Properties

Modulus $1584$
Structure \(C_{2}\times C_{2}\times C_{2}\times C_{60}\)
Order $480$

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Show commands: PariGP / SageMath

sage: H = DirichletGroup(1584)
 
pari: g = idealstar(,1584,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 480
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{2}\times C_{60}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1584}(991,\cdot)$, $\chi_{1584}(1189,\cdot)$, $\chi_{1584}(353,\cdot)$, $\chi_{1584}(145,\cdot)$

First 32 of 480 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 \(-1\) \(1\) \(5\) \(7\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{1584}(1,\cdot)\) 1584.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1584}(5,\cdot)\) 1584.dn 60 yes \(-1\) \(1\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{13}{20}\right)\)
\(\chi_{1584}(7,\cdot)\) 1584.dc 30 no \(1\) \(1\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{1584}(13,\cdot)\) 1584.dr 60 yes \(-1\) \(1\) \(e\left(\frac{49}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{1}{60}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{1584}(17,\cdot)\) 1584.cd 10 no \(1\) \(1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{7}{10}\right)\) \(-1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1584}(19,\cdot)\) 1584.cu 20 no \(1\) \(1\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{1584}(23,\cdot)\) 1584.bg 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\)
\(\chi_{1584}(25,\cdot)\) 1584.da 30 no \(1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{1584}(29,\cdot)\) 1584.dp 60 yes \(1\) \(1\) \(e\left(\frac{23}{60}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{17}{60}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{19}{60}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{9}{20}\right)\)
\(\chi_{1584}(31,\cdot)\) 1584.dg 30 no \(-1\) \(1\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{1}{10}\right)\)
\(\chi_{1584}(35,\cdot)\) 1584.cs 20 no \(-1\) \(1\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(-1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{1584}(37,\cdot)\) 1584.cr 20 no \(1\) \(1\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{7}{20}\right)\) \(-1\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{19}{20}\right)\)
\(\chi_{1584}(41,\cdot)\) 1584.df 30 no \(1\) \(1\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{3}{10}\right)\)
\(\chi_{1584}(43,\cdot)\) 1584.cj 12 yes \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\)
\(\chi_{1584}(47,\cdot)\) 1584.cy 30 no \(1\) \(1\) \(e\left(\frac{1}{30}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{23}{30}\right)\) \(e\left(\frac{19}{30}\right)\) \(e\left(\frac{4}{5}\right)\)
\(\chi_{1584}(49,\cdot)\) 1584.cm 15 no \(1\) \(1\) \(e\left(\frac{4}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{8}{15}\right)\) \(e\left(\frac{2}{15}\right)\) \(e\left(\frac{1}{15}\right)\) \(e\left(\frac{2}{5}\right)\)
\(\chi_{1584}(53,\cdot)\) 1584.ct 20 no \(-1\) \(1\) \(e\left(\frac{3}{20}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{11}{20}\right)\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{17}{20}\right)\)
\(\chi_{1584}(59,\cdot)\) 1584.dq 60 yes \(1\) \(1\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{17}{20}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{59}{60}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{19}{20}\right)\)
\(\chi_{1584}(61,\cdot)\) 1584.dr 60 yes \(-1\) \(1\) \(e\left(\frac{41}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{19}{20}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{13}{60}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{1584}(65,\cdot)\) 1584.bn 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\)
\(\chi_{1584}(67,\cdot)\) 1584.ch 12 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\)
\(\chi_{1584}(71,\cdot)\) 1584.bu 10 no \(1\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(1\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{9}{10}\right)\)
\(\chi_{1584}(73,\cdot)\) 1584.ca 10 no \(-1\) \(1\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{3}{5}\right)\) \(1\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{1}{5}\right)\)
\(\chi_{1584}(79,\cdot)\) 1584.dh 30 no \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{13}{30}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{1584}(83,\cdot)\) 1584.dk 60 yes \(-1\) \(1\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{3}{20}\right)\)
\(\chi_{1584}(85,\cdot)\) 1584.dr 60 yes \(-1\) \(1\) \(e\left(\frac{7}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{43}{60}\right)\) \(e\left(\frac{7}{10}\right)\) \(e\left(\frac{13}{20}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{1584}(89,\cdot)\) 1584.n 2 no \(-1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1584}(91,\cdot)\) 1584.co 20 no \(-1\) \(1\) \(e\left(\frac{9}{20}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{11}{20}\right)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{13}{20}\right)\) \(1\) \(e\left(\frac{9}{10}\right)\) \(e\left(\frac{7}{20}\right)\) \(e\left(\frac{3}{10}\right)\) \(e\left(\frac{1}{20}\right)\)
\(\chi_{1584}(95,\cdot)\) 1584.cz 30 no \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{7}{10}\right)\)
\(\chi_{1584}(97,\cdot)\) 1584.cm 15 no \(1\) \(1\) \(e\left(\frac{11}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{15}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{3}{5}\right)\)
\(\chi_{1584}(101,\cdot)\) 1584.dp 60 yes \(1\) \(1\) \(e\left(\frac{29}{60}\right)\) \(e\left(\frac{13}{15}\right)\) \(e\left(\frac{11}{60}\right)\) \(e\left(\frac{2}{5}\right)\) \(e\left(\frac{1}{20}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{37}{60}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{20}\right)\)
\(\chi_{1584}(103,\cdot)\) 1584.cv 30 no \(-1\) \(1\) \(e\left(\frac{29}{30}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{4}{5}\right)\) \(e\left(\frac{3}{5}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{14}{15}\right)\) \(e\left(\frac{7}{30}\right)\) \(e\left(\frac{11}{30}\right)\) \(e\left(\frac{1}{5}\right)\)
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