Properties

 Modulus $6422$ Structure $$C_{6}\times C_{468}$$ Order $2808$

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(6422)

pari: g = idealstar(,6422,2)

Character group

 sage: G.order()  pari: g.no Order = 2808 sage: H.invariants()  pari: g.cyc Structure = $$C_{6}\times C_{468}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{6422}(4903,\cdot)$, $\chi_{6422}(4733,\cdot)$

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 $$-1$$ $$1$$ $$3$$ $$5$$ $$7$$ $$9$$ $$11$$ $$15$$ $$17$$ $$21$$ $$23$$ $$25$$
$$\chi_{6422}(1,\cdot)$$ 6422.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{6422}(3,\cdot)$$ 6422.dd 234 no $$-1$$ $$1$$ $$e\left(\frac{223}{234}\right)$$ $$e\left(\frac{83}{117}\right)$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{106}{117}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{155}{234}\right)$$ $$e\left(\frac{32}{117}\right)$$ $$e\left(\frac{79}{234}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{49}{117}\right)$$
$$\chi_{6422}(5,\cdot)$$ 6422.dq 468 no $$-1$$ $$1$$ $$e\left(\frac{83}{117}\right)$$ $$e\left(\frac{347}{468}\right)$$ $$e\left(\frac{79}{156}\right)$$ $$e\left(\frac{49}{117}\right)$$ $$e\left(\frac{95}{156}\right)$$ $$e\left(\frac{211}{468}\right)$$ $$e\left(\frac{73}{234}\right)$$ $$e\left(\frac{101}{468}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{113}{234}\right)$$
$$\chi_{6422}(7,\cdot)$$ 6422.cv 156 no $$-1$$ $$1$$ $$e\left(\frac{5}{13}\right)$$ $$e\left(\frac{79}{156}\right)$$ $$e\left(\frac{61}{156}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{101}{156}\right)$$ $$e\left(\frac{139}{156}\right)$$ $$e\left(\frac{37}{78}\right)$$ $$e\left(\frac{121}{156}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{78}\right)$$
$$\chi_{6422}(9,\cdot)$$ 6422.cs 117 no $$1$$ $$1$$ $$e\left(\frac{106}{117}\right)$$ $$e\left(\frac{49}{117}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{95}{117}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{38}{117}\right)$$ $$e\left(\frac{64}{117}\right)$$ $$e\left(\frac{79}{117}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{98}{117}\right)$$
$$\chi_{6422}(11,\cdot)$$ 6422.cv 156 no $$-1$$ $$1$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{95}{156}\right)$$ $$e\left(\frac{101}{156}\right)$$ $$e\left(\frac{1}{13}\right)$$ $$e\left(\frac{1}{156}\right)$$ $$e\left(\frac{23}{156}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{29}{156}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{17}{78}\right)$$
$$\chi_{6422}(15,\cdot)$$ 6422.dn 468 no $$1$$ $$1$$ $$e\left(\frac{155}{234}\right)$$ $$e\left(\frac{211}{468}\right)$$ $$e\left(\frac{139}{156}\right)$$ $$e\left(\frac{38}{117}\right)$$ $$e\left(\frac{23}{156}\right)$$ $$e\left(\frac{53}{468}\right)$$ $$e\left(\frac{137}{234}\right)$$ $$e\left(\frac{259}{468}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{211}{234}\right)$$
