LMFDB - Group of Dirichlet characters of modulus 309680

sage:H = DirichletGroup(309680)

pari:g = idealstar(,309680,2)

Character group

sage:G.order() pari:g.no
Order	=	104832
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{2}\times C_{12}\times C_{1092}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{309680}(193551,\cdot)$, $\chi_{309680}(232261,\cdot)$, $\chi_{309680}(61937,\cdot)$, $\chi_{309680}(297041,\cdot)$, $\chi_{309680}(82321,\cdot)$

First 32 of 104832 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	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{309680}(1,\cdot)$	309680.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{309680}(3,\cdot)$	309680.ccq	1092	yes	$1$	$1$	$e\left(\frac{10}{273}\right)$	$e\left(\frac{20}{273}\right)$	$e\left(\frac{27}{364}\right)$	$e\left(\frac{197}{273}\right)$	$e\left(\frac{671}{1092}\right)$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{10}{91}\right)$	$e\left(\frac{349}{1092}\right)$	$e\left(\frac{5}{13}\right)$
$\chi_{309680}(9,\cdot)$	309680.bya	546	no	$1$	$1$	$e\left(\frac{20}{273}\right)$	$e\left(\frac{40}{273}\right)$	$e\left(\frac{27}{182}\right)$	$e\left(\frac{121}{273}\right)$	$e\left(\frac{125}{546}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{20}{91}\right)$	$e\left(\frac{349}{546}\right)$	$e\left(\frac{10}{13}\right)$
$\chi_{309680}(11,\cdot)$	309680.cds	1092	no	$-1$	$1$	$e\left(\frac{27}{364}\right)$	$e\left(\frac{27}{182}\right)$	$e\left(\frac{139}{1092}\right)$	$e\left(\frac{895}{1092}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{81}{364}\right)$	$e\left(\frac{527}{1092}\right)$	$e\left(\frac{77}{78}\right)$
$\chi_{309680}(13,\cdot)$	309680.ccs	1092	yes	$1$	$1$	$e\left(\frac{197}{273}\right)$	$e\left(\frac{121}{273}\right)$	$e\left(\frac{895}{1092}\right)$	$e\left(\frac{68}{273}\right)$	$e\left(\frac{199}{364}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{15}{91}\right)$	$e\left(\frac{751}{1092}\right)$	$e\left(\frac{71}{78}\right)$
$\chi_{309680}(17,\cdot)$	309680.cfm	1092	no	$-1$	$1$	$e\left(\frac{671}{1092}\right)$	$e\left(\frac{125}{546}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{199}{364}\right)$	$e\left(\frac{857}{1092}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{307}{364}\right)$	$e\left(\frac{16}{91}\right)$	$e\left(\frac{19}{78}\right)$
$\chi_{309680}(19,\cdot)$	309680.bqf	156	no	$1$	$1$	$e\left(\frac{77}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{31}{156}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{4}{13}\right)$
$\chi_{309680}(23,\cdot)$	309680.bgw	84	no	$1$	$1$	$e\left(\frac{41}{84}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{67}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{20}{21}\right)$	$-1$
$\chi_{309680}(27,\cdot)$	309680.bxh	364	yes	$1$	$1$	$e\left(\frac{10}{91}\right)$	$e\left(\frac{20}{91}\right)$	$e\left(\frac{81}{364}\right)$	$e\left(\frac{15}{91}\right)$	$e\left(\frac{307}{364}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{30}{91}\right)$	$e\left(\frac{349}{364}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{309680}(29,\cdot)$	309680.chi	1092	yes	$-1$	$1$	$e\left(\frac{349}{1092}\right)$	$e\left(\frac{349}{546}\right)$	$e\left(\frac{527}{1092}\right)$	$e\left(\frac{751}{1092}\right)$	$e\left(\frac{16}{91}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{349}{364}\right)$	$e\left(\frac{563}{1092}\right)$	$e\left(\frac{35}{39}\right)$
