LMFDB - Group of Dirichlet characters of modulus 91091

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(91091)

gp:g = idealstar(,91091,2)

magma:G = FullDirichletGroup(91091);

Character group

Order	=	65520	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{6}\times C_{5460}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{91091}(59489,\cdot)$, $\chi_{91091}(41406,\cdot)$, $\chi_{91091}(19944,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 65520 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$12$	$15$
$\chi_{91091}(1,\cdot)$	91091.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{91091}(2,\cdot)$	91091.si	5460	yes	$1$	$1$	$e\left(\frac{367}{1820}\right)$	$e\left(\frac{292}{1365}\right)$	$e\left(\frac{367}{910}\right)$	$e\left(\frac{2239}{5460}\right)$	$e\left(\frac{2269}{5460}\right)$	$e\left(\frac{1101}{1820}\right)$	$e\left(\frac{584}{1365}\right)$	$e\left(\frac{167}{273}\right)$	$e\left(\frac{337}{546}\right)$	$e\left(\frac{3407}{5460}\right)$
$\chi_{91091}(3,\cdot)$	91091.rq	2730	yes	$-1$	$1$	$e\left(\frac{292}{1365}\right)$	$e\left(\frac{899}{910}\right)$	$e\left(\frac{584}{1365}\right)$	$e\left(\frac{121}{2730}\right)$	$e\left(\frac{551}{2730}\right)$	$e\left(\frac{292}{455}\right)$	$e\left(\frac{444}{455}\right)$	$e\left(\frac{47}{182}\right)$	$e\left(\frac{227}{546}\right)$	$e\left(\frac{44}{1365}\right)$
$\chi_{91091}(4,\cdot)$	91091.ru	2730	yes	$1$	$1$	$e\left(\frac{367}{910}\right)$	$e\left(\frac{584}{1365}\right)$	$e\left(\frac{367}{455}\right)$	$e\left(\frac{2239}{2730}\right)$	$e\left(\frac{2269}{2730}\right)$	$e\left(\frac{191}{910}\right)$	$e\left(\frac{1168}{1365}\right)$	$e\left(\frac{61}{273}\right)$	$e\left(\frac{64}{273}\right)$	$e\left(\frac{677}{2730}\right)$
$\chi_{91091}(5,\cdot)$	91091.ry	5460	yes	$1$	$1$	$e\left(\frac{2239}{5460}\right)$	$e\left(\frac{121}{2730}\right)$	$e\left(\frac{2239}{2730}\right)$	$e\left(\frac{781}{5460}\right)$	$e\left(\frac{827}{1820}\right)$	$e\left(\frac{419}{1820}\right)$	$e\left(\frac{121}{1365}\right)$	$e\left(\frac{151}{273}\right)$	$e\left(\frac{236}{273}\right)$	$e\left(\frac{341}{1820}\right)$
$\chi_{91091}(6,\cdot)$	91091.sb	5460	yes	$-1$	$1$	$e\left(\frac{2269}{5460}\right)$	$e\left(\frac{551}{2730}\right)$	$e\left(\frac{2269}{2730}\right)$	$e\left(\frac{827}{1820}\right)$	$e\left(\frac{3371}{5460}\right)$	$e\left(\frac{449}{1820}\right)$	$e\left(\frac{551}{1365}\right)$	$e\left(\frac{475}{546}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{3583}{5460}\right)$
$\chi_{91091}(8,\cdot)$	91091.qr	1820	yes	$1$	$1$	$e\left(\frac{1101}{1820}\right)$	$e\left(\frac{292}{455}\right)$	$e\left(\frac{191}{910}\right)$	$e\left(\frac{419}{1820}\right)$	$e\left(\frac{449}{1820}\right)$	$e\left(\frac{1483}{1820}\right)$	$e\left(\frac{129}{455}\right)$	$e\left(\frac{76}{91}\right)$	$e\left(\frac{155}{182}\right)$	$e\left(\frac{1587}{1820}\right)$
