LMFDB - Group of Dirichlet characters of modulus 5641

Show commands: PariGP / SageMath

sage: H = DirichletGroup(5641)

pari: g = idealstar(,5641,2)

Character group

sage: G.order() pari: g.no
Order	=	5640
sage: H.invariants() pari: g.cyc
Structure	=	$C_{5640}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{5641}(14,\cdot)$

First 32 of 5640 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{5641}(1,\cdot)$	5641.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{5641}(2,\cdot)$	5641.y	564	yes	$1$	$1$	$e\left(\frac{185}{282}\right)$	$e\left(\frac{143}{282}\right)$	$e\left(\frac{44}{141}\right)$	$e\left(\frac{43}{282}\right)$	$e\left(\frac{23}{141}\right)$	$e\left(\frac{7}{188}\right)$	$e\left(\frac{91}{94}\right)$	$e\left(\frac{2}{141}\right)$	$e\left(\frac{38}{47}\right)$	$e\left(\frac{31}{282}\right)$
$\chi_{5641}(3,\cdot)$	5641.be	2820	yes	$1$	$1$	$e\left(\frac{143}{282}\right)$	$e\left(\frac{949}{1410}\right)$	$e\left(\frac{2}{141}\right)$	$e\left(\frac{593}{1410}\right)$	$e\left(\frac{127}{705}\right)$	$e\left(\frac{149}{940}\right)$	$e\left(\frac{49}{94}\right)$	$e\left(\frac{244}{705}\right)$	$e\left(\frac{218}{235}\right)$	$e\left(\frac{1103}{1410}\right)$
$\chi_{5641}(4,\cdot)$	5641.v	282	yes	$1$	$1$	$e\left(\frac{44}{141}\right)$	$e\left(\frac{2}{141}\right)$	$e\left(\frac{88}{141}\right)$	$e\left(\frac{43}{141}\right)$	$e\left(\frac{46}{141}\right)$	$e\left(\frac{7}{94}\right)$	$e\left(\frac{44}{47}\right)$	$e\left(\frac{4}{141}\right)$	$e\left(\frac{29}{47}\right)$	$e\left(\frac{31}{141}\right)$
$\chi_{5641}(5,\cdot)$	5641.be	2820	yes	$1$	$1$	$e\left(\frac{43}{282}\right)$	$e\left(\frac{593}{1410}\right)$	$e\left(\frac{43}{141}\right)$	$e\left(\frac{271}{1410}\right)$	$e\left(\frac{404}{705}\right)$	$e\left(\frac{783}{940}\right)$	$e\left(\frac{43}{94}\right)$	$e\left(\frac{593}{705}\right)$	$e\left(\frac{81}{235}\right)$	$e\left(\frac{661}{1410}\right)$
$\chi_{5641}(6,\cdot)$	5641.z	705	yes	$1$	$1$	$e\left(\frac{23}{141}\right)$	$e\left(\frac{127}{705}\right)$	$e\left(\frac{46}{141}\right)$	$e\left(\frac{404}{705}\right)$	$e\left(\frac{242}{705}\right)$	$e\left(\frac{46}{235}\right)$	$e\left(\frac{23}{47}\right)$	$e\left(\frac{254}{705}\right)$	$e\left(\frac{173}{235}\right)$	$e\left(\frac{629}{705}\right)$
$\chi_{5641}(7,\cdot)$	5641.bd	1880	yes	$-1$	$1$	$e\left(\frac{7}{188}\right)$	$e\left(\frac{149}{940}\right)$	$e\left(\frac{7}{94}\right)$	$e\left(\frac{783}{940}\right)$	$e\left(\frac{46}{235}\right)$	$e\left(\frac{507}{1880}\right)$	$e\left(\frac{21}{188}\right)$	$e\left(\frac{149}{470}\right)$	$e\left(\frac{409}{470}\right)$	$e\left(\frac{453}{940}\right)$
$\chi_{5641}(8,\cdot)$	5641.t	188	yes	$1$	$1$	$e\left(\frac{91}{94}\right)$	$e\left(\frac{49}{94}\right)$	$e\left(\frac{44}{47}\right)$	$e\left(\frac{43}{94}\right)$	$e\left(\frac{23}{47}\right)$	$e\left(\frac{21}{188}\right)$	$e\left(\frac{85}{94}\right)$	$e\left(\frac{2}{47}\right)$	$e\left(\frac{20}{47}\right)$	$e\left(\frac{31}{94}\right)$