$\chi_{309680}(31,\cdot)$	309680.bar	78	no	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{4}{13}\right)$	$-1$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{35}{39}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{309680}(33,\cdot)$	309680.cfm	1092	no	$-1$	$1$	$e\left(\frac{121}{1092}\right)$	$e\left(\frac{121}{546}\right)$	$e\left(\frac{55}{273}\right)$	$e\left(\frac{197}{364}\right)$	$e\left(\frac{799}{1092}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{29}{84}\right)$	$e\left(\frac{121}{364}\right)$	$e\left(\frac{73}{91}\right)$	$e\left(\frac{29}{78}\right)$
$\chi_{309680}(37,\cdot)$	309680.cjn	1092	yes	$1$	$1$	$e\left(\frac{46}{91}\right)$	$e\left(\frac{1}{91}\right)$	$e\left(\frac{317}{1092}\right)$	$e\left(\frac{505}{546}\right)$	$e\left(\frac{451}{1092}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{47}{91}\right)$	$e\left(\frac{703}{1092}\right)$	$e\left(\frac{38}{39}\right)$
$\chi_{309680}(39,\cdot)$	309680.cbp	546	no	$1$	$1$	$e\left(\frac{69}{91}\right)$	$e\left(\frac{47}{91}\right)$	$e\left(\frac{244}{273}\right)$	$e\left(\frac{265}{273}\right)$	$e\left(\frac{44}{273}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{25}{91}\right)$	$e\left(\frac{2}{273}\right)$	$e\left(\frac{23}{78}\right)$
$\chi_{309680}(41,\cdot)$	309680.buk	182	no	$1$	$1$	$e\left(\frac{149}{182}\right)$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{31}{182}\right)$	$e\left(\frac{89}{91}\right)$	$e\left(\frac{11}{91}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{83}{182}\right)$	$e\left(\frac{46}{91}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{309680}(43,\cdot)$	309680.cct	1092	yes	$-1$	$1$	$e\left(\frac{74}{273}\right)$	$e\left(\frac{148}{273}\right)$	$e\left(\frac{199}{1092}\right)$	$e\left(\frac{20}{273}\right)$	$e\left(\frac{187}{364}\right)$	$e\left(\frac{133}{156}\right)$	$e\left(\frac{1}{84}\right)$	$e\left(\frac{74}{91}\right)$	$e\left(\frac{799}{1092}\right)$	$e\left(\frac{53}{78}\right)$
$\chi_{309680}(47,\cdot)$	309680.ceq	1092	no	$1$	$1$	$e\left(\frac{137}{1092}\right)$	$e\left(\frac{137}{546}\right)$	$e\left(\frac{127}{182}\right)$	$e\left(\frac{433}{1092}\right)$	$e\left(\frac{121}{1092}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{137}{364}\right)$	$e\left(\frac{263}{273}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{309680}(51,\cdot)$	309680.cds	1092	no	$-1$	$1$	$e\left(\frac{237}{364}\right)$	$e\left(\frac{55}{182}\right)$	$e\left(\frac{209}{1092}\right)$	$e\left(\frac{293}{1092}\right)$	$e\left(\frac{109}{273}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{347}{364}\right)$	$e\left(\frac{541}{1092}\right)$	$e\left(\frac{49}{78}\right)$