$\chi_{91091}(9,\cdot)$	91091.qn	1365	yes	$1$	$1$	$e\left(\frac{584}{1365}\right)$	$e\left(\frac{444}{455}\right)$	$e\left(\frac{1168}{1365}\right)$	$e\left(\frac{121}{1365}\right)$	$e\left(\frac{551}{1365}\right)$	$e\left(\frac{129}{455}\right)$	$e\left(\frac{433}{455}\right)$	$e\left(\frac{47}{91}\right)$	$e\left(\frac{227}{273}\right)$	$e\left(\frac{88}{1365}\right)$
$\chi_{91091}(10,\cdot)$	91091.ob	546	yes	$1$	$1$	$e\left(\frac{167}{273}\right)$	$e\left(\frac{47}{182}\right)$	$e\left(\frac{61}{273}\right)$	$e\left(\frac{151}{273}\right)$	$e\left(\frac{475}{546}\right)$	$e\left(\frac{76}{91}\right)$	$e\left(\frac{47}{91}\right)$	$e\left(\frac{15}{91}\right)$	$e\left(\frac{263}{546}\right)$	$e\left(\frac{443}{546}\right)$
$\chi_{91091}(12,\cdot)$	91091.or	546	no	$-1$	$1$	$e\left(\frac{337}{546}\right)$	$e\left(\frac{227}{546}\right)$	$e\left(\frac{64}{273}\right)$	$e\left(\frac{236}{273}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{155}{182}\right)$	$e\left(\frac{227}{273}\right)$	$e\left(\frac{263}{546}\right)$	$e\left(\frac{355}{546}\right)$	$e\left(\frac{51}{182}\right)$
$\chi_{91091}(15,\cdot)$	91091.sg	5460	yes	$-1$	$1$	$e\left(\frac{3407}{5460}\right)$	$e\left(\frac{44}{1365}\right)$	$e\left(\frac{677}{2730}\right)$	$e\left(\frac{341}{1820}\right)$	$e\left(\frac{3583}{5460}\right)$	$e\left(\frac{1587}{1820}\right)$	$e\left(\frac{88}{1365}\right)$	$e\left(\frac{443}{546}\right)$	$e\left(\frac{51}{182}\right)$	$e\left(\frac{1199}{5460}\right)$
$\chi_{91091}(16,\cdot)$	91091.qm	1365	yes	$1$	$1$	$e\left(\frac{367}{455}\right)$	$e\left(\frac{1168}{1365}\right)$	$e\left(\frac{279}{455}\right)$	$e\left(\frac{874}{1365}\right)$	$e\left(\frac{904}{1365}\right)$	$e\left(\frac{191}{455}\right)$	$e\left(\frac{971}{1365}\right)$	$e\left(\frac{122}{273}\right)$	$e\left(\frac{128}{273}\right)$	$e\left(\frac{677}{1365}\right)$
$\chi_{91091}(17,\cdot)$	91091.qv	2730	yes	$1$	$1$	$e\left(\frac{142}{455}\right)$	$e\left(\frac{2311}{2730}\right)$	$e\left(\frac{284}{455}\right)$	$e\left(\frac{389}{1365}\right)$	$e\left(\frac{433}{2730}\right)$	$e\left(\frac{426}{455}\right)$	$e\left(\frac{946}{1365}\right)$	$e\left(\frac{163}{273}\right)$	$e\left(\frac{257}{546}\right)$	$e\left(\frac{359}{2730}\right)$
$\chi_{91091}(18,\cdot)$	91091.pf	780	no	$1$	$1$	$e\left(\frac{491}{780}\right)$	$e\left(\frac{37}{195}\right)$	$e\left(\frac{101}{390}\right)$	$e\left(\frac{389}{780}\right)$	$e\left(\frac{213}{260}\right)$	$e\left(\frac{231}{260}\right)$	$e\left(\frac{74}{195}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{179}{260}\right)$
$\chi_{91091}(19,\cdot)$	91091.gx	60	no	$-1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{60}\right)$
$\chi_{91091}(20,\cdot)$	91091.rz	5460	yes	$1$	$1$	$e\left(\frac{4441}{5460}\right)$	$e\left(\frac{1289}{2730}\right)$	$e\left(\frac{1711}{2730}\right)$	$e\left(\frac{1753}{1820}\right)$	$e\left(\frac{1559}{5460}\right)$	$e\left(\frac{801}{1820}\right)$	$e\left(\frac{1289}{1365}\right)$	$e\left(\frac{212}{273}\right)$	$e\left(\frac{9}{91}\right)$	$e\left(\frac{2377}{5460}\right)$
