LMFDB - Group of Dirichlet characters of modulus 13685

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(13685)

gp:g = idealstar(,13685,2)

magma:G = FullDirichletGroup(13685);

Character group

Order	=	8448	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{528}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{13685}(8212,\cdot)$, $\chi_{13685}(1956,\cdot)$, $\chi_{13685}(4831,\cdot)$, $\chi_{13685}(8331,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 8448 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	$-1$	$1$	$2$	$3$	$4$	$6$	$8$	$9$	$11$	$12$	$13$	$16$
$\chi_{13685}(1,\cdot)$	13685.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{13685}(2,\cdot)$	13685.jy	264	yes	$-1$	$1$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{109}{264}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{73}{264}\right)$	$e\left(\frac{29}{264}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{13}{33}\right)$
$\chi_{13685}(3,\cdot)$	13685.km	528	yes	$-1$	$1$	$e\left(\frac{109}{264}\right)$	$e\left(\frac{61}{528}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{93}{176}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{61}{264}\right)$	$e\left(\frac{343}{528}\right)$	$e\left(\frac{497}{528}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{43}{66}\right)$
$\chi_{13685}(4,\cdot)$	13685.je	132	yes	$1$	$1$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{26}{33}\right)$
$\chi_{13685}(6,\cdot)$	13685.jl	176	no	$1$	$1$	$e\left(\frac{67}{88}\right)$	$e\left(\frac{93}{176}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{51}{176}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{163}{176}\right)$	$e\left(\frac{9}{176}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{13685}(8,\cdot)$	13685.ig	88	no	$-1$	$1$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{25}{88}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{2}{11}\right)$
$\chi_{13685}(9,\cdot)$	13685.ka	264	yes	$1$	$1$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{61}{264}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{61}{132}\right)$	$e\left(\frac{79}{264}\right)$	$e\left(\frac{233}{264}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{10}{33}\right)$
$\chi_{13685}(11,\cdot)$	13685.kx	528	no	$1$	$1$	$e\left(\frac{73}{264}\right)$	$e\left(\frac{343}{528}\right)$	$e\left(\frac{73}{132}\right)$	$e\left(\frac{163}{176}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{79}{264}\right)$	$e\left(\frac{217}{528}\right)$	$e\left(\frac{107}{528}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{7}{66}\right)$
$\chi_{13685}(12,\cdot)$	13685.lb	528	yes	$-1$	$1$	$e\left(\frac{29}{264}\right)$	$e\left(\frac{497}{528}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{9}{176}\right)$	$e\left(\frac{29}{88}\right)$	$e\left(\frac{233}{264}\right)$	$e\left(\frac{107}{528}\right)$	$e\left(\frac{85}{528}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{29}{66}\right)$
$\chi_{13685}(13,\cdot)$	13685.fv	44	yes	$1$	$1$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{13685}(16,\cdot)$	13685.hl	66	no	$1$	$1$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{19}{33}\right)$
$\chi_{13685}(18,\cdot)$	13685.it	132	no	$-1$	$1$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{85}{132}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{131}{132}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{23}{33}\right)$
$\chi_{13685}(19,\cdot)$	13685.ke	264	yes	$1$	$1$	$e\left(\frac{103}{132}\right)$	$e\left(\frac{31}{264}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{79}{88}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{31}{132}\right)$	$e\left(\frac{157}{264}\right)$	$e\left(\frac{179}{264}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{4}{33}\right)$
$\chi_{13685}(22,\cdot)$	13685.ei	16	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{16}\right)$	$i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$1$	$-1$
$\chi_{13685}(24,\cdot)$	13685.gx	48	no	$1$	$1$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{13}{48}\right)$	$-i$	$e\left(\frac{5}{6}\right)$
$\chi_{13685}(26,\cdot)$	13685.kc	264	no	$-1$	$1$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{157}{264}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{41}{88}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{199}{264}\right)$	$e\left(\frac{89}{264}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{16}{33}\right)$
$\chi_{13685}(27,\cdot)$	13685.jj	176	yes	$-1$	$1$	$e\left(\frac{21}{88}\right)$	$e\left(\frac{61}{176}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{103}{176}\right)$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{61}{88}\right)$	$e\left(\frac{167}{176}\right)$	$e\left(\frac{145}{176}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{21}{22}\right)$
