LMFDB - Group of Dirichlet characters of modulus 56644

sage:H = DirichletGroup(56644)

pari:g = idealstar(,56644,2)

Character group

sage:G.order() pari:g.no
Order	=	22848
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{5712}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{56644}(28323,\cdot)$, $\chi_{56644}(50865,\cdot)$, $\chi_{56644}(34105,\cdot)$

First 32 of 22848 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$19$	$23$	$25$	$27$
$\chi_{56644}(1,\cdot)$	56644.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{56644}(3,\cdot)$	56644.gb	5712	yes	$-1$	$1$	$e\left(\frac{3013}{5712}\right)$	$e\left(\frac{3041}{5712}\right)$	$e\left(\frac{157}{2856}\right)$	$e\left(\frac{3067}{5712}\right)$	$e\left(\frac{241}{476}\right)$	$e\left(\frac{57}{952}\right)$	$e\left(\frac{157}{408}\right)$	$e\left(\frac{1283}{5712}\right)$	$e\left(\frac{185}{2856}\right)$	$e\left(\frac{1109}{1904}\right)$
$\chi_{56644}(5,\cdot)$	56644.ga	5712	no	$1$	$1$	$e\left(\frac{3041}{5712}\right)$	$e\left(\frac{4693}{5712}\right)$	$e\left(\frac{185}{2856}\right)$	$e\left(\frac{5615}{5712}\right)$	$e\left(\frac{381}{476}\right)$	$e\left(\frac{337}{952}\right)$	$e\left(\frac{389}{408}\right)$	$e\left(\frac{5623}{5712}\right)$	$e\left(\frac{1837}{2856}\right)$	$e\left(\frac{1137}{1904}\right)$
$\chi_{56644}(9,\cdot)$	56644.fx	2856	no	$1$	$1$	$e\left(\frac{157}{2856}\right)$	$e\left(\frac{185}{2856}\right)$	$e\left(\frac{157}{1428}\right)$	$e\left(\frac{211}{2856}\right)$	$e\left(\frac{3}{238}\right)$	$e\left(\frac{57}{476}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{1283}{2856}\right)$	$e\left(\frac{185}{1428}\right)$	$e\left(\frac{157}{952}\right)$
$\chi_{56644}(11,\cdot)$	56644.gd	5712	yes	$1$	$1$	$e\left(\frac{3067}{5712}\right)$	$e\left(\frac{5615}{5712}\right)$	$e\left(\frac{211}{2856}\right)$	$e\left(\frac{3085}{5712}\right)$	$e\left(\frac{1}{476}\right)$	$e\left(\frac{495}{952}\right)$	$e\left(\frac{7}{408}\right)$	$e\left(\frac{3125}{5712}\right)$	$e\left(\frac{2759}{2856}\right)$	$e\left(\frac{1163}{1904}\right)$
$\chi_{56644}(13,\cdot)$	56644.ev	476	no	$-1$	$1$	$e\left(\frac{241}{476}\right)$	$e\left(\frac{381}{476}\right)$	$e\left(\frac{3}{238}\right)$	$e\left(\frac{1}{476}\right)$	$e\left(\frac{39}{238}\right)$	$e\left(\frac{73}{238}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{261}{476}\right)$	$e\left(\frac{143}{238}\right)$	$e\left(\frac{247}{476}\right)$
$\chi_{56644}(15,\cdot)$	56644.fl	952	yes	$-1$	$1$	$e\left(\frac{57}{952}\right)$	$e\left(\frac{337}{952}\right)$	$e\left(\frac{57}{476}\right)$	$e\left(\frac{495}{952}\right)$	$e\left(\frac{73}{238}\right)$	$e\left(\frac{197}{476}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{199}{952}\right)$	$e\left(\frac{337}{476}\right)$	$e\left(\frac{171}{952}\right)$
$\chi_{56644}(19,\cdot)$	56644.er	408	no	$1$	$1$	$e\left(\frac{157}{408}\right)$	$e\left(\frac{389}{408}\right)$	$e\left(\frac{157}{204}\right)$	$e\left(\frac{7}{408}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{79}{204}\right)$	$e\left(\frac{263}{408}\right)$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{21}{136}\right)$
