LMFDB - Group of Dirichlet characters of modulus 586971

Show commands: PariGP / SageMath

sage: H = DirichletGroup(586971)

pari: g = idealstar(,586971,2)

Character group

sage: G.order() pari: g.no
Order	=	304920
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{25410}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{586971}(130439,\cdot)$, $\chi_{586971}(179686,\cdot)$, $\chi_{586971}(73207,\cdot)$

First 32 of 304920 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$13$	$16$	$17$	$19$	$20$
$\chi_{586971}(1,\cdot)$	586971.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{586971}(2,\cdot)$	586971.sk	25410	yes	$1$	$1$	$e\left(\frac{3338}{12705}\right)$	$e\left(\frac{6676}{12705}\right)$	$e\left(\frac{7943}{8470}\right)$	$e\left(\frac{3338}{4235}\right)$	$e\left(\frac{1019}{5082}\right)$	$e\left(\frac{19171}{25410}\right)$	$e\left(\frac{647}{12705}\right)$	$e\left(\frac{1367}{12705}\right)$	$e\left(\frac{2009}{3630}\right)$	$e\left(\frac{11771}{25410}\right)$
$\chi_{586971}(4,\cdot)$	586971.rg	12705	yes	$1$	$1$	$e\left(\frac{6676}{12705}\right)$	$e\left(\frac{647}{12705}\right)$	$e\left(\frac{3708}{4235}\right)$	$e\left(\frac{2441}{4235}\right)$	$e\left(\frac{1019}{2541}\right)$	$e\left(\frac{6466}{12705}\right)$	$e\left(\frac{1294}{12705}\right)$	$e\left(\frac{2734}{12705}\right)$	$e\left(\frac{194}{1815}\right)$	$e\left(\frac{11771}{12705}\right)$
$\chi_{586971}(5,\cdot)$	586971.rx	25410	yes	$1$	$1$	$e\left(\frac{7943}{8470}\right)$	$e\left(\frac{3708}{4235}\right)$	$e\left(\frac{2168}{12705}\right)$	$e\left(\frac{6889}{8470}\right)$	$e\left(\frac{551}{5082}\right)$	$e\left(\frac{2129}{25410}\right)$	$e\left(\frac{3181}{4235}\right)$	$e\left(\frac{11948}{12705}\right)$	$e\left(\frac{1211}{3630}\right)$	$e\left(\frac{587}{12705}\right)$
$\chi_{586971}(8,\cdot)$	586971.rd	8470	no	$1$	$1$	$e\left(\frac{3338}{4235}\right)$	$e\left(\frac{2441}{4235}\right)$	$e\left(\frac{6889}{8470}\right)$	$e\left(\frac{1544}{4235}\right)$	$e\left(\frac{1019}{1694}\right)$	$e\left(\frac{2231}{8470}\right)$	$e\left(\frac{647}{4235}\right)$	$e\left(\frac{1367}{4235}\right)$	$e\left(\frac{799}{1210}\right)$	$e\left(\frac{3301}{8470}\right)$
$\chi_{586971}(10,\cdot)$	586971.qd	5082	no	$1$	$1$	$e\left(\frac{1019}{5082}\right)$	$e\left(\frac{1019}{2541}\right)$	$e\left(\frac{551}{5082}\right)$	$e\left(\frac{1019}{1694}\right)$	$e\left(\frac{785}{2541}\right)$	$e\left(\frac{710}{847}\right)$	$e\left(\frac{2038}{2541}\right)$	$e\left(\frac{122}{2541}\right)$	$e\left(\frac{322}{363}\right)$	$e\left(\frac{863}{1694}\right)$
$\chi_{586971}(13,\cdot)$	586971.sg	25410	yes	$1$	$1$	$e\left(\frac{19171}{25410}\right)$	$e\left(\frac{6466}{12705}\right)$	$e\left(\frac{2129}{25410}\right)$	$e\left(\frac{2231}{8470}\right)$	$e\left(\frac{710}{847}\right)$	$e\left(\frac{8413}{12705}\right)$	$e\left(\frac{227}{12705}\right)$	$e\left(\frac{1949}{4235}\right)$	$e\left(\frac{314}{605}\right)$	$e\left(\frac{15061}{25410}\right)$
$\chi_{586971}(16,\cdot)$	586971.rg	12705	yes	$1$	$1$	$e\left(\frac{647}{12705}\right)$	$e\left(\frac{1294}{12705}\right)$	$e\left(\frac{3181}{4235}\right)$	$e\left(\frac{647}{4235}\right)$	$e\left(\frac{2038}{2541}\right)$	$e\left(\frac{227}{12705}\right)$	$e\left(\frac{2588}{12705}\right)$	$e\left(\frac{5468}{12705}\right)$	$e\left(\frac{388}{1815}\right)$	$e\left(\frac{10837}{12705}\right)$
