Properties

Modulus 485
Structure \(C_{96}\times C_{4}\)
Order 384

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Show commands for: Pari/GP / SageMath

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(485)
 
pari: g = idealstar(,485,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 384
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{96}\times C_{4}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{485}(296,\cdot)$, $\chi_{485}(292,\cdot)$

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.

orbit label order primitive -1 1 2 3 4 6 7 8 9 11 12 13
\(\chi_{485}(1,\cdot)\) 485.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{485}(2,\cdot)\) 485.bm 48 yes \(-1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{29}{48}\right)\)
\(\chi_{485}(3,\cdot)\) 485.bm 48 yes \(-1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{48}\right)\)
\(\chi_{485}(4,\cdot)\) 485.bd 24 yes \(1\) \(1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{11}{24}\right)\) \(-i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{12}\right)\) \(i\) \(e\left(\frac{5}{24}\right)\)
\(\chi_{485}(6,\cdot)\) 485.x 12 no \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{485}(7,\cdot)\) 485.br 96 yes \(1\) \(1\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{79}{96}\right)\)
\(\chi_{485}(8,\cdot)\) 485.ba 16 yes \(-1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{485}(9,\cdot)\) 485.bd 24 yes \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{17}{24}\right)\) \(i\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(-i\) \(e\left(\frac{23}{24}\right)\)
\(\chi_{485}(11,\cdot)\) 485.bk 48 no \(1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{19}{48}\right)\)
\(\chi_{485}(12,\cdot)\) 485.ba 16 yes \(-1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(i\) \(-1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{485}(13,\cdot)\) 485.br 96 yes \(1\) \(1\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{73}{96}\right)\)
\(\chi_{485}(14,\cdot)\) 485.bp 96 yes \(-1\) \(1\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{41}{96}\right)\)
\(\chi_{485}(16,\cdot)\) 485.x 12 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{485}(17,\cdot)\) 485.bo 96 yes \(1\) \(1\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{89}{96}\right)\)
\(\chi_{485}(18,\cdot)\) 485.ba 16 yes \(-1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(-1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{485}(19,\cdot)\) 485.bi 32 yes \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{19}{32}\right)\)
\(\chi_{485}(21,\cdot)\) 485.bq 96 no \(-1\) \(1\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{29}{96}\right)\)
\(\chi_{485}(22,\cdot)\) 485.j 4 yes \(-1\) \(1\) \(-i\) \(i\) \(-1\) \(1\) \(1\) \(i\) \(-1\) \(-1\) \(-i\) \(1\)
\(\chi_{485}(23,\cdot)\) 485.br 96 yes \(1\) \(1\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{29}{96}\right)\)
\(\chi_{485}(24,\cdot)\) 485.bd 24 yes \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{24}\right)\) \(i\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{12}\right)\) \(-i\) \(e\left(\frac{7}{24}\right)\)
\(\chi_{485}(26,\cdot)\) 485.bq 96 no \(-1\) \(1\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{35}{96}\right)\)
\(\chi_{485}(27,\cdot)\) 485.ba 16 yes \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(i\) \(-1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{485}(28,\cdot)\) 485.bg 32 yes \(1\) \(1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{32}\right)\)
\(\chi_{485}(29,\cdot)\) 485.bp 96 yes \(-1\) \(1\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{85}{96}\right)\)
\(\chi_{485}(31,\cdot)\) 485.bk 48 no \(1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{47}{48}\right)\)
\(\chi_{485}(32,\cdot)\) 485.bm 48 yes \(-1\) \(1\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{48}\right)\)
\(\chi_{485}(33,\cdot)\) 485.r 8 yes \(-1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(1\) \(1\) \(-i\) \(1\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{485}(34,\cdot)\) 485.bi 32 yes \(-1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{17}{32}\right)\)
\(\chi_{485}(36,\cdot)\) 485.l 6 no \(1\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{485}(37,\cdot)\) 485.br 96 yes \(1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{43}{96}\right)\)
\(\chi_{485}(38,\cdot)\) 485.bo 96 yes \(1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{19}{96}\right)\)
\(\chi_{485}(39,\cdot)\) 485.bp 96 yes \(-1\) \(1\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{23}{96}\right)\)