LMFDB - Group of Dirichlet characters of modulus 8464

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(8464)

gp:g = idealstar(,8464,2)

magma:G = FullDirichletGroup(8464);

Character group

Order	=	4048	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{1012}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{8464}(7407,\cdot)$, $\chi_{8464}(2117,\cdot)$, $\chi_{8464}(6353,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 4048 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8464}(1,\cdot)$	8464.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8464}(3,\cdot)$	8464.bv	1012	yes	$-1$	$1$	$e\left(\frac{259}{1012}\right)$	$e\left(\frac{791}{1012}\right)$	$e\left(\frac{20}{253}\right)$	$e\left(\frac{259}{506}\right)$	$e\left(\frac{453}{1012}\right)$	$e\left(\frac{261}{1012}\right)$	$e\left(\frac{19}{506}\right)$	$e\left(\frac{232}{253}\right)$	$e\left(\frac{535}{1012}\right)$	$e\left(\frac{339}{1012}\right)$
$\chi_{8464}(5,\cdot)$	8464.bu	1012	yes	$-1$	$1$	$e\left(\frac{791}{1012}\right)$	$e\left(\frac{255}{1012}\right)$	$e\left(\frac{191}{253}\right)$	$e\left(\frac{285}{506}\right)$	$e\left(\frac{139}{1012}\right)$	$e\left(\frac{127}{1012}\right)$	$e\left(\frac{17}{506}\right)$	$e\left(\frac{29}{506}\right)$	$e\left(\frac{745}{1012}\right)$	$e\left(\frac{543}{1012}\right)$
$\chi_{8464}(7,\cdot)$	8464.br	506	no	$1$	$1$	$e\left(\frac{20}{253}\right)$	$e\left(\frac{191}{253}\right)$	$e\left(\frac{98}{253}\right)$	$e\left(\frac{40}{253}\right)$	$e\left(\frac{237}{506}\right)$	$e\left(\frac{475}{506}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{199}{506}\right)$	$e\left(\frac{109}{506}\right)$	$e\left(\frac{118}{253}\right)$
$\chi_{8464}(9,\cdot)$	8464.bl	506	no	$1$	$1$	$e\left(\frac{259}{506}\right)$	$e\left(\frac{285}{506}\right)$	$e\left(\frac{40}{253}\right)$	$e\left(\frac{6}{253}\right)$	$e\left(\frac{453}{506}\right)$	$e\left(\frac{261}{506}\right)$	$e\left(\frac{19}{253}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{29}{506}\right)$	$e\left(\frac{339}{506}\right)$
$\chi_{8464}(11,\cdot)$	8464.bs	1012	yes	$1$	$1$	$e\left(\frac{453}{1012}\right)$	$e\left(\frac{139}{1012}\right)$	$e\left(\frac{237}{506}\right)$	$e\left(\frac{453}{506}\right)$	$e\left(\frac{173}{1012}\right)$	$e\left(\frac{351}{1012}\right)$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{371}{506}\right)$	$e\left(\frac{39}{1012}\right)$	$e\left(\frac{927}{1012}\right)$
$\chi_{8464}(13,\cdot)$	8464.bt	1012	yes	$1$	$1$	$e\left(\frac{261}{1012}\right)$	$e\left(\frac{127}{1012}\right)$	$e\left(\frac{475}{506}\right)$	$e\left(\frac{261}{506}\right)$	$e\left(\frac{351}{1012}\right)$	$e\left(\frac{601}{1012}\right)$	$e\left(\frac{97}{253}\right)$	$e\left(\frac{225}{253}\right)$	$e\left(\frac{629}{1012}\right)$	$e\left(\frac{199}{1012}\right)$
