LMFDB - Group of Dirichlet characters of modulus 4563

sage:H = DirichletGroup(4563)

pari:g = idealstar(,4563,2)

Character group

sage:G.order() pari:g.no
Order	=	2808
sage:H.invariants() pari:g.cyc
Structure	=	$C_{6}\times C_{468}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{4563}(677,\cdot)$, $\chi_{4563}(3889,\cdot)$

First 32 of 2808 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{4563}(1,\cdot)$	4563.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4563}(2,\cdot)$	4563.dm	468	yes	$1$	$1$	$e\left(\frac{29}{468}\right)$	$e\left(\frac{29}{234}\right)$	$e\left(\frac{157}{468}\right)$	$e\left(\frac{269}{468}\right)$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{179}{468}\right)$	$e\left(\frac{149}{234}\right)$	$e\left(\frac{29}{117}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{4563}(4,\cdot)$	4563.df	234	yes	$1$	$1$	$e\left(\frac{29}{234}\right)$	$e\left(\frac{29}{117}\right)$	$e\left(\frac{157}{234}\right)$	$e\left(\frac{35}{234}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{179}{234}\right)$	$e\left(\frac{32}{117}\right)$	$e\left(\frac{58}{117}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{4563}(5,\cdot)$	4563.do	468	yes	$1$	$1$	$e\left(\frac{157}{468}\right)$	$e\left(\frac{157}{234}\right)$	$e\left(\frac{425}{468}\right)$	$e\left(\frac{289}{468}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{259}{468}\right)$	$e\left(\frac{223}{234}\right)$	$e\left(\frac{40}{117}\right)$	$e\left(\frac{23}{39}\right)$
$\chi_{4563}(7,\cdot)$	4563.dq	468	yes	$-1$	$1$	$e\left(\frac{269}{468}\right)$	$e\left(\frac{35}{234}\right)$	$e\left(\frac{289}{468}\right)$	$e\left(\frac{287}{468}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{95}{468}\right)$	$e\left(\frac{22}{117}\right)$	$e\left(\frac{35}{117}\right)$	$e\left(\frac{37}{78}\right)$
$\chi_{4563}(8,\cdot)$	4563.cz	156	no	$1$	$1$	$e\left(\frac{29}{156}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{1}{156}\right)$	$e\left(\frac{113}{156}\right)$	$e\left(\frac{29}{52}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{4563}(10,\cdot)$	4563.ck	78	no	$1$	$1$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{14}{39}\right)$
$\chi_{4563}(11,\cdot)$	4563.dm	468	yes	$1$	$1$	$e\left(\frac{179}{468}\right)$	$e\left(\frac{179}{234}\right)$	$e\left(\frac{259}{468}\right)$	$e\left(\frac{95}{468}\right)$	$e\left(\frac{23}{156}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{185}{468}\right)$	$e\left(\frac{137}{234}\right)$	$e\left(\frac{62}{117}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{4563}(14,\cdot)$	4563.dg	234	yes	$-1$	$1$	$e\left(\frac{149}{234}\right)$	$e\left(\frac{32}{117}\right)$	$e\left(\frac{223}{234}\right)$	$e\left(\frac{22}{117}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{137}{234}\right)$	$e\left(\frac{193}{234}\right)$	$e\left(\frac{64}{117}\right)$	$e\left(\frac{19}{78}\right)$
$\chi_{4563}(16,\cdot)$	4563.ct	117	yes	$1$	$1$	$e\left(\frac{29}{117}\right)$	$e\left(\frac{58}{117}\right)$	$e\left(\frac{40}{117}\right)$	$e\left(\frac{35}{117}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{62}{117}\right)$	$e\left(\frac{64}{117}\right)$	$e\left(\frac{116}{117}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{4563}(17,\cdot)$	4563.cg	78	no	$-1$	$1$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{14}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{11}{78}\right)$
$\chi_{4563}(19,\cdot)$	4563.be	12	no	$-1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$i$	$i$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{4563}(20,\cdot)$	4563.dr	468	yes	$1$	$1$	$e\left(\frac{215}{468}\right)$	$e\left(\frac{215}{234}\right)$	$e\left(\frac{271}{468}\right)$	$e\left(\frac{359}{468}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{149}{468}\right)$	$e\left(\frac{53}{234}\right)$	$e\left(\frac{98}{117}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{4563}(22,\cdot)$	4563.x	9	no	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$1$
