Properties

Modulus 6004
Structure \(C_{234}\times C_{6}\times C_{2}\)
Order 2808

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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(6004)
 
pari: g = idealstar(,6004,2)
 

Character group

sage: G.order()
 
pari: g.no
 
Order = 2808
sage: H.invariants()
 
pari: g.cyc
 
Structure = \(C_{234}\times C_{6}\times C_{2}\)
sage: H.gens()
 
pari: g.gen
 
Generators = $\chi_{6004}(2689,\cdot)$, $\chi_{6004}(577,\cdot)$, $\chi_{6004}(3003,\cdot)$

First 32 of 2808 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 3 5 7 9 11 13 15 17 21 23
\(\chi_{6004}(1,\cdot)\) 6004.a 1 no \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\) \(1\)
\(\chi_{6004}(3,\cdot)\) 6004.es 234 yes \(-1\) \(1\) \(e\left(\frac{211}{234}\right)\) \(e\left(\frac{41}{117}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{94}{117}\right)\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{11}{234}\right)\) \(e\left(\frac{59}{234}\right)\) \(e\left(\frac{115}{234}\right)\) \(e\left(\frac{97}{234}\right)\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{6004}(5,\cdot)\) 6004.ea 117 no \(1\) \(1\) \(e\left(\frac{41}{117}\right)\) \(e\left(\frac{59}{117}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{82}{117}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{55}{117}\right)\) \(e\left(\frac{100}{117}\right)\) \(e\left(\frac{68}{117}\right)\) \(e\left(\frac{95}{117}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{6004}(7,\cdot)\) 6004.dp 78 yes \(1\) \(1\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{55}{78}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{47}{78}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{6004}(9,\cdot)\) 6004.eb 117 no \(1\) \(1\) \(e\left(\frac{94}{117}\right)\) \(e\left(\frac{82}{117}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{71}{117}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{11}{117}\right)\) \(e\left(\frac{59}{117}\right)\) \(e\left(\frac{115}{117}\right)\) \(e\left(\frac{97}{117}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{6004}(11,\cdot)\) 6004.dw 78 yes \(-1\) \(1\) \(e\left(\frac{1}{26}\right)\) \(e\left(\frac{28}{39}\right)\) \(e\left(\frac{55}{78}\right)\) \(e\left(\frac{1}{13}\right)\) \(e\left(\frac{61}{78}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{59}{78}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{29}{39}\right)\) \(-1\)
\(\chi_{6004}(13,\cdot)\) 6004.ef 234 no \(-1\) \(1\) \(e\left(\frac{11}{234}\right)\) \(e\left(\frac{55}{117}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{11}{117}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{49}{234}\right)\) \(e\left(\frac{121}{234}\right)\) \(e\left(\frac{109}{117}\right)\) \(e\left(\frac{191}{234}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{6004}(15,\cdot)\) 6004.ep 234 yes \(-1\) \(1\) \(e\left(\frac{59}{234}\right)\) \(e\left(\frac{100}{117}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{59}{117}\right)\) \(e\left(\frac{59}{78}\right)\) \(e\left(\frac{121}{234}\right)\) \(e\left(\frac{25}{234}\right)\) \(e\left(\frac{17}{234}\right)\) \(e\left(\frac{53}{234}\right)\) \(e\left(\frac{13}{18}\right)\)
\(\chi_{6004}(17,\cdot)\) 6004.ek 234 no \(-1\) \(1\) \(e\left(\frac{115}{234}\right)\) \(e\left(\frac{68}{117}\right)\) \(e\left(\frac{47}{78}\right)\) \(e\left(\frac{115}{117}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{109}{117}\right)\) \(e\left(\frac{17}{234}\right)\) \(e\left(\frac{49}{234}\right)\) \(e\left(\frac{11}{117}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{6004}(21,\cdot)\) 6004.er 234 no \(-1\) \(1\) \(e\left(\frac{97}{234}\right)\) \(e\left(\frac{95}{117}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{97}{117}\right)\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{191}{234}\right)\) \(e\left(\frac{53}{234}\right)\) \(e\left(\frac{11}{117}\right)\) \(e\left(\frac{103}{234}\right)\) \(e\left(\frac{1}{9}\right)\)