$\chi_{56644}(23,\cdot)$	56644.gd	5712	yes	$1$	$1$	$e\left(\frac{1283}{5712}\right)$	$e\left(\frac{5623}{5712}\right)$	$e\left(\frac{1283}{2856}\right)$	$e\left(\frac{3125}{5712}\right)$	$e\left(\frac{261}{476}\right)$	$e\left(\frac{199}{952}\right)$	$e\left(\frac{263}{408}\right)$	$e\left(\frac{4045}{5712}\right)$	$e\left(\frac{2767}{2856}\right)$	$e\left(\frac{1283}{1904}\right)$
$\chi_{56644}(25,\cdot)$	56644.fx	2856	no	$1$	$1$	$e\left(\frac{185}{2856}\right)$	$e\left(\frac{1837}{2856}\right)$	$e\left(\frac{185}{1428}\right)$	$e\left(\frac{2759}{2856}\right)$	$e\left(\frac{143}{238}\right)$	$e\left(\frac{337}{476}\right)$	$e\left(\frac{185}{204}\right)$	$e\left(\frac{2767}{2856}\right)$	$e\left(\frac{409}{1428}\right)$	$e\left(\frac{185}{952}\right)$
$\chi_{56644}(27,\cdot)$	56644.fu	1904	yes	$-1$	$1$	$e\left(\frac{1109}{1904}\right)$	$e\left(\frac{1137}{1904}\right)$	$e\left(\frac{157}{952}\right)$	$e\left(\frac{1163}{1904}\right)$	$e\left(\frac{247}{476}\right)$	$e\left(\frac{171}{952}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{1283}{1904}\right)$	$e\left(\frac{185}{952}\right)$	$e\left(\frac{1423}{1904}\right)$
$\chi_{56644}(29,\cdot)$	56644.ft	1904	no	$-1$	$1$	$e\left(\frac{1691}{1904}\right)$	$e\left(\frac{1271}{1904}\right)$	$e\left(\frac{739}{952}\right)$	$e\left(\frac{1357}{1904}\right)$	$e\left(\frac{103}{476}\right)$	$e\left(\frac{529}{952}\right)$	$e\left(\frac{59}{136}\right)$	$e\left(\frac{1461}{1904}\right)$	$e\left(\frac{319}{952}\right)$	$e\left(\frac{1265}{1904}\right)$
$\chi_{56644}(31,\cdot)$	56644.fj	816	no	$-1$	$1$	$e\left(\frac{571}{816}\right)$	$e\left(\frac{335}{816}\right)$	$e\left(\frac{163}{408}\right)$	$e\left(\frac{757}{816}\right)$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{325}{408}\right)$	$e\left(\frac{173}{816}\right)$	$e\left(\frac{335}{408}\right)$	$e\left(\frac{27}{272}\right)$
$\chi_{56644}(33,\cdot)$	56644.ez	714	no	$-1$	$1$	$e\left(\frac{23}{357}\right)$	$e\left(\frac{184}{357}\right)$	$e\left(\frac{46}{357}\right)$	$e\left(\frac{55}{714}\right)$	$e\left(\frac{121}{238}\right)$	$e\left(\frac{69}{119}\right)$	$e\left(\frac{41}{102}\right)$	$e\left(\frac{551}{714}\right)$	$e\left(\frac{11}{357}\right)$	$e\left(\frac{23}{119}\right)$
$\chi_{56644}(37,\cdot)$	56644.gc	5712	no	$-1$	$1$	$e\left(\frac{1349}{5712}\right)$	$e\left(\frac{4009}{5712}\right)$	$e\left(\frac{1349}{2856}\right)$	$e\left(\frac{2195}{5712}\right)$	$e\left(\frac{47}{476}\right)$	$e\left(\frac{893}{952}\right)$	$e\left(\frac{125}{408}\right)$	$e\left(\frac{4075}{5712}\right)$	$e\left(\frac{1153}{2856}\right)$	$e\left(\frac{1349}{1904}\right)$
$\chi_{56644}(39,\cdot)$	56644.gd	5712	yes	$1$	$1$	$e\left(\frac{193}{5712}\right)$	$e\left(\frac{1901}{5712}\right)$	$e\left(\frac{193}{2856}\right)$	$e\left(\frac{3079}{5712}\right)$	$e\left(\frac{319}{476}\right)$	$e\left(\frac{349}{952}\right)$	$e\left(\frac{397}{408}\right)$	$e\left(\frac{4415}{5712}\right)$	$e\left(\frac{1901}{2856}\right)$	$e\left(\frac{193}{1904}\right)$