$\chi_{8464}(15,\cdot)$	8464.bm	506	no	$1$	$1$	$e\left(\frac{19}{506}\right)$	$e\left(\frac{17}{506}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{19}{253}\right)$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{97}{253}\right)$	$e\left(\frac{18}{253}\right)$	$e\left(\frac{493}{506}\right)$	$e\left(\frac{67}{253}\right)$	$e\left(\frac{441}{506}\right)$
$\chi_{8464}(17,\cdot)$	8464.bp	506	no	$-1$	$1$	$e\left(\frac{232}{253}\right)$	$e\left(\frac{29}{506}\right)$	$e\left(\frac{199}{506}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{371}{506}\right)$	$e\left(\frac{225}{253}\right)$	$e\left(\frac{493}{506}\right)$	$e\left(\frac{335}{506}\right)$	$e\left(\frac{303}{506}\right)$	$e\left(\frac{157}{506}\right)$
$\chi_{8464}(19,\cdot)$	8464.bs	1012	yes	$1$	$1$	$e\left(\frac{535}{1012}\right)$	$e\left(\frac{745}{1012}\right)$	$e\left(\frac{109}{506}\right)$	$e\left(\frac{29}{506}\right)$	$e\left(\frac{39}{1012}\right)$	$e\left(\frac{629}{1012}\right)$	$e\left(\frac{67}{253}\right)$	$e\left(\frac{303}{506}\right)$	$e\left(\frac{857}{1012}\right)$	$e\left(\frac{753}{1012}\right)$
$\chi_{8464}(21,\cdot)$	8464.bu	1012	yes	$-1$	$1$	$e\left(\frac{339}{1012}\right)$	$e\left(\frac{543}{1012}\right)$	$e\left(\frac{118}{253}\right)$	$e\left(\frac{339}{506}\right)$	$e\left(\frac{927}{1012}\right)$	$e\left(\frac{199}{1012}\right)$	$e\left(\frac{441}{506}\right)$	$e\left(\frac{157}{506}\right)$	$e\left(\frac{753}{1012}\right)$	$e\left(\frac{811}{1012}\right)$
$\chi_{8464}(25,\cdot)$	8464.bl	506	no	$1$	$1$	$e\left(\frac{285}{506}\right)$	$e\left(\frac{255}{506}\right)$	$e\left(\frac{129}{253}\right)$	$e\left(\frac{32}{253}\right)$	$e\left(\frac{139}{506}\right)$	$e\left(\frac{127}{506}\right)$	$e\left(\frac{17}{253}\right)$	$e\left(\frac{29}{253}\right)$	$e\left(\frac{239}{506}\right)$	$e\left(\frac{37}{506}\right)$
$\chi_{8464}(27,\cdot)$	8464.bv	1012	yes	$-1$	$1$	$e\left(\frac{777}{1012}\right)$	$e\left(\frac{349}{1012}\right)$	$e\left(\frac{60}{253}\right)$	$e\left(\frac{271}{506}\right)$	$e\left(\frac{347}{1012}\right)$	$e\left(\frac{783}{1012}\right)$	$e\left(\frac{57}{506}\right)$	$e\left(\frac{190}{253}\right)$	$e\left(\frac{593}{1012}\right)$	$e\left(\frac{5}{1012}\right)$
$\chi_{8464}(29,\cdot)$	8464.bt	1012	yes	$1$	$1$	$e\left(\frac{1005}{1012}\right)$	$e\left(\frac{47}{1012}\right)$	$e\left(\frac{375}{506}\right)$	$e\left(\frac{499}{506}\right)$	$e\left(\frac{863}{1012}\right)$	$e\left(\frac{581}{1012}\right)$	$e\left(\frac{10}{253}\right)$	$e\left(\frac{151}{253}\right)$	$e\left(\frac{177}{1012}\right)$	$e\left(\frac{743}{1012}\right)$
$\chi_{8464}(31,\cdot)$	8464.bn	506	no	$-1$	$1$	$e\left(\frac{459}{506}\right)$	$e\left(\frac{212}{253}\right)$	$e\left(\frac{301}{506}\right)$	$e\left(\frac{206}{253}\right)$	$e\left(\frac{373}{506}\right)$	$e\left(\frac{53}{253}\right)$	$e\left(\frac{377}{506}\right)$	$e\left(\frac{76}{253}\right)$	$e\left(\frac{321}{506}\right)$	$e\left(\frac{127}{253}\right)$
