LMFDB - Group of Dirichlet characters of modulus 373527

sage:H = DirichletGroup(373527)

pari:g = idealstar(,373527,2)

Character group

sage:G.order() pari:g.no
Order	=	194040
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{16170}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{373527}(290522,\cdot)$, $\chi_{373527}(286408,\cdot)$, $\chi_{373527}(126568,\cdot)$

First 32 of 194040 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{373527}(1,\cdot)$	373527.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{373527}(2,\cdot)$	373527.sf	16170	yes	$1$	$1$	$e\left(\frac{1531}{8085}\right)$	$e\left(\frac{3062}{8085}\right)$	$e\left(\frac{3461}{5390}\right)$	$e\left(\frac{1531}{2695}\right)$	$e\left(\frac{2689}{3234}\right)$	$e\left(\frac{5057}{16170}\right)$	$e\left(\frac{6124}{8085}\right)$	$e\left(\frac{3574}{8085}\right)$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{337}{16170}\right)$
$\chi_{373527}(4,\cdot)$	373527.ri	8085	yes	$1$	$1$	$e\left(\frac{3062}{8085}\right)$	$e\left(\frac{6124}{8085}\right)$	$e\left(\frac{766}{2695}\right)$	$e\left(\frac{367}{2695}\right)$	$e\left(\frac{1072}{1617}\right)$	$e\left(\frac{5057}{8085}\right)$	$e\left(\frac{4163}{8085}\right)$	$e\left(\frac{7148}{8085}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{337}{8085}\right)$
$\chi_{373527}(5,\cdot)$	373527.sh	16170	yes	$1$	$1$	$e\left(\frac{3461}{5390}\right)$	$e\left(\frac{766}{2695}\right)$	$e\left(\frac{6541}{8085}\right)$	$e\left(\frac{4993}{5390}\right)$	$e\left(\frac{1459}{3234}\right)$	$e\left(\frac{11713}{16170}\right)$	$e\left(\frac{1532}{2695}\right)$	$e\left(\frac{7516}{8085}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{754}{8085}\right)$
$\chi_{373527}(8,\cdot)$	373527.qz	5390	no	$1$	$1$	$e\left(\frac{1531}{2695}\right)$	$e\left(\frac{367}{2695}\right)$	$e\left(\frac{4993}{5390}\right)$	$e\left(\frac{1898}{2695}\right)$	$e\left(\frac{533}{1078}\right)$	$e\left(\frac{5057}{5390}\right)$	$e\left(\frac{734}{2695}\right)$	$e\left(\frac{879}{2695}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{337}{5390}\right)$
$\chi_{373527}(10,\cdot)$	373527.qq	3234	no	$1$	$1$	$e\left(\frac{2689}{3234}\right)$	$e\left(\frac{1072}{1617}\right)$	$e\left(\frac{1459}{3234}\right)$	$e\left(\frac{533}{1078}\right)$	$e\left(\frac{457}{1617}\right)$	$e\left(\frac{20}{539}\right)$	$e\left(\frac{527}{1617}\right)$	$e\left(\frac{601}{1617}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{123}{1078}\right)$
$\chi_{373527}(13,\cdot)$	373527.sj	16170	yes	$1$	$1$	$e\left(\frac{5057}{16170}\right)$	$e\left(\frac{5057}{8085}\right)$	$e\left(\frac{11713}{16170}\right)$	$e\left(\frac{5057}{5390}\right)$	$e\left(\frac{20}{539}\right)$	$e\left(\frac{5486}{8085}\right)$	$e\left(\frac{2029}{8085}\right)$	$e\left(\frac{608}{2695}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{5657}{16170}\right)$
$\chi_{373527}(16,\cdot)$	373527.ri	8085	yes	$1$	$1$	$e\left(\frac{6124}{8085}\right)$	$e\left(\frac{4163}{8085}\right)$	$e\left(\frac{1532}{2695}\right)$	$e\left(\frac{734}{2695}\right)$	$e\left(\frac{527}{1617}\right)$	$e\left(\frac{2029}{8085}\right)$	$e\left(\frac{241}{8085}\right)$	$e\left(\frac{6211}{8085}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{674}{8085}\right)$
