LMFDB - Group of Dirichlet characters of modulus 451584

Show commands: PariGP / SageMath

sage: H = DirichletGroup(451584)

pari: g = idealstar(,451584,2)

Character group

sage: G.order() pari: g.no
Order	=	129024
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{5376}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{451584}(330751,\cdot)$, $\chi_{451584}(241669,\cdot)$, $\chi_{451584}(50177,\cdot)$, $\chi_{451584}(230401,\cdot)$

First 32 of 129024 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	$-1$	$1$	$5$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$
$\chi_{451584}(1,\cdot)$	451584.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{451584}(5,\cdot)$	451584.bbk	5376	yes	$1$	$1$	$e\left(\frac{1045}{5376}\right)$	$e\left(\frac{1529}{5376}\right)$	$e\left(\frac{2075}{5376}\right)$	$e\left(\frac{499}{1344}\right)$	$e\left(\frac{581}{768}\right)$	$e\left(\frac{2579}{2688}\right)$	$e\left(\frac{1045}{2688}\right)$	$e\left(\frac{3991}{5376}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{1037}{5376}\right)$
$\chi_{451584}(11,\cdot)$	451584.bau	5376	yes	$1$	$1$	$e\left(\frac{1529}{5376}\right)$	$e\left(\frac{5293}{5376}\right)$	$e\left(\frac{3319}{5376}\right)$	$e\left(\frac{143}{1344}\right)$	$e\left(\frac{361}{768}\right)$	$e\left(\frac{1807}{2688}\right)$	$e\left(\frac{1529}{2688}\right)$	$e\left(\frac{3491}{5376}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{1489}{5376}\right)$
$\chi_{451584}(13,\cdot)$	451584.bbo	5376	yes	$-1$	$1$	$e\left(\frac{2075}{5376}\right)$	$e\left(\frac{3319}{5376}\right)$	$e\left(\frac{3893}{5376}\right)$	$e\left(\frac{127}{448}\right)$	$e\left(\frac{121}{256}\right)$	$e\left(\frac{253}{2688}\right)$	$e\left(\frac{2075}{2688}\right)$	$e\left(\frac{1657}{5376}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{865}{1792}\right)$
$\chi_{451584}(17,\cdot)$	451584.yv	1344	no	$1$	$1$	$e\left(\frac{499}{1344}\right)$	$e\left(\frac{143}{1344}\right)$	$e\left(\frac{127}{448}\right)$	$e\left(\frac{149}{336}\right)$	$e\left(\frac{163}{192}\right)$	$e\left(\frac{437}{672}\right)$	$e\left(\frac{499}{672}\right)$	$e\left(\frac{75}{448}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{379}{1344}\right)$
$\chi_{451584}(19,\cdot)$	451584.ww	768	no	$1$	$1$	$e\left(\frac{581}{768}\right)$	$e\left(\frac{361}{768}\right)$	$e\left(\frac{121}{256}\right)$	$e\left(\frac{163}{192}\right)$	$e\left(\frac{563}{768}\right)$	$e\left(\frac{355}{384}\right)$	$e\left(\frac{197}{384}\right)$	$e\left(\frac{141}{256}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{317}{768}\right)$
$\chi_{451584}(23,\cdot)$	451584.zx	2688	no	$1$	$1$	$e\left(\frac{2579}{2688}\right)$	$e\left(\frac{1807}{2688}\right)$	$e\left(\frac{253}{2688}\right)$	$e\left(\frac{437}{672}\right)$	$e\left(\frac{355}{384}\right)$	$e\left(\frac{1093}{1344}\right)$	$e\left(\frac{1235}{1344}\right)$	$e\left(\frac{929}{2688}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{2203}{2688}\right)$