$\chi_{8464}(33,\cdot)$	8464.bp	506	no	$-1$	$1$	$e\left(\frac{178}{253}\right)$	$e\left(\frac{465}{506}\right)$	$e\left(\frac{277}{506}\right)$	$e\left(\frac{103}{253}\right)$	$e\left(\frac{313}{506}\right)$	$e\left(\frac{153}{253}\right)$	$e\left(\frac{315}{506}\right)$	$e\left(\frac{329}{506}\right)$	$e\left(\frac{287}{506}\right)$	$e\left(\frac{127}{506}\right)$
$\chi_{8464}(35,\cdot)$	8464.bv	1012	yes	$-1$	$1$	$e\left(\frac{871}{1012}\right)$	$e\left(\frac{7}{1012}\right)$	$e\left(\frac{36}{253}\right)$	$e\left(\frac{365}{506}\right)$	$e\left(\frac{613}{1012}\right)$	$e\left(\frac{65}{1012}\right)$	$e\left(\frac{439}{506}\right)$	$e\left(\frac{114}{253}\right)$	$e\left(\frac{963}{1012}\right)$	$e\left(\frac{3}{1012}\right)$
$\chi_{8464}(37,\cdot)$	8464.bu	1012	yes	$-1$	$1$	$e\left(\frac{551}{1012}\right)$	$e\left(\frac{999}{1012}\right)$	$e\left(\frac{150}{253}\right)$	$e\left(\frac{45}{506}\right)$	$e\left(\frac{235}{1012}\right)$	$e\left(\frac{819}{1012}\right)$	$e\left(\frac{269}{506}\right)$	$e\left(\frac{191}{506}\right)$	$e\left(\frac{597}{1012}\right)$	$e\left(\frac{139}{1012}\right)$
$\chi_{8464}(39,\cdot)$	8464.bq	506	no	$-1$	$1$	$e\left(\frac{130}{253}\right)$	$e\left(\frac{459}{506}\right)$	$e\left(\frac{9}{506}\right)$	$e\left(\frac{7}{253}\right)$	$e\left(\frac{201}{253}\right)$	$e\left(\frac{431}{506}\right)$	$e\left(\frac{213}{506}\right)$	$e\left(\frac{204}{253}\right)$	$e\left(\frac{38}{253}\right)$	$e\left(\frac{269}{506}\right)$
$\chi_{8464}(41,\cdot)$	8464.bl	506	no	$1$	$1$	$e\left(\frac{71}{506}\right)$	$e\left(\frac{463}{506}\right)$	$e\left(\frac{136}{253}\right)$	$e\left(\frac{71}{253}\right)$	$e\left(\frac{427}{506}\right)$	$e\left(\frac{179}{506}\right)$	$e\left(\frac{14}{253}\right)$	$e\left(\frac{9}{253}\right)$	$e\left(\frac{301}{506}\right)$	$e\left(\frac{343}{506}\right)$
$\chi_{8464}(43,\cdot)$	8464.bs	1012	yes	$1$	$1$	$e\left(\frac{105}{1012}\right)$	$e\left(\frac{307}{1012}\right)$	$e\left(\frac{447}{506}\right)$	$e\left(\frac{105}{506}\right)$	$e\left(\frac{717}{1012}\right)$	$e\left(\frac{899}{1012}\right)$	$e\left(\frac{103}{253}\right)$	$e\left(\frac{277}{506}\right)$	$e\left(\frac{887}{1012}\right)$	$e\left(\frac{999}{1012}\right)$
$\chi_{8464}(45,\cdot)$	8464.bh	92	yes	$-1$	$1$	$e\left(\frac{27}{92}\right)$	$e\left(\frac{75}{92}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{3}{92}\right)$	$e\left(\frac{59}{92}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{73}{92}\right)$	$e\left(\frac{19}{92}\right)$
$\chi_{8464}(47,\cdot)$	8464.bd	46	no	$-1$	$1$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{1}{23}\right)$
$\chi_{8464}(49,\cdot)$	8464.bk	253	no	$1$	$1$	$e\left(\frac{40}{253}\right)$	$e\left(\frac{129}{253}\right)$	$e\left(\frac{196}{253}\right)$	$e\left(\frac{80}{253}\right)$	$e\left(\frac{237}{253}\right)$	$e\left(\frac{222}{253}\right)$	$e\left(\frac{169}{253}\right)$	$e\left(\frac{199}{253}\right)$	$e\left(\frac{109}{253}\right)$	$e\left(\frac{236}{253}\right)$
