LMFDB - Group of Dirichlet characters of modulus 186576

sage:H = DirichletGroup(186576)

pari:g = idealstar(,186576,2)

Character group

sage:G.order() pari:g.no
Order	=	54912
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{1716}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{186576}(69967,\cdot)$, $\chi_{186576}(46645,\cdot)$, $\chi_{186576}(124385,\cdot)$, $\chi_{186576}(85009,\cdot)$, $\chi_{186576}(48673,\cdot)$

First 32 of 54912 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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$25$	$29$	$31$	$35$	$37$
$\chi_{186576}(1,\cdot)$	186576.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{186576}(5,\cdot)$	186576.vh	572	yes	$-1$	$1$	$e\left(\frac{45}{143}\right)$	$e\left(\frac{307}{572}\right)$	$e\left(\frac{29}{286}\right)$	$e\left(\frac{69}{286}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{90}{143}\right)$	$e\left(\frac{215}{572}\right)$	$e\left(\frac{277}{572}\right)$	$e\left(\frac{487}{572}\right)$	$e\left(\frac{131}{143}\right)$
$\chi_{186576}(7,\cdot)$	186576.xp	1716	no	$-1$	$1$	$e\left(\frac{307}{572}\right)$	$e\left(\frac{515}{1716}\right)$	$e\left(\frac{721}{1716}\right)$	$e\left(\frac{80}{429}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{21}{286}\right)$	$e\left(\frac{413}{858}\right)$	$e\left(\frac{49}{572}\right)$	$e\left(\frac{359}{429}\right)$	$e\left(\frac{355}{1716}\right)$
$\chi_{186576}(11,\cdot)$	186576.xb	1716	yes	$1$	$1$	$e\left(\frac{29}{286}\right)$	$e\left(\frac{721}{1716}\right)$	$e\left(\frac{805}{858}\right)$	$e\left(\frac{653}{858}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{29}{143}\right)$	$e\left(\frac{41}{1716}\right)$	$e\left(\frac{469}{572}\right)$	$e\left(\frac{895}{1716}\right)$	$e\left(\frac{463}{858}\right)$
$\chi_{186576}(17,\cdot)$	186576.vu	858	no	$1$	$1$	$e\left(\frac{69}{286}\right)$	$e\left(\frac{80}{429}\right)$	$e\left(\frac{653}{858}\right)$	$e\left(\frac{158}{429}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{69}{143}\right)$	$e\left(\frac{569}{858}\right)$	$e\left(\frac{161}{286}\right)$	$e\left(\frac{367}{858}\right)$	$e\left(\frac{1}{429}\right)$
$\chi_{186576}(19,\cdot)$	186576.pb	132	no	$-1$	$1$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{71}{132}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{65}{66}\right)$
$\chi_{186576}(25,\cdot)$	186576.tj	286	no	$1$	$1$	$e\left(\frac{90}{143}\right)$	$e\left(\frac{21}{286}\right)$	$e\left(\frac{29}{143}\right)$	$e\left(\frac{69}{143}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{37}{143}\right)$	$e\left(\frac{215}{286}\right)$	$e\left(\frac{277}{286}\right)$	$e\left(\frac{201}{286}\right)$	$e\left(\frac{119}{143}\right)$
$\chi_{186576}(29,\cdot)$	186576.yg	1716	yes	$-1$	$1$	$e\left(\frac{215}{572}\right)$	$e\left(\frac{413}{858}\right)$	$e\left(\frac{41}{1716}\right)$	$e\left(\frac{569}{858}\right)$	$e\left(\frac{25}{132}\right)$	$e\left(\frac{215}{286}\right)$	$e\left(\frac{1259}{1716}\right)$	$e\left(\frac{42}{143}\right)$	$e\left(\frac{1471}{1716}\right)$	$e\left(\frac{1115}{1716}\right)$
