LMFDB - Group of Dirichlet characters of modulus 61936

sage:H = DirichletGroup(61936)

pari:g = idealstar(,61936,2)

Character group

sage:G.order() pari:g.no
Order	=	26208
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{1092}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{61936}(7743,\cdot)$, $\chi_{61936}(46453,\cdot)$, $\chi_{61936}(49297,\cdot)$, $\chi_{61936}(20385,\cdot)$

First 32 of 26208 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{61936}(1,\cdot)$	61936.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{61936}(3,\cdot)$	61936.se	1092	yes	$-1$	$1$	$e\left(\frac{859}{1092}\right)$	$e\left(\frac{257}{1092}\right)$	$e\left(\frac{313}{546}\right)$	$e\left(\frac{27}{364}\right)$	$e\left(\frac{515}{1092}\right)$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{236}{273}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{257}{546}\right)$
$\chi_{61936}(5,\cdot)$	61936.sh	1092	yes	$-1$	$1$	$e\left(\frac{257}{1092}\right)$	$e\left(\frac{607}{1092}\right)$	$e\left(\frac{257}{546}\right)$	$e\left(\frac{335}{364}\right)$	$e\left(\frac{613}{1092}\right)$	$e\left(\frac{72}{91}\right)$	$e\left(\frac{521}{546}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{61}{546}\right)$
$\chi_{61936}(9,\cdot)$	61936.qn	546	no	$1$	$1$	$e\left(\frac{313}{546}\right)$	$e\left(\frac{257}{546}\right)$	$e\left(\frac{40}{273}\right)$	$e\left(\frac{27}{182}\right)$	$e\left(\frac{515}{546}\right)$	$e\left(\frac{4}{91}\right)$	$e\left(\frac{199}{273}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{257}{273}\right)$
$\chi_{61936}(11,\cdot)$	61936.rg	1092	yes	$-1$	$1$	$e\left(\frac{27}{364}\right)$	$e\left(\frac{335}{364}\right)$	$e\left(\frac{27}{182}\right)$	$e\left(\frac{139}{1092}\right)$	$e\left(\frac{895}{1092}\right)$	$e\left(\frac{181}{182}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{153}{182}\right)$
$\chi_{61936}(13,\cdot)$	61936.sa	1092	yes	$-1$	$1$	$e\left(\frac{515}{1092}\right)$	$e\left(\frac{613}{1092}\right)$	$e\left(\frac{515}{546}\right)$	$e\left(\frac{895}{1092}\right)$	$e\left(\frac{1091}{1092}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{145}{182}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{67}{546}\right)$
$\chi_{61936}(15,\cdot)$	61936.ok	182	no	$1$	$1$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{72}{91}\right)$	$e\left(\frac{4}{91}\right)$	$e\left(\frac{181}{182}\right)$	$e\left(\frac{3}{91}\right)$	$e\left(\frac{74}{91}\right)$	$e\left(\frac{149}{182}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{53}{91}\right)$
$\chi_{61936}(17,\cdot)$	61936.pr	546	no	$1$	$1$	$e\left(\frac{236}{273}\right)$	$e\left(\frac{521}{546}\right)$	$e\left(\frac{199}{273}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{145}{182}\right)$	$e\left(\frac{149}{182}\right)$	$e\left(\frac{146}{273}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{248}{273}\right)$
$\chi_{61936}(19,\cdot)$	61936.nf	156	no	$1$	$1$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{35}{78}\right)$	$e\left(\frac{7}{156}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{55}{78}\right)$
$\chi_{61936}(23,\cdot)$	61936.hr	42	no	$-1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{61936}(25,\cdot)$	61936.qn	546	no	$1$	$1$	$e\left(\frac{257}{546}\right)$	$e\left(\frac{61}{546}\right)$	$e\left(\frac{257}{273}\right)$	$e\left(\frac{153}{182}\right)$	$e\left(\frac{67}{546}\right)$	$e\left(\frac{53}{91}\right)$	$e\left(\frac{248}{273}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{61}{273}\right)$