$\chi_{451584}(25,\cdot)$	451584.zm	2688	no	$1$	$1$	$e\left(\frac{1045}{2688}\right)$	$e\left(\frac{1529}{2688}\right)$	$e\left(\frac{2075}{2688}\right)$	$e\left(\frac{499}{672}\right)$	$e\left(\frac{197}{384}\right)$	$e\left(\frac{1235}{1344}\right)$	$e\left(\frac{1045}{1344}\right)$	$e\left(\frac{1303}{2688}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1037}{2688}\right)$
$\chi_{451584}(29,\cdot)$	451584.bbq	5376	yes	$-1$	$1$	$e\left(\frac{3991}{5376}\right)$	$e\left(\frac{3491}{5376}\right)$	$e\left(\frac{1657}{5376}\right)$	$e\left(\frac{75}{448}\right)$	$e\left(\frac{141}{256}\right)$	$e\left(\frac{929}{2688}\right)$	$e\left(\frac{1303}{2688}\right)$	$e\left(\frac{5261}{5376}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{1301}{1792}\right)$
$\chi_{451584}(31,\cdot)$	451584.nw	96	no	$1$	$1$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{59}{96}\right)$
$\chi_{451584}(37,\cdot)$	451584.bbh	5376	no	$1$	$1$	$e\left(\frac{1037}{5376}\right)$	$e\left(\frac{1489}{5376}\right)$	$e\left(\frac{865}{1792}\right)$	$e\left(\frac{379}{1344}\right)$	$e\left(\frac{317}{768}\right)$	$e\left(\frac{2203}{2688}\right)$	$e\left(\frac{1037}{2688}\right)$	$e\left(\frac{1301}{1792}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{4421}{5376}\right)$
$\chi_{451584}(41,\cdot)$	451584.zt	2688	no	$1$	$1$	$e\left(\frac{1387}{2688}\right)$	$e\left(\frac{1223}{2688}\right)$	$e\left(\frac{1573}{2688}\right)$	$e\left(\frac{47}{224}\right)$	$e\left(\frac{41}{128}\right)$	$e\left(\frac{845}{1344}\right)$	$e\left(\frac{43}{1344}\right)$	$e\left(\frac{809}{2688}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{209}{896}\right)$
$\chi_{451584}(43,\cdot)$	451584.bao	5376	yes	$-1$	$1$	$e\left(\frac{3841}{5376}\right)$	$e\left(\frac{3413}{5376}\right)$	$e\left(\frac{5359}{5376}\right)$	$e\left(\frac{333}{448}\right)$	$e\left(\frac{123}{256}\right)$	$e\left(\frac{263}{2688}\right)$	$e\left(\frac{1153}{2688}\right)$	$e\left(\frac{2939}{5376}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{947}{1792}\right)$
$\chi_{451584}(47,\cdot)$	451584.xs	1344	no	$-1$	$1$	$e\left(\frac{429}{448}\right)$	$e\left(\frac{241}{448}\right)$	$e\left(\frac{1129}{1344}\right)$	$e\left(\frac{97}{336}\right)$	$e\left(\frac{23}{192}\right)$	$e\left(\frac{59}{224}\right)$	$e\left(\frac{205}{224}\right)$	$e\left(\frac{1277}{1344}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{815}{1344}\right)$
$\chi_{451584}(53,\cdot)$	451584.bay	5376	no	$-1$	$1$	$e\left(\frac{2281}{5376}\right)$	$e\left(\frac{989}{5376}\right)$	$e\left(\frac{941}{1792}\right)$	$e\left(\frac{671}{1344}\right)$	$e\left(\frac{217}{768}\right)$	$e\left(\frac{863}{2688}\right)$	$e\left(\frac{2281}{2688}\right)$	$e\left(\frac{337}{1792}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{577}{5376}\right)$
$\chi_{451584}(55,\cdot)$	451584.xk	896	no	$1$	$1$	$e\left(\frac{429}{896}\right)$	$e\left(\frac{241}{896}\right)$	$e\left(\frac{3}{896}\right)$	$e\left(\frac{107}{224}\right)$	$e\left(\frac{29}{128}\right)$	$e\left(\frac{283}{448}\right)$	$e\left(\frac{429}{448}\right)$	$e\left(\frac{351}{896}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{421}{896}\right)$
