LMFDB - Group of Dirichlet characters of modulus 27584

Show commands: PariGP / SageMath

sage: H = DirichletGroup(27584)

pari: g = idealstar(,27584,2)

Character group

sage: G.order() pari: g.no
Order	=	13760
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{3440}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{27584}(14655,\cdot)$, $\chi_{27584}(25861,\cdot)$, $\chi_{27584}(16385,\cdot)$

First 32 of 13760 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{27584}(1,\cdot)$	27584.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{27584}(3,\cdot)$	27584.cm	688	yes	$-1$	$1$	$e\left(\frac{267}{688}\right)$	$e\left(\frac{609}{688}\right)$	$e\left(\frac{9}{344}\right)$	$e\left(\frac{267}{344}\right)$	$e\left(\frac{429}{688}\right)$	$e\left(\frac{383}{688}\right)$	$e\left(\frac{47}{172}\right)$	$e\left(\frac{75}{172}\right)$	$e\left(\frac{79}{688}\right)$	$e\left(\frac{285}{688}\right)$
$\chi_{27584}(5,\cdot)$	27584.cz	3440	yes	$1$	$1$	$e\left(\frac{609}{688}\right)$	$e\left(\frac{247}{3440}\right)$	$e\left(\frac{723}{1720}\right)$	$e\left(\frac{265}{344}\right)$	$e\left(\frac{2643}{3440}\right)$	$e\left(\frac{2617}{3440}\right)$	$e\left(\frac{823}{860}\right)$	$e\left(\frac{349}{860}\right)$	$e\left(\frac{2849}{3440}\right)$	$e\left(\frac{1051}{3440}\right)$
$\chi_{27584}(7,\cdot)$	27584.cx	1720	no	$1$	$1$	$e\left(\frac{9}{344}\right)$	$e\left(\frac{723}{1720}\right)$	$e\left(\frac{647}{860}\right)$	$e\left(\frac{9}{172}\right)$	$e\left(\frac{1027}{1720}\right)$	$e\left(\frac{1313}{1720}\right)$	$e\left(\frac{96}{215}\right)$	$e\left(\frac{123}{215}\right)$	$e\left(\frac{481}{1720}\right)$	$e\left(\frac{1339}{1720}\right)$
$\chi_{27584}(9,\cdot)$	27584.ce	344	no	$1$	$1$	$e\left(\frac{267}{344}\right)$	$e\left(\frac{265}{344}\right)$	$e\left(\frac{9}{172}\right)$	$e\left(\frac{95}{172}\right)$	$e\left(\frac{85}{344}\right)$	$e\left(\frac{39}{344}\right)$	$e\left(\frac{47}{86}\right)$	$e\left(\frac{75}{86}\right)$	$e\left(\frac{79}{344}\right)$	$e\left(\frac{285}{344}\right)$
$\chi_{27584}(11,\cdot)$	27584.db	3440	yes	$-1$	$1$	$e\left(\frac{429}{688}\right)$	$e\left(\frac{2643}{3440}\right)$	$e\left(\frac{1027}{1720}\right)$	$e\left(\frac{85}{344}\right)$	$e\left(\frac{1367}{3440}\right)$	$e\left(\frac{93}{3440}\right)$	$e\left(\frac{337}{860}\right)$	$e\left(\frac{761}{860}\right)$	$e\left(\frac{2861}{3440}\right)$	$e\left(\frac{759}{3440}\right)$
$\chi_{27584}(13,\cdot)$	27584.da	3440	yes	$-1$	$1$	$e\left(\frac{383}{688}\right)$	$e\left(\frac{2617}{3440}\right)$	$e\left(\frac{1313}{1720}\right)$	$e\left(\frac{39}{344}\right)$	$e\left(\frac{93}{3440}\right)$	$e\left(\frac{3167}{3440}\right)$	$e\left(\frac{273}{860}\right)$	$e\left(\frac{249}{860}\right)$	$e\left(\frac{479}{3440}\right)$	$e\left(\frac{1101}{3440}\right)$
$\chi_{27584}(15,\cdot)$	27584.cs	860	no	$-1$	$1$	$e\left(\frac{47}{172}\right)$	$e\left(\frac{823}{860}\right)$	$e\left(\frac{96}{215}\right)$	$e\left(\frac{47}{86}\right)$	$e\left(\frac{337}{860}\right)$	$e\left(\frac{273}{860}\right)$	$e\left(\frac{99}{430}\right)$	$e\left(\frac{181}{215}\right)$	$e\left(\frac{811}{860}\right)$	$e\left(\frac{619}{860}\right)$