$\chi_{373527}(17,\cdot)$	373527.rp	16170	no	$-1$	$1$	$e\left(\frac{3574}{8085}\right)$	$e\left(\frac{7148}{8085}\right)$	$e\left(\frac{7516}{8085}\right)$	$e\left(\frac{879}{2695}\right)$	$e\left(\frac{601}{1617}\right)$	$e\left(\frac{608}{2695}\right)$	$e\left(\frac{6211}{8085}\right)$	$e\left(\frac{7327}{16170}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{2193}{2695}\right)$
$\chi_{373527}(19,\cdot)$	373527.la	330	no	$1$	$1$	$e\left(\frac{139}{330}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{29}{110}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{93}{110}\right)$
$\chi_{373527}(20,\cdot)$	373527.rk	16170	yes	$1$	$1$	$e\left(\frac{337}{16170}\right)$	$e\left(\frac{337}{8085}\right)$	$e\left(\frac{754}{8085}\right)$	$e\left(\frac{337}{5390}\right)$	$e\left(\frac{123}{1078}\right)$	$e\left(\frac{5657}{16170}\right)$	$e\left(\frac{674}{8085}\right)$	$e\left(\frac{2193}{2695}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{1091}{8085}\right)$
$\chi_{373527}(23,\cdot)$	373527.qu	3234	yes	$-1$	$1$	$e\left(\frac{741}{1078}\right)$	$e\left(\frac{202}{539}\right)$	$e\left(\frac{1405}{3234}\right)$	$e\left(\frac{67}{1078}\right)$	$e\left(\frac{197}{1617}\right)$	$e\left(\frac{1486}{1617}\right)$	$e\left(\frac{404}{539}\right)$	$e\left(\frac{2029}{3234}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{2617}{3234}\right)$
$\chi_{373527}(25,\cdot)$	373527.rg	8085	yes	$1$	$1$	$e\left(\frac{766}{2695}\right)$	$e\left(\frac{1532}{2695}\right)$	$e\left(\frac{4997}{8085}\right)$	$e\left(\frac{2298}{2695}\right)$	$e\left(\frac{1459}{1617}\right)$	$e\left(\frac{3628}{8085}\right)$	$e\left(\frac{369}{2695}\right)$	$e\left(\frac{6947}{8085}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{1508}{8085}\right)$
$\chi_{373527}(26,\cdot)$	373527.sc	16170	no	$1$	$1$	$e\left(\frac{8119}{16170}\right)$	$e\left(\frac{34}{8085}\right)$	$e\left(\frac{2963}{8085}\right)$	$e\left(\frac{2729}{5390}\right)$	$e\left(\frac{2809}{3234}\right)$	$e\left(\frac{5343}{5390}\right)$	$e\left(\frac{68}{8085}\right)$	$e\left(\frac{5398}{8085}\right)$	$e\left(\frac{43}{330}\right)$	$e\left(\frac{999}{2695}\right)$
$\chi_{373527}(29,\cdot)$	373527.rn	16170	yes	$1$	$1$	$e\left(\frac{6227}{8085}\right)$	$e\left(\frac{4369}{8085}\right)$	$e\left(\frac{12281}{16170}\right)$	$e\left(\frac{837}{2695}\right)$	$e\left(\frac{571}{1078}\right)$	$e\left(\frac{15569}{16170}\right)$	$e\left(\frac{653}{8085}\right)$	$e\left(\frac{1241}{2695}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{4849}{16170}\right)$
$\chi_{373527}(31,\cdot)$	373527.pq	2310	no	$-1$	$1$	$e\left(\frac{1013}{1155}\right)$	$e\left(\frac{871}{1155}\right)$	$e\left(\frac{493}{770}\right)$	$e\left(\frac{243}{385}\right)$	$e\left(\frac{239}{462}\right)$	$e\left(\frac{1291}{2310}\right)$	$e\left(\frac{587}{1155}\right)$	$e\left(\frac{1429}{2310}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{911}{2310}\right)$