$\chi_{451584}(59,\cdot)$	451584.bbm	5376	yes	$-1$	$1$	$e\left(\frac{1719}{1792}\right)$	$e\left(\frac{1091}{1792}\right)$	$e\left(\frac{11}{5376}\right)$	$e\left(\frac{803}{1344}\right)$	$e\left(\frac{469}{768}\right)$	$e\left(\frac{321}{896}\right)$	$e\left(\frac{823}{896}\right)$	$e\left(\frac{4423}{5376}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{1693}{5376}\right)$
$\chi_{451584}(61,\cdot)$	451584.bba	5376	yes	$-1$	$1$	$e\left(\frac{453}{1792}\right)$	$e\left(\frac{361}{1792}\right)$	$e\left(\frac{2497}{5376}\right)$	$e\left(\frac{169}{1344}\right)$	$e\left(\frac{95}{768}\right)$	$e\left(\frac{291}{896}\right)$	$e\left(\frac{453}{896}\right)$	$e\left(\frac{1397}{5376}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{2615}{5376}\right)$
$\chi_{451584}(65,\cdot)$	451584.sz	336	no	$-1$	$1$	$e\left(\frac{65}{112}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{37}{336}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{17}{336}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{227}{336}\right)$
$\chi_{451584}(67,\cdot)$	451584.wt	768	no	$-1$	$1$	$e\left(\frac{243}{256}\right)$	$e\left(\frac{175}{256}\right)$	$e\left(\frac{407}{768}\right)$	$e\left(\frac{143}{192}\right)$	$e\left(\frac{127}{768}\right)$	$e\left(\frac{37}{128}\right)$	$e\left(\frac{115}{128}\right)$	$e\left(\frac{67}{768}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{49}{768}\right)$
$\chi_{451584}(71,\cdot)$	451584.xn	896	no	$1$	$1$	$e\left(\frac{379}{896}\right)$	$e\left(\frac{663}{896}\right)$	$e\left(\frac{789}{896}\right)$	$e\left(\frac{141}{224}\right)$	$e\left(\frac{75}{128}\right)$	$e\left(\frac{285}{448}\right)$	$e\left(\frac{379}{448}\right)$	$e\left(\frac{25}{896}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{67}{896}\right)$
$\chi_{451584}(73,\cdot)$	451584.zw	2688	no	$-1$	$1$	$e\left(\frac{695}{2688}\right)$	$e\left(\frac{1795}{2688}\right)$	$e\left(\frac{883}{896}\right)$	$e\left(\frac{625}{672}\right)$	$e\left(\frac{71}{384}\right)$	$e\left(\frac{577}{1344}\right)$	$e\left(\frac{695}{1344}\right)$	$e\left(\frac{271}{896}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{2591}{2688}\right)$
$\chi_{451584}(79,\cdot)$	451584.rm	192	no	$-1$	$1$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{73}{192}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{65}{192}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{29}{192}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{47}{192}\right)$
$\chi_{451584}(83,\cdot)$	451584.bam	5376	yes	$-1$	$1$	$e\left(\frac{5107}{5376}\right)$	$e\left(\frac{2351}{5376}\right)$	$e\left(\frac{349}{5376}\right)$	$e\left(\frac{279}{448}\right)$	$e\left(\frac{65}{256}\right)$	$e\left(\frac{1637}{2688}\right)$	$e\left(\frac{2419}{2688}\right)$	$e\left(\frac{65}{5376}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{745}{1792}\right)$