$\chi_{5641}(9,\cdot)$	5641.bc	1410	yes	$1$	$1$	$e\left(\frac{2}{141}\right)$	$e\left(\frac{244}{705}\right)$	$e\left(\frac{4}{141}\right)$	$e\left(\frac{593}{705}\right)$	$e\left(\frac{254}{705}\right)$	$e\left(\frac{149}{470}\right)$	$e\left(\frac{2}{47}\right)$	$e\left(\frac{488}{705}\right)$	$e\left(\frac{201}{235}\right)$	$e\left(\frac{398}{705}\right)$
$\chi_{5641}(10,\cdot)$	5641.x	470	yes	$1$	$1$	$e\left(\frac{38}{47}\right)$	$e\left(\frac{218}{235}\right)$	$e\left(\frac{29}{47}\right)$	$e\left(\frac{81}{235}\right)$	$e\left(\frac{173}{235}\right)$	$e\left(\frac{409}{470}\right)$	$e\left(\frac{20}{47}\right)$	$e\left(\frac{201}{235}\right)$	$e\left(\frac{36}{235}\right)$	$e\left(\frac{136}{235}\right)$
$\chi_{5641}(11,\cdot)$	5641.be	2820	yes	$1$	$1$	$e\left(\frac{31}{282}\right)$	$e\left(\frac{1103}{1410}\right)$	$e\left(\frac{31}{141}\right)$	$e\left(\frac{661}{1410}\right)$	$e\left(\frac{629}{705}\right)$	$e\left(\frac{453}{940}\right)$	$e\left(\frac{31}{94}\right)$	$e\left(\frac{398}{705}\right)$	$e\left(\frac{136}{235}\right)$	$e\left(\frac{811}{1410}\right)$
$\chi_{5641}(12,\cdot)$	5641.ba	940	yes	$1$	$1$	$e\left(\frac{77}{94}\right)$	$e\left(\frac{323}{470}\right)$	$e\left(\frac{30}{47}\right)$	$e\left(\frac{341}{470}\right)$	$e\left(\frac{119}{235}\right)$	$e\left(\frac{219}{940}\right)$	$e\left(\frac{43}{94}\right)$	$e\left(\frac{88}{235}\right)$	$e\left(\frac{128}{235}\right)$	$e\left(\frac{1}{470}\right)$
$\chi_{5641}(13,\cdot)$	5641.ba	940	yes	$1$	$1$	$e\left(\frac{15}{94}\right)$	$e\left(\frac{373}{470}\right)$	$e\left(\frac{15}{47}\right)$	$e\left(\frac{241}{470}\right)$	$e\left(\frac{224}{235}\right)$	$e\left(\frac{509}{940}\right)$	$e\left(\frac{45}{94}\right)$	$e\left(\frac{138}{235}\right)$	$e\left(\frac{158}{235}\right)$	$e\left(\frac{71}{470}\right)$
$\chi_{5641}(14,\cdot)$	5641.bf	5640	yes	$-1$	$1$	$e\left(\frac{391}{564}\right)$	$e\left(\frac{1877}{2820}\right)$	$e\left(\frac{109}{282}\right)$	$e\left(\frac{2779}{2820}\right)$	$e\left(\frac{253}{705}\right)$	$e\left(\frac{577}{1880}\right)$	$e\left(\frac{15}{188}\right)$	$e\left(\frac{467}{1410}\right)$	$e\left(\frac{319}{470}\right)$	$e\left(\frac{1669}{2820}\right)$
$\chi_{5641}(15,\cdot)$	5641.u	235	yes	$1$	$1$	$e\left(\frac{31}{47}\right)$	$e\left(\frac{22}{235}\right)$	$e\left(\frac{15}{47}\right)$	$e\left(\frac{144}{235}\right)$	$e\left(\frac{177}{235}\right)$	$e\left(\frac{233}{235}\right)$	$e\left(\frac{46}{47}\right)$	$e\left(\frac{44}{235}\right)$	$e\left(\frac{64}{235}\right)$	$e\left(\frac{59}{235}\right)$
$\chi_{5641}(16,\cdot)$	5641.s	141	yes	$1$	$1$	$e\left(\frac{88}{141}\right)$	$e\left(\frac{4}{141}\right)$	$e\left(\frac{35}{141}\right)$	$e\left(\frac{86}{141}\right)$	$e\left(\frac{92}{141}\right)$	$e\left(\frac{7}{47}\right)$	$e\left(\frac{41}{47}\right)$	$e\left(\frac{8}{141}\right)$	$e\left(\frac{11}{47}\right)$	$e\left(\frac{62}{141}\right)$