$\chi_{309680}(53,\cdot)$	309680.ccg	1092	yes	$1$	$1$	$e\left(\frac{41}{182}\right)$	$e\left(\frac{41}{91}\right)$	$e\left(\frac{985}{1092}\right)$	$e\left(\frac{115}{273}\right)$	$e\left(\frac{473}{1092}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{123}{182}\right)$	$e\left(\frac{431}{1092}\right)$	$e\left(\frac{37}{39}\right)$
$\chi_{309680}(57,\cdot)$	309680.bvw	364	no	$1$	$1$	$e\left(\frac{193}{364}\right)$	$e\left(\frac{11}{182}\right)$	$e\left(\frac{101}{182}\right)$	$e\left(\frac{335}{364}\right)$	$e\left(\frac{205}{364}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{215}{364}\right)$	$e\left(\frac{15}{182}\right)$	$e\left(\frac{9}{13}\right)$
$\chi_{309680}(59,\cdot)$	309680.cgm	1092	yes	$-1$	$1$	$e\left(\frac{499}{1092}\right)$	$e\left(\frac{499}{546}\right)$	$e\left(\frac{57}{364}\right)$	$e\left(\frac{1067}{1092}\right)$	$e\left(\frac{319}{546}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{135}{364}\right)$	$e\left(\frac{757}{1092}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{309680}(61,\cdot)$	309680.cfy	1092	no	$1$	$1$	$e\left(\frac{97}{1092}\right)$	$e\left(\frac{97}{546}\right)$	$e\left(\frac{499}{1092}\right)$	$e\left(\frac{185}{364}\right)$	$e\left(\frac{181}{273}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{97}{364}\right)$	$e\left(\frac{113}{364}\right)$	$e\left(\frac{11}{78}\right)$
$\chi_{309680}(67,\cdot)$	309680.bnd	156	no	$1$	$1$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{131}{156}\right)$	$e\left(\frac{43}{156}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{49}{78}\right)$
$\chi_{309680}(69,\cdot)$	309680.bwh	364	yes	$1$	$1$	$e\left(\frac{191}{364}\right)$	$e\left(\frac{9}{182}\right)$	$e\left(\frac{339}{364}\right)$	$e\left(\frac{241}{364}\right)$	$e\left(\frac{179}{182}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{209}{364}\right)$	$e\left(\frac{99}{364}\right)$	$e\left(\frac{23}{26}\right)$
$\chi_{309680}(71,\cdot)$	309680.buo	182	no	$1$	$1$	$e\left(\frac{41}{182}\right)$	$e\left(\frac{41}{91}\right)$	$e\left(\frac{29}{91}\right)$	$e\left(\frac{107}{182}\right)$	$e\left(\frac{3}{182}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{123}{182}\right)$	$e\left(\frac{89}{91}\right)$	$e\left(\frac{3}{26}\right)$
$\chi_{309680}(73,\cdot)$	309680.cem	1092	no	$1$	$1$	$e\left(\frac{71}{364}\right)$	$e\left(\frac{71}{182}\right)$	$e\left(\frac{53}{546}\right)$	$e\left(\frac{1}{1092}\right)$	$e\left(\frac{677}{1092}\right)$	$e\left(\frac{23}{26}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{213}{364}\right)$	$e\left(\frac{17}{273}\right)$	$e\left(\frac{59}{78}\right)$
$\chi_{309680}(81,\cdot)$	309680.bvm	273	no	$1$	$1$	$e\left(\frac{40}{273}\right)$	$e\left(\frac{80}{273}\right)$	$e\left(\frac{27}{91}\right)$	$e\left(\frac{242}{273}\right)$	$e\left(\frac{125}{273}\right)$	$e\left(\frac{38}{39}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{40}{91}\right)$	$e\left(\frac{76}{273}\right)$	$e\left(\frac{7}{13}\right)$
$\chi_{309680}(83,\cdot)$	309680.cir	1092	yes	$-1$	$1$	$e\left(\frac{173}{546}\right)$	$e\left(\frac{173}{273}\right)$	$e\left(\frac{869}{1092}\right)$	$e\left(\frac{16}{273}\right)$	$e\left(\frac{95}{364}\right)$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{173}{182}\right)$	$e\left(\frac{803}{1092}\right)$	$e\left(\frac{29}{39}\right)$