$\chi_{586971}(17,\cdot)$	586971.sd	25410	no	$-1$	$1$	$e\left(\frac{1367}{12705}\right)$	$e\left(\frac{2734}{12705}\right)$	$e\left(\frac{11948}{12705}\right)$	$e\left(\frac{1367}{4235}\right)$	$e\left(\frac{122}{2541}\right)$	$e\left(\frac{1949}{4235}\right)$	$e\left(\frac{5468}{12705}\right)$	$e\left(\frac{6971}{25410}\right)$	$e\left(\frac{1508}{1815}\right)$	$e\left(\frac{659}{4235}\right)$
$\chi_{586971}(19,\cdot)$	586971.oz	3630	no	$1$	$1$	$e\left(\frac{2009}{3630}\right)$	$e\left(\frac{194}{1815}\right)$	$e\left(\frac{1211}{3630}\right)$	$e\left(\frac{799}{1210}\right)$	$e\left(\frac{322}{363}\right)$	$e\left(\frac{314}{605}\right)$	$e\left(\frac{388}{1815}\right)$	$e\left(\frac{1508}{1815}\right)$	$e\left(\frac{1231}{1815}\right)$	$e\left(\frac{533}{1210}\right)$
$\chi_{586971}(20,\cdot)$	586971.rp	25410	yes	$1$	$1$	$e\left(\frac{11771}{25410}\right)$	$e\left(\frac{11771}{12705}\right)$	$e\left(\frac{587}{12705}\right)$	$e\left(\frac{3301}{8470}\right)$	$e\left(\frac{863}{1694}\right)$	$e\left(\frac{15061}{25410}\right)$	$e\left(\frac{10837}{12705}\right)$	$e\left(\frac{659}{4235}\right)$	$e\left(\frac{533}{1210}\right)$	$e\left(\frac{12358}{12705}\right)$
$\chi_{586971}(23,\cdot)$	586971.qh	5082	yes	$-1$	$1$	$e\left(\frac{1011}{1694}\right)$	$e\left(\frac{164}{847}\right)$	$e\left(\frac{2561}{5082}\right)$	$e\left(\frac{1339}{1694}\right)$	$e\left(\frac{256}{2541}\right)$	$e\left(\frac{932}{2541}\right)$	$e\left(\frac{328}{847}\right)$	$e\left(\frac{1151}{5082}\right)$	$e\left(\frac{302}{363}\right)$	$e\left(\frac{3545}{5082}\right)$
$\chi_{586971}(25,\cdot)$	586971.rh	12705	yes	$1$	$1$	$e\left(\frac{3708}{4235}\right)$	$e\left(\frac{3181}{4235}\right)$	$e\left(\frac{4336}{12705}\right)$	$e\left(\frac{2654}{4235}\right)$	$e\left(\frac{551}{2541}\right)$	$e\left(\frac{2129}{12705}\right)$	$e\left(\frac{2127}{4235}\right)$	$e\left(\frac{11191}{12705}\right)$	$e\left(\frac{1211}{1815}\right)$	$e\left(\frac{1174}{12705}\right)$
$\chi_{586971}(26,\cdot)$	586971.rq	25410	no	$1$	$1$	$e\left(\frac{437}{25410}\right)$	$e\left(\frac{437}{12705}\right)$	$e\left(\frac{274}{12705}\right)$	$e\left(\frac{437}{8470}\right)$	$e\left(\frac{197}{5082}\right)$	$e\left(\frac{3529}{8470}\right)$	$e\left(\frac{874}{12705}\right)$	$e\left(\frac{7214}{12705}\right)$	$e\left(\frac{263}{3630}\right)$	$e\left(\frac{237}{4235}\right)$
$\chi_{586971}(29,\cdot)$	586971.rr	25410	yes	$1$	$1$	$e\left(\frac{7576}{12705}\right)$	$e\left(\frac{2447}{12705}\right)$	$e\left(\frac{733}{25410}\right)$	$e\left(\frac{3341}{4235}\right)$	$e\left(\frac{1059}{1694}\right)$	$e\left(\frac{22747}{25410}\right)$	$e\left(\frac{4894}{12705}\right)$	$e\left(\frac{3438}{4235}\right)$	$e\left(\frac{861}{1210}\right)$	$e\left(\frac{5627}{25410}\right)$
$\chi_{586971}(31,\cdot)$	586971.ou	3630	no	$-1$	$1$	$e\left(\frac{844}{1815}\right)$	$e\left(\frac{1688}{1815}\right)$	$e\left(\frac{479}{1210}\right)$	$e\left(\frac{239}{605}\right)$	$e\left(\frac{625}{726}\right)$	$e\left(\frac{3563}{3630}\right)$	$e\left(\frac{1561}{1815}\right)$	$e\left(\frac{377}{3630}\right)$	$e\left(\frac{1669}{3630}\right)$	$e\left(\frac{1183}{3630}\right)$