$\chi_{8464}(51,\cdot)$	8464.bs	1012	yes	$1$	$1$	$e\left(\frac{175}{1012}\right)$	$e\left(\frac{849}{1012}\right)$	$e\left(\frac{239}{506}\right)$	$e\left(\frac{175}{506}\right)$	$e\left(\frac{183}{1012}\right)$	$e\left(\frac{149}{1012}\right)$	$e\left(\frac{3}{253}\right)$	$e\left(\frac{293}{506}\right)$	$e\left(\frac{129}{1012}\right)$	$e\left(\frac{653}{1012}\right)$
$\chi_{8464}(53,\cdot)$	8464.bu	1012	yes	$-1$	$1$	$e\left(\frac{399}{1012}\right)$	$e\left(\frac{863}{1012}\right)$	$e\left(\frac{65}{253}\right)$	$e\left(\frac{399}{506}\right)$	$e\left(\frac{903}{1012}\right)$	$e\left(\frac{279}{1012}\right)$	$e\left(\frac{125}{506}\right)$	$e\left(\frac{243}{506}\right)$	$e\left(\frac{537}{1012}\right)$	$e\left(\frac{659}{1012}\right)$
$\chi_{8464}(55,\cdot)$	8464.bq	506	no	$-1$	$1$	$e\left(\frac{58}{253}\right)$	$e\left(\frac{197}{506}\right)$	$e\left(\frac{113}{506}\right)$	$e\left(\frac{116}{253}\right)$	$e\left(\frac{78}{253}\right)$	$e\left(\frac{239}{506}\right)$	$e\left(\frac{313}{506}\right)$	$e\left(\frac{200}{253}\right)$	$e\left(\frac{196}{253}\right)$	$e\left(\frac{229}{506}\right)$
$\chi_{8464}(57,\cdot)$	8464.bo	506	no	$-1$	$1$	$e\left(\frac{397}{506}\right)$	$e\left(\frac{131}{253}\right)$	$e\left(\frac{149}{506}\right)$	$e\left(\frac{144}{253}\right)$	$e\left(\frac{123}{253}\right)$	$e\left(\frac{445}{506}\right)$	$e\left(\frac{153}{506}\right)$	$e\left(\frac{261}{506}\right)$	$e\left(\frac{95}{253}\right)$	$e\left(\frac{20}{253}\right)$
$\chi_{8464}(59,\cdot)$	8464.bv	1012	yes	$-1$	$1$	$e\left(\frac{569}{1012}\right)$	$e\left(\frac{589}{1012}\right)$	$e\left(\frac{210}{253}\right)$	$e\left(\frac{63}{506}\right)$	$e\left(\frac{835}{1012}\right)$	$e\left(\frac{843}{1012}\right)$	$e\left(\frac{73}{506}\right)$	$e\left(\frac{159}{253}\right)$	$e\left(\frac{937}{1012}\right)$	$e\left(\frac{397}{1012}\right)$
$\chi_{8464}(61,\cdot)$	8464.bu	1012	yes	$-1$	$1$	$e\left(\frac{929}{1012}\right)$	$e\left(\frac{485}{1012}\right)$	$e\left(\frac{145}{253}\right)$	$e\left(\frac{423}{506}\right)$	$e\left(\frac{185}{1012}\right)$	$e\left(\frac{817}{1012}\right)$	$e\left(\frac{201}{506}\right)$	$e\left(\frac{75}{506}\right)$	$e\left(\frac{147}{1012}\right)$	$e\left(\frac{497}{1012}\right)$
$\chi_{8464}(63,\cdot)$	8464.s	22	no	$1$	$1$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{8464}(65,\cdot)$	8464.bp	506	no	$-1$	$1$	$e\left(\frac{10}{253}\right)$	$e\left(\frac{191}{506}\right)$	$e\left(\frac{351}{506}\right)$	$e\left(\frac{20}{253}\right)$	$e\left(\frac{245}{506}\right)$	$e\left(\frac{182}{253}\right)$	$e\left(\frac{211}{506}\right)$	$e\left(\frac{479}{506}\right)$	$e\left(\frac{181}{506}\right)$	$e\left(\frac{371}{506}\right)$

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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	$8464$
Structure	\(C_{2}\times C_{2}\times C_{1012}\)