$\chi_{61936}(27,\cdot)$	61936.ow	364	yes	$-1$	$1$	$e\left(\frac{131}{364}\right)$	$e\left(\frac{257}{364}\right)$	$e\left(\frac{131}{182}\right)$	$e\left(\frac{81}{364}\right)$	$e\left(\frac{151}{364}\right)$	$e\left(\frac{6}{91}\right)$	$e\left(\frac{54}{91}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{75}{182}\right)$
$\chi_{61936}(29,\cdot)$	61936.ro	1092	yes	$-1$	$1$	$e\left(\frac{895}{1092}\right)$	$e\left(\frac{1007}{1092}\right)$	$e\left(\frac{349}{546}\right)$	$e\left(\frac{527}{1092}\right)$	$e\left(\frac{205}{1092}\right)$	$e\left(\frac{135}{182}\right)$	$e\left(\frac{123}{182}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{461}{546}\right)$
$\chi_{61936}(31,\cdot)$	61936.jf	78	no	$1$	$1$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{4}{13}\right)$	$-1$	$e\left(\frac{9}{13}\right)$
$\chi_{61936}(33,\cdot)$	61936.pr	546	no	$1$	$1$	$e\left(\frac{235}{273}\right)$	$e\left(\frac{85}{546}\right)$	$e\left(\frac{197}{273}\right)$	$e\left(\frac{55}{273}\right)$	$e\left(\frac{53}{182}\right)$	$e\left(\frac{3}{182}\right)$	$e\left(\frac{268}{273}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{85}{273}\right)$
$\chi_{61936}(37,\cdot)$	61936.rj	1092	yes	$-1$	$1$	$e\left(\frac{275}{364}\right)$	$e\left(\frac{163}{364}\right)$	$e\left(\frac{93}{182}\right)$	$e\left(\frac{317}{1092}\right)$	$e\left(\frac{191}{1092}\right)$	$e\left(\frac{37}{182}\right)$	$e\left(\frac{89}{546}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{163}{182}\right)$
$\chi_{61936}(39,\cdot)$	61936.oy	546	no	$1$	$1$	$e\left(\frac{47}{182}\right)$	$e\left(\frac{145}{182}\right)$	$e\left(\frac{47}{91}\right)$	$e\left(\frac{244}{273}\right)$	$e\left(\frac{257}{546}\right)$	$e\left(\frac{5}{91}\right)$	$e\left(\frac{361}{546}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{54}{91}\right)$
$\chi_{61936}(41,\cdot)$	61936.ob	182	no	$1$	$1$	$e\left(\frac{149}{182}\right)$	$e\left(\frac{43}{91}\right)$	$e\left(\frac{58}{91}\right)$	$e\left(\frac{31}{182}\right)$	$e\left(\frac{89}{91}\right)$	$e\left(\frac{53}{182}\right)$	$e\left(\frac{11}{91}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{86}{91}\right)$
$\chi_{61936}(43,\cdot)$	61936.sb	1092	yes	$1$	$1$	$e\left(\frac{23}{1092}\right)$	$e\left(\frac{373}{1092}\right)$	$e\left(\frac{23}{546}\right)$	$e\left(\frac{199}{1092}\right)$	$e\left(\frac{899}{1092}\right)$	$e\left(\frac{33}{91}\right)$	$e\left(\frac{139}{182}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{373}{546}\right)$
$\chi_{61936}(45,\cdot)$	61936.sh	1092	yes	$-1$	$1$	$e\left(\frac{883}{1092}\right)$	$e\left(\frac{29}{1092}\right)$	$e\left(\frac{337}{546}\right)$	$e\left(\frac{25}{364}\right)$	$e\left(\frac{551}{1092}\right)$	$e\left(\frac{76}{91}\right)$	$e\left(\frac{373}{546}\right)$	$e\left(\frac{53}{156}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{29}{546}\right)$
$\chi_{61936}(47,\cdot)$	61936.qo	546	no	$-1$	$1$	$e\left(\frac{205}{546}\right)$	$e\left(\frac{191}{546}\right)$	$e\left(\frac{205}{273}\right)$	$e\left(\frac{127}{182}\right)$	$e\left(\frac{353}{546}\right)$	$e\left(\frac{66}{91}\right)$	$e\left(\frac{235}{273}\right)$	$e\left(\frac{34}{39}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{191}{273}\right)$
$\chi_{61936}(51,\cdot)$	61936.rg	1092	yes	$-1$	$1$	$e\left(\frac{237}{364}\right)$	$e\left(\frac{69}{364}\right)$	$e\left(\frac{55}{182}\right)$	$e\left(\frac{209}{1092}\right)$	$e\left(\frac{293}{1092}\right)$	$e\left(\frac{153}{182}\right)$	$e\left(\frac{109}{273}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{69}{182}\right)$