$\chi_{373527}(32,\cdot)$	373527.qd	3234	yes	$1$	$1$	$e\left(\frac{1531}{1617}\right)$	$e\left(\frac{1445}{1617}\right)$	$e\left(\frac{227}{1078}\right)$	$e\left(\frac{453}{539}\right)$	$e\left(\frac{509}{3234}\right)$	$e\left(\frac{1823}{3234}\right)$	$e\left(\frac{1273}{1617}\right)$	$e\left(\frac{340}{1617}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{337}{3234}\right)$
$\chi_{373527}(34,\cdot)$	373527.qx	3234	yes	$-1$	$1$	$e\left(\frac{1021}{1617}\right)$	$e\left(\frac{425}{1617}\right)$	$e\left(\frac{1849}{3234}\right)$	$e\left(\frac{482}{539}\right)$	$e\left(\frac{219}{1078}\right)$	$e\left(\frac{1741}{3234}\right)$	$e\left(\frac{850}{1617}\right)$	$e\left(\frac{965}{1078}\right)$	$e\left(\frac{5}{22}\right)$	$e\left(\frac{2699}{3234}\right)$
$\chi_{373527}(37,\cdot)$	373527.rh	8085	no	$1$	$1$	$e\left(\frac{1712}{8085}\right)$	$e\left(\frac{3424}{8085}\right)$	$e\left(\frac{4478}{8085}\right)$	$e\left(\frac{1712}{2695}\right)$	$e\left(\frac{1238}{1617}\right)$	$e\left(\frac{804}{2695}\right)$	$e\left(\frac{6848}{8085}\right)$	$e\left(\frac{13}{8085}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{2634}{2695}\right)$
$\chi_{373527}(38,\cdot)$	373527.sh	16170	yes	$1$	$1$	$e\left(\frac{3291}{5390}\right)$	$e\left(\frac{596}{2695}\right)$	$e\left(\frac{5216}{8085}\right)$	$e\left(\frac{4483}{5390}\right)$	$e\left(\frac{827}{3234}\right)$	$e\left(\frac{353}{16170}\right)$	$e\left(\frac{1192}{2695}\right)$	$e\left(\frac{2006}{8085}\right)$	$e\left(\frac{71}{330}\right)$	$e\left(\frac{7004}{8085}\right)$
$\chi_{373527}(40,\cdot)$	373527.oe	1470	no	$1$	$1$	$e\left(\frac{103}{490}\right)$	$e\left(\frac{103}{245}\right)$	$e\left(\frac{1081}{1470}\right)$	$e\left(\frac{309}{490}\right)$	$e\left(\frac{139}{147}\right)$	$e\left(\frac{487}{735}\right)$	$e\left(\frac{206}{245}\right)$	$e\left(\frac{188}{735}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{229}{1470}\right)$
$\chi_{373527}(41,\cdot)$	373527.sk	16170	yes	$-1$	$1$	$e\left(\frac{6448}{8085}\right)$	$e\left(\frac{4811}{8085}\right)$	$e\left(\frac{5582}{8085}\right)$	$e\left(\frac{1058}{2695}\right)$	$e\left(\frac{263}{539}\right)$	$e\left(\frac{1478}{8085}\right)$	$e\left(\frac{1537}{8085}\right)$	$e\left(\frac{1653}{5390}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{2308}{8085}\right)$
$\chi_{373527}(43,\cdot)$	373527.qw	3234	yes	$-1$	$1$	$e\left(\frac{2759}{3234}\right)$	$e\left(\frac{1142}{1617}\right)$	$e\left(\frac{1202}{1617}\right)$	$e\left(\frac{603}{1078}\right)$	$e\left(\frac{643}{1078}\right)$	$e\left(\frac{337}{3234}\right)$	$e\left(\frac{667}{1617}\right)$	$e\left(\frac{697}{1078}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{727}{1617}\right)$
$\chi_{373527}(46,\cdot)$	373527.sg	16170	no	$-1$	$1$	$e\left(\frac{14177}{16170}\right)$	$e\left(\frac{6092}{8085}\right)$	$e\left(\frac{619}{8085}\right)$	$e\left(\frac{3397}{5390}\right)$	$e\left(\frac{3083}{3234}\right)$	$e\left(\frac{1249}{5390}\right)$	$e\left(\frac{4099}{8085}\right)$	$e\left(\frac{1123}{16170}\right)$	$e\left(\frac{299}{330}\right)$	$e\left(\frac{2237}{2695}\right)$
$\chi_{373527}(47,\cdot)$	373527.sa	16170	yes	$1$	$1$	$e\left(\frac{15011}{16170}\right)$	$e\left(\frac{6926}{8085}\right)$	$e\left(\frac{2609}{2695}\right)$	$e\left(\frac{4231}{5390}\right)$	$e\left(\frac{2899}{3234}\right)$	$e\left(\frac{11861}{16170}\right)$	$e\left(\frac{5767}{8085}\right)$	$e\left(\frac{3532}{8085}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{6668}{8085}\right)$
