi_{8820}(139,\cdot)\) 8820.gm 42 yes \(1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{10}{21}\right)\)