Properties

Modulus $735$
Structure \(C_{2}\times C_{2}\times C_{84}\)
Order $336$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(735)
 
pari: g = idealstar(,735,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 336
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{84}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{735}(491,\cdot)$, $\chi_{735}(442,\cdot)$, $\chi_{735}(346,\cdot)$

First 32 of 336 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 \(-1\) \(1\) \(2\) \(4\) \(8\) \(11\) \(13\) \(16\) \(17\) \(19\) \(22\) \(23\)
\(\chi_{735}(1,\cdot)\) 735.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{735}(2,\cdot)\) 735.bt 84 yes \(1\) \(1\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{65}{84}\right)\)
\(\chi_{735}(4,\cdot)\) 735.bo 42 no \(1\) \(1\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{23}{42}\right)\)
\(\chi_{735}(8,\cdot)\) 735.bj 28 yes \(1\) \(1\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{19}{28}\right)\) \(-1\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{9}{28}\right)\)
\(\chi_{735}(11,\cdot)\) 735.bl 42 no \(-1\) \(1\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{29}{42}\right)\)
\(\chi_{735}(13,\cdot)\) 735.bi 28 no \(1\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(1\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{3}{28}\right)\)
\(\chi_{735}(16,\cdot)\) 735.bg 21 no \(1\) \(1\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{2}{21}\right)\)
\(\chi_{735}(17,\cdot)\) 735.bs 84 yes \(-1\) \(1\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{73}{84}\right)\)
\(\chi_{735}(19,\cdot)\) 735.r 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{735}(22,\cdot)\) 735.bh 28 no \(-1\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{15}{28}\right)\) \(-1\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{13}{28}\right)\)
\(\chi_{735}(23,\cdot)\) 735.bt 84 yes \(1\) \(1\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{11}{84}\right)\)
\(\chi_{735}(26,\cdot)\) 735.bm 42 no \(1\) \(1\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{37}{42}\right)\)
\(\chi_{735}(29,\cdot)\) 735.bb 14 yes \(-1\) \(1\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{7}\right)\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{7}\right)\)
\(\chi_{735}(31,\cdot)\) 735.n 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{735}(32,\cdot)\) 735.bt 84 yes \(1\) \(1\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{73}{84}\right)\)
\(\chi_{735}(34,\cdot)\) 735.bc 14 no \(-1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{6}{7}\right)\) \(-1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{9}{14}\right)\)
\(\chi_{735}(37,\cdot)\) 735.bv 84 no \(-1\) \(1\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{59}{84}\right)\)
\(\chi_{735}(38,\cdot)\) 735.bs 84 yes \(-1\) \(1\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{79}{84}\right)\)
\(\chi_{735}(41,\cdot)\) 735.bf 14 no \(1\) \(1\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{7}\right)\) \(-1\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{14}\right)\)
\(\chi_{735}(43,\cdot)\) 735.bh 28 no \(-1\) \(1\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{9}{28}\right)\) \(-1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{19}{28}\right)\)
\(\chi_{735}(44,\cdot)\) 735.bq 42 yes \(-1\) \(1\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{5}{21}\right)\)
\(\chi_{735}(46,\cdot)\) 735.bg 21 no \(1\) \(1\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{19}{21}\right)\)
\(\chi_{735}(47,\cdot)\) 735.bs 84 yes \(-1\) \(1\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{8}{21}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{65}{84}\right)\)
\(\chi_{735}(52,\cdot)\) 735.bu 84 no \(1\) \(1\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{55}{84}\right)\)
\(\chi_{735}(53,\cdot)\) 735.bt 84 yes \(1\) \(1\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{16}{21}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{67}{84}\right)\)
\(\chi_{735}(58,\cdot)\) 735.bv 84 no \(-1\) \(1\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{19}{21}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{20}{21}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{5}{84}\right)\)
\(\chi_{735}(59,\cdot)\) 735.bp 42 yes \(1\) \(1\) \(e\left(\frac{1}{21}\right)\) \(e\left(\frac{2}{21}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{16}{21}\right)\)
\(\chi_{735}(61,\cdot)\) 735.br 42 no \(-1\) \(1\) \(e\left(\frac{17}{21}\right)\) \(e\left(\frac{13}{21}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{10}{21}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{5}{21}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{20}{21}\right)\)
\(\chi_{735}(62,\cdot)\) 735.bk 28 yes \(-1\) \(1\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{11}{28}\right)\) \(1\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{3}{28}\right)\)
\(\chi_{735}(64,\cdot)\) 735.bd 14 no \(1\) \(1\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{14}\right)\) \(1\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{9}{14}\right)\)
\(\chi_{735}(67,\cdot)\) 735.w 12 no \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{735}(68,\cdot)\) 735.x 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\)
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