$\chi_{451584}(85,\cdot)$	451584.ban	5376	yes	$1$	$1$	$e\left(\frac{3041}{5376}\right)$	$e\left(\frac{2101}{5376}\right)$	$e\left(\frac{3599}{5376}\right)$	$e\left(\frac{365}{448}\right)$	$e\left(\frac{155}{256}\right)$	$e\left(\frac{1639}{2688}\right)$	$e\left(\frac{353}{2688}\right)$	$e\left(\frac{4891}{5376}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{851}{1792}\right)$
$\chi_{451584}(89,\cdot)$	451584.zq	2688	no	$1$	$1$	$e\left(\frac{2221}{2688}\right)$	$e\left(\frac{689}{2688}\right)$	$e\left(\frac{449}{896}\right)$	$e\left(\frac{443}{672}\right)$	$e\left(\frac{157}{384}\right)$	$e\left(\frac{731}{1344}\right)$	$e\left(\frac{877}{1344}\right)$	$e\left(\frac{117}{896}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{1765}{2688}\right)$
$\chi_{451584}(95,\cdot)$	451584.vz	672	no	$1$	$1$	$e\left(\frac{213}{224}\right)$	$e\left(\frac{169}{224}\right)$	$e\left(\frac{577}{672}\right)$	$e\left(\frac{37}{168}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{99}{112}\right)$	$e\left(\frac{101}{112}\right)$	$e\left(\frac{197}{672}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{407}{672}\right)$
$\chi_{451584}(97,\cdot)$	451584.og	96	no	$-1$	$1$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{32}\right)$
$\chi_{451584}(101,\cdot)$	451584.bbk	5376	yes	$1$	$1$	$e\left(\frac{4349}{5376}\right)$	$e\left(\frac{4609}{5376}\right)$	$e\left(\frac{1459}{5376}\right)$	$e\left(\frac{779}{1344}\right)$	$e\left(\frac{685}{768}\right)$	$e\left(\frac{619}{2688}\right)$	$e\left(\frac{1661}{2688}\right)$	$e\left(\frac{3599}{5376}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{4789}{5376}\right)$
$\chi_{451584}(103,\cdot)$	451584.baf	2688	no	$1$	$1$	$e\left(\frac{2213}{2688}\right)$	$e\left(\frac{1993}{2688}\right)$	$e\left(\frac{523}{2688}\right)$	$e\left(\frac{659}{672}\right)$	$e\left(\frac{277}{384}\right)$	$e\left(\frac{355}{1344}\right)$	$e\left(\frac{869}{1344}\right)$	$e\left(\frac{263}{2688}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1117}{2688}\right)$
$\chi_{451584}(107,\cdot)$	451584.bat	5376	no	$1$	$1$	$e\left(\frac{5009}{5376}\right)$	$e\left(\frac{3877}{5376}\right)$	$e\left(\frac{1269}{1792}\right)$	$e\left(\frac{823}{1344}\right)$	$e\left(\frac{641}{768}\right)$	$e\left(\frac{55}{2688}\right)$	$e\left(\frac{2321}{2688}\right)$	$e\left(\frac{1081}{1792}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{4265}{5376}\right)$
$\chi_{451584}(109,\cdot)$	451584.bbh	5376	no	$1$	$1$	$e\left(\frac{3139}{5376}\right)$	$e\left(\frac{3263}{5376}\right)$	$e\left(\frac{47}{1792}\right)$	$e\left(\frac{437}{1344}\right)$	$e\left(\frac{19}{768}\right)$	$e\left(\frac{533}{2688}\right)$	$e\left(\frac{451}{2688}\right)$	$e\left(\frac{1467}{1792}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{3211}{5376}\right)$

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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 $\F_{q}$

Modulus	$451584$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{5376}\)