$\chi_{4563}(23,\cdot)$	4563.bk	18	no	$-1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{4563}(25,\cdot)$	4563.dh	234	yes	$1$	$1$	$e\left(\frac{157}{234}\right)$	$e\left(\frac{40}{117}\right)$	$e\left(\frac{191}{234}\right)$	$e\left(\frac{55}{234}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{25}{234}\right)$	$e\left(\frac{106}{117}\right)$	$e\left(\frac{80}{117}\right)$	$e\left(\frac{7}{39}\right)$
$\chi_{4563}(28,\cdot)$	4563.cv	156	no	$-1$	$1$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{151}{156}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{1}{78}\right)$
$\chi_{4563}(29,\cdot)$	4563.di	234	yes	$-1$	$1$	$e\left(\frac{73}{234}\right)$	$e\left(\frac{73}{117}\right)$	$e\left(\frac{137}{234}\right)$	$e\left(\frac{38}{117}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{31}{234}\right)$	$e\left(\frac{149}{234}\right)$	$e\left(\frac{29}{117}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{4563}(31,\cdot)$	4563.dn	468	yes	$-1$	$1$	$e\left(\frac{115}{468}\right)$	$e\left(\frac{115}{234}\right)$	$e\left(\frac{359}{468}\right)$	$e\left(\frac{85}{468}\right)$	$e\left(\frac{115}{156}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{145}{468}\right)$	$e\left(\frac{50}{117}\right)$	$e\left(\frac{115}{117}\right)$	$e\left(\frac{25}{78}\right)$
$\chi_{4563}(32,\cdot)$	4563.dm	468	yes	$1$	$1$	$e\left(\frac{145}{468}\right)$	$e\left(\frac{145}{234}\right)$	$e\left(\frac{317}{468}\right)$	$e\left(\frac{409}{468}\right)$	$e\left(\frac{145}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{427}{468}\right)$	$e\left(\frac{43}{234}\right)$	$e\left(\frac{28}{117}\right)$	$e\left(\frac{11}{13}\right)$
$\chi_{4563}(34,\cdot)$	4563.dn	468	yes	$-1$	$1$	$e\left(\frac{389}{468}\right)$	$e\left(\frac{155}{234}\right)$	$e\left(\frac{433}{468}\right)$	$e\left(\frac{23}{468}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{287}{468}\right)$	$e\left(\frac{103}{117}\right)$	$e\left(\frac{38}{117}\right)$	$e\left(\frac{71}{78}\right)$
$\chi_{4563}(35,\cdot)$	4563.ch	78	no	$-1$	$1$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{5}{78}\right)$
$\chi_{4563}(37,\cdot)$	4563.cx	156	no	$-1$	$1$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{47}{78}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{8}{39}\right)$	$e\left(\frac{25}{78}\right)$
$\chi_{4563}(38,\cdot)$	4563.dk	234	yes	$-1$	$1$	$e\left(\frac{17}{117}\right)$	$e\left(\frac{34}{117}\right)$	$e\left(\frac{49}{117}\right)$	$e\left(\frac{193}{234}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{113}{117}\right)$	$e\left(\frac{227}{234}\right)$	$e\left(\frac{68}{117}\right)$	$e\left(\frac{47}{78}\right)$
$\chi_{4563}(40,\cdot)$	4563.cu	117	yes	$1$	$1$	$e\left(\frac{61}{117}\right)$	$e\left(\frac{5}{117}\right)$	$e\left(\frac{107}{117}\right)$	$e\left(\frac{40}{117}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{17}{39}\right)$	$e\left(\frac{82}{117}\right)$	$e\left(\frac{101}{117}\right)$	$e\left(\frac{10}{117}\right)$	$e\left(\frac{35}{39}\right)$
$\chi_{4563}(41,\cdot)$	4563.dr	468	yes	$1$	$1$	$e\left(\frac{229}{468}\right)$	$e\left(\frac{229}{234}\right)$	$e\left(\frac{293}{468}\right)$	$e\left(\frac{193}{468}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{187}{468}\right)$	$e\left(\frac{211}{234}\right)$	$e\left(\frac{112}{117}\right)$	$e\left(\frac{28}{39}\right)$