$\chi_{309680}(87,\cdot)$	309680.cfn	1092	no	$-1$	$1$	$e\left(\frac{389}{1092}\right)$	$e\left(\frac{389}{546}\right)$	$e\left(\frac{152}{273}\right)$	$e\left(\frac{149}{364}\right)$	$e\left(\frac{863}{1092}\right)$	$e\left(\frac{10}{39}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{25}{364}\right)$	$e\left(\frac{76}{91}\right)$	$e\left(\frac{11}{39}\right)$
$\chi_{309680}(89,\cdot)$	309680.cat	546	no	$-1$	$1$	$e\left(\frac{215}{546}\right)$	$e\left(\frac{215}{273}\right)$	$e\left(\frac{515}{546}\right)$	$e\left(\frac{153}{182}\right)$	$e\left(\frac{262}{273}\right)$	$e\left(\frac{29}{39}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{33}{182}\right)$	$e\left(\frac{121}{182}\right)$	$e\left(\frac{17}{78}\right)$
$\chi_{309680}(93,\cdot)$	309680.cco	1092	yes	$1$	$1$	$e\left(\frac{115}{273}\right)$	$e\left(\frac{230}{273}\right)$	$e\left(\frac{67}{1092}\right)$	$e\left(\frac{115}{182}\right)$	$e\left(\frac{937}{1092}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{83}{84}\right)$	$e\left(\frac{24}{91}\right)$	$e\left(\frac{79}{364}\right)$	$e\left(\frac{10}{39}\right)$
$\chi_{309680}(97,\cdot)$	309680.zf	52	no	$1$	$1$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{6}{13}\right)$	$-i$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{21}{26}\right)$

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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	$309680$
Structure	\(C_{2}\times C_{2}\times C_{2}\times C_{12}\times C_{1092}\)
Order	$104832$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(27\)	\(29\)	\(31\)
\(\chi_{309680}(1,\cdot)\)	309680.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{309680}(3,\cdot)\)	309680.ccq	1092	yes	\(1\)	\(1\)	\(e\left(\frac{10}{273}\right)\)	\(e\left(\frac{20}{273}\right)\)	\(e\left(\frac{27}{364}\right)\)	\(e\left(\frac{197}{273}\right)\)	\(e\left(\frac{671}{1092}\right)\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{10}{91}\right)\)	\(e\left(\frac{349}{1092}\right)\)	\(e\left(\frac{5}{13}\right)\)
\(\chi_{309680}(9,\cdot)\)	309680.bya	546	no	\(1\)	\(1\)	\(e\left(\frac{20}{273}\right)\)	\(e\left(\frac{40}{273}\right)\)	\(e\left(\frac{27}{182}\right)\)	\(e\left(\frac{121}{273}\right)\)	\(e\left(\frac{125}{546}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{20}{91}\right)\)	\(e\left(\frac{349}{546}\right)\)	\(e\left(\frac{10}{13}\right)\)
\(\chi_{309680}(11,\cdot)\)	309680.cds	1092	no	\(-1\)	\(1\)	\(e\left(\frac{27}{364}\right)\)	\(e\left(\frac{27}{182}\right)\)	\(e\left(\frac{139}{1092}\right)\)	\(e\left(\frac{895}{1092}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{81}{364}\right)\)	\(e\left(\frac{527}{1092}\right)\)	\(e\left(\frac{77}{78}\right)\)
\(\chi_{309680}(13,\cdot)\)	309680.ccs	1092	yes	\(1\)	\(1\)	\(e\left(\frac{197}{273}\right)\)	\(e\left(\frac{121}{273}\right)\)	\(e\left(\frac{895}{1092}\right)\)	\(e\left(\frac{68}{273}\right)\)	\(e\left(\frac{199}{364}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{15}{91}\right)\)	\(e\left(\frac{751}{1092}\right)\)	\(e\left(\frac{71}{78}\right)\)