$\chi_{373527}(50,\cdot)$	373527.pk	2310	no	$1$	$1$	$e\left(\frac{547}{1155}\right)$	$e\left(\frac{1094}{1155}\right)$	$e\left(\frac{601}{2310}\right)$	$e\left(\frac{162}{385}\right)$	$e\left(\frac{113}{154}\right)$	$e\left(\frac{1759}{2310}\right)$	$e\left(\frac{1033}{1155}\right)$	$e\left(\frac{116}{385}\right)$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{479}{2310}\right)$
$\chi_{373527}(52,\cdot)$	373527.rv	16170	yes	$1$	$1$	$e\left(\frac{3727}{5390}\right)$	$e\left(\frac{1032}{2695}\right)$	$e\left(\frac{139}{16170}\right)$	$e\left(\frac{401}{5390}\right)$	$e\left(\frac{1132}{1617}\right)$	$e\left(\frac{2458}{8085}\right)$	$e\left(\frac{2064}{2695}\right)$	$e\left(\frac{887}{8085}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{6331}{16170}\right)$
$\chi_{373527}(53,\cdot)$	373527.ru	16170	no	$-1$	$1$	$e\left(\frac{1007}{16170}\right)$	$e\left(\frac{1007}{8085}\right)$	$e\left(\frac{12863}{16170}\right)$	$e\left(\frac{1007}{5390}\right)$	$e\left(\frac{1387}{1617}\right)$	$e\left(\frac{57}{2695}\right)$	$e\left(\frac{2014}{8085}\right)$	$e\left(\frac{9193}{16170}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{4959}{5390}\right)$
$\chi_{373527}(58,\cdot)$	373527.rg	8085	yes	$1$	$1$	$e\left(\frac{2586}{2695}\right)$	$e\left(\frac{2477}{2695}\right)$	$e\left(\frac{3247}{8085}\right)$	$e\left(\frac{2368}{2695}\right)$	$e\left(\frac{584}{1617}\right)$	$e\left(\frac{2228}{8085}\right)$	$e\left(\frac{2259}{2695}\right)$	$e\left(\frac{7297}{8085}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{2593}{8085}\right)$
$\chi_{373527}(59,\cdot)$	373527.sa	16170	yes	$1$	$1$	$e\left(\frac{11359}{16170}\right)$	$e\left(\frac{3274}{8085}\right)$	$e\left(\frac{2631}{2695}\right)$	$e\left(\frac{579}{5390}\right)$	$e\left(\frac{2195}{3234}\right)$	$e\left(\frac{10519}{16170}\right)$	$e\left(\frac{6548}{8085}\right)$	$e\left(\frac{6953}{8085}\right)$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{3082}{8085}\right)$
$\chi_{373527}(61,\cdot)$	373527.rq	16170	yes	$1$	$1$	$e\left(\frac{3263}{16170}\right)$	$e\left(\frac{3263}{8085}\right)$	$e\left(\frac{3249}{5390}\right)$	$e\left(\frac{3263}{5390}\right)$	$e\left(\frac{1301}{1617}\right)$	$e\left(\frac{2944}{8085}\right)$	$e\left(\frac{6526}{8085}\right)$	$e\left(\frac{7426}{8085}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{103}{16170}\right)$
$\chi_{373527}(62,\cdot)$	373527.re	5390	no	$-1$	$1$	$e\left(\frac{179}{2695}\right)$	$e\left(\frac{358}{2695}\right)$	$e\left(\frac{761}{2695}\right)$	$e\left(\frac{537}{2695}\right)$	$e\left(\frac{188}{539}\right)$	$e\left(\frac{2349}{2695}\right)$	$e\left(\frac{716}{2695}\right)$	$e\left(\frac{327}{5390}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{1119}{2695}\right)$

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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	$373527$
Structure	\(C_{2}\times C_{6}\times C_{16170}\)