$\chi_{4563}(43,\cdot)$	4563.de	234	yes	$1$	$1$	$e\left(\frac{1}{234}\right)$	$e\left(\frac{1}{117}\right)$	$e\left(\frac{35}{234}\right)$	$e\left(\frac{55}{234}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{103}{234}\right)$	$e\left(\frac{28}{117}\right)$	$e\left(\frac{2}{117}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{4563}(44,\cdot)$	4563.cz	156	no	$1$	$1$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{35}{156}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{4563}(46,\cdot)$	4563.cx	156	no	$-1$	$1$	$e\left(\frac{79}{156}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{139}{156}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{25}{156}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{47}{78}\right)$
$\chi_{4563}(47,\cdot)$	4563.do	468	yes	$1$	$1$	$e\left(\frac{371}{468}\right)$	$e\left(\frac{137}{234}\right)$	$e\left(\frac{271}{468}\right)$	$e\left(\frac{203}{468}\right)$	$e\left(\frac{59}{156}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{305}{468}\right)$	$e\left(\frac{53}{234}\right)$	$e\left(\frac{20}{117}\right)$	$e\left(\frac{31}{39}\right)$
$\chi_{4563}(49,\cdot)$	4563.de	234	yes	$1$	$1$	$e\left(\frac{35}{234}\right)$	$e\left(\frac{35}{117}\right)$	$e\left(\frac{55}{234}\right)$	$e\left(\frac{53}{234}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{95}{234}\right)$	$e\left(\frac{44}{117}\right)$	$e\left(\frac{70}{117}\right)$	$e\left(\frac{37}{39}\right)$
$\chi_{4563}(50,\cdot)$	4563.dr	468	yes	$1$	$1$	$e\left(\frac{343}{468}\right)$	$e\left(\frac{109}{234}\right)$	$e\left(\frac{71}{468}\right)$	$e\left(\frac{379}{468}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{229}{468}\right)$	$e\left(\frac{127}{234}\right)$	$e\left(\frac{109}{117}\right)$	$e\left(\frac{37}{39}\right)$

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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	$4563$
Structure	\(C_{6}\times C_{468}\)
Order	$2808$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(14\)	\(16\)	\(17\)
\(\chi_{4563}(1,\cdot)\)	4563.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4563}(2,\cdot)\)	4563.dm	468	yes	\(1\)	\(1\)	\(e\left(\frac{29}{468}\right)\)	\(e\left(\frac{29}{234}\right)\)	\(e\left(\frac{157}{468}\right)\)	\(e\left(\frac{269}{468}\right)\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{179}{468}\right)\)	\(e\left(\frac{149}{234}\right)\)	\(e\left(\frac{29}{117}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{4563}(4,\cdot)\)	4563.df	234	yes	\(1\)	\(1\)	\(e\left(\frac{29}{234}\right)\)	\(e\left(\frac{29}{117}\right)\)	\(e\left(\frac{157}{234}\right)\)	\(e\left(\frac{35}{234}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{179}{234}\right)\)	\(e\left(\frac{32}{117}\right)\)	\(e\left(\frac{58}{117}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{4563}(5,\cdot)\)	4563.do	468	yes	\(1\)	\(1\)	\(e\left(\frac{157}{468}\right)\)	\(e\left(\frac{157}{234}\right)\)	\(e\left(\frac{425}{468}\right)\)	\(e\left(\frac{289}{468}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{259}{468}\right)\)	\(e\left(\frac{223}{234}\right)\)	\(e\left(\frac{40}{117}\right)\)	\(e\left(\frac{23}{39}\right)\)
\(\chi_{4563}(7,\cdot)\)	4563.dq	468	yes	\(-1\)	\(1\)	\(e\left(\frac{269}{468}\right)\)	\(e\left(\frac{35}{234}\right)\)	\(e\left(\frac{289}{468}\right)\)	\(e\left(\frac{287}{468}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{95}{468}\right)\)	\(e\left(\frac{22}{117}\right)\)	\(e\left(\frac{35}{117}\right)\)	\(e\left(\frac{37}{78}\right)\)
\(\chi_{4563}(8,\cdot)\)	4563.cz	156	no	\(1\)	\(1\)	\(e\left(\frac{29}{156}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{1}{156}\right)\)	\(e\left(\frac{113}{156}\right)\)	\(e\left(\frac{29}{52}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{4563}(10,\cdot)\)	4563.ck	78	no	\(1\)	\(1\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)