\(\chi_{309680}(17,\cdot)\)	309680.cfm	1092	no	\(-1\)	\(1\)	\(e\left(\frac{671}{1092}\right)\)	\(e\left(\frac{125}{546}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{199}{364}\right)\)	\(e\left(\frac{857}{1092}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{307}{364}\right)\)	\(e\left(\frac{16}{91}\right)\)	\(e\left(\frac{19}{78}\right)\)
\(\chi_{309680}(19,\cdot)\)	309680.bqf	156	no	\(1\)	\(1\)	\(e\left(\frac{77}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{31}{156}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{4}{13}\right)\)
\(\chi_{309680}(23,\cdot)\)	309680.bgw	84	no	\(1\)	\(1\)	\(e\left(\frac{41}{84}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{31}{84}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{67}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(-1\)
\(\chi_{309680}(27,\cdot)\)	309680.bxh	364	yes	\(1\)	\(1\)	\(e\left(\frac{10}{91}\right)\)	\(e\left(\frac{20}{91}\right)\)	\(e\left(\frac{81}{364}\right)\)	\(e\left(\frac{15}{91}\right)\)	\(e\left(\frac{307}{364}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{30}{91}\right)\)	\(e\left(\frac{349}{364}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{309680}(29,\cdot)\)	309680.chi	1092	yes	\(-1\)	\(1\)	\(e\left(\frac{349}{1092}\right)\)	\(e\left(\frac{349}{546}\right)\)	\(e\left(\frac{527}{1092}\right)\)	\(e\left(\frac{751}{1092}\right)\)	\(e\left(\frac{16}{91}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{349}{364}\right)\)	\(e\left(\frac{563}{1092}\right)\)	\(e\left(\frac{35}{39}\right)\)
\(\chi_{309680}(31,\cdot)\)	309680.bar	78	no	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(-1\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{309680}(33,\cdot)\)	309680.cfm	1092	no	\(-1\)	\(1\)	\(e\left(\frac{121}{1092}\right)\)	\(e\left(\frac{121}{546}\right)\)	\(e\left(\frac{55}{273}\right)\)	\(e\left(\frac{197}{364}\right)\)	\(e\left(\frac{799}{1092}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{29}{84}\right)\)	\(e\left(\frac{121}{364}\right)\)	\(e\left(\frac{73}{91}\right)\)	\(e\left(\frac{29}{78}\right)\)
\(\chi_{309680}(37,\cdot)\)	309680.cjn	1092	yes	\(1\)	\(1\)	\(e\left(\frac{46}{91}\right)\)	\(e\left(\frac{1}{91}\right)\)	\(e\left(\frac{317}{1092}\right)\)	\(e\left(\frac{505}{546}\right)\)	\(e\left(\frac{451}{1092}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{47}{91}\right)\)	\(e\left(\frac{703}{1092}\right)\)	\(e\left(\frac{38}{39}\right)\)
\(\chi_{309680}(39,\cdot)\)	309680.cbp	546	no	\(1\)	\(1\)	\(e\left(\frac{69}{91}\right)\)	\(e\left(\frac{47}{91}\right)\)	\(e\left(\frac{244}{273}\right)\)	\(e\left(\frac{265}{273}\right)\)	\(e\left(\frac{44}{273}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{25}{91}\right)\)	\(e\left(\frac{2}{273}\right)\)	\(e\left(\frac{23}{78}\right)\)
