Properties

Modulus $1960$
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(1960)
 
pari: g = idealstar(,1960,2)
 

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 = $\chi_{1960}(1471,\cdot)$, $\chi_{1960}(981,\cdot)$, $\chi_{1960}(1177,\cdot)$, $\chi_{1960}(1081,\cdot)$

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 \(-1\) \(1\) \(3\) \(9\) \(11\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{1960}(1,\cdot)\) 1960.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1960}(3,\cdot)\) 1960.do 84 yes \(-1\) \(1\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1960}(9,\cdot)\) 1960.db 42 no \(1\) \(1\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1960}(11,\cdot)\) 1960.di 42 no \(-1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1960}(13,\cdot)\) 1960.cr 28 yes \(1\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(-1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(-1\)
\(\chi_{1960}(17,\cdot)\) 1960.dp 84 no \(1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1960}(19,\cdot)\) 1960.ba 6 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1960}(23,\cdot)\) 1960.dl 84 no \(1\) \(1\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1960}(27,\cdot)\) 1960.cp 28 yes \(-1\) \(1\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{1}{28}\right)\) \(1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(1\)
\(\chi_{1960}(29,\cdot)\) 1960.ca 14 yes \(1\) \(1\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(-1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(1\)
\(\chi_{1960}(31,\cdot)\) 1960.bc 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1960}(33,\cdot)\) 1960.dp 84 no \(1\) \(1\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1960}(37,\cdot)\) 1960.dk 84 yes \(-1\) \(1\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1960}(39,\cdot)\) 1960.dg 42 no \(-1\) \(1\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1960}(41,\cdot)\) 1960.cg 14 no \(-1\) \(1\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{13}{14}\right)\) \(-1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\)
\(\chi_{1960}(43,\cdot)\) 1960.cn 28 yes \(1\) \(1\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{9}{28}\right)\) \(-1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(-1\)
\(\chi_{1960}(47,\cdot)\) 1960.dn 84 no \(-1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1960}(51,\cdot)\) 1960.di 42 no \(-1\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1960}(53,\cdot)\) 1960.dk 84 yes \(-1\) \(1\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1960}(57,\cdot)\) 1960.co 28 no \(-1\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{19}{28}\right)\) \(-1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(1\)
\(\chi_{1960}(59,\cdot)\) 1960.dj 42 yes \(1\) \(1\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1960}(61,\cdot)\) 1960.dd 42 no \(-1\) \(1\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1960}(67,\cdot)\) 1960.bs 12 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1960}(69,\cdot)\) 1960.cl 14 yes \(-1\) \(1\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{7}\right)\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(-1\)
\(\chi_{1960}(71,\cdot)\) 1960.ci 14 no \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(-1\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(-1\)
\(\chi_{1960}(73,\cdot)\) 1960.dp 84 no \(1\) \(1\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1960}(79,\cdot)\) 1960.bd 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1960}(81,\cdot)\) 1960.cm 21 no \(1\) \(1\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1960}(83,\cdot)\) 1960.cp 28 yes \(-1\) \(1\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{3}{28}\right)\) \(1\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(1\)
\(\chi_{1960}(87,\cdot)\) 1960.dn 84 no \(-1\) \(1\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1960}(89,\cdot)\) 1960.dh 42 no \(-1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1960}(93,\cdot)\) 1960.dk 84 yes \(-1\) \(1\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{3}\right)\)
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