Properties

Modulus $2960$
Structure \(C_{36}\times C_{4}\times C_{4}\times C_{2}\)
Order $1152$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(2960)
 
pari: g = idealstar(,2960,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1152
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{36}\times C_{4}\times C_{4}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2960}(2591,\cdot)$, $\chi_{2960}(741,\cdot)$, $\chi_{2960}(1777,\cdot)$, $\chi_{2960}(2481,\cdot)$

First 32 of 1152 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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\)
\(\chi_{2960}(1,\cdot)\) 2960.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2960}(3,\cdot)\) 2960.hb 36 yes \(1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2960}(7,\cdot)\) 2960.gi 36 no \(1\) \(1\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{2960}(9,\cdot)\) 2960.gb 18 no \(1\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2960}(11,\cdot)\) 2960.eb 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(-i\)
\(\chi_{2960}(13,\cdot)\) 2960.gq 36 yes \(1\) \(1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2960}(17,\cdot)\) 2960.hx 36 no \(1\) \(1\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{2960}(19,\cdot)\) 2960.hf 36 yes \(1\) \(1\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{2960}(21,\cdot)\) 2960.gs 36 no \(1\) \(1\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{2960}(23,\cdot)\) 2960.ef 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(i\)
\(\chi_{2960}(27,\cdot)\) 2960.do 12 yes \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(1\)
\(\chi_{2960}(29,\cdot)\) 2960.ed 12 yes \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(-i\)
\(\chi_{2960}(31,\cdot)\) 2960.ck 4 no \(1\) \(1\) \(1\) \(-1\) \(1\) \(1\) \(-i\) \(-i\) \(i\) \(-1\) \(i\) \(1\)
\(\chi_{2960}(33,\cdot)\) 2960.gk 36 no \(-1\) \(1\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{2960}(39,\cdot)\) 2960.hy 36 no \(1\) \(1\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2960}(41,\cdot)\) 2960.gd 18 no \(1\) \(1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{2960}(43,\cdot)\) 2960.cp 4 yes \(-1\) \(1\) \(1\) \(-i\) \(1\) \(i\) \(i\) \(1\) \(1\) \(-i\) \(-1\) \(1\)
\(\chi_{2960}(47,\cdot)\) 2960.eh 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(-i\)
\(\chi_{2960}(49,\cdot)\) 2960.fu 18 no \(1\) \(1\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{2960}(51,\cdot)\) 2960.dx 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(-i\)
\(\chi_{2960}(53,\cdot)\) 2960.ha 36 yes \(-1\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2960}(57,\cdot)\) 2960.gp 36 no \(1\) \(1\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{2960}(59,\cdot)\) 2960.hg 36 yes \(1\) \(1\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{2960}(61,\cdot)\) 2960.hh 36 no \(-1\) \(1\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{2960}(63,\cdot)\) 2960.eh 12 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(i\)
\(\chi_{2960}(67,\cdot)\) 2960.hm 36 yes \(1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{2960}(69,\cdot)\) 2960.hc 36 yes \(-1\) \(1\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{2960}(71,\cdot)\) 2960.ft 18 no \(-1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2960}(73,\cdot)\) 2960.bn 4 no \(-1\) \(1\) \(-i\) \(-i\) \(-1\) \(-1\) \(i\) \(i\) \(-1\) \(-1\) \(-i\) \(i\)
\(\chi_{2960}(77,\cdot)\) 2960.gz 36 yes \(-1\) \(1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2960}(79,\cdot)\) 2960.gm 36 no \(1\) \(1\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{2960}(81,\cdot)\) 2960.dk 9 no \(1\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)