Properties

Modulus $2880$
Structure \(C_{48}\times C_{4}\times C_{2}\times C_{2}\)
Order $768$

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Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(2880)
 
pari: g = idealstar(,2880,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 768
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{48}\times C_{4}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{2880}(2431,\cdot)$, $\chi_{2880}(901,\cdot)$, $\chi_{2880}(641,\cdot)$, $\chi_{2880}(577,\cdot)$

First 32 of 768 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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{2880}(1,\cdot)\) 2880.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{2880}(7,\cdot)\) 2880.ej 24 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{2880}(11,\cdot)\) 2880.ff 48 no \(1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{24}\right)\)
\(\chi_{2880}(13,\cdot)\) 2880.fm 48 yes \(-1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{2880}(17,\cdot)\) 2880.bg 4 no \(1\) \(1\) \(-i\) \(i\) \(1\) \(-i\) \(-i\) \(-i\) \(i\) \(1\) \(1\) \(1\)
\(\chi_{2880}(19,\cdot)\) 2880.ec 16 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{2880}(23,\cdot)\) 2880.el 24 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{2880}(29,\cdot)\) 2880.fh 48 yes \(-1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{11}{24}\right)\)
\(\chi_{2880}(31,\cdot)\) 2880.bz 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2880}(37,\cdot)\) 2880.ee 16 no \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(-1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{2880}(41,\cdot)\) 2880.eq 24 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{2880}(43,\cdot)\) 2880.ey 48 yes \(1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{2880}(47,\cdot)\) 2880.de 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2880}(49,\cdot)\) 2880.cu 12 no \(1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{2880}(53,\cdot)\) 2880.ef 16 no \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(-1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{2880}(59,\cdot)\) 2880.fd 48 yes \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(-i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{24}\right)\)
\(\chi_{2880}(61,\cdot)\) 2880.fi 48 no \(1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{23}{24}\right)\)
\(\chi_{2880}(67,\cdot)\) 2880.ey 48 yes \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(-1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{2880}(71,\cdot)\) 2880.cn 8 no \(1\) \(1\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(i\)
\(\chi_{2880}(73,\cdot)\) 2880.cf 8 no \(-1\) \(1\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\)
\(\chi_{2880}(77,\cdot)\) 2880.fn 48 yes \(1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{2880}(79,\cdot)\) 2880.dp 12 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(-i\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{2880}(83,\cdot)\) 2880.ez 48 yes \(-1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(-1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{23}{24}\right)\)
\(\chi_{2880}(89,\cdot)\) 2880.ck 8 no \(-1\) \(1\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\)
\(\chi_{2880}(91,\cdot)\) 2880.ea 16 no \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{2880}(97,\cdot)\) 2880.dm 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(i\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{2880}(101,\cdot)\) 2880.fj 48 no \(-1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{2880}(103,\cdot)\) 2880.ex 24 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{2880}(107,\cdot)\) 2880.dv 16 no \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{2880}(109,\cdot)\) 2880.dy 16 no \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(-1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{2880}(113,\cdot)\) 2880.dc 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(i\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{2880}(119,\cdot)\) 2880.ep 24 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{12}\right)\)