LMFDB - Group of Dirichlet characters of modulus 666

Show commands: PariGP / SageMath

sage: H = DirichletGroup(666)

pari: g = idealstar(,666,2)

Character group

sage: G.order() pari: g.no
Order	=	216
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{36}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{666}(371,\cdot)$, $\chi_{666}(631,\cdot)$

First 32 of 216 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{666}(1,\cdot)$	666.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{666}(5,\cdot)$	666.bv	36	no	$1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{9}\right)$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{36}\right)$	$-i$	$e\left(\frac{13}{18}\right)$	$i$	$e\left(\frac{5}{12}\right)$
$\chi_{666}(7,\cdot)$	666.w	9	no	$1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{666}(11,\cdot)$	666.v	6	no	$-1$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{666}(13,\cdot)$	666.bq	36	no	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{9}\right)$	$-1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{25}{36}\right)$	$i$	$e\left(\frac{7}{18}\right)$	$-i$	$e\left(\frac{5}{12}\right)$
$\chi_{666}(17,\cdot)$	666.bs	36	no	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{12}\right)$	$-i$
$\chi_{666}(19,\cdot)$	666.bt	36	no	$-1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{12}\right)$	$-i$
$\chi_{666}(23,\cdot)$	666.ba	12	no	$1$	$1$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{666}(25,\cdot)$	666.bp	18	no	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{9}\right)$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$-1$	$e\left(\frac{4}{9}\right)$	$-1$	$e\left(\frac{5}{6}\right)$
$\chi_{666}(29,\cdot)$	666.ba	12	no	$1$	$1$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{666}(31,\cdot)$	666.bd	12	no	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$-i$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{666}(35,\cdot)$	666.bs	36	no	$1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{12}\right)$	$-i$
$\chi_{666}(41,\cdot)$	666.bi	18	no	$-1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$-1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{18}\right)$	$1$	$e\left(\frac{8}{9}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{666}(43,\cdot)$	666.bd	12	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{666}(47,\cdot)$	666.u	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{666}(49,\cdot)$	666.w	9	no	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{666}(53,\cdot)$	666.bo	18	no	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{6}\right)$	$1$
$\chi_{666}(55,\cdot)$	666.bt	36	no	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{12}\right)$	$i$
$\chi_{666}(59,\cdot)$	666.br	36	no	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{666}(61,\cdot)$	666.bu	36	no	$-1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$
$\chi_{666}(65,\cdot)$	666.bi	18	no	$-1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$-1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$1$	$e\left(\frac{1}{9}\right)$	$1$	$e\left(\frac{5}{6}\right)$
$\chi_{666}(67,\cdot)$	666.bp	18	no	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{9}\right)$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{18}\right)$	$-1$	$e\left(\frac{2}{9}\right)$	$-1$	$e\left(\frac{1}{6}\right)$
$\chi_{666}(71,\cdot)$	666.bo	18	no	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{6}\right)$	$1$
$\chi_{666}(73,\cdot)$	666.c	2	no	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$-1$	$-1$
$\chi_{666}(77,\cdot)$	666.bi	18	no	$-1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{4}{9}\right)$	$-1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{18}\right)$	$1$	$e\left(\frac{5}{9}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{666}(79,\cdot)$	666.bu	36	no	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{666}(83,\cdot)$	666.bh	18	no	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{8}{9}\right)$	$-1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$-1$	$e\left(\frac{1}{9}\right)$	$-1$	$e\left(\frac{1}{3}\right)$
$\chi_{666}(85,\cdot)$	666.t	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{666}(89,\cdot)$	666.bs	36	no	$1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{12}\right)$	$i$
$\chi_{666}(91,\cdot)$	666.bt	36	no	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{12}\right)$	$-i$
$\chi_{666}(95,\cdot)$	666.bm	18	no	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{666}(97,\cdot)$	666.bg	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{12}\right)$

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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	$666$
Structure	\(C_{6}\times C_{36}\)
Order	$216$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{666}(1,\cdot)\)	666.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{666}(5,\cdot)\)	666.bv	36	no	\(1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(-i\)	\(e\left(\frac{13}{18}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{666}(7,\cdot)\)	666.w	9	no	\(1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{666}(11,\cdot)\)	666.v	6	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{666}(13,\cdot)\)	666.bq	36	no	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(-1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(i\)	\(e\left(\frac{7}{18}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{666}(17,\cdot)\)	666.bs	36	no	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)
\(\chi_{666}(19,\cdot)\)	666.bt	36	no	\(-1\)	\(1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)
\(\chi_{666}(23,\cdot)\)	666.ba	12	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{666}(25,\cdot)\)	666.bp	18	no	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(-1\)	\(e\left(\frac{4}{9}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{666}(29,\cdot)\)	666.ba	12	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{666}(31,\cdot)\)	666.bd	12	no	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{666}(35,\cdot)\)	666.bs	36	no	\(1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)
\(\chi_{666}(41,\cdot)\)	666.bi	18	no	\(-1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(-1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{666}(43,\cdot)\)	666.bd	12	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{666}(47,\cdot)\)	666.u	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{666}(49,\cdot)\)	666.w	9	no	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{666}(53,\cdot)\)	666.bo	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)
\(\chi_{666}(55,\cdot)\)	666.bt	36	no	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)
\(\chi_{666}(59,\cdot)\)	666.br	36	no	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{666}(61,\cdot)\)	666.bu	36	no	\(-1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)
\(\chi_{666}(65,\cdot)\)	666.bi	18	no	\(-1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(-1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{666}(67,\cdot)\)	666.bp	18	no	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(-1\)	\(e\left(\frac{2}{9}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{666}(71,\cdot)\)	666.bo	18	no	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)
\(\chi_{666}(73,\cdot)\)	666.c	2	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{666}(77,\cdot)\)	666.bi	18	no	\(-1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(-1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{666}(79,\cdot)\)	666.bu	36	no	\(-1\)	\(1\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{666}(83,\cdot)\)	666.bh	18	no	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(-1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(-1\)	\(e\left(\frac{1}{9}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{666}(85,\cdot)\)	666.t	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{666}(89,\cdot)\)	666.bs	36	no	\(1\)	\(1\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)
\(\chi_{666}(91,\cdot)\)	666.bt	36	no	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)
\(\chi_{666}(95,\cdot)\)	666.bm	18	no	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{666}(97,\cdot)\)	666.bg	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)

Introduction

L-functions

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Character group

First 32 of 216 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.