LMFDB - Group of Dirichlet characters of modulus 2667

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2667)

pari: g = idealstar(,2667,2)

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	=	$\chi_{2667}(890,\cdot)$, $\chi_{2667}(1144,\cdot)$, $\chi_{2667}(2416,\cdot)$

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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{2667}(1,\cdot)$	2667.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2667}(2,\cdot)$	2667.db	42	yes	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{2667}(4,\cdot)$	2667.cw	21	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2667}(5,\cdot)$	2667.df	42	yes	$-1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2667}(8,\cdot)$	2667.bx	14	no	$-1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$	$1$
$\chi_{2667}(10,\cdot)$	2667.du	42	no	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2667}(11,\cdot)$	2667.em	126	yes	$-1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{109}{126}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{2667}(13,\cdot)$	2667.ee	126	no	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2667}(16,\cdot)$	2667.cw	21	no	$1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{2667}(17,\cdot)$	2667.eh	126	yes	$1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2667}(19,\cdot)$	2667.v	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2667}(20,\cdot)$	2667.n	6	yes	$-1$	$1$	$-1$	$1$	$-1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{2667}(22,\cdot)$	2667.br	9	no	$1$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{9}\right)$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2667}(23,\cdot)$	2667.eg	126	yes	$1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{41}{126}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2667}(25,\cdot)$	2667.cv	21	no	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2667}(26,\cdot)$	2667.eh	126	yes	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{53}{126}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2667}(29,\cdot)$	2667.ew	126	no	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2667}(31,\cdot)$	2667.ep	126	no	$-1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{126}\right)$	$-1$
$\chi_{2667}(32,\cdot)$	2667.db	42	yes	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2667}(34,\cdot)$	2667.ee	126	no	$-1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2667}(37,\cdot)$	2667.bp	9	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$1$
$\chi_{2667}(38,\cdot)$	2667.dl	42	yes	$1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2667}(40,\cdot)$	2667.dt	42	no	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2667}(41,\cdot)$	2667.ex	126	yes	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{2667}(43,\cdot)$	2667.ed	126	no	$-1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2667}(44,\cdot)$	2667.ej	126	yes	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{97}{126}\right)$	$1$
$\chi_{2667}(46,\cdot)$	2667.eq	126	no	$-1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{55}{63}\right)$	$1$
$\chi_{2667}(47,\cdot)$	2667.dl	42	yes	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{2667}(50,\cdot)$	2667.dz	42	no	$-1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{29}{42}\right)$	$1$
$\chi_{2667}(52,\cdot)$	2667.cg	18	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{18}\right)$	$-1$
$\chi_{2667}(53,\cdot)$	2667.eg	126	yes	$1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{2667}(55,\cdot)$	2667.ef	126	no	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{17}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{5}{6}\right)$

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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	$2667$
Structure	\(C_{2}\times C_{6}\times C_{126}\)
Order	$1512$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{2667}(1,\cdot)\)	2667.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2667}(2,\cdot)\)	2667.db	42	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2667}(4,\cdot)\)	2667.cw	21	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2667}(5,\cdot)\)	2667.df	42	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2667}(8,\cdot)\)	2667.bx	14	no	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(1\)
\(\chi_{2667}(10,\cdot)\)	2667.du	42	no	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2667}(11,\cdot)\)	2667.em	126	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{109}{126}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2667}(13,\cdot)\)	2667.ee	126	no	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2667}(16,\cdot)\)	2667.cw	21	no	\(1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2667}(17,\cdot)\)	2667.eh	126	yes	\(1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2667}(19,\cdot)\)	2667.v	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2667}(20,\cdot)\)	2667.n	6	yes	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{2667}(22,\cdot)\)	2667.br	9	no	\(1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2667}(23,\cdot)\)	2667.eg	126	yes	\(1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{41}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2667}(25,\cdot)\)	2667.cv	21	no	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2667}(26,\cdot)\)	2667.eh	126	yes	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{53}{126}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2667}(29,\cdot)\)	2667.ew	126	no	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2667}(31,\cdot)\)	2667.ep	126	no	\(-1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{126}\right)\)	\(-1\)
\(\chi_{2667}(32,\cdot)\)	2667.db	42	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2667}(34,\cdot)\)	2667.ee	126	no	\(-1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2667}(37,\cdot)\)	2667.bp	9	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(1\)
\(\chi_{2667}(38,\cdot)\)	2667.dl	42	yes	\(1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2667}(40,\cdot)\)	2667.dt	42	no	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2667}(41,\cdot)\)	2667.ex	126	yes	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{2667}(43,\cdot)\)	2667.ed	126	no	\(-1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2667}(44,\cdot)\)	2667.ej	126	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(1\)
\(\chi_{2667}(46,\cdot)\)	2667.eq	126	no	\(-1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(1\)
\(\chi_{2667}(47,\cdot)\)	2667.dl	42	yes	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{2667}(50,\cdot)\)	2667.dz	42	no	\(-1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(1\)
\(\chi_{2667}(52,\cdot)\)	2667.cg	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(-1\)
\(\chi_{2667}(53,\cdot)\)	2667.eg	126	yes	\(1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2667}(55,\cdot)\)	2667.ef	126	no	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{17}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{5}{6}\right)\)

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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.