$\chi_{61936}(53,\cdot)$	61936.rj	1092	yes	$-1$	$1$	$e\left(\frac{355}{364}\right)$	$e\left(\frac{131}{364}\right)$	$e\left(\frac{173}{182}\right)$	$e\left(\frac{985}{1092}\right)$	$e\left(\frac{187}{1092}\right)$	$e\left(\frac{61}{182}\right)$	$e\left(\frac{373}{546}\right)$	$e\left(\frac{35}{52}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{131}{182}\right)$
$\chi_{61936}(55,\cdot)$	61936.ho	42	no	$1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{61936}(57,\cdot)$	61936.og	182	no	$-1$	$1$	$e\left(\frac{71}{91}\right)$	$e\left(\frac{107}{182}\right)$	$e\left(\frac{51}{91}\right)$	$e\left(\frac{101}{182}\right)$	$e\left(\frac{31}{182}\right)$	$e\left(\frac{67}{182}\right)$	$e\left(\frac{57}{182}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{16}{91}\right)$
$\chi_{61936}(59,\cdot)$	61936.se	1092	yes	$-1$	$1$	$e\left(\frac{1045}{1092}\right)$	$e\left(\frac{947}{1092}\right)$	$e\left(\frac{499}{546}\right)$	$e\left(\frac{57}{364}\right)$	$e\left(\frac{521}{1092}\right)$	$e\left(\frac{75}{91}\right)$	$e\left(\frac{23}{273}\right)$	$e\left(\frac{125}{156}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{401}{546}\right)$
$\chi_{61936}(61,\cdot)$	61936.rq	1092	yes	$1$	$1$	$e\left(\frac{97}{1092}\right)$	$e\left(\frac{125}{1092}\right)$	$e\left(\frac{97}{546}\right)$	$e\left(\frac{499}{1092}\right)$	$e\left(\frac{185}{364}\right)$	$e\left(\frac{37}{182}\right)$	$e\left(\frac{181}{273}\right)$	$e\left(\frac{137}{156}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{125}{546}\right)$
$\chi_{61936}(65,\cdot)$	61936.on	273	no	$1$	$1$	$e\left(\frac{193}{273}\right)$	$e\left(\frac{32}{273}\right)$	$e\left(\frac{113}{273}\right)$	$e\left(\frac{202}{273}\right)$	$e\left(\frac{51}{91}\right)$	$e\left(\frac{75}{91}\right)$	$e\left(\frac{205}{273}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{64}{273}\right)$
$\chi_{61936}(67,\cdot)$	61936.nj	156	no	$-1$	$1$	$e\left(\frac{5}{156}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{119}{156}\right)$	$e\left(\frac{9}{52}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{23}{39}\right)$	$e\left(\frac{121}{156}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{37}{78}\right)$
$\chi_{61936}(69,\cdot)$	61936.ot	364	yes	$1$	$1$	$e\left(\frac{9}{364}\right)$	$e\left(\frac{233}{364}\right)$	$e\left(\frac{9}{182}\right)$	$e\left(\frac{339}{364}\right)$	$e\left(\frac{59}{364}\right)$	$e\left(\frac{121}{182}\right)$	$e\left(\frac{44}{91}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{51}{182}\right)$
$\chi_{61936}(71,\cdot)$	61936.nz	182	no	$1$	$1$	$e\left(\frac{41}{182}\right)$	$e\left(\frac{111}{182}\right)$	$e\left(\frac{41}{91}\right)$	$e\left(\frac{29}{91}\right)$	$e\left(\frac{107}{182}\right)$	$e\left(\frac{76}{91}\right)$	$e\left(\frac{3}{182}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{20}{91}\right)$
$\chi_{61936}(73,\cdot)$	61936.re	546	no	$-1$	$1$	$e\left(\frac{86}{91}\right)$	$e\left(\frac{2}{91}\right)$	$e\left(\frac{81}{91}\right)$	$e\left(\frac{53}{546}\right)$	$e\left(\frac{205}{273}\right)$	$e\left(\frac{88}{91}\right)$	$e\left(\frac{475}{546}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{91}\right)$

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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	$61936$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{1092}\)