$\chi_{91091}(23,\cdot)$	91091.gd	42	no	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{41}{42}\right)$
$\chi_{91091}(24,\cdot)$	91091.sk	5460	yes	$-1$	$1$	$e\left(\frac{4471}{5460}\right)$	$e\left(\frac{573}{910}\right)$	$e\left(\frac{1741}{2730}\right)$	$e\left(\frac{1499}{5460}\right)$	$e\left(\frac{2449}{5460}\right)$	$e\left(\frac{831}{1820}\right)$	$e\left(\frac{118}{455}\right)$	$e\left(\frac{17}{182}\right)$	$e\left(\frac{73}{273}\right)$	$e\left(\frac{4937}{5460}\right)$
$\chi_{91091}(25,\cdot)$	91091.re	2730	yes	$1$	$1$	$e\left(\frac{2239}{2730}\right)$	$e\left(\frac{121}{1365}\right)$	$e\left(\frac{874}{1365}\right)$	$e\left(\frac{781}{2730}\right)$	$e\left(\frac{827}{910}\right)$	$e\left(\frac{419}{910}\right)$	$e\left(\frac{242}{1365}\right)$	$e\left(\frac{29}{273}\right)$	$e\left(\frac{199}{273}\right)$	$e\left(\frac{341}{910}\right)$
$\chi_{91091}(27,\cdot)$	91091.pr	910	yes	$-1$	$1$	$e\left(\frac{292}{455}\right)$	$e\left(\frac{877}{910}\right)$	$e\left(\frac{129}{455}\right)$	$e\left(\frac{121}{910}\right)$	$e\left(\frac{551}{910}\right)$	$e\left(\frac{421}{455}\right)$	$e\left(\frac{422}{455}\right)$	$e\left(\frac{141}{182}\right)$	$e\left(\frac{45}{182}\right)$	$e\left(\frac{44}{455}\right)$
$\chi_{91091}(29,\cdot)$	91091.rd	2730	yes	$-1$	$1$	$e\left(\frac{271}{2730}\right)$	$e\left(\frac{1124}{1365}\right)$	$e\left(\frac{271}{1365}\right)$	$e\left(\frac{244}{455}\right)$	$e\left(\frac{2519}{2730}\right)$	$e\left(\frac{271}{910}\right)$	$e\left(\frac{883}{1365}\right)$	$e\left(\frac{347}{546}\right)$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{491}{1365}\right)$
$\chi_{91091}(30,\cdot)$	91091.mq	390	no	$-1$	$1$	$e\left(\frac{161}{195}\right)$	$e\left(\frac{16}{65}\right)$	$e\left(\frac{127}{195}\right)$	$e\left(\frac{233}{390}\right)$	$e\left(\frac{14}{195}\right)$	$e\left(\frac{31}{65}\right)$	$e\left(\frac{32}{65}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{329}{390}\right)$
$\chi_{91091}(31,\cdot)$	91091.pm	780	no	$1$	$1$	$e\left(\frac{53}{780}\right)$	$e\left(\frac{257}{390}\right)$	$e\left(\frac{53}{390}\right)$	$e\left(\frac{347}{780}\right)$	$e\left(\frac{189}{260}\right)$	$e\left(\frac{53}{260}\right)$	$e\left(\frac{62}{195}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{27}{260}\right)$
$\chi_{91091}(32,\cdot)$	91091.py	1092	yes	$1$	$1$	$e\left(\frac{3}{364}\right)$	$e\left(\frac{19}{273}\right)$	$e\left(\frac{3}{182}\right)$	$e\left(\frac{55}{1092}\right)$	$e\left(\frac{85}{1092}\right)$	$e\left(\frac{9}{364}\right)$	$e\left(\frac{38}{273}\right)$	$e\left(\frac{16}{273}\right)$	$e\left(\frac{47}{546}\right)$	$e\left(\frac{131}{1092}\right)$
$\chi_{91091}(34,\cdot)$	91091.mb	364	no	$1$	$1$	$e\left(\frac{187}{364}\right)$	$e\left(\frac{11}{182}\right)$	$e\left(\frac{5}{182}\right)$	$e\left(\frac{253}{364}\right)$	$e\left(\frac{209}{364}\right)$	$e\left(\frac{197}{364}\right)$	$e\left(\frac{11}{91}\right)$	$e\left(\frac{19}{91}\right)$	$e\left(\frac{8}{91}\right)$	$e\left(\frac{275}{364}\right)$