Order	$129024$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)
\(\chi_{451584}(1,\cdot)\)	451584.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{451584}(5,\cdot)\)	451584.bbk	5376	yes	\(1\)	\(1\)	\(e\left(\frac{1045}{5376}\right)\)	\(e\left(\frac{1529}{5376}\right)\)	\(e\left(\frac{2075}{5376}\right)\)	\(e\left(\frac{499}{1344}\right)\)	\(e\left(\frac{581}{768}\right)\)	\(e\left(\frac{2579}{2688}\right)\)	\(e\left(\frac{1045}{2688}\right)\)	\(e\left(\frac{3991}{5376}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{1037}{5376}\right)\)
\(\chi_{451584}(11,\cdot)\)	451584.bau	5376	yes	\(1\)	\(1\)	\(e\left(\frac{1529}{5376}\right)\)	\(e\left(\frac{5293}{5376}\right)\)	\(e\left(\frac{3319}{5376}\right)\)	\(e\left(\frac{143}{1344}\right)\)	\(e\left(\frac{361}{768}\right)\)	\(e\left(\frac{1807}{2688}\right)\)	\(e\left(\frac{1529}{2688}\right)\)	\(e\left(\frac{3491}{5376}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{1489}{5376}\right)\)
\(\chi_{451584}(13,\cdot)\)	451584.bbo	5376	yes	\(-1\)	\(1\)	\(e\left(\frac{2075}{5376}\right)\)	\(e\left(\frac{3319}{5376}\right)\)	\(e\left(\frac{3893}{5376}\right)\)	\(e\left(\frac{127}{448}\right)\)	\(e\left(\frac{121}{256}\right)\)	\(e\left(\frac{253}{2688}\right)\)	\(e\left(\frac{2075}{2688}\right)\)	\(e\left(\frac{1657}{5376}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{865}{1792}\right)\)
\(\chi_{451584}(17,\cdot)\)	451584.yv	1344	no	\(1\)	\(1\)	\(e\left(\frac{499}{1344}\right)\)	\(e\left(\frac{143}{1344}\right)\)	\(e\left(\frac{127}{448}\right)\)	\(e\left(\frac{149}{336}\right)\)	\(e\left(\frac{163}{192}\right)\)	\(e\left(\frac{437}{672}\right)\)	\(e\left(\frac{499}{672}\right)\)	\(e\left(\frac{75}{448}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{379}{1344}\right)\)
\(\chi_{451584}(19,\cdot)\)	451584.ww	768	no	\(1\)	\(1\)	\(e\left(\frac{581}{768}\right)\)	\(e\left(\frac{361}{768}\right)\)	\(e\left(\frac{121}{256}\right)\)	\(e\left(\frac{163}{192}\right)\)	\(e\left(\frac{563}{768}\right)\)	\(e\left(\frac{355}{384}\right)\)	\(e\left(\frac{197}{384}\right)\)	\(e\left(\frac{141}{256}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{317}{768}\right)\)
\(\chi_{451584}(23,\cdot)\)	451584.zx	2688	no	\(1\)	\(1\)	\(e\left(\frac{2579}{2688}\right)\)	\(e\left(\frac{1807}{2688}\right)\)	\(e\left(\frac{253}{2688}\right)\)	\(e\left(\frac{437}{672}\right)\)	\(e\left(\frac{355}{384}\right)\)	\(e\left(\frac{1093}{1344}\right)\)	\(e\left(\frac{1235}{1344}\right)\)	\(e\left(\frac{929}{2688}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{2203}{2688}\right)\)
\(\chi_{451584}(25,\cdot)\)	451584.zm	2688	no	\(1\)	\(1\)	\(e\left(\frac{1045}{2688}\right)\)	\(e\left(\frac{1529}{2688}\right)\)	\(e\left(\frac{2075}{2688}\right)\)	\(e\left(\frac{499}{672}\right)\)	\(e\left(\frac{197}{384}\right)\)	\(e\left(\frac{1235}{1344}\right)\)	\(e\left(\frac{1045}{1344}\right)\)	\(e\left(\frac{1303}{2688}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1037}{2688}\right)\)
