Properties

Modulus $896$
Structure \(C_{96}\times C_{2}\times C_{2}\)
Order $384$

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Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(896)
 
pari: g = idealstar(,896,2)
 

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 = $\chi_{896}(127,\cdot)$, $\chi_{896}(645,\cdot)$, $\chi_{896}(129,\cdot)$

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 \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\)
\(\chi_{896}(1,\cdot)\) 896.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{896}(3,\cdot)\) 896.bt 96 yes \(1\) \(1\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{41}{48}\right)\)
\(\chi_{896}(5,\cdot)\) 896.bv 96 yes \(-1\) \(1\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{19}{48}\right)\)
\(\chi_{896}(9,\cdot)\) 896.br 48 no \(1\) \(1\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{17}{24}\right)\)
\(\chi_{896}(11,\cdot)\) 896.bs 96 yes \(-1\) \(1\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{47}{48}\right)\)
\(\chi_{896}(13,\cdot)\) 896.bm 32 yes \(-1\) \(1\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{896}(15,\cdot)\) 896.w 8 no \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(i\) \(i\)
\(\chi_{896}(17,\cdot)\) 896.bg 24 no \(-1\) \(1\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{896}(19,\cdot)\) 896.bt 96 yes \(1\) \(1\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{37}{48}\right)\)
\(\chi_{896}(23,\cdot)\) 896.bp 48 no \(-1\) \(1\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{9}{16}\right)\) \(i\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{24}\right)\)
\(\chi_{896}(25,\cdot)\) 896.br 48 no \(1\) \(1\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{15}{16}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{896}(27,\cdot)\) 896.bk 32 yes \(1\) \(1\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{896}(29,\cdot)\) 896.bn 32 no \(1\) \(1\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{896}(31,\cdot)\) 896.z 12 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(-1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{896}(33,\cdot)\) 896.bb 12 no \(-1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{896}(37,\cdot)\) 896.bu 96 yes \(1\) \(1\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{43}{48}\right)\)
\(\chi_{896}(39,\cdot)\) 896.bp 48 no \(-1\) \(1\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{7}{16}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{19}{24}\right)\)
\(\chi_{896}(41,\cdot)\) 896.bf 16 no \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{896}(43,\cdot)\) 896.bl 32 no \(-1\) \(1\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{896}(45,\cdot)\) 896.bv 96 yes \(-1\) \(1\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{5}{48}\right)\)
\(\chi_{896}(47,\cdot)\) 896.bi 24 no \(1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{896}(51,\cdot)\) 896.bs 96 yes \(-1\) \(1\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{13}{48}\right)\)
\(\chi_{896}(53,\cdot)\) 896.bu 96 yes \(1\) \(1\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{47}{48}\right)\)
\(\chi_{896}(55,\cdot)\) 896.bd 16 no \(1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(i\) \(-i\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{896}(57,\cdot)\) 896.bc 16 no \(1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(i\) \(-i\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{896}(59,\cdot)\) 896.bt 96 yes \(1\) \(1\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{35}{48}\right)\)
\(\chi_{896}(61,\cdot)\) 896.bv 96 yes \(-1\) \(1\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{25}{48}\right)\)
\(\chi_{896}(65,\cdot)\) 896.t 6 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{896}(67,\cdot)\) 896.bs 96 yes \(-1\) \(1\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{41}{48}\right)\)
\(\chi_{896}(69,\cdot)\) 896.bm 32 yes \(-1\) \(1\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{896}(71,\cdot)\) 896.be 16 no \(-1\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(-i\) \(-i\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{896}(73,\cdot)\) 896.bo 48 no \(-1\) \(1\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{13}{16}\right)\) \(-i\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{1}{24}\right)\)