$\chi_{586971}(32,\cdot)$	586971.qa	5082	yes	$1$	$1$	$e\left(\frac{797}{2541}\right)$	$e\left(\frac{1594}{2541}\right)$	$e\left(\frac{1167}{1694}\right)$	$e\left(\frac{797}{847}\right)$	$e\left(\frac{13}{5082}\right)$	$e\left(\frac{3925}{5082}\right)$	$e\left(\frac{647}{2541}\right)$	$e\left(\frac{1367}{2541}\right)$	$e\left(\frac{557}{726}\right)$	$e\left(\frac{1607}{5082}\right)$
$\chi_{586971}(34,\cdot)$	586971.qt	5082	yes	$-1$	$1$	$e\left(\frac{941}{2541}\right)$	$e\left(\frac{1882}{2541}\right)$	$e\left(\frac{4463}{5082}\right)$	$e\left(\frac{94}{847}\right)$	$e\left(\frac{421}{1694}\right)$	$e\left(\frac{1091}{5082}\right)$	$e\left(\frac{1223}{2541}\right)$	$e\left(\frac{647}{1694}\right)$	$e\left(\frac{93}{242}\right)$	$e\left(\frac{3145}{5082}\right)$
$\chi_{586971}(37,\cdot)$	586971.rj	12705	no	$1$	$1$	$e\left(\frac{9571}{12705}\right)$	$e\left(\frac{6437}{12705}\right)$	$e\left(\frac{9589}{12705}\right)$	$e\left(\frac{1101}{4235}\right)$	$e\left(\frac{1291}{2541}\right)$	$e\left(\frac{2747}{4235}\right)$	$e\left(\frac{169}{12705}\right)$	$e\left(\frac{1424}{12705}\right)$	$e\left(\frac{664}{1815}\right)$	$e\left(\frac{1107}{4235}\right)$
$\chi_{586971}(38,\cdot)$	586971.rx	25410	yes	$1$	$1$	$e\left(\frac{6913}{8470}\right)$	$e\left(\frac{2678}{4235}\right)$	$e\left(\frac{3448}{12705}\right)$	$e\left(\frac{3799}{8470}\right)$	$e\left(\frac{445}{5082}\right)$	$e\left(\frac{6949}{25410}\right)$	$e\left(\frac{1121}{4235}\right)$	$e\left(\frac{11923}{12705}\right)$	$e\left(\frac{841}{3630}\right)$	$e\left(\frac{11482}{12705}\right)$
$\chi_{586971}(40,\cdot)$	586971.on	2310	no	$1$	$1$	$e\left(\frac{559}{770}\right)$	$e\left(\frac{174}{385}\right)$	$e\left(\frac{2273}{2310}\right)$	$e\left(\frac{137}{770}\right)$	$e\left(\frac{164}{231}\right)$	$e\left(\frac{401}{1155}\right)$	$e\left(\frac{348}{385}\right)$	$e\left(\frac{304}{1155}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{1007}{2310}\right)$
$\chi_{586971}(41,\cdot)$	586971.sc	25410	yes	$-1$	$1$	$e\left(\frac{6374}{12705}\right)$	$e\left(\frac{43}{12705}\right)$	$e\left(\frac{11821}{12705}\right)$	$e\left(\frac{2139}{4235}\right)$	$e\left(\frac{366}{847}\right)$	$e\left(\frac{109}{12705}\right)$	$e\left(\frac{86}{12705}\right)$	$e\left(\frac{2279}{8470}\right)$	$e\left(\frac{47}{605}\right)$	$e\left(\frac{11864}{12705}\right)$
$\chi_{586971}(43,\cdot)$	586971.qr	5082	yes	$-1$	$1$	$e\left(\frac{2965}{5082}\right)$	$e\left(\frac{424}{2541}\right)$	$e\left(\frac{1861}{2541}\right)$	$e\left(\frac{1271}{1694}\right)$	$e\left(\frac{535}{1694}\right)$	$e\left(\frac{1145}{5082}\right)$	$e\left(\frac{848}{2541}\right)$	$e\left(\frac{1297}{1694}\right)$	$e\left(\frac{63}{242}\right)$	$e\left(\frac{2285}{2541}\right)$
$\chi_{586971}(46,\cdot)$	586971.ro	25410	no	$-1$	$1$	$e\left(\frac{21841}{25410}\right)$	$e\left(\frac{9136}{12705}\right)$	$e\left(\frac{5612}{12705}\right)$	$e\left(\frac{4901}{8470}\right)$	$e\left(\frac{1531}{5082}\right)$	$e\left(\frac{1027}{8470}\right)$	$e\left(\frac{5567}{12705}\right)$	$e\left(\frac{8489}{25410}\right)$	$e\left(\frac{1399}{3630}\right)$	$e\left(\frac{681}{4235}\right)$
$\chi_{586971}(47,\cdot)$	586971.sj	25410	yes	$1$	$1$	$e\left(\frac{24883}{25410}\right)$	$e\left(\frac{12178}{12705}\right)$	$e\left(\frac{1182}{4235}\right)$	$e\left(\frac{7943}{8470}\right)$	$e\left(\frac{1313}{5082}\right)$	$e\left(\frac{20473}{25410}\right)$	$e\left(\frac{11651}{12705}\right)$	$e\left(\frac{6806}{12705}\right)$	$e\left(\frac{3227}{3630}\right)$	$e\left(\frac{3019}{12705}\right)$
