LMFDB - Group of Dirichlet characters of modulus 987696

sage:H = DirichletGroup(987696)

pari:g = idealstar(,987696,2)

Character group

sage:G.order() pari:g.no
Order	=	311904
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{6}\times C_{12996}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{987696}(617311,\cdot)$, $\chi_{987696}(740773,\cdot)$, $\chi_{987696}(438977,\cdot)$, $\chi_{987696}(857377,\cdot)$

First 32 of 311904 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$35$
$\chi_{987696}(1,\cdot)$	987696.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{987696}(5,\cdot)$	987696.vr	12996	yes	$-1$	$1$	$e\left(\frac{7727}{12996}\right)$	$e\left(\frac{2005}{2166}\right)$	$e\left(\frac{667}{1444}\right)$	$e\left(\frac{9643}{12996}\right)$	$e\left(\frac{5749}{6498}\right)$	$e\left(\frac{2515}{3249}\right)$	$e\left(\frac{1229}{6498}\right)$	$e\left(\frac{9997}{12996}\right)$	$e\left(\frac{99}{361}\right)$	$e\left(\frac{6761}{12996}\right)$
$\chi_{987696}(7,\cdot)$	987696.qy	2166	no	$-1$	$1$	$e\left(\frac{2005}{2166}\right)$	$e\left(\frac{907}{2166}\right)$	$e\left(\frac{650}{1083}\right)$	$e\left(\frac{119}{722}\right)$	$e\left(\frac{235}{1083}\right)$	$e\left(\frac{527}{722}\right)$	$e\left(\frac{922}{1083}\right)$	$e\left(\frac{2009}{2166}\right)$	$e\left(\frac{1109}{2166}\right)$	$e\left(\frac{373}{1083}\right)$
$\chi_{987696}(11,\cdot)$	987696.sq	4332	yes	$1$	$1$	$e\left(\frac{667}{1444}\right)$	$e\left(\frac{650}{1083}\right)$	$e\left(\frac{191}{4332}\right)$	$e\left(\frac{617}{4332}\right)$	$e\left(\frac{1927}{2166}\right)$	$e\left(\frac{1753}{2166}\right)$	$e\left(\frac{667}{722}\right)$	$e\left(\frac{341}{1444}\right)$	$e\left(\frac{251}{2166}\right)$	$e\left(\frac{269}{4332}\right)$
$\chi_{987696}(13,\cdot)$	987696.wb	12996	yes	$-1$	$1$	$e\left(\frac{9643}{12996}\right)$	$e\left(\frac{119}{722}\right)$	$e\left(\frac{617}{4332}\right)$	$e\left(\frac{623}{12996}\right)$	$e\left(\frac{1780}{3249}\right)$	$e\left(\frac{1921}{6498}\right)$	$e\left(\frac{3145}{6498}\right)$	$e\left(\frac{5771}{12996}\right)$	$e\left(\frac{17}{2166}\right)$	$e\left(\frac{11785}{12996}\right)$
$\chi_{987696}(17,\cdot)$	987696.tz	6498	no	$-1$	$1$	$e\left(\frac{5749}{6498}\right)$	$e\left(\frac{235}{1083}\right)$	$e\left(\frac{1927}{2166}\right)$	$e\left(\frac{1780}{3249}\right)$	$e\left(\frac{3709}{6498}\right)$	$e\left(\frac{4781}{6498}\right)$	$e\left(\frac{2500}{3249}\right)$	$e\left(\frac{4355}{6498}\right)$	$e\left(\frac{355}{1083}\right)$	$e\left(\frac{661}{6498}\right)$