Order	$194040$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{373527}(1,\cdot)\)	373527.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{373527}(2,\cdot)\)	373527.sf	16170	yes	\(1\)	\(1\)	\(e\left(\frac{1531}{8085}\right)\)	\(e\left(\frac{3062}{8085}\right)\)	\(e\left(\frac{3461}{5390}\right)\)	\(e\left(\frac{1531}{2695}\right)\)	\(e\left(\frac{2689}{3234}\right)\)	\(e\left(\frac{5057}{16170}\right)\)	\(e\left(\frac{6124}{8085}\right)\)	\(e\left(\frac{3574}{8085}\right)\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{337}{16170}\right)\)
\(\chi_{373527}(4,\cdot)\)	373527.ri	8085	yes	\(1\)	\(1\)	\(e\left(\frac{3062}{8085}\right)\)	\(e\left(\frac{6124}{8085}\right)\)	\(e\left(\frac{766}{2695}\right)\)	\(e\left(\frac{367}{2695}\right)\)	\(e\left(\frac{1072}{1617}\right)\)	\(e\left(\frac{5057}{8085}\right)\)	\(e\left(\frac{4163}{8085}\right)\)	\(e\left(\frac{7148}{8085}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{337}{8085}\right)\)
\(\chi_{373527}(5,\cdot)\)	373527.sh	16170	yes	\(1\)	\(1\)	\(e\left(\frac{3461}{5390}\right)\)	\(e\left(\frac{766}{2695}\right)\)	\(e\left(\frac{6541}{8085}\right)\)	\(e\left(\frac{4993}{5390}\right)\)	\(e\left(\frac{1459}{3234}\right)\)	\(e\left(\frac{11713}{16170}\right)\)	\(e\left(\frac{1532}{2695}\right)\)	\(e\left(\frac{7516}{8085}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{754}{8085}\right)\)
\(\chi_{373527}(8,\cdot)\)	373527.qz	5390	no	\(1\)	\(1\)	\(e\left(\frac{1531}{2695}\right)\)	\(e\left(\frac{367}{2695}\right)\)	\(e\left(\frac{4993}{5390}\right)\)	\(e\left(\frac{1898}{2695}\right)\)	\(e\left(\frac{533}{1078}\right)\)	\(e\left(\frac{5057}{5390}\right)\)	\(e\left(\frac{734}{2695}\right)\)	\(e\left(\frac{879}{2695}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{337}{5390}\right)\)
\(\chi_{373527}(10,\cdot)\)	373527.qq	3234	no	\(1\)	\(1\)	\(e\left(\frac{2689}{3234}\right)\)	\(e\left(\frac{1072}{1617}\right)\)	\(e\left(\frac{1459}{3234}\right)\)	\(e\left(\frac{533}{1078}\right)\)	\(e\left(\frac{457}{1617}\right)\)	\(e\left(\frac{20}{539}\right)\)	\(e\left(\frac{527}{1617}\right)\)	\(e\left(\frac{601}{1617}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{123}{1078}\right)\)
\(\chi_{373527}(13,\cdot)\)	373527.sj	16170	yes	\(1\)	\(1\)	\(e\left(\frac{5057}{16170}\right)\)	\(e\left(\frac{5057}{8085}\right)\)	\(e\left(\frac{11713}{16170}\right)\)	\(e\left(\frac{5057}{5390}\right)\)	\(e\left(\frac{20}{539}\right)\)	\(e\left(\frac{5486}{8085}\right)\)	\(e\left(\frac{2029}{8085}\right)\)	\(e\left(\frac{608}{2695}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{5657}{16170}\right)\)
\(\chi_{373527}(16,\cdot)\)	373527.ri	8085	yes	\(1\)	\(1\)	\(e\left(\frac{6124}{8085}\right)\)	\(e\left(\frac{4163}{8085}\right)\)	\(e\left(\frac{1532}{2695}\right)\)	\(e\left(\frac{734}{2695}\right)\)	\(e\left(\frac{527}{1617}\right)\)	\(e\left(\frac{2029}{8085}\right)\)	\(e\left(\frac{241}{8085}\right)\)	\(e\left(\frac{6211}{8085}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{674}{8085}\right)\)
\(\chi_{373527}(17,\cdot)\)	373527.rp	16170	no	\(-1\)	\(1\)	\(e\left(\frac{3574}{8085}\right)\)	\(e\left(\frac{7148}{8085}\right)\)	\(e\left(\frac{7516}{8085}\right)\)	\(e\left(\frac{879}{2695}\right)\)	\(e\left(\frac{601}{1617}\right)\)	\(e\left(\frac{608}{2695}\right)\)	\(e\left(\frac{6211}{8085}\right)\)	\(e\left(\frac{7327}{16170}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{2193}{2695}\right)\)