$\chi_{586971}(50,\cdot)$	586971.pn	3630	no	$1$	$1$	$e\left(\frac{251}{1815}\right)$	$e\left(\frac{502}{1815}\right)$	$e\left(\frac{1013}{3630}\right)$	$e\left(\frac{251}{605}\right)$	$e\left(\frac{101}{242}\right)$	$e\left(\frac{3347}{3630}\right)$	$e\left(\frac{1004}{1815}\right)$	$e\left(\frac{598}{605}\right)$	$e\left(\frac{267}{1210}\right)$	$e\left(\frac{2017}{3630}\right)$
$\chi_{586971}(52,\cdot)$	586971.rz	25410	yes	$1$	$1$	$e\left(\frac{2371}{8470}\right)$	$e\left(\frac{2371}{4235}\right)$	$e\left(\frac{24377}{25410}\right)$	$e\left(\frac{7113}{8470}\right)$	$e\left(\frac{608}{2541}\right)$	$e\left(\frac{2174}{12705}\right)$	$e\left(\frac{507}{4235}\right)$	$e\left(\frac{8581}{12705}\right)$	$e\left(\frac{1136}{1815}\right)$	$e\left(\frac{13193}{25410}\right)$
$\chi_{586971}(53,\cdot)$	586971.sf	25410	no	$-1$	$1$	$e\left(\frac{10531}{25410}\right)$	$e\left(\frac{10531}{12705}\right)$	$e\left(\frac{15619}{25410}\right)$	$e\left(\frac{2061}{8470}\right)$	$e\left(\frac{74}{2541}\right)$	$e\left(\frac{1446}{4235}\right)$	$e\left(\frac{8357}{12705}\right)$	$e\left(\frac{14309}{25410}\right)$	$e\left(\frac{272}{1815}\right)$	$e\left(\frac{3757}{8470}\right)$
$\chi_{586971}(58,\cdot)$	586971.rh	12705	yes	$1$	$1$	$e\left(\frac{3638}{4235}\right)$	$e\left(\frac{3041}{4235}\right)$	$e\left(\frac{12281}{12705}\right)$	$e\left(\frac{2444}{4235}\right)$	$e\left(\frac{2098}{2541}\right)$	$e\left(\frac{8254}{12705}\right)$	$e\left(\frac{1847}{4235}\right)$	$e\left(\frac{11681}{12705}\right)$	$e\left(\frac{481}{1815}\right)$	$e\left(\frac{8699}{12705}\right)$
$\chi_{586971}(59,\cdot)$	586971.sj	25410	yes	$1$	$1$	$e\left(\frac{16127}{25410}\right)$	$e\left(\frac{3422}{12705}\right)$	$e\left(\frac{3503}{4235}\right)$	$e\left(\frac{7657}{8470}\right)$	$e\left(\frac{2347}{5082}\right)$	$e\left(\frac{2477}{25410}\right)$	$e\left(\frac{6844}{12705}\right)$	$e\left(\frac{1009}{12705}\right)$	$e\left(\frac{2083}{3630}\right)$	$e\left(\frac{1226}{12705}\right)$
$\chi_{586971}(61,\cdot)$	586971.rm	25410	yes	$1$	$1$	$e\left(\frac{7459}{25410}\right)$	$e\left(\frac{7459}{12705}\right)$	$e\left(\frac{2727}{8470}\right)$	$e\left(\frac{7459}{8470}\right)$	$e\left(\frac{1564}{2541}\right)$	$e\left(\frac{7877}{12705}\right)$	$e\left(\frac{2213}{12705}\right)$	$e\left(\frac{6443}{12705}\right)$	$e\left(\frac{343}{1815}\right)$	$e\left(\frac{23099}{25410}\right)$
$\chi_{586971}(62,\cdot)$	586971.rb	8470	no	$-1$	$1$	$e\left(\frac{3082}{4235}\right)$	$e\left(\frac{1929}{4235}\right)$	$e\left(\frac{1413}{4235}\right)$	$e\left(\frac{776}{4235}\right)$	$e\left(\frac{52}{847}\right)$	$e\left(\frac{3117}{4235}\right)$	$e\left(\frac{3858}{4235}\right)$	$e\left(\frac{1791}{8470}\right)$	$e\left(\frac{8}{605}\right)$	$e\left(\frac{3342}{4235}\right)$

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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	$586971$
Structure	\(C_{2}\times C_{6}\times C_{25410}\)
Order	$304920$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(13\)	\(16\)	\(17\)	\(19\)	\(20\)
