LMFDB - Group of Dirichlet characters of modulus 10053

Show commands: PariGP / SageMath

sage: H = DirichletGroup(10053)

pari: g = idealstar(,10053,2)

Character group

sage: G.order() pari: g.no
Order	=	6696
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{1116}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{10053}(1118,\cdot)$, $\chi_{10053}(8938,\cdot)$

First 32 of 6696 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{10053}(1,\cdot)$	10053.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{10053}(2,\cdot)$	10053.dr	1116	yes	$1$	$1$	$e\left(\frac{187}{1116}\right)$	$e\left(\frac{187}{558}\right)$	$e\left(\frac{63}{124}\right)$	$e\left(\frac{545}{558}\right)$	$e\left(\frac{187}{372}\right)$	$e\left(\frac{377}{558}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{82}{93}\right)$	$e\left(\frac{161}{1116}\right)$	$e\left(\frac{187}{279}\right)$
$\chi_{10053}(4,\cdot)$	10053.dk	558	yes	$1$	$1$	$e\left(\frac{187}{558}\right)$	$e\left(\frac{187}{279}\right)$	$e\left(\frac{1}{62}\right)$	$e\left(\frac{266}{279}\right)$	$e\left(\frac{1}{186}\right)$	$e\left(\frac{98}{279}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{71}{93}\right)$	$e\left(\frac{161}{558}\right)$	$e\left(\frac{95}{279}\right)$
$\chi_{10053}(5,\cdot)$	10053.dc	372	yes	$1$	$1$	$e\left(\frac{63}{124}\right)$	$e\left(\frac{1}{62}\right)$	$e\left(\frac{89}{372}\right)$	$e\left(\frac{49}{62}\right)$	$e\left(\frac{65}{124}\right)$	$e\left(\frac{139}{186}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{56}{93}\right)$	$e\left(\frac{37}{124}\right)$	$e\left(\frac{1}{31}\right)$
$\chi_{10053}(7,\cdot)$	10053.dk	558	yes	$1$	$1$	$e\left(\frac{545}{558}\right)$	$e\left(\frac{266}{279}\right)$	$e\left(\frac{49}{62}\right)$	$e\left(\frac{262}{279}\right)$	$e\left(\frac{173}{186}\right)$	$e\left(\frac{214}{279}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{93}\right)$	$e\left(\frac{511}{558}\right)$	$e\left(\frac{253}{279}\right)$
$\chi_{10053}(8,\cdot)$	10053.cv	372	no	$1$	$1$	$e\left(\frac{187}{372}\right)$	$e\left(\frac{1}{186}\right)$	$e\left(\frac{65}{124}\right)$	$e\left(\frac{173}{186}\right)$	$e\left(\frac{63}{124}\right)$	$e\left(\frac{5}{186}\right)$	$-i$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{161}{372}\right)$	$e\left(\frac{1}{93}\right)$
$\chi_{10053}(10,\cdot)$	10053.dg	558	no	$1$	$1$	$e\left(\frac{377}{558}\right)$	$e\left(\frac{98}{279}\right)$	$e\left(\frac{139}{186}\right)$	$e\left(\frac{214}{279}\right)$	$e\left(\frac{5}{186}\right)$	$e\left(\frac{118}{279}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{247}{558}\right)$	$e\left(\frac{196}{279}\right)$
$\chi_{10053}(11,\cdot)$	10053.bd	12	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{10053}(13,\cdot)$	10053.cc	93	yes	$1$	$1$	$e\left(\frac{82}{93}\right)$	$e\left(\frac{71}{93}\right)$	$e\left(\frac{56}{93}\right)$	$e\left(\frac{7}{93}\right)$	$e\left(\frac{20}{31}\right)$	$e\left(\frac{15}{31}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{26}{93}\right)$	$e\left(\frac{89}{93}\right)$	$e\left(\frac{49}{93}\right)$