$\chi_{987696}(23,\cdot)$	987696.tt	6498	no	$1$	$1$	$e\left(\frac{2515}{3249}\right)$	$e\left(\frac{527}{722}\right)$	$e\left(\frac{1753}{2166}\right)$	$e\left(\frac{1921}{6498}\right)$	$e\left(\frac{4781}{6498}\right)$	$e\left(\frac{3248}{3249}\right)$	$e\left(\frac{1781}{3249}\right)$	$e\left(\frac{3179}{3249}\right)$	$e\left(\frac{1313}{2166}\right)$	$e\left(\frac{3275}{6498}\right)$
$\chi_{987696}(25,\cdot)$	987696.ui	6498	no	$1$	$1$	$e\left(\frac{1229}{6498}\right)$	$e\left(\frac{922}{1083}\right)$	$e\left(\frac{667}{722}\right)$	$e\left(\frac{3145}{6498}\right)$	$e\left(\frac{2500}{3249}\right)$	$e\left(\frac{1781}{3249}\right)$	$e\left(\frac{1229}{3249}\right)$	$e\left(\frac{3499}{6498}\right)$	$e\left(\frac{198}{361}\right)$	$e\left(\frac{263}{6498}\right)$
$\chi_{987696}(29,\cdot)$	987696.vs	12996	yes	$1$	$1$	$e\left(\frac{9997}{12996}\right)$	$e\left(\frac{2009}{2166}\right)$	$e\left(\frac{341}{1444}\right)$	$e\left(\frac{5771}{12996}\right)$	$e\left(\frac{4355}{6498}\right)$	$e\left(\frac{3179}{3249}\right)$	$e\left(\frac{3499}{6498}\right)$	$e\left(\frac{5309}{12996}\right)$	$e\left(\frac{433}{722}\right)$	$e\left(\frac{9055}{12996}\right)$
$\chi_{987696}(31,\cdot)$	987696.ro	2166	no	$1$	$1$	$e\left(\frac{99}{361}\right)$	$e\left(\frac{1109}{2166}\right)$	$e\left(\frac{251}{2166}\right)$	$e\left(\frac{17}{2166}\right)$	$e\left(\frac{355}{1083}\right)$	$e\left(\frac{1313}{2166}\right)$	$e\left(\frac{198}{361}\right)$	$e\left(\frac{433}{722}\right)$	$e\left(\frac{35}{1083}\right)$	$e\left(\frac{1703}{2166}\right)$
$\chi_{987696}(35,\cdot)$	987696.vj	12996	no	$1$	$1$	$e\left(\frac{6761}{12996}\right)$	$e\left(\frac{373}{1083}\right)$	$e\left(\frac{269}{4332}\right)$	$e\left(\frac{11785}{12996}\right)$	$e\left(\frac{661}{6498}\right)$	$e\left(\frac{3275}{6498}\right)$	$e\left(\frac{263}{6498}\right)$	$e\left(\frac{9055}{12996}\right)$	$e\left(\frac{1703}{2166}\right)$	$e\left(\frac{11237}{12996}\right)$
$\chi_{987696}(37,\cdot)$	987696.ps	1444	no	$-1$	$1$	$e\left(\frac{857}{1444}\right)$	$e\left(\frac{85}{722}\right)$	$e\left(\frac{697}{1444}\right)$	$e\left(\frac{1333}{1444}\right)$	$e\left(\frac{147}{361}\right)$	$e\left(\frac{141}{722}\right)$	$e\left(\frac{135}{722}\right)$	$e\left(\frac{1329}{1444}\right)$	$e\left(\frac{451}{722}\right)$	$e\left(\frac{1027}{1444}\right)$
$\chi_{987696}(41,\cdot)$	987696.tx	6498	no	$1$	$1$	$e\left(\frac{191}{3249}\right)$	$e\left(\frac{98}{1083}\right)$	$e\left(\frac{158}{361}\right)$	$e\left(\frac{1303}{3249}\right)$	$e\left(\frac{6421}{6498}\right)$	$e\left(\frac{3341}{6498}\right)$	$e\left(\frac{382}{3249}\right)$	$e\left(\frac{5357}{6498}\right)$	$e\left(\frac{685}{722}\right)$	$e\left(\frac{485}{3249}\right)$