$$\chi_{6422}(17,\cdot)$$ 6422.dg 234 no $$1$$ $$1$$ $$e\left(\frac{32}{117}\right)$$ $$e\left(\frac{73}{234}\right)$$ $$e\left(\frac{37}{78}\right)$$ $$e\left(\frac{64}{117}\right)$$ $$e\left(\frac{5}{78}\right)$$ $$e\left(\frac{137}{234}\right)$$ $$e\left(\frac{23}{117}\right)$$ $$e\left(\frac{175}{234}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{73}{117}\right)$$
$$\chi_{6422}(21,\cdot)$$ 6422.dm 468 no $$1$$ $$1$$ $$e\left(\frac{79}{234}\right)$$ $$e\left(\frac{101}{468}\right)$$ $$e\left(\frac{121}{156}\right)$$ $$e\left(\frac{79}{117}\right)$$ $$e\left(\frac{29}{156}\right)$$ $$e\left(\frac{259}{468}\right)$$ $$e\left(\frac{175}{234}\right)$$ $$e\left(\frac{53}{468}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{101}{234}\right)$$
$$\chi_{6422}(23,\cdot)$$ 6422.bn 18 no $$1$$ $$1$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{9}\right)$$
$$\chi_{6422}(25,\cdot)$$ 6422.dh 234 no $$1$$ $$1$$ $$e\left(\frac{49}{117}\right)$$ $$e\left(\frac{113}{234}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{98}{117}\right)$$ $$e\left(\frac{17}{78}\right)$$ $$e\left(\frac{211}{234}\right)$$ $$e\left(\frac{73}{117}\right)$$ $$e\left(\frac{101}{234}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{113}{117}\right)$$
$$\chi_{6422}(27,\cdot)$$ 6422.ck 78 no $$-1$$ $$1$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{5}{39}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{32}{39}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{10}{39}\right)$$
$$\chi_{6422}(29,\cdot)$$ 6422.di 234 no $$-1$$ $$1$$ $$e\left(\frac{17}{234}\right)$$ $$e\left(\frac{49}{117}\right)$$ $$e\left(\frac{4}{39}\right)$$ $$e\left(\frac{17}{117}\right)$$ $$e\left(\frac{29}{39}\right)$$ $$e\left(\frac{115}{234}\right)$$ $$e\left(\frac{103}{117}\right)$$ $$e\left(\frac{41}{234}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{98}{117}\right)$$
$$\chi_{6422}(31,\cdot)$$ 6422.cw 156 no $$1$$ $$1$$ $$e\left(\frac{41}{78}\right)$$ $$e\left(\frac{85}{156}\right)$$ $$e\left(\frac{21}{52}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{45}{52}\right)$$ $$e\left(\frac{11}{156}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{145}{156}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{7}{78}\right)$$
$$\chi_{6422}(33,\cdot)$$ 6422.dn 468 no $$1$$ $$1$$ $$e\left(\frac{115}{234}\right)$$ $$e\left(\frac{149}{468}\right)$$ $$e\left(\frac{5}{156}\right)$$ $$e\left(\frac{115}{117}\right)$$ $$e\left(\frac{85}{156}\right)$$ $$e\left(\frac{379}{468}\right)$$ $$e\left(\frac{79}{234}\right)$$ $$e\left(\frac{245}{468}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{149}{234}\right)$$
$$\chi_{6422}(35,\cdot)$$ 6422.cu 117 no $$1$$ $$1$$ $$e\left(\frac{11}{117}\right)$$ $$e\left(\frac{29}{117}\right)$$ $$e\left(\frac{35}{39}\right)$$ $$e\left(\frac{22}{117}\right)$$ $$e\left(\frac{10}{39}\right)$$ $$e\left(\frac{40}{117}\right)$$ $$e\left(\frac{92}{117}\right)$$ $$e\left(\frac{116}{117}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{58}{117}\right)$$
