Properties

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

Show commands for: Pari/GP / SageMath

sage: H = DirichletGroup(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 = $\chi_{6004}(3003,\cdot)$, $\chi_{6004}(2529,\cdot)$, $\chi_{6004}(3953,\cdot)$

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.

Character Orbit 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 $$1$$ $$1$$ $$e\left(\frac{46}{117}\right)$$ $$e\left(\frac{31}{117}\right)$$ $$e\left(\frac{61}{78}\right)$$ $$e\left(\frac{92}{117}\right)$$ $$e\left(\frac{53}{78}\right)$$ $$e\left(\frac{151}{234}\right)$$ $$e\left(\frac{77}{117}\right)$$ $$e\left(\frac{43}{117}\right)$$ $$e\left(\frac{41}{234}\right)$$ $$e\left(\frac{7}{18}\right)$$