$\chi_{5641}(17,\cdot)$	5641.bb	1128	yes	$-1$	$1$	$e\left(\frac{407}{564}\right)$	$e\left(\frac{89}{564}\right)$	$e\left(\frac{125}{282}\right)$	$e\left(\frac{151}{564}\right)$	$e\left(\frac{124}{141}\right)$	$e\left(\frac{53}{376}\right)$	$e\left(\frac{31}{188}\right)$	$e\left(\frac{89}{282}\right)$	$e\left(\frac{93}{94}\right)$	$e\left(\frac{181}{564}\right)$
$\chi_{5641}(18,\cdot)$	5641.ba	940	yes	$1$	$1$	$e\left(\frac{63}{94}\right)$	$e\left(\frac{401}{470}\right)$	$e\left(\frac{16}{47}\right)$	$e\left(\frac{467}{470}\right)$	$e\left(\frac{123}{235}\right)$	$e\left(\frac{333}{940}\right)$	$e\left(\frac{1}{94}\right)$	$e\left(\frac{166}{235}\right)$	$e\left(\frac{156}{235}\right)$	$e\left(\frac{317}{470}\right)$
$\chi_{5641}(19,\cdot)$	5641.y	564	yes	$1$	$1$	$e\left(\frac{7}{282}\right)$	$e\left(\frac{199}{282}\right)$	$e\left(\frac{7}{141}\right)$	$e\left(\frac{119}{282}\right)$	$e\left(\frac{103}{141}\right)$	$e\left(\frac{15}{188}\right)$	$e\left(\frac{7}{94}\right)$	$e\left(\frac{58}{141}\right)$	$e\left(\frac{21}{47}\right)$	$e\left(\frac{53}{282}\right)$
$\chi_{5641}(20,\cdot)$	5641.be	2820	yes	$1$	$1$	$e\left(\frac{131}{282}\right)$	$e\left(\frac{613}{1410}\right)$	$e\left(\frac{131}{141}\right)$	$e\left(\frac{701}{1410}\right)$	$e\left(\frac{634}{705}\right)$	$e\left(\frac{853}{940}\right)$	$e\left(\frac{37}{94}\right)$	$e\left(\frac{613}{705}\right)$	$e\left(\frac{226}{235}\right)$	$e\left(\frac{971}{1410}\right)$
$\chi_{5641}(21,\cdot)$	5641.bb	1128	yes	$-1$	$1$	$e\left(\frac{307}{564}\right)$	$e\left(\frac{469}{564}\right)$	$e\left(\frac{25}{282}\right)$	$e\left(\frac{143}{564}\right)$	$e\left(\frac{53}{141}\right)$	$e\left(\frac{161}{376}\right)$	$e\left(\frac{119}{188}\right)$	$e\left(\frac{187}{282}\right)$	$e\left(\frac{75}{94}\right)$	$e\left(\frac{149}{564}\right)$
$\chi_{5641}(22,\cdot)$	5641.u	235	yes	$1$	$1$	$e\left(\frac{36}{47}\right)$	$e\left(\frac{68}{235}\right)$	$e\left(\frac{25}{47}\right)$	$e\left(\frac{146}{235}\right)$	$e\left(\frac{13}{235}\right)$	$e\left(\frac{122}{235}\right)$	$e\left(\frac{14}{47}\right)$	$e\left(\frac{136}{235}\right)$	$e\left(\frac{91}{235}\right)$	$e\left(\frac{161}{235}\right)$
$\chi_{5641}(23,\cdot)$	5641.u	235	yes	$1$	$1$	$e\left(\frac{44}{47}\right)$	$e\left(\frac{104}{235}\right)$	$e\left(\frac{41}{47}\right)$	$e\left(\frac{168}{235}\right)$	$e\left(\frac{89}{235}\right)$	$e\left(\frac{76}{235}\right)$	$e\left(\frac{38}{47}\right)$	$e\left(\frac{208}{235}\right)$	$e\left(\frac{153}{235}\right)$	$e\left(\frac{108}{235}\right)$
$\chi_{5641}(24,\cdot)$	5641.bc	1410	yes	$1$	$1$	$e\left(\frac{67}{141}\right)$	$e\left(\frac{137}{705}\right)$	$e\left(\frac{134}{141}\right)$	$e\left(\frac{619}{705}\right)$	$e\left(\frac{472}{705}\right)$	$e\left(\frac{127}{470}\right)$	$e\left(\frac{20}{47}\right)$	$e\left(\frac{274}{705}\right)$	$e\left(\frac{83}{235}\right)$	$e\left(\frac{79}{705}\right)$
$\chi_{5641}(25,\cdot)$	5641.bc	1410	yes	$1$	$1$	$e\left(\frac{43}{141}\right)$	$e\left(\frac{593}{705}\right)$	$e\left(\frac{86}{141}\right)$	$e\left(\frac{271}{705}\right)$	$e\left(\frac{103}{705}\right)$	$e\left(\frac{313}{470}\right)$	$e\left(\frac{43}{47}\right)$	$e\left(\frac{481}{705}\right)$	$e\left(\frac{162}{235}\right)$	$e\left(\frac{661}{705}\right)$
