Properties

Modulus $469$
Structure \(C_{66}\times C_{6}\)
Order $396$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(469)
 
pari: g = idealstar(,469,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 396
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{66}\times C_{6}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{469}(269,\cdot)$, $\chi_{469}(337,\cdot)$

First 32 of 396 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 \(-1\) \(1\) \(2\) \(3\) \(4\) \(5\) \(6\) \(8\) \(9\) \(10\) \(11\) \(12\)
\(\chi_{469}(1,\cdot)\) 469.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{469}(2,\cdot)\) 469.bm 66 yes \(-1\) \(1\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{19}{66}\right)\)
\(\chi_{469}(3,\cdot)\) 469.bh 66 yes \(1\) \(1\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{2}{33}\right)\)
\(\chi_{469}(4,\cdot)\) 469.y 33 yes \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{19}{33}\right)\)
\(\chi_{469}(5,\cdot)\) 469.bh 66 yes \(1\) \(1\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{16}{33}\right)\)
\(\chi_{469}(6,\cdot)\) 469.bl 66 yes \(-1\) \(1\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{23}{66}\right)\)
\(\chi_{469}(8,\cdot)\) 469.x 22 no \(-1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{19}{22}\right)\)
\(\chi_{469}(9,\cdot)\) 469.ba 33 yes \(1\) \(1\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{28}{33}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{4}{33}\right)\)
\(\chi_{469}(10,\cdot)\) 469.bj 66 yes \(-1\) \(1\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{17}{22}\right)\)
\(\chi_{469}(11,\cdot)\) 469.bm 66 yes \(-1\) \(1\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{65}{66}\right)\)
\(\chi_{469}(12,\cdot)\) 469.bg 66 yes \(1\) \(1\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{7}{11}\right)\)
\(\chi_{469}(13,\cdot)\) 469.bd 66 yes \(1\) \(1\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{10}{33}\right)\)
\(\chi_{469}(15,\cdot)\) 469.u 11 no \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{6}{11}\right)\)
\(\chi_{469}(16,\cdot)\) 469.y 33 yes \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{33}\right)\)
\(\chi_{469}(17,\cdot)\) 469.bj 66 yes \(-1\) \(1\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{20}{33}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{469}(18,\cdot)\) 469.bf 66 yes \(-1\) \(1\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{2}{33}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{23}{33}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{9}{22}\right)\)
\(\chi_{469}(19,\cdot)\) 469.bc 66 yes \(-1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{25}{66}\right)\)
\(\chi_{469}(20,\cdot)\) 469.bd 66 yes \(1\) \(1\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{2}{33}\right)\)
\(\chi_{469}(22,\cdot)\) 469.u 11 no \(1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{3}{11}\right)\)
\(\chi_{469}(23,\cdot)\) 469.y 33 yes \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{25}{33}\right)\) \(e\left(\frac{4}{33}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{2}{33}\right)\)
\(\chi_{469}(24,\cdot)\) 469.bk 66 yes \(-1\) \(1\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{61}{66}\right)\)
\(\chi_{469}(25,\cdot)\) 469.ba 33 yes \(1\) \(1\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{19}{33}\right)\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{26}{33}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{32}{33}\right)\)
\(\chi_{469}(26,\cdot)\) 469.bj 66 yes \(-1\) \(1\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{13}{22}\right)\)
\(\chi_{469}(27,\cdot)\) 469.w 22 yes \(1\) \(1\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{2}{11}\right)\)
\(\chi_{469}(29,\cdot)\) 469.g 3 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{469}(30,\cdot)\) 469.j 6 yes \(-1\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{469}(31,\cdot)\) 469.bn 66 yes \(1\) \(1\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{33}\right)\)
\(\chi_{469}(32,\cdot)\) 469.bm 66 yes \(-1\) \(1\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{1}{33}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{8}{33}\right)\) \(e\left(\frac{29}{33}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{29}{66}\right)\)
\(\chi_{469}(33,\cdot)\) 469.bj 66 yes \(-1\) \(1\) \(e\left(\frac{5}{33}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{10}{33}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{31}{33}\right)\) \(e\left(\frac{1}{22}\right)\)
\(\chi_{469}(34,\cdot)\) 469.bd 66 yes \(1\) \(1\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{32}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{29}{33}\right)\)
\(\chi_{469}(36,\cdot)\) 469.z 33 no \(1\) \(1\) \(e\left(\frac{7}{33}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{14}{33}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{16}{33}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{13}{33}\right)\) \(e\left(\frac{17}{33}\right)\) \(e\left(\frac{23}{33}\right)\)
\(\chi_{469}(37,\cdot)\) 469.h 3 yes \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)