$\chi_{10053}(14,\cdot)$	10053.dr	1116	yes	$1$	$1$	$e\left(\frac{161}{1116}\right)$	$e\left(\frac{161}{558}\right)$	$e\left(\frac{37}{124}\right)$	$e\left(\frac{511}{558}\right)$	$e\left(\frac{161}{372}\right)$	$e\left(\frac{247}{558}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{89}{93}\right)$	$e\left(\frac{67}{1116}\right)$	$e\left(\frac{161}{279}\right)$
$\chi_{10053}(16,\cdot)$	10053.cs	279	yes	$1$	$1$	$e\left(\frac{187}{279}\right)$	$e\left(\frac{95}{279}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{253}{279}\right)$	$e\left(\frac{1}{93}\right)$	$e\left(\frac{196}{279}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{49}{93}\right)$	$e\left(\frac{161}{279}\right)$	$e\left(\frac{190}{279}\right)$
$\chi_{10053}(17,\cdot)$	10053.dn	1116	no	$1$	$1$	$e\left(\frac{857}{1116}\right)$	$e\left(\frac{299}{558}\right)$	$e\left(\frac{91}{372}\right)$	$e\left(\frac{391}{558}\right)$	$e\left(\frac{113}{372}\right)$	$e\left(\frac{7}{558}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{30}{31}\right)$	$e\left(\frac{523}{1116}\right)$	$e\left(\frac{20}{279}\right)$
$\chi_{10053}(19,\cdot)$	10053.cw	372	no	$-1$	$1$	$e\left(\frac{145}{372}\right)$	$e\left(\frac{145}{186}\right)$	$e\left(\frac{63}{124}\right)$	$e\left(\frac{161}{186}\right)$	$e\left(\frac{21}{124}\right)$	$e\left(\frac{167}{186}\right)$	$i$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{95}{372}\right)$	$e\left(\frac{52}{93}\right)$
$\chi_{10053}(20,\cdot)$	10053.do	1116	yes	$1$	$1$	$e\left(\frac{941}{1116}\right)$	$e\left(\frac{383}{558}\right)$	$e\left(\frac{95}{372}\right)$	$e\left(\frac{415}{558}\right)$	$e\left(\frac{197}{372}\right)$	$e\left(\frac{55}{558}\right)$	$-i$	$e\left(\frac{34}{93}\right)$	$e\left(\frac{655}{1116}\right)$	$e\left(\frac{104}{279}\right)$
$\chi_{10053}(22,\cdot)$	10053.de	558	yes	$1$	$1$	$e\left(\frac{419}{558}\right)$	$e\left(\frac{140}{279}\right)$	$e\left(\frac{17}{186}\right)$	$e\left(\frac{226}{279}\right)$	$e\left(\frac{47}{186}\right)$	$e\left(\frac{235}{279}\right)$	$-1$	$e\left(\frac{20}{93}\right)$	$e\left(\frac{313}{558}\right)$	$e\left(\frac{1}{279}\right)$
$\chi_{10053}(23,\cdot)$	10053.bp	18	yes	$-1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{10053}(25,\cdot)$	10053.cr	186	yes	$1$	$1$	$e\left(\frac{1}{62}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{89}{186}\right)$	$e\left(\frac{18}{31}\right)$	$e\left(\frac{3}{62}\right)$	$e\left(\frac{46}{93}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{93}\right)$	$e\left(\frac{37}{62}\right)$	$e\left(\frac{2}{31}\right)$
$\chi_{10053}(26,\cdot)$	10053.dn	1116	no	$1$	$1$	$e\left(\frac{55}{1116}\right)$	$e\left(\frac{55}{558}\right)$	$e\left(\frac{41}{372}\right)$	$e\left(\frac{29}{558}\right)$	$e\left(\frac{55}{372}\right)$	$e\left(\frac{89}{558}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{31}\right)$	$e\left(\frac{113}{1116}\right)$	$e\left(\frac{55}{279}\right)$
$\chi_{10053}(28,\cdot)$	10053.cb	93	no	$1$	$1$	$e\left(\frac{29}{93}\right)$	$e\left(\frac{58}{93}\right)$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{83}{93}\right)$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{11}{93}\right)$	$1$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{19}{93}\right)$	$e\left(\frac{23}{93}\right)$
