Properties

Modulus $1620$
Structure \(C_{2}\times C_{2}\times C_{108}\)
Order $432$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1620)
 
pari: g = idealstar(,1620,2)
 

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 = $\chi_{1620}(811,\cdot)$, $\chi_{1620}(1541,\cdot)$, $\chi_{1620}(1297,\cdot)$

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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{1620}(1,\cdot)\) 1620.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1620}(7,\cdot)\) 1620.bv 108 yes \(1\) \(1\) \(e\left(\frac{53}{108}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{13}{108}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{55}{108}\right)\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{19}{27}\right)\)
\(\chi_{1620}(11,\cdot)\) 1620.bo 54 no \(1\) \(1\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{41}{54}\right)\)
\(\chi_{1620}(13,\cdot)\) 1620.bu 108 no \(-1\) \(1\) \(e\left(\frac{13}{108}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{47}{108}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{95}{108}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{23}{27}\right)\)
\(\chi_{1620}(17,\cdot)\) 1620.bk 36 no \(1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{1620}(19,\cdot)\) 1620.bf 18 no \(-1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{1620}(23,\cdot)\) 1620.bt 108 yes \(-1\) \(1\) \(e\left(\frac{55}{108}\right)\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{95}{108}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{107}{108}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{43}{54}\right)\)
\(\chi_{1620}(29,\cdot)\) 1620.bl 54 no \(-1\) \(1\) \(e\left(\frac{25}{54}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{27}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{17}{54}\right)\)
\(\chi_{1620}(31,\cdot)\) 1620.bn 54 no \(-1\) \(1\) \(e\left(\frac{23}{54}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{49}{54}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{27}\right)\)
\(\chi_{1620}(37,\cdot)\) 1620.bj 36 no \(-1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{1620}(41,\cdot)\) 1620.bq 54 no \(-1\) \(1\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{17}{54}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{54}\right)\)
\(\chi_{1620}(43,\cdot)\) 1620.bv 108 yes \(1\) \(1\) \(e\left(\frac{83}{108}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{55}{108}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{25}{108}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{16}{27}\right)\)
\(\chi_{1620}(47,\cdot)\) 1620.bt 108 yes \(-1\) \(1\) \(e\left(\frac{89}{108}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{85}{108}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{73}{108}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{47}{54}\right)\)
\(\chi_{1620}(49,\cdot)\) 1620.br 54 no \(1\) \(1\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{27}\right)\)
\(\chi_{1620}(53,\cdot)\) 1620.x 12 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1620}(59,\cdot)\) 1620.bm 54 yes \(1\) \(1\) \(e\left(\frac{4}{27}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{19}{54}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{13}{54}\right)\)
\(\chi_{1620}(61,\cdot)\) 1620.bg 27 no \(1\) \(1\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{16}{27}\right)\) \(e\left(\frac{17}{27}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{27}\right)\)
\(\chi_{1620}(67,\cdot)\) 1620.bv 108 yes \(1\) \(1\) \(e\left(\frac{85}{108}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{29}{108}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{23}{108}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{43}{54}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{5}{27}\right)\)
\(\chi_{1620}(71,\cdot)\) 1620.be 18 no \(1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{1620}(73,\cdot)\) 1620.bj 36 no \(-1\) \(1\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{1620}(77,\cdot)\) 1620.bs 108 no \(1\) \(1\) \(e\left(\frac{91}{108}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{5}{108}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{71}{108}\right)\) \(e\left(\frac{10}{27}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{25}{54}\right)\)
\(\chi_{1620}(79,\cdot)\) 1620.bp 54 yes \(-1\) \(1\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{13}{27}\right)\)
\(\chi_{1620}(83,\cdot)\) 1620.bt 108 yes \(-1\) \(1\) \(e\left(\frac{59}{108}\right)\) \(e\left(\frac{20}{27}\right)\) \(e\left(\frac{43}{108}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{103}{108}\right)\) \(e\left(\frac{5}{27}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{53}{54}\right)\)
\(\chi_{1620}(89,\cdot)\) 1620.z 18 no \(-1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{18}\right)\)
\(\chi_{1620}(91,\cdot)\) 1620.ba 18 no \(-1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{1620}(97,\cdot)\) 1620.bu 108 no \(-1\) \(1\) \(e\left(\frac{47}{108}\right)\) \(e\left(\frac{26}{27}\right)\) \(e\left(\frac{37}{108}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{61}{108}\right)\) \(e\left(\frac{13}{54}\right)\) \(e\left(\frac{13}{27}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{25}{27}\right)\)
\(\chi_{1620}(101,\cdot)\) 1620.bq 54 no \(-1\) \(1\) \(e\left(\frac{11}{27}\right)\) \(e\left(\frac{1}{54}\right)\) \(e\left(\frac{19}{27}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{7}{54}\right)\) \(e\left(\frac{7}{27}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{29}{54}\right)\)
\(\chi_{1620}(103,\cdot)\) 1620.bv 108 yes \(1\) \(1\) \(e\left(\frac{43}{108}\right)\) \(e\left(\frac{47}{54}\right)\) \(e\left(\frac{35}{108}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{65}{108}\right)\) \(e\left(\frac{5}{54}\right)\) \(e\left(\frac{37}{54}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{20}{27}\right)\)
\(\chi_{1620}(107,\cdot)\) 1620.w 12 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1620}(109,\cdot)\) 1620.r 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1620}(113,\cdot)\) 1620.bs 108 no \(1\) \(1\) \(e\left(\frac{25}{108}\right)\) \(e\left(\frac{11}{54}\right)\) \(e\left(\frac{107}{108}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{29}{108}\right)\) \(e\left(\frac{25}{27}\right)\) \(e\left(\frac{23}{27}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{49}{54}\right)\)
\(\chi_{1620}(119,\cdot)\) 1620.bm 54 yes \(1\) \(1\) \(e\left(\frac{14}{27}\right)\) \(e\left(\frac{8}{27}\right)\) \(e\left(\frac{41}{54}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{53}{54}\right)\) \(e\left(\frac{31}{54}\right)\) \(e\left(\frac{35}{54}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{54}\right)\)
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