$\chi_{56644}(41,\cdot)$	56644.fv	1904	no	$1$	$1$	$e\left(\frac{1877}{1904}\right)$	$e\left(\frac{617}{1904}\right)$	$e\left(\frac{925}{952}\right)$	$e\left(\frac{1419}{1904}\right)$	$e\left(\frac{3}{476}\right)$	$e\left(\frac{295}{952}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{1459}{1904}\right)$	$e\left(\frac{617}{952}\right)$	$e\left(\frac{1823}{1904}\right)$
$\chi_{56644}(43,\cdot)$	56644.fl	952	yes	$-1$	$1$	$e\left(\frac{451}{952}\right)$	$e\left(\frac{395}{952}\right)$	$e\left(\frac{451}{476}\right)$	$e\left(\frac{309}{952}\right)$	$e\left(\frac{135}{238}\right)$	$e\left(\frac{423}{476}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{205}{952}\right)$	$e\left(\frac{395}{476}\right)$	$e\left(\frac{401}{952}\right)$
$\chi_{56644}(45,\cdot)$	56644.ga	5712	no	$1$	$1$	$e\left(\frac{3355}{5712}\right)$	$e\left(\frac{5063}{5712}\right)$	$e\left(\frac{499}{2856}\right)$	$e\left(\frac{325}{5712}\right)$	$e\left(\frac{387}{476}\right)$	$e\left(\frac{451}{952}\right)$	$e\left(\frac{295}{408}\right)$	$e\left(\frac{2477}{5712}\right)$	$e\left(\frac{2207}{2856}\right)$	$e\left(\frac{1451}{1904}\right)$
$\chi_{56644}(47,\cdot)$	56644.fp	1428	yes	$1$	$1$	$e\left(\frac{1409}{1428}\right)$	$e\left(\frac{919}{1428}\right)$	$e\left(\frac{695}{714}\right)$	$e\left(\frac{1025}{1428}\right)$	$e\left(\frac{235}{238}\right)$	$e\left(\frac{75}{119}\right)$	$e\left(\frac{83}{102}\right)$	$e\left(\frac{13}{1428}\right)$	$e\left(\frac{205}{714}\right)$	$e\left(\frac{457}{476}\right)$
$\chi_{56644}(53,\cdot)$	56644.fx	2856	no	$1$	$1$	$e\left(\frac{2843}{2856}\right)$	$e\left(\frac{967}{2856}\right)$	$e\left(\frac{1415}{1428}\right)$	$e\left(\frac{2693}{2856}\right)$	$e\left(\frac{71}{238}\right)$	$e\left(\frac{159}{476}\right)$	$e\left(\frac{191}{204}\right)$	$e\left(\frac{2677}{2856}\right)$	$e\left(\frac{967}{1428}\right)$	$e\left(\frac{939}{952}\right)$
$\chi_{56644}(55,\cdot)$	56644.ew	476	yes	$1$	$1$	$e\left(\frac{33}{476}\right)$	$e\left(\frac{383}{476}\right)$	$e\left(\frac{33}{238}\right)$	$e\left(\frac{249}{476}\right)$	$e\left(\frac{191}{238}\right)$	$e\left(\frac{104}{119}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{253}{476}\right)$	$e\left(\frac{145}{238}\right)$	$e\left(\frac{99}{476}\right)$
$\chi_{56644}(57,\cdot)$	56644.ft	1904	no	$-1$	$1$	$e\left(\frac{1737}{1904}\right)$	$e\left(\frac{925}{1904}\right)$	$e\left(\frac{785}{952}\right)$	$e\left(\frac{1055}{1904}\right)$	$e\left(\frac{45}{476}\right)$	$e\left(\frac{379}{952}\right)$	$e\left(\frac{105}{136}\right)$	$e\left(\frac{1655}{1904}\right)$	$e\left(\frac{925}{952}\right)$	$e\left(\frac{1403}{1904}\right)$
$\chi_{56644}(59,\cdot)$	56644.fz	2856	yes	$1$	$1$	$e\left(\frac{1913}{2856}\right)$	$e\left(\frac{2809}{2856}\right)$	$e\left(\frac{485}{1428}\right)$	$e\left(\frac{1907}{2856}\right)$	$e\left(\frac{99}{119}\right)$	$e\left(\frac{311}{476}\right)$	$e\left(\frac{77}{204}\right)$	$e\left(\frac{307}{2856}\right)$	$e\left(\frac{1381}{1428}\right)$	$e\left(\frac{9}{952}\right)$