$\chi_{27584}(17,\cdot)$	27584.ct	860	no	$-1$	$1$	$e\left(\frac{75}{172}\right)$	$e\left(\frac{349}{860}\right)$	$e\left(\frac{123}{215}\right)$	$e\left(\frac{75}{86}\right)$	$e\left(\frac{761}{860}\right)$	$e\left(\frac{249}{860}\right)$	$e\left(\frac{181}{215}\right)$	$e\left(\frac{101}{430}\right)$	$e\left(\frac{683}{860}\right)$	$e\left(\frac{7}{860}\right)$
$\chi_{27584}(19,\cdot)$	27584.db	3440	yes	$-1$	$1$	$e\left(\frac{79}{688}\right)$	$e\left(\frac{2849}{3440}\right)$	$e\left(\frac{481}{1720}\right)$	$e\left(\frac{79}{344}\right)$	$e\left(\frac{2861}{3440}\right)$	$e\left(\frac{479}{3440}\right)$	$e\left(\frac{811}{860}\right)$	$e\left(\frac{683}{860}\right)$	$e\left(\frac{3343}{3440}\right)$	$e\left(\frac{1357}{3440}\right)$
$\chi_{27584}(21,\cdot)$	27584.da	3440	yes	$-1$	$1$	$e\left(\frac{285}{688}\right)$	$e\left(\frac{1051}{3440}\right)$	$e\left(\frac{1339}{1720}\right)$	$e\left(\frac{285}{344}\right)$	$e\left(\frac{759}{3440}\right)$	$e\left(\frac{1101}{3440}\right)$	$e\left(\frac{619}{860}\right)$	$e\left(\frac{7}{860}\right)$	$e\left(\frac{1357}{3440}\right)$	$e\left(\frac{663}{3440}\right)$
$\chi_{27584}(23,\cdot)$	27584.cw	1720	no	$-1$	$1$	$e\left(\frac{139}{344}\right)$	$e\left(\frac{273}{1720}\right)$	$e\left(\frac{7}{860}\right)$	$e\left(\frac{139}{172}\right)$	$e\left(\frac{1337}{1720}\right)$	$e\left(\frac{1263}{1720}\right)$	$e\left(\frac{121}{215}\right)$	$e\left(\frac{1}{430}\right)$	$e\left(\frac{931}{1720}\right)$	$e\left(\frac{709}{1720}\right)$
$\chi_{27584}(25,\cdot)$	27584.cu	1720	no	$1$	$1$	$e\left(\frac{265}{344}\right)$	$e\left(\frac{247}{1720}\right)$	$e\left(\frac{723}{860}\right)$	$e\left(\frac{93}{172}\right)$	$e\left(\frac{923}{1720}\right)$	$e\left(\frac{897}{1720}\right)$	$e\left(\frac{393}{430}\right)$	$e\left(\frac{349}{430}\right)$	$e\left(\frac{1129}{1720}\right)$	$e\left(\frac{1051}{1720}\right)$
$\chi_{27584}(27,\cdot)$	27584.cm	688	yes	$-1$	$1$	$e\left(\frac{113}{688}\right)$	$e\left(\frac{451}{688}\right)$	$e\left(\frac{27}{344}\right)$	$e\left(\frac{113}{344}\right)$	$e\left(\frac{599}{688}\right)$	$e\left(\frac{461}{688}\right)$	$e\left(\frac{141}{172}\right)$	$e\left(\frac{53}{172}\right)$	$e\left(\frac{237}{688}\right)$	$e\left(\frac{167}{688}\right)$
$\chi_{27584}(29,\cdot)$	27584.cz	3440	yes	$1$	$1$	$e\left(\frac{379}{688}\right)$	$e\left(\frac{3213}{3440}\right)$	$e\left(\frac{777}{1720}\right)$	$e\left(\frac{35}{344}\right)$	$e\left(\frac{1777}{3440}\right)$	$e\left(\frac{2163}{3440}\right)$	$e\left(\frac{417}{860}\right)$	$e\left(\frac{111}{860}\right)$	$e\left(\frac{571}{3440}\right)$	$e\left(\frac{9}{3440}\right)$
$\chi_{27584}(31,\cdot)$	27584.cg	430	no	$1$	$1$	$e\left(\frac{18}{43}\right)$	$e\left(\frac{183}{430}\right)$	$e\left(\frac{137}{215}\right)$	$e\left(\frac{36}{43}\right)$	$e\left(\frac{76}{215}\right)$	$e\left(\frac{89}{215}\right)$	$e\left(\frac{363}{430}\right)$	$e\left(\frac{109}{430}\right)$	$e\left(\frac{188}{215}\right)$	$e\left(\frac{12}{215}\right)$