$\chi_{186576}(31,\cdot)$	186576.uo	572	no	$1$	$1$	$e\left(\frac{277}{572}\right)$	$e\left(\frac{49}{572}\right)$	$e\left(\frac{469}{572}\right)$	$e\left(\frac{161}{286}\right)$	$e\left(\frac{15}{44}\right)$	$e\left(\frac{277}{286}\right)$	$e\left(\frac{42}{143}\right)$	$e\left(\frac{551}{572}\right)$	$e\left(\frac{163}{286}\right)$	$e\left(\frac{31}{572}\right)$
$\chi_{186576}(35,\cdot)$	186576.xg	1716	yes	$1$	$1$	$e\left(\frac{487}{572}\right)$	$e\left(\frac{359}{429}\right)$	$e\left(\frac{895}{1716}\right)$	$e\left(\frac{367}{858}\right)$	$e\left(\frac{95}{132}\right)$	$e\left(\frac{201}{286}\right)$	$e\left(\frac{1471}{1716}\right)$	$e\left(\frac{163}{286}\right)$	$e\left(\frac{1181}{1716}\right)$	$e\left(\frac{211}{1716}\right)$
$\chi_{186576}(37,\cdot)$	186576.ym	1716	no	$1$	$1$	$e\left(\frac{131}{143}\right)$	$e\left(\frac{355}{1716}\right)$	$e\left(\frac{463}{858}\right)$	$e\left(\frac{1}{429}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{119}{143}\right)$	$e\left(\frac{1115}{1716}\right)$	$e\left(\frac{31}{572}\right)$	$e\left(\frac{211}{1716}\right)$	$e\left(\frac{391}{858}\right)$
$\chi_{186576}(41,\cdot)$	186576.xl	1716	no	$1$	$1$	$e\left(\frac{257}{572}\right)$	$e\left(\frac{1141}{1716}\right)$	$e\left(\frac{53}{1716}\right)$	$e\left(\frac{373}{429}\right)$	$e\left(\frac{13}{132}\right)$	$e\left(\frac{257}{286}\right)$	$e\left(\frac{263}{429}\right)$	$e\left(\frac{409}{572}\right)$	$e\left(\frac{49}{429}\right)$	$e\left(\frac{395}{1716}\right)$
$\chi_{186576}(43,\cdot)$	186576.xi	1716	no	$1$	$1$	$e\left(\frac{295}{572}\right)$	$e\left(\frac{428}{429}\right)$	$e\left(\frac{595}{1716}\right)$	$e\left(\frac{661}{858}\right)$	$e\left(\frac{65}{132}\right)$	$e\left(\frac{9}{286}\right)$	$e\left(\frac{211}{1716}\right)$	$e\left(\frac{41}{143}\right)$	$e\left(\frac{881}{1716}\right)$	$e\left(\frac{193}{1716}\right)$
$\chi_{186576}(47,\cdot)$	186576.lj	52	no	$-1$	$1$	$e\left(\frac{7}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{6}{13}\right)$	$-i$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{51}{52}\right)$
$\chi_{186576}(49,\cdot)$	186576.wb	858	no	$1$	$1$	$e\left(\frac{21}{286}\right)$	$e\left(\frac{515}{858}\right)$	$e\left(\frac{721}{858}\right)$	$e\left(\frac{160}{429}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{21}{143}\right)$	$e\left(\frac{413}{429}\right)$	$e\left(\frac{49}{286}\right)$	$e\left(\frac{289}{429}\right)$	$e\left(\frac{355}{858}\right)$
$\chi_{186576}(53,\cdot)$	186576.vg	572	yes	$1$	$1$	$e\left(\frac{307}{572}\right)$	$e\left(\frac{31}{143}\right)$	$e\left(\frac{431}{572}\right)$	$e\left(\frac{122}{143}\right)$	$e\left(\frac{31}{44}\right)$	$e\left(\frac{21}{286}\right)$	$e\left(\frac{323}{572}\right)$	$e\left(\frac{48}{143}\right)$	$e\left(\frac{431}{572}\right)$	$e\left(\frac{309}{572}\right)$