$\chi_{56644}(61,\cdot)$	56644.ga	5712	no	$1$	$1$	$e\left(\frac{1223}{5712}\right)$	$e\left(\frac{3715}{5712}\right)$	$e\left(\frac{1223}{2856}\right)$	$e\left(\frac{2153}{5712}\right)$	$e\left(\frac{131}{476}\right)$	$e\left(\frac{823}{952}\right)$	$e\left(\frac{203}{408}\right)$	$e\left(\frac{1681}{5712}\right)$	$e\left(\frac{859}{2856}\right)$	$e\left(\frac{1223}{1904}\right)$
$\chi_{56644}(65,\cdot)$	56644.en	336	no	$-1$	$1$	$e\left(\frac{13}{336}\right)$	$e\left(\frac{209}{336}\right)$	$e\left(\frac{13}{168}\right)$	$e\left(\frac{331}{336}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{179}{336}\right)$	$e\left(\frac{41}{168}\right)$	$e\left(\frac{13}{112}\right)$
$\chi_{56644}(67,\cdot)$	56644.di	102	no	$-1$	$1$	$e\left(\frac{43}{51}\right)$	$e\left(\frac{25}{102}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{37}{51}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{31}{102}\right)$	$e\left(\frac{35}{51}\right)$	$e\left(\frac{25}{51}\right)$	$e\left(\frac{9}{17}\right)$
$\chi_{56644}(69,\cdot)$	56644.ec	238	no	$-1$	$1$	$e\left(\frac{179}{238}\right)$	$e\left(\frac{123}{238}\right)$	$e\left(\frac{60}{119}\right)$	$e\left(\frac{10}{119}\right)$	$e\left(\frac{13}{238}\right)$	$e\left(\frac{32}{119}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{111}{119}\right)$	$e\left(\frac{4}{119}\right)$	$e\left(\frac{61}{238}\right)$
$\chi_{56644}(71,\cdot)$	56644.fs	1904	yes	$1$	$1$	$e\left(\frac{31}{1904}\right)$	$e\left(\frac{1795}{1904}\right)$	$e\left(\frac{31}{952}\right)$	$e\left(\frac{169}{1904}\right)$	$e\left(\frac{23}{476}\right)$	$e\left(\frac{913}{952}\right)$	$e\left(\frac{99}{136}\right)$	$e\left(\frac{1745}{1904}\right)$	$e\left(\frac{843}{952}\right)$	$e\left(\frac{93}{1904}\right)$
$\chi_{56644}(73,\cdot)$	56644.ga	5712	no	$1$	$1$	$e\left(\frac{2785}{5712}\right)$	$e\left(\frac{2645}{5712}\right)$	$e\left(\frac{2785}{2856}\right)$	$e\left(\frac{1087}{5712}\right)$	$e\left(\frac{461}{476}\right)$	$e\left(\frac{905}{952}\right)$	$e\left(\frac{133}{408}\right)$	$e\left(\frac{4295}{5712}\right)$	$e\left(\frac{2645}{2856}\right)$	$e\left(\frac{881}{1904}\right)$
$\chi_{56644}(75,\cdot)$	56644.eo	336	no	$-1$	$1$	$e\left(\frac{199}{336}\right)$	$e\left(\frac{59}{336}\right)$	$e\left(\frac{31}{168}\right)$	$e\left(\frac{169}{336}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{43}{56}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{65}{336}\right)$	$e\left(\frac{59}{168}\right)$	$e\left(\frac{87}{112}\right)$
$\chi_{56644}(79,\cdot)$	56644.fh	816	no	$1$	$1$	$e\left(\frac{365}{816}\right)$	$e\left(\frac{217}{816}\right)$	$e\left(\frac{365}{408}\right)$	$e\left(\frac{779}{816}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{311}{408}\right)$	$e\left(\frac{67}{816}\right)$	$e\left(\frac{217}{408}\right)$	$e\left(\frac{93}{272}\right)$

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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	$56644$
Structure	\(C_{2}\times C_{2}\times C_{5712}\)
Order	$22848$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(23\)	\(25\)	\(27\)