$\chi_{27584}(33,\cdot)$	27584.cj	430	no	$1$	$1$	$e\left(\frac{1}{86}\right)$	$e\left(\frac{281}{430}\right)$	$e\left(\frac{134}{215}\right)$	$e\left(\frac{1}{43}\right)$	$e\left(\frac{9}{430}\right)$	$e\left(\frac{251}{430}\right)$	$e\left(\frac{143}{215}\right)$	$e\left(\frac{69}{215}\right)$	$e\left(\frac{407}{430}\right)$	$e\left(\frac{273}{430}\right)$
$\chi_{27584}(35,\cdot)$	27584.cy	3440	yes	$1$	$1$	$e\left(\frac{627}{688}\right)$	$e\left(\frac{1693}{3440}\right)$	$e\left(\frac{297}{1720}\right)$	$e\left(\frac{283}{344}\right)$	$e\left(\frac{1257}{3440}\right)$	$e\left(\frac{1803}{3440}\right)$	$e\left(\frac{347}{860}\right)$	$e\left(\frac{841}{860}\right)$	$e\left(\frac{371}{3440}\right)$	$e\left(\frac{289}{3440}\right)$
$\chi_{27584}(37,\cdot)$	27584.da	3440	yes	$-1$	$1$	$e\left(\frac{409}{688}\right)$	$e\left(\frac{2527}{3440}\right)$	$e\left(\frac{583}{1720}\right)$	$e\left(\frac{65}{344}\right)$	$e\left(\frac{843}{3440}\right)$	$e\left(\frac{2297}{3440}\right)$	$e\left(\frac{283}{860}\right)$	$e\left(\frac{759}{860}\right)$	$e\left(\frac{569}{3440}\right)$	$e\left(\frac{3211}{3440}\right)$
$\chi_{27584}(39,\cdot)$	27584.cx	1720	no	$1$	$1$	$e\left(\frac{325}{344}\right)$	$e\left(\frac{1111}{1720}\right)$	$e\left(\frac{679}{860}\right)$	$e\left(\frac{153}{172}\right)$	$e\left(\frac{1119}{1720}\right)$	$e\left(\frac{821}{1720}\right)$	$e\left(\frac{127}{215}\right)$	$e\left(\frac{156}{215}\right)$	$e\left(\frac{437}{1720}\right)$	$e\left(\frac{1263}{1720}\right)$
$\chi_{27584}(41,\cdot)$	27584.cu	1720	no	$1$	$1$	$e\left(\frac{223}{344}\right)$	$e\left(\frac{657}{1720}\right)$	$e\left(\frac{513}{860}\right)$	$e\left(\frac{51}{172}\right)$	$e\left(\frac{373}{1720}\right)$	$e\left(\frac{847}{1720}\right)$	$e\left(\frac{13}{430}\right)$	$e\left(\frac{319}{430}\right)$	$e\left(\frac{719}{1720}\right)$	$e\left(\frac{421}{1720}\right)$
$\chi_{27584}(43,\cdot)$	27584.cy	3440	yes	$1$	$1$	$e\left(\frac{677}{688}\right)$	$e\left(\frac{2843}{3440}\right)$	$e\left(\frac{1407}{1720}\right)$	$e\left(\frac{333}{344}\right)$	$e\left(\frac{847}{3440}\right)$	$e\left(\frac{1453}{3440}\right)$	$e\left(\frac{697}{860}\right)$	$e\left(\frac{631}{860}\right)$	$e\left(\frac{2661}{3440}\right)$	$e\left(\frac{2759}{3440}\right)$
$\chi_{27584}(45,\cdot)$	27584.cz	3440	yes	$1$	$1$	$e\left(\frac{455}{688}\right)$	$e\left(\frac{2897}{3440}\right)$	$e\left(\frac{813}{1720}\right)$	$e\left(\frac{111}{344}\right)$	$e\left(\frac{53}{3440}\right)$	$e\left(\frac{3007}{3440}\right)$	$e\left(\frac{433}{860}\right)$	$e\left(\frac{239}{860}\right)$	$e\left(\frac{199}{3440}\right)$	$e\left(\frac{461}{3440}\right)$
$\chi_{27584}(47,\cdot)$	27584.bz	172	no	$1$	$1$	$e\left(\frac{149}{172}\right)$	$e\left(\frac{49}{172}\right)$	$e\left(\frac{63}{86}\right)$	$e\left(\frac{63}{86}\right)$	$e\left(\frac{79}{172}\right)$	$e\left(\frac{101}{172}\right)$	$e\left(\frac{13}{86}\right)$	$e\left(\frac{61}{86}\right)$	$e\left(\frac{37}{172}\right)$	$e\left(\frac{103}{172}\right)$
$\chi_{27584}(49,\cdot)$	27584.cr	860	no	$1$	$1$	$e\left(\frac{9}{172}\right)$	$e\left(\frac{723}{860}\right)$	$e\left(\frac{217}{430}\right)$	$e\left(\frac{9}{86}\right)$	$e\left(\frac{167}{860}\right)$	$e\left(\frac{453}{860}\right)$	$e\left(\frac{192}{215}\right)$	$e\left(\frac{31}{215}\right)$	$e\left(\frac{481}{860}\right)$	$e\left(\frac{479}{860}\right)$