$\chi_{13685}(29,\cdot)$	13685.jp	176	no	$-1$	$1$	$e\left(\frac{45}{88}\right)$	$e\left(\frac{71}{176}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{161}{176}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{9}{176}\right)$	$e\left(\frac{75}{176}\right)$	$e\left(\frac{9}{44}\right)$	$e\left(\frac{1}{22}\right)$
$\chi_{13685}(31,\cdot)$	13685.kw	528	no	$1$	$1$	$e\left(\frac{199}{264}\right)$	$e\left(\frac{49}{528}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{149}{176}\right)$	$e\left(\frac{23}{88}\right)$	$e\left(\frac{49}{264}\right)$	$e\left(\frac{31}{528}\right)$	$e\left(\frac{317}{528}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{1}{66}\right)$
$\chi_{13685}(32,\cdot)$	13685.jy	264	yes	$-1$	$1$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{17}{264}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{101}{264}\right)$	$e\left(\frac{145}{264}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{32}{33}\right)$
$\chi_{13685}(33,\cdot)$	13685.is	132	yes	$-1$	$1$	$e\left(\frac{91}{132}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{3}{44}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{19}{132}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{25}{33}\right)$
$\chi_{13685}(36,\cdot)$	13685.ia	88	no	$1$	$1$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{5}{88}\right)$	$e\left(\frac{1}{22}\right)$	$e\left(\frac{51}{88}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{5}{44}\right)$	$e\left(\frac{75}{88}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{13685}(37,\cdot)$	13685.kp	528	yes	$-1$	$1$	$e\left(\frac{185}{264}\right)$	$e\left(\frac{221}{528}\right)$	$e\left(\frac{53}{132}\right)$	$e\left(\frac{21}{176}\right)$	$e\left(\frac{9}{88}\right)$	$e\left(\frac{221}{264}\right)$	$e\left(\frac{191}{528}\right)$	$e\left(\frac{433}{528}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{53}{66}\right)$
$\chi_{13685}(38,\cdot)$	13685.ip	132	yes	$-1$	$1$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{17}{44}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{25}{44}\right)$	$e\left(\frac{17}{33}\right)$
$\chi_{13685}(39,\cdot)$	13685.ks	528	yes	$-1$	$1$	$e\left(\frac{247}{264}\right)$	$e\left(\frac{157}{528}\right)$	$e\left(\frac{115}{132}\right)$	$e\left(\frac{41}{176}\right)$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{157}{264}\right)$	$e\left(\frac{67}{528}\right)$	$e\left(\frac{89}{528}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{49}{66}\right)$
$\chi_{13685}(41,\cdot)$	13685.jl	176	no	$1$	$1$	$e\left(\frac{63}{88}\right)$	$e\left(\frac{161}{176}\right)$	$e\left(\frac{19}{44}\right)$	$e\left(\frac{111}{176}\right)$	$e\left(\frac{13}{88}\right)$	$e\left(\frac{73}{88}\right)$	$e\left(\frac{127}{176}\right)$	$e\left(\frac{61}{176}\right)$	$e\left(\frac{39}{44}\right)$	$e\left(\frac{19}{22}\right)$
$\chi_{13685}(43,\cdot)$	13685.if	88	no	$1$	$1$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{88}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{85}{88}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{1}{44}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{41}{44}\right)$	$e\left(\frac{9}{11}\right)$
$\chi_{13685}(44,\cdot)$	13685.kq	528	yes	$1$	$1$	$e\left(\frac{257}{264}\right)$	$e\left(\frac{251}{528}\right)$	$e\left(\frac{125}{132}\right)$	$e\left(\frac{79}{176}\right)$	$e\left(\frac{81}{88}\right)$	$e\left(\frac{251}{264}\right)$	$e\left(\frac{509}{528}\right)$	$e\left(\frac{223}{528}\right)$	$e\left(\frac{23}{44}\right)$	$e\left(\frac{59}{66}\right)$
$\chi_{13685}(47,\cdot)$	13685.dn	12	no	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$i$	$e\left(\frac{2}{3}\right)$
$\chi_{13685}(48,\cdot)$	13685.jj	176	yes	$-1$	$1$	$e\left(\frac{71}{88}\right)$	$e\left(\frac{135}{176}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{101}{176}\right)$	$e\left(\frac{37}{88}\right)$	$e\left(\frac{47}{88}\right)$	$e\left(\frac{133}{176}\right)$	$e\left(\frac{67}{176}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{13685}(52,\cdot)$	13685.iw	132	no	$1$	$1$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{1}{132}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{29}{44}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{29}{33}\right)$
$\chi_{13685}(53,\cdot)$	13685.kk	264	yes	$1$	$1$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{161}{264}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{59}{88}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{29}{132}\right)$	$e\left(\frac{149}{264}\right)$	$e\left(\frac{193}{264}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{8}{33}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$13685$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{528}\)