$\chi_{5641}(26,\cdot)$	5641.z	705	yes	$1$	$1$	$e\left(\frac{115}{141}\right)$	$e\left(\frac{212}{705}\right)$	$e\left(\frac{89}{141}\right)$	$e\left(\frac{469}{705}\right)$	$e\left(\frac{82}{705}\right)$	$e\left(\frac{136}{235}\right)$	$e\left(\frac{21}{47}\right)$	$e\left(\frac{424}{705}\right)$	$e\left(\frac{113}{235}\right)$	$e\left(\frac{184}{705}\right)$
$\chi_{5641}(27,\cdot)$	5641.ba	940	yes	$1$	$1$	$e\left(\frac{49}{94}\right)$	$e\left(\frac{9}{470}\right)$	$e\left(\frac{2}{47}\right)$	$e\left(\frac{123}{470}\right)$	$e\left(\frac{127}{235}\right)$	$e\left(\frac{447}{940}\right)$	$e\left(\frac{53}{94}\right)$	$e\left(\frac{9}{235}\right)$	$e\left(\frac{184}{235}\right)$	$e\left(\frac{163}{470}\right)$
$\chi_{5641}(28,\cdot)$	5641.bf	5640	yes	$-1$	$1$	$e\left(\frac{197}{564}\right)$	$e\left(\frac{487}{2820}\right)$	$e\left(\frac{197}{282}\right)$	$e\left(\frac{389}{2820}\right)$	$e\left(\frac{368}{705}\right)$	$e\left(\frac{647}{1880}\right)$	$e\left(\frac{9}{188}\right)$	$e\left(\frac{487}{1410}\right)$	$e\left(\frac{229}{470}\right)$	$e\left(\frac{1979}{2820}\right)$
$\chi_{5641}(29,\cdot)$	5641.bb	1128	yes	$-1$	$1$	$e\left(\frac{493}{564}\right)$	$e\left(\frac{439}{564}\right)$	$e\left(\frac{211}{282}\right)$	$e\left(\frac{485}{564}\right)$	$e\left(\frac{92}{141}\right)$	$e\left(\frac{291}{376}\right)$	$e\left(\frac{117}{188}\right)$	$e\left(\frac{157}{282}\right)$	$e\left(\frac{69}{94}\right)$	$e\left(\frac{107}{564}\right)$
$\chi_{5641}(30,\cdot)$	5641.be	2820	yes	$1$	$1$	$e\left(\frac{89}{282}\right)$	$e\left(\frac{847}{1410}\right)$	$e\left(\frac{89}{141}\right)$	$e\left(\frac{1079}{1410}\right)$	$e\left(\frac{646}{705}\right)$	$e\left(\frac{27}{940}\right)$	$e\left(\frac{89}{94}\right)$	$e\left(\frac{142}{705}\right)$	$e\left(\frac{19}{235}\right)$	$e\left(\frac{509}{1410}\right)$
$\chi_{5641}(31,\cdot)$	5641.bb	1128	yes	$-1$	$1$	$e\left(\frac{83}{564}\right)$	$e\left(\frac{305}{564}\right)$	$e\left(\frac{83}{282}\right)$	$e\left(\frac{283}{564}\right)$	$e\left(\frac{97}{141}\right)$	$e\left(\frac{57}{376}\right)$	$e\left(\frac{83}{188}\right)$	$e\left(\frac{23}{282}\right)$	$e\left(\frac{61}{94}\right)$	$e\left(\frac{145}{564}\right)$
$\chi_{5641}(32,\cdot)$	5641.y	564	yes	$1$	$1$	$e\left(\frac{79}{282}\right)$	$e\left(\frac{151}{282}\right)$	$e\left(\frac{79}{141}\right)$	$e\left(\frac{215}{282}\right)$	$e\left(\frac{115}{141}\right)$	$e\left(\frac{35}{188}\right)$	$e\left(\frac{79}{94}\right)$	$e\left(\frac{10}{141}\right)$	$e\left(\frac{2}{47}\right)$	$e\left(\frac{155}{282}\right)$

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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	$5641$
Structure	\(C_{5640}\)