$\chi_{91091}(36,\cdot)$	91091.rg	2730	yes	$1$	$1$	$e\left(\frac{2269}{2730}\right)$	$e\left(\frac{551}{1365}\right)$	$e\left(\frac{904}{1365}\right)$	$e\left(\frac{827}{910}\right)$	$e\left(\frac{641}{2730}\right)$	$e\left(\frac{449}{910}\right)$	$e\left(\frac{1102}{1365}\right)$	$e\left(\frac{202}{273}\right)$	$e\left(\frac{6}{91}\right)$	$e\left(\frac{853}{2730}\right)$
$\chi_{91091}(37,\cdot)$	91091.sj	5460	yes	$-1$	$1$	$e\left(\frac{1779}{1820}\right)$	$e\left(\frac{529}{1365}\right)$	$e\left(\frac{869}{910}\right)$	$e\left(\frac{3313}{5460}\right)$	$e\left(\frac{1993}{5460}\right)$	$e\left(\frac{1697}{1820}\right)$	$e\left(\frac{1058}{1365}\right)$	$e\left(\frac{319}{546}\right)$	$e\left(\frac{187}{546}\right)$	$e\left(\frac{5429}{5460}\right)$
$\chi_{91091}(38,\cdot)$	91091.rb	2730	yes	$-1$	$1$	$e\left(\frac{1597}{2730}\right)$	$e\left(\frac{311}{2730}\right)$	$e\left(\frac{232}{1365}\right)$	$e\left(\frac{719}{1365}\right)$	$e\left(\frac{318}{455}\right)$	$e\left(\frac{687}{910}\right)$	$e\left(\frac{311}{1365}\right)$	$e\left(\frac{61}{546}\right)$	$e\left(\frac{155}{546}\right)$	$e\left(\frac{583}{910}\right)$
$\chi_{91091}(40,\cdot)$	91091.ra	2730	yes	$1$	$1$	$e\left(\frac{41}{2730}\right)$	$e\left(\frac{1873}{2730}\right)$	$e\left(\frac{41}{1365}\right)$	$e\left(\frac{1019}{2730}\right)$	$e\left(\frac{319}{455}\right)$	$e\left(\frac{41}{910}\right)$	$e\left(\frac{508}{1365}\right)$	$e\left(\frac{106}{273}\right)$	$e\left(\frac{391}{546}\right)$	$e\left(\frac{27}{455}\right)$
$\chi_{91091}(41,\cdot)$	91091.sb	5460	yes	$-1$	$1$	$e\left(\frac{713}{5460}\right)$	$e\left(\frac{877}{2730}\right)$	$e\left(\frac{713}{2730}\right)$	$e\left(\frac{839}{1820}\right)$	$e\left(\frac{2467}{5460}\right)$	$e\left(\frac{713}{1820}\right)$	$e\left(\frac{877}{1365}\right)$	$e\left(\frac{323}{546}\right)$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{4271}{5460}\right)$
$\chi_{91091}(43,\cdot)$	91091.od	546	yes	$-1$	$1$	$e\left(\frac{272}{273}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{271}{273}\right)$	$e\left(\frac{33}{182}\right)$	$e\left(\frac{31}{273}\right)$	$e\left(\frac{90}{91}\right)$	$e\left(\frac{64}{273}\right)$	$e\left(\frac{97}{546}\right)$	$e\left(\frac{10}{91}\right)$	$e\left(\frac{163}{546}\right)$
$\chi_{91091}(45,\cdot)$	91091.qe	1092	no	$1$	$1$	$e\left(\frac{305}{364}\right)$	$e\left(\frac{11}{546}\right)$	$e\left(\frac{123}{182}\right)$	$e\left(\frac{253}{1092}\right)$	$e\left(\frac{937}{1092}\right)$	$e\left(\frac{187}{364}\right)$	$e\left(\frac{11}{273}\right)$	$e\left(\frac{19}{273}\right)$	$e\left(\frac{190}{273}\right)$	$e\left(\frac{275}{1092}\right)$

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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	$91091$
Structure	\(C_{2}\times C_{6}\times C_{5460}\)
Order	$65520$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(15\)