\(\chi_{586971}(1,\cdot)\)	586971.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{586971}(2,\cdot)\)	586971.sk	25410	yes	\(1\)	\(1\)	\(e\left(\frac{3338}{12705}\right)\)	\(e\left(\frac{6676}{12705}\right)\)	\(e\left(\frac{7943}{8470}\right)\)	\(e\left(\frac{3338}{4235}\right)\)	\(e\left(\frac{1019}{5082}\right)\)	\(e\left(\frac{19171}{25410}\right)\)	\(e\left(\frac{647}{12705}\right)\)	\(e\left(\frac{1367}{12705}\right)\)	\(e\left(\frac{2009}{3630}\right)\)	\(e\left(\frac{11771}{25410}\right)\)
\(\chi_{586971}(4,\cdot)\)	586971.rg	12705	yes	\(1\)	\(1\)	\(e\left(\frac{6676}{12705}\right)\)	\(e\left(\frac{647}{12705}\right)\)	\(e\left(\frac{3708}{4235}\right)\)	\(e\left(\frac{2441}{4235}\right)\)	\(e\left(\frac{1019}{2541}\right)\)	\(e\left(\frac{6466}{12705}\right)\)	\(e\left(\frac{1294}{12705}\right)\)	\(e\left(\frac{2734}{12705}\right)\)	\(e\left(\frac{194}{1815}\right)\)	\(e\left(\frac{11771}{12705}\right)\)
\(\chi_{586971}(5,\cdot)\)	586971.rx	25410	yes	\(1\)	\(1\)	\(e\left(\frac{7943}{8470}\right)\)	\(e\left(\frac{3708}{4235}\right)\)	\(e\left(\frac{2168}{12705}\right)\)	\(e\left(\frac{6889}{8470}\right)\)	\(e\left(\frac{551}{5082}\right)\)	\(e\left(\frac{2129}{25410}\right)\)	\(e\left(\frac{3181}{4235}\right)\)	\(e\left(\frac{11948}{12705}\right)\)	\(e\left(\frac{1211}{3630}\right)\)	\(e\left(\frac{587}{12705}\right)\)
\(\chi_{586971}(8,\cdot)\)	586971.rd	8470	no	\(1\)	\(1\)	\(e\left(\frac{3338}{4235}\right)\)	\(e\left(\frac{2441}{4235}\right)\)	\(e\left(\frac{6889}{8470}\right)\)	\(e\left(\frac{1544}{4235}\right)\)	\(e\left(\frac{1019}{1694}\right)\)	\(e\left(\frac{2231}{8470}\right)\)	\(e\left(\frac{647}{4235}\right)\)	\(e\left(\frac{1367}{4235}\right)\)	\(e\left(\frac{799}{1210}\right)\)	\(e\left(\frac{3301}{8470}\right)\)
\(\chi_{586971}(10,\cdot)\)	586971.qd	5082	no	\(1\)	\(1\)	\(e\left(\frac{1019}{5082}\right)\)	\(e\left(\frac{1019}{2541}\right)\)	\(e\left(\frac{551}{5082}\right)\)	\(e\left(\frac{1019}{1694}\right)\)	\(e\left(\frac{785}{2541}\right)\)	\(e\left(\frac{710}{847}\right)\)	\(e\left(\frac{2038}{2541}\right)\)	\(e\left(\frac{122}{2541}\right)\)	\(e\left(\frac{322}{363}\right)\)	\(e\left(\frac{863}{1694}\right)\)
\(\chi_{586971}(13,\cdot)\)	586971.sg	25410	yes	\(1\)	\(1\)	\(e\left(\frac{19171}{25410}\right)\)	\(e\left(\frac{6466}{12705}\right)\)	\(e\left(\frac{2129}{25410}\right)\)	\(e\left(\frac{2231}{8470}\right)\)	\(e\left(\frac{710}{847}\right)\)	\(e\left(\frac{8413}{12705}\right)\)	\(e\left(\frac{227}{12705}\right)\)	\(e\left(\frac{1949}{4235}\right)\)	\(e\left(\frac{314}{605}\right)\)	\(e\left(\frac{15061}{25410}\right)\)
\(\chi_{586971}(16,\cdot)\)	586971.rg	12705	yes	\(1\)	\(1\)	\(e\left(\frac{647}{12705}\right)\)	\(e\left(\frac{1294}{12705}\right)\)	\(e\left(\frac{3181}{4235}\right)\)	\(e\left(\frac{647}{4235}\right)\)	\(e\left(\frac{2038}{2541}\right)\)	\(e\left(\frac{227}{12705}\right)\)	\(e\left(\frac{2588}{12705}\right)\)	\(e\left(\frac{5468}{12705}\right)\)	\(e\left(\frac{388}{1815}\right)\)	\(e\left(\frac{10837}{12705}\right)\)
\(\chi_{586971}(17,\cdot)\)	586971.sd	25410	no	\(-1\)	\(1\)	\(e\left(\frac{1367}{12705}\right)\)	\(e\left(\frac{2734}{12705}\right)\)	\(e\left(\frac{11948}{12705}\right)\)	\(e\left(\frac{1367}{4235}\right)\)	\(e\left(\frac{122}{2541}\right)\)	\(e\left(\frac{1949}{4235}\right)\)	\(e\left(\frac{5468}{12705}\right)\)	\(e\left(\frac{6971}{25410}\right)\)	\(e\left(\frac{1508}{1815}\right)\)	\(e\left(\frac{659}{4235}\right)\)
