LMFDB - Group of Dirichlet characters of modulus 5586

Show commands: PariGP / SageMath

sage: H = DirichletGroup(5586)

pari: g = idealstar(,5586,2)

Character group

sage: G.order() pari: g.no
Order	=	1512
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{126}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{5586}(3725,\cdot)$, $\chi_{5586}(4903,\cdot)$, $\chi_{5586}(4999,\cdot)$

First 32 of 1512 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	$-1$	$1$	$5$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{5586}(1,\cdot)$	5586.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{5586}(5,\cdot)$	5586.ex	126	no	$1$	$1$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{26}{63}\right)$
$\chi_{5586}(11,\cdot)$	5586.dx	42	no	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{19}{42}\right)$
$\chi_{5586}(13,\cdot)$	5586.eq	126	no	$1$	$1$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{25}{63}\right)$
$\chi_{5586}(17,\cdot)$	5586.eh	126	no	$1$	$1$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{83}{126}\right)$	$-1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{41}{63}\right)$
$\chi_{5586}(23,\cdot)$	5586.en	126	no	$-1$	$1$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{85}{126}\right)$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{65}{126}\right)$
$\chi_{5586}(25,\cdot)$	5586.ea	63	no	$1$	$1$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{52}{63}\right)$
$\chi_{5586}(29,\cdot)$	5586.el	126	no	$1$	$1$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{13}{63}\right)$
$\chi_{5586}(31,\cdot)$	5586.bc	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{5586}(37,\cdot)$	5586.dt	42	no	$-1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{5586}(41,\cdot)$	5586.ej	126	no	$-1$	$1$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{31}{126}\right)$
$\chi_{5586}(43,\cdot)$	5586.eb	63	no	$1$	$1$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{44}{63}\right)$
$\chi_{5586}(47,\cdot)$	5586.eh	126	no	$1$	$1$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{25}{126}\right)$	$-1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{4}{63}\right)$
$\chi_{5586}(53,\cdot)$	5586.ew	126	no	$1$	$1$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{1}{63}\right)$
$\chi_{5586}(55,\cdot)$	5586.er	126	no	$-1$	$1$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{109}{126}\right)$
$\chi_{5586}(59,\cdot)$	5586.em	126	no	$-1$	$1$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{1}{63}\right)$	$1$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{109}{126}\right)$
$\chi_{5586}(61,\cdot)$	5586.ep	126	no	$-1$	$1$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{38}{63}\right)$	$-1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{47}{126}\right)$
$\chi_{5586}(65,\cdot)$	5586.de	42	no	$1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{5586}(67,\cdot)$	5586.ct	18	no	$-1$	$1$	$e\left(\frac{4}{9}\right)$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{5586}(71,\cdot)$	5586.el	126	no	$1$	$1$	$e\left(\frac{37}{126}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{8}{63}\right)$
$\chi_{5586}(73,\cdot)$	5586.ep	126	no	$-1$	$1$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{40}{63}\right)$	$-1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{13}{126}\right)$
$\chi_{5586}(79,\cdot)$	5586.ct	18	no	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$
$\chi_{5586}(83,\cdot)$	5586.du	42	no	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{42}\right)$	$-1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{5586}(85,\cdot)$	5586.eb	63	no	$1$	$1$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{63}\right)$
$\chi_{5586}(89,\cdot)$	5586.em	126	no	$-1$	$1$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{5}{63}\right)$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{41}{126}\right)$
$\chi_{5586}(97,\cdot)$	5586.cf	18	no	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{9}\right)$
$\chi_{5586}(101,\cdot)$	5586.ex	126	no	$1$	$1$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{61}{63}\right)$
$\chi_{5586}(103,\cdot)$	5586.dj	42	no	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{5586}(107,\cdot)$	5586.dw	42	no	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{5586}(109,\cdot)$	5586.eo	126	no	$-1$	$1$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{47}{126}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{95}{126}\right)$	$-1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{43}{126}\right)$
$\chi_{5586}(113,\cdot)$	5586.by	14	no	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$-1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{5586}(115,\cdot)$	5586.dk	42	no	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{14}\right)$

