LMFDB - Group of Dirichlet characters of modulus 266

Show commands: PariGP / SageMath

sage: H = DirichletGroup(266)

pari: g = idealstar(,266,2)

Character group

sage: G.order() pari: g.no
Order	=	108
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{18}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{266}(115,\cdot)$, $\chi_{266}(211,\cdot)$

First 32 of 108 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$23$	$25$	$27$
$\chi_{266}(1,\cdot)$	266.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{266}(3,\cdot)$	266.y	18	no	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{266}(5,\cdot)$	266.be	18	no	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{266}(9,\cdot)$	266.v	9	no	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{266}(11,\cdot)$	266.g	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$
$\chi_{266}(13,\cdot)$	266.x	18	no	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{266}(15,\cdot)$	266.bb	18	no	$-1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{266}(17,\cdot)$	266.z	18	no	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{266}(23,\cdot)$	266.v	9	no	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{266}(25,\cdot)$	266.w	9	no	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{266}(27,\cdot)$	266.m	6	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{266}(29,\cdot)$	266.bb	18	no	$-1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{266}(31,\cdot)$	266.t	6	no	$1$	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{266}(33,\cdot)$	266.bd	18	no	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{266}(37,\cdot)$	266.o	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{266}(39,\cdot)$	266.e	3	no	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{266}(41,\cdot)$	266.x	18	no	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{266}(43,\cdot)$	266.u	9	no	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{266}(45,\cdot)$	266.j	6	no	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{266}(47,\cdot)$	266.z	18	no	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{266}(51,\cdot)$	266.ba	18	no	$-1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{266}(53,\cdot)$	266.bf	18	no	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{266}(55,\cdot)$	266.bc	18	no	$-1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{266}(59,\cdot)$	266.y	18	no	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{266}(61,\cdot)$	266.z	18	no	$-1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{266}(65,\cdot)$	266.i	6	no	$-1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{266}(67,\cdot)$	266.bf	18	no	$-1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{266}(69,\cdot)$	266.m	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{266}(71,\cdot)$	266.bb	18	no	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{266}(73,\cdot)$	266.z	18	no	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{266}(75,\cdot)$	266.l	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{266}(79,\cdot)$	266.bf	18	no	$-1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$

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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	$266$
Structure	\(C_{6}\times C_{18}\)
Order	$108$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(23\)	\(25\)	\(27\)
\(\chi_{266}(1,\cdot)\)	266.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{266}(3,\cdot)\)	266.y	18	no	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{266}(5,\cdot)\)	266.be	18	no	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{266}(9,\cdot)\)	266.v	9	no	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{266}(11,\cdot)\)	266.g	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)
\(\chi_{266}(13,\cdot)\)	266.x	18	no	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{266}(15,\cdot)\)	266.bb	18	no	\(-1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{266}(17,\cdot)\)	266.z	18	no	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{266}(23,\cdot)\)	266.v	9	no	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{266}(25,\cdot)\)	266.w	9	no	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{266}(27,\cdot)\)	266.m	6	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{266}(29,\cdot)\)	266.bb	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{266}(31,\cdot)\)	266.t	6	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{266}(33,\cdot)\)	266.bd	18	no	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{266}(37,\cdot)\)	266.o	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{266}(39,\cdot)\)	266.e	3	no	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{266}(41,\cdot)\)	266.x	18	no	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{266}(43,\cdot)\)	266.u	9	no	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{266}(45,\cdot)\)	266.j	6	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{266}(47,\cdot)\)	266.z	18	no	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{266}(51,\cdot)\)	266.ba	18	no	\(-1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{266}(53,\cdot)\)	266.bf	18	no	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{266}(55,\cdot)\)	266.bc	18	no	\(-1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{266}(59,\cdot)\)	266.y	18	no	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{266}(61,\cdot)\)	266.z	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{266}(65,\cdot)\)	266.i	6	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{266}(67,\cdot)\)	266.bf	18	no	\(-1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{266}(69,\cdot)\)	266.m	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{266}(71,\cdot)\)	266.bb	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{266}(73,\cdot)\)	266.z	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{266}(75,\cdot)\)	266.l	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{266}(79,\cdot)\)	266.bf	18	no	\(-1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)

Introduction

L-functions

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Character group

First 32 of 108 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.