Order	$4048$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8464}(1,\cdot)\)	8464.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8464}(3,\cdot)\)	8464.bv	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{259}{1012}\right)\)	\(e\left(\frac{791}{1012}\right)\)	\(e\left(\frac{20}{253}\right)\)	\(e\left(\frac{259}{506}\right)\)	\(e\left(\frac{453}{1012}\right)\)	\(e\left(\frac{261}{1012}\right)\)	\(e\left(\frac{19}{506}\right)\)	\(e\left(\frac{232}{253}\right)\)	\(e\left(\frac{535}{1012}\right)\)	\(e\left(\frac{339}{1012}\right)\)
\(\chi_{8464}(5,\cdot)\)	8464.bu	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{791}{1012}\right)\)	\(e\left(\frac{255}{1012}\right)\)	\(e\left(\frac{191}{253}\right)\)	\(e\left(\frac{285}{506}\right)\)	\(e\left(\frac{139}{1012}\right)\)	\(e\left(\frac{127}{1012}\right)\)	\(e\left(\frac{17}{506}\right)\)	\(e\left(\frac{29}{506}\right)\)	\(e\left(\frac{745}{1012}\right)\)	\(e\left(\frac{543}{1012}\right)\)
\(\chi_{8464}(7,\cdot)\)	8464.br	506	no	\(1\)	\(1\)	\(e\left(\frac{20}{253}\right)\)	\(e\left(\frac{191}{253}\right)\)	\(e\left(\frac{98}{253}\right)\)	\(e\left(\frac{40}{253}\right)\)	\(e\left(\frac{237}{506}\right)\)	\(e\left(\frac{475}{506}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{199}{506}\right)\)	\(e\left(\frac{109}{506}\right)\)	\(e\left(\frac{118}{253}\right)\)
\(\chi_{8464}(9,\cdot)\)	8464.bl	506	no	\(1\)	\(1\)	\(e\left(\frac{259}{506}\right)\)	\(e\left(\frac{285}{506}\right)\)	\(e\left(\frac{40}{253}\right)\)	\(e\left(\frac{6}{253}\right)\)	\(e\left(\frac{453}{506}\right)\)	\(e\left(\frac{261}{506}\right)\)	\(e\left(\frac{19}{253}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{29}{506}\right)\)	\(e\left(\frac{339}{506}\right)\)
\(\chi_{8464}(11,\cdot)\)	8464.bs	1012	yes	\(1\)	\(1\)	\(e\left(\frac{453}{1012}\right)\)	\(e\left(\frac{139}{1012}\right)\)	\(e\left(\frac{237}{506}\right)\)	\(e\left(\frac{453}{506}\right)\)	\(e\left(\frac{173}{1012}\right)\)	\(e\left(\frac{351}{1012}\right)\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{371}{506}\right)\)	\(e\left(\frac{39}{1012}\right)\)	\(e\left(\frac{927}{1012}\right)\)
\(\chi_{8464}(13,\cdot)\)	8464.bt	1012	yes	\(1\)	\(1\)	\(e\left(\frac{261}{1012}\right)\)	\(e\left(\frac{127}{1012}\right)\)	\(e\left(\frac{475}{506}\right)\)	\(e\left(\frac{261}{506}\right)\)	\(e\left(\frac{351}{1012}\right)\)	\(e\left(\frac{601}{1012}\right)\)	\(e\left(\frac{97}{253}\right)\)	\(e\left(\frac{225}{253}\right)\)	\(e\left(\frac{629}{1012}\right)\)	\(e\left(\frac{199}{1012}\right)\)
\(\chi_{8464}(15,\cdot)\)	8464.bm	506	no	\(1\)	\(1\)	\(e\left(\frac{19}{506}\right)\)	\(e\left(\frac{17}{506}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{19}{253}\right)\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{97}{253}\right)\)	\(e\left(\frac{18}{253}\right)\)	\(e\left(\frac{493}{506}\right)\)	\(e\left(\frac{67}{253}\right)\)	\(e\left(\frac{441}{506}\right)\)
\(\chi_{8464}(17,\cdot)\)	8464.bp	506	no	\(-1\)	\(1\)	\(e\left(\frac{232}{253}\right)\)	\(e\left(\frac{29}{506}\right)\)	\(e\left(\frac{199}{506}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{371}{506}\right)\)	\(e\left(\frac{225}{253}\right)\)	\(e\left(\frac{493}{506}\right)\)	\(e\left(\frac{335}{506}\right)\)	\(e\left(\frac{303}{506}\right)\)	\(e\left(\frac{157}{506}\right)\)