Order	$26208$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{61936}(1,\cdot)\)	61936.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{61936}(3,\cdot)\)	61936.se	1092	yes	\(-1\)	\(1\)	\(e\left(\frac{859}{1092}\right)\)	\(e\left(\frac{257}{1092}\right)\)	\(e\left(\frac{313}{546}\right)\)	\(e\left(\frac{27}{364}\right)\)	\(e\left(\frac{515}{1092}\right)\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{236}{273}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{257}{546}\right)\)
\(\chi_{61936}(5,\cdot)\)	61936.sh	1092	yes	\(-1\)	\(1\)	\(e\left(\frac{257}{1092}\right)\)	\(e\left(\frac{607}{1092}\right)\)	\(e\left(\frac{257}{546}\right)\)	\(e\left(\frac{335}{364}\right)\)	\(e\left(\frac{613}{1092}\right)\)	\(e\left(\frac{72}{91}\right)\)	\(e\left(\frac{521}{546}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{61}{546}\right)\)
\(\chi_{61936}(9,\cdot)\)	61936.qn	546	no	\(1\)	\(1\)	\(e\left(\frac{313}{546}\right)\)	\(e\left(\frac{257}{546}\right)\)	\(e\left(\frac{40}{273}\right)\)	\(e\left(\frac{27}{182}\right)\)	\(e\left(\frac{515}{546}\right)\)	\(e\left(\frac{4}{91}\right)\)	\(e\left(\frac{199}{273}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{257}{273}\right)\)
\(\chi_{61936}(11,\cdot)\)	61936.rg	1092	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{364}\right)\)	\(e\left(\frac{335}{364}\right)\)	\(e\left(\frac{27}{182}\right)\)	\(e\left(\frac{139}{1092}\right)\)	\(e\left(\frac{895}{1092}\right)\)	\(e\left(\frac{181}{182}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{153}{182}\right)\)
\(\chi_{61936}(13,\cdot)\)	61936.sa	1092	yes	\(-1\)	\(1\)	\(e\left(\frac{515}{1092}\right)\)	\(e\left(\frac{613}{1092}\right)\)	\(e\left(\frac{515}{546}\right)\)	\(e\left(\frac{895}{1092}\right)\)	\(e\left(\frac{1091}{1092}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{145}{182}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{67}{546}\right)\)
\(\chi_{61936}(15,\cdot)\)	61936.ok	182	no	\(1\)	\(1\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{72}{91}\right)\)	\(e\left(\frac{4}{91}\right)\)	\(e\left(\frac{181}{182}\right)\)	\(e\left(\frac{3}{91}\right)\)	\(e\left(\frac{74}{91}\right)\)	\(e\left(\frac{149}{182}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{53}{91}\right)\)
\(\chi_{61936}(17,\cdot)\)	61936.pr	546	no	\(1\)	\(1\)	\(e\left(\frac{236}{273}\right)\)	\(e\left(\frac{521}{546}\right)\)	\(e\left(\frac{199}{273}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{145}{182}\right)\)	\(e\left(\frac{149}{182}\right)\)	\(e\left(\frac{146}{273}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{248}{273}\right)\)
\(\chi_{61936}(19,\cdot)\)	61936.nf	156	no	\(1\)	\(1\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{25}{52}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{35}{78}\right)\)	\(e\left(\frac{7}{156}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{55}{78}\right)\)
\(\chi_{61936}(23,\cdot)\)	61936.hr	42	no	\(-1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{61936}(25,\cdot)\)	61936.qn	546	no	\(1\)	\(1\)	\(e\left(\frac{257}{546}\right)\)	\(e\left(\frac{61}{546}\right)\)	\(e\left(\frac{257}{273}\right)\)	\(e\left(\frac{153}{182}\right)\)	\(e\left(\frac{67}{546}\right)\)	\(e\left(\frac{53}{91}\right)\)	\(e\left(\frac{248}{273}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{61}{273}\right)\)
\(\chi_{61936}(27,\cdot)\)	61936.ow	364	yes	\(-1\)	\(1\)	\(e\left(\frac{131}{364}\right)\)	\(e\left(\frac{257}{364}\right)\)	\(e\left(\frac{131}{182}\right)\)	\(e\left(\frac{81}{364}\right)\)	\(e\left(\frac{151}{364}\right)\)	\(e\left(\frac{6}{91}\right)\)	\(e\left(\frac{54}{91}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{75}{182}\right)\)