$\chi_{27584}(51,\cdot)$	27584.cy	3440	yes	$1$	$1$	$e\left(\frac{567}{688}\right)$	$e\left(\frac{1001}{3440}\right)$	$e\left(\frac{1029}{1720}\right)$	$e\left(\frac{223}{344}\right)$	$e\left(\frac{1749}{3440}\right)$	$e\left(\frac{2911}{3440}\right)$	$e\left(\frac{99}{860}\right)$	$e\left(\frac{577}{860}\right)$	$e\left(\frac{3127}{3440}\right)$	$e\left(\frac{1453}{3440}\right)$
$\chi_{27584}(53,\cdot)$	27584.cz	3440	yes	$1$	$1$	$e\left(\frac{565}{688}\right)$	$e\left(\frac{611}{3440}\right)$	$e\left(\frac{159}{1720}\right)$	$e\left(\frac{221}{344}\right)$	$e\left(\frac{3279}{3440}\right)$	$e\left(\frac{861}{3440}\right)$	$e\left(\frac{859}{860}\right)$	$e\left(\frac{637}{860}\right)$	$e\left(\frac{1797}{3440}\right)$	$e\left(\frac{3143}{3440}\right)$
$\chi_{27584}(55,\cdot)$	27584.cc	344	no	$-1$	$1$	$e\left(\frac{175}{344}\right)$	$e\left(\frac{289}{344}\right)$	$e\left(\frac{3}{172}\right)$	$e\left(\frac{3}{172}\right)$	$e\left(\frac{57}{344}\right)$	$e\left(\frac{271}{344}\right)$	$e\left(\frac{15}{43}\right)$	$e\left(\frac{25}{86}\right)$	$e\left(\frac{227}{344}\right)$	$e\left(\frac{181}{344}\right)$
$\chi_{27584}(57,\cdot)$	27584.cu	1720	no	$1$	$1$	$e\left(\frac{173}{344}\right)$	$e\left(\frac{1227}{1720}\right)$	$e\left(\frac{263}{860}\right)$	$e\left(\frac{1}{172}\right)$	$e\left(\frac{783}{1720}\right)$	$e\left(\frac{1197}{1720}\right)$	$e\left(\frac{93}{430}\right)$	$e\left(\frac{99}{430}\right)$	$e\left(\frac{149}{1720}\right)$	$e\left(\frac{1391}{1720}\right)$
$\chi_{27584}(59,\cdot)$	27584.db	3440	yes	$-1$	$1$	$e\left(\frac{649}{688}\right)$	$e\left(\frac{2199}{3440}\right)$	$e\left(\frac{751}{1720}\right)$	$e\left(\frac{305}{344}\right)$	$e\left(\frac{251}{3440}\right)$	$e\left(\frac{3369}{3440}\right)$	$e\left(\frac{501}{860}\right)$	$e\left(\frac{353}{860}\right)$	$e\left(\frac{553}{3440}\right)$	$e\left(\frac{1307}{3440}\right)$
$\chi_{27584}(61,\cdot)$	27584.cz	3440	yes	$1$	$1$	$e\left(\frac{291}{688}\right)$	$e\left(\frac{1189}{3440}\right)$	$e\left(\frac{681}{1720}\right)$	$e\left(\frac{291}{344}\right)$	$e\left(\frac{2361}{3440}\right)$	$e\left(\frac{2779}{3440}\right)$	$e\left(\frac{661}{860}\right)$	$e\left(\frac{343}{860}\right)$	$e\left(\frac{3283}{3440}\right)$	$e\left(\frac{2817}{3440}\right)$
$\chi_{27584}(63,\cdot)$	27584.cl	430	no	$1$	$1$	$e\left(\frac{69}{86}\right)$	$e\left(\frac{41}{215}\right)$	$e\left(\frac{173}{215}\right)$	$e\left(\frac{26}{43}\right)$	$e\left(\frac{363}{430}\right)$	$e\left(\frac{377}{430}\right)$	$e\left(\frac{427}{430}\right)$	$e\left(\frac{191}{430}\right)$	$e\left(\frac{219}{430}\right)$	$e\left(\frac{261}{430}\right)$

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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	$27584$
Structure	\(C_{2}\times C_{2}\times C_{3440}\)