\(\chi_{8464}(19,\cdot)\)	8464.bs	1012	yes	\(1\)	\(1\)	\(e\left(\frac{535}{1012}\right)\)	\(e\left(\frac{745}{1012}\right)\)	\(e\left(\frac{109}{506}\right)\)	\(e\left(\frac{29}{506}\right)\)	\(e\left(\frac{39}{1012}\right)\)	\(e\left(\frac{629}{1012}\right)\)	\(e\left(\frac{67}{253}\right)\)	\(e\left(\frac{303}{506}\right)\)	\(e\left(\frac{857}{1012}\right)\)	\(e\left(\frac{753}{1012}\right)\)
\(\chi_{8464}(21,\cdot)\)	8464.bu	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{339}{1012}\right)\)	\(e\left(\frac{543}{1012}\right)\)	\(e\left(\frac{118}{253}\right)\)	\(e\left(\frac{339}{506}\right)\)	\(e\left(\frac{927}{1012}\right)\)	\(e\left(\frac{199}{1012}\right)\)	\(e\left(\frac{441}{506}\right)\)	\(e\left(\frac{157}{506}\right)\)	\(e\left(\frac{753}{1012}\right)\)	\(e\left(\frac{811}{1012}\right)\)
\(\chi_{8464}(25,\cdot)\)	8464.bl	506	no	\(1\)	\(1\)	\(e\left(\frac{285}{506}\right)\)	\(e\left(\frac{255}{506}\right)\)	\(e\left(\frac{129}{253}\right)\)	\(e\left(\frac{32}{253}\right)\)	\(e\left(\frac{139}{506}\right)\)	\(e\left(\frac{127}{506}\right)\)	\(e\left(\frac{17}{253}\right)\)	\(e\left(\frac{29}{253}\right)\)	\(e\left(\frac{239}{506}\right)\)	\(e\left(\frac{37}{506}\right)\)
\(\chi_{8464}(27,\cdot)\)	8464.bv	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{777}{1012}\right)\)	\(e\left(\frac{349}{1012}\right)\)	\(e\left(\frac{60}{253}\right)\)	\(e\left(\frac{271}{506}\right)\)	\(e\left(\frac{347}{1012}\right)\)	\(e\left(\frac{783}{1012}\right)\)	\(e\left(\frac{57}{506}\right)\)	\(e\left(\frac{190}{253}\right)\)	\(e\left(\frac{593}{1012}\right)\)	\(e\left(\frac{5}{1012}\right)\)
\(\chi_{8464}(29,\cdot)\)	8464.bt	1012	yes	\(1\)	\(1\)	\(e\left(\frac{1005}{1012}\right)\)	\(e\left(\frac{47}{1012}\right)\)	\(e\left(\frac{375}{506}\right)\)	\(e\left(\frac{499}{506}\right)\)	\(e\left(\frac{863}{1012}\right)\)	\(e\left(\frac{581}{1012}\right)\)	\(e\left(\frac{10}{253}\right)\)	\(e\left(\frac{151}{253}\right)\)	\(e\left(\frac{177}{1012}\right)\)	\(e\left(\frac{743}{1012}\right)\)
\(\chi_{8464}(31,\cdot)\)	8464.bn	506	no	\(-1\)	\(1\)	\(e\left(\frac{459}{506}\right)\)	\(e\left(\frac{212}{253}\right)\)	\(e\left(\frac{301}{506}\right)\)	\(e\left(\frac{206}{253}\right)\)	\(e\left(\frac{373}{506}\right)\)	\(e\left(\frac{53}{253}\right)\)	\(e\left(\frac{377}{506}\right)\)	\(e\left(\frac{76}{253}\right)\)	\(e\left(\frac{321}{506}\right)\)	\(e\left(\frac{127}{253}\right)\)
\(\chi_{8464}(33,\cdot)\)	8464.bp	506	no	\(-1\)	\(1\)	\(e\left(\frac{178}{253}\right)\)	\(e\left(\frac{465}{506}\right)\)	\(e\left(\frac{277}{506}\right)\)	\(e\left(\frac{103}{253}\right)\)	\(e\left(\frac{313}{506}\right)\)	\(e\left(\frac{153}{253}\right)\)	\(e\left(\frac{315}{506}\right)\)	\(e\left(\frac{329}{506}\right)\)	\(e\left(\frac{287}{506}\right)\)	\(e\left(\frac{127}{506}\right)\)
