LMFDB - Group of Dirichlet characters of modulus 713293

Show commands: PariGP / SageMath

sage: H = DirichletGroup(713293)

pari: g = idealstar(,713293,2)

Character group

sage: G.order() pari: g.no
Order	=	611352
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{101892}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{713293}(363926,\cdot)$, $\chi_{713293}(174686,\cdot)$

First 32 of 611352 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{713293}(1,\cdot)$	713293.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{713293}(2,\cdot)$	713293.em	101892	yes	$-1$	$1$	$e\left(\frac{3237}{33964}\right)$	$e\left(\frac{38909}{50946}\right)$	$e\left(\frac{3237}{16982}\right)$	$e\left(\frac{59275}{101892}\right)$	$e\left(\frac{87529}{101892}\right)$	$e\left(\frac{9711}{33964}\right)$	$e\left(\frac{13436}{25473}\right)$	$e\left(\frac{34493}{50946}\right)$	$e\left(\frac{18187}{50946}\right)$	$e\left(\frac{24310}{25473}\right)$
$\chi_{713293}(3,\cdot)$	713293.ee	50946	yes	$-1$	$1$	$e\left(\frac{38909}{50946}\right)$	$e\left(\frac{36955}{50946}\right)$	$e\left(\frac{13436}{25473}\right)$	$e\left(\frac{3256}{25473}\right)$	$e\left(\frac{4153}{8491}\right)$	$e\left(\frac{4945}{16982}\right)$	$e\left(\frac{11482}{25473}\right)$	$e\left(\frac{45421}{50946}\right)$	$e\left(\frac{4919}{25473}\right)$	$e\left(\frac{12881}{50946}\right)$
$\chi_{713293}(4,\cdot)$	713293.dw	50946	yes	$1$	$1$	$e\left(\frac{3237}{16982}\right)$	$e\left(\frac{13436}{25473}\right)$	$e\left(\frac{3237}{8491}\right)$	$e\left(\frac{8329}{50946}\right)$	$e\left(\frac{36583}{50946}\right)$	$e\left(\frac{9711}{16982}\right)$	$e\left(\frac{1399}{25473}\right)$	$e\left(\frac{9020}{25473}\right)$	$e\left(\frac{18187}{25473}\right)$	$e\left(\frac{23147}{25473}\right)$
$\chi_{713293}(5,\cdot)$	713293.ek	101892	yes	$1$	$1$	$e\left(\frac{59275}{101892}\right)$	$e\left(\frac{3256}{25473}\right)$	$e\left(\frac{8329}{50946}\right)$	$e\left(\frac{20831}{33964}\right)$	$e\left(\frac{72299}{101892}\right)$	$e\left(\frac{25311}{33964}\right)$	$e\left(\frac{6512}{25473}\right)$	$e\left(\frac{4969}{25473}\right)$	$e\left(\frac{2661}{16982}\right)$	$e\left(\frac{4947}{16982}\right)$
$\chi_{713293}(6,\cdot)$	713293.ep	101892	yes	$1$	$1$	$e\left(\frac{87529}{101892}\right)$	$e\left(\frac{4153}{8491}\right)$	$e\left(\frac{36583}{50946}\right)$	$e\left(\frac{72299}{101892}\right)$	$e\left(\frac{35473}{101892}\right)$	$e\left(\frac{19601}{33964}\right)$	$e\left(\frac{8306}{8491}\right)$	$e\left(\frac{4828}{8491}\right)$	$e\left(\frac{28025}{50946}\right)$	$e\left(\frac{10555}{50946}\right)$
$\chi_{713293}(8,\cdot)$	713293.du	33964	yes	$-1$	$1$	$e\left(\frac{9711}{33964}\right)$	$e\left(\frac{4945}{16982}\right)$	$e\left(\frac{9711}{16982}\right)$	$e\left(\frac{25311}{33964}\right)$	$e\left(\frac{19601}{33964}\right)$	$e\left(\frac{29133}{33964}\right)$	$e\left(\frac{4945}{8491}\right)$	$e\left(\frac{529}{16982}\right)$	$e\left(\frac{1205}{16982}\right)$	$e\left(\frac{7328}{8491}\right)$
$\chi_{713293}(9,\cdot)$	713293.dq	25473	yes	$1$	$1$	$e\left(\frac{13436}{25473}\right)$	$e\left(\frac{11482}{25473}\right)$	$e\left(\frac{1399}{25473}\right)$	$e\left(\frac{6512}{25473}\right)$	$e\left(\frac{8306}{8491}\right)$	$e\left(\frac{4945}{8491}\right)$	$e\left(\frac{22964}{25473}\right)$	$e\left(\frac{19948}{25473}\right)$	$e\left(\frac{9838}{25473}\right)$	$e\left(\frac{12881}{25473}\right)$