\(\chi_{451584}(29,\cdot)\)	451584.bbq	5376	yes	\(-1\)	\(1\)	\(e\left(\frac{3991}{5376}\right)\)	\(e\left(\frac{3491}{5376}\right)\)	\(e\left(\frac{1657}{5376}\right)\)	\(e\left(\frac{75}{448}\right)\)	\(e\left(\frac{141}{256}\right)\)	\(e\left(\frac{929}{2688}\right)\)	\(e\left(\frac{1303}{2688}\right)\)	\(e\left(\frac{5261}{5376}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{1301}{1792}\right)\)
\(\chi_{451584}(31,\cdot)\)	451584.nw	96	no	\(1\)	\(1\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{59}{96}\right)\)
\(\chi_{451584}(37,\cdot)\)	451584.bbh	5376	no	\(1\)	\(1\)	\(e\left(\frac{1037}{5376}\right)\)	\(e\left(\frac{1489}{5376}\right)\)	\(e\left(\frac{865}{1792}\right)\)	\(e\left(\frac{379}{1344}\right)\)	\(e\left(\frac{317}{768}\right)\)	\(e\left(\frac{2203}{2688}\right)\)	\(e\left(\frac{1037}{2688}\right)\)	\(e\left(\frac{1301}{1792}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{4421}{5376}\right)\)
\(\chi_{451584}(41,\cdot)\)	451584.zt	2688	no	\(1\)	\(1\)	\(e\left(\frac{1387}{2688}\right)\)	\(e\left(\frac{1223}{2688}\right)\)	\(e\left(\frac{1573}{2688}\right)\)	\(e\left(\frac{47}{224}\right)\)	\(e\left(\frac{41}{128}\right)\)	\(e\left(\frac{845}{1344}\right)\)	\(e\left(\frac{43}{1344}\right)\)	\(e\left(\frac{809}{2688}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{209}{896}\right)\)
\(\chi_{451584}(43,\cdot)\)	451584.bao	5376	yes	\(-1\)	\(1\)	\(e\left(\frac{3841}{5376}\right)\)	\(e\left(\frac{3413}{5376}\right)\)	\(e\left(\frac{5359}{5376}\right)\)	\(e\left(\frac{333}{448}\right)\)	\(e\left(\frac{123}{256}\right)\)	\(e\left(\frac{263}{2688}\right)\)	\(e\left(\frac{1153}{2688}\right)\)	\(e\left(\frac{2939}{5376}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{947}{1792}\right)\)
\(\chi_{451584}(47,\cdot)\)	451584.xs	1344	no	\(-1\)	\(1\)	\(e\left(\frac{429}{448}\right)\)	\(e\left(\frac{241}{448}\right)\)	\(e\left(\frac{1129}{1344}\right)\)	\(e\left(\frac{97}{336}\right)\)	\(e\left(\frac{23}{192}\right)\)	\(e\left(\frac{59}{224}\right)\)	\(e\left(\frac{205}{224}\right)\)	\(e\left(\frac{1277}{1344}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{815}{1344}\right)\)
\(\chi_{451584}(53,\cdot)\)	451584.bay	5376	no	\(-1\)	\(1\)	\(e\left(\frac{2281}{5376}\right)\)	\(e\left(\frac{989}{5376}\right)\)	\(e\left(\frac{941}{1792}\right)\)	\(e\left(\frac{671}{1344}\right)\)	\(e\left(\frac{217}{768}\right)\)	\(e\left(\frac{863}{2688}\right)\)	\(e\left(\frac{2281}{2688}\right)\)	\(e\left(\frac{337}{1792}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{577}{5376}\right)\)
\(\chi_{451584}(55,\cdot)\)	451584.xk	896	no	\(1\)	\(1\)	\(e\left(\frac{429}{896}\right)\)	\(e\left(\frac{241}{896}\right)\)	\(e\left(\frac{3}{896}\right)\)	\(e\left(\frac{107}{224}\right)\)	\(e\left(\frac{29}{128}\right)\)	\(e\left(\frac{283}{448}\right)\)	\(e\left(\frac{429}{448}\right)\)	\(e\left(\frac{351}{896}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{421}{896}\right)\)