\(\chi_{56644}(1,\cdot)\)	56644.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{56644}(3,\cdot)\)	56644.gb	5712	yes	\(-1\)	\(1\)	\(e\left(\frac{3013}{5712}\right)\)	\(e\left(\frac{3041}{5712}\right)\)	\(e\left(\frac{157}{2856}\right)\)	\(e\left(\frac{3067}{5712}\right)\)	\(e\left(\frac{241}{476}\right)\)	\(e\left(\frac{57}{952}\right)\)	\(e\left(\frac{157}{408}\right)\)	\(e\left(\frac{1283}{5712}\right)\)	\(e\left(\frac{185}{2856}\right)\)	\(e\left(\frac{1109}{1904}\right)\)
\(\chi_{56644}(5,\cdot)\)	56644.ga	5712	no	\(1\)	\(1\)	\(e\left(\frac{3041}{5712}\right)\)	\(e\left(\frac{4693}{5712}\right)\)	\(e\left(\frac{185}{2856}\right)\)	\(e\left(\frac{5615}{5712}\right)\)	\(e\left(\frac{381}{476}\right)\)	\(e\left(\frac{337}{952}\right)\)	\(e\left(\frac{389}{408}\right)\)	\(e\left(\frac{5623}{5712}\right)\)	\(e\left(\frac{1837}{2856}\right)\)	\(e\left(\frac{1137}{1904}\right)\)
\(\chi_{56644}(9,\cdot)\)	56644.fx	2856	no	\(1\)	\(1\)	\(e\left(\frac{157}{2856}\right)\)	\(e\left(\frac{185}{2856}\right)\)	\(e\left(\frac{157}{1428}\right)\)	\(e\left(\frac{211}{2856}\right)\)	\(e\left(\frac{3}{238}\right)\)	\(e\left(\frac{57}{476}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{1283}{2856}\right)\)	\(e\left(\frac{185}{1428}\right)\)	\(e\left(\frac{157}{952}\right)\)
\(\chi_{56644}(11,\cdot)\)	56644.gd	5712	yes	\(1\)	\(1\)	\(e\left(\frac{3067}{5712}\right)\)	\(e\left(\frac{5615}{5712}\right)\)	\(e\left(\frac{211}{2856}\right)\)	\(e\left(\frac{3085}{5712}\right)\)	\(e\left(\frac{1}{476}\right)\)	\(e\left(\frac{495}{952}\right)\)	\(e\left(\frac{7}{408}\right)\)	\(e\left(\frac{3125}{5712}\right)\)	\(e\left(\frac{2759}{2856}\right)\)	\(e\left(\frac{1163}{1904}\right)\)
\(\chi_{56644}(13,\cdot)\)	56644.ev	476	no	\(-1\)	\(1\)	\(e\left(\frac{241}{476}\right)\)	\(e\left(\frac{381}{476}\right)\)	\(e\left(\frac{3}{238}\right)\)	\(e\left(\frac{1}{476}\right)\)	\(e\left(\frac{39}{238}\right)\)	\(e\left(\frac{73}{238}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{261}{476}\right)\)	\(e\left(\frac{143}{238}\right)\)	\(e\left(\frac{247}{476}\right)\)
\(\chi_{56644}(15,\cdot)\)	56644.fl	952	yes	\(-1\)	\(1\)	\(e\left(\frac{57}{952}\right)\)	\(e\left(\frac{337}{952}\right)\)	\(e\left(\frac{57}{476}\right)\)	\(e\left(\frac{495}{952}\right)\)	\(e\left(\frac{73}{238}\right)\)	\(e\left(\frac{197}{476}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{199}{952}\right)\)	\(e\left(\frac{337}{476}\right)\)	\(e\left(\frac{171}{952}\right)\)
\(\chi_{56644}(19,\cdot)\)	56644.er	408	no	\(1\)	\(1\)	\(e\left(\frac{157}{408}\right)\)	\(e\left(\frac{389}{408}\right)\)	\(e\left(\frac{157}{204}\right)\)	\(e\left(\frac{7}{408}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{79}{204}\right)\)	\(e\left(\frac{263}{408}\right)\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{21}{136}\right)\)
\(\chi_{56644}(23,\cdot)\)	56644.gd	5712	yes	\(1\)	\(1\)	\(e\left(\frac{1283}{5712}\right)\)	\(e\left(\frac{5623}{5712}\right)\)	\(e\left(\frac{1283}{2856}\right)\)	\(e\left(\frac{3125}{5712}\right)\)	\(e\left(\frac{261}{476}\right)\)	\(e\left(\frac{199}{952}\right)\)	\(e\left(\frac{263}{408}\right)\)	\(e\left(\frac{4045}{5712}\right)\)	\(e\left(\frac{2767}{2856}\right)\)	\(e\left(\frac{1283}{1904}\right)\)