\(\chi_{8464}(35,\cdot)\)	8464.bv	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{871}{1012}\right)\)	\(e\left(\frac{7}{1012}\right)\)	\(e\left(\frac{36}{253}\right)\)	\(e\left(\frac{365}{506}\right)\)	\(e\left(\frac{613}{1012}\right)\)	\(e\left(\frac{65}{1012}\right)\)	\(e\left(\frac{439}{506}\right)\)	\(e\left(\frac{114}{253}\right)\)	\(e\left(\frac{963}{1012}\right)\)	\(e\left(\frac{3}{1012}\right)\)
\(\chi_{8464}(37,\cdot)\)	8464.bu	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{551}{1012}\right)\)	\(e\left(\frac{999}{1012}\right)\)	\(e\left(\frac{150}{253}\right)\)	\(e\left(\frac{45}{506}\right)\)	\(e\left(\frac{235}{1012}\right)\)	\(e\left(\frac{819}{1012}\right)\)	\(e\left(\frac{269}{506}\right)\)	\(e\left(\frac{191}{506}\right)\)	\(e\left(\frac{597}{1012}\right)\)	\(e\left(\frac{139}{1012}\right)\)
\(\chi_{8464}(39,\cdot)\)	8464.bq	506	no	\(-1\)	\(1\)	\(e\left(\frac{130}{253}\right)\)	\(e\left(\frac{459}{506}\right)\)	\(e\left(\frac{9}{506}\right)\)	\(e\left(\frac{7}{253}\right)\)	\(e\left(\frac{201}{253}\right)\)	\(e\left(\frac{431}{506}\right)\)	\(e\left(\frac{213}{506}\right)\)	\(e\left(\frac{204}{253}\right)\)	\(e\left(\frac{38}{253}\right)\)	\(e\left(\frac{269}{506}\right)\)
\(\chi_{8464}(41,\cdot)\)	8464.bl	506	no	\(1\)	\(1\)	\(e\left(\frac{71}{506}\right)\)	\(e\left(\frac{463}{506}\right)\)	\(e\left(\frac{136}{253}\right)\)	\(e\left(\frac{71}{253}\right)\)	\(e\left(\frac{427}{506}\right)\)	\(e\left(\frac{179}{506}\right)\)	\(e\left(\frac{14}{253}\right)\)	\(e\left(\frac{9}{253}\right)\)	\(e\left(\frac{301}{506}\right)\)	\(e\left(\frac{343}{506}\right)\)
\(\chi_{8464}(43,\cdot)\)	8464.bs	1012	yes	\(1\)	\(1\)	\(e\left(\frac{105}{1012}\right)\)	\(e\left(\frac{307}{1012}\right)\)	\(e\left(\frac{447}{506}\right)\)	\(e\left(\frac{105}{506}\right)\)	\(e\left(\frac{717}{1012}\right)\)	\(e\left(\frac{899}{1012}\right)\)	\(e\left(\frac{103}{253}\right)\)	\(e\left(\frac{277}{506}\right)\)	\(e\left(\frac{887}{1012}\right)\)	\(e\left(\frac{999}{1012}\right)\)
\(\chi_{8464}(45,\cdot)\)	8464.bh	92	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{92}\right)\)	\(e\left(\frac{75}{92}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{3}{92}\right)\)	\(e\left(\frac{59}{92}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{73}{92}\right)\)	\(e\left(\frac{19}{92}\right)\)
\(\chi_{8464}(47,\cdot)\)	8464.bd	46	no	\(-1\)	\(1\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{1}{23}\right)\)
\(\chi_{8464}(49,\cdot)\)	8464.bk	253	no	\(1\)	\(1\)	\(e\left(\frac{40}{253}\right)\)	\(e\left(\frac{129}{253}\right)\)	\(e\left(\frac{196}{253}\right)\)	\(e\left(\frac{80}{253}\right)\)	\(e\left(\frac{237}{253}\right)\)	\(e\left(\frac{222}{253}\right)\)	\(e\left(\frac{169}{253}\right)\)	\(e\left(\frac{199}{253}\right)\)	\(e\left(\frac{109}{253}\right)\)	\(e\left(\frac{236}{253}\right)\)