Order	$13760$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{27584}(1,\cdot)\)	27584.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{27584}(3,\cdot)\)	27584.cm	688	yes	\(-1\)	\(1\)	\(e\left(\frac{267}{688}\right)\)	\(e\left(\frac{609}{688}\right)\)	\(e\left(\frac{9}{344}\right)\)	\(e\left(\frac{267}{344}\right)\)	\(e\left(\frac{429}{688}\right)\)	\(e\left(\frac{383}{688}\right)\)	\(e\left(\frac{47}{172}\right)\)	\(e\left(\frac{75}{172}\right)\)	\(e\left(\frac{79}{688}\right)\)	\(e\left(\frac{285}{688}\right)\)
\(\chi_{27584}(5,\cdot)\)	27584.cz	3440	yes	\(1\)	\(1\)	\(e\left(\frac{609}{688}\right)\)	\(e\left(\frac{247}{3440}\right)\)	\(e\left(\frac{723}{1720}\right)\)	\(e\left(\frac{265}{344}\right)\)	\(e\left(\frac{2643}{3440}\right)\)	\(e\left(\frac{2617}{3440}\right)\)	\(e\left(\frac{823}{860}\right)\)	\(e\left(\frac{349}{860}\right)\)	\(e\left(\frac{2849}{3440}\right)\)	\(e\left(\frac{1051}{3440}\right)\)
\(\chi_{27584}(7,\cdot)\)	27584.cx	1720	no	\(1\)	\(1\)	\(e\left(\frac{9}{344}\right)\)	\(e\left(\frac{723}{1720}\right)\)	\(e\left(\frac{647}{860}\right)\)	\(e\left(\frac{9}{172}\right)\)	\(e\left(\frac{1027}{1720}\right)\)	\(e\left(\frac{1313}{1720}\right)\)	\(e\left(\frac{96}{215}\right)\)	\(e\left(\frac{123}{215}\right)\)	\(e\left(\frac{481}{1720}\right)\)	\(e\left(\frac{1339}{1720}\right)\)
\(\chi_{27584}(9,\cdot)\)	27584.ce	344	no	\(1\)	\(1\)	\(e\left(\frac{267}{344}\right)\)	\(e\left(\frac{265}{344}\right)\)	\(e\left(\frac{9}{172}\right)\)	\(e\left(\frac{95}{172}\right)\)	\(e\left(\frac{85}{344}\right)\)	\(e\left(\frac{39}{344}\right)\)	\(e\left(\frac{47}{86}\right)\)	\(e\left(\frac{75}{86}\right)\)	\(e\left(\frac{79}{344}\right)\)	\(e\left(\frac{285}{344}\right)\)
\(\chi_{27584}(11,\cdot)\)	27584.db	3440	yes	\(-1\)	\(1\)	\(e\left(\frac{429}{688}\right)\)	\(e\left(\frac{2643}{3440}\right)\)	\(e\left(\frac{1027}{1720}\right)\)	\(e\left(\frac{85}{344}\right)\)	\(e\left(\frac{1367}{3440}\right)\)	\(e\left(\frac{93}{3440}\right)\)	\(e\left(\frac{337}{860}\right)\)	\(e\left(\frac{761}{860}\right)\)	\(e\left(\frac{2861}{3440}\right)\)	\(e\left(\frac{759}{3440}\right)\)
\(\chi_{27584}(13,\cdot)\)	27584.da	3440	yes	\(-1\)	\(1\)	\(e\left(\frac{383}{688}\right)\)	\(e\left(\frac{2617}{3440}\right)\)	\(e\left(\frac{1313}{1720}\right)\)	\(e\left(\frac{39}{344}\right)\)	\(e\left(\frac{93}{3440}\right)\)	\(e\left(\frac{3167}{3440}\right)\)	\(e\left(\frac{273}{860}\right)\)	\(e\left(\frac{249}{860}\right)\)	\(e\left(\frac{479}{3440}\right)\)	\(e\left(\frac{1101}{3440}\right)\)
\(\chi_{27584}(15,\cdot)\)	27584.cs	860	no	\(-1\)	\(1\)	\(e\left(\frac{47}{172}\right)\)	\(e\left(\frac{823}{860}\right)\)	\(e\left(\frac{96}{215}\right)\)	\(e\left(\frac{47}{86}\right)\)	\(e\left(\frac{337}{860}\right)\)	\(e\left(\frac{273}{860}\right)\)	\(e\left(\frac{99}{430}\right)\)	\(e\left(\frac{181}{215}\right)\)	\(e\left(\frac{811}{860}\right)\)	\(e\left(\frac{619}{860}\right)\)
\(\chi_{27584}(17,\cdot)\)	27584.ct	860	no	\(-1\)	\(1\)	\(e\left(\frac{75}{172}\right)\)	\(e\left(\frac{349}{860}\right)\)	\(e\left(\frac{123}{215}\right)\)	\(e\left(\frac{75}{86}\right)\)	\(e\left(\frac{761}{860}\right)\)	\(e\left(\frac{249}{860}\right)\)	\(e\left(\frac{181}{215}\right)\)	\(e\left(\frac{101}{430}\right)\)	\(e\left(\frac{683}{860}\right)\)	\(e\left(\frac{7}{860}\right)\)