$\chi_{10053}(29,\cdot)$	10053.do	1116	yes	$1$	$1$	$e\left(\frac{1049}{1116}\right)$	$e\left(\frac{491}{558}\right)$	$e\left(\frac{47}{372}\right)$	$e\left(\frac{127}{558}\right)$	$e\left(\frac{305}{372}\right)$	$e\left(\frac{37}{558}\right)$	$-i$	$e\left(\frac{55}{93}\right)$	$e\left(\frac{187}{1116}\right)$	$e\left(\frac{212}{279}\right)$
$\chi_{10053}(31,\cdot)$	10053.cu	279	yes	$1$	$1$	$e\left(\frac{238}{279}\right)$	$e\left(\frac{197}{279}\right)$	$e\left(\frac{1}{93}\right)$	$e\left(\frac{43}{279}\right)$	$e\left(\frac{52}{93}\right)$	$e\left(\frac{241}{279}\right)$	$1$	$e\left(\frac{68}{93}\right)$	$e\left(\frac{2}{279}\right)$	$e\left(\frac{115}{279}\right)$
$\chi_{10053}(32,\cdot)$	10053.dr	1116	yes	$1$	$1$	$e\left(\frac{935}{1116}\right)$	$e\left(\frac{377}{558}\right)$	$e\left(\frac{67}{124}\right)$	$e\left(\frac{493}{558}\right)$	$e\left(\frac{191}{372}\right)$	$e\left(\frac{211}{558}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{38}{93}\right)$	$e\left(\frac{805}{1116}\right)$	$e\left(\frac{98}{279}\right)$
$\chi_{10053}(34,\cdot)$	10053.ca	93	yes	$1$	$1$	$e\left(\frac{29}{31}\right)$	$e\left(\frac{27}{31}\right)$	$e\left(\frac{70}{93}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{25}{31}\right)$	$e\left(\frac{64}{93}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{79}{93}\right)$	$e\left(\frac{19}{31}\right)$	$e\left(\frac{23}{31}\right)$
$\chi_{10053}(35,\cdot)$	10053.dn	1116	no	$1$	$1$	$e\left(\frac{541}{1116}\right)$	$e\left(\frac{541}{558}\right)$	$e\left(\frac{11}{372}\right)$	$e\left(\frac{407}{558}\right)$	$e\left(\frac{169}{372}\right)$	$e\left(\frac{287}{558}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{21}{31}\right)$	$e\left(\frac{239}{1116}\right)$	$e\left(\frac{262}{279}\right)$
$\chi_{10053}(37,\cdot)$	10053.bz	62	no	$1$	$1$	$e\left(\frac{9}{62}\right)$	$e\left(\frac{9}{31}\right)$	$e\left(\frac{19}{62}\right)$	$e\left(\frac{7}{31}\right)$	$e\left(\frac{27}{62}\right)$	$e\left(\frac{14}{31}\right)$	$-1$	$e\left(\frac{26}{31}\right)$	$e\left(\frac{23}{62}\right)$	$e\left(\frac{18}{31}\right)$
$\chi_{10053}(38,\cdot)$	10053.dl	558	yes	$-1$	$1$	$e\left(\frac{311}{558}\right)$	$e\left(\frac{32}{279}\right)$	$e\left(\frac{1}{62}\right)$	$e\left(\frac{235}{279}\right)$	$e\left(\frac{125}{186}\right)$	$e\left(\frac{160}{279}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{40}{93}\right)$	$e\left(\frac{223}{558}\right)$	$e\left(\frac{64}{279}\right)$
$\chi_{10053}(40,\cdot)$	10053.cc	93	yes	$1$	$1$	$e\left(\frac{1}{93}\right)$	$e\left(\frac{2}{93}\right)$	$e\left(\frac{71}{93}\right)$	$e\left(\frac{67}{93}\right)$	$e\left(\frac{1}{31}\right)$	$e\left(\frac{24}{31}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{93}\right)$	$e\left(\frac{68}{93}\right)$	$e\left(\frac{4}{93}\right)$
$\chi_{10053}(41,\cdot)$	10053.df	558	yes	$-1$	$1$	$e\left(\frac{23}{558}\right)$	$e\left(\frac{23}{279}\right)$	$e\left(\frac{131}{186}\right)$	$e\left(\frac{73}{279}\right)$	$e\left(\frac{23}{186}\right)$	$e\left(\frac{208}{279}\right)$	$-1$	$e\left(\frac{83}{93}\right)$	$e\left(\frac{169}{558}\right)$	$e\left(\frac{46}{279}\right)$