$\chi_{713293}(10,\cdot)$	713293.ee	50946	yes	$-1$	$1$	$e\left(\frac{34493}{50946}\right)$	$e\left(\frac{45421}{50946}\right)$	$e\left(\frac{9020}{25473}\right)$	$e\left(\frac{4969}{25473}\right)$	$e\left(\frac{4828}{8491}\right)$	$e\left(\frac{529}{16982}\right)$	$e\left(\frac{19948}{25473}\right)$	$e\left(\frac{44431}{50946}\right)$	$e\left(\frac{13085}{25473}\right)$	$e\left(\frac{12515}{50946}\right)$
$\chi_{713293}(11,\cdot)$	713293.ec	50946	yes	$1$	$1$	$e\left(\frac{18187}{50946}\right)$	$e\left(\frac{4919}{25473}\right)$	$e\left(\frac{18187}{25473}\right)$	$e\left(\frac{2661}{16982}\right)$	$e\left(\frac{28025}{50946}\right)$	$e\left(\frac{1205}{16982}\right)$	$e\left(\frac{9838}{25473}\right)$	$e\left(\frac{13085}{25473}\right)$	$e\left(\frac{5837}{8491}\right)$	$e\left(\frac{7702}{8491}\right)$
$\chi_{713293}(12,\cdot)$	713293.dz	50946	yes	$-1$	$1$	$e\left(\frac{24310}{25473}\right)$	$e\left(\frac{12881}{50946}\right)$	$e\left(\frac{23147}{25473}\right)$	$e\left(\frac{4947}{16982}\right)$	$e\left(\frac{10555}{50946}\right)$	$e\left(\frac{7328}{8491}\right)$	$e\left(\frac{12881}{25473}\right)$	$e\left(\frac{12515}{50946}\right)$	$e\left(\frac{7702}{8491}\right)$	$e\left(\frac{2743}{16982}\right)$
$\chi_{713293}(13,\cdot)$	713293.dp	16982	yes	$-1$	$1$	$e\left(\frac{6012}{8491}\right)$	$e\left(\frac{6021}{16982}\right)$	$e\left(\frac{3533}{8491}\right)$	$e\left(\frac{547}{16982}\right)$	$e\left(\frac{1063}{16982}\right)$	$e\left(\frac{1054}{8491}\right)$	$e\left(\frac{6021}{8491}\right)$	$e\left(\frac{12571}{16982}\right)$	$e\left(\frac{1854}{8491}\right)$	$e\left(\frac{13087}{16982}\right)$
$\chi_{713293}(15,\cdot)$	713293.ei	101892	yes	$-1$	$1$	$e\left(\frac{35201}{101892}\right)$	$e\left(\frac{14489}{16982}\right)$	$e\left(\frac{35201}{50946}\right)$	$e\left(\frac{75517}{101892}\right)$	$e\left(\frac{20243}{101892}\right)$	$e\left(\frac{1237}{33964}\right)$	$e\left(\frac{5998}{8491}\right)$	$e\left(\frac{1471}{16982}\right)$	$e\left(\frac{17821}{50946}\right)$	$e\left(\frac{13861}{25473}\right)$
$\chi_{713293}(16,\cdot)$	713293.dt	25473	yes	$1$	$1$	$e\left(\frac{3237}{8491}\right)$	$e\left(\frac{1399}{25473}\right)$	$e\left(\frac{6474}{8491}\right)$	$e\left(\frac{8329}{25473}\right)$	$e\left(\frac{11110}{25473}\right)$	$e\left(\frac{1220}{8491}\right)$	$e\left(\frac{2798}{25473}\right)$	$e\left(\frac{18040}{25473}\right)$	$e\left(\frac{10901}{25473}\right)$	$e\left(\frac{20821}{25473}\right)$
$\chi_{713293}(17,\cdot)$	713293.ek	101892	yes	$1$	$1$	$e\left(\frac{95063}{101892}\right)$	$e\left(\frac{15026}{25473}\right)$	$e\left(\frac{44117}{50946}\right)$	$e\left(\frac{30327}{33964}\right)$	$e\left(\frac{53275}{101892}\right)$	$e\left(\frac{27135}{33964}\right)$	$e\left(\frac{4579}{25473}\right)$	$e\left(\frac{21038}{25473}\right)$	$e\left(\frac{8551}{16982}\right)$	$e\left(\frac{7741}{16982}\right)$
$\chi_{713293}(18,\cdot)$	713293.dh	14556	no	$-1$	$1$	$e\left(\frac{9065}{14556}\right)$	$e\left(\frac{1561}{7278}\right)$	$e\left(\frac{1787}{7278}\right)$	$e\left(\frac{4063}{4852}\right)$	$e\left(\frac{12187}{14556}\right)$	$e\left(\frac{4213}{4852}\right)$	$e\left(\frac{1561}{3639}\right)$	$e\left(\frac{3349}{7278}\right)$	$e\left(\frac{1803}{2426}\right)$	$e\left(\frac{558}{1213}\right)$