Order	$5640$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{5641}(1,\cdot)\)	5641.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{5641}(2,\cdot)\)	5641.y	564	yes	\(1\)	\(1\)	\(e\left(\frac{185}{282}\right)\)	\(e\left(\frac{143}{282}\right)\)	\(e\left(\frac{44}{141}\right)\)	\(e\left(\frac{43}{282}\right)\)	\(e\left(\frac{23}{141}\right)\)	\(e\left(\frac{7}{188}\right)\)	\(e\left(\frac{91}{94}\right)\)	\(e\left(\frac{2}{141}\right)\)	\(e\left(\frac{38}{47}\right)\)	\(e\left(\frac{31}{282}\right)\)
\(\chi_{5641}(3,\cdot)\)	5641.be	2820	yes	\(1\)	\(1\)	\(e\left(\frac{143}{282}\right)\)	\(e\left(\frac{949}{1410}\right)\)	\(e\left(\frac{2}{141}\right)\)	\(e\left(\frac{593}{1410}\right)\)	\(e\left(\frac{127}{705}\right)\)	\(e\left(\frac{149}{940}\right)\)	\(e\left(\frac{49}{94}\right)\)	\(e\left(\frac{244}{705}\right)\)	\(e\left(\frac{218}{235}\right)\)	\(e\left(\frac{1103}{1410}\right)\)
\(\chi_{5641}(4,\cdot)\)	5641.v	282	yes	\(1\)	\(1\)	\(e\left(\frac{44}{141}\right)\)	\(e\left(\frac{2}{141}\right)\)	\(e\left(\frac{88}{141}\right)\)	\(e\left(\frac{43}{141}\right)\)	\(e\left(\frac{46}{141}\right)\)	\(e\left(\frac{7}{94}\right)\)	\(e\left(\frac{44}{47}\right)\)	\(e\left(\frac{4}{141}\right)\)	\(e\left(\frac{29}{47}\right)\)	\(e\left(\frac{31}{141}\right)\)
\(\chi_{5641}(5,\cdot)\)	5641.be	2820	yes	\(1\)	\(1\)	\(e\left(\frac{43}{282}\right)\)	\(e\left(\frac{593}{1410}\right)\)	\(e\left(\frac{43}{141}\right)\)	\(e\left(\frac{271}{1410}\right)\)	\(e\left(\frac{404}{705}\right)\)	\(e\left(\frac{783}{940}\right)\)	\(e\left(\frac{43}{94}\right)\)	\(e\left(\frac{593}{705}\right)\)	\(e\left(\frac{81}{235}\right)\)	\(e\left(\frac{661}{1410}\right)\)
\(\chi_{5641}(6,\cdot)\)	5641.z	705	yes	\(1\)	\(1\)	\(e\left(\frac{23}{141}\right)\)	\(e\left(\frac{127}{705}\right)\)	\(e\left(\frac{46}{141}\right)\)	\(e\left(\frac{404}{705}\right)\)	\(e\left(\frac{242}{705}\right)\)	\(e\left(\frac{46}{235}\right)\)	\(e\left(\frac{23}{47}\right)\)	\(e\left(\frac{254}{705}\right)\)	\(e\left(\frac{173}{235}\right)\)	\(e\left(\frac{629}{705}\right)\)
\(\chi_{5641}(7,\cdot)\)	5641.bd	1880	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{188}\right)\)	\(e\left(\frac{149}{940}\right)\)	\(e\left(\frac{7}{94}\right)\)	\(e\left(\frac{783}{940}\right)\)	\(e\left(\frac{46}{235}\right)\)	\(e\left(\frac{507}{1880}\right)\)	\(e\left(\frac{21}{188}\right)\)	\(e\left(\frac{149}{470}\right)\)	\(e\left(\frac{409}{470}\right)\)	\(e\left(\frac{453}{940}\right)\)
\(\chi_{5641}(8,\cdot)\)	5641.t	188	yes	\(1\)	\(1\)	\(e\left(\frac{91}{94}\right)\)	\(e\left(\frac{49}{94}\right)\)	\(e\left(\frac{44}{47}\right)\)	\(e\left(\frac{43}{94}\right)\)	\(e\left(\frac{23}{47}\right)\)	\(e\left(\frac{21}{188}\right)\)	\(e\left(\frac{85}{94}\right)\)	\(e\left(\frac{2}{47}\right)\)	\(e\left(\frac{20}{47}\right)\)	\(e\left(\frac{31}{94}\right)\)
\(\chi_{5641}(9,\cdot)\)	5641.bc	1410	yes	\(1\)	\(1\)	\(e\left(\frac{2}{141}\right)\)	\(e\left(\frac{244}{705}\right)\)	\(e\left(\frac{4}{141}\right)\)	\(e\left(\frac{593}{705}\right)\)	\(e\left(\frac{254}{705}\right)\)	\(e\left(\frac{149}{470}\right)\)	\(e\left(\frac{2}{47}\right)\)	\(e\left(\frac{488}{705}\right)\)	\(e\left(\frac{201}{235}\right)\)	\(e\left(\frac{398}{705}\right)\)