$\chi_{186576}(55,\cdot)$	186576.vy	858	no	$-1$	$1$	$e\left(\frac{119}{286}\right)$	$e\left(\frac{821}{858}\right)$	$e\left(\frac{17}{429}\right)$	$e\left(\frac{1}{429}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{119}{143}\right)$	$e\left(\frac{343}{858}\right)$	$e\left(\frac{87}{286}\right)$	$e\left(\frac{160}{429}\right)$	$e\left(\frac{391}{858}\right)$
$\chi_{186576}(59,\cdot)$	186576.yi	1716	yes	$-1$	$1$	$e\left(\frac{58}{143}\right)$	$e\left(\frac{167}{1716}\right)$	$e\left(\frac{37}{429}\right)$	$e\left(\frac{305}{429}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{116}{143}\right)$	$e\left(\frac{1165}{1716}\right)$	$e\left(\frac{17}{572}\right)$	$e\left(\frac{863}{1716}\right)$	$e\left(\frac{211}{429}\right)$
$\chi_{186576}(61,\cdot)$	186576.xj	1716	no	$-1$	$1$	$e\left(\frac{343}{572}\right)$	$e\left(\frac{89}{429}\right)$	$e\left(\frac{241}{1716}\right)$	$e\left(\frac{373}{858}\right)$	$e\left(\frac{23}{132}\right)$	$e\left(\frac{57}{286}\right)$	$e\left(\frac{97}{1716}\right)$	$e\left(\frac{69}{143}\right)$	$e\left(\frac{1385}{1716}\right)$	$e\left(\frac{841}{1716}\right)$
$\chi_{186576}(67,\cdot)$	186576.yj	1716	no	$-1$	$1$	$e\left(\frac{68}{143}\right)$	$e\left(\frac{1039}{1716}\right)$	$e\left(\frac{428}{429}\right)$	$e\left(\frac{328}{429}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{136}{143}\right)$	$e\left(\frac{641}{1716}\right)$	$e\left(\frac{15}{572}\right)$	$e\left(\frac{139}{1716}\right)$	$e\left(\frac{835}{858}\right)$
$\chi_{186576}(71,\cdot)$	186576.xn	1716	no	$-1$	$1$	$e\left(\frac{569}{572}\right)$	$e\left(\frac{335}{1716}\right)$	$e\left(\frac{1327}{1716}\right)$	$e\left(\frac{152}{429}\right)$	$e\left(\frac{59}{132}\right)$	$e\left(\frac{283}{286}\right)$	$e\left(\frac{328}{429}\right)$	$e\left(\frac{279}{572}\right)$	$e\left(\frac{163}{858}\right)$	$e\left(\frac{31}{1716}\right)$
$\chi_{186576}(73,\cdot)$	186576.uj	572	no	$-1$	$1$	$e\left(\frac{357}{572}\right)$	$e\left(\frac{249}{572}\right)$	$e\left(\frac{463}{572}\right)$	$e\left(\frac{1}{286}\right)$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{71}{286}\right)$	$e\left(\frac{243}{286}\right)$	$e\left(\frac{547}{572}\right)$	$e\left(\frac{17}{286}\right)$	$e\left(\frac{391}{572}\right)$
$\chi_{186576}(77,\cdot)$	186576.uz	572	yes	$-1$	$1$	$e\left(\frac{365}{572}\right)$	$e\left(\frac{103}{143}\right)$	$e\left(\frac{205}{572}\right)$	$e\left(\frac{271}{286}\right)$	$e\left(\frac{37}{44}\right)$	$e\left(\frac{79}{286}\right)$	$e\left(\frac{289}{572}\right)$	$e\left(\frac{259}{286}\right)$	$e\left(\frac{205}{572}\right)$	$e\left(\frac{427}{572}\right)$
$\chi_{186576}(79,\cdot)$	186576.sz	286	no	$1$	$1$	$e\left(\frac{149}{286}\right)$	$e\left(\frac{79}{143}\right)$	$e\left(\frac{82}{143}\right)$	$e\left(\frac{119}{286}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{6}{143}\right)$	$e\left(\frac{87}{143}\right)$	$e\left(\frac{157}{286}\right)$	$e\left(\frac{21}{286}\right)$	$e\left(\frac{27}{286}\right)$