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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	$5586$
Structure	\(C_{2}\times C_{6}\times C_{126}\)
Order	$1512$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{5586}(1,\cdot)\)	5586.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{5586}(5,\cdot)\)	5586.ex	126	no	\(1\)	\(1\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{26}{63}\right)\)
\(\chi_{5586}(11,\cdot)\)	5586.dx	42	no	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)
\(\chi_{5586}(13,\cdot)\)	5586.eq	126	no	\(1\)	\(1\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{25}{63}\right)\)
\(\chi_{5586}(17,\cdot)\)	5586.eh	126	no	\(1\)	\(1\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(-1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{41}{63}\right)\)
\(\chi_{5586}(23,\cdot)\)	5586.en	126	no	\(-1\)	\(1\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{65}{126}\right)\)
\(\chi_{5586}(25,\cdot)\)	5586.ea	63	no	\(1\)	\(1\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{52}{63}\right)\)
\(\chi_{5586}(29,\cdot)\)	5586.el	126	no	\(1\)	\(1\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{13}{63}\right)\)
\(\chi_{5586}(31,\cdot)\)	5586.bc	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{5586}(37,\cdot)\)	5586.dt	42	no	\(-1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{5586}(41,\cdot)\)	5586.ej	126	no	\(-1\)	\(1\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{31}{126}\right)\)
\(\chi_{5586}(43,\cdot)\)	5586.eb	63	no	\(1\)	\(1\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{44}{63}\right)\)
\(\chi_{5586}(47,\cdot)\)	5586.eh	126	no	\(1\)	\(1\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(-1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{4}{63}\right)\)
\(\chi_{5586}(53,\cdot)\)	5586.ew	126	no	\(1\)	\(1\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{1}{63}\right)\)
\(\chi_{5586}(55,\cdot)\)	5586.er	126	no	\(-1\)	\(1\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{109}{126}\right)\)
\(\chi_{5586}(59,\cdot)\)	5586.em	126	no	\(-1\)	\(1\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(1\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{109}{126}\right)\)
\(\chi_{5586}(61,\cdot)\)	5586.ep	126	no	\(-1\)	\(1\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(-1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{47}{126}\right)\)
\(\chi_{5586}(65,\cdot)\)	5586.de	42	no	\(1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{5586}(67,\cdot)\)	5586.ct	18	no	\(-1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{5586}(71,\cdot)\)	5586.el	126	no	\(1\)	\(1\)	\(e\left(\frac{37}{126}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{8}{63}\right)\)
\(\chi_{5586}(73,\cdot)\)	5586.ep	126	no	\(-1\)	\(1\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(-1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{13}{126}\right)\)
\(\chi_{5586}(79,\cdot)\)	5586.ct	18	no	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)
\(\chi_{5586}(83,\cdot)\)	5586.du	42	no	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(-1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{5586}(85,\cdot)\)	5586.eb	63	no	\(1\)	\(1\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{63}\right)\)
\(\chi_{5586}(89,\cdot)\)	5586.em	126	no	\(-1\)	\(1\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{41}{126}\right)\)
\(\chi_{5586}(97,\cdot)\)	5586.cf	18	no	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{5586}(101,\cdot)\)	5586.ex	126	no	\(1\)	\(1\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{61}{63}\right)\)
\(\chi_{5586}(103,\cdot)\)	5586.dj	42	no	\(1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{5586}(107,\cdot)\)	5586.dw	42	no	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{5586}(109,\cdot)\)	5586.eo	126	no	\(-1\)	\(1\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{47}{126}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(-1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{43}{126}\right)\)
\(\chi_{5586}(113,\cdot)\)	5586.by	14	no	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(-1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{5586}(115,\cdot)\)	5586.dk	42	no	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)

Introduction

L-functions

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Character group

First 32 of 1512 characters

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