\(\chi_{61936}(29,\cdot)\)	61936.ro	1092	yes	\(-1\)	\(1\)	\(e\left(\frac{895}{1092}\right)\)	\(e\left(\frac{1007}{1092}\right)\)	\(e\left(\frac{349}{546}\right)\)	\(e\left(\frac{527}{1092}\right)\)	\(e\left(\frac{205}{1092}\right)\)	\(e\left(\frac{135}{182}\right)\)	\(e\left(\frac{123}{182}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{461}{546}\right)\)
\(\chi_{61936}(31,\cdot)\)	61936.jf	78	no	\(1\)	\(1\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(-1\)	\(e\left(\frac{9}{13}\right)\)
\(\chi_{61936}(33,\cdot)\)	61936.pr	546	no	\(1\)	\(1\)	\(e\left(\frac{235}{273}\right)\)	\(e\left(\frac{85}{546}\right)\)	\(e\left(\frac{197}{273}\right)\)	\(e\left(\frac{55}{273}\right)\)	\(e\left(\frac{53}{182}\right)\)	\(e\left(\frac{3}{182}\right)\)	\(e\left(\frac{268}{273}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{85}{273}\right)\)
\(\chi_{61936}(37,\cdot)\)	61936.rj	1092	yes	\(-1\)	\(1\)	\(e\left(\frac{275}{364}\right)\)	\(e\left(\frac{163}{364}\right)\)	\(e\left(\frac{93}{182}\right)\)	\(e\left(\frac{317}{1092}\right)\)	\(e\left(\frac{191}{1092}\right)\)	\(e\left(\frac{37}{182}\right)\)	\(e\left(\frac{89}{546}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{163}{182}\right)\)
\(\chi_{61936}(39,\cdot)\)	61936.oy	546	no	\(1\)	\(1\)	\(e\left(\frac{47}{182}\right)\)	\(e\left(\frac{145}{182}\right)\)	\(e\left(\frac{47}{91}\right)\)	\(e\left(\frac{244}{273}\right)\)	\(e\left(\frac{257}{546}\right)\)	\(e\left(\frac{5}{91}\right)\)	\(e\left(\frac{361}{546}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{54}{91}\right)\)
\(\chi_{61936}(41,\cdot)\)	61936.ob	182	no	\(1\)	\(1\)	\(e\left(\frac{149}{182}\right)\)	\(e\left(\frac{43}{91}\right)\)	\(e\left(\frac{58}{91}\right)\)	\(e\left(\frac{31}{182}\right)\)	\(e\left(\frac{89}{91}\right)\)	\(e\left(\frac{53}{182}\right)\)	\(e\left(\frac{11}{91}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{86}{91}\right)\)
\(\chi_{61936}(43,\cdot)\)	61936.sb	1092	yes	\(1\)	\(1\)	\(e\left(\frac{23}{1092}\right)\)	\(e\left(\frac{373}{1092}\right)\)	\(e\left(\frac{23}{546}\right)\)	\(e\left(\frac{199}{1092}\right)\)	\(e\left(\frac{899}{1092}\right)\)	\(e\left(\frac{33}{91}\right)\)	\(e\left(\frac{139}{182}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{373}{546}\right)\)
\(\chi_{61936}(45,\cdot)\)	61936.sh	1092	yes	\(-1\)	\(1\)	\(e\left(\frac{883}{1092}\right)\)	\(e\left(\frac{29}{1092}\right)\)	\(e\left(\frac{337}{546}\right)\)	\(e\left(\frac{25}{364}\right)\)	\(e\left(\frac{551}{1092}\right)\)	\(e\left(\frac{76}{91}\right)\)	\(e\left(\frac{373}{546}\right)\)	\(e\left(\frac{53}{156}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{29}{546}\right)\)
\(\chi_{61936}(47,\cdot)\)	61936.qo	546	no	\(-1\)	\(1\)	\(e\left(\frac{205}{546}\right)\)	\(e\left(\frac{191}{546}\right)\)	\(e\left(\frac{205}{273}\right)\)	\(e\left(\frac{127}{182}\right)\)	\(e\left(\frac{353}{546}\right)\)	\(e\left(\frac{66}{91}\right)\)	\(e\left(\frac{235}{273}\right)\)	\(e\left(\frac{34}{39}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{191}{273}\right)\)
\(\chi_{61936}(51,\cdot)\)	61936.rg	1092	yes	\(-1\)	\(1\)	\(e\left(\frac{237}{364}\right)\)	\(e\left(\frac{69}{364}\right)\)	\(e\left(\frac{55}{182}\right)\)	\(e\left(\frac{209}{1092}\right)\)	\(e\left(\frac{293}{1092}\right)\)	\(e\left(\frac{153}{182}\right)\)	\(e\left(\frac{109}{273}\right)\)	\(e\left(\frac{23}{52}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{69}{182}\right)\)