\(\chi_{56644}(25,\cdot)\)	56644.fx	2856	no	\(1\)	\(1\)	\(e\left(\frac{185}{2856}\right)\)	\(e\left(\frac{1837}{2856}\right)\)	\(e\left(\frac{185}{1428}\right)\)	\(e\left(\frac{2759}{2856}\right)\)	\(e\left(\frac{143}{238}\right)\)	\(e\left(\frac{337}{476}\right)\)	\(e\left(\frac{185}{204}\right)\)	\(e\left(\frac{2767}{2856}\right)\)	\(e\left(\frac{409}{1428}\right)\)	\(e\left(\frac{185}{952}\right)\)
\(\chi_{56644}(27,\cdot)\)	56644.fu	1904	yes	\(-1\)	\(1\)	\(e\left(\frac{1109}{1904}\right)\)	\(e\left(\frac{1137}{1904}\right)\)	\(e\left(\frac{157}{952}\right)\)	\(e\left(\frac{1163}{1904}\right)\)	\(e\left(\frac{247}{476}\right)\)	\(e\left(\frac{171}{952}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{1283}{1904}\right)\)	\(e\left(\frac{185}{952}\right)\)	\(e\left(\frac{1423}{1904}\right)\)
\(\chi_{56644}(29,\cdot)\)	56644.ft	1904	no	\(-1\)	\(1\)	\(e\left(\frac{1691}{1904}\right)\)	\(e\left(\frac{1271}{1904}\right)\)	\(e\left(\frac{739}{952}\right)\)	\(e\left(\frac{1357}{1904}\right)\)	\(e\left(\frac{103}{476}\right)\)	\(e\left(\frac{529}{952}\right)\)	\(e\left(\frac{59}{136}\right)\)	\(e\left(\frac{1461}{1904}\right)\)	\(e\left(\frac{319}{952}\right)\)	\(e\left(\frac{1265}{1904}\right)\)
\(\chi_{56644}(31,\cdot)\)	56644.fj	816	no	\(-1\)	\(1\)	\(e\left(\frac{571}{816}\right)\)	\(e\left(\frac{335}{816}\right)\)	\(e\left(\frac{163}{408}\right)\)	\(e\left(\frac{757}{816}\right)\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{325}{408}\right)\)	\(e\left(\frac{173}{816}\right)\)	\(e\left(\frac{335}{408}\right)\)	\(e\left(\frac{27}{272}\right)\)
\(\chi_{56644}(33,\cdot)\)	56644.ez	714	no	\(-1\)	\(1\)	\(e\left(\frac{23}{357}\right)\)	\(e\left(\frac{184}{357}\right)\)	\(e\left(\frac{46}{357}\right)\)	\(e\left(\frac{55}{714}\right)\)	\(e\left(\frac{121}{238}\right)\)	\(e\left(\frac{69}{119}\right)\)	\(e\left(\frac{41}{102}\right)\)	\(e\left(\frac{551}{714}\right)\)	\(e\left(\frac{11}{357}\right)\)	\(e\left(\frac{23}{119}\right)\)
\(\chi_{56644}(37,\cdot)\)	56644.gc	5712	no	\(-1\)	\(1\)	\(e\left(\frac{1349}{5712}\right)\)	\(e\left(\frac{4009}{5712}\right)\)	\(e\left(\frac{1349}{2856}\right)\)	\(e\left(\frac{2195}{5712}\right)\)	\(e\left(\frac{47}{476}\right)\)	\(e\left(\frac{893}{952}\right)\)	\(e\left(\frac{125}{408}\right)\)	\(e\left(\frac{4075}{5712}\right)\)	\(e\left(\frac{1153}{2856}\right)\)	\(e\left(\frac{1349}{1904}\right)\)
\(\chi_{56644}(39,\cdot)\)	56644.gd	5712	yes	\(1\)	\(1\)	\(e\left(\frac{193}{5712}\right)\)	\(e\left(\frac{1901}{5712}\right)\)	\(e\left(\frac{193}{2856}\right)\)	\(e\left(\frac{3079}{5712}\right)\)	\(e\left(\frac{319}{476}\right)\)	\(e\left(\frac{349}{952}\right)\)	\(e\left(\frac{397}{408}\right)\)	\(e\left(\frac{4415}{5712}\right)\)	\(e\left(\frac{1901}{2856}\right)\)	\(e\left(\frac{193}{1904}\right)\)