$\chi_{186576}(83,\cdot)$	186576.tt	572	yes	$1$	$1$	$e\left(\frac{229}{286}\right)$	$e\left(\frac{1}{572}\right)$	$e\left(\frac{15}{286}\right)$	$e\left(\frac{85}{286}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{86}{143}\right)$	$e\left(\frac{269}{572}\right)$	$e\left(\frac{163}{572}\right)$	$e\left(\frac{459}{572}\right)$	$e\left(\frac{101}{286}\right)$
$\chi_{186576}(85,\cdot)$	186576.wx	1716	no	$-1$	$1$	$e\left(\frac{159}{286}\right)$	$e\left(\frac{1241}{1716}\right)$	$e\left(\frac{370}{429}\right)$	$e\left(\frac{523}{858}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{16}{143}\right)$	$e\left(\frac{67}{1716}\right)$	$e\left(\frac{27}{572}\right)$	$e\left(\frac{479}{1716}\right)$	$e\left(\frac{394}{429}\right)$
$\chi_{186576}(89,\cdot)$	186576.pr	132	no	$-1$	$1$	$e\left(\frac{21}{44}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{17}{132}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{109}{132}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{27}{44}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{47}{132}\right)$
$\chi_{186576}(95,\cdot)$	186576.wl	858	no	$1$	$1$	$e\left(\frac{71}{143}\right)$	$e\left(\frac{32}{429}\right)$	$e\left(\frac{347}{858}\right)$	$e\left(\frac{727}{858}\right)$	$e\left(\frac{8}{33}\right)$	$e\left(\frac{142}{143}\right)$	$e\left(\frac{485}{858}\right)$	$e\left(\frac{118}{143}\right)$	$e\left(\frac{245}{429}\right)$	$e\left(\frac{773}{858}\right)$
$\chi_{186576}(97,\cdot)$	186576.xk	1716	no	$1$	$1$	$e\left(\frac{15}{572}\right)$	$e\left(\frac{899}{1716}\right)$	$e\left(\frac{1087}{1716}\right)$	$e\left(\frac{98}{429}\right)$	$e\left(\frac{101}{132}\right)$	$e\left(\frac{15}{286}\right)$	$e\left(\frac{76}{429}\right)$	$e\left(\frac{321}{572}\right)$	$e\left(\frac{236}{429}\right)$	$e\left(\frac{703}{1716}\right)$
$\chi_{186576}(101,\cdot)$	186576.xh	1716	yes	$-1$	$1$	$e\left(\frac{139}{572}\right)$	$e\left(\frac{64}{429}\right)$	$e\left(\frac{101}{1716}\right)$	$e\left(\frac{167}{858}\right)$	$e\left(\frac{97}{132}\right)$	$e\left(\frac{139}{286}\right)$	$e\left(\frac{653}{1716}\right)$	$e\left(\frac{43}{286}\right)$	$e\left(\frac{673}{1716}\right)$	$e\left(\frac{947}{1716}\right)$
$\chi_{186576}(103,\cdot)$	186576.sr	286	no	$1$	$1$	$e\left(\frac{161}{286}\right)$	$e\left(\frac{45}{286}\right)$	$e\left(\frac{103}{143}\right)$	$e\left(\frac{71}{286}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{18}{143}\right)$	$e\left(\frac{93}{286}\right)$	$e\left(\frac{21}{143}\right)$	$e\left(\frac{103}{143}\right)$	$e\left(\frac{81}{286}\right)$
$\chi_{186576}(107,\cdot)$	186576.ya	1716	yes	$-1$	$1$	$e\left(\frac{167}{572}\right)$	$e\left(\frac{233}{858}\right)$	$e\left(\frac{395}{1716}\right)$	$e\left(\frac{214}{429}\right)$	$e\left(\frac{67}{132}\right)$	$e\left(\frac{167}{286}\right)$	$e\left(\frac{1373}{1716}\right)$	$e\left(\frac{171}{286}\right)$	$e\left(\frac{967}{1716}\right)$	$e\left(\frac{467}{1716}\right)$

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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	$186576$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{4}\times C_{1716}\)
Order	$54912$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(25\)	\(29\)	\(31\)	\(35\)	\(37\)
