Properties

Modulus $4560$
Structure \(C_{36}\times C_{4}\times C_{2}\times C_{2}\times C_{2}\)
Order $1152$

Learn more

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(4560)
 
pari: g = idealstar(,4560,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 1152
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{36}\times C_{4}\times C_{2}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{4560}(1711,\cdot)$, $\chi_{4560}(1141,\cdot)$, $\chi_{4560}(3041,\cdot)$, $\chi_{4560}(2737,\cdot)$, $\chi_{4560}(1921,\cdot)$

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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{4560}(1,\cdot)\) 4560.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{4560}(7,\cdot)\) 4560.fq 12 no \(1\) \(1\) \(-i\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{4560}(11,\cdot)\) 4560.gd 12 no \(1\) \(1\) \(1\) \(i\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{4560}(13,\cdot)\) 4560.ip 36 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{4560}(17,\cdot)\) 4560.iq 36 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{23}{36}\right)\)
\(\chi_{4560}(23,\cdot)\) 4560.iv 36 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{1}{36}\right)\)
\(\chi_{4560}(29,\cdot)\) 4560.hq 36 yes \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(-i\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{13}{36}\right)\)
\(\chi_{4560}(31,\cdot)\) 4560.di 6 no \(1\) \(1\) \(-1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4560}(37,\cdot)\) 4560.ch 4 no \(1\) \(1\) \(-i\) \(i\) \(1\) \(i\) \(i\) \(-i\) \(-1\) \(1\) \(1\) \(1\)
\(\chi_{4560}(41,\cdot)\) 4560.gk 18 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{4560}(43,\cdot)\) 4560.in 36 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{4560}(47,\cdot)\) 4560.hz 36 no \(-1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(i\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{13}{36}\right)\)
\(\chi_{4560}(49,\cdot)\) 4560.ds 6 no \(1\) \(1\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4560}(53,\cdot)\) 4560.il 36 yes \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{13}{36}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{4560}(59,\cdot)\) 4560.iy 36 yes \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{19}{36}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{36}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{36}\right)\)
\(\chi_{4560}(61,\cdot)\) 4560.jb 36 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{17}{18}\right)\) \(e\left(\frac{19}{36}\right)\)
\(\chi_{4560}(67,\cdot)\) 4560.ib 36 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{4560}(71,\cdot)\) 4560.hf 18 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{4560}(73,\cdot)\) 4560.ir 36 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{35}{36}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{11}{36}\right)\)
\(\chi_{4560}(77,\cdot)\) 4560.cm 4 no \(1\) \(1\) \(-i\) \(i\) \(1\) \(-i\) \(-i\) \(i\) \(1\) \(1\) \(1\) \(-1\)
\(\chi_{4560}(79,\cdot)\) 4560.go 18 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{4560}(83,\cdot)\) 4560.fi 12 yes \(-1\) \(1\) \(-i\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4560}(89,\cdot)\) 4560.gz 18 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{4560}(91,\cdot)\) 4560.hm 36 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{5}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{19}{36}\right)\)
\(\chi_{4560}(97,\cdot)\) 4560.hx 36 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{36}\right)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{23}{36}\right)\)
\(\chi_{4560}(101,\cdot)\) 4560.ja 36 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{23}{36}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{36}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{25}{36}\right)\)
\(\chi_{4560}(103,\cdot)\) 4560.fv 12 no \(-1\) \(1\) \(i\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{4560}(107,\cdot)\) 4560.ff 12 yes \(1\) \(1\) \(i\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4560}(109,\cdot)\) 4560.hr 36 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{25}{36}\right)\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{7}{9}\right)\) \(e\left(\frac{31}{36}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{36}\right)\)
\(\chi_{4560}(113,\cdot)\) 4560.br 4 no \(-1\) \(1\) \(-i\) \(-1\) \(-i\) \(i\) \(-i\) \(-1\) \(-1\) \(i\) \(1\) \(i\)
\(\chi_{4560}(119,\cdot)\) 4560.gs 18 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{18}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{4560}(121,\cdot)\) 4560.dx 6 no \(1\) \(1\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\)