LMFDB - Group of Dirichlet characters of modulus 2013

Show commands: PariGP / SageMath

sage: H = DirichletGroup(2013)

pari: g = idealstar(,2013,2)

Character group

sage: G.order() pari: g.no
Order	=	1200
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{10}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{2013}(1343,\cdot)$, $\chi_{2013}(1465,\cdot)$, $\chi_{2013}(1222,\cdot)$

First 32 of 1200 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{2013}(1,\cdot)$	2013.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{2013}(2,\cdot)$	2013.ga	60	yes	$-1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{60}\right)$
$\chi_{2013}(4,\cdot)$	2013.en	30	no	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{2013}(5,\cdot)$	2013.fj	30	yes	$-1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2013}(7,\cdot)$	2013.fr	60	no	$1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{41}{60}\right)$
$\chi_{2013}(8,\cdot)$	2013.dk	20	yes	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$
$\chi_{2013}(10,\cdot)$	2013.fx	60	no	$1$	$1$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{31}{60}\right)$
$\chi_{2013}(13,\cdot)$	2013.ep	30	no	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{30}\right)$
$\chi_{2013}(14,\cdot)$	2013.fb	30	yes	$-1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$
$\chi_{2013}(16,\cdot)$	2013.cz	15	no	$1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$
$\chi_{2013}(17,\cdot)$	2013.fo	60	yes	$-1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{2013}(19,\cdot)$	2013.fe	30	no	$-1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$
$\chi_{2013}(20,\cdot)$	2013.bc	10	yes	$-1$	$1$	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{7}{10}\right)$
$\chi_{2013}(23,\cdot)$	2013.dn	20	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{17}{20}\right)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{2013}(25,\cdot)$	2013.cv	15	no	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{2013}(26,\cdot)$	2013.fp	60	yes	$1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{2013}(28,\cdot)$	2013.dd	20	no	$1$	$1$	$-i$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$i$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{1}{20}\right)$
$\chi_{2013}(29,\cdot)$	2013.gb	60	yes	$-1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{60}\right)$
$\chi_{2013}(31,\cdot)$	2013.gj	60	no	$-1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{23}{60}\right)$	$-i$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{37}{60}\right)$
$\chi_{2013}(32,\cdot)$	2013.cr	12	yes	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{2013}(34,\cdot)$	2013.o	5	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$
$\chi_{2013}(35,\cdot)$	2013.ga	60	yes	$-1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{60}\right)$
$\chi_{2013}(37,\cdot)$	2013.dp	20	no	$-1$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{2013}(38,\cdot)$	2013.dw	20	yes	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$i$
$\chi_{2013}(40,\cdot)$	2013.fs	60	no	$1$	$1$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{53}{60}\right)$
$\chi_{2013}(41,\cdot)$	2013.bu	10	yes	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$-1$
$\chi_{2013}(43,\cdot)$	2013.fx	60	no	$1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{11}{60}\right)$
$\chi_{2013}(46,\cdot)$	2013.ev	30	no	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{2013}(47,\cdot)$	2013.eg	30	yes	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{2013}(49,\cdot)$	2013.es	30	no	$1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$
$\chi_{2013}(50,\cdot)$	2013.dl	20	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{20}\right)$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{2013}(52,\cdot)$	2013.cn	10	no	$-1$	$1$	$1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$e\left(\frac{3}{5}\right)$

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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	$2013$
Structure	\(C_{2}\times C_{10}\times C_{60}\)
Order	$1200$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\(\chi_{2013}(1,\cdot)\)	2013.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{2013}(2,\cdot)\)	2013.ga	60	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)
\(\chi_{2013}(4,\cdot)\)	2013.en	30	no	\(1\)	\(1\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{2013}(5,\cdot)\)	2013.fj	30	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2013}(7,\cdot)\)	2013.fr	60	no	\(1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)
\(\chi_{2013}(8,\cdot)\)	2013.dk	20	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)
\(\chi_{2013}(10,\cdot)\)	2013.fx	60	no	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{31}{60}\right)\)
\(\chi_{2013}(13,\cdot)\)	2013.ep	30	no	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)
\(\chi_{2013}(14,\cdot)\)	2013.fb	30	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)
\(\chi_{2013}(16,\cdot)\)	2013.cz	15	no	\(1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)
\(\chi_{2013}(17,\cdot)\)	2013.fo	60	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{2013}(19,\cdot)\)	2013.fe	30	no	\(-1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)
\(\chi_{2013}(20,\cdot)\)	2013.bc	10	yes	\(-1\)	\(1\)	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{2013}(23,\cdot)\)	2013.dn	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{2013}(25,\cdot)\)	2013.cv	15	no	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{2013}(26,\cdot)\)	2013.fp	60	yes	\(1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{2013}(28,\cdot)\)	2013.dd	20	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(i\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{2013}(29,\cdot)\)	2013.gb	60	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{60}\right)\)
\(\chi_{2013}(31,\cdot)\)	2013.gj	60	no	\(-1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(-i\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{37}{60}\right)\)
\(\chi_{2013}(32,\cdot)\)	2013.cr	12	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{2013}(34,\cdot)\)	2013.o	5	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)
\(\chi_{2013}(35,\cdot)\)	2013.ga	60	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{60}\right)\)
\(\chi_{2013}(37,\cdot)\)	2013.dp	20	no	\(-1\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{2013}(38,\cdot)\)	2013.dw	20	yes	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(i\)
\(\chi_{2013}(40,\cdot)\)	2013.fs	60	no	\(1\)	\(1\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{53}{60}\right)\)
\(\chi_{2013}(41,\cdot)\)	2013.bu	10	yes	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)
\(\chi_{2013}(43,\cdot)\)	2013.fx	60	no	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{11}{60}\right)\)
\(\chi_{2013}(46,\cdot)\)	2013.ev	30	no	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{2013}(47,\cdot)\)	2013.eg	30	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{2013}(49,\cdot)\)	2013.es	30	no	\(1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)
\(\chi_{2013}(50,\cdot)\)	2013.dl	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(-i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{2013}(52,\cdot)\)	2013.cn	10	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(e\left(\frac{3}{5}\right)\)

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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.