\(\chi_{5641}(10,\cdot)\)	5641.x	470	yes	\(1\)	\(1\)	\(e\left(\frac{38}{47}\right)\)	\(e\left(\frac{218}{235}\right)\)	\(e\left(\frac{29}{47}\right)\)	\(e\left(\frac{81}{235}\right)\)	\(e\left(\frac{173}{235}\right)\)	\(e\left(\frac{409}{470}\right)\)	\(e\left(\frac{20}{47}\right)\)	\(e\left(\frac{201}{235}\right)\)	\(e\left(\frac{36}{235}\right)\)	\(e\left(\frac{136}{235}\right)\)
\(\chi_{5641}(11,\cdot)\)	5641.be	2820	yes	\(1\)	\(1\)	\(e\left(\frac{31}{282}\right)\)	\(e\left(\frac{1103}{1410}\right)\)	\(e\left(\frac{31}{141}\right)\)	\(e\left(\frac{661}{1410}\right)\)	\(e\left(\frac{629}{705}\right)\)	\(e\left(\frac{453}{940}\right)\)	\(e\left(\frac{31}{94}\right)\)	\(e\left(\frac{398}{705}\right)\)	\(e\left(\frac{136}{235}\right)\)	\(e\left(\frac{811}{1410}\right)\)
\(\chi_{5641}(12,\cdot)\)	5641.ba	940	yes	\(1\)	\(1\)	\(e\left(\frac{77}{94}\right)\)	\(e\left(\frac{323}{470}\right)\)	\(e\left(\frac{30}{47}\right)\)	\(e\left(\frac{341}{470}\right)\)	\(e\left(\frac{119}{235}\right)\)	\(e\left(\frac{219}{940}\right)\)	\(e\left(\frac{43}{94}\right)\)	\(e\left(\frac{88}{235}\right)\)	\(e\left(\frac{128}{235}\right)\)	\(e\left(\frac{1}{470}\right)\)
\(\chi_{5641}(13,\cdot)\)	5641.ba	940	yes	\(1\)	\(1\)	\(e\left(\frac{15}{94}\right)\)	\(e\left(\frac{373}{470}\right)\)	\(e\left(\frac{15}{47}\right)\)	\(e\left(\frac{241}{470}\right)\)	\(e\left(\frac{224}{235}\right)\)	\(e\left(\frac{509}{940}\right)\)	\(e\left(\frac{45}{94}\right)\)	\(e\left(\frac{138}{235}\right)\)	\(e\left(\frac{158}{235}\right)\)	\(e\left(\frac{71}{470}\right)\)
\(\chi_{5641}(14,\cdot)\)	5641.bf	5640	yes	\(-1\)	\(1\)	\(e\left(\frac{391}{564}\right)\)	\(e\left(\frac{1877}{2820}\right)\)	\(e\left(\frac{109}{282}\right)\)	\(e\left(\frac{2779}{2820}\right)\)	\(e\left(\frac{253}{705}\right)\)	\(e\left(\frac{577}{1880}\right)\)	\(e\left(\frac{15}{188}\right)\)	\(e\left(\frac{467}{1410}\right)\)	\(e\left(\frac{319}{470}\right)\)	\(e\left(\frac{1669}{2820}\right)\)
\(\chi_{5641}(15,\cdot)\)	5641.u	235	yes	\(1\)	\(1\)	\(e\left(\frac{31}{47}\right)\)	\(e\left(\frac{22}{235}\right)\)	\(e\left(\frac{15}{47}\right)\)	\(e\left(\frac{144}{235}\right)\)	\(e\left(\frac{177}{235}\right)\)	\(e\left(\frac{233}{235}\right)\)	\(e\left(\frac{46}{47}\right)\)	\(e\left(\frac{44}{235}\right)\)	\(e\left(\frac{64}{235}\right)\)	\(e\left(\frac{59}{235}\right)\)
\(\chi_{5641}(16,\cdot)\)	5641.s	141	yes	\(1\)	\(1\)	\(e\left(\frac{88}{141}\right)\)	\(e\left(\frac{4}{141}\right)\)	\(e\left(\frac{35}{141}\right)\)	\(e\left(\frac{86}{141}\right)\)	\(e\left(\frac{92}{141}\right)\)	\(e\left(\frac{7}{47}\right)\)	\(e\left(\frac{41}{47}\right)\)	\(e\left(\frac{8}{141}\right)\)	\(e\left(\frac{11}{47}\right)\)	\(e\left(\frac{62}{141}\right)\)
\(\chi_{5641}(17,\cdot)\)	5641.bb	1128	yes	\(-1\)	\(1\)	\(e\left(\frac{407}{564}\right)\)	\(e\left(\frac{89}{564}\right)\)	\(e\left(\frac{125}{282}\right)\)	\(e\left(\frac{151}{564}\right)\)	\(e\left(\frac{124}{141}\right)\)	\(e\left(\frac{53}{376}\right)\)	\(e\left(\frac{31}{188}\right)\)	\(e\left(\frac{89}{282}\right)\)	\(e\left(\frac{93}{94}\right)\)	\(e\left(\frac{181}{564}\right)\)