\(\chi_{4563}(11,\cdot)\)	4563.dm	468	yes	\(1\)	\(1\)	\(e\left(\frac{179}{468}\right)\)	\(e\left(\frac{179}{234}\right)\)	\(e\left(\frac{259}{468}\right)\)	\(e\left(\frac{95}{468}\right)\)	\(e\left(\frac{23}{156}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{185}{468}\right)\)	\(e\left(\frac{137}{234}\right)\)	\(e\left(\frac{62}{117}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{4563}(14,\cdot)\)	4563.dg	234	yes	\(-1\)	\(1\)	\(e\left(\frac{149}{234}\right)\)	\(e\left(\frac{32}{117}\right)\)	\(e\left(\frac{223}{234}\right)\)	\(e\left(\frac{22}{117}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{137}{234}\right)\)	\(e\left(\frac{193}{234}\right)\)	\(e\left(\frac{64}{117}\right)\)	\(e\left(\frac{19}{78}\right)\)
\(\chi_{4563}(16,\cdot)\)	4563.ct	117	yes	\(1\)	\(1\)	\(e\left(\frac{29}{117}\right)\)	\(e\left(\frac{58}{117}\right)\)	\(e\left(\frac{40}{117}\right)\)	\(e\left(\frac{35}{117}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{62}{117}\right)\)	\(e\left(\frac{64}{117}\right)\)	\(e\left(\frac{116}{117}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{4563}(17,\cdot)\)	4563.cg	78	no	\(-1\)	\(1\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{11}{78}\right)\)
\(\chi_{4563}(19,\cdot)\)	4563.be	12	no	\(-1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(i\)	\(i\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{4563}(20,\cdot)\)	4563.dr	468	yes	\(1\)	\(1\)	\(e\left(\frac{215}{468}\right)\)	\(e\left(\frac{215}{234}\right)\)	\(e\left(\frac{271}{468}\right)\)	\(e\left(\frac{359}{468}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{149}{468}\right)\)	\(e\left(\frac{53}{234}\right)\)	\(e\left(\frac{98}{117}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{4563}(22,\cdot)\)	4563.x	9	no	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)
\(\chi_{4563}(23,\cdot)\)	4563.bk	18	no	\(-1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{4563}(25,\cdot)\)	4563.dh	234	yes	\(1\)	\(1\)	\(e\left(\frac{157}{234}\right)\)	\(e\left(\frac{40}{117}\right)\)	\(e\left(\frac{191}{234}\right)\)	\(e\left(\frac{55}{234}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{25}{234}\right)\)	\(e\left(\frac{106}{117}\right)\)	\(e\left(\frac{80}{117}\right)\)	\(e\left(\frac{7}{39}\right)\)
\(\chi_{4563}(28,\cdot)\)	4563.cv	156	no	\(-1\)	\(1\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{15}{52}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{151}{156}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{1}{78}\right)\)
\(\chi_{4563}(29,\cdot)\)	4563.di	234	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{234}\right)\)	\(e\left(\frac{73}{117}\right)\)	\(e\left(\frac{137}{234}\right)\)	\(e\left(\frac{38}{117}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{31}{234}\right)\)	\(e\left(\frac{149}{234}\right)\)	\(e\left(\frac{29}{117}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{4563}(31,\cdot)\)	4563.dn	468	yes	\(-1\)	\(1\)	\(e\left(\frac{115}{468}\right)\)	\(e\left(\frac{115}{234}\right)\)	\(e\left(\frac{359}{468}\right)\)	\(e\left(\frac{85}{468}\right)\)	\(e\left(\frac{115}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{145}{468}\right)\)	\(e\left(\frac{50}{117}\right)\)	\(e\left(\frac{115}{117}\right)\)	\(e\left(\frac{25}{78}\right)\)
\(\chi_{4563}(32,\cdot)\)	4563.dm	468	yes	\(1\)	\(1\)	\(e\left(\frac{145}{468}\right)\)	\(e\left(\frac{145}{234}\right)\)	\(e\left(\frac{317}{468}\right)\)	\(e\left(\frac{409}{468}\right)\)	\(e\left(\frac{145}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{427}{468}\right)\)	\(e\left(\frac{43}{234}\right)\)	\(e\left(\frac{28}{117}\right)\)	\(e\left(\frac{11}{13}\right)\)