\(\chi_{56644}(41,\cdot)\)	56644.fv	1904	no	\(1\)	\(1\)	\(e\left(\frac{1877}{1904}\right)\)	\(e\left(\frac{617}{1904}\right)\)	\(e\left(\frac{925}{952}\right)\)	\(e\left(\frac{1419}{1904}\right)\)	\(e\left(\frac{3}{476}\right)\)	\(e\left(\frac{295}{952}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{1459}{1904}\right)\)	\(e\left(\frac{617}{952}\right)\)	\(e\left(\frac{1823}{1904}\right)\)
\(\chi_{56644}(43,\cdot)\)	56644.fl	952	yes	\(-1\)	\(1\)	\(e\left(\frac{451}{952}\right)\)	\(e\left(\frac{395}{952}\right)\)	\(e\left(\frac{451}{476}\right)\)	\(e\left(\frac{309}{952}\right)\)	\(e\left(\frac{135}{238}\right)\)	\(e\left(\frac{423}{476}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{205}{952}\right)\)	\(e\left(\frac{395}{476}\right)\)	\(e\left(\frac{401}{952}\right)\)
\(\chi_{56644}(45,\cdot)\)	56644.ga	5712	no	\(1\)	\(1\)	\(e\left(\frac{3355}{5712}\right)\)	\(e\left(\frac{5063}{5712}\right)\)	\(e\left(\frac{499}{2856}\right)\)	\(e\left(\frac{325}{5712}\right)\)	\(e\left(\frac{387}{476}\right)\)	\(e\left(\frac{451}{952}\right)\)	\(e\left(\frac{295}{408}\right)\)	\(e\left(\frac{2477}{5712}\right)\)	\(e\left(\frac{2207}{2856}\right)\)	\(e\left(\frac{1451}{1904}\right)\)
\(\chi_{56644}(47,\cdot)\)	56644.fp	1428	yes	\(1\)	\(1\)	\(e\left(\frac{1409}{1428}\right)\)	\(e\left(\frac{919}{1428}\right)\)	\(e\left(\frac{695}{714}\right)\)	\(e\left(\frac{1025}{1428}\right)\)	\(e\left(\frac{235}{238}\right)\)	\(e\left(\frac{75}{119}\right)\)	\(e\left(\frac{83}{102}\right)\)	\(e\left(\frac{13}{1428}\right)\)	\(e\left(\frac{205}{714}\right)\)	\(e\left(\frac{457}{476}\right)\)
\(\chi_{56644}(53,\cdot)\)	56644.fx	2856	no	\(1\)	\(1\)	\(e\left(\frac{2843}{2856}\right)\)	\(e\left(\frac{967}{2856}\right)\)	\(e\left(\frac{1415}{1428}\right)\)	\(e\left(\frac{2693}{2856}\right)\)	\(e\left(\frac{71}{238}\right)\)	\(e\left(\frac{159}{476}\right)\)	\(e\left(\frac{191}{204}\right)\)	\(e\left(\frac{2677}{2856}\right)\)	\(e\left(\frac{967}{1428}\right)\)	\(e\left(\frac{939}{952}\right)\)
\(\chi_{56644}(55,\cdot)\)	56644.ew	476	yes	\(1\)	\(1\)	\(e\left(\frac{33}{476}\right)\)	\(e\left(\frac{383}{476}\right)\)	\(e\left(\frac{33}{238}\right)\)	\(e\left(\frac{249}{476}\right)\)	\(e\left(\frac{191}{238}\right)\)	\(e\left(\frac{104}{119}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{253}{476}\right)\)	\(e\left(\frac{145}{238}\right)\)	\(e\left(\frac{99}{476}\right)\)
\(\chi_{56644}(57,\cdot)\)	56644.ft	1904	no	\(-1\)	\(1\)	\(e\left(\frac{1737}{1904}\right)\)	\(e\left(\frac{925}{1904}\right)\)	\(e\left(\frac{785}{952}\right)\)	\(e\left(\frac{1055}{1904}\right)\)	\(e\left(\frac{45}{476}\right)\)	\(e\left(\frac{379}{952}\right)\)	\(e\left(\frac{105}{136}\right)\)	\(e\left(\frac{1655}{1904}\right)\)	\(e\left(\frac{925}{952}\right)\)	\(e\left(\frac{1403}{1904}\right)\)
\(\chi_{56644}(59,\cdot)\)	56644.fz	2856	yes	\(1\)	\(1\)	\(e\left(\frac{1913}{2856}\right)\)	\(e\left(\frac{2809}{2856}\right)\)	\(e\left(\frac{485}{1428}\right)\)	\(e\left(\frac{1907}{2856}\right)\)	\(e\left(\frac{99}{119}\right)\)	\(e\left(\frac{311}{476}\right)\)	\(e\left(\frac{77}{204}\right)\)	\(e\left(\frac{307}{2856}\right)\)	\(e\left(\frac{1381}{1428}\right)\)	\(e\left(\frac{9}{952}\right)\)