\(\chi_{6004}(23,\cdot)\) 6004.cd 18 yes \(-1\) \(1\) \(e\left(\frac{5}{18}\right)\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{9}\right)\) \(-1\) \(e\left(\frac{8}{9}\right)\) \(e\left(\frac{13}{18}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{1}{9}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{6004}(25,\cdot)\) 6004.ea 117 no \(1\) \(1\) \(e\left(\frac{82}{117}\right)\) \(e\left(\frac{1}{117}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{47}{117}\right)\) \(e\left(\frac{17}{39}\right)\) \(e\left(\frac{110}{117}\right)\) \(e\left(\frac{83}{117}\right)\) \(e\left(\frac{19}{117}\right)\) \(e\left(\frac{73}{117}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{6004}(27,\cdot)\) 6004.dg 78 yes \(-1\) \(1\) \(e\left(\frac{55}{78}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{11}{78}\right)\) \(e\left(\frac{59}{78}\right)\) \(e\left(\frac{37}{78}\right)\) \(e\left(\frac{19}{78}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{6004}(29,\cdot)\) 6004.eh 234 no \(1\) \(1\) \(e\left(\frac{49}{117}\right)\) \(e\left(\frac{100}{117}\right)\) \(e\left(\frac{11}{78}\right)\) \(e\left(\frac{98}{117}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{121}{234}\right)\) \(e\left(\frac{32}{117}\right)\) \(e\left(\frac{95}{234}\right)\) \(e\left(\frac{131}{234}\right)\) \(e\left(\frac{5}{9}\right)\)
\(\chi_{6004}(31,\cdot)\) 6004.dn 78 yes \(1\) \(1\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{43}{78}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{25}{78}\right)\) \(e\left(\frac{15}{26}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{47}{78}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{6004}(33,\cdot)\) 6004.el 234 no \(1\) \(1\) \(e\left(\frac{110}{117}\right)\) \(e\left(\frac{8}{117}\right)\) \(e\left(\frac{17}{78}\right)\) \(e\left(\frac{103}{117}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{5}{234}\right)\) \(e\left(\frac{1}{117}\right)\) \(e\left(\frac{109}{234}\right)\) \(e\left(\frac{37}{234}\right)\) \(e\left(\frac{7}{9}\right)\)
\(\chi_{6004}(35,\cdot)\) 6004.et 234 yes \(1\) \(1\) \(e\left(\frac{101}{117}\right)\) \(e\left(\frac{113}{117}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{85}{117}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{28}{117}\right)\) \(e\left(\frac{97}{117}\right)\) \(e\left(\frac{43}{234}\right)\) \(e\left(\frac{98}{117}\right)\) \(e\left(\frac{5}{18}\right)\)
\(\chi_{6004}(37,\cdot)\) 6004.ds 78 no \(1\) \(1\) \(e\left(\frac{29}{39}\right)\) \(e\left(\frac{4}{39}\right)\) \(e\left(\frac{71}{78}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{61}{78}\right)\) \(e\left(\frac{11}{13}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{17}{26}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{6004}(39,\cdot)\) 6004.dt 78 no \(1\) \(1\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{32}{39}\right)\) \(e\left(\frac{11}{39}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{1}{78}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{10}{13}\right)\) \(e\left(\frac{11}{26}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{6004}(41,\cdot)\) 6004.el 234 no \(1\) \(1\) \(e\left(\frac{41}{117}\right)\) \(e\left(\frac{20}{117}\right)\) \(e\left(\frac{23}{78}\right)\) \(e\left(\frac{82}{117}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{71}{234}\right)\) \(e\left(\frac{61}{117}\right)\) \(e\left(\frac{97}{234}\right)\) \(e\left(\frac{151}{234}\right)\) \(e\left(\frac{4}{9}\right)\)
\(\chi_{6004}(43,\cdot)\) 6004.et 234 yes \(1\) \(1\) \(e\left(\frac{80}{117}\right)\) \(e\left(\frac{20}{117}\right)\) \(e\left(\frac{5}{39}\right)\) \(e\left(\frac{43}{117}\right)\) \(e\left(\frac{23}{26}\right)\) \(e\left(\frac{94}{117}\right)\) \(e\left(\frac{100}{117}\right)\) \(e\left(\frac{19}{234}\right)\) \(e\left(\frac{95}{117}\right)\) \(e\left(\frac{11}{18}\right)\)