\(\chi_{373527}(19,\cdot)\)	373527.la	330	no	\(1\)	\(1\)	\(e\left(\frac{139}{330}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{29}{110}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{93}{110}\right)\)
\(\chi_{373527}(20,\cdot)\)	373527.rk	16170	yes	\(1\)	\(1\)	\(e\left(\frac{337}{16170}\right)\)	\(e\left(\frac{337}{8085}\right)\)	\(e\left(\frac{754}{8085}\right)\)	\(e\left(\frac{337}{5390}\right)\)	\(e\left(\frac{123}{1078}\right)\)	\(e\left(\frac{5657}{16170}\right)\)	\(e\left(\frac{674}{8085}\right)\)	\(e\left(\frac{2193}{2695}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{1091}{8085}\right)\)
\(\chi_{373527}(23,\cdot)\)	373527.qu	3234	yes	\(-1\)	\(1\)	\(e\left(\frac{741}{1078}\right)\)	\(e\left(\frac{202}{539}\right)\)	\(e\left(\frac{1405}{3234}\right)\)	\(e\left(\frac{67}{1078}\right)\)	\(e\left(\frac{197}{1617}\right)\)	\(e\left(\frac{1486}{1617}\right)\)	\(e\left(\frac{404}{539}\right)\)	\(e\left(\frac{2029}{3234}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{2617}{3234}\right)\)
\(\chi_{373527}(25,\cdot)\)	373527.rg	8085	yes	\(1\)	\(1\)	\(e\left(\frac{766}{2695}\right)\)	\(e\left(\frac{1532}{2695}\right)\)	\(e\left(\frac{4997}{8085}\right)\)	\(e\left(\frac{2298}{2695}\right)\)	\(e\left(\frac{1459}{1617}\right)\)	\(e\left(\frac{3628}{8085}\right)\)	\(e\left(\frac{369}{2695}\right)\)	\(e\left(\frac{6947}{8085}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{1508}{8085}\right)\)
\(\chi_{373527}(26,\cdot)\)	373527.sc	16170	no	\(1\)	\(1\)	\(e\left(\frac{8119}{16170}\right)\)	\(e\left(\frac{34}{8085}\right)\)	\(e\left(\frac{2963}{8085}\right)\)	\(e\left(\frac{2729}{5390}\right)\)	\(e\left(\frac{2809}{3234}\right)\)	\(e\left(\frac{5343}{5390}\right)\)	\(e\left(\frac{68}{8085}\right)\)	\(e\left(\frac{5398}{8085}\right)\)	\(e\left(\frac{43}{330}\right)\)	\(e\left(\frac{999}{2695}\right)\)
\(\chi_{373527}(29,\cdot)\)	373527.rn	16170	yes	\(1\)	\(1\)	\(e\left(\frac{6227}{8085}\right)\)	\(e\left(\frac{4369}{8085}\right)\)	\(e\left(\frac{12281}{16170}\right)\)	\(e\left(\frac{837}{2695}\right)\)	\(e\left(\frac{571}{1078}\right)\)	\(e\left(\frac{15569}{16170}\right)\)	\(e\left(\frac{653}{8085}\right)\)	\(e\left(\frac{1241}{2695}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{4849}{16170}\right)\)
\(\chi_{373527}(31,\cdot)\)	373527.pq	2310	no	\(-1\)	\(1\)	\(e\left(\frac{1013}{1155}\right)\)	\(e\left(\frac{871}{1155}\right)\)	\(e\left(\frac{493}{770}\right)\)	\(e\left(\frac{243}{385}\right)\)	\(e\left(\frac{239}{462}\right)\)	\(e\left(\frac{1291}{2310}\right)\)	\(e\left(\frac{587}{1155}\right)\)	\(e\left(\frac{1429}{2310}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{911}{2310}\right)\)
\(\chi_{373527}(32,\cdot)\)	373527.qd	3234	yes	\(1\)	\(1\)	\(e\left(\frac{1531}{1617}\right)\)	\(e\left(\frac{1445}{1617}\right)\)	\(e\left(\frac{227}{1078}\right)\)	\(e\left(\frac{453}{539}\right)\)	\(e\left(\frac{509}{3234}\right)\)	\(e\left(\frac{1823}{3234}\right)\)	\(e\left(\frac{1273}{1617}\right)\)	\(e\left(\frac{340}{1617}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{337}{3234}\right)\)