\(\chi_{91091}(1,\cdot)\)	91091.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{91091}(2,\cdot)\)	91091.si	5460	yes	\(1\)	\(1\)	\(e\left(\frac{367}{1820}\right)\)	\(e\left(\frac{292}{1365}\right)\)	\(e\left(\frac{367}{910}\right)\)	\(e\left(\frac{2239}{5460}\right)\)	\(e\left(\frac{2269}{5460}\right)\)	\(e\left(\frac{1101}{1820}\right)\)	\(e\left(\frac{584}{1365}\right)\)	\(e\left(\frac{167}{273}\right)\)	\(e\left(\frac{337}{546}\right)\)	\(e\left(\frac{3407}{5460}\right)\)
\(\chi_{91091}(3,\cdot)\)	91091.rq	2730	yes	\(-1\)	\(1\)	\(e\left(\frac{292}{1365}\right)\)	\(e\left(\frac{899}{910}\right)\)	\(e\left(\frac{584}{1365}\right)\)	\(e\left(\frac{121}{2730}\right)\)	\(e\left(\frac{551}{2730}\right)\)	\(e\left(\frac{292}{455}\right)\)	\(e\left(\frac{444}{455}\right)\)	\(e\left(\frac{47}{182}\right)\)	\(e\left(\frac{227}{546}\right)\)	\(e\left(\frac{44}{1365}\right)\)
\(\chi_{91091}(4,\cdot)\)	91091.ru	2730	yes	\(1\)	\(1\)	\(e\left(\frac{367}{910}\right)\)	\(e\left(\frac{584}{1365}\right)\)	\(e\left(\frac{367}{455}\right)\)	\(e\left(\frac{2239}{2730}\right)\)	\(e\left(\frac{2269}{2730}\right)\)	\(e\left(\frac{191}{910}\right)\)	\(e\left(\frac{1168}{1365}\right)\)	\(e\left(\frac{61}{273}\right)\)	\(e\left(\frac{64}{273}\right)\)	\(e\left(\frac{677}{2730}\right)\)
\(\chi_{91091}(5,\cdot)\)	91091.ry	5460	yes	\(1\)	\(1\)	\(e\left(\frac{2239}{5460}\right)\)	\(e\left(\frac{121}{2730}\right)\)	\(e\left(\frac{2239}{2730}\right)\)	\(e\left(\frac{781}{5460}\right)\)	\(e\left(\frac{827}{1820}\right)\)	\(e\left(\frac{419}{1820}\right)\)	\(e\left(\frac{121}{1365}\right)\)	\(e\left(\frac{151}{273}\right)\)	\(e\left(\frac{236}{273}\right)\)	\(e\left(\frac{341}{1820}\right)\)
\(\chi_{91091}(6,\cdot)\)	91091.sb	5460	yes	\(-1\)	\(1\)	\(e\left(\frac{2269}{5460}\right)\)	\(e\left(\frac{551}{2730}\right)\)	\(e\left(\frac{2269}{2730}\right)\)	\(e\left(\frac{827}{1820}\right)\)	\(e\left(\frac{3371}{5460}\right)\)	\(e\left(\frac{449}{1820}\right)\)	\(e\left(\frac{551}{1365}\right)\)	\(e\left(\frac{475}{546}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{3583}{5460}\right)\)
\(\chi_{91091}(8,\cdot)\)	91091.qr	1820	yes	\(1\)	\(1\)	\(e\left(\frac{1101}{1820}\right)\)	\(e\left(\frac{292}{455}\right)\)	\(e\left(\frac{191}{910}\right)\)	\(e\left(\frac{419}{1820}\right)\)	\(e\left(\frac{449}{1820}\right)\)	\(e\left(\frac{1483}{1820}\right)\)	\(e\left(\frac{129}{455}\right)\)	\(e\left(\frac{76}{91}\right)\)	\(e\left(\frac{155}{182}\right)\)	\(e\left(\frac{1587}{1820}\right)\)
\(\chi_{91091}(9,\cdot)\)	91091.qn	1365	yes	\(1\)	\(1\)	\(e\left(\frac{584}{1365}\right)\)	\(e\left(\frac{444}{455}\right)\)	\(e\left(\frac{1168}{1365}\right)\)	\(e\left(\frac{121}{1365}\right)\)	\(e\left(\frac{551}{1365}\right)\)	\(e\left(\frac{129}{455}\right)\)	\(e\left(\frac{433}{455}\right)\)	\(e\left(\frac{47}{91}\right)\)	\(e\left(\frac{227}{273}\right)\)	\(e\left(\frac{88}{1365}\right)\)