\(\chi_{27584}(19,\cdot)\)	27584.db	3440	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{688}\right)\)	\(e\left(\frac{2849}{3440}\right)\)	\(e\left(\frac{481}{1720}\right)\)	\(e\left(\frac{79}{344}\right)\)	\(e\left(\frac{2861}{3440}\right)\)	\(e\left(\frac{479}{3440}\right)\)	\(e\left(\frac{811}{860}\right)\)	\(e\left(\frac{683}{860}\right)\)	\(e\left(\frac{3343}{3440}\right)\)	\(e\left(\frac{1357}{3440}\right)\)
\(\chi_{27584}(21,\cdot)\)	27584.da	3440	yes	\(-1\)	\(1\)	\(e\left(\frac{285}{688}\right)\)	\(e\left(\frac{1051}{3440}\right)\)	\(e\left(\frac{1339}{1720}\right)\)	\(e\left(\frac{285}{344}\right)\)	\(e\left(\frac{759}{3440}\right)\)	\(e\left(\frac{1101}{3440}\right)\)	\(e\left(\frac{619}{860}\right)\)	\(e\left(\frac{7}{860}\right)\)	\(e\left(\frac{1357}{3440}\right)\)	\(e\left(\frac{663}{3440}\right)\)
\(\chi_{27584}(23,\cdot)\)	27584.cw	1720	no	\(-1\)	\(1\)	\(e\left(\frac{139}{344}\right)\)	\(e\left(\frac{273}{1720}\right)\)	\(e\left(\frac{7}{860}\right)\)	\(e\left(\frac{139}{172}\right)\)	\(e\left(\frac{1337}{1720}\right)\)	\(e\left(\frac{1263}{1720}\right)\)	\(e\left(\frac{121}{215}\right)\)	\(e\left(\frac{1}{430}\right)\)	\(e\left(\frac{931}{1720}\right)\)	\(e\left(\frac{709}{1720}\right)\)
\(\chi_{27584}(25,\cdot)\)	27584.cu	1720	no	\(1\)	\(1\)	\(e\left(\frac{265}{344}\right)\)	\(e\left(\frac{247}{1720}\right)\)	\(e\left(\frac{723}{860}\right)\)	\(e\left(\frac{93}{172}\right)\)	\(e\left(\frac{923}{1720}\right)\)	\(e\left(\frac{897}{1720}\right)\)	\(e\left(\frac{393}{430}\right)\)	\(e\left(\frac{349}{430}\right)\)	\(e\left(\frac{1129}{1720}\right)\)	\(e\left(\frac{1051}{1720}\right)\)
\(\chi_{27584}(27,\cdot)\)	27584.cm	688	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{688}\right)\)	\(e\left(\frac{451}{688}\right)\)	\(e\left(\frac{27}{344}\right)\)	\(e\left(\frac{113}{344}\right)\)	\(e\left(\frac{599}{688}\right)\)	\(e\left(\frac{461}{688}\right)\)	\(e\left(\frac{141}{172}\right)\)	\(e\left(\frac{53}{172}\right)\)	\(e\left(\frac{237}{688}\right)\)	\(e\left(\frac{167}{688}\right)\)
\(\chi_{27584}(29,\cdot)\)	27584.cz	3440	yes	\(1\)	\(1\)	\(e\left(\frac{379}{688}\right)\)	\(e\left(\frac{3213}{3440}\right)\)	\(e\left(\frac{777}{1720}\right)\)	\(e\left(\frac{35}{344}\right)\)	\(e\left(\frac{1777}{3440}\right)\)	\(e\left(\frac{2163}{3440}\right)\)	\(e\left(\frac{417}{860}\right)\)	\(e\left(\frac{111}{860}\right)\)	\(e\left(\frac{571}{3440}\right)\)	\(e\left(\frac{9}{3440}\right)\)
\(\chi_{27584}(31,\cdot)\)	27584.cg	430	no	\(1\)	\(1\)	\(e\left(\frac{18}{43}\right)\)	\(e\left(\frac{183}{430}\right)\)	\(e\left(\frac{137}{215}\right)\)	\(e\left(\frac{36}{43}\right)\)	\(e\left(\frac{76}{215}\right)\)	\(e\left(\frac{89}{215}\right)\)	\(e\left(\frac{363}{430}\right)\)	\(e\left(\frac{109}{430}\right)\)	\(e\left(\frac{188}{215}\right)\)	\(e\left(\frac{12}{215}\right)\)
\(\chi_{27584}(33,\cdot)\)	27584.cj	430	no	\(1\)	\(1\)	\(e\left(\frac{1}{86}\right)\)	\(e\left(\frac{281}{430}\right)\)	\(e\left(\frac{134}{215}\right)\)	\(e\left(\frac{1}{43}\right)\)	\(e\left(\frac{9}{430}\right)\)	\(e\left(\frac{251}{430}\right)\)	\(e\left(\frac{143}{215}\right)\)	\(e\left(\frac{69}{215}\right)\)	\(e\left(\frac{407}{430}\right)\)	\(e\left(\frac{273}{430}\right)\)