$\chi_{713293}(19,\cdot)$	713293.dk	14556	no	$1$	$1$	$e\left(\frac{5623}{14556}\right)$	$e\left(\frac{1396}{3639}\right)$	$e\left(\frac{5623}{7278}\right)$	$e\left(\frac{3583}{4852}\right)$	$e\left(\frac{11207}{14556}\right)$	$e\left(\frac{771}{4852}\right)$	$e\left(\frac{2792}{3639}\right)$	$e\left(\frac{454}{3639}\right)$	$e\left(\frac{1959}{2426}\right)$	$e\left(\frac{379}{2426}\right)$
$\chi_{713293}(20,\cdot)$	713293.ep	101892	yes	$1$	$1$	$e\left(\frac{78697}{101892}\right)$	$e\left(\frac{5564}{8491}\right)$	$e\left(\frac{27751}{50946}\right)$	$e\left(\frac{79151}{101892}\right)$	$e\left(\frac{43573}{101892}\right)$	$e\left(\frac{10769}{33964}\right)$	$e\left(\frac{2637}{8491}\right)$	$e\left(\frac{4663}{8491}\right)$	$e\left(\frac{44357}{50946}\right)$	$e\left(\frac{10189}{50946}\right)$
$\chi_{713293}(22,\cdot)$	713293.ei	101892	yes	$-1$	$1$	$e\left(\frac{46085}{101892}\right)$	$e\left(\frac{16249}{16982}\right)$	$e\left(\frac{46085}{50946}\right)$	$e\left(\frac{75241}{101892}\right)$	$e\left(\frac{41687}{101892}\right)$	$e\left(\frac{12121}{33964}\right)$	$e\left(\frac{7758}{8491}\right)$	$e\left(\frac{3239}{16982}\right)$	$e\left(\frac{2263}{50946}\right)$	$e\left(\frac{21943}{25473}\right)$
$\chi_{713293}(23,\cdot)$	713293.em	101892	yes	$-1$	$1$	$e\left(\frac{727}{33964}\right)$	$e\left(\frac{42839}{50946}\right)$	$e\left(\frac{727}{16982}\right)$	$e\left(\frac{72385}{101892}\right)$	$e\left(\frac{87859}{101892}\right)$	$e\left(\frac{2181}{33964}\right)$	$e\left(\frac{17366}{25473}\right)$	$e\left(\frac{37283}{50946}\right)$	$e\left(\frac{18475}{50946}\right)$	$e\left(\frac{22510}{25473}\right)$
$\chi_{713293}(24,\cdot)$	713293.el	101892	yes	$1$	$1$	$e\left(\frac{5059}{101892}\right)$	$e\left(\frac{422}{25473}\right)$	$e\left(\frac{5059}{50946}\right)$	$e\left(\frac{88957}{101892}\right)$	$e\left(\frac{2249}{33964}\right)$	$e\left(\frac{5059}{33964}\right)$	$e\left(\frac{844}{25473}\right)$	$e\left(\frac{23504}{25473}\right)$	$e\left(\frac{13453}{50946}\right)$	$e\left(\frac{5903}{50946}\right)$
$\chi_{713293}(25,\cdot)$	713293.ec	50946	yes	$1$	$1$	$e\left(\frac{8329}{50946}\right)$	$e\left(\frac{6512}{25473}\right)$	$e\left(\frac{8329}{25473}\right)$	$e\left(\frac{3849}{16982}\right)$	$e\left(\frac{21353}{50946}\right)$	$e\left(\frac{8329}{16982}\right)$	$e\left(\frac{13024}{25473}\right)$	$e\left(\frac{9938}{25473}\right)$	$e\left(\frac{2661}{8491}\right)$	$e\left(\frac{4947}{8491}\right)$
$\chi_{713293}(26,\cdot)$	713293.ej	101892	yes	$1$	$1$	$e\left(\frac{27285}{33964}\right)$	$e\left(\frac{3013}{25473}\right)$	$e\left(\frac{10303}{16982}\right)$	$e\left(\frac{62557}{101892}\right)$	$e\left(\frac{93907}{101892}\right)$	$e\left(\frac{13927}{33964}\right)$	$e\left(\frac{6026}{25473}\right)$	$e\left(\frac{10630}{25473}\right)$	$e\left(\frac{29311}{50946}\right)$	$e\left(\frac{36935}{50946}\right)$
$\chi_{713293}(27,\cdot)$	713293.dn	16982	yes	$-1$	$1$	$e\left(\frac{4945}{16982}\right)$	$e\left(\frac{2991}{16982}\right)$	$e\left(\frac{4945}{8491}\right)$	$e\left(\frac{3256}{8491}\right)$	$e\left(\frac{3968}{8491}\right)$	$e\left(\frac{14835}{16982}\right)$	$e\left(\frac{2991}{8491}\right)$	$e\left(\frac{11457}{16982}\right)$	$e\left(\frac{4919}{8491}\right)$	$e\left(\frac{12881}{16982}\right)$