$\chi_{10053}(43,\cdot)$	10053.dp	1116	yes	$-1$	$1$	$e\left(\frac{131}{1116}\right)$	$e\left(\frac{131}{558}\right)$	$e\left(\frac{269}{372}\right)$	$e\left(\frac{343}{558}\right)$	$e\left(\frac{131}{372}\right)$	$e\left(\frac{469}{558}\right)$	$i$	$e\left(\frac{16}{93}\right)$	$e\left(\frac{817}{1116}\right)$	$e\left(\frac{131}{279}\right)$
$\chi_{10053}(44,\cdot)$	10053.dn	1116	no	$1$	$1$	$e\left(\frac{1025}{1116}\right)$	$e\left(\frac{467}{558}\right)$	$e\left(\frac{223}{372}\right)$	$e\left(\frac{439}{558}\right)$	$e\left(\frac{281}{372}\right)$	$e\left(\frac{289}{558}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{31}\right)$	$e\left(\frac{787}{1116}\right)$	$e\left(\frac{188}{279}\right)$
$\chi_{10053}(46,\cdot)$	10053.ce	124	no	$-1$	$1$	$e\left(\frac{7}{124}\right)$	$e\left(\frac{7}{62}\right)$	$e\left(\frac{63}{124}\right)$	$e\left(\frac{33}{62}\right)$	$e\left(\frac{21}{124}\right)$	$e\left(\frac{35}{62}\right)$	$i$	$e\left(\frac{17}{31}\right)$	$e\left(\frac{73}{124}\right)$	$e\left(\frac{7}{31}\right)$
$\chi_{10053}(47,\cdot)$	10053.cp	186	yes	$-1$	$1$	$e\left(\frac{55}{93}\right)$	$e\left(\frac{17}{93}\right)$	$e\left(\frac{61}{93}\right)$	$e\left(\frac{58}{93}\right)$	$e\left(\frac{24}{31}\right)$	$e\left(\frac{23}{93}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{25}{93}\right)$	$e\left(\frac{20}{93}\right)$	$e\left(\frac{34}{93}\right)$

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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	$10053$
Structure	\(C_{6}\times C_{1116}\)
Order	$6696$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{10053}(1,\cdot)\)	10053.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{10053}(2,\cdot)\)	10053.dr	1116	yes	\(1\)	\(1\)	\(e\left(\frac{187}{1116}\right)\)	\(e\left(\frac{187}{558}\right)\)	\(e\left(\frac{63}{124}\right)\)	\(e\left(\frac{545}{558}\right)\)	\(e\left(\frac{187}{372}\right)\)	\(e\left(\frac{377}{558}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{82}{93}\right)\)	\(e\left(\frac{161}{1116}\right)\)	\(e\left(\frac{187}{279}\right)\)
\(\chi_{10053}(4,\cdot)\)	10053.dk	558	yes	\(1\)	\(1\)	\(e\left(\frac{187}{558}\right)\)	\(e\left(\frac{187}{279}\right)\)	\(e\left(\frac{1}{62}\right)\)	\(e\left(\frac{266}{279}\right)\)	\(e\left(\frac{1}{186}\right)\)	\(e\left(\frac{98}{279}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{71}{93}\right)\)	\(e\left(\frac{161}{558}\right)\)	\(e\left(\frac{95}{279}\right)\)
\(\chi_{10053}(5,\cdot)\)	10053.dc	372	yes	\(1\)	\(1\)	\(e\left(\frac{63}{124}\right)\)	\(e\left(\frac{1}{62}\right)\)	\(e\left(\frac{89}{372}\right)\)	\(e\left(\frac{49}{62}\right)\)	\(e\left(\frac{65}{124}\right)\)	\(e\left(\frac{139}{186}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{56}{93}\right)\)	\(e\left(\frac{37}{124}\right)\)	\(e\left(\frac{1}{31}\right)\)
\(\chi_{10053}(7,\cdot)\)	10053.dk	558	yes	\(1\)	\(1\)	\(e\left(\frac{545}{558}\right)\)	\(e\left(\frac{266}{279}\right)\)	\(e\left(\frac{49}{62}\right)\)	\(e\left(\frac{262}{279}\right)\)	\(e\left(\frac{173}{186}\right)\)	\(e\left(\frac{214}{279}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{93}\right)\)	\(e\left(\frac{511}{558}\right)\)	\(e\left(\frac{253}{279}\right)\)