\(\chi_{186576}(1,\cdot)\)	186576.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{186576}(5,\cdot)\)	186576.vh	572	yes	\(-1\)	\(1\)	\(e\left(\frac{45}{143}\right)\)	\(e\left(\frac{307}{572}\right)\)	\(e\left(\frac{29}{286}\right)\)	\(e\left(\frac{69}{286}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{90}{143}\right)\)	\(e\left(\frac{215}{572}\right)\)	\(e\left(\frac{277}{572}\right)\)	\(e\left(\frac{487}{572}\right)\)	\(e\left(\frac{131}{143}\right)\)
\(\chi_{186576}(7,\cdot)\)	186576.xp	1716	no	\(-1\)	\(1\)	\(e\left(\frac{307}{572}\right)\)	\(e\left(\frac{515}{1716}\right)\)	\(e\left(\frac{721}{1716}\right)\)	\(e\left(\frac{80}{429}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{21}{286}\right)\)	\(e\left(\frac{413}{858}\right)\)	\(e\left(\frac{49}{572}\right)\)	\(e\left(\frac{359}{429}\right)\)	\(e\left(\frac{355}{1716}\right)\)
\(\chi_{186576}(11,\cdot)\)	186576.xb	1716	yes	\(1\)	\(1\)	\(e\left(\frac{29}{286}\right)\)	\(e\left(\frac{721}{1716}\right)\)	\(e\left(\frac{805}{858}\right)\)	\(e\left(\frac{653}{858}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{29}{143}\right)\)	\(e\left(\frac{41}{1716}\right)\)	\(e\left(\frac{469}{572}\right)\)	\(e\left(\frac{895}{1716}\right)\)	\(e\left(\frac{463}{858}\right)\)
\(\chi_{186576}(17,\cdot)\)	186576.vu	858	no	\(1\)	\(1\)	\(e\left(\frac{69}{286}\right)\)	\(e\left(\frac{80}{429}\right)\)	\(e\left(\frac{653}{858}\right)\)	\(e\left(\frac{158}{429}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{69}{143}\right)\)	\(e\left(\frac{569}{858}\right)\)	\(e\left(\frac{161}{286}\right)\)	\(e\left(\frac{367}{858}\right)\)	\(e\left(\frac{1}{429}\right)\)
\(\chi_{186576}(19,\cdot)\)	186576.pb	132	no	\(-1\)	\(1\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{71}{132}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{65}{66}\right)\)
\(\chi_{186576}(25,\cdot)\)	186576.tj	286	no	\(1\)	\(1\)	\(e\left(\frac{90}{143}\right)\)	\(e\left(\frac{21}{286}\right)\)	\(e\left(\frac{29}{143}\right)\)	\(e\left(\frac{69}{143}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{37}{143}\right)\)	\(e\left(\frac{215}{286}\right)\)	\(e\left(\frac{277}{286}\right)\)	\(e\left(\frac{201}{286}\right)\)	\(e\left(\frac{119}{143}\right)\)
\(\chi_{186576}(29,\cdot)\)	186576.yg	1716	yes	\(-1\)	\(1\)	\(e\left(\frac{215}{572}\right)\)	\(e\left(\frac{413}{858}\right)\)	\(e\left(\frac{41}{1716}\right)\)	\(e\left(\frac{569}{858}\right)\)	\(e\left(\frac{25}{132}\right)\)	\(e\left(\frac{215}{286}\right)\)	\(e\left(\frac{1259}{1716}\right)\)	\(e\left(\frac{42}{143}\right)\)	\(e\left(\frac{1471}{1716}\right)\)	\(e\left(\frac{1115}{1716}\right)\)
\(\chi_{186576}(31,\cdot)\)	186576.uo	572	no	\(1\)	\(1\)	\(e\left(\frac{277}{572}\right)\)	\(e\left(\frac{49}{572}\right)\)	\(e\left(\frac{469}{572}\right)\)	\(e\left(\frac{161}{286}\right)\)	\(e\left(\frac{15}{44}\right)\)	\(e\left(\frac{277}{286}\right)\)	\(e\left(\frac{42}{143}\right)\)	\(e\left(\frac{551}{572}\right)\)	\(e\left(\frac{163}{286}\right)\)	\(e\left(\frac{31}{572}\right)\)