\(\chi_{586971}(19,\cdot)\)	586971.oz	3630	no	\(1\)	\(1\)	\(e\left(\frac{2009}{3630}\right)\)	\(e\left(\frac{194}{1815}\right)\)	\(e\left(\frac{1211}{3630}\right)\)	\(e\left(\frac{799}{1210}\right)\)	\(e\left(\frac{322}{363}\right)\)	\(e\left(\frac{314}{605}\right)\)	\(e\left(\frac{388}{1815}\right)\)	\(e\left(\frac{1508}{1815}\right)\)	\(e\left(\frac{1231}{1815}\right)\)	\(e\left(\frac{533}{1210}\right)\)
\(\chi_{586971}(20,\cdot)\)	586971.rp	25410	yes	\(1\)	\(1\)	\(e\left(\frac{11771}{25410}\right)\)	\(e\left(\frac{11771}{12705}\right)\)	\(e\left(\frac{587}{12705}\right)\)	\(e\left(\frac{3301}{8470}\right)\)	\(e\left(\frac{863}{1694}\right)\)	\(e\left(\frac{15061}{25410}\right)\)	\(e\left(\frac{10837}{12705}\right)\)	\(e\left(\frac{659}{4235}\right)\)	\(e\left(\frac{533}{1210}\right)\)	\(e\left(\frac{12358}{12705}\right)\)
\(\chi_{586971}(23,\cdot)\)	586971.qh	5082	yes	\(-1\)	\(1\)	\(e\left(\frac{1011}{1694}\right)\)	\(e\left(\frac{164}{847}\right)\)	\(e\left(\frac{2561}{5082}\right)\)	\(e\left(\frac{1339}{1694}\right)\)	\(e\left(\frac{256}{2541}\right)\)	\(e\left(\frac{932}{2541}\right)\)	\(e\left(\frac{328}{847}\right)\)	\(e\left(\frac{1151}{5082}\right)\)	\(e\left(\frac{302}{363}\right)\)	\(e\left(\frac{3545}{5082}\right)\)
\(\chi_{586971}(25,\cdot)\)	586971.rh	12705	yes	\(1\)	\(1\)	\(e\left(\frac{3708}{4235}\right)\)	\(e\left(\frac{3181}{4235}\right)\)	\(e\left(\frac{4336}{12705}\right)\)	\(e\left(\frac{2654}{4235}\right)\)	\(e\left(\frac{551}{2541}\right)\)	\(e\left(\frac{2129}{12705}\right)\)	\(e\left(\frac{2127}{4235}\right)\)	\(e\left(\frac{11191}{12705}\right)\)	\(e\left(\frac{1211}{1815}\right)\)	\(e\left(\frac{1174}{12705}\right)\)
\(\chi_{586971}(26,\cdot)\)	586971.rq	25410	no	\(1\)	\(1\)	\(e\left(\frac{437}{25410}\right)\)	\(e\left(\frac{437}{12705}\right)\)	\(e\left(\frac{274}{12705}\right)\)	\(e\left(\frac{437}{8470}\right)\)	\(e\left(\frac{197}{5082}\right)\)	\(e\left(\frac{3529}{8470}\right)\)	\(e\left(\frac{874}{12705}\right)\)	\(e\left(\frac{7214}{12705}\right)\)	\(e\left(\frac{263}{3630}\right)\)	\(e\left(\frac{237}{4235}\right)\)
\(\chi_{586971}(29,\cdot)\)	586971.rr	25410	yes	\(1\)	\(1\)	\(e\left(\frac{7576}{12705}\right)\)	\(e\left(\frac{2447}{12705}\right)\)	\(e\left(\frac{733}{25410}\right)\)	\(e\left(\frac{3341}{4235}\right)\)	\(e\left(\frac{1059}{1694}\right)\)	\(e\left(\frac{22747}{25410}\right)\)	\(e\left(\frac{4894}{12705}\right)\)	\(e\left(\frac{3438}{4235}\right)\)	\(e\left(\frac{861}{1210}\right)\)	\(e\left(\frac{5627}{25410}\right)\)
\(\chi_{586971}(31,\cdot)\)	586971.ou	3630	no	\(-1\)	\(1\)	\(e\left(\frac{844}{1815}\right)\)	\(e\left(\frac{1688}{1815}\right)\)	\(e\left(\frac{479}{1210}\right)\)	\(e\left(\frac{239}{605}\right)\)	\(e\left(\frac{625}{726}\right)\)	\(e\left(\frac{3563}{3630}\right)\)	\(e\left(\frac{1561}{1815}\right)\)	\(e\left(\frac{377}{3630}\right)\)	\(e\left(\frac{1669}{3630}\right)\)	\(e\left(\frac{1183}{3630}\right)\)
\(\chi_{586971}(32,\cdot)\)	586971.qa	5082	yes	\(1\)	\(1\)	\(e\left(\frac{797}{2541}\right)\)	\(e\left(\frac{1594}{2541}\right)\)	\(e\left(\frac{1167}{1694}\right)\)	\(e\left(\frac{797}{847}\right)\)	\(e\left(\frac{13}{5082}\right)\)	\(e\left(\frac{3925}{5082}\right)\)	\(e\left(\frac{647}{2541}\right)\)	\(e\left(\frac{1367}{2541}\right)\)	\(e\left(\frac{557}{726}\right)\)	\(e\left(\frac{1607}{5082}\right)\)
