Properties

Modulus $966$
Structure \(C_{66}\times C_{2}\times C_{2}\)
Order $264$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(966)
 
pari: g = idealstar(,966,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 264
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{66}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{966}(323,\cdot)$, $\chi_{966}(829,\cdot)$, $\chi_{966}(925,\cdot)$

First 32 of 264 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 \(-1\) \(1\) \(5\) \(11\) \(13\) \(17\) \(19\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{966}(1,\cdot)\) 966.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{966}(5,\cdot)\) 966.bc 66 no \(-1\) \(1\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{966}(11,\cdot)\) 966.bf 66 no \(1\) \(1\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{966}(13,\cdot)\) 966.v 22 no \(-1\) \(1\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{22}\right)\)
\(\chi_{966}(17,\cdot)\) 966.bc 66 no \(-1\) \(1\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{966}(19,\cdot)\) 966.be 66 no \(1\) \(1\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{966}(25,\cdot)\) 966.y 33 no \(1\) \(1\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{966}(29,\cdot)\) 966.w 22 no \(-1\) \(1\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{22}\right)\)
\(\chi_{966}(31,\cdot)\) 966.bb 66 no \(-1\) \(1\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{966}(37,\cdot)\) 966.z 66 no \(-1\) \(1\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{966}(41,\cdot)\) 966.t 22 no \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{966}(43,\cdot)\) 966.x 22 no \(-1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{966}(47,\cdot)\) 966.l 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\)
\(\chi_{966}(53,\cdot)\) 966.bf 66 no \(1\) \(1\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{966}(55,\cdot)\) 966.v 22 no \(-1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{21}{22}\right)\)
\(\chi_{966}(59,\cdot)\) 966.bd 66 no \(1\) \(1\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{966}(61,\cdot)\) 966.be 66 no \(1\) \(1\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{966}(65,\cdot)\) 966.bf 66 no \(1\) \(1\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{966}(67,\cdot)\) 966.z 66 no \(-1\) \(1\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{1}{11}\right)\)
\(\chi_{966}(71,\cdot)\) 966.w 22 no \(-1\) \(1\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{966}(73,\cdot)\) 966.bb 66 no \(-1\) \(1\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{15}{22}\right)\)
\(\chi_{966}(79,\cdot)\) 966.z 66 no \(-1\) \(1\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{966}(83,\cdot)\) 966.u 22 no \(-1\) \(1\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{966}(85,\cdot)\) 966.q 11 no \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\)
\(\chi_{966}(89,\cdot)\) 966.bc 66 no \(-1\) \(1\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{8}{11}\right)\)
\(\chi_{966}(95,\cdot)\) 966.ba 66 no \(-1\) \(1\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{5}{22}\right)\)
\(\chi_{966}(97,\cdot)\) 966.s 22 no \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{966}(101,\cdot)\) 966.bd 66 no \(1\) \(1\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{5}{11}\right)\)
\(\chi_{966}(103,\cdot)\) 966.be 66 no \(1\) \(1\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{966}(107,\cdot)\) 966.bf 66 no \(1\) \(1\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{966}(109,\cdot)\) 966.z 66 no \(-1\) \(1\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{9}{11}\right)\)
\(\chi_{966}(113,\cdot)\) 966.r 22 no \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{13}{22}\right)\)