Order	$8448$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)	\(16\)
\(\chi_{13685}(1,\cdot)\)	13685.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{13685}(2,\cdot)\)	13685.jy	264	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{109}{264}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{73}{264}\right)\)	\(e\left(\frac{29}{264}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{13}{33}\right)\)
\(\chi_{13685}(3,\cdot)\)	13685.km	528	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{264}\right)\)	\(e\left(\frac{61}{528}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{93}{176}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{61}{264}\right)\)	\(e\left(\frac{343}{528}\right)\)	\(e\left(\frac{497}{528}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{43}{66}\right)\)
\(\chi_{13685}(4,\cdot)\)	13685.je	132	yes	\(1\)	\(1\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{26}{33}\right)\)
\(\chi_{13685}(6,\cdot)\)	13685.jl	176	no	\(1\)	\(1\)	\(e\left(\frac{67}{88}\right)\)	\(e\left(\frac{93}{176}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{51}{176}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{163}{176}\right)\)	\(e\left(\frac{9}{176}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{13685}(8,\cdot)\)	13685.ig	88	no	\(-1\)	\(1\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{25}{88}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{13685}(9,\cdot)\)	13685.ka	264	yes	\(1\)	\(1\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{61}{264}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{61}{132}\right)\)	\(e\left(\frac{79}{264}\right)\)	\(e\left(\frac{233}{264}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)
\(\chi_{13685}(11,\cdot)\)	13685.kx	528	no	\(1\)	\(1\)	\(e\left(\frac{73}{264}\right)\)	\(e\left(\frac{343}{528}\right)\)	\(e\left(\frac{73}{132}\right)\)	\(e\left(\frac{163}{176}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{79}{264}\right)\)	\(e\left(\frac{217}{528}\right)\)	\(e\left(\frac{107}{528}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{7}{66}\right)\)
\(\chi_{13685}(12,\cdot)\)	13685.lb	528	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{264}\right)\)	\(e\left(\frac{497}{528}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{9}{176}\right)\)	\(e\left(\frac{29}{88}\right)\)	\(e\left(\frac{233}{264}\right)\)	\(e\left(\frac{107}{528}\right)\)	\(e\left(\frac{85}{528}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{29}{66}\right)\)
\(\chi_{13685}(13,\cdot)\)	13685.fv	44	yes	\(1\)	\(1\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{13685}(16,\cdot)\)	13685.hl	66	no	\(1\)	\(1\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{19}{33}\right)\)
\(\chi_{13685}(18,\cdot)\)	13685.it	132	no	\(-1\)	\(1\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{85}{132}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{131}{132}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{23}{33}\right)\)
\(\chi_{13685}(19,\cdot)\)	13685.ke	264	yes	\(1\)	\(1\)	\(e\left(\frac{103}{132}\right)\)	\(e\left(\frac{31}{264}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{79}{88}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{31}{132}\right)\)	\(e\left(\frac{157}{264}\right)\)	\(e\left(\frac{179}{264}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{4}{33}\right)\)
\(\chi_{13685}(22,\cdot)\)	13685.ei	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(1\)	\(-1\)
\(\chi_{13685}(24,\cdot)\)	13685.gx	48	no	\(1\)	\(1\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(-i\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{13685}(26,\cdot)\)	13685.kc	264	no	\(-1\)	\(1\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{157}{264}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{41}{88}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{199}{264}\right)\)	\(e\left(\frac{89}{264}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{16}{33}\right)\)
\(\chi_{13685}(27,\cdot)\)	13685.jj	176	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{88}\right)\)	\(e\left(\frac{61}{176}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{103}{176}\right)\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{61}{88}\right)\)	\(e\left(\frac{167}{176}\right)\)	\(e\left(\frac{145}{176}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{13685}(29,\cdot)\)	13685.jp	176	no	\(-1\)	\(1\)	\(e\left(\frac{45}{88}\right)\)	\(e\left(\frac{71}{176}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{161}{176}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{9}{176}\right)\)	\(e\left(\frac{75}{176}\right)\)	\(e\left(\frac{9}{44}\right)\)	\(e\left(\frac{1}{22}\right)\)