\(\chi_{5641}(18,\cdot)\)	5641.ba	940	yes	\(1\)	\(1\)	\(e\left(\frac{63}{94}\right)\)	\(e\left(\frac{401}{470}\right)\)	\(e\left(\frac{16}{47}\right)\)	\(e\left(\frac{467}{470}\right)\)	\(e\left(\frac{123}{235}\right)\)	\(e\left(\frac{333}{940}\right)\)	\(e\left(\frac{1}{94}\right)\)	\(e\left(\frac{166}{235}\right)\)	\(e\left(\frac{156}{235}\right)\)	\(e\left(\frac{317}{470}\right)\)
\(\chi_{5641}(19,\cdot)\)	5641.y	564	yes	\(1\)	\(1\)	\(e\left(\frac{7}{282}\right)\)	\(e\left(\frac{199}{282}\right)\)	\(e\left(\frac{7}{141}\right)\)	\(e\left(\frac{119}{282}\right)\)	\(e\left(\frac{103}{141}\right)\)	\(e\left(\frac{15}{188}\right)\)	\(e\left(\frac{7}{94}\right)\)	\(e\left(\frac{58}{141}\right)\)	\(e\left(\frac{21}{47}\right)\)	\(e\left(\frac{53}{282}\right)\)
\(\chi_{5641}(20,\cdot)\)	5641.be	2820	yes	\(1\)	\(1\)	\(e\left(\frac{131}{282}\right)\)	\(e\left(\frac{613}{1410}\right)\)	\(e\left(\frac{131}{141}\right)\)	\(e\left(\frac{701}{1410}\right)\)	\(e\left(\frac{634}{705}\right)\)	\(e\left(\frac{853}{940}\right)\)	\(e\left(\frac{37}{94}\right)\)	\(e\left(\frac{613}{705}\right)\)	\(e\left(\frac{226}{235}\right)\)	\(e\left(\frac{971}{1410}\right)\)
\(\chi_{5641}(21,\cdot)\)	5641.bb	1128	yes	\(-1\)	\(1\)	\(e\left(\frac{307}{564}\right)\)	\(e\left(\frac{469}{564}\right)\)	\(e\left(\frac{25}{282}\right)\)	\(e\left(\frac{143}{564}\right)\)	\(e\left(\frac{53}{141}\right)\)	\(e\left(\frac{161}{376}\right)\)	\(e\left(\frac{119}{188}\right)\)	\(e\left(\frac{187}{282}\right)\)	\(e\left(\frac{75}{94}\right)\)	\(e\left(\frac{149}{564}\right)\)
\(\chi_{5641}(22,\cdot)\)	5641.u	235	yes	\(1\)	\(1\)	\(e\left(\frac{36}{47}\right)\)	\(e\left(\frac{68}{235}\right)\)	\(e\left(\frac{25}{47}\right)\)	\(e\left(\frac{146}{235}\right)\)	\(e\left(\frac{13}{235}\right)\)	\(e\left(\frac{122}{235}\right)\)	\(e\left(\frac{14}{47}\right)\)	\(e\left(\frac{136}{235}\right)\)	\(e\left(\frac{91}{235}\right)\)	\(e\left(\frac{161}{235}\right)\)
\(\chi_{5641}(23,\cdot)\)	5641.u	235	yes	\(1\)	\(1\)	\(e\left(\frac{44}{47}\right)\)	\(e\left(\frac{104}{235}\right)\)	\(e\left(\frac{41}{47}\right)\)	\(e\left(\frac{168}{235}\right)\)	\(e\left(\frac{89}{235}\right)\)	\(e\left(\frac{76}{235}\right)\)	\(e\left(\frac{38}{47}\right)\)	\(e\left(\frac{208}{235}\right)\)	\(e\left(\frac{153}{235}\right)\)	\(e\left(\frac{108}{235}\right)\)
\(\chi_{5641}(24,\cdot)\)	5641.bc	1410	yes	\(1\)	\(1\)	\(e\left(\frac{67}{141}\right)\)	\(e\left(\frac{137}{705}\right)\)	\(e\left(\frac{134}{141}\right)\)	\(e\left(\frac{619}{705}\right)\)	\(e\left(\frac{472}{705}\right)\)	\(e\left(\frac{127}{470}\right)\)	\(e\left(\frac{20}{47}\right)\)	\(e\left(\frac{274}{705}\right)\)	\(e\left(\frac{83}{235}\right)\)	\(e\left(\frac{79}{705}\right)\)
\(\chi_{5641}(25,\cdot)\)	5641.bc	1410	yes	\(1\)	\(1\)	\(e\left(\frac{43}{141}\right)\)	\(e\left(\frac{593}{705}\right)\)	\(e\left(\frac{86}{141}\right)\)	\(e\left(\frac{271}{705}\right)\)	\(e\left(\frac{103}{705}\right)\)	\(e\left(\frac{313}{470}\right)\)	\(e\left(\frac{43}{47}\right)\)	\(e\left(\frac{481}{705}\right)\)	\(e\left(\frac{162}{235}\right)\)	\(e\left(\frac{661}{705}\right)\)
