Properties

Modulus $1131$
Structure \(C_{2}\times C_{4}\times C_{84}\)
Order $672$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(1131)
 
pari: g = idealstar(,1131,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 672
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{4}\times C_{84}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1131}(755,\cdot)$, $\chi_{1131}(262,\cdot)$, $\chi_{1131}(118,\cdot)$

First 32 of 672 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 \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(14\) \(16\) \(17\)
\(\chi_{1131}(1,\cdot)\) 1131.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1131}(2,\cdot)\) 1131.da 84 yes \(-1\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1131}(4,\cdot)\) 1131.co 42 no \(1\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1131}(5,\cdot)\) 1131.cb 28 yes \(1\) \(1\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(-1\)
\(\chi_{1131}(7,\cdot)\) 1131.cu 84 no \(-1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1131}(8,\cdot)\) 1131.by 28 yes \(-1\) \(1\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(i\)
\(\chi_{1131}(10,\cdot)\) 1131.cs 84 no \(-1\) \(1\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{1131}(11,\cdot)\) 1131.cr 84 yes \(-1\) \(1\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1131}(14,\cdot)\) 1131.bz 28 no \(1\) \(1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(i\)
\(\chi_{1131}(16,\cdot)\) 1131.bw 21 no \(1\) \(1\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1131}(17,\cdot)\) 1131.bg 12 yes \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{1131}(19,\cdot)\) 1131.cq 84 no \(1\) \(1\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{1131}(20,\cdot)\) 1131.cv 84 yes \(1\) \(1\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1131}(22,\cdot)\) 1131.ck 42 no \(1\) \(1\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1131}(23,\cdot)\) 1131.cn 42 yes \(-1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1131}(25,\cdot)\) 1131.bv 14 no \(1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(1\)
\(\chi_{1131}(28,\cdot)\) 1131.bh 12 no \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1131}(31,\cdot)\) 1131.ci 28 no \(1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(i\)
\(\chi_{1131}(32,\cdot)\) 1131.da 84 yes \(-1\) \(1\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1131}(34,\cdot)\) 1131.cc 28 no \(-1\) \(1\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(1\)
\(\chi_{1131}(35,\cdot)\) 1131.cp 42 yes \(-1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1131}(37,\cdot)\) 1131.cq 84 no \(1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1131}(38,\cdot)\) 1131.bt 14 yes \(-1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(1\)
\(\chi_{1131}(40,\cdot)\) 1131.cf 28 no \(-1\) \(1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(-i\)
\(\chi_{1131}(41,\cdot)\) 1131.bn 12 yes \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{1131}(43,\cdot)\) 1131.cs 84 no \(-1\) \(1\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1131}(44,\cdot)\) 1131.ch 28 yes \(-1\) \(1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(i\)
\(\chi_{1131}(46,\cdot)\) 1131.bd 12 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{1}{12}\right)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{1131}(47,\cdot)\) 1131.by 28 yes \(-1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(i\)
\(\chi_{1131}(49,\cdot)\) 1131.cl 42 no \(1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1131}(50,\cdot)\) 1131.cr 84 yes \(-1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1131}(53,\cdot)\) 1131.bu 14 no \(-1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(-1\)
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