\(\chi_{186576}(35,\cdot)\)	186576.xg	1716	yes	\(1\)	\(1\)	\(e\left(\frac{487}{572}\right)\)	\(e\left(\frac{359}{429}\right)\)	\(e\left(\frac{895}{1716}\right)\)	\(e\left(\frac{367}{858}\right)\)	\(e\left(\frac{95}{132}\right)\)	\(e\left(\frac{201}{286}\right)\)	\(e\left(\frac{1471}{1716}\right)\)	\(e\left(\frac{163}{286}\right)\)	\(e\left(\frac{1181}{1716}\right)\)	\(e\left(\frac{211}{1716}\right)\)
\(\chi_{186576}(37,\cdot)\)	186576.ym	1716	no	\(1\)	\(1\)	\(e\left(\frac{131}{143}\right)\)	\(e\left(\frac{355}{1716}\right)\)	\(e\left(\frac{463}{858}\right)\)	\(e\left(\frac{1}{429}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{119}{143}\right)\)	\(e\left(\frac{1115}{1716}\right)\)	\(e\left(\frac{31}{572}\right)\)	\(e\left(\frac{211}{1716}\right)\)	\(e\left(\frac{391}{858}\right)\)
\(\chi_{186576}(41,\cdot)\)	186576.xl	1716	no	\(1\)	\(1\)	\(e\left(\frac{257}{572}\right)\)	\(e\left(\frac{1141}{1716}\right)\)	\(e\left(\frac{53}{1716}\right)\)	\(e\left(\frac{373}{429}\right)\)	\(e\left(\frac{13}{132}\right)\)	\(e\left(\frac{257}{286}\right)\)	\(e\left(\frac{263}{429}\right)\)	\(e\left(\frac{409}{572}\right)\)	\(e\left(\frac{49}{429}\right)\)	\(e\left(\frac{395}{1716}\right)\)
\(\chi_{186576}(43,\cdot)\)	186576.xi	1716	no	\(1\)	\(1\)	\(e\left(\frac{295}{572}\right)\)	\(e\left(\frac{428}{429}\right)\)	\(e\left(\frac{595}{1716}\right)\)	\(e\left(\frac{661}{858}\right)\)	\(e\left(\frac{65}{132}\right)\)	\(e\left(\frac{9}{286}\right)\)	\(e\left(\frac{211}{1716}\right)\)	\(e\left(\frac{41}{143}\right)\)	\(e\left(\frac{881}{1716}\right)\)	\(e\left(\frac{193}{1716}\right)\)
\(\chi_{186576}(47,\cdot)\)	186576.lj	52	no	\(-1\)	\(1\)	\(e\left(\frac{7}{52}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(-i\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{51}{52}\right)\)
\(\chi_{186576}(49,\cdot)\)	186576.wb	858	no	\(1\)	\(1\)	\(e\left(\frac{21}{286}\right)\)	\(e\left(\frac{515}{858}\right)\)	\(e\left(\frac{721}{858}\right)\)	\(e\left(\frac{160}{429}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{21}{143}\right)\)	\(e\left(\frac{413}{429}\right)\)	\(e\left(\frac{49}{286}\right)\)	\(e\left(\frac{289}{429}\right)\)	\(e\left(\frac{355}{858}\right)\)
\(\chi_{186576}(53,\cdot)\)	186576.vg	572	yes	\(1\)	\(1\)	\(e\left(\frac{307}{572}\right)\)	\(e\left(\frac{31}{143}\right)\)	\(e\left(\frac{431}{572}\right)\)	\(e\left(\frac{122}{143}\right)\)	\(e\left(\frac{31}{44}\right)\)	\(e\left(\frac{21}{286}\right)\)	\(e\left(\frac{323}{572}\right)\)	\(e\left(\frac{48}{143}\right)\)	\(e\left(\frac{431}{572}\right)\)	\(e\left(\frac{309}{572}\right)\)
\(\chi_{186576}(55,\cdot)\)	186576.vy	858	no	\(-1\)	\(1\)	\(e\left(\frac{119}{286}\right)\)	\(e\left(\frac{821}{858}\right)\)	\(e\left(\frac{17}{429}\right)\)	\(e\left(\frac{1}{429}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{119}{143}\right)\)	\(e\left(\frac{343}{858}\right)\)	\(e\left(\frac{87}{286}\right)\)	\(e\left(\frac{160}{429}\right)\)	\(e\left(\frac{391}{858}\right)\)