\(\chi_{27584}(35,\cdot)\)	27584.cy	3440	yes	\(1\)	\(1\)	\(e\left(\frac{627}{688}\right)\)	\(e\left(\frac{1693}{3440}\right)\)	\(e\left(\frac{297}{1720}\right)\)	\(e\left(\frac{283}{344}\right)\)	\(e\left(\frac{1257}{3440}\right)\)	\(e\left(\frac{1803}{3440}\right)\)	\(e\left(\frac{347}{860}\right)\)	\(e\left(\frac{841}{860}\right)\)	\(e\left(\frac{371}{3440}\right)\)	\(e\left(\frac{289}{3440}\right)\)
\(\chi_{27584}(37,\cdot)\)	27584.da	3440	yes	\(-1\)	\(1\)	\(e\left(\frac{409}{688}\right)\)	\(e\left(\frac{2527}{3440}\right)\)	\(e\left(\frac{583}{1720}\right)\)	\(e\left(\frac{65}{344}\right)\)	\(e\left(\frac{843}{3440}\right)\)	\(e\left(\frac{2297}{3440}\right)\)	\(e\left(\frac{283}{860}\right)\)	\(e\left(\frac{759}{860}\right)\)	\(e\left(\frac{569}{3440}\right)\)	\(e\left(\frac{3211}{3440}\right)\)
\(\chi_{27584}(39,\cdot)\)	27584.cx	1720	no	\(1\)	\(1\)	\(e\left(\frac{325}{344}\right)\)	\(e\left(\frac{1111}{1720}\right)\)	\(e\left(\frac{679}{860}\right)\)	\(e\left(\frac{153}{172}\right)\)	\(e\left(\frac{1119}{1720}\right)\)	\(e\left(\frac{821}{1720}\right)\)	\(e\left(\frac{127}{215}\right)\)	\(e\left(\frac{156}{215}\right)\)	\(e\left(\frac{437}{1720}\right)\)	\(e\left(\frac{1263}{1720}\right)\)
\(\chi_{27584}(41,\cdot)\)	27584.cu	1720	no	\(1\)	\(1\)	\(e\left(\frac{223}{344}\right)\)	\(e\left(\frac{657}{1720}\right)\)	\(e\left(\frac{513}{860}\right)\)	\(e\left(\frac{51}{172}\right)\)	\(e\left(\frac{373}{1720}\right)\)	\(e\left(\frac{847}{1720}\right)\)	\(e\left(\frac{13}{430}\right)\)	\(e\left(\frac{319}{430}\right)\)	\(e\left(\frac{719}{1720}\right)\)	\(e\left(\frac{421}{1720}\right)\)
\(\chi_{27584}(43,\cdot)\)	27584.cy	3440	yes	\(1\)	\(1\)	\(e\left(\frac{677}{688}\right)\)	\(e\left(\frac{2843}{3440}\right)\)	\(e\left(\frac{1407}{1720}\right)\)	\(e\left(\frac{333}{344}\right)\)	\(e\left(\frac{847}{3440}\right)\)	\(e\left(\frac{1453}{3440}\right)\)	\(e\left(\frac{697}{860}\right)\)	\(e\left(\frac{631}{860}\right)\)	\(e\left(\frac{2661}{3440}\right)\)	\(e\left(\frac{2759}{3440}\right)\)
\(\chi_{27584}(45,\cdot)\)	27584.cz	3440	yes	\(1\)	\(1\)	\(e\left(\frac{455}{688}\right)\)	\(e\left(\frac{2897}{3440}\right)\)	\(e\left(\frac{813}{1720}\right)\)	\(e\left(\frac{111}{344}\right)\)	\(e\left(\frac{53}{3440}\right)\)	\(e\left(\frac{3007}{3440}\right)\)	\(e\left(\frac{433}{860}\right)\)	\(e\left(\frac{239}{860}\right)\)	\(e\left(\frac{199}{3440}\right)\)	\(e\left(\frac{461}{3440}\right)\)
\(\chi_{27584}(47,\cdot)\)	27584.bz	172	no	\(1\)	\(1\)	\(e\left(\frac{149}{172}\right)\)	\(e\left(\frac{49}{172}\right)\)	\(e\left(\frac{63}{86}\right)\)	\(e\left(\frac{63}{86}\right)\)	\(e\left(\frac{79}{172}\right)\)	\(e\left(\frac{101}{172}\right)\)	\(e\left(\frac{13}{86}\right)\)	\(e\left(\frac{61}{86}\right)\)	\(e\left(\frac{37}{172}\right)\)	\(e\left(\frac{103}{172}\right)\)