$\chi_{713293}(29,\cdot)$	713293.do	16982	yes	$1$	$1$	$e\left(\frac{10511}{16982}\right)$	$e\left(\frac{671}{8491}\right)$	$e\left(\frac{2020}{8491}\right)$	$e\left(\frac{15461}{16982}\right)$	$e\left(\frac{11853}{16982}\right)$	$e\left(\frac{14551}{16982}\right)$	$e\left(\frac{1342}{8491}\right)$	$e\left(\frac{4495}{8491}\right)$	$e\left(\frac{464}{8491}\right)$	$e\left(\frac{2691}{8491}\right)$
$\chi_{713293}(30,\cdot)$	713293.cp	3639	no	$1$	$1$	$e\left(\frac{1604}{3639}\right)$	$e\left(\frac{2245}{3639}\right)$	$e\left(\frac{3208}{3639}\right)$	$e\left(\frac{1175}{3639}\right)$	$e\left(\frac{70}{1213}\right)$	$e\left(\frac{391}{1213}\right)$	$e\left(\frac{851}{3639}\right)$	$e\left(\frac{2779}{3639}\right)$	$e\left(\frac{2572}{3639}\right)$	$e\left(\frac{1814}{3639}\right)$
$\chi_{713293}(31,\cdot)$	713293.cs	7278	no	$-1$	$1$	$e\left(\frac{892}{1213}\right)$	$e\left(\frac{6181}{7278}\right)$	$e\left(\frac{571}{1213}\right)$	$e\left(\frac{6277}{7278}\right)$	$e\left(\frac{4255}{7278}\right)$	$e\left(\frac{250}{1213}\right)$	$e\left(\frac{2542}{3639}\right)$	$e\left(\frac{4351}{7278}\right)$	$e\left(\frac{295}{3639}\right)$	$e\left(\frac{2329}{7278}\right)$
$\chi_{713293}(32,\cdot)$	713293.em	101892	yes	$-1$	$1$	$e\left(\frac{16185}{33964}\right)$	$e\left(\frac{41707}{50946}\right)$	$e\left(\frac{16185}{16982}\right)$	$e\left(\frac{92591}{101892}\right)$	$e\left(\frac{30077}{101892}\right)$	$e\left(\frac{14591}{33964}\right)$	$e\left(\frac{16234}{25473}\right)$	$e\left(\frac{19627}{50946}\right)$	$e\left(\frac{39989}{50946}\right)$	$e\left(\frac{19658}{25473}\right)$
$\chi_{713293}(33,\cdot)$	713293.eh	50946	yes	$-1$	$1$	$e\left(\frac{1025}{8491}\right)$	$e\left(\frac{46793}{50946}\right)$	$e\left(\frac{2050}{8491}\right)$	$e\left(\frac{14495}{50946}\right)$	$e\left(\frac{1997}{50946}\right)$	$e\left(\frac{3075}{8491}\right)$	$e\left(\frac{21320}{25473}\right)$	$e\left(\frac{20645}{50946}\right)$	$e\left(\frac{22430}{25473}\right)$	$e\left(\frac{8147}{50946}\right)$
$\chi_{713293}(34,\cdot)$	713293.eb	50946	yes	$-1$	$1$	$e\left(\frac{1441}{50946}\right)$	$e\left(\frac{6005}{16982}\right)$	$e\left(\frac{1441}{25473}\right)$	$e\left(\frac{12091}{25473}\right)$	$e\left(\frac{9728}{25473}\right)$	$e\left(\frac{1441}{16982}\right)$	$e\left(\frac{6005}{8491}\right)$	$e\left(\frac{8541}{16982}\right)$	$e\left(\frac{21920}{25473}\right)$	$e\left(\frac{20897}{50946}\right)$
$\chi_{713293}(36,\cdot)$	713293.eg	50946	yes	$1$	$1$	$e\left(\frac{36583}{50946}\right)$	$e\left(\frac{8306}{8491}\right)$	$e\left(\frac{11110}{25473}\right)$	$e\left(\frac{21353}{50946}\right)$	$e\left(\frac{35473}{50946}\right)$	$e\left(\frac{2619}{16982}\right)$	$e\left(\frac{8121}{8491}\right)$	$e\left(\frac{1165}{8491}\right)$	$e\left(\frac{2552}{25473}\right)$	$e\left(\frac{10555}{25473}\right)$
$\chi_{713293}(37,\cdot)$	713293.dt	25473	yes	$1$	$1$	$e\left(\frac{2326}{8491}\right)$	$e\left(\frac{20794}{25473}\right)$	$e\left(\frac{4652}{8491}\right)$	$e\left(\frac{14914}{25473}\right)$	$e\left(\frac{2299}{25473}\right)$	$e\left(\frac{6978}{8491}\right)$	$e\left(\frac{16115}{25473}\right)$	$e\left(\frac{21892}{25473}\right)$	$e\left(\frac{5711}{25473}\right)$	$e\left(\frac{9277}{25473}\right)$

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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	$713293$
Structure	\(C_{6}\times C_{101892}\)