\(\chi_{309680}(41,\cdot)\)	309680.buk	182	no	\(1\)	\(1\)	\(e\left(\frac{149}{182}\right)\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{31}{182}\right)\)	\(e\left(\frac{89}{91}\right)\)	\(e\left(\frac{11}{91}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{83}{182}\right)\)	\(e\left(\frac{46}{91}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{309680}(43,\cdot)\)	309680.cct	1092	yes	\(-1\)	\(1\)	\(e\left(\frac{74}{273}\right)\)	\(e\left(\frac{148}{273}\right)\)	\(e\left(\frac{199}{1092}\right)\)	\(e\left(\frac{20}{273}\right)\)	\(e\left(\frac{187}{364}\right)\)	\(e\left(\frac{133}{156}\right)\)	\(e\left(\frac{1}{84}\right)\)	\(e\left(\frac{74}{91}\right)\)	\(e\left(\frac{799}{1092}\right)\)	\(e\left(\frac{53}{78}\right)\)
\(\chi_{309680}(47,\cdot)\)	309680.ceq	1092	no	\(1\)	\(1\)	\(e\left(\frac{137}{1092}\right)\)	\(e\left(\frac{137}{546}\right)\)	\(e\left(\frac{127}{182}\right)\)	\(e\left(\frac{433}{1092}\right)\)	\(e\left(\frac{121}{1092}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{137}{364}\right)\)	\(e\left(\frac{263}{273}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{309680}(51,\cdot)\)	309680.cds	1092	no	\(-1\)	\(1\)	\(e\left(\frac{237}{364}\right)\)	\(e\left(\frac{55}{182}\right)\)	\(e\left(\frac{209}{1092}\right)\)	\(e\left(\frac{293}{1092}\right)\)	\(e\left(\frac{109}{273}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{347}{364}\right)\)	\(e\left(\frac{541}{1092}\right)\)	\(e\left(\frac{49}{78}\right)\)
\(\chi_{309680}(53,\cdot)\)	309680.ccg	1092	yes	\(1\)	\(1\)	\(e\left(\frac{41}{182}\right)\)	\(e\left(\frac{41}{91}\right)\)	\(e\left(\frac{985}{1092}\right)\)	\(e\left(\frac{115}{273}\right)\)	\(e\left(\frac{473}{1092}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{123}{182}\right)\)	\(e\left(\frac{431}{1092}\right)\)	\(e\left(\frac{37}{39}\right)\)
\(\chi_{309680}(57,\cdot)\)	309680.bvw	364	no	\(1\)	\(1\)	\(e\left(\frac{193}{364}\right)\)	\(e\left(\frac{11}{182}\right)\)	\(e\left(\frac{101}{182}\right)\)	\(e\left(\frac{335}{364}\right)\)	\(e\left(\frac{205}{364}\right)\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{215}{364}\right)\)	\(e\left(\frac{15}{182}\right)\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{309680}(59,\cdot)\)	309680.cgm	1092	yes	\(-1\)	\(1\)	\(e\left(\frac{499}{1092}\right)\)	\(e\left(\frac{499}{546}\right)\)	\(e\left(\frac{57}{364}\right)\)	\(e\left(\frac{1067}{1092}\right)\)	\(e\left(\frac{319}{546}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{135}{364}\right)\)	\(e\left(\frac{757}{1092}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{309680}(61,\cdot)\)	309680.cfy	1092	no	\(1\)	\(1\)	\(e\left(\frac{97}{1092}\right)\)	\(e\left(\frac{97}{546}\right)\)	\(e\left(\frac{499}{1092}\right)\)	\(e\left(\frac{185}{364}\right)\)	\(e\left(\frac{181}{273}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{97}{364}\right)\)	\(e\left(\frac{113}{364}\right)\)	\(e\left(\frac{11}{78}\right)\)
\(\chi_{309680}(67,\cdot)\)	309680.bnd	156	no	\(1\)	\(1\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{131}{156}\right)\)	\(e\left(\frac{43}{156}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{49}{78}\right)\)
\(\chi_{309680}(69,\cdot)\)	309680.bwh	364	yes	\(1\)	\(1\)	\(e\left(\frac{191}{364}\right)\)	\(e\left(\frac{9}{182}\right)\)	\(e\left(\frac{339}{364}\right)\)	\(e\left(\frac{241}{364}\right)\)	\(e\left(\frac{179}{182}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{209}{364}\right)\)	\(e\left(\frac{99}{364}\right)\)	\(e\left(\frac{23}{26}\right)\)
