Properties

Modulus $576$
Structure \(C_{2}\times C_{2}\times C_{48}\)
Order $192$

Learn more

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(576)
 
pari: g = idealstar(,576,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 192
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{2}\times C_{2}\times C_{48}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{576}(127,\cdot)$, $\chi_{576}(325,\cdot)$, $\chi_{576}(65,\cdot)$

First 32 of 192 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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{576}(1,\cdot)\) 576.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{576}(5,\cdot)\) 576.bn 48 yes \(-1\) \(1\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{576}(7,\cdot)\) 576.bh 24 no \(-1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{576}(11,\cdot)\) 576.bl 48 yes \(1\) \(1\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{576}(13,\cdot)\) 576.bm 48 yes \(1\) \(1\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{576}(17,\cdot)\) 576.j 4 no \(-1\) \(1\) \(i\) \(-1\) \(i\) \(i\) \(-1\) \(i\) \(1\) \(-1\) \(-i\) \(1\)
\(\chi_{576}(19,\cdot)\) 576.bf 16 no \(-1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(1\)
\(\chi_{576}(23,\cdot)\) 576.bj 24 no \(1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{576}(25,\cdot)\) 576.bg 24 no \(1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{576}(29,\cdot)\) 576.bn 48 yes \(-1\) \(1\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(-i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{576}(31,\cdot)\) 576.t 6 no \(-1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{576}(35,\cdot)\) 576.be 16 no \(1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(-i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(1\)
\(\chi_{576}(37,\cdot)\) 576.bd 16 no \(1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(-1\)
\(\chi_{576}(41,\cdot)\) 576.bi 24 no \(-1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{576}(43,\cdot)\) 576.bk 48 yes \(-1\) \(1\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(-i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{576}(47,\cdot)\) 576.y 12 no \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(-i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{576}(49,\cdot)\) 576.bb 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(1\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{576}(53,\cdot)\) 576.bc 16 no \(-1\) \(1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(-1\)
\(\chi_{576}(55,\cdot)\) 576.u 8 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(-1\)
\(\chi_{576}(59,\cdot)\) 576.bl 48 yes \(1\) \(1\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{576}(61,\cdot)\) 576.bm 48 yes \(1\) \(1\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{576}(65,\cdot)\) 576.q 6 no \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{576}(67,\cdot)\) 576.bk 48 yes \(-1\) \(1\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{576}(71,\cdot)\) 576.w 8 no \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(i\) \(e\left(\frac{3}{8}\right)\) \(-1\)
\(\chi_{576}(73,\cdot)\) 576.v 8 no \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(1\)
\(\chi_{576}(77,\cdot)\) 576.bn 48 yes \(-1\) \(1\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{576}(79,\cdot)\) 576.z 12 no \(-1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(1\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{576}(83,\cdot)\) 576.bl 48 yes \(1\) \(1\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{576}(85,\cdot)\) 576.bm 48 yes \(1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(-i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{576}(89,\cdot)\) 576.x 8 no \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(1\)
\(\chi_{576}(91,\cdot)\) 576.bf 16 no \(-1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(1\)
\(\chi_{576}(95,\cdot)\) 576.p 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
Click here to search among the remaining 160 characters.