LMFDB - Group of Dirichlet characters of modulus 6223

sage:H = DirichletGroup(6223)

pari:g = idealstar(,6223,2)

Character group

sage:G.order() pari:g.no
Order	=	5292
sage:H.invariants() pari:g.cyc
Structure	=	$C_{42}\times C_{126}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{6223}(5589,\cdot)$, $\chi_{6223}(638,\cdot)$

First 32 of 5292 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{6223}(1,\cdot)$	6223.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6223}(2,\cdot)$	6223.de	21	yes	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6223}(3,\cdot)$	6223.kh	126	yes	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{26}{63}\right)$
$\chi_{6223}(4,\cdot)$	6223.de	21	yes	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6223}(5,\cdot)$	6223.dy	42	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{21}\right)$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{6223}(6,\cdot)$	6223.jd	126	yes	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{63}\right)$
$\chi_{6223}(8,\cdot)$	6223.z	7	yes	$1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{6}{7}\right)$	$1$
$\chi_{6223}(9,\cdot)$	6223.ie	63	yes	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{52}{63}\right)$
$\chi_{6223}(10,\cdot)$	6223.fc	42	yes	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{6223}(11,\cdot)$	6223.hy	63	yes	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{46}{63}\right)$
$\chi_{6223}(12,\cdot)$	6223.ii	126	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{63}\right)$	$1$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{47}{63}\right)$
$\chi_{6223}(13,\cdot)$	6223.ja	126	yes	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{103}{126}\right)$
$\chi_{6223}(15,\cdot)$	6223.hn	63	yes	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{8}{63}\right)$
$\chi_{6223}(16,\cdot)$	6223.de	21	yes	$1$	$1$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6223}(17,\cdot)$	6223.jk	126	yes	$-1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{8}{21}\right)$	$-1$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{5}{18}\right)$
$\chi_{6223}(18,\cdot)$	6223.hv	63	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{31}{63}\right)$
$\chi_{6223}(19,\cdot)$	6223.j	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{6223}(20,\cdot)$	6223.ep	42	yes	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{6223}(22,\cdot)$	6223.hr	63	yes	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{25}{63}\right)$
$\chi_{6223}(23,\cdot)$	6223.im	126	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{67}{126}\right)$	$1$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{25}{126}\right)$
$\chi_{6223}(24,\cdot)$	6223.kg	126	yes	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{26}{63}\right)$
$\chi_{6223}(25,\cdot)$	6223.co	21	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{21}\right)$	$1$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{6223}(26,\cdot)$	6223.ks	126	yes	$-1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{61}{126}\right)$
$\chi_{6223}(27,\cdot)$	6223.eo	42	yes	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{6223}(29,\cdot)$	6223.iz	126	yes	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{5}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{95}{126}\right)$
$\chi_{6223}(30,\cdot)$	6223.hv	63	no	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{50}{63}\right)$
$\chi_{6223}(31,\cdot)$	6223.jy	126	no	$-1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{97}{126}\right)$
$\chi_{6223}(32,\cdot)$	6223.de	21	yes	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6223}(33,\cdot)$	6223.gg	42	yes	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{6223}(34,\cdot)$	6223.ji	126	yes	$-1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{65}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{17}{18}\right)$
$\chi_{6223}(36,\cdot)$	6223.hp	63	yes	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{10}{63}\right)$
$\chi_{6223}(37,\cdot)$	6223.id	63	yes	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{10}{63}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$6223$
Structure	\(C_{42}\times C_{126}\)
Order	$5292$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{6223}(1,\cdot)\)	6223.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6223}(2,\cdot)\)	6223.de	21	yes	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6223}(3,\cdot)\)	6223.kh	126	yes	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)
\(\chi_{6223}(4,\cdot)\)	6223.de	21	yes	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6223}(5,\cdot)\)	6223.dy	42	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{6223}(6,\cdot)\)	6223.jd	126	yes	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{63}\right)\)
\(\chi_{6223}(8,\cdot)\)	6223.z	7	yes	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(1\)
\(\chi_{6223}(9,\cdot)\)	6223.ie	63	yes	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)
\(\chi_{6223}(10,\cdot)\)	6223.fc	42	yes	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{6223}(11,\cdot)\)	6223.hy	63	yes	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{46}{63}\right)\)
\(\chi_{6223}(12,\cdot)\)	6223.ii	126	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(1\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{47}{63}\right)\)
\(\chi_{6223}(13,\cdot)\)	6223.ja	126	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{103}{126}\right)\)
\(\chi_{6223}(15,\cdot)\)	6223.hn	63	yes	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)
\(\chi_{6223}(16,\cdot)\)	6223.de	21	yes	\(1\)	\(1\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6223}(17,\cdot)\)	6223.jk	126	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(-1\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{5}{18}\right)\)
\(\chi_{6223}(18,\cdot)\)	6223.hv	63	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{16}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)
\(\chi_{6223}(19,\cdot)\)	6223.j	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{6223}(20,\cdot)\)	6223.ep	42	yes	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{6223}(22,\cdot)\)	6223.hr	63	yes	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{25}{63}\right)\)
\(\chi_{6223}(23,\cdot)\)	6223.im	126	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(1\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{25}{126}\right)\)
\(\chi_{6223}(24,\cdot)\)	6223.kg	126	yes	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)
\(\chi_{6223}(25,\cdot)\)	6223.co	21	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(1\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{6223}(26,\cdot)\)	6223.ks	126	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{61}{126}\right)\)
\(\chi_{6223}(27,\cdot)\)	6223.eo	42	yes	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{6223}(29,\cdot)\)	6223.iz	126	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{95}{126}\right)\)
\(\chi_{6223}(30,\cdot)\)	6223.hv	63	no	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)
\(\chi_{6223}(31,\cdot)\)	6223.jy	126	no	\(-1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{97}{126}\right)\)
\(\chi_{6223}(32,\cdot)\)	6223.de	21	yes	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6223}(33,\cdot)\)	6223.gg	42	yes	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{6223}(34,\cdot)\)	6223.ji	126	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{65}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{17}{18}\right)\)
\(\chi_{6223}(36,\cdot)\)	6223.hp	63	yes	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{10}{63}\right)\)
\(\chi_{6223}(37,\cdot)\)	6223.id	63	yes	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)

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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.