LMFDB - Group of Dirichlet characters of modulus 6422

Show commands: PariGP / 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	$-1$	$1$	$e\left(\frac{50}{117}\right)$	$e\left(\frac{233}{468}\right)$	$e\left(\frac{49}{156}\right)$	$e\left(\frac{100}{117}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{433}{468}\right)$	$e\left(\frac{223}{234}\right)$	$e\left(\frac{347}{468}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{233}{234}\right)$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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	\(-1\)	\(1\)	\(e\left(\frac{50}{117}\right)\)	\(e\left(\frac{233}{468}\right)\)	\(e\left(\frac{49}{156}\right)\)	\(e\left(\frac{100}{117}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{433}{468}\right)\)	\(e\left(\frac{223}{234}\right)\)	\(e\left(\frac{347}{468}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{233}{234}\right)\)

Introduction

L-functions

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.