$\chi_{987696}(43,\cdot)$	987696.vq	12996	yes	$-1$	$1$	$e\left(\frac{245}{12996}\right)$	$e\left(\frac{351}{361}\right)$	$e\left(\frac{4201}{4332}\right)$	$e\left(\frac{8623}{12996}\right)$	$e\left(\frac{1430}{3249}\right)$	$e\left(\frac{2314}{3249}\right)$	$e\left(\frac{245}{6498}\right)$	$e\left(\frac{7867}{12996}\right)$	$e\left(\frac{1699}{2166}\right)$	$e\left(\frac{12881}{12996}\right)$
$\chi_{987696}(47,\cdot)$	987696.uj	6498	no	$1$	$1$	$e\left(\frac{2555}{6498}\right)$	$e\left(\frac{863}{2166}\right)$	$e\left(\frac{331}{361}\right)$	$e\left(\frac{1256}{3249}\right)$	$e\left(\frac{1943}{6498}\right)$	$e\left(\frac{2468}{3249}\right)$	$e\left(\frac{2555}{3249}\right)$	$e\left(\frac{2209}{6498}\right)$	$e\left(\frac{71}{722}\right)$	$e\left(\frac{2572}{3249}\right)$
$\chi_{987696}(49,\cdot)$	987696.pl	1083	no	$1$	$1$	$e\left(\frac{922}{1083}\right)$	$e\left(\frac{907}{1083}\right)$	$e\left(\frac{217}{1083}\right)$	$e\left(\frac{119}{361}\right)$	$e\left(\frac{470}{1083}\right)$	$e\left(\frac{166}{361}\right)$	$e\left(\frac{761}{1083}\right)$	$e\left(\frac{926}{1083}\right)$	$e\left(\frac{26}{1083}\right)$	$e\left(\frac{746}{1083}\right)$
$\chi_{987696}(53,\cdot)$	987696.vw	12996	no	$1$	$1$	$e\left(\frac{1063}{12996}\right)$	$e\left(\frac{1471}{2166}\right)$	$e\left(\frac{2965}{4332}\right)$	$e\left(\frac{10325}{12996}\right)$	$e\left(\frac{5933}{6498}\right)$	$e\left(\frac{1955}{3249}\right)$	$e\left(\frac{1063}{6498}\right)$	$e\left(\frac{2651}{12996}\right)$	$e\left(\frac{517}{2166}\right)$	$e\left(\frac{9889}{12996}\right)$
$\chi_{987696}(55,\cdot)$	987696.ty	6498	no	$-1$	$1$	$e\left(\frac{367}{6498}\right)$	$e\left(\frac{1139}{2166}\right)$	$e\left(\frac{548}{1083}\right)$	$e\left(\frac{5747}{6498}\right)$	$e\left(\frac{2516}{3249}\right)$	$e\left(\frac{3791}{6498}\right)$	$e\left(\frac{367}{3249}\right)$	$e\left(\frac{35}{6498}\right)$	$e\left(\frac{845}{2166}\right)$	$e\left(\frac{1892}{3249}\right)$
$\chi_{987696}(59,\cdot)$	987696.wd	12996	yes	$-1$	$1$	$e\left(\frac{3215}{12996}\right)$	$e\left(\frac{41}{1083}\right)$	$e\left(\frac{537}{1444}\right)$	$e\left(\frac{6181}{12996}\right)$	$e\left(\frac{1747}{6498}\right)$	$e\left(\frac{149}{6498}\right)$	$e\left(\frac{3215}{6498}\right)$	$e\left(\frac{8947}{12996}\right)$	$e\left(\frac{333}{361}\right)$	$e\left(\frac{3707}{12996}\right)$
$\chi_{987696}(61,\cdot)$	987696.vl	12996	yes	$1$	$1$	$e\left(\frac{679}{12996}\right)$	$e\left(\frac{401}{2166}\right)$	$e\left(\frac{711}{1444}\right)$	$e\left(\frac{9293}{12996}\right)$	$e\left(\frac{1333}{3249}\right)$	$e\left(\frac{2089}{6498}\right)$	$e\left(\frac{679}{6498}\right)$	$e\left(\frac{5465}{12996}\right)$	$e\left(\frac{92}{361}\right)$	$e\left(\frac{3085}{12996}\right)$