\(\chi_{10053}(8,\cdot)\)	10053.cv	372	no	\(1\)	\(1\)	\(e\left(\frac{187}{372}\right)\)	\(e\left(\frac{1}{186}\right)\)	\(e\left(\frac{65}{124}\right)\)	\(e\left(\frac{173}{186}\right)\)	\(e\left(\frac{63}{124}\right)\)	\(e\left(\frac{5}{186}\right)\)	\(-i\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{161}{372}\right)\)	\(e\left(\frac{1}{93}\right)\)
\(\chi_{10053}(10,\cdot)\)	10053.dg	558	no	\(1\)	\(1\)	\(e\left(\frac{377}{558}\right)\)	\(e\left(\frac{98}{279}\right)\)	\(e\left(\frac{139}{186}\right)\)	\(e\left(\frac{214}{279}\right)\)	\(e\left(\frac{5}{186}\right)\)	\(e\left(\frac{118}{279}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{247}{558}\right)\)	\(e\left(\frac{196}{279}\right)\)
\(\chi_{10053}(11,\cdot)\)	10053.bd	12	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{10053}(13,\cdot)\)	10053.cc	93	yes	\(1\)	\(1\)	\(e\left(\frac{82}{93}\right)\)	\(e\left(\frac{71}{93}\right)\)	\(e\left(\frac{56}{93}\right)\)	\(e\left(\frac{7}{93}\right)\)	\(e\left(\frac{20}{31}\right)\)	\(e\left(\frac{15}{31}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{26}{93}\right)\)	\(e\left(\frac{89}{93}\right)\)	\(e\left(\frac{49}{93}\right)\)
\(\chi_{10053}(14,\cdot)\)	10053.dr	1116	yes	\(1\)	\(1\)	\(e\left(\frac{161}{1116}\right)\)	\(e\left(\frac{161}{558}\right)\)	\(e\left(\frac{37}{124}\right)\)	\(e\left(\frac{511}{558}\right)\)	\(e\left(\frac{161}{372}\right)\)	\(e\left(\frac{247}{558}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{89}{93}\right)\)	\(e\left(\frac{67}{1116}\right)\)	\(e\left(\frac{161}{279}\right)\)
\(\chi_{10053}(16,\cdot)\)	10053.cs	279	yes	\(1\)	\(1\)	\(e\left(\frac{187}{279}\right)\)	\(e\left(\frac{95}{279}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{253}{279}\right)\)	\(e\left(\frac{1}{93}\right)\)	\(e\left(\frac{196}{279}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{49}{93}\right)\)	\(e\left(\frac{161}{279}\right)\)	\(e\left(\frac{190}{279}\right)\)
\(\chi_{10053}(17,\cdot)\)	10053.dn	1116	no	\(1\)	\(1\)	\(e\left(\frac{857}{1116}\right)\)	\(e\left(\frac{299}{558}\right)\)	\(e\left(\frac{91}{372}\right)\)	\(e\left(\frac{391}{558}\right)\)	\(e\left(\frac{113}{372}\right)\)	\(e\left(\frac{7}{558}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{30}{31}\right)\)	\(e\left(\frac{523}{1116}\right)\)	\(e\left(\frac{20}{279}\right)\)
\(\chi_{10053}(19,\cdot)\)	10053.cw	372	no	\(-1\)	\(1\)	\(e\left(\frac{145}{372}\right)\)	\(e\left(\frac{145}{186}\right)\)	\(e\left(\frac{63}{124}\right)\)	\(e\left(\frac{161}{186}\right)\)	\(e\left(\frac{21}{124}\right)\)	\(e\left(\frac{167}{186}\right)\)	\(i\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{95}{372}\right)\)	\(e\left(\frac{52}{93}\right)\)
\(\chi_{10053}(20,\cdot)\)	10053.do	1116	yes	\(1\)	\(1\)	\(e\left(\frac{941}{1116}\right)\)	\(e\left(\frac{383}{558}\right)\)	\(e\left(\frac{95}{372}\right)\)	\(e\left(\frac{415}{558}\right)\)	\(e\left(\frac{197}{372}\right)\)	\(e\left(\frac{55}{558}\right)\)	\(-i\)	\(e\left(\frac{34}{93}\right)\)	\(e\left(\frac{655}{1116}\right)\)	\(e\left(\frac{104}{279}\right)\)