$$\chi_{6422}(37,\cdot)$$ 6422.cx 156 no $$1$$ $$1$$ $$e\left(\frac{41}{78}\right)$$ $$e\left(\frac{37}{52}\right)$$ $$e\left(\frac{89}{156}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{109}{156}\right)$$ $$e\left(\frac{37}{156}\right)$$ $$e\left(\frac{25}{78}\right)$$ $$e\left(\frac{5}{52}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{11}{26}\right)$$
$$\chi_{6422}(41,\cdot)$$ 6422.do 468 no $$1$$ $$1$$ $$e\left(\frac{223}{234}\right)$$ $$e\left(\frac{215}{468}\right)$$ $$e\left(\frac{33}{52}\right)$$ $$e\left(\frac{106}{117}\right)$$ $$e\left(\frac{41}{52}\right)$$ $$e\left(\frac{193}{468}\right)$$ $$e\left(\frac{181}{234}\right)$$ $$e\left(\frac{275}{468}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{215}{234}\right)$$
$$\chi_{6422}(43,\cdot)$$ 6422.dg 234 no $$1$$ $$1$$ $$e\left(\frac{62}{117}\right)$$ $$e\left(\frac{61}{234}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{7}{117}\right)$$ $$e\left(\frac{17}{78}\right)$$ $$e\left(\frac{185}{234}\right)$$ $$e\left(\frac{8}{117}\right)$$ $$e\left(\frac{127}{234}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{61}{117}\right)$$
$$\chi_{6422}(45,\cdot)$$ 6422.cv 156 no $$-1$$ $$1$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{25}{156}\right)$$ $$e\left(\frac{43}{156}\right)$$ $$e\left(\frac{3}{13}\right)$$ $$e\left(\frac{107}{156}\right)$$ $$e\left(\frac{121}{156}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{139}{156}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{25}{78}\right)$$
$$\chi_{6422}(47,\cdot)$$ 6422.dq 468 no $$-1$$ $$1$$ $$e\left(\frac{100}{117}\right)$$ $$e\left(\frac{349}{468}\right)$$ $$e\left(\frac{137}{156}\right)$$ $$e\left(\frac{83}{117}\right)$$ $$e\left(\frac{145}{156}\right)$$ $$e\left(\frac{281}{468}\right)$$ $$e\left(\frac{95}{234}\right)$$ $$e\left(\frac{343}{468}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{115}{234}\right)$$
$$\chi_{6422}(49,\cdot)$$ 6422.cg 78 no $$1$$ $$1$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{1}{78}\right)$$ $$e\left(\frac{61}{78}\right)$$ $$e\left(\frac{7}{13}\right)$$ $$e\left(\frac{23}{78}\right)$$ $$e\left(\frac{61}{78}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{43}{78}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{1}{39}\right)$$
$$\chi_{6422}(51,\cdot)$$ 6422.de 234 no $$-1$$ $$1$$ $$e\left(\frac{53}{234}\right)$$ $$e\left(\frac{5}{234}\right)$$ $$e\left(\frac{67}{78}\right)$$ $$e\left(\frac{53}{117}\right)$$ $$e\left(\frac{47}{78}\right)$$ $$e\left(\frac{29}{117}\right)$$ $$e\left(\frac{55}{117}\right)$$ $$e\left(\frac{10}{117}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{5}{117}\right)$$
$$\chi_{6422}(53,\cdot)$$ 6422.dj 234 no $$-1$$ $$1$$ $$e\left(\frac{77}{234}\right)$$ $$e\left(\frac{82}{117}\right)$$ $$e\left(\frac{38}{39}\right)$$ $$e\left(\frac{77}{117}\right)$$ $$e\left(\frac{22}{39}\right)$$ $$e\left(\frac{7}{234}\right)$$ $$e\left(\frac{49}{117}\right)$$ $$e\left(\frac{71}{234}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{47}{117}\right)$$
