Properties

Modulus 291
Structure \(C_{96}\times C_{2}\)
Order 192

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Show commands for: SageMath / Pari/GP

sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(291)
 
pari: g = idealstar(,291,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 192
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{96}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{291}(199,\cdot)$, $\chi_{291}(98,\cdot)$

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.

orbit label order primitive -1 1 2 4 5 7 8 10 11 13 14 16
\(\chi_{291}(1,\cdot)\) 291.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{291}(2,\cdot)\) 291.v 48 yes \(-1\) \(1\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{291}(4,\cdot)\) 291.q 24 no \(1\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{23}{24}\right)\) \(i\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{291}(5,\cdot)\) 291.x 96 yes \(1\) \(1\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{291}(7,\cdot)\) 291.w 96 no \(-1\) \(1\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{291}(8,\cdot)\) 291.o 16 yes \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-1\)
\(\chi_{291}(10,\cdot)\) 291.w 96 no \(-1\) \(1\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{291}(11,\cdot)\) 291.v 48 yes \(-1\) \(1\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{291}(13,\cdot)\) 291.w 96 no \(-1\) \(1\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{291}(14,\cdot)\) 291.x 96 yes \(1\) \(1\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{291}(16,\cdot)\) 291.n 12 no \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{291}(17,\cdot)\) 291.x 96 yes \(1\) \(1\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{291}(19,\cdot)\) 291.t 32 no \(-1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(-i\)
\(\chi_{291}(20,\cdot)\) 291.s 32 yes \(1\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(-i\)
\(\chi_{291}(22,\cdot)\) 291.f 4 no \(1\) \(1\) \(-1\) \(1\) \(i\) \(-i\) \(-1\) \(-i\) \(-1\) \(i\) \(i\) \(1\)
\(\chi_{291}(23,\cdot)\) 291.x 96 yes \(1\) \(1\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{291}(25,\cdot)\) 291.u 48 no \(1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{291}(26,\cdot)\) 291.x 96 yes \(1\) \(1\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{291}(28,\cdot)\) 291.t 32 no \(-1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(i\)
\(\chi_{291}(29,\cdot)\) 291.x 96 yes \(1\) \(1\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{291}(31,\cdot)\) 291.u 48 no \(1\) \(1\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{291}(32,\cdot)\) 291.v 48 yes \(-1\) \(1\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{291}(34,\cdot)\) 291.t 32 no \(-1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(i\)
\(\chi_{291}(35,\cdot)\) 291.j 6 yes \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{291}(37,\cdot)\) 291.w 96 no \(-1\) \(1\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{291}(38,\cdot)\) 291.x 96 yes \(1\) \(1\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{291}(40,\cdot)\) 291.w 96 no \(-1\) \(1\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{291}(41,\cdot)\) 291.x 96 yes \(1\) \(1\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{291}(43,\cdot)\) 291.q 24 no \(1\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{7}{24}\right)\) \(i\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{291}(44,\cdot)\) 291.v 48 yes \(-1\) \(1\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{291}(46,\cdot)\) 291.t 32 no \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(i\)
\(\chi_{291}(47,\cdot)\) 291.k 8 yes \(-1\) \(1\) \(i\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\)