\(\chi_{451584}(59,\cdot)\)	451584.bbm	5376	yes	\(-1\)	\(1\)	\(e\left(\frac{1719}{1792}\right)\)	\(e\left(\frac{1091}{1792}\right)\)	\(e\left(\frac{11}{5376}\right)\)	\(e\left(\frac{803}{1344}\right)\)	\(e\left(\frac{469}{768}\right)\)	\(e\left(\frac{321}{896}\right)\)	\(e\left(\frac{823}{896}\right)\)	\(e\left(\frac{4423}{5376}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{1693}{5376}\right)\)
\(\chi_{451584}(61,\cdot)\)	451584.bba	5376	yes	\(-1\)	\(1\)	\(e\left(\frac{453}{1792}\right)\)	\(e\left(\frac{361}{1792}\right)\)	\(e\left(\frac{2497}{5376}\right)\)	\(e\left(\frac{169}{1344}\right)\)	\(e\left(\frac{95}{768}\right)\)	\(e\left(\frac{291}{896}\right)\)	\(e\left(\frac{453}{896}\right)\)	\(e\left(\frac{1397}{5376}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{2615}{5376}\right)\)
\(\chi_{451584}(65,\cdot)\)	451584.sz	336	no	\(-1\)	\(1\)	\(e\left(\frac{65}{112}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{37}{336}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{17}{336}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{227}{336}\right)\)
\(\chi_{451584}(67,\cdot)\)	451584.wt	768	no	\(-1\)	\(1\)	\(e\left(\frac{243}{256}\right)\)	\(e\left(\frac{175}{256}\right)\)	\(e\left(\frac{407}{768}\right)\)	\(e\left(\frac{143}{192}\right)\)	\(e\left(\frac{127}{768}\right)\)	\(e\left(\frac{37}{128}\right)\)	\(e\left(\frac{115}{128}\right)\)	\(e\left(\frac{67}{768}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{49}{768}\right)\)
\(\chi_{451584}(71,\cdot)\)	451584.xn	896	no	\(1\)	\(1\)	\(e\left(\frac{379}{896}\right)\)	\(e\left(\frac{663}{896}\right)\)	\(e\left(\frac{789}{896}\right)\)	\(e\left(\frac{141}{224}\right)\)	\(e\left(\frac{75}{128}\right)\)	\(e\left(\frac{285}{448}\right)\)	\(e\left(\frac{379}{448}\right)\)	\(e\left(\frac{25}{896}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{67}{896}\right)\)
\(\chi_{451584}(73,\cdot)\)	451584.zw	2688	no	\(-1\)	\(1\)	\(e\left(\frac{695}{2688}\right)\)	\(e\left(\frac{1795}{2688}\right)\)	\(e\left(\frac{883}{896}\right)\)	\(e\left(\frac{625}{672}\right)\)	\(e\left(\frac{71}{384}\right)\)	\(e\left(\frac{577}{1344}\right)\)	\(e\left(\frac{695}{1344}\right)\)	\(e\left(\frac{271}{896}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{2591}{2688}\right)\)
\(\chi_{451584}(79,\cdot)\)	451584.rm	192	no	\(-1\)	\(1\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{73}{192}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{65}{192}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{29}{192}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{47}{192}\right)\)
\(\chi_{451584}(83,\cdot)\)	451584.bam	5376	yes	\(-1\)	\(1\)	\(e\left(\frac{5107}{5376}\right)\)	\(e\left(\frac{2351}{5376}\right)\)	\(e\left(\frac{349}{5376}\right)\)	\(e\left(\frac{279}{448}\right)\)	\(e\left(\frac{65}{256}\right)\)	\(e\left(\frac{1637}{2688}\right)\)	\(e\left(\frac{2419}{2688}\right)\)	\(e\left(\frac{65}{5376}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{745}{1792}\right)\)