\(\chi_{6004}(45,\cdot)\) 6004.cu 39 no \(1\) \(1\) \(e\left(\frac{2}{13}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{19}{39}\right)\) \(e\left(\frac{4}{13}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{14}{39}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{25}{39}\right)\) \(1\)
\(\chi_{6004}(47,\cdot)\) 6004.et 234 yes \(1\) \(1\) \(e\left(\frac{4}{117}\right)\) \(e\left(\frac{1}{117}\right)\) \(e\left(\frac{10}{39}\right)\) \(e\left(\frac{8}{117}\right)\) \(e\left(\frac{7}{26}\right)\) \(e\left(\frac{110}{117}\right)\) \(e\left(\frac{5}{117}\right)\) \(e\left(\frac{77}{234}\right)\) \(e\left(\frac{34}{117}\right)\) \(e\left(\frac{1}{18}\right)\)
\(\chi_{6004}(49,\cdot)\) 6004.cv 39 no \(1\) \(1\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{12}{13}\right)\) \(e\left(\frac{1}{39}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{16}{39}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{37}{39}\right)\) \(e\left(\frac{8}{39}\right)\) \(e\left(\frac{2}{39}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{6004}(51,\cdot)\) 6004.ev 234 yes \(1\) \(1\) \(e\left(\frac{46}{117}\right)\) \(e\left(\frac{109}{117}\right)\) \(e\left(\frac{3}{26}\right)\) \(e\left(\frac{92}{117}\right)\) \(e\left(\frac{1}{78}\right)\) \(e\left(\frac{229}{234}\right)\) \(e\left(\frac{38}{117}\right)\) \(e\left(\frac{82}{117}\right)\) \(e\left(\frac{119}{234}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{6004}(53,\cdot)\) 6004.eh 234 no \(1\) \(1\) \(e\left(\frac{109}{117}\right)\) \(e\left(\frac{115}{117}\right)\) \(e\left(\frac{77}{78}\right)\) \(e\left(\frac{101}{117}\right)\) \(e\left(\frac{6}{13}\right)\) \(e\left(\frac{145}{234}\right)\) \(e\left(\frac{107}{117}\right)\) \(e\left(\frac{197}{234}\right)\) \(e\left(\frac{215}{234}\right)\) \(e\left(\frac{8}{9}\right)\)
\(\chi_{6004}(55,\cdot)\) 6004.cd 18 yes \(-1\) \(1\) \(e\left(\frac{7}{18}\right)\) \(e\left(\frac{2}{9}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{7}{9}\right)\) \(-1\) \(e\left(\frac{4}{9}\right)\) \(e\left(\frac{11}{18}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{5}{9}\right)\) \(e\left(\frac{17}{18}\right)\)
\(\chi_{6004}(59,\cdot)\) 6004.es 234 yes \(-1\) \(1\) \(e\left(\frac{145}{234}\right)\) \(e\left(\frac{62}{117}\right)\) \(e\left(\frac{35}{39}\right)\) \(e\left(\frac{28}{117}\right)\) \(e\left(\frac{5}{26}\right)\) \(e\left(\frac{185}{234}\right)\) \(e\left(\frac{35}{234}\right)\) \(e\left(\frac{211}{234}\right)\) \(e\left(\frac{121}{234}\right)\) \(e\left(\frac{17}{18}\right)\)
\(\chi_{6004}(61,\cdot)\) 6004.ek 234 no \(-1\) \(1\) \(e\left(\frac{5}{234}\right)\) \(e\left(\frac{64}{117}\right)\) \(e\left(\frac{19}{78}\right)\) \(e\left(\frac{5}{117}\right)\) \(e\left(\frac{22}{39}\right)\) \(e\left(\frac{20}{117}\right)\) \(e\left(\frac{133}{234}\right)\) \(e\left(\frac{53}{234}\right)\) \(e\left(\frac{31}{117}\right)\) \(e\left(\frac{2}{9}\right)\)
\(\chi_{6004}(63,\cdot)\) 6004.ee 234 yes \(1\) \(1\) \(e\left(\frac{37}{117}\right)\) \(e\left(\frac{19}{117}\right)\) \(e\left(\frac{7}{13}\right)\) \(e\left(\frac{74}{117}\right)\) \(e\left(\frac{61}{78}\right)\) \(e\left(\frac{101}{117}\right)\) \(e\left(\frac{56}{117}\right)\) \(e\left(\frac{137}{234}\right)\) \(e\left(\frac{100}{117}\right)\) \(e\left(\frac{7}{18}\right)\)
\(\chi_{6004}(65,\cdot)\) 6004.df 78 no \(-1\) \(1\) \(e\left(\frac{31}{78}\right)\) \(e\left(\frac{38}{39}\right)\) \(e\left(\frac{3}{13}\right)\) \(e\left(\frac{31}{39}\right)\) \(e\left(\frac{9}{13}\right)\) \(e\left(\frac{53}{78}\right)\) \(e\left(\frac{29}{78}\right)\) \(e\left(\frac{20}{39}\right)\) \(e\left(\frac{49}{78}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{6004}(67,\cdot)\) 6004.ej 234 yes \(1\) \(1\) \(e\left(\frac{46}{117}\right)\) \(e\left(\frac{31}{117}\right)\) \(e\left(\frac{61}{78}\right)\) \(e\left(\frac{92}{117}\right)\) \(e\left(\frac{53}{78}\right)\) \(e\left(\frac{151}{234}\right)\) \(e\left(\frac{77}{117}\right)\) \(e\left(\frac{43}{117}\right)\) \(e\left(\frac{41}{234}\right)\) \(e\left(\frac{7}{18}\right)\)