Order	$611352$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{713293}(1,\cdot)\)	713293.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{713293}(2,\cdot)\)	713293.em	101892	yes	\(-1\)	\(1\)	\(e\left(\frac{3237}{33964}\right)\)	\(e\left(\frac{38909}{50946}\right)\)	\(e\left(\frac{3237}{16982}\right)\)	\(e\left(\frac{59275}{101892}\right)\)	\(e\left(\frac{87529}{101892}\right)\)	\(e\left(\frac{9711}{33964}\right)\)	\(e\left(\frac{13436}{25473}\right)\)	\(e\left(\frac{34493}{50946}\right)\)	\(e\left(\frac{18187}{50946}\right)\)	\(e\left(\frac{24310}{25473}\right)\)
\(\chi_{713293}(3,\cdot)\)	713293.ee	50946	yes	\(-1\)	\(1\)	\(e\left(\frac{38909}{50946}\right)\)	\(e\left(\frac{36955}{50946}\right)\)	\(e\left(\frac{13436}{25473}\right)\)	\(e\left(\frac{3256}{25473}\right)\)	\(e\left(\frac{4153}{8491}\right)\)	\(e\left(\frac{4945}{16982}\right)\)	\(e\left(\frac{11482}{25473}\right)\)	\(e\left(\frac{45421}{50946}\right)\)	\(e\left(\frac{4919}{25473}\right)\)	\(e\left(\frac{12881}{50946}\right)\)
\(\chi_{713293}(4,\cdot)\)	713293.dw	50946	yes	\(1\)	\(1\)	\(e\left(\frac{3237}{16982}\right)\)	\(e\left(\frac{13436}{25473}\right)\)	\(e\left(\frac{3237}{8491}\right)\)	\(e\left(\frac{8329}{50946}\right)\)	\(e\left(\frac{36583}{50946}\right)\)	\(e\left(\frac{9711}{16982}\right)\)	\(e\left(\frac{1399}{25473}\right)\)	\(e\left(\frac{9020}{25473}\right)\)	\(e\left(\frac{18187}{25473}\right)\)	\(e\left(\frac{23147}{25473}\right)\)
\(\chi_{713293}(5,\cdot)\)	713293.ek	101892	yes	\(1\)	\(1\)	\(e\left(\frac{59275}{101892}\right)\)	\(e\left(\frac{3256}{25473}\right)\)	\(e\left(\frac{8329}{50946}\right)\)	\(e\left(\frac{20831}{33964}\right)\)	\(e\left(\frac{72299}{101892}\right)\)	\(e\left(\frac{25311}{33964}\right)\)	\(e\left(\frac{6512}{25473}\right)\)	\(e\left(\frac{4969}{25473}\right)\)	\(e\left(\frac{2661}{16982}\right)\)	\(e\left(\frac{4947}{16982}\right)\)
\(\chi_{713293}(6,\cdot)\)	713293.ep	101892	yes	\(1\)	\(1\)	\(e\left(\frac{87529}{101892}\right)\)	\(e\left(\frac{4153}{8491}\right)\)	\(e\left(\frac{36583}{50946}\right)\)	\(e\left(\frac{72299}{101892}\right)\)	\(e\left(\frac{35473}{101892}\right)\)	\(e\left(\frac{19601}{33964}\right)\)	\(e\left(\frac{8306}{8491}\right)\)	\(e\left(\frac{4828}{8491}\right)\)	\(e\left(\frac{28025}{50946}\right)\)	\(e\left(\frac{10555}{50946}\right)\)
\(\chi_{713293}(8,\cdot)\)	713293.du	33964	yes	\(-1\)	\(1\)	\(e\left(\frac{9711}{33964}\right)\)	\(e\left(\frac{4945}{16982}\right)\)	\(e\left(\frac{9711}{16982}\right)\)	\(e\left(\frac{25311}{33964}\right)\)	\(e\left(\frac{19601}{33964}\right)\)	\(e\left(\frac{29133}{33964}\right)\)	\(e\left(\frac{4945}{8491}\right)\)	\(e\left(\frac{529}{16982}\right)\)	\(e\left(\frac{1205}{16982}\right)\)	\(e\left(\frac{7328}{8491}\right)\)
\(\chi_{713293}(9,\cdot)\)	713293.dq	25473	yes	\(1\)	\(1\)	\(e\left(\frac{13436}{25473}\right)\)	\(e\left(\frac{11482}{25473}\right)\)	\(e\left(\frac{1399}{25473}\right)\)	\(e\left(\frac{6512}{25473}\right)\)	\(e\left(\frac{8306}{8491}\right)\)	\(e\left(\frac{4945}{8491}\right)\)	\(e\left(\frac{22964}{25473}\right)\)	\(e\left(\frac{19948}{25473}\right)\)	\(e\left(\frac{9838}{25473}\right)\)	\(e\left(\frac{12881}{25473}\right)\)
\(\chi_{713293}(10,\cdot)\)	713293.ee	50946	yes	\(-1\)	\(1\)	\(e\left(\frac{34493}{50946}\right)\)	\(e\left(\frac{45421}{50946}\right)\)	\(e\left(\frac{9020}{25473}\right)\)	\(e\left(\frac{4969}{25473}\right)\)	\(e\left(\frac{4828}{8491}\right)\)	\(e\left(\frac{529}{16982}\right)\)	\(e\left(\frac{19948}{25473}\right)\)	\(e\left(\frac{44431}{50946}\right)\)	\(e\left(\frac{13085}{25473}\right)\)	\(e\left(\frac{12515}{50946}\right)\)