\(\chi_{56644}(61,\cdot)\)	56644.ga	5712	no	\(1\)	\(1\)	\(e\left(\frac{1223}{5712}\right)\)	\(e\left(\frac{3715}{5712}\right)\)	\(e\left(\frac{1223}{2856}\right)\)	\(e\left(\frac{2153}{5712}\right)\)	\(e\left(\frac{131}{476}\right)\)	\(e\left(\frac{823}{952}\right)\)	\(e\left(\frac{203}{408}\right)\)	\(e\left(\frac{1681}{5712}\right)\)	\(e\left(\frac{859}{2856}\right)\)	\(e\left(\frac{1223}{1904}\right)\)
\(\chi_{56644}(65,\cdot)\)	56644.en	336	no	\(-1\)	\(1\)	\(e\left(\frac{13}{336}\right)\)	\(e\left(\frac{209}{336}\right)\)	\(e\left(\frac{13}{168}\right)\)	\(e\left(\frac{331}{336}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{179}{336}\right)\)	\(e\left(\frac{41}{168}\right)\)	\(e\left(\frac{13}{112}\right)\)
\(\chi_{56644}(67,\cdot)\)	56644.di	102	no	\(-1\)	\(1\)	\(e\left(\frac{43}{51}\right)\)	\(e\left(\frac{25}{102}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{37}{51}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{31}{102}\right)\)	\(e\left(\frac{35}{51}\right)\)	\(e\left(\frac{25}{51}\right)\)	\(e\left(\frac{9}{17}\right)\)
\(\chi_{56644}(69,\cdot)\)	56644.ec	238	no	\(-1\)	\(1\)	\(e\left(\frac{179}{238}\right)\)	\(e\left(\frac{123}{238}\right)\)	\(e\left(\frac{60}{119}\right)\)	\(e\left(\frac{10}{119}\right)\)	\(e\left(\frac{13}{238}\right)\)	\(e\left(\frac{32}{119}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{111}{119}\right)\)	\(e\left(\frac{4}{119}\right)\)	\(e\left(\frac{61}{238}\right)\)
\(\chi_{56644}(71,\cdot)\)	56644.fs	1904	yes	\(1\)	\(1\)	\(e\left(\frac{31}{1904}\right)\)	\(e\left(\frac{1795}{1904}\right)\)	\(e\left(\frac{31}{952}\right)\)	\(e\left(\frac{169}{1904}\right)\)	\(e\left(\frac{23}{476}\right)\)	\(e\left(\frac{913}{952}\right)\)	\(e\left(\frac{99}{136}\right)\)	\(e\left(\frac{1745}{1904}\right)\)	\(e\left(\frac{843}{952}\right)\)	\(e\left(\frac{93}{1904}\right)\)
\(\chi_{56644}(73,\cdot)\)	56644.ga	5712	no	\(1\)	\(1\)	\(e\left(\frac{2785}{5712}\right)\)	\(e\left(\frac{2645}{5712}\right)\)	\(e\left(\frac{2785}{2856}\right)\)	\(e\left(\frac{1087}{5712}\right)\)	\(e\left(\frac{461}{476}\right)\)	\(e\left(\frac{905}{952}\right)\)	\(e\left(\frac{133}{408}\right)\)	\(e\left(\frac{4295}{5712}\right)\)	\(e\left(\frac{2645}{2856}\right)\)	\(e\left(\frac{881}{1904}\right)\)
\(\chi_{56644}(75,\cdot)\)	56644.eo	336	no	\(-1\)	\(1\)	\(e\left(\frac{199}{336}\right)\)	\(e\left(\frac{59}{336}\right)\)	\(e\left(\frac{31}{168}\right)\)	\(e\left(\frac{169}{336}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{65}{336}\right)\)	\(e\left(\frac{59}{168}\right)\)	\(e\left(\frac{87}{112}\right)\)
\(\chi_{56644}(79,\cdot)\)	56644.fh	816	no	\(1\)	\(1\)	\(e\left(\frac{365}{816}\right)\)	\(e\left(\frac{217}{816}\right)\)	\(e\left(\frac{365}{408}\right)\)	\(e\left(\frac{779}{816}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{311}{408}\right)\)	\(e\left(\frac{67}{816}\right)\)	\(e\left(\frac{217}{408}\right)\)	\(e\left(\frac{93}{272}\right)\)

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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.