\(\chi_{586971}(34,\cdot)\)	586971.qt	5082	yes	\(-1\)	\(1\)	\(e\left(\frac{941}{2541}\right)\)	\(e\left(\frac{1882}{2541}\right)\)	\(e\left(\frac{4463}{5082}\right)\)	\(e\left(\frac{94}{847}\right)\)	\(e\left(\frac{421}{1694}\right)\)	\(e\left(\frac{1091}{5082}\right)\)	\(e\left(\frac{1223}{2541}\right)\)	\(e\left(\frac{647}{1694}\right)\)	\(e\left(\frac{93}{242}\right)\)	\(e\left(\frac{3145}{5082}\right)\)
\(\chi_{586971}(37,\cdot)\)	586971.rj	12705	no	\(1\)	\(1\)	\(e\left(\frac{9571}{12705}\right)\)	\(e\left(\frac{6437}{12705}\right)\)	\(e\left(\frac{9589}{12705}\right)\)	\(e\left(\frac{1101}{4235}\right)\)	\(e\left(\frac{1291}{2541}\right)\)	\(e\left(\frac{2747}{4235}\right)\)	\(e\left(\frac{169}{12705}\right)\)	\(e\left(\frac{1424}{12705}\right)\)	\(e\left(\frac{664}{1815}\right)\)	\(e\left(\frac{1107}{4235}\right)\)
\(\chi_{586971}(38,\cdot)\)	586971.rx	25410	yes	\(1\)	\(1\)	\(e\left(\frac{6913}{8470}\right)\)	\(e\left(\frac{2678}{4235}\right)\)	\(e\left(\frac{3448}{12705}\right)\)	\(e\left(\frac{3799}{8470}\right)\)	\(e\left(\frac{445}{5082}\right)\)	\(e\left(\frac{6949}{25410}\right)\)	\(e\left(\frac{1121}{4235}\right)\)	\(e\left(\frac{11923}{12705}\right)\)	\(e\left(\frac{841}{3630}\right)\)	\(e\left(\frac{11482}{12705}\right)\)
\(\chi_{586971}(40,\cdot)\)	586971.on	2310	no	\(1\)	\(1\)	\(e\left(\frac{559}{770}\right)\)	\(e\left(\frac{174}{385}\right)\)	\(e\left(\frac{2273}{2310}\right)\)	\(e\left(\frac{137}{770}\right)\)	\(e\left(\frac{164}{231}\right)\)	\(e\left(\frac{401}{1155}\right)\)	\(e\left(\frac{348}{385}\right)\)	\(e\left(\frac{304}{1155}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{1007}{2310}\right)\)
\(\chi_{586971}(41,\cdot)\)	586971.sc	25410	yes	\(-1\)	\(1\)	\(e\left(\frac{6374}{12705}\right)\)	\(e\left(\frac{43}{12705}\right)\)	\(e\left(\frac{11821}{12705}\right)\)	\(e\left(\frac{2139}{4235}\right)\)	\(e\left(\frac{366}{847}\right)\)	\(e\left(\frac{109}{12705}\right)\)	\(e\left(\frac{86}{12705}\right)\)	\(e\left(\frac{2279}{8470}\right)\)	\(e\left(\frac{47}{605}\right)\)	\(e\left(\frac{11864}{12705}\right)\)
\(\chi_{586971}(43,\cdot)\)	586971.qr	5082	yes	\(-1\)	\(1\)	\(e\left(\frac{2965}{5082}\right)\)	\(e\left(\frac{424}{2541}\right)\)	\(e\left(\frac{1861}{2541}\right)\)	\(e\left(\frac{1271}{1694}\right)\)	\(e\left(\frac{535}{1694}\right)\)	\(e\left(\frac{1145}{5082}\right)\)	\(e\left(\frac{848}{2541}\right)\)	\(e\left(\frac{1297}{1694}\right)\)	\(e\left(\frac{63}{242}\right)\)	\(e\left(\frac{2285}{2541}\right)\)
\(\chi_{586971}(46,\cdot)\)	586971.ro	25410	no	\(-1\)	\(1\)	\(e\left(\frac{21841}{25410}\right)\)	\(e\left(\frac{9136}{12705}\right)\)	\(e\left(\frac{5612}{12705}\right)\)	\(e\left(\frac{4901}{8470}\right)\)	\(e\left(\frac{1531}{5082}\right)\)	\(e\left(\frac{1027}{8470}\right)\)	\(e\left(\frac{5567}{12705}\right)\)	\(e\left(\frac{8489}{25410}\right)\)	\(e\left(\frac{1399}{3630}\right)\)	\(e\left(\frac{681}{4235}\right)\)