\(\chi_{713293}(11,\cdot)\)	713293.ec	50946	yes	\(1\)	\(1\)	\(e\left(\frac{18187}{50946}\right)\)	\(e\left(\frac{4919}{25473}\right)\)	\(e\left(\frac{18187}{25473}\right)\)	\(e\left(\frac{2661}{16982}\right)\)	\(e\left(\frac{28025}{50946}\right)\)	\(e\left(\frac{1205}{16982}\right)\)	\(e\left(\frac{9838}{25473}\right)\)	\(e\left(\frac{13085}{25473}\right)\)	\(e\left(\frac{5837}{8491}\right)\)	\(e\left(\frac{7702}{8491}\right)\)
\(\chi_{713293}(12,\cdot)\)	713293.dz	50946	yes	\(-1\)	\(1\)	\(e\left(\frac{24310}{25473}\right)\)	\(e\left(\frac{12881}{50946}\right)\)	\(e\left(\frac{23147}{25473}\right)\)	\(e\left(\frac{4947}{16982}\right)\)	\(e\left(\frac{10555}{50946}\right)\)	\(e\left(\frac{7328}{8491}\right)\)	\(e\left(\frac{12881}{25473}\right)\)	\(e\left(\frac{12515}{50946}\right)\)	\(e\left(\frac{7702}{8491}\right)\)	\(e\left(\frac{2743}{16982}\right)\)
\(\chi_{713293}(13,\cdot)\)	713293.dp	16982	yes	\(-1\)	\(1\)	\(e\left(\frac{6012}{8491}\right)\)	\(e\left(\frac{6021}{16982}\right)\)	\(e\left(\frac{3533}{8491}\right)\)	\(e\left(\frac{547}{16982}\right)\)	\(e\left(\frac{1063}{16982}\right)\)	\(e\left(\frac{1054}{8491}\right)\)	\(e\left(\frac{6021}{8491}\right)\)	\(e\left(\frac{12571}{16982}\right)\)	\(e\left(\frac{1854}{8491}\right)\)	\(e\left(\frac{13087}{16982}\right)\)
\(\chi_{713293}(15,\cdot)\)	713293.ei	101892	yes	\(-1\)	\(1\)	\(e\left(\frac{35201}{101892}\right)\)	\(e\left(\frac{14489}{16982}\right)\)	\(e\left(\frac{35201}{50946}\right)\)	\(e\left(\frac{75517}{101892}\right)\)	\(e\left(\frac{20243}{101892}\right)\)	\(e\left(\frac{1237}{33964}\right)\)	\(e\left(\frac{5998}{8491}\right)\)	\(e\left(\frac{1471}{16982}\right)\)	\(e\left(\frac{17821}{50946}\right)\)	\(e\left(\frac{13861}{25473}\right)\)
\(\chi_{713293}(16,\cdot)\)	713293.dt	25473	yes	\(1\)	\(1\)	\(e\left(\frac{3237}{8491}\right)\)	\(e\left(\frac{1399}{25473}\right)\)	\(e\left(\frac{6474}{8491}\right)\)	\(e\left(\frac{8329}{25473}\right)\)	\(e\left(\frac{11110}{25473}\right)\)	\(e\left(\frac{1220}{8491}\right)\)	\(e\left(\frac{2798}{25473}\right)\)	\(e\left(\frac{18040}{25473}\right)\)	\(e\left(\frac{10901}{25473}\right)\)	\(e\left(\frac{20821}{25473}\right)\)
\(\chi_{713293}(17,\cdot)\)	713293.ek	101892	yes	\(1\)	\(1\)	\(e\left(\frac{95063}{101892}\right)\)	\(e\left(\frac{15026}{25473}\right)\)	\(e\left(\frac{44117}{50946}\right)\)	\(e\left(\frac{30327}{33964}\right)\)	\(e\left(\frac{53275}{101892}\right)\)	\(e\left(\frac{27135}{33964}\right)\)	\(e\left(\frac{4579}{25473}\right)\)	\(e\left(\frac{21038}{25473}\right)\)	\(e\left(\frac{8551}{16982}\right)\)	\(e\left(\frac{7741}{16982}\right)\)
\(\chi_{713293}(18,\cdot)\)	713293.dh	14556	no	\(-1\)	\(1\)	\(e\left(\frac{9065}{14556}\right)\)	\(e\left(\frac{1561}{7278}\right)\)	\(e\left(\frac{1787}{7278}\right)\)	\(e\left(\frac{4063}{4852}\right)\)	\(e\left(\frac{12187}{14556}\right)\)	\(e\left(\frac{4213}{4852}\right)\)	\(e\left(\frac{1561}{3639}\right)\)	\(e\left(\frac{3349}{7278}\right)\)	\(e\left(\frac{1803}{2426}\right)\)	\(e\left(\frac{558}{1213}\right)\)
\(\chi_{713293}(19,\cdot)\)	713293.dk	14556	no	\(1\)	\(1\)	\(e\left(\frac{5623}{14556}\right)\)	\(e\left(\frac{1396}{3639}\right)\)	\(e\left(\frac{5623}{7278}\right)\)	\(e\left(\frac{3583}{4852}\right)\)	\(e\left(\frac{11207}{14556}\right)\)	\(e\left(\frac{771}{4852}\right)\)	\(e\left(\frac{2792}{3639}\right)\)	\(e\left(\frac{454}{3639}\right)\)	\(e\left(\frac{1959}{2426}\right)\)	\(e\left(\frac{379}{2426}\right)\)