\(\chi_{8464}(51,\cdot)\)	8464.bs	1012	yes	\(1\)	\(1\)	\(e\left(\frac{175}{1012}\right)\)	\(e\left(\frac{849}{1012}\right)\)	\(e\left(\frac{239}{506}\right)\)	\(e\left(\frac{175}{506}\right)\)	\(e\left(\frac{183}{1012}\right)\)	\(e\left(\frac{149}{1012}\right)\)	\(e\left(\frac{3}{253}\right)\)	\(e\left(\frac{293}{506}\right)\)	\(e\left(\frac{129}{1012}\right)\)	\(e\left(\frac{653}{1012}\right)\)
\(\chi_{8464}(53,\cdot)\)	8464.bu	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{399}{1012}\right)\)	\(e\left(\frac{863}{1012}\right)\)	\(e\left(\frac{65}{253}\right)\)	\(e\left(\frac{399}{506}\right)\)	\(e\left(\frac{903}{1012}\right)\)	\(e\left(\frac{279}{1012}\right)\)	\(e\left(\frac{125}{506}\right)\)	\(e\left(\frac{243}{506}\right)\)	\(e\left(\frac{537}{1012}\right)\)	\(e\left(\frac{659}{1012}\right)\)
\(\chi_{8464}(55,\cdot)\)	8464.bq	506	no	\(-1\)	\(1\)	\(e\left(\frac{58}{253}\right)\)	\(e\left(\frac{197}{506}\right)\)	\(e\left(\frac{113}{506}\right)\)	\(e\left(\frac{116}{253}\right)\)	\(e\left(\frac{78}{253}\right)\)	\(e\left(\frac{239}{506}\right)\)	\(e\left(\frac{313}{506}\right)\)	\(e\left(\frac{200}{253}\right)\)	\(e\left(\frac{196}{253}\right)\)	\(e\left(\frac{229}{506}\right)\)
\(\chi_{8464}(57,\cdot)\)	8464.bo	506	no	\(-1\)	\(1\)	\(e\left(\frac{397}{506}\right)\)	\(e\left(\frac{131}{253}\right)\)	\(e\left(\frac{149}{506}\right)\)	\(e\left(\frac{144}{253}\right)\)	\(e\left(\frac{123}{253}\right)\)	\(e\left(\frac{445}{506}\right)\)	\(e\left(\frac{153}{506}\right)\)	\(e\left(\frac{261}{506}\right)\)	\(e\left(\frac{95}{253}\right)\)	\(e\left(\frac{20}{253}\right)\)
\(\chi_{8464}(59,\cdot)\)	8464.bv	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{569}{1012}\right)\)	\(e\left(\frac{589}{1012}\right)\)	\(e\left(\frac{210}{253}\right)\)	\(e\left(\frac{63}{506}\right)\)	\(e\left(\frac{835}{1012}\right)\)	\(e\left(\frac{843}{1012}\right)\)	\(e\left(\frac{73}{506}\right)\)	\(e\left(\frac{159}{253}\right)\)	\(e\left(\frac{937}{1012}\right)\)	\(e\left(\frac{397}{1012}\right)\)
\(\chi_{8464}(61,\cdot)\)	8464.bu	1012	yes	\(-1\)	\(1\)	\(e\left(\frac{929}{1012}\right)\)	\(e\left(\frac{485}{1012}\right)\)	\(e\left(\frac{145}{253}\right)\)	\(e\left(\frac{423}{506}\right)\)	\(e\left(\frac{185}{1012}\right)\)	\(e\left(\frac{817}{1012}\right)\)	\(e\left(\frac{201}{506}\right)\)	\(e\left(\frac{75}{506}\right)\)	\(e\left(\frac{147}{1012}\right)\)	\(e\left(\frac{497}{1012}\right)\)
\(\chi_{8464}(63,\cdot)\)	8464.s	22	no	\(1\)	\(1\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{8464}(65,\cdot)\)	8464.bp	506	no	\(-1\)	\(1\)	\(e\left(\frac{10}{253}\right)\)	\(e\left(\frac{191}{506}\right)\)	\(e\left(\frac{351}{506}\right)\)	\(e\left(\frac{20}{253}\right)\)	\(e\left(\frac{245}{506}\right)\)	\(e\left(\frac{182}{253}\right)\)	\(e\left(\frac{211}{506}\right)\)	\(e\left(\frac{479}{506}\right)\)	\(e\left(\frac{181}{506}\right)\)	\(e\left(\frac{371}{506}\right)\)

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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.