\(\chi_{10053}(22,\cdot)\)	10053.de	558	yes	\(1\)	\(1\)	\(e\left(\frac{419}{558}\right)\)	\(e\left(\frac{140}{279}\right)\)	\(e\left(\frac{17}{186}\right)\)	\(e\left(\frac{226}{279}\right)\)	\(e\left(\frac{47}{186}\right)\)	\(e\left(\frac{235}{279}\right)\)	\(-1\)	\(e\left(\frac{20}{93}\right)\)	\(e\left(\frac{313}{558}\right)\)	\(e\left(\frac{1}{279}\right)\)
\(\chi_{10053}(23,\cdot)\)	10053.bp	18	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{10053}(25,\cdot)\)	10053.cr	186	yes	\(1\)	\(1\)	\(e\left(\frac{1}{62}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{89}{186}\right)\)	\(e\left(\frac{18}{31}\right)\)	\(e\left(\frac{3}{62}\right)\)	\(e\left(\frac{46}{93}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{93}\right)\)	\(e\left(\frac{37}{62}\right)\)	\(e\left(\frac{2}{31}\right)\)
\(\chi_{10053}(26,\cdot)\)	10053.dn	1116	no	\(1\)	\(1\)	\(e\left(\frac{55}{1116}\right)\)	\(e\left(\frac{55}{558}\right)\)	\(e\left(\frac{41}{372}\right)\)	\(e\left(\frac{29}{558}\right)\)	\(e\left(\frac{55}{372}\right)\)	\(e\left(\frac{89}{558}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{31}\right)\)	\(e\left(\frac{113}{1116}\right)\)	\(e\left(\frac{55}{279}\right)\)
\(\chi_{10053}(28,\cdot)\)	10053.cb	93	no	\(1\)	\(1\)	\(e\left(\frac{29}{93}\right)\)	\(e\left(\frac{58}{93}\right)\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{83}{93}\right)\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{11}{93}\right)\)	\(1\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{19}{93}\right)\)	\(e\left(\frac{23}{93}\right)\)
\(\chi_{10053}(29,\cdot)\)	10053.do	1116	yes	\(1\)	\(1\)	\(e\left(\frac{1049}{1116}\right)\)	\(e\left(\frac{491}{558}\right)\)	\(e\left(\frac{47}{372}\right)\)	\(e\left(\frac{127}{558}\right)\)	\(e\left(\frac{305}{372}\right)\)	\(e\left(\frac{37}{558}\right)\)	\(-i\)	\(e\left(\frac{55}{93}\right)\)	\(e\left(\frac{187}{1116}\right)\)	\(e\left(\frac{212}{279}\right)\)
\(\chi_{10053}(31,\cdot)\)	10053.cu	279	yes	\(1\)	\(1\)	\(e\left(\frac{238}{279}\right)\)	\(e\left(\frac{197}{279}\right)\)	\(e\left(\frac{1}{93}\right)\)	\(e\left(\frac{43}{279}\right)\)	\(e\left(\frac{52}{93}\right)\)	\(e\left(\frac{241}{279}\right)\)	\(1\)	\(e\left(\frac{68}{93}\right)\)	\(e\left(\frac{2}{279}\right)\)	\(e\left(\frac{115}{279}\right)\)
\(\chi_{10053}(32,\cdot)\)	10053.dr	1116	yes	\(1\)	\(1\)	\(e\left(\frac{935}{1116}\right)\)	\(e\left(\frac{377}{558}\right)\)	\(e\left(\frac{67}{124}\right)\)	\(e\left(\frac{493}{558}\right)\)	\(e\left(\frac{191}{372}\right)\)	\(e\left(\frac{211}{558}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{38}{93}\right)\)	\(e\left(\frac{805}{1116}\right)\)	\(e\left(\frac{98}{279}\right)\)
\(\chi_{10053}(34,\cdot)\)	10053.ca	93	yes	\(1\)	\(1\)	\(e\left(\frac{29}{31}\right)\)	\(e\left(\frac{27}{31}\right)\)	\(e\left(\frac{70}{93}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{25}{31}\right)\)	\(e\left(\frac{64}{93}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{79}{93}\right)\)	\(e\left(\frac{19}{31}\right)\)	\(e\left(\frac{23}{31}\right)\)
\(\chi_{10053}(35,\cdot)\)	10053.dn	1116	no	\(1\)	\(1\)	\(e\left(\frac{541}{1116}\right)\)	\(e\left(\frac{541}{558}\right)\)	\(e\left(\frac{11}{372}\right)\)	\(e\left(\frac{407}{558}\right)\)	\(e\left(\frac{169}{372}\right)\)	\(e\left(\frac{287}{558}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{21}{31}\right)\)	\(e\left(\frac{239}{1116}\right)\)	\(e\left(\frac{262}{279}\right)\)