\(\chi_{5641}(26,\cdot)\)	5641.z	705	yes	\(1\)	\(1\)	\(e\left(\frac{115}{141}\right)\)	\(e\left(\frac{212}{705}\right)\)	\(e\left(\frac{89}{141}\right)\)	\(e\left(\frac{469}{705}\right)\)	\(e\left(\frac{82}{705}\right)\)	\(e\left(\frac{136}{235}\right)\)	\(e\left(\frac{21}{47}\right)\)	\(e\left(\frac{424}{705}\right)\)	\(e\left(\frac{113}{235}\right)\)	\(e\left(\frac{184}{705}\right)\)
\(\chi_{5641}(27,\cdot)\)	5641.ba	940	yes	\(1\)	\(1\)	\(e\left(\frac{49}{94}\right)\)	\(e\left(\frac{9}{470}\right)\)	\(e\left(\frac{2}{47}\right)\)	\(e\left(\frac{123}{470}\right)\)	\(e\left(\frac{127}{235}\right)\)	\(e\left(\frac{447}{940}\right)\)	\(e\left(\frac{53}{94}\right)\)	\(e\left(\frac{9}{235}\right)\)	\(e\left(\frac{184}{235}\right)\)	\(e\left(\frac{163}{470}\right)\)
\(\chi_{5641}(28,\cdot)\)	5641.bf	5640	yes	\(-1\)	\(1\)	\(e\left(\frac{197}{564}\right)\)	\(e\left(\frac{487}{2820}\right)\)	\(e\left(\frac{197}{282}\right)\)	\(e\left(\frac{389}{2820}\right)\)	\(e\left(\frac{368}{705}\right)\)	\(e\left(\frac{647}{1880}\right)\)	\(e\left(\frac{9}{188}\right)\)	\(e\left(\frac{487}{1410}\right)\)	\(e\left(\frac{229}{470}\right)\)	\(e\left(\frac{1979}{2820}\right)\)
\(\chi_{5641}(29,\cdot)\)	5641.bb	1128	yes	\(-1\)	\(1\)	\(e\left(\frac{493}{564}\right)\)	\(e\left(\frac{439}{564}\right)\)	\(e\left(\frac{211}{282}\right)\)	\(e\left(\frac{485}{564}\right)\)	\(e\left(\frac{92}{141}\right)\)	\(e\left(\frac{291}{376}\right)\)	\(e\left(\frac{117}{188}\right)\)	\(e\left(\frac{157}{282}\right)\)	\(e\left(\frac{69}{94}\right)\)	\(e\left(\frac{107}{564}\right)\)
\(\chi_{5641}(30,\cdot)\)	5641.be	2820	yes	\(1\)	\(1\)	\(e\left(\frac{89}{282}\right)\)	\(e\left(\frac{847}{1410}\right)\)	\(e\left(\frac{89}{141}\right)\)	\(e\left(\frac{1079}{1410}\right)\)	\(e\left(\frac{646}{705}\right)\)	\(e\left(\frac{27}{940}\right)\)	\(e\left(\frac{89}{94}\right)\)	\(e\left(\frac{142}{705}\right)\)	\(e\left(\frac{19}{235}\right)\)	\(e\left(\frac{509}{1410}\right)\)
\(\chi_{5641}(31,\cdot)\)	5641.bb	1128	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{564}\right)\)	\(e\left(\frac{305}{564}\right)\)	\(e\left(\frac{83}{282}\right)\)	\(e\left(\frac{283}{564}\right)\)	\(e\left(\frac{97}{141}\right)\)	\(e\left(\frac{57}{376}\right)\)	\(e\left(\frac{83}{188}\right)\)	\(e\left(\frac{23}{282}\right)\)	\(e\left(\frac{61}{94}\right)\)	\(e\left(\frac{145}{564}\right)\)
\(\chi_{5641}(32,\cdot)\)	5641.y	564	yes	\(1\)	\(1\)	\(e\left(\frac{79}{282}\right)\)	\(e\left(\frac{151}{282}\right)\)	\(e\left(\frac{79}{141}\right)\)	\(e\left(\frac{215}{282}\right)\)	\(e\left(\frac{115}{141}\right)\)	\(e\left(\frac{35}{188}\right)\)	\(e\left(\frac{79}{94}\right)\)	\(e\left(\frac{10}{141}\right)\)	\(e\left(\frac{2}{47}\right)\)	\(e\left(\frac{155}{282}\right)\)

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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.