LMFDB - Group of Dirichlet characters of modulus 660

Show commands: PariGP / SageMath

sage: H = DirichletGroup(660)

pari: g = idealstar(,660,2)

Character group

sage: G.order() pari: g.no
Order	=	160
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{20}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{660}(331,\cdot)$, $\chi_{660}(221,\cdot)$, $\chi_{660}(397,\cdot)$, $\chi_{660}(541,\cdot)$

First 32 of 160 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	$-1$	$1$	$7$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{660}(1,\cdot)$	660.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{660}(7,\cdot)$	660.bt	20	no	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{10}\right)$	$-i$
$\chi_{660}(13,\cdot)$	660.bo	20	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-i$
$\chi_{660}(17,\cdot)$	660.bq	20	no	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{5}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{5}\right)$	$i$
$\chi_{660}(19,\cdot)$	660.bg	10	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$-1$
$\chi_{660}(23,\cdot)$	660.w	4	no	$-1$	$1$	$i$	$i$	$i$	$1$	$i$	$1$	$-1$	$-i$	$-1$	$-i$
$\chi_{660}(29,\cdot)$	660.bb	10	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$1$
$\chi_{660}(31,\cdot)$	660.bh	10	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$-1$
$\chi_{660}(37,\cdot)$	660.bu	20	no	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{5}\right)$	$-i$
$\chi_{660}(41,\cdot)$	660.bl	10	no	$1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$-1$
$\chi_{660}(43,\cdot)$	660.s	4	no	$-1$	$1$	$-i$	$-i$	$i$	$-1$	$-i$	$1$	$-1$	$-i$	$-1$	$i$
$\chi_{660}(47,\cdot)$	660.bp	20	yes	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{2}{5}\right)$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$	$i$
$\chi_{660}(49,\cdot)$	660.bm	10	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$-1$
$\chi_{660}(53,\cdot)$	660.bs	20	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$	$i$
$\chi_{660}(59,\cdot)$	660.bd	10	yes	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$1$
$\chi_{660}(61,\cdot)$	660.bn	10	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$-1$
$\chi_{660}(67,\cdot)$	660.u	4	no	$1$	$1$	$-i$	$-i$	$i$	$1$	$i$	$-1$	$-1$	$i$	$1$	$i$
$\chi_{660}(71,\cdot)$	660.bj	10	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$-1$
$\chi_{660}(73,\cdot)$	660.bo	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$i$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{10}\right)$	$-i$
$\chi_{660}(79,\cdot)$	660.bg	10	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$-1$
$\chi_{660}(83,\cdot)$	660.bv	20	yes	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{5}\right)$	$i$
$\chi_{660}(89,\cdot)$	660.e	2	no	$-1$	$1$	$-1$	$-1$	$1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$
$\chi_{660}(91,\cdot)$	660.bh	10	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$-1$
$\chi_{660}(97,\cdot)$	660.bu	20	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-i$
$\chi_{660}(101,\cdot)$	660.bl	10	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$-1$
$\chi_{660}(103,\cdot)$	660.br	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{5}\right)$	$-i$
$\chi_{660}(107,\cdot)$	660.bv	20	yes	$1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{2}{5}\right)$	$-i$
$\chi_{660}(109,\cdot)$	660.p	2	no	$-1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$
$\chi_{660}(113,\cdot)$	660.bs	20	no	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$-i$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{10}\right)$	$i$
$\chi_{660}(119,\cdot)$	660.bd	10	yes	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{10}\right)$	$1$
$\chi_{660}(127,\cdot)$	660.bt	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$	$-i$
$\chi_{660}(131,\cdot)$	660.m	2	no	$-1$	$1$	$1$	$-1$	$1$	$1$	$1$	$1$	$-1$	$1$	$1$	$1$

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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	$660$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{20}\)
Order	$160$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{660}(1,\cdot)\)	660.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{660}(7,\cdot)\)	660.bt	20	no	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-i\)
\(\chi_{660}(13,\cdot)\)	660.bo	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)
\(\chi_{660}(17,\cdot)\)	660.bq	20	no	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(i\)
\(\chi_{660}(19,\cdot)\)	660.bg	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)
\(\chi_{660}(23,\cdot)\)	660.w	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(i\)	\(1\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(-1\)	\(-i\)
\(\chi_{660}(29,\cdot)\)	660.bb	10	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(1\)
\(\chi_{660}(31,\cdot)\)	660.bh	10	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)
\(\chi_{660}(37,\cdot)\)	660.bu	20	no	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)
\(\chi_{660}(41,\cdot)\)	660.bl	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)
\(\chi_{660}(43,\cdot)\)	660.s	4	no	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(i\)	\(-1\)	\(-i\)	\(1\)	\(-1\)	\(-i\)	\(-1\)	\(i\)
\(\chi_{660}(47,\cdot)\)	660.bp	20	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)
\(\chi_{660}(49,\cdot)\)	660.bm	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(-1\)
\(\chi_{660}(53,\cdot)\)	660.bs	20	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(i\)
\(\chi_{660}(59,\cdot)\)	660.bd	10	yes	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)
\(\chi_{660}(61,\cdot)\)	660.bn	10	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)
\(\chi_{660}(67,\cdot)\)	660.u	4	no	\(1\)	\(1\)	\(-i\)	\(-i\)	\(i\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(1\)	\(i\)
\(\chi_{660}(71,\cdot)\)	660.bj	10	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)
\(\chi_{660}(73,\cdot)\)	660.bo	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(i\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(-i\)
\(\chi_{660}(79,\cdot)\)	660.bg	10	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)
\(\chi_{660}(83,\cdot)\)	660.bv	20	yes	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(i\)
\(\chi_{660}(89,\cdot)\)	660.e	2	no	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)
\(\chi_{660}(91,\cdot)\)	660.bh	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)
\(\chi_{660}(97,\cdot)\)	660.bu	20	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-i\)
\(\chi_{660}(101,\cdot)\)	660.bl	10	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)
\(\chi_{660}(103,\cdot)\)	660.br	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)
\(\chi_{660}(107,\cdot)\)	660.bv	20	yes	\(1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-i\)
\(\chi_{660}(109,\cdot)\)	660.p	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{660}(113,\cdot)\)	660.bs	20	no	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)
\(\chi_{660}(119,\cdot)\)	660.bd	10	yes	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)
\(\chi_{660}(127,\cdot)\)	660.bt	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-i\)
\(\chi_{660}(131,\cdot)\)	660.m	2	no	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)

Introduction

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.