Properties

Modulus $2205$
Structure \(C_{84}\times C_{6}\times C_{2}\)
Order $1008$

Learn more about

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(2205)
 
pari: g = idealstar(,2205,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1008
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{84}\times C_{6}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2205}(1226,\cdot)$, $\chi_{2205}(442,\cdot)$, $\chi_{2205}(1081,\cdot)$

First 32 of 1008 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 \(-1\) \(1\) \(2\) \(4\) \(8\) \(11\) \(13\) \(16\) \(17\) \(19\) \(22\) \(23\)
\(\chi_{2205}(1,\cdot)\) 2205.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2205}(2,\cdot)\) 2205.el 84 yes \(1\) \(1\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{3}{28}\right)\)
\(\chi_{2205}(4,\cdot)\) 2205.db 42 yes \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{3}{14}\right)\)
\(\chi_{2205}(8,\cdot)\) 2205.cw 28 no \(1\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{19}{28}\right)\) \(-1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{2205}(11,\cdot)\) 2205.dx 42 no \(-1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{1}{42}\right)\)
\(\chi_{2205}(13,\cdot)\) 2205.ej 84 yes \(1\) \(1\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{11}{28}\right)\) \(1\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{65}{84}\right)\)
\(\chi_{2205}(16,\cdot)\) 2205.cr 21 no \(1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{2205}(17,\cdot)\) 2205.ed 84 no \(-1\) \(1\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{73}{84}\right)\)
\(\chi_{2205}(19,\cdot)\) 2205.bi 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{2205}(22,\cdot)\) 2205.eg 84 yes \(-1\) \(1\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{15}{28}\right)\) \(-1\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{11}{84}\right)\)
\(\chi_{2205}(23,\cdot)\) 2205.en 84 yes \(1\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{67}{84}\right)\)
\(\chi_{2205}(26,\cdot)\) 2205.dg 42 no \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{37}{42}\right)\)
\(\chi_{2205}(29,\cdot)\) 2205.dp 42 yes \(-1\) \(1\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{13}{21}\right)\)
\(\chi_{2205}(31,\cdot)\) 2205.bc 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)
\(\chi_{2205}(32,\cdot)\) 2205.el 84 yes \(1\) \(1\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{15}{28}\right)\)
\(\chi_{2205}(34,\cdot)\) 2205.dj 42 yes \(-1\) \(1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(-1\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{41}{42}\right)\)
\(\chi_{2205}(37,\cdot)\) 2205.ei 84 no \(-1\) \(1\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{59}{84}\right)\)
\(\chi_{2205}(38,\cdot)\) 2205.em 84 yes \(-1\) \(1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{23}{84}\right)\)
\(\chi_{2205}(41,\cdot)\) 2205.de 42 no \(1\) \(1\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{31}{42}\right)\)
\(\chi_{2205}(43,\cdot)\) 2205.eg 84 yes \(-1\) \(1\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{9}{28}\right)\) \(-1\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{1}{84}\right)\)
\(\chi_{2205}(44,\cdot)\) 2205.dr 42 no \(-1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{2205}(46,\cdot)\) 2205.cs 21 no \(1\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{2205}(47,\cdot)\) 2205.ek 84 yes \(-1\) \(1\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{3}{28}\right)\)
\(\chi_{2205}(52,\cdot)\) 2205.eo 84 yes \(1\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{83}{84}\right)\)
\(\chi_{2205}(53,\cdot)\) 2205.ee 84 no \(1\) \(1\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{67}{84}\right)\)
\(\chi_{2205}(58,\cdot)\) 2205.ep 84 yes \(-1\) \(1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{61}{84}\right)\)
\(\chi_{2205}(59,\cdot)\) 2205.dv 42 yes \(1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{3}{7}\right)\)
\(\chi_{2205}(61,\cdot)\) 2205.dn 42 no \(-1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{2205}(62,\cdot)\) 2205.cx 28 no \(-1\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{3}{28}\right)\)
\(\chi_{2205}(64,\cdot)\) 2205.cn 14 no \(1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{9}{14}\right)\)
\(\chi_{2205}(67,\cdot)\) 2205.ci 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\)
\(\chi_{2205}(68,\cdot)\) 2205.bv 12 no \(-1\) \(1\) \(i\) \(-1\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\)