\(\chi_{91091}(10,\cdot)\)	91091.ob	546	yes	\(1\)	\(1\)	\(e\left(\frac{167}{273}\right)\)	\(e\left(\frac{47}{182}\right)\)	\(e\left(\frac{61}{273}\right)\)	\(e\left(\frac{151}{273}\right)\)	\(e\left(\frac{475}{546}\right)\)	\(e\left(\frac{76}{91}\right)\)	\(e\left(\frac{47}{91}\right)\)	\(e\left(\frac{15}{91}\right)\)	\(e\left(\frac{263}{546}\right)\)	\(e\left(\frac{443}{546}\right)\)
\(\chi_{91091}(12,\cdot)\)	91091.or	546	no	\(-1\)	\(1\)	\(e\left(\frac{337}{546}\right)\)	\(e\left(\frac{227}{546}\right)\)	\(e\left(\frac{64}{273}\right)\)	\(e\left(\frac{236}{273}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{155}{182}\right)\)	\(e\left(\frac{227}{273}\right)\)	\(e\left(\frac{263}{546}\right)\)	\(e\left(\frac{355}{546}\right)\)	\(e\left(\frac{51}{182}\right)\)
\(\chi_{91091}(15,\cdot)\)	91091.sg	5460	yes	\(-1\)	\(1\)	\(e\left(\frac{3407}{5460}\right)\)	\(e\left(\frac{44}{1365}\right)\)	\(e\left(\frac{677}{2730}\right)\)	\(e\left(\frac{341}{1820}\right)\)	\(e\left(\frac{3583}{5460}\right)\)	\(e\left(\frac{1587}{1820}\right)\)	\(e\left(\frac{88}{1365}\right)\)	\(e\left(\frac{443}{546}\right)\)	\(e\left(\frac{51}{182}\right)\)	\(e\left(\frac{1199}{5460}\right)\)
\(\chi_{91091}(16,\cdot)\)	91091.qm	1365	yes	\(1\)	\(1\)	\(e\left(\frac{367}{455}\right)\)	\(e\left(\frac{1168}{1365}\right)\)	\(e\left(\frac{279}{455}\right)\)	\(e\left(\frac{874}{1365}\right)\)	\(e\left(\frac{904}{1365}\right)\)	\(e\left(\frac{191}{455}\right)\)	\(e\left(\frac{971}{1365}\right)\)	\(e\left(\frac{122}{273}\right)\)	\(e\left(\frac{128}{273}\right)\)	\(e\left(\frac{677}{1365}\right)\)
\(\chi_{91091}(17,\cdot)\)	91091.qv	2730	yes	\(1\)	\(1\)	\(e\left(\frac{142}{455}\right)\)	\(e\left(\frac{2311}{2730}\right)\)	\(e\left(\frac{284}{455}\right)\)	\(e\left(\frac{389}{1365}\right)\)	\(e\left(\frac{433}{2730}\right)\)	\(e\left(\frac{426}{455}\right)\)	\(e\left(\frac{946}{1365}\right)\)	\(e\left(\frac{163}{273}\right)\)	\(e\left(\frac{257}{546}\right)\)	\(e\left(\frac{359}{2730}\right)\)
\(\chi_{91091}(18,\cdot)\)	91091.pf	780	no	\(1\)	\(1\)	\(e\left(\frac{491}{780}\right)\)	\(e\left(\frac{37}{195}\right)\)	\(e\left(\frac{101}{390}\right)\)	\(e\left(\frac{389}{780}\right)\)	\(e\left(\frac{213}{260}\right)\)	\(e\left(\frac{231}{260}\right)\)	\(e\left(\frac{74}{195}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{179}{260}\right)\)
\(\chi_{91091}(19,\cdot)\)	91091.gx	60	no	\(-1\)	\(1\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{60}\right)\)
\(\chi_{91091}(20,\cdot)\)	91091.rz	5460	yes	\(1\)	\(1\)	\(e\left(\frac{4441}{5460}\right)\)	\(e\left(\frac{1289}{2730}\right)\)	\(e\left(\frac{1711}{2730}\right)\)	\(e\left(\frac{1753}{1820}\right)\)	\(e\left(\frac{1559}{5460}\right)\)	\(e\left(\frac{801}{1820}\right)\)	\(e\left(\frac{1289}{1365}\right)\)	\(e\left(\frac{212}{273}\right)\)	\(e\left(\frac{9}{91}\right)\)	\(e\left(\frac{2377}{5460}\right)\)
\(\chi_{91091}(23,\cdot)\)	91091.gd	42	no	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)