\(\chi_{186576}(59,\cdot)\)	186576.yi	1716	yes	\(-1\)	\(1\)	\(e\left(\frac{58}{143}\right)\)	\(e\left(\frac{167}{1716}\right)\)	\(e\left(\frac{37}{429}\right)\)	\(e\left(\frac{305}{429}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{116}{143}\right)\)	\(e\left(\frac{1165}{1716}\right)\)	\(e\left(\frac{17}{572}\right)\)	\(e\left(\frac{863}{1716}\right)\)	\(e\left(\frac{211}{429}\right)\)
\(\chi_{186576}(61,\cdot)\)	186576.xj	1716	no	\(-1\)	\(1\)	\(e\left(\frac{343}{572}\right)\)	\(e\left(\frac{89}{429}\right)\)	\(e\left(\frac{241}{1716}\right)\)	\(e\left(\frac{373}{858}\right)\)	\(e\left(\frac{23}{132}\right)\)	\(e\left(\frac{57}{286}\right)\)	\(e\left(\frac{97}{1716}\right)\)	\(e\left(\frac{69}{143}\right)\)	\(e\left(\frac{1385}{1716}\right)\)	\(e\left(\frac{841}{1716}\right)\)
\(\chi_{186576}(67,\cdot)\)	186576.yj	1716	no	\(-1\)	\(1\)	\(e\left(\frac{68}{143}\right)\)	\(e\left(\frac{1039}{1716}\right)\)	\(e\left(\frac{428}{429}\right)\)	\(e\left(\frac{328}{429}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{136}{143}\right)\)	\(e\left(\frac{641}{1716}\right)\)	\(e\left(\frac{15}{572}\right)\)	\(e\left(\frac{139}{1716}\right)\)	\(e\left(\frac{835}{858}\right)\)
\(\chi_{186576}(71,\cdot)\)	186576.xn	1716	no	\(-1\)	\(1\)	\(e\left(\frac{569}{572}\right)\)	\(e\left(\frac{335}{1716}\right)\)	\(e\left(\frac{1327}{1716}\right)\)	\(e\left(\frac{152}{429}\right)\)	\(e\left(\frac{59}{132}\right)\)	\(e\left(\frac{283}{286}\right)\)	\(e\left(\frac{328}{429}\right)\)	\(e\left(\frac{279}{572}\right)\)	\(e\left(\frac{163}{858}\right)\)	\(e\left(\frac{31}{1716}\right)\)
\(\chi_{186576}(73,\cdot)\)	186576.uj	572	no	\(-1\)	\(1\)	\(e\left(\frac{357}{572}\right)\)	\(e\left(\frac{249}{572}\right)\)	\(e\left(\frac{463}{572}\right)\)	\(e\left(\frac{1}{286}\right)\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{71}{286}\right)\)	\(e\left(\frac{243}{286}\right)\)	\(e\left(\frac{547}{572}\right)\)	\(e\left(\frac{17}{286}\right)\)	\(e\left(\frac{391}{572}\right)\)
\(\chi_{186576}(77,\cdot)\)	186576.uz	572	yes	\(-1\)	\(1\)	\(e\left(\frac{365}{572}\right)\)	\(e\left(\frac{103}{143}\right)\)	\(e\left(\frac{205}{572}\right)\)	\(e\left(\frac{271}{286}\right)\)	\(e\left(\frac{37}{44}\right)\)	\(e\left(\frac{79}{286}\right)\)	\(e\left(\frac{289}{572}\right)\)	\(e\left(\frac{259}{286}\right)\)	\(e\left(\frac{205}{572}\right)\)	\(e\left(\frac{427}{572}\right)\)
\(\chi_{186576}(79,\cdot)\)	186576.sz	286	no	\(1\)	\(1\)	\(e\left(\frac{149}{286}\right)\)	\(e\left(\frac{79}{143}\right)\)	\(e\left(\frac{82}{143}\right)\)	\(e\left(\frac{119}{286}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{6}{143}\right)\)	\(e\left(\frac{87}{143}\right)\)	\(e\left(\frac{157}{286}\right)\)	\(e\left(\frac{21}{286}\right)\)	\(e\left(\frac{27}{286}\right)\)
\(\chi_{186576}(83,\cdot)\)	186576.tt	572	yes	\(1\)	\(1\)	\(e\left(\frac{229}{286}\right)\)	\(e\left(\frac{1}{572}\right)\)	\(e\left(\frac{15}{286}\right)\)	\(e\left(\frac{85}{286}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{86}{143}\right)\)	\(e\left(\frac{269}{572}\right)\)	\(e\left(\frac{163}{572}\right)\)	\(e\left(\frac{459}{572}\right)\)	\(e\left(\frac{101}{286}\right)\)
