Properties

Modulus $1296$
Structure \(C_{2}\times C_{2}\times C_{108}\)
Order $432$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1296)
 
pari: g = idealstar(,1296,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 432
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{108}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1296}(1135,\cdot)$, $\chi_{1296}(325,\cdot)$, $\chi_{1296}(1217,\cdot)$

First 32 of 432 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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{1296}(1,\cdot)\) 1296.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1296}(5,\cdot)\) 1296.bu 108 yes \(-1\) \(1\) \(e\left(\frac{5}{108}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{85}{108}\right)\) \(e\left(\frac{17}{108}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{55}{108}\right)\) \(e\left(\frac{14}{27}\right)\)
\(\chi_{1296}(7,\cdot)\) 1296.br 54 no \(-1\) \(1\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{23}{54}\right)\)
\(\chi_{1296}(11,\cdot)\) 1296.bs 108 yes \(1\) \(1\) \(e\left(\frac{85}{108}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{95}{108}\right)\) \(e\left(\frac{73}{108}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{71}{108}\right)\) \(e\left(\frac{17}{54}\right)\)
\(\chi_{1296}(13,\cdot)\) 1296.bv 108 yes \(1\) \(1\) \(e\left(\frac{17}{108}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{73}{108}\right)\) \(e\left(\frac{47}{108}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{7}{54}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{79}{108}\right)\) \(e\left(\frac{26}{27}\right)\)
\(\chi_{1296}(17,\cdot)\) 1296.bc 18 no \(-1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{1296}(19,\cdot)\) 1296.bi 36 no \(-1\) \(1\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{1296}(23,\cdot)\) 1296.bn 54 no \(1\) \(1\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{7}{54}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{31}{54}\right)\)
\(\chi_{1296}(25,\cdot)\) 1296.bp 54 no \(1\) \(1\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{1}{27}\right)\)
\(\chi_{1296}(29,\cdot)\) 1296.bu 108 yes \(-1\) \(1\) \(e\left(\frac{55}{108}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{71}{108}\right)\) \(e\left(\frac{79}{108}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{65}{108}\right)\) \(e\left(\frac{19}{27}\right)\)
\(\chi_{1296}(31,\cdot)\) 1296.bm 54 no \(-1\) \(1\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{49}{54}\right)\)
\(\chi_{1296}(35,\cdot)\) 1296.bk 36 no \(1\) \(1\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{17}{18}\right)\)
\(\chi_{1296}(37,\cdot)\) 1296.bh 36 no \(1\) \(1\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{1296}(41,\cdot)\) 1296.bl 54 no \(-1\) \(1\) \(e\left(\frac{2}{27}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{22}{27}\right)\) \(e\left(\frac{17}{27}\right)\)
\(\chi_{1296}(43,\cdot)\) 1296.bt 108 yes \(-1\) \(1\) \(e\left(\frac{67}{108}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{5}{108}\right)\) \(e\left(\frac{1}{108}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{89}{108}\right)\) \(e\left(\frac{35}{54}\right)\)
\(\chi_{1296}(47,\cdot)\) 1296.bq 54 no \(1\) \(1\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{5}{54}\right)\)
\(\chi_{1296}(49,\cdot)\) 1296.bg 27 no \(1\) \(1\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{23}{27}\right)\)
\(\chi_{1296}(53,\cdot)\) 1296.x 12 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1296}(55,\cdot)\) 1296.t 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1296}(59,\cdot)\) 1296.bs 108 yes \(1\) \(1\) \(e\left(\frac{77}{108}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{67}{108}\right)\) \(e\left(\frac{89}{108}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{91}{108}\right)\) \(e\left(\frac{37}{54}\right)\)
\(\chi_{1296}(61,\cdot)\) 1296.bv 108 yes \(1\) \(1\) \(e\left(\frac{97}{108}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{29}{108}\right)\) \(e\left(\frac{103}{108}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{95}{108}\right)\) \(e\left(\frac{7}{27}\right)\)
\(\chi_{1296}(65,\cdot)\) 1296.bo 54 no \(-1\) \(1\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{13}{27}\right)\)
\(\chi_{1296}(67,\cdot)\) 1296.bt 108 yes \(-1\) \(1\) \(e\left(\frac{53}{108}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{91}{108}\right)\) \(e\left(\frac{83}{108}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{43}{108}\right)\) \(e\left(\frac{43}{54}\right)\)
\(\chi_{1296}(71,\cdot)\) 1296.bd 18 no \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{1296}(73,\cdot)\) 1296.bb 18 no \(1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{1296}(77,\cdot)\) 1296.bu 108 yes \(-1\) \(1\) \(e\left(\frac{11}{108}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{79}{108}\right)\) \(e\left(\frac{59}{108}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{13}{108}\right)\) \(e\left(\frac{20}{27}\right)\)
\(\chi_{1296}(79,\cdot)\) 1296.bm 54 no \(-1\) \(1\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{47}{54}\right)\)
\(\chi_{1296}(83,\cdot)\) 1296.bs 108 yes \(1\) \(1\) \(e\left(\frac{19}{108}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{53}{108}\right)\) \(e\left(\frac{43}{108}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{101}{108}\right)\) \(e\left(\frac{47}{54}\right)\)
\(\chi_{1296}(85,\cdot)\) 1296.bv 108 yes \(1\) \(1\) \(e\left(\frac{11}{108}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{79}{108}\right)\) \(e\left(\frac{5}{108}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{13}{108}\right)\) \(e\left(\frac{20}{27}\right)\)
\(\chi_{1296}(89,\cdot)\) 1296.bf 18 no \(-1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{1296}(91,\cdot)\) 1296.bi 36 no \(-1\) \(1\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{1296}(95,\cdot)\) 1296.bq 54 no \(1\) \(1\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{29}{54}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{43}{54}\right)\)
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