\(\chi_{713293}(20,\cdot)\)	713293.ep	101892	yes	\(1\)	\(1\)	\(e\left(\frac{78697}{101892}\right)\)	\(e\left(\frac{5564}{8491}\right)\)	\(e\left(\frac{27751}{50946}\right)\)	\(e\left(\frac{79151}{101892}\right)\)	\(e\left(\frac{43573}{101892}\right)\)	\(e\left(\frac{10769}{33964}\right)\)	\(e\left(\frac{2637}{8491}\right)\)	\(e\left(\frac{4663}{8491}\right)\)	\(e\left(\frac{44357}{50946}\right)\)	\(e\left(\frac{10189}{50946}\right)\)
\(\chi_{713293}(22,\cdot)\)	713293.ei	101892	yes	\(-1\)	\(1\)	\(e\left(\frac{46085}{101892}\right)\)	\(e\left(\frac{16249}{16982}\right)\)	\(e\left(\frac{46085}{50946}\right)\)	\(e\left(\frac{75241}{101892}\right)\)	\(e\left(\frac{41687}{101892}\right)\)	\(e\left(\frac{12121}{33964}\right)\)	\(e\left(\frac{7758}{8491}\right)\)	\(e\left(\frac{3239}{16982}\right)\)	\(e\left(\frac{2263}{50946}\right)\)	\(e\left(\frac{21943}{25473}\right)\)
\(\chi_{713293}(23,\cdot)\)	713293.em	101892	yes	\(-1\)	\(1\)	\(e\left(\frac{727}{33964}\right)\)	\(e\left(\frac{42839}{50946}\right)\)	\(e\left(\frac{727}{16982}\right)\)	\(e\left(\frac{72385}{101892}\right)\)	\(e\left(\frac{87859}{101892}\right)\)	\(e\left(\frac{2181}{33964}\right)\)	\(e\left(\frac{17366}{25473}\right)\)	\(e\left(\frac{37283}{50946}\right)\)	\(e\left(\frac{18475}{50946}\right)\)	\(e\left(\frac{22510}{25473}\right)\)
\(\chi_{713293}(24,\cdot)\)	713293.el	101892	yes	\(1\)	\(1\)	\(e\left(\frac{5059}{101892}\right)\)	\(e\left(\frac{422}{25473}\right)\)	\(e\left(\frac{5059}{50946}\right)\)	\(e\left(\frac{88957}{101892}\right)\)	\(e\left(\frac{2249}{33964}\right)\)	\(e\left(\frac{5059}{33964}\right)\)	\(e\left(\frac{844}{25473}\right)\)	\(e\left(\frac{23504}{25473}\right)\)	\(e\left(\frac{13453}{50946}\right)\)	\(e\left(\frac{5903}{50946}\right)\)
\(\chi_{713293}(25,\cdot)\)	713293.ec	50946	yes	\(1\)	\(1\)	\(e\left(\frac{8329}{50946}\right)\)	\(e\left(\frac{6512}{25473}\right)\)	\(e\left(\frac{8329}{25473}\right)\)	\(e\left(\frac{3849}{16982}\right)\)	\(e\left(\frac{21353}{50946}\right)\)	\(e\left(\frac{8329}{16982}\right)\)	\(e\left(\frac{13024}{25473}\right)\)	\(e\left(\frac{9938}{25473}\right)\)	\(e\left(\frac{2661}{8491}\right)\)	\(e\left(\frac{4947}{8491}\right)\)
\(\chi_{713293}(26,\cdot)\)	713293.ej	101892	yes	\(1\)	\(1\)	\(e\left(\frac{27285}{33964}\right)\)	\(e\left(\frac{3013}{25473}\right)\)	\(e\left(\frac{10303}{16982}\right)\)	\(e\left(\frac{62557}{101892}\right)\)	\(e\left(\frac{93907}{101892}\right)\)	\(e\left(\frac{13927}{33964}\right)\)	\(e\left(\frac{6026}{25473}\right)\)	\(e\left(\frac{10630}{25473}\right)\)	\(e\left(\frac{29311}{50946}\right)\)	\(e\left(\frac{36935}{50946}\right)\)
\(\chi_{713293}(27,\cdot)\)	713293.dn	16982	yes	\(-1\)	\(1\)	\(e\left(\frac{4945}{16982}\right)\)	\(e\left(\frac{2991}{16982}\right)\)	\(e\left(\frac{4945}{8491}\right)\)	\(e\left(\frac{3256}{8491}\right)\)	\(e\left(\frac{3968}{8491}\right)\)	\(e\left(\frac{14835}{16982}\right)\)	\(e\left(\frac{2991}{8491}\right)\)	\(e\left(\frac{11457}{16982}\right)\)	\(e\left(\frac{4919}{8491}\right)\)	\(e\left(\frac{12881}{16982}\right)\)