\(\chi_{186576}(85,\cdot)\)	186576.wx	1716	no	\(-1\)	\(1\)	\(e\left(\frac{159}{286}\right)\)	\(e\left(\frac{1241}{1716}\right)\)	\(e\left(\frac{370}{429}\right)\)	\(e\left(\frac{523}{858}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{16}{143}\right)\)	\(e\left(\frac{67}{1716}\right)\)	\(e\left(\frac{27}{572}\right)\)	\(e\left(\frac{479}{1716}\right)\)	\(e\left(\frac{394}{429}\right)\)
\(\chi_{186576}(89,\cdot)\)	186576.pr	132	no	\(-1\)	\(1\)	\(e\left(\frac{21}{44}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{17}{132}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{109}{132}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{27}{44}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{47}{132}\right)\)
\(\chi_{186576}(95,\cdot)\)	186576.wl	858	no	\(1\)	\(1\)	\(e\left(\frac{71}{143}\right)\)	\(e\left(\frac{32}{429}\right)\)	\(e\left(\frac{347}{858}\right)\)	\(e\left(\frac{727}{858}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{142}{143}\right)\)	\(e\left(\frac{485}{858}\right)\)	\(e\left(\frac{118}{143}\right)\)	\(e\left(\frac{245}{429}\right)\)	\(e\left(\frac{773}{858}\right)\)
\(\chi_{186576}(97,\cdot)\)	186576.xk	1716	no	\(1\)	\(1\)	\(e\left(\frac{15}{572}\right)\)	\(e\left(\frac{899}{1716}\right)\)	\(e\left(\frac{1087}{1716}\right)\)	\(e\left(\frac{98}{429}\right)\)	\(e\left(\frac{101}{132}\right)\)	\(e\left(\frac{15}{286}\right)\)	\(e\left(\frac{76}{429}\right)\)	\(e\left(\frac{321}{572}\right)\)	\(e\left(\frac{236}{429}\right)\)	\(e\left(\frac{703}{1716}\right)\)
\(\chi_{186576}(101,\cdot)\)	186576.xh	1716	yes	\(-1\)	\(1\)	\(e\left(\frac{139}{572}\right)\)	\(e\left(\frac{64}{429}\right)\)	\(e\left(\frac{101}{1716}\right)\)	\(e\left(\frac{167}{858}\right)\)	\(e\left(\frac{97}{132}\right)\)	\(e\left(\frac{139}{286}\right)\)	\(e\left(\frac{653}{1716}\right)\)	\(e\left(\frac{43}{286}\right)\)	\(e\left(\frac{673}{1716}\right)\)	\(e\left(\frac{947}{1716}\right)\)
\(\chi_{186576}(103,\cdot)\)	186576.sr	286	no	\(1\)	\(1\)	\(e\left(\frac{161}{286}\right)\)	\(e\left(\frac{45}{286}\right)\)	\(e\left(\frac{103}{143}\right)\)	\(e\left(\frac{71}{286}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{18}{143}\right)\)	\(e\left(\frac{93}{286}\right)\)	\(e\left(\frac{21}{143}\right)\)	\(e\left(\frac{103}{143}\right)\)	\(e\left(\frac{81}{286}\right)\)
\(\chi_{186576}(107,\cdot)\)	186576.ya	1716	yes	\(-1\)	\(1\)	\(e\left(\frac{167}{572}\right)\)	\(e\left(\frac{233}{858}\right)\)	\(e\left(\frac{395}{1716}\right)\)	\(e\left(\frac{214}{429}\right)\)	\(e\left(\frac{67}{132}\right)\)	\(e\left(\frac{167}{286}\right)\)	\(e\left(\frac{1373}{1716}\right)\)	\(e\left(\frac{171}{286}\right)\)	\(e\left(\frac{967}{1716}\right)\)	\(e\left(\frac{467}{1716}\right)\)

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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.