\(\chi_{4563}(34,\cdot)\)	4563.dn	468	yes	\(-1\)	\(1\)	\(e\left(\frac{389}{468}\right)\)	\(e\left(\frac{155}{234}\right)\)	\(e\left(\frac{433}{468}\right)\)	\(e\left(\frac{23}{468}\right)\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{287}{468}\right)\)	\(e\left(\frac{103}{117}\right)\)	\(e\left(\frac{38}{117}\right)\)	\(e\left(\frac{71}{78}\right)\)
\(\chi_{4563}(35,\cdot)\)	4563.ch	78	no	\(-1\)	\(1\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{5}{78}\right)\)
\(\chi_{4563}(37,\cdot)\)	4563.cx	156	no	\(-1\)	\(1\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{47}{78}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{8}{39}\right)\)	\(e\left(\frac{25}{78}\right)\)
\(\chi_{4563}(38,\cdot)\)	4563.dk	234	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{117}\right)\)	\(e\left(\frac{34}{117}\right)\)	\(e\left(\frac{49}{117}\right)\)	\(e\left(\frac{193}{234}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{113}{117}\right)\)	\(e\left(\frac{227}{234}\right)\)	\(e\left(\frac{68}{117}\right)\)	\(e\left(\frac{47}{78}\right)\)
\(\chi_{4563}(40,\cdot)\)	4563.cu	117	yes	\(1\)	\(1\)	\(e\left(\frac{61}{117}\right)\)	\(e\left(\frac{5}{117}\right)\)	\(e\left(\frac{107}{117}\right)\)	\(e\left(\frac{40}{117}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{82}{117}\right)\)	\(e\left(\frac{101}{117}\right)\)	\(e\left(\frac{10}{117}\right)\)	\(e\left(\frac{35}{39}\right)\)
\(\chi_{4563}(41,\cdot)\)	4563.dr	468	yes	\(1\)	\(1\)	\(e\left(\frac{229}{468}\right)\)	\(e\left(\frac{229}{234}\right)\)	\(e\left(\frac{293}{468}\right)\)	\(e\left(\frac{193}{468}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{187}{468}\right)\)	\(e\left(\frac{211}{234}\right)\)	\(e\left(\frac{112}{117}\right)\)	\(e\left(\frac{28}{39}\right)\)
\(\chi_{4563}(43,\cdot)\)	4563.de	234	yes	\(1\)	\(1\)	\(e\left(\frac{1}{234}\right)\)	\(e\left(\frac{1}{117}\right)\)	\(e\left(\frac{35}{234}\right)\)	\(e\left(\frac{55}{234}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{103}{234}\right)\)	\(e\left(\frac{28}{117}\right)\)	\(e\left(\frac{2}{117}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{4563}(44,\cdot)\)	4563.cz	156	no	\(1\)	\(1\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{35}{156}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{4563}(46,\cdot)\)	4563.cx	156	no	\(-1\)	\(1\)	\(e\left(\frac{79}{156}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{139}{156}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{25}{156}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{47}{78}\right)\)
\(\chi_{4563}(47,\cdot)\)	4563.do	468	yes	\(1\)	\(1\)	\(e\left(\frac{371}{468}\right)\)	\(e\left(\frac{137}{234}\right)\)	\(e\left(\frac{271}{468}\right)\)	\(e\left(\frac{203}{468}\right)\)	\(e\left(\frac{59}{156}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{305}{468}\right)\)	\(e\left(\frac{53}{234}\right)\)	\(e\left(\frac{20}{117}\right)\)	\(e\left(\frac{31}{39}\right)\)
\(\chi_{4563}(49,\cdot)\)	4563.de	234	yes	\(1\)	\(1\)	\(e\left(\frac{35}{234}\right)\)	\(e\left(\frac{35}{117}\right)\)	\(e\left(\frac{55}{234}\right)\)	\(e\left(\frac{53}{234}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{95}{234}\right)\)	\(e\left(\frac{44}{117}\right)\)	\(e\left(\frac{70}{117}\right)\)	\(e\left(\frac{37}{39}\right)\)
\(\chi_{4563}(50,\cdot)\)	4563.dr	468	yes	\(1\)	\(1\)	\(e\left(\frac{343}{468}\right)\)	\(e\left(\frac{109}{234}\right)\)	\(e\left(\frac{71}{468}\right)\)	\(e\left(\frac{379}{468}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{229}{468}\right)\)	\(e\left(\frac{127}{234}\right)\)	\(e\left(\frac{109}{117}\right)\)	\(e\left(\frac{37}{39}\right)\)

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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.