\(\chi_{373527}(34,\cdot)\)	373527.qx	3234	yes	\(-1\)	\(1\)	\(e\left(\frac{1021}{1617}\right)\)	\(e\left(\frac{425}{1617}\right)\)	\(e\left(\frac{1849}{3234}\right)\)	\(e\left(\frac{482}{539}\right)\)	\(e\left(\frac{219}{1078}\right)\)	\(e\left(\frac{1741}{3234}\right)\)	\(e\left(\frac{850}{1617}\right)\)	\(e\left(\frac{965}{1078}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{2699}{3234}\right)\)
\(\chi_{373527}(37,\cdot)\)	373527.rh	8085	no	\(1\)	\(1\)	\(e\left(\frac{1712}{8085}\right)\)	\(e\left(\frac{3424}{8085}\right)\)	\(e\left(\frac{4478}{8085}\right)\)	\(e\left(\frac{1712}{2695}\right)\)	\(e\left(\frac{1238}{1617}\right)\)	\(e\left(\frac{804}{2695}\right)\)	\(e\left(\frac{6848}{8085}\right)\)	\(e\left(\frac{13}{8085}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{2634}{2695}\right)\)
\(\chi_{373527}(38,\cdot)\)	373527.sh	16170	yes	\(1\)	\(1\)	\(e\left(\frac{3291}{5390}\right)\)	\(e\left(\frac{596}{2695}\right)\)	\(e\left(\frac{5216}{8085}\right)\)	\(e\left(\frac{4483}{5390}\right)\)	\(e\left(\frac{827}{3234}\right)\)	\(e\left(\frac{353}{16170}\right)\)	\(e\left(\frac{1192}{2695}\right)\)	\(e\left(\frac{2006}{8085}\right)\)	\(e\left(\frac{71}{330}\right)\)	\(e\left(\frac{7004}{8085}\right)\)
\(\chi_{373527}(40,\cdot)\)	373527.oe	1470	no	\(1\)	\(1\)	\(e\left(\frac{103}{490}\right)\)	\(e\left(\frac{103}{245}\right)\)	\(e\left(\frac{1081}{1470}\right)\)	\(e\left(\frac{309}{490}\right)\)	\(e\left(\frac{139}{147}\right)\)	\(e\left(\frac{487}{735}\right)\)	\(e\left(\frac{206}{245}\right)\)	\(e\left(\frac{188}{735}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{229}{1470}\right)\)
\(\chi_{373527}(41,\cdot)\)	373527.sk	16170	yes	\(-1\)	\(1\)	\(e\left(\frac{6448}{8085}\right)\)	\(e\left(\frac{4811}{8085}\right)\)	\(e\left(\frac{5582}{8085}\right)\)	\(e\left(\frac{1058}{2695}\right)\)	\(e\left(\frac{263}{539}\right)\)	\(e\left(\frac{1478}{8085}\right)\)	\(e\left(\frac{1537}{8085}\right)\)	\(e\left(\frac{1653}{5390}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{2308}{8085}\right)\)
\(\chi_{373527}(43,\cdot)\)	373527.qw	3234	yes	\(-1\)	\(1\)	\(e\left(\frac{2759}{3234}\right)\)	\(e\left(\frac{1142}{1617}\right)\)	\(e\left(\frac{1202}{1617}\right)\)	\(e\left(\frac{603}{1078}\right)\)	\(e\left(\frac{643}{1078}\right)\)	\(e\left(\frac{337}{3234}\right)\)	\(e\left(\frac{667}{1617}\right)\)	\(e\left(\frac{697}{1078}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{727}{1617}\right)\)
\(\chi_{373527}(46,\cdot)\)	373527.sg	16170	no	\(-1\)	\(1\)	\(e\left(\frac{14177}{16170}\right)\)	\(e\left(\frac{6092}{8085}\right)\)	\(e\left(\frac{619}{8085}\right)\)	\(e\left(\frac{3397}{5390}\right)\)	\(e\left(\frac{3083}{3234}\right)\)	\(e\left(\frac{1249}{5390}\right)\)	\(e\left(\frac{4099}{8085}\right)\)	\(e\left(\frac{1123}{16170}\right)\)	\(e\left(\frac{299}{330}\right)\)	\(e\left(\frac{2237}{2695}\right)\)
\(\chi_{373527}(47,\cdot)\)	373527.sa	16170	yes	\(1\)	\(1\)	\(e\left(\frac{15011}{16170}\right)\)	\(e\left(\frac{6926}{8085}\right)\)	\(e\left(\frac{2609}{2695}\right)\)	\(e\left(\frac{4231}{5390}\right)\)	\(e\left(\frac{2899}{3234}\right)\)	\(e\left(\frac{11861}{16170}\right)\)	\(e\left(\frac{5767}{8085}\right)\)	\(e\left(\frac{3532}{8085}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{6668}{8085}\right)\)