\(\chi_{586971}(47,\cdot)\)	586971.sj	25410	yes	\(1\)	\(1\)	\(e\left(\frac{24883}{25410}\right)\)	\(e\left(\frac{12178}{12705}\right)\)	\(e\left(\frac{1182}{4235}\right)\)	\(e\left(\frac{7943}{8470}\right)\)	\(e\left(\frac{1313}{5082}\right)\)	\(e\left(\frac{20473}{25410}\right)\)	\(e\left(\frac{11651}{12705}\right)\)	\(e\left(\frac{6806}{12705}\right)\)	\(e\left(\frac{3227}{3630}\right)\)	\(e\left(\frac{3019}{12705}\right)\)
\(\chi_{586971}(50,\cdot)\)	586971.pn	3630	no	\(1\)	\(1\)	\(e\left(\frac{251}{1815}\right)\)	\(e\left(\frac{502}{1815}\right)\)	\(e\left(\frac{1013}{3630}\right)\)	\(e\left(\frac{251}{605}\right)\)	\(e\left(\frac{101}{242}\right)\)	\(e\left(\frac{3347}{3630}\right)\)	\(e\left(\frac{1004}{1815}\right)\)	\(e\left(\frac{598}{605}\right)\)	\(e\left(\frac{267}{1210}\right)\)	\(e\left(\frac{2017}{3630}\right)\)
\(\chi_{586971}(52,\cdot)\)	586971.rz	25410	yes	\(1\)	\(1\)	\(e\left(\frac{2371}{8470}\right)\)	\(e\left(\frac{2371}{4235}\right)\)	\(e\left(\frac{24377}{25410}\right)\)	\(e\left(\frac{7113}{8470}\right)\)	\(e\left(\frac{608}{2541}\right)\)	\(e\left(\frac{2174}{12705}\right)\)	\(e\left(\frac{507}{4235}\right)\)	\(e\left(\frac{8581}{12705}\right)\)	\(e\left(\frac{1136}{1815}\right)\)	\(e\left(\frac{13193}{25410}\right)\)
\(\chi_{586971}(53,\cdot)\)	586971.sf	25410	no	\(-1\)	\(1\)	\(e\left(\frac{10531}{25410}\right)\)	\(e\left(\frac{10531}{12705}\right)\)	\(e\left(\frac{15619}{25410}\right)\)	\(e\left(\frac{2061}{8470}\right)\)	\(e\left(\frac{74}{2541}\right)\)	\(e\left(\frac{1446}{4235}\right)\)	\(e\left(\frac{8357}{12705}\right)\)	\(e\left(\frac{14309}{25410}\right)\)	\(e\left(\frac{272}{1815}\right)\)	\(e\left(\frac{3757}{8470}\right)\)
\(\chi_{586971}(58,\cdot)\)	586971.rh	12705	yes	\(1\)	\(1\)	\(e\left(\frac{3638}{4235}\right)\)	\(e\left(\frac{3041}{4235}\right)\)	\(e\left(\frac{12281}{12705}\right)\)	\(e\left(\frac{2444}{4235}\right)\)	\(e\left(\frac{2098}{2541}\right)\)	\(e\left(\frac{8254}{12705}\right)\)	\(e\left(\frac{1847}{4235}\right)\)	\(e\left(\frac{11681}{12705}\right)\)	\(e\left(\frac{481}{1815}\right)\)	\(e\left(\frac{8699}{12705}\right)\)
\(\chi_{586971}(59,\cdot)\)	586971.sj	25410	yes	\(1\)	\(1\)	\(e\left(\frac{16127}{25410}\right)\)	\(e\left(\frac{3422}{12705}\right)\)	\(e\left(\frac{3503}{4235}\right)\)	\(e\left(\frac{7657}{8470}\right)\)	\(e\left(\frac{2347}{5082}\right)\)	\(e\left(\frac{2477}{25410}\right)\)	\(e\left(\frac{6844}{12705}\right)\)	\(e\left(\frac{1009}{12705}\right)\)	\(e\left(\frac{2083}{3630}\right)\)	\(e\left(\frac{1226}{12705}\right)\)
\(\chi_{586971}(61,\cdot)\)	586971.rm	25410	yes	\(1\)	\(1\)	\(e\left(\frac{7459}{25410}\right)\)	\(e\left(\frac{7459}{12705}\right)\)	\(e\left(\frac{2727}{8470}\right)\)	\(e\left(\frac{7459}{8470}\right)\)	\(e\left(\frac{1564}{2541}\right)\)	\(e\left(\frac{7877}{12705}\right)\)	\(e\left(\frac{2213}{12705}\right)\)	\(e\left(\frac{6443}{12705}\right)\)	\(e\left(\frac{343}{1815}\right)\)	\(e\left(\frac{23099}{25410}\right)\)
\(\chi_{586971}(62,\cdot)\)	586971.rb	8470	no	\(-1\)	\(1\)	\(e\left(\frac{3082}{4235}\right)\)	\(e\left(\frac{1929}{4235}\right)\)	\(e\left(\frac{1413}{4235}\right)\)	\(e\left(\frac{776}{4235}\right)\)	\(e\left(\frac{52}{847}\right)\)	\(e\left(\frac{3117}{4235}\right)\)	\(e\left(\frac{3858}{4235}\right)\)	\(e\left(\frac{1791}{8470}\right)\)	\(e\left(\frac{8}{605}\right)\)	\(e\left(\frac{3342}{4235}\right)\)

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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.