Properties

Modulus $1152$
Structure \(C_{96}\times C_{2}\times C_{2}\)
Order $384$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(1152)
 
pari: g = idealstar(,1152,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 384
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{96}\times C_{2}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{1152}(127,\cdot)$, $\chi_{1152}(901,\cdot)$, $\chi_{1152}(641,\cdot)$

First 32 of 384 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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{1152}(1,\cdot)\) 1152.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{1152}(5,\cdot)\) 1152.bt 96 yes \(-1\) \(1\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{1152}(7,\cdot)\) 1152.bo 48 no \(-1\) \(1\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(-i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1152}(11,\cdot)\) 1152.bs 96 yes \(1\) \(1\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1152}(13,\cdot)\) 1152.bv 96 yes \(1\) \(1\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1152}(17,\cdot)\) 1152.x 8 no \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(1\)
\(\chi_{1152}(19,\cdot)\) 1152.bk 32 no \(-1\) \(1\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(i\)
\(\chi_{1152}(23,\cdot)\) 1152.bp 48 no \(1\) \(1\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1152}(25,\cdot)\) 1152.bq 48 no \(1\) \(1\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(-i\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1152}(29,\cdot)\) 1152.bt 96 yes \(-1\) \(1\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1152}(31,\cdot)\) 1152.z 12 no \(-1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(1\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1152}(35,\cdot)\) 1152.bm 32 no \(1\) \(1\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{25}{32}\right)\) \(i\)
\(\chi_{1152}(37,\cdot)\) 1152.bl 32 no \(1\) \(1\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{32}\right)\) \(i\)
\(\chi_{1152}(41,\cdot)\) 1152.br 48 no \(-1\) \(1\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(-i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{1152}(43,\cdot)\) 1152.bu 96 yes \(-1\) \(1\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1152}(47,\cdot)\) 1152.bj 24 no \(1\) \(1\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1152}(49,\cdot)\) 1152.bg 24 no \(1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{1152}(53,\cdot)\) 1152.bn 32 no \(-1\) \(1\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{23}{32}\right)\) \(i\)
\(\chi_{1152}(55,\cdot)\) 1152.bf 16 no \(-1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(i\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(1\)
\(\chi_{1152}(59,\cdot)\) 1152.bs 96 yes \(1\) \(1\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1152}(61,\cdot)\) 1152.bv 96 yes \(1\) \(1\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{1152}(65,\cdot)\) 1152.n 6 no \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{1152}(67,\cdot)\) 1152.bu 96 yes \(-1\) \(1\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{1152}(71,\cdot)\) 1152.be 16 no \(1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(1\)
\(\chi_{1152}(73,\cdot)\) 1152.bd 16 no \(1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(-1\)
\(\chi_{1152}(77,\cdot)\) 1152.bt 96 yes \(-1\) \(1\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{1152}(79,\cdot)\) 1152.bh 24 no \(-1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{1152}(83,\cdot)\) 1152.bs 96 yes \(1\) \(1\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{1152}(85,\cdot)\) 1152.bv 96 yes \(1\) \(1\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{1152}(89,\cdot)\) 1152.bc 16 no \(-1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(i\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(-1\)
\(\chi_{1152}(91,\cdot)\) 1152.bk 32 no \(-1\) \(1\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{32}\right)\) \(-i\)
\(\chi_{1152}(95,\cdot)\) 1152.y 12 no \(1\) \(1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\)