\(\chi_{13685}(31,\cdot)\)	13685.kw	528	no	\(1\)	\(1\)	\(e\left(\frac{199}{264}\right)\)	\(e\left(\frac{49}{528}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{149}{176}\right)\)	\(e\left(\frac{23}{88}\right)\)	\(e\left(\frac{49}{264}\right)\)	\(e\left(\frac{31}{528}\right)\)	\(e\left(\frac{317}{528}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{1}{66}\right)\)
\(\chi_{13685}(32,\cdot)\)	13685.jy	264	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{17}{264}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{101}{264}\right)\)	\(e\left(\frac{145}{264}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{32}{33}\right)\)
\(\chi_{13685}(33,\cdot)\)	13685.is	132	yes	\(-1\)	\(1\)	\(e\left(\frac{91}{132}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{3}{44}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{19}{132}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{25}{33}\right)\)
\(\chi_{13685}(36,\cdot)\)	13685.ia	88	no	\(1\)	\(1\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{5}{88}\right)\)	\(e\left(\frac{1}{22}\right)\)	\(e\left(\frac{51}{88}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{5}{44}\right)\)	\(e\left(\frac{75}{88}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{13685}(37,\cdot)\)	13685.kp	528	yes	\(-1\)	\(1\)	\(e\left(\frac{185}{264}\right)\)	\(e\left(\frac{221}{528}\right)\)	\(e\left(\frac{53}{132}\right)\)	\(e\left(\frac{21}{176}\right)\)	\(e\left(\frac{9}{88}\right)\)	\(e\left(\frac{221}{264}\right)\)	\(e\left(\frac{191}{528}\right)\)	\(e\left(\frac{433}{528}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{53}{66}\right)\)
\(\chi_{13685}(38,\cdot)\)	13685.ip	132	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{17}{44}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{25}{44}\right)\)	\(e\left(\frac{17}{33}\right)\)
\(\chi_{13685}(39,\cdot)\)	13685.ks	528	yes	\(-1\)	\(1\)	\(e\left(\frac{247}{264}\right)\)	\(e\left(\frac{157}{528}\right)\)	\(e\left(\frac{115}{132}\right)\)	\(e\left(\frac{41}{176}\right)\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{157}{264}\right)\)	\(e\left(\frac{67}{528}\right)\)	\(e\left(\frac{89}{528}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{49}{66}\right)\)
\(\chi_{13685}(41,\cdot)\)	13685.jl	176	no	\(1\)	\(1\)	\(e\left(\frac{63}{88}\right)\)	\(e\left(\frac{161}{176}\right)\)	\(e\left(\frac{19}{44}\right)\)	\(e\left(\frac{111}{176}\right)\)	\(e\left(\frac{13}{88}\right)\)	\(e\left(\frac{73}{88}\right)\)	\(e\left(\frac{127}{176}\right)\)	\(e\left(\frac{61}{176}\right)\)	\(e\left(\frac{39}{44}\right)\)	\(e\left(\frac{19}{22}\right)\)
\(\chi_{13685}(43,\cdot)\)	13685.if	88	no	\(1\)	\(1\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{88}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{85}{88}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{1}{44}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{41}{44}\right)\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{13685}(44,\cdot)\)	13685.kq	528	yes	\(1\)	\(1\)	\(e\left(\frac{257}{264}\right)\)	\(e\left(\frac{251}{528}\right)\)	\(e\left(\frac{125}{132}\right)\)	\(e\left(\frac{79}{176}\right)\)	\(e\left(\frac{81}{88}\right)\)	\(e\left(\frac{251}{264}\right)\)	\(e\left(\frac{509}{528}\right)\)	\(e\left(\frac{223}{528}\right)\)	\(e\left(\frac{23}{44}\right)\)	\(e\left(\frac{59}{66}\right)\)
\(\chi_{13685}(47,\cdot)\)	13685.dn	12	no	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{13685}(48,\cdot)\)	13685.jj	176	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{88}\right)\)	\(e\left(\frac{135}{176}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{101}{176}\right)\)	\(e\left(\frac{37}{88}\right)\)	\(e\left(\frac{47}{88}\right)\)	\(e\left(\frac{133}{176}\right)\)	\(e\left(\frac{67}{176}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{13685}(52,\cdot)\)	13685.iw	132	no	\(1\)	\(1\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{1}{132}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{29}{44}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{29}{33}\right)\)
\(\chi_{13685}(53,\cdot)\)	13685.kk	264	yes	\(1\)	\(1\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{161}{264}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{59}{88}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{29}{132}\right)\)	\(e\left(\frac{149}{264}\right)\)	\(e\left(\frac{193}{264}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{8}{33}\right)\)

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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.