Properties

Modulus $2736$
Structure \(C_{36}\times C_{6}\times C_{2}\times C_{2}\)
Order $864$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(2736)
 
pari: g = idealstar(,2736,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 864
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{36}\times C_{6}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2736}(1711,\cdot)$, $\chi_{2736}(2053,\cdot)$, $\chi_{2736}(1217,\cdot)$, $\chi_{2736}(1009,\cdot)$

First 32 of 864 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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(23\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{2736}(1,\cdot)\) 2736.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2736}(5,\cdot)\) 2736.he 36 yes \(-1\) \(1\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{25}{36}\right)\) \(1\) \(e\left(\frac{29}{36}\right)\)
\(\chi_{2736}(7,\cdot)\) 2736.cr 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2736}(11,\cdot)\) 2736.ea 12 yes \(1\) \(1\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{2736}(13,\cdot)\) 2736.gp 36 yes \(-1\) \(1\) \(e\left(\frac{31}{36}\right)\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{36}\right)\)
\(\chi_{2736}(17,\cdot)\) 2736.fj 18 no \(-1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{2736}(23,\cdot)\) 2736.ez 18 no \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{18}\right)\)
\(\chi_{2736}(25,\cdot)\) 2736.fd 18 no \(1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(1\) \(e\left(\frac{11}{18}\right)\)
\(\chi_{2736}(29,\cdot)\) 2736.gz 36 yes \(1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{17}{36}\right)\) \(-1\) \(e\left(\frac{19}{36}\right)\)
\(\chi_{2736}(31,\cdot)\) 2736.di 6 no \(1\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{2736}(35,\cdot)\) 2736.gv 36 no \(1\) \(1\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{36}\right)\)
\(\chi_{2736}(37,\cdot)\) 2736.w 4 no \(-1\) \(1\) \(i\) \(-1\) \(i\) \(i\) \(1\) \(-1\) \(-1\) \(i\) \(-1\) \(-i\)
\(\chi_{2736}(41,\cdot)\) 2736.fn 18 no \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(-1\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{2736}(43,\cdot)\) 2736.hi 36 yes \(-1\) \(1\) \(e\left(\frac{29}{36}\right)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{29}{36}\right)\)
\(\chi_{2736}(47,\cdot)\) 2736.gc 18 no \(1\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(-1\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{2736}(49,\cdot)\) 2736.r 3 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2736}(53,\cdot)\) 2736.hc 36 no \(1\) \(1\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{25}{36}\right)\)
\(\chi_{2736}(55,\cdot)\) 2736.fv 18 no \(-1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{2736}(59,\cdot)\) 2736.gx 36 yes \(-1\) \(1\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{19}{36}\right)\) \(1\) \(e\left(\frac{35}{36}\right)\)
\(\chi_{2736}(61,\cdot)\) 2736.hf 36 yes \(1\) \(1\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{29}{36}\right)\) \(1\) \(e\left(\frac{25}{36}\right)\)
\(\chi_{2736}(65,\cdot)\) 2736.bf 6 no \(1\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{2736}(67,\cdot)\) 2736.hh 36 yes \(1\) \(1\) \(e\left(\frac{19}{36}\right)\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{19}{36}\right)\)
\(\chi_{2736}(71,\cdot)\) 2736.fy 18 no \(-1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{2736}(73,\cdot)\) 2736.fi 18 no \(1\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{2736}(77,\cdot)\) 2736.ed 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\)
\(\chi_{2736}(79,\cdot)\) 2736.ex 18 no \(1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{2736}(83,\cdot)\) 2736.dy 12 yes \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{2736}(85,\cdot)\) 2736.gm 36 yes \(1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{19}{36}\right)\)
\(\chi_{2736}(89,\cdot)\) 2736.fh 18 no \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{2736}(91,\cdot)\) 2736.gt 36 no \(1\) \(1\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{25}{36}\right)\)
\(\chi_{2736}(97,\cdot)\) 2736.gg 18 no \(-1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{2736}(101,\cdot)\) 2736.he 36 yes \(-1\) \(1\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{36}\right)\) \(1\) \(e\left(\frac{13}{36}\right)\)