$$\chi_{6422}(55,\cdot)$$ 6422.cs 117 no $$1$$ $$1$$ $$e\left(\frac{29}{117}\right)$$ $$e\left(\frac{41}{117}\right)$$ $$e\left(\frac{2}{13}\right)$$ $$e\left(\frac{58}{117}\right)$$ $$e\left(\frac{8}{13}\right)$$ $$e\left(\frac{70}{117}\right)$$ $$e\left(\frac{44}{117}\right)$$ $$e\left(\frac{47}{117}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{82}{117}\right)$$
$$\chi_{6422}(59,\cdot)$$ 6422.dn 468 no $$1$$ $$1$$ $$e\left(\frac{127}{234}\right)$$ $$e\left(\frac{425}{468}\right)$$ $$e\left(\frac{53}{156}\right)$$ $$e\left(\frac{10}{117}\right)$$ $$e\left(\frac{121}{156}\right)$$ $$e\left(\frac{211}{468}\right)$$ $$e\left(\frac{73}{234}\right)$$ $$e\left(\frac{413}{468}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{191}{234}\right)$$
$$\chi_{6422}(61,\cdot)$$ 6422.cs 117 no $$1$$ $$1$$ $$e\left(\frac{85}{117}\right)$$ $$e\left(\frac{100}{117}\right)$$ $$e\left(\frac{9}{13}\right)$$ $$e\left(\frac{53}{117}\right)$$ $$e\left(\frac{10}{13}\right)$$ $$e\left(\frac{68}{117}\right)$$ $$e\left(\frac{16}{117}\right)$$ $$e\left(\frac{49}{117}\right)$$ $$e\left(\frac{8}{9}\right)$$ $$e\left(\frac{83}{117}\right)$$
$$\chi_{6422}(63,\cdot)$$ 6422.dp 468 no $$-1$$ $$1$$ $$e\left(\frac{34}{117}\right)$$ $$e\left(\frac{433}{468}\right)$$ $$e\left(\frac{25}{156}\right)$$ $$e\left(\frac{68}{117}\right)$$ $$e\left(\frac{113}{156}\right)$$ $$e\left(\frac{101}{468}\right)$$ $$e\left(\frac{5}{234}\right)$$ $$e\left(\frac{211}{468}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{199}{234}\right)$$
$$\chi_{6422}(67,\cdot)$$ 6422.dn 468 no $$1$$ $$1$$ $$e\left(\frac{161}{234}\right)$$ $$e\left(\frac{115}{468}\right)$$ $$e\left(\frac{7}{156}\right)$$ $$e\left(\frac{44}{117}\right)$$ $$e\left(\frac{119}{156}\right)$$ $$e\left(\frac{437}{468}\right)$$ $$e\left(\frac{17}{234}\right)$$ $$e\left(\frac{343}{468}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{115}{234}\right)$$
$$\chi_{6422}(69,\cdot)$$ 6422.cq 78 no $$-1$$ $$1$$ $$e\left(\frac{19}{26}\right)$$ $$e\left(\frac{77}{78}\right)$$ $$e\left(\frac{17}{78}\right)$$ $$e\left(\frac{6}{13}\right)$$ $$e\left(\frac{55}{78}\right)$$ $$e\left(\frac{28}{39}\right)$$ $$e\left(\frac{2}{39}\right)$$ $$e\left(\frac{37}{39}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{38}{39}\right)$$
$$\chi_{6422}(71,\cdot)$$ 6422.dn 468 no $$1$$ $$1$$ $$e\left(\frac{223}{234}\right)$$ $$e\left(\frac{59}{468}\right)$$ $$e\left(\frac{47}{156}\right)$$ $$e\left(\frac{106}{117}\right)$$ $$e\left(\frac{19}{156}\right)$$ $$e\left(\frac{37}{468}\right)$$ $$e\left(\frac{25}{234}\right)$$ $$e\left(\frac{119}{468}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{59}{234}\right)$$
$$\chi_{6422}(73,\cdot)$$ 6422.dq 468 no $$-1$$ $$1$$ $$e\left(\frac{50}{117}\right)$$ $$e\left(\frac{233}{468}\right)$$ $$e\left(\frac{49}{156}\right)$$ $$e\left(\frac{100}{117}\right)$$ $$e\left(\frac{53}{156}\right)$$ $$e\left(\frac{433}{468}\right)$$ $$e\left(\frac{223}{234}\right)$$ $$e\left(\frac{347}{468}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{233}{234}\right)$$