\(\chi_{27584}(49,\cdot)\)	27584.cr	860	no	\(1\)	\(1\)	\(e\left(\frac{9}{172}\right)\)	\(e\left(\frac{723}{860}\right)\)	\(e\left(\frac{217}{430}\right)\)	\(e\left(\frac{9}{86}\right)\)	\(e\left(\frac{167}{860}\right)\)	\(e\left(\frac{453}{860}\right)\)	\(e\left(\frac{192}{215}\right)\)	\(e\left(\frac{31}{215}\right)\)	\(e\left(\frac{481}{860}\right)\)	\(e\left(\frac{479}{860}\right)\)
\(\chi_{27584}(51,\cdot)\)	27584.cy	3440	yes	\(1\)	\(1\)	\(e\left(\frac{567}{688}\right)\)	\(e\left(\frac{1001}{3440}\right)\)	\(e\left(\frac{1029}{1720}\right)\)	\(e\left(\frac{223}{344}\right)\)	\(e\left(\frac{1749}{3440}\right)\)	\(e\left(\frac{2911}{3440}\right)\)	\(e\left(\frac{99}{860}\right)\)	\(e\left(\frac{577}{860}\right)\)	\(e\left(\frac{3127}{3440}\right)\)	\(e\left(\frac{1453}{3440}\right)\)
\(\chi_{27584}(53,\cdot)\)	27584.cz	3440	yes	\(1\)	\(1\)	\(e\left(\frac{565}{688}\right)\)	\(e\left(\frac{611}{3440}\right)\)	\(e\left(\frac{159}{1720}\right)\)	\(e\left(\frac{221}{344}\right)\)	\(e\left(\frac{3279}{3440}\right)\)	\(e\left(\frac{861}{3440}\right)\)	\(e\left(\frac{859}{860}\right)\)	\(e\left(\frac{637}{860}\right)\)	\(e\left(\frac{1797}{3440}\right)\)	\(e\left(\frac{3143}{3440}\right)\)
\(\chi_{27584}(55,\cdot)\)	27584.cc	344	no	\(-1\)	\(1\)	\(e\left(\frac{175}{344}\right)\)	\(e\left(\frac{289}{344}\right)\)	\(e\left(\frac{3}{172}\right)\)	\(e\left(\frac{3}{172}\right)\)	\(e\left(\frac{57}{344}\right)\)	\(e\left(\frac{271}{344}\right)\)	\(e\left(\frac{15}{43}\right)\)	\(e\left(\frac{25}{86}\right)\)	\(e\left(\frac{227}{344}\right)\)	\(e\left(\frac{181}{344}\right)\)
\(\chi_{27584}(57,\cdot)\)	27584.cu	1720	no	\(1\)	\(1\)	\(e\left(\frac{173}{344}\right)\)	\(e\left(\frac{1227}{1720}\right)\)	\(e\left(\frac{263}{860}\right)\)	\(e\left(\frac{1}{172}\right)\)	\(e\left(\frac{783}{1720}\right)\)	\(e\left(\frac{1197}{1720}\right)\)	\(e\left(\frac{93}{430}\right)\)	\(e\left(\frac{99}{430}\right)\)	\(e\left(\frac{149}{1720}\right)\)	\(e\left(\frac{1391}{1720}\right)\)
\(\chi_{27584}(59,\cdot)\)	27584.db	3440	yes	\(-1\)	\(1\)	\(e\left(\frac{649}{688}\right)\)	\(e\left(\frac{2199}{3440}\right)\)	\(e\left(\frac{751}{1720}\right)\)	\(e\left(\frac{305}{344}\right)\)	\(e\left(\frac{251}{3440}\right)\)	\(e\left(\frac{3369}{3440}\right)\)	\(e\left(\frac{501}{860}\right)\)	\(e\left(\frac{353}{860}\right)\)	\(e\left(\frac{553}{3440}\right)\)	\(e\left(\frac{1307}{3440}\right)\)
\(\chi_{27584}(61,\cdot)\)	27584.cz	3440	yes	\(1\)	\(1\)	\(e\left(\frac{291}{688}\right)\)	\(e\left(\frac{1189}{3440}\right)\)	\(e\left(\frac{681}{1720}\right)\)	\(e\left(\frac{291}{344}\right)\)	\(e\left(\frac{2361}{3440}\right)\)	\(e\left(\frac{2779}{3440}\right)\)	\(e\left(\frac{661}{860}\right)\)	\(e\left(\frac{343}{860}\right)\)	\(e\left(\frac{3283}{3440}\right)\)	\(e\left(\frac{2817}{3440}\right)\)
\(\chi_{27584}(63,\cdot)\)	27584.cl	430	no	\(1\)	\(1\)	\(e\left(\frac{69}{86}\right)\)	\(e\left(\frac{41}{215}\right)\)	\(e\left(\frac{173}{215}\right)\)	\(e\left(\frac{26}{43}\right)\)	\(e\left(\frac{363}{430}\right)\)	\(e\left(\frac{377}{430}\right)\)	\(e\left(\frac{427}{430}\right)\)	\(e\left(\frac{191}{430}\right)\)	\(e\left(\frac{219}{430}\right)\)	\(e\left(\frac{261}{430}\right)\)

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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.