\(\chi_{373527}(50,\cdot)\)	373527.pk	2310	no	\(1\)	\(1\)	\(e\left(\frac{547}{1155}\right)\)	\(e\left(\frac{1094}{1155}\right)\)	\(e\left(\frac{601}{2310}\right)\)	\(e\left(\frac{162}{385}\right)\)	\(e\left(\frac{113}{154}\right)\)	\(e\left(\frac{1759}{2310}\right)\)	\(e\left(\frac{1033}{1155}\right)\)	\(e\left(\frac{116}{385}\right)\)	\(e\left(\frac{47}{110}\right)\)	\(e\left(\frac{479}{2310}\right)\)
\(\chi_{373527}(52,\cdot)\)	373527.rv	16170	yes	\(1\)	\(1\)	\(e\left(\frac{3727}{5390}\right)\)	\(e\left(\frac{1032}{2695}\right)\)	\(e\left(\frac{139}{16170}\right)\)	\(e\left(\frac{401}{5390}\right)\)	\(e\left(\frac{1132}{1617}\right)\)	\(e\left(\frac{2458}{8085}\right)\)	\(e\left(\frac{2064}{2695}\right)\)	\(e\left(\frac{887}{8085}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{6331}{16170}\right)\)
\(\chi_{373527}(53,\cdot)\)	373527.ru	16170	no	\(-1\)	\(1\)	\(e\left(\frac{1007}{16170}\right)\)	\(e\left(\frac{1007}{8085}\right)\)	\(e\left(\frac{12863}{16170}\right)\)	\(e\left(\frac{1007}{5390}\right)\)	\(e\left(\frac{1387}{1617}\right)\)	\(e\left(\frac{57}{2695}\right)\)	\(e\left(\frac{2014}{8085}\right)\)	\(e\left(\frac{9193}{16170}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{4959}{5390}\right)\)
\(\chi_{373527}(58,\cdot)\)	373527.rg	8085	yes	\(1\)	\(1\)	\(e\left(\frac{2586}{2695}\right)\)	\(e\left(\frac{2477}{2695}\right)\)	\(e\left(\frac{3247}{8085}\right)\)	\(e\left(\frac{2368}{2695}\right)\)	\(e\left(\frac{584}{1617}\right)\)	\(e\left(\frac{2228}{8085}\right)\)	\(e\left(\frac{2259}{2695}\right)\)	\(e\left(\frac{7297}{8085}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{2593}{8085}\right)\)
\(\chi_{373527}(59,\cdot)\)	373527.sa	16170	yes	\(1\)	\(1\)	\(e\left(\frac{11359}{16170}\right)\)	\(e\left(\frac{3274}{8085}\right)\)	\(e\left(\frac{2631}{2695}\right)\)	\(e\left(\frac{579}{5390}\right)\)	\(e\left(\frac{2195}{3234}\right)\)	\(e\left(\frac{10519}{16170}\right)\)	\(e\left(\frac{6548}{8085}\right)\)	\(e\left(\frac{6953}{8085}\right)\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{3082}{8085}\right)\)
\(\chi_{373527}(61,\cdot)\)	373527.rq	16170	yes	\(1\)	\(1\)	\(e\left(\frac{3263}{16170}\right)\)	\(e\left(\frac{3263}{8085}\right)\)	\(e\left(\frac{3249}{5390}\right)\)	\(e\left(\frac{3263}{5390}\right)\)	\(e\left(\frac{1301}{1617}\right)\)	\(e\left(\frac{2944}{8085}\right)\)	\(e\left(\frac{6526}{8085}\right)\)	\(e\left(\frac{7426}{8085}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{103}{16170}\right)\)
\(\chi_{373527}(62,\cdot)\)	373527.re	5390	no	\(-1\)	\(1\)	\(e\left(\frac{179}{2695}\right)\)	\(e\left(\frac{358}{2695}\right)\)	\(e\left(\frac{761}{2695}\right)\)	\(e\left(\frac{537}{2695}\right)\)	\(e\left(\frac{188}{539}\right)\)	\(e\left(\frac{2349}{2695}\right)\)	\(e\left(\frac{716}{2695}\right)\)	\(e\left(\frac{327}{5390}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{1119}{2695}\right)\)

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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.