\(\chi_{61936}(53,\cdot)\)	61936.rj	1092	yes	\(-1\)	\(1\)	\(e\left(\frac{355}{364}\right)\)	\(e\left(\frac{131}{364}\right)\)	\(e\left(\frac{173}{182}\right)\)	\(e\left(\frac{985}{1092}\right)\)	\(e\left(\frac{187}{1092}\right)\)	\(e\left(\frac{61}{182}\right)\)	\(e\left(\frac{373}{546}\right)\)	\(e\left(\frac{35}{52}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{131}{182}\right)\)
\(\chi_{61936}(55,\cdot)\)	61936.ho	42	no	\(1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{61936}(57,\cdot)\)	61936.og	182	no	\(-1\)	\(1\)	\(e\left(\frac{71}{91}\right)\)	\(e\left(\frac{107}{182}\right)\)	\(e\left(\frac{51}{91}\right)\)	\(e\left(\frac{101}{182}\right)\)	\(e\left(\frac{31}{182}\right)\)	\(e\left(\frac{67}{182}\right)\)	\(e\left(\frac{57}{182}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{16}{91}\right)\)
\(\chi_{61936}(59,\cdot)\)	61936.se	1092	yes	\(-1\)	\(1\)	\(e\left(\frac{1045}{1092}\right)\)	\(e\left(\frac{947}{1092}\right)\)	\(e\left(\frac{499}{546}\right)\)	\(e\left(\frac{57}{364}\right)\)	\(e\left(\frac{521}{1092}\right)\)	\(e\left(\frac{75}{91}\right)\)	\(e\left(\frac{23}{273}\right)\)	\(e\left(\frac{125}{156}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{401}{546}\right)\)
\(\chi_{61936}(61,\cdot)\)	61936.rq	1092	yes	\(1\)	\(1\)	\(e\left(\frac{97}{1092}\right)\)	\(e\left(\frac{125}{1092}\right)\)	\(e\left(\frac{97}{546}\right)\)	\(e\left(\frac{499}{1092}\right)\)	\(e\left(\frac{185}{364}\right)\)	\(e\left(\frac{37}{182}\right)\)	\(e\left(\frac{181}{273}\right)\)	\(e\left(\frac{137}{156}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{125}{546}\right)\)
\(\chi_{61936}(65,\cdot)\)	61936.on	273	no	\(1\)	\(1\)	\(e\left(\frac{193}{273}\right)\)	\(e\left(\frac{32}{273}\right)\)	\(e\left(\frac{113}{273}\right)\)	\(e\left(\frac{202}{273}\right)\)	\(e\left(\frac{51}{91}\right)\)	\(e\left(\frac{75}{91}\right)\)	\(e\left(\frac{205}{273}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{64}{273}\right)\)
\(\chi_{61936}(67,\cdot)\)	61936.nj	156	no	\(-1\)	\(1\)	\(e\left(\frac{5}{156}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{119}{156}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{23}{39}\right)\)	\(e\left(\frac{121}{156}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{37}{78}\right)\)
\(\chi_{61936}(69,\cdot)\)	61936.ot	364	yes	\(1\)	\(1\)	\(e\left(\frac{9}{364}\right)\)	\(e\left(\frac{233}{364}\right)\)	\(e\left(\frac{9}{182}\right)\)	\(e\left(\frac{339}{364}\right)\)	\(e\left(\frac{59}{364}\right)\)	\(e\left(\frac{121}{182}\right)\)	\(e\left(\frac{44}{91}\right)\)	\(e\left(\frac{17}{52}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{51}{182}\right)\)
\(\chi_{61936}(71,\cdot)\)	61936.nz	182	no	\(1\)	\(1\)	\(e\left(\frac{41}{182}\right)\)	\(e\left(\frac{111}{182}\right)\)	\(e\left(\frac{41}{91}\right)\)	\(e\left(\frac{29}{91}\right)\)	\(e\left(\frac{107}{182}\right)\)	\(e\left(\frac{76}{91}\right)\)	\(e\left(\frac{3}{182}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{20}{91}\right)\)
\(\chi_{61936}(73,\cdot)\)	61936.re	546	no	\(-1\)	\(1\)	\(e\left(\frac{86}{91}\right)\)	\(e\left(\frac{2}{91}\right)\)	\(e\left(\frac{81}{91}\right)\)	\(e\left(\frac{53}{546}\right)\)	\(e\left(\frac{205}{273}\right)\)	\(e\left(\frac{88}{91}\right)\)	\(e\left(\frac{475}{546}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{91}\right)\)

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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.