\(\chi_{451584}(85,\cdot)\)	451584.ban	5376	yes	\(1\)	\(1\)	\(e\left(\frac{3041}{5376}\right)\)	\(e\left(\frac{2101}{5376}\right)\)	\(e\left(\frac{3599}{5376}\right)\)	\(e\left(\frac{365}{448}\right)\)	\(e\left(\frac{155}{256}\right)\)	\(e\left(\frac{1639}{2688}\right)\)	\(e\left(\frac{353}{2688}\right)\)	\(e\left(\frac{4891}{5376}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{851}{1792}\right)\)
\(\chi_{451584}(89,\cdot)\)	451584.zq	2688	no	\(1\)	\(1\)	\(e\left(\frac{2221}{2688}\right)\)	\(e\left(\frac{689}{2688}\right)\)	\(e\left(\frac{449}{896}\right)\)	\(e\left(\frac{443}{672}\right)\)	\(e\left(\frac{157}{384}\right)\)	\(e\left(\frac{731}{1344}\right)\)	\(e\left(\frac{877}{1344}\right)\)	\(e\left(\frac{117}{896}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{1765}{2688}\right)\)
\(\chi_{451584}(95,\cdot)\)	451584.vz	672	no	\(1\)	\(1\)	\(e\left(\frac{213}{224}\right)\)	\(e\left(\frac{169}{224}\right)\)	\(e\left(\frac{577}{672}\right)\)	\(e\left(\frac{37}{168}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{99}{112}\right)\)	\(e\left(\frac{101}{112}\right)\)	\(e\left(\frac{197}{672}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{407}{672}\right)\)
\(\chi_{451584}(97,\cdot)\)	451584.og	96	no	\(-1\)	\(1\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{32}\right)\)
\(\chi_{451584}(101,\cdot)\)	451584.bbk	5376	yes	\(1\)	\(1\)	\(e\left(\frac{4349}{5376}\right)\)	\(e\left(\frac{4609}{5376}\right)\)	\(e\left(\frac{1459}{5376}\right)\)	\(e\left(\frac{779}{1344}\right)\)	\(e\left(\frac{685}{768}\right)\)	\(e\left(\frac{619}{2688}\right)\)	\(e\left(\frac{1661}{2688}\right)\)	\(e\left(\frac{3599}{5376}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{4789}{5376}\right)\)
\(\chi_{451584}(103,\cdot)\)	451584.baf	2688	no	\(1\)	\(1\)	\(e\left(\frac{2213}{2688}\right)\)	\(e\left(\frac{1993}{2688}\right)\)	\(e\left(\frac{523}{2688}\right)\)	\(e\left(\frac{659}{672}\right)\)	\(e\left(\frac{277}{384}\right)\)	\(e\left(\frac{355}{1344}\right)\)	\(e\left(\frac{869}{1344}\right)\)	\(e\left(\frac{263}{2688}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1117}{2688}\right)\)
\(\chi_{451584}(107,\cdot)\)	451584.bat	5376	no	\(1\)	\(1\)	\(e\left(\frac{5009}{5376}\right)\)	\(e\left(\frac{3877}{5376}\right)\)	\(e\left(\frac{1269}{1792}\right)\)	\(e\left(\frac{823}{1344}\right)\)	\(e\left(\frac{641}{768}\right)\)	\(e\left(\frac{55}{2688}\right)\)	\(e\left(\frac{2321}{2688}\right)\)	\(e\left(\frac{1081}{1792}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{4265}{5376}\right)\)
\(\chi_{451584}(109,\cdot)\)	451584.bbh	5376	no	\(1\)	\(1\)	\(e\left(\frac{3139}{5376}\right)\)	\(e\left(\frac{3263}{5376}\right)\)	\(e\left(\frac{47}{1792}\right)\)	\(e\left(\frac{437}{1344}\right)\)	\(e\left(\frac{19}{768}\right)\)	\(e\left(\frac{533}{2688}\right)\)	\(e\left(\frac{451}{2688}\right)\)	\(e\left(\frac{1467}{1792}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{3211}{5376}\right)\)

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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.