\(\chi_{713293}(29,\cdot)\)	713293.do	16982	yes	\(1\)	\(1\)	\(e\left(\frac{10511}{16982}\right)\)	\(e\left(\frac{671}{8491}\right)\)	\(e\left(\frac{2020}{8491}\right)\)	\(e\left(\frac{15461}{16982}\right)\)	\(e\left(\frac{11853}{16982}\right)\)	\(e\left(\frac{14551}{16982}\right)\)	\(e\left(\frac{1342}{8491}\right)\)	\(e\left(\frac{4495}{8491}\right)\)	\(e\left(\frac{464}{8491}\right)\)	\(e\left(\frac{2691}{8491}\right)\)
\(\chi_{713293}(30,\cdot)\)	713293.cp	3639	no	\(1\)	\(1\)	\(e\left(\frac{1604}{3639}\right)\)	\(e\left(\frac{2245}{3639}\right)\)	\(e\left(\frac{3208}{3639}\right)\)	\(e\left(\frac{1175}{3639}\right)\)	\(e\left(\frac{70}{1213}\right)\)	\(e\left(\frac{391}{1213}\right)\)	\(e\left(\frac{851}{3639}\right)\)	\(e\left(\frac{2779}{3639}\right)\)	\(e\left(\frac{2572}{3639}\right)\)	\(e\left(\frac{1814}{3639}\right)\)
\(\chi_{713293}(31,\cdot)\)	713293.cs	7278	no	\(-1\)	\(1\)	\(e\left(\frac{892}{1213}\right)\)	\(e\left(\frac{6181}{7278}\right)\)	\(e\left(\frac{571}{1213}\right)\)	\(e\left(\frac{6277}{7278}\right)\)	\(e\left(\frac{4255}{7278}\right)\)	\(e\left(\frac{250}{1213}\right)\)	\(e\left(\frac{2542}{3639}\right)\)	\(e\left(\frac{4351}{7278}\right)\)	\(e\left(\frac{295}{3639}\right)\)	\(e\left(\frac{2329}{7278}\right)\)
\(\chi_{713293}(32,\cdot)\)	713293.em	101892	yes	\(-1\)	\(1\)	\(e\left(\frac{16185}{33964}\right)\)	\(e\left(\frac{41707}{50946}\right)\)	\(e\left(\frac{16185}{16982}\right)\)	\(e\left(\frac{92591}{101892}\right)\)	\(e\left(\frac{30077}{101892}\right)\)	\(e\left(\frac{14591}{33964}\right)\)	\(e\left(\frac{16234}{25473}\right)\)	\(e\left(\frac{19627}{50946}\right)\)	\(e\left(\frac{39989}{50946}\right)\)	\(e\left(\frac{19658}{25473}\right)\)
\(\chi_{713293}(33,\cdot)\)	713293.eh	50946	yes	\(-1\)	\(1\)	\(e\left(\frac{1025}{8491}\right)\)	\(e\left(\frac{46793}{50946}\right)\)	\(e\left(\frac{2050}{8491}\right)\)	\(e\left(\frac{14495}{50946}\right)\)	\(e\left(\frac{1997}{50946}\right)\)	\(e\left(\frac{3075}{8491}\right)\)	\(e\left(\frac{21320}{25473}\right)\)	\(e\left(\frac{20645}{50946}\right)\)	\(e\left(\frac{22430}{25473}\right)\)	\(e\left(\frac{8147}{50946}\right)\)
\(\chi_{713293}(34,\cdot)\)	713293.eb	50946	yes	\(-1\)	\(1\)	\(e\left(\frac{1441}{50946}\right)\)	\(e\left(\frac{6005}{16982}\right)\)	\(e\left(\frac{1441}{25473}\right)\)	\(e\left(\frac{12091}{25473}\right)\)	\(e\left(\frac{9728}{25473}\right)\)	\(e\left(\frac{1441}{16982}\right)\)	\(e\left(\frac{6005}{8491}\right)\)	\(e\left(\frac{8541}{16982}\right)\)	\(e\left(\frac{21920}{25473}\right)\)	\(e\left(\frac{20897}{50946}\right)\)
\(\chi_{713293}(36,\cdot)\)	713293.eg	50946	yes	\(1\)	\(1\)	\(e\left(\frac{36583}{50946}\right)\)	\(e\left(\frac{8306}{8491}\right)\)	\(e\left(\frac{11110}{25473}\right)\)	\(e\left(\frac{21353}{50946}\right)\)	\(e\left(\frac{35473}{50946}\right)\)	\(e\left(\frac{2619}{16982}\right)\)	\(e\left(\frac{8121}{8491}\right)\)	\(e\left(\frac{1165}{8491}\right)\)	\(e\left(\frac{2552}{25473}\right)\)	\(e\left(\frac{10555}{25473}\right)\)
\(\chi_{713293}(37,\cdot)\)	713293.dt	25473	yes	\(1\)	\(1\)	\(e\left(\frac{2326}{8491}\right)\)	\(e\left(\frac{20794}{25473}\right)\)	\(e\left(\frac{4652}{8491}\right)\)	\(e\left(\frac{14914}{25473}\right)\)	\(e\left(\frac{2299}{25473}\right)\)	\(e\left(\frac{6978}{8491}\right)\)	\(e\left(\frac{16115}{25473}\right)\)	\(e\left(\frac{21892}{25473}\right)\)	\(e\left(\frac{5711}{25473}\right)\)	\(e\left(\frac{9277}{25473}\right)\)

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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.