Properties

Modulus $2352$
Structure \(C_{2}\times C_{2}\times C_{2}\times C_{84}\)
Order $672$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(2352)
 
pari: g = idealstar(,2352,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 672
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{2}\times C_{84}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2352}(1471,\cdot)$, $\chi_{2352}(1765,\cdot)$, $\chi_{2352}(785,\cdot)$, $\chi_{2352}(2257,\cdot)$

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 \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\)
\(\chi_{2352}(1,\cdot)\) 2352.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2352}(5,\cdot)\) 2352.dr 84 yes \(1\) \(1\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{29}{84}\right)\)
\(\chi_{2352}(11,\cdot)\) 2352.dl 84 yes \(1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{61}{84}\right)\)
\(\chi_{2352}(13,\cdot)\) 2352.cu 28 no \(-1\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(-i\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(-1\) \(e\left(\frac{25}{28}\right)\)
\(\chi_{2352}(17,\cdot)\) 2352.dg 42 no \(1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{21}\right)\)
\(\chi_{2352}(19,\cdot)\) 2352.bt 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{2352}(23,\cdot)\) 2352.df 42 no \(1\) \(1\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{42}\right)\)
\(\chi_{2352}(25,\cdot)\) 2352.cy 42 no \(1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{29}{42}\right)\)
\(\chi_{2352}(29,\cdot)\) 2352.cs 28 yes \(-1\) \(1\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(i\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{13}{28}\right)\) \(1\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{2352}(31,\cdot)\) 2352.bl 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2352}(37,\cdot)\) 2352.dp 84 no \(1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{53}{84}\right)\)
\(\chi_{2352}(41,\cdot)\) 2352.ce 14 no \(1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{13}{14}\right)\)
\(\chi_{2352}(43,\cdot)\) 2352.co 28 no \(-1\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(i\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(-1\) \(e\left(\frac{23}{28}\right)\)
\(\chi_{2352}(47,\cdot)\) 2352.dj 42 no \(-1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{21}\right)\)
\(\chi_{2352}(53,\cdot)\) 2352.dm 84 yes \(-1\) \(1\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{73}{84}\right)\)
\(\chi_{2352}(55,\cdot)\) 2352.bx 14 no \(1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(-1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(1\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{2352}(59,\cdot)\) 2352.do 84 yes \(-1\) \(1\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{84}\right)\)
\(\chi_{2352}(61,\cdot)\) 2352.dk 84 no \(-1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{84}\right)\)
\(\chi_{2352}(65,\cdot)\) 2352.cv 42 no \(-1\) \(1\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{2352}(67,\cdot)\) 2352.bq 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{2352}(71,\cdot)\) 2352.cd 14 no \(1\) \(1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(1\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(-1\) \(e\left(\frac{11}{14}\right)\)
\(\chi_{2352}(73,\cdot)\) 2352.dd 42 no \(-1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{29}{42}\right)\)
\(\chi_{2352}(79,\cdot)\) 2352.be 6 no \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2352}(83,\cdot)\) 2352.cq 28 yes \(-1\) \(1\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(i\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(1\) \(e\left(\frac{17}{28}\right)\)
\(\chi_{2352}(85,\cdot)\) 2352.cp 28 no \(1\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(-i\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{25}{28}\right)\) \(1\) \(e\left(\frac{11}{28}\right)\)
\(\chi_{2352}(89,\cdot)\) 2352.da 42 no \(1\) \(1\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{42}\right)\)
\(\chi_{2352}(95,\cdot)\) 2352.cz 42 no \(1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{16}{21}\right)\)
\(\chi_{2352}(97,\cdot)\) 2352.f 2 no \(-1\) \(1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(-1\) \(1\)
\(\chi_{2352}(101,\cdot)\) 2352.dr 84 yes \(1\) \(1\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{84}\right)\)
\(\chi_{2352}(103,\cdot)\) 2352.dh 42 no \(1\) \(1\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{25}{42}\right)\)
\(\chi_{2352}(107,\cdot)\) 2352.dl 84 yes \(1\) \(1\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{65}{84}\right)\)
\(\chi_{2352}(109,\cdot)\) 2352.dp 84 no \(1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{84}\right)\)
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