\(\chi_{91091}(24,\cdot)\)	91091.sk	5460	yes	\(-1\)	\(1\)	\(e\left(\frac{4471}{5460}\right)\)	\(e\left(\frac{573}{910}\right)\)	\(e\left(\frac{1741}{2730}\right)\)	\(e\left(\frac{1499}{5460}\right)\)	\(e\left(\frac{2449}{5460}\right)\)	\(e\left(\frac{831}{1820}\right)\)	\(e\left(\frac{118}{455}\right)\)	\(e\left(\frac{17}{182}\right)\)	\(e\left(\frac{73}{273}\right)\)	\(e\left(\frac{4937}{5460}\right)\)
\(\chi_{91091}(25,\cdot)\)	91091.re	2730	yes	\(1\)	\(1\)	\(e\left(\frac{2239}{2730}\right)\)	\(e\left(\frac{121}{1365}\right)\)	\(e\left(\frac{874}{1365}\right)\)	\(e\left(\frac{781}{2730}\right)\)	\(e\left(\frac{827}{910}\right)\)	\(e\left(\frac{419}{910}\right)\)	\(e\left(\frac{242}{1365}\right)\)	\(e\left(\frac{29}{273}\right)\)	\(e\left(\frac{199}{273}\right)\)	\(e\left(\frac{341}{910}\right)\)
\(\chi_{91091}(27,\cdot)\)	91091.pr	910	yes	\(-1\)	\(1\)	\(e\left(\frac{292}{455}\right)\)	\(e\left(\frac{877}{910}\right)\)	\(e\left(\frac{129}{455}\right)\)	\(e\left(\frac{121}{910}\right)\)	\(e\left(\frac{551}{910}\right)\)	\(e\left(\frac{421}{455}\right)\)	\(e\left(\frac{422}{455}\right)\)	\(e\left(\frac{141}{182}\right)\)	\(e\left(\frac{45}{182}\right)\)	\(e\left(\frac{44}{455}\right)\)
\(\chi_{91091}(29,\cdot)\)	91091.rd	2730	yes	\(-1\)	\(1\)	\(e\left(\frac{271}{2730}\right)\)	\(e\left(\frac{1124}{1365}\right)\)	\(e\left(\frac{271}{1365}\right)\)	\(e\left(\frac{244}{455}\right)\)	\(e\left(\frac{2519}{2730}\right)\)	\(e\left(\frac{271}{910}\right)\)	\(e\left(\frac{883}{1365}\right)\)	\(e\left(\frac{347}{546}\right)\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{491}{1365}\right)\)
\(\chi_{91091}(30,\cdot)\)	91091.mq	390	no	\(-1\)	\(1\)	\(e\left(\frac{161}{195}\right)\)	\(e\left(\frac{16}{65}\right)\)	\(e\left(\frac{127}{195}\right)\)	\(e\left(\frac{233}{390}\right)\)	\(e\left(\frac{14}{195}\right)\)	\(e\left(\frac{31}{65}\right)\)	\(e\left(\frac{32}{65}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{329}{390}\right)\)
\(\chi_{91091}(31,\cdot)\)	91091.pm	780	no	\(1\)	\(1\)	\(e\left(\frac{53}{780}\right)\)	\(e\left(\frac{257}{390}\right)\)	\(e\left(\frac{53}{390}\right)\)	\(e\left(\frac{347}{780}\right)\)	\(e\left(\frac{189}{260}\right)\)	\(e\left(\frac{53}{260}\right)\)	\(e\left(\frac{62}{195}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{27}{260}\right)\)
\(\chi_{91091}(32,\cdot)\)	91091.py	1092	yes	\(1\)	\(1\)	\(e\left(\frac{3}{364}\right)\)	\(e\left(\frac{19}{273}\right)\)	\(e\left(\frac{3}{182}\right)\)	\(e\left(\frac{55}{1092}\right)\)	\(e\left(\frac{85}{1092}\right)\)	\(e\left(\frac{9}{364}\right)\)	\(e\left(\frac{38}{273}\right)\)	\(e\left(\frac{16}{273}\right)\)	\(e\left(\frac{47}{546}\right)\)	\(e\left(\frac{131}{1092}\right)\)
\(\chi_{91091}(34,\cdot)\)	91091.mb	364	no	\(1\)	\(1\)	\(e\left(\frac{187}{364}\right)\)	\(e\left(\frac{11}{182}\right)\)	\(e\left(\frac{5}{182}\right)\)	\(e\left(\frac{253}{364}\right)\)	\(e\left(\frac{209}{364}\right)\)	\(e\left(\frac{197}{364}\right)\)	\(e\left(\frac{11}{91}\right)\)	\(e\left(\frac{19}{91}\right)\)	\(e\left(\frac{8}{91}\right)\)	\(e\left(\frac{275}{364}\right)\)