\(\chi_{10053}(37,\cdot)\)	10053.bz	62	no	\(1\)	\(1\)	\(e\left(\frac{9}{62}\right)\)	\(e\left(\frac{9}{31}\right)\)	\(e\left(\frac{19}{62}\right)\)	\(e\left(\frac{7}{31}\right)\)	\(e\left(\frac{27}{62}\right)\)	\(e\left(\frac{14}{31}\right)\)	\(-1\)	\(e\left(\frac{26}{31}\right)\)	\(e\left(\frac{23}{62}\right)\)	\(e\left(\frac{18}{31}\right)\)
\(\chi_{10053}(38,\cdot)\)	10053.dl	558	yes	\(-1\)	\(1\)	\(e\left(\frac{311}{558}\right)\)	\(e\left(\frac{32}{279}\right)\)	\(e\left(\frac{1}{62}\right)\)	\(e\left(\frac{235}{279}\right)\)	\(e\left(\frac{125}{186}\right)\)	\(e\left(\frac{160}{279}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{40}{93}\right)\)	\(e\left(\frac{223}{558}\right)\)	\(e\left(\frac{64}{279}\right)\)
\(\chi_{10053}(40,\cdot)\)	10053.cc	93	yes	\(1\)	\(1\)	\(e\left(\frac{1}{93}\right)\)	\(e\left(\frac{2}{93}\right)\)	\(e\left(\frac{71}{93}\right)\)	\(e\left(\frac{67}{93}\right)\)	\(e\left(\frac{1}{31}\right)\)	\(e\left(\frac{24}{31}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{93}\right)\)	\(e\left(\frac{68}{93}\right)\)	\(e\left(\frac{4}{93}\right)\)
\(\chi_{10053}(41,\cdot)\)	10053.df	558	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{558}\right)\)	\(e\left(\frac{23}{279}\right)\)	\(e\left(\frac{131}{186}\right)\)	\(e\left(\frac{73}{279}\right)\)	\(e\left(\frac{23}{186}\right)\)	\(e\left(\frac{208}{279}\right)\)	\(-1\)	\(e\left(\frac{83}{93}\right)\)	\(e\left(\frac{169}{558}\right)\)	\(e\left(\frac{46}{279}\right)\)
\(\chi_{10053}(43,\cdot)\)	10053.dp	1116	yes	\(-1\)	\(1\)	\(e\left(\frac{131}{1116}\right)\)	\(e\left(\frac{131}{558}\right)\)	\(e\left(\frac{269}{372}\right)\)	\(e\left(\frac{343}{558}\right)\)	\(e\left(\frac{131}{372}\right)\)	\(e\left(\frac{469}{558}\right)\)	\(i\)	\(e\left(\frac{16}{93}\right)\)	\(e\left(\frac{817}{1116}\right)\)	\(e\left(\frac{131}{279}\right)\)
\(\chi_{10053}(44,\cdot)\)	10053.dn	1116	no	\(1\)	\(1\)	\(e\left(\frac{1025}{1116}\right)\)	\(e\left(\frac{467}{558}\right)\)	\(e\left(\frac{223}{372}\right)\)	\(e\left(\frac{439}{558}\right)\)	\(e\left(\frac{281}{372}\right)\)	\(e\left(\frac{289}{558}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{3}{31}\right)\)	\(e\left(\frac{787}{1116}\right)\)	\(e\left(\frac{188}{279}\right)\)
\(\chi_{10053}(46,\cdot)\)	10053.ce	124	no	\(-1\)	\(1\)	\(e\left(\frac{7}{124}\right)\)	\(e\left(\frac{7}{62}\right)\)	\(e\left(\frac{63}{124}\right)\)	\(e\left(\frac{33}{62}\right)\)	\(e\left(\frac{21}{124}\right)\)	\(e\left(\frac{35}{62}\right)\)	\(i\)	\(e\left(\frac{17}{31}\right)\)	\(e\left(\frac{73}{124}\right)\)	\(e\left(\frac{7}{31}\right)\)
\(\chi_{10053}(47,\cdot)\)	10053.cp	186	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{93}\right)\)	\(e\left(\frac{17}{93}\right)\)	\(e\left(\frac{61}{93}\right)\)	\(e\left(\frac{58}{93}\right)\)	\(e\left(\frac{24}{31}\right)\)	\(e\left(\frac{23}{93}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{25}{93}\right)\)	\(e\left(\frac{20}{93}\right)\)	\(e\left(\frac{34}{93}\right)\)

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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.