\(\chi_{309680}(71,\cdot)\)	309680.buo	182	no	\(1\)	\(1\)	\(e\left(\frac{41}{182}\right)\)	\(e\left(\frac{41}{91}\right)\)	\(e\left(\frac{29}{91}\right)\)	\(e\left(\frac{107}{182}\right)\)	\(e\left(\frac{3}{182}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{123}{182}\right)\)	\(e\left(\frac{89}{91}\right)\)	\(e\left(\frac{3}{26}\right)\)
\(\chi_{309680}(73,\cdot)\)	309680.cem	1092	no	\(1\)	\(1\)	\(e\left(\frac{71}{364}\right)\)	\(e\left(\frac{71}{182}\right)\)	\(e\left(\frac{53}{546}\right)\)	\(e\left(\frac{1}{1092}\right)\)	\(e\left(\frac{677}{1092}\right)\)	\(e\left(\frac{23}{26}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{213}{364}\right)\)	\(e\left(\frac{17}{273}\right)\)	\(e\left(\frac{59}{78}\right)\)
\(\chi_{309680}(81,\cdot)\)	309680.bvm	273	no	\(1\)	\(1\)	\(e\left(\frac{40}{273}\right)\)	\(e\left(\frac{80}{273}\right)\)	\(e\left(\frac{27}{91}\right)\)	\(e\left(\frac{242}{273}\right)\)	\(e\left(\frac{125}{273}\right)\)	\(e\left(\frac{38}{39}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{40}{91}\right)\)	\(e\left(\frac{76}{273}\right)\)	\(e\left(\frac{7}{13}\right)\)
\(\chi_{309680}(83,\cdot)\)	309680.cir	1092	yes	\(-1\)	\(1\)	\(e\left(\frac{173}{546}\right)\)	\(e\left(\frac{173}{273}\right)\)	\(e\left(\frac{869}{1092}\right)\)	\(e\left(\frac{16}{273}\right)\)	\(e\left(\frac{95}{364}\right)\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{173}{182}\right)\)	\(e\left(\frac{803}{1092}\right)\)	\(e\left(\frac{29}{39}\right)\)
\(\chi_{309680}(87,\cdot)\)	309680.cfn	1092	no	\(-1\)	\(1\)	\(e\left(\frac{389}{1092}\right)\)	\(e\left(\frac{389}{546}\right)\)	\(e\left(\frac{152}{273}\right)\)	\(e\left(\frac{149}{364}\right)\)	\(e\left(\frac{863}{1092}\right)\)	\(e\left(\frac{10}{39}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{25}{364}\right)\)	\(e\left(\frac{76}{91}\right)\)	\(e\left(\frac{11}{39}\right)\)
\(\chi_{309680}(89,\cdot)\)	309680.cat	546	no	\(-1\)	\(1\)	\(e\left(\frac{215}{546}\right)\)	\(e\left(\frac{215}{273}\right)\)	\(e\left(\frac{515}{546}\right)\)	\(e\left(\frac{153}{182}\right)\)	\(e\left(\frac{262}{273}\right)\)	\(e\left(\frac{29}{39}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{33}{182}\right)\)	\(e\left(\frac{121}{182}\right)\)	\(e\left(\frac{17}{78}\right)\)
\(\chi_{309680}(93,\cdot)\)	309680.cco	1092	yes	\(1\)	\(1\)	\(e\left(\frac{115}{273}\right)\)	\(e\left(\frac{230}{273}\right)\)	\(e\left(\frac{67}{1092}\right)\)	\(e\left(\frac{115}{182}\right)\)	\(e\left(\frac{937}{1092}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{83}{84}\right)\)	\(e\left(\frac{24}{91}\right)\)	\(e\left(\frac{79}{364}\right)\)	\(e\left(\frac{10}{39}\right)\)
\(\chi_{309680}(97,\cdot)\)	309680.zf	52	no	\(1\)	\(1\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{19}{52}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(-i\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{21}{26}\right)\)

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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.