\(\chi_{91091}(36,\cdot)\)	91091.rg	2730	yes	\(1\)	\(1\)	\(e\left(\frac{2269}{2730}\right)\)	\(e\left(\frac{551}{1365}\right)\)	\(e\left(\frac{904}{1365}\right)\)	\(e\left(\frac{827}{910}\right)\)	\(e\left(\frac{641}{2730}\right)\)	\(e\left(\frac{449}{910}\right)\)	\(e\left(\frac{1102}{1365}\right)\)	\(e\left(\frac{202}{273}\right)\)	\(e\left(\frac{6}{91}\right)\)	\(e\left(\frac{853}{2730}\right)\)
\(\chi_{91091}(37,\cdot)\)	91091.sj	5460	yes	\(-1\)	\(1\)	\(e\left(\frac{1779}{1820}\right)\)	\(e\left(\frac{529}{1365}\right)\)	\(e\left(\frac{869}{910}\right)\)	\(e\left(\frac{3313}{5460}\right)\)	\(e\left(\frac{1993}{5460}\right)\)	\(e\left(\frac{1697}{1820}\right)\)	\(e\left(\frac{1058}{1365}\right)\)	\(e\left(\frac{319}{546}\right)\)	\(e\left(\frac{187}{546}\right)\)	\(e\left(\frac{5429}{5460}\right)\)
\(\chi_{91091}(38,\cdot)\)	91091.rb	2730	yes	\(-1\)	\(1\)	\(e\left(\frac{1597}{2730}\right)\)	\(e\left(\frac{311}{2730}\right)\)	\(e\left(\frac{232}{1365}\right)\)	\(e\left(\frac{719}{1365}\right)\)	\(e\left(\frac{318}{455}\right)\)	\(e\left(\frac{687}{910}\right)\)	\(e\left(\frac{311}{1365}\right)\)	\(e\left(\frac{61}{546}\right)\)	\(e\left(\frac{155}{546}\right)\)	\(e\left(\frac{583}{910}\right)\)
\(\chi_{91091}(40,\cdot)\)	91091.ra	2730	yes	\(1\)	\(1\)	\(e\left(\frac{41}{2730}\right)\)	\(e\left(\frac{1873}{2730}\right)\)	\(e\left(\frac{41}{1365}\right)\)	\(e\left(\frac{1019}{2730}\right)\)	\(e\left(\frac{319}{455}\right)\)	\(e\left(\frac{41}{910}\right)\)	\(e\left(\frac{508}{1365}\right)\)	\(e\left(\frac{106}{273}\right)\)	\(e\left(\frac{391}{546}\right)\)	\(e\left(\frac{27}{455}\right)\)
\(\chi_{91091}(41,\cdot)\)	91091.sb	5460	yes	\(-1\)	\(1\)	\(e\left(\frac{713}{5460}\right)\)	\(e\left(\frac{877}{2730}\right)\)	\(e\left(\frac{713}{2730}\right)\)	\(e\left(\frac{839}{1820}\right)\)	\(e\left(\frac{2467}{5460}\right)\)	\(e\left(\frac{713}{1820}\right)\)	\(e\left(\frac{877}{1365}\right)\)	\(e\left(\frac{323}{546}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{4271}{5460}\right)\)
\(\chi_{91091}(43,\cdot)\)	91091.od	546	yes	\(-1\)	\(1\)	\(e\left(\frac{272}{273}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{271}{273}\right)\)	\(e\left(\frac{33}{182}\right)\)	\(e\left(\frac{31}{273}\right)\)	\(e\left(\frac{90}{91}\right)\)	\(e\left(\frac{64}{273}\right)\)	\(e\left(\frac{97}{546}\right)\)	\(e\left(\frac{10}{91}\right)\)	\(e\left(\frac{163}{546}\right)\)
\(\chi_{91091}(45,\cdot)\)	91091.qe	1092	no	\(1\)	\(1\)	\(e\left(\frac{305}{364}\right)\)	\(e\left(\frac{11}{546}\right)\)	\(e\left(\frac{123}{182}\right)\)	\(e\left(\frac{253}{1092}\right)\)	\(e\left(\frac{937}{1092}\right)\)	\(e\left(\frac{187}{364}\right)\)	\(e\left(\frac{11}{273}\right)\)	\(e\left(\frac{19}{273}\right)\)	\(e\left(\frac{190}{273}\right)\)	\(e\left(\frac{275}{1092}\right)\)

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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.