$\chi_{987696}(65,\cdot)$	987696.ql	2166	no	$1$	$1$	$e\left(\frac{243}{722}\right)$	$e\left(\frac{98}{1083}\right)$	$e\left(\frac{1309}{2166}\right)$	$e\left(\frac{1711}{2166}\right)$	$e\left(\frac{937}{2166}\right)$	$e\left(\frac{151}{2166}\right)$	$e\left(\frac{243}{361}\right)$	$e\left(\frac{77}{361}\right)$	$e\left(\frac{611}{2166}\right)$	$e\left(\frac{925}{2166}\right)$
$\chi_{987696}(67,\cdot)$	987696.vu	12996	yes	$1$	$1$	$e\left(\frac{3007}{12996}\right)$	$e\left(\frac{253}{361}\right)$	$e\left(\frac{2123}{4332}\right)$	$e\left(\frac{11759}{12996}\right)$	$e\left(\frac{643}{3249}\right)$	$e\left(\frac{1454}{3249}\right)$	$e\left(\frac{3007}{6498}\right)$	$e\left(\frac{995}{12996}\right)$	$e\left(\frac{655}{1083}\right)$	$e\left(\frac{12115}{12996}\right)$
$\chi_{987696}(71,\cdot)$	987696.ud	6498	no	$-1$	$1$	$e\left(\frac{614}{3249}\right)$	$e\left(\frac{1955}{2166}\right)$	$e\left(\frac{2059}{2166}\right)$	$e\left(\frac{1966}{3249}\right)$	$e\left(\frac{3319}{6498}\right)$	$e\left(\frac{2518}{3249}\right)$	$e\left(\frac{1228}{3249}\right)$	$e\left(\frac{2711}{6498}\right)$	$e\left(\frac{313}{1083}\right)$	$e\left(\frac{595}{6498}\right)$
$\chi_{987696}(73,\cdot)$	987696.ub	6498	no	$1$	$1$	$e\left(\frac{3583}{6498}\right)$	$e\left(\frac{235}{1083}\right)$	$e\left(\frac{1927}{2166}\right)$	$e\left(\frac{2477}{6498}\right)$	$e\left(\frac{2396}{3249}\right)$	$e\left(\frac{1849}{3249}\right)$	$e\left(\frac{334}{3249}\right)$	$e\left(\frac{23}{6498}\right)$	$e\left(\frac{355}{1083}\right)$	$e\left(\frac{4993}{6498}\right)$
$\chi_{987696}(77,\cdot)$	987696.si	4332	yes	$-1$	$1$	$e\left(\frac{1679}{4332}\right)$	$e\left(\frac{41}{2166}\right)$	$e\left(\frac{2791}{4332}\right)$	$e\left(\frac{1331}{4332}\right)$	$e\left(\frac{77}{722}\right)$	$e\left(\frac{584}{1083}\right)$	$e\left(\frac{1679}{2166}\right)$	$e\left(\frac{709}{4332}\right)$	$e\left(\frac{680}{1083}\right)$	$e\left(\frac{587}{1444}\right)$
$\chi_{987696}(79,\cdot)$	987696.vf	6498	no	$1$	$1$	$e\left(\frac{2042}{3249}\right)$	$e\left(\frac{151}{722}\right)$	$e\left(\frac{305}{2166}\right)$	$e\left(\frac{5651}{6498}\right)$	$e\left(\frac{1658}{3249}\right)$	$e\left(\frac{581}{6498}\right)$	$e\left(\frac{835}{3249}\right)$	$e\left(\frac{4931}{6498}\right)$	$e\left(\frac{707}{1083}\right)$	$e\left(\frac{5443}{6498}\right)$
$\chi_{987696}(83,\cdot)$	987696.sn	4332	yes	$1$	$1$	$e\left(\frac{3251}{4332}\right)$	$e\left(\frac{14}{1083}\right)$	$e\left(\frac{1457}{4332}\right)$	$e\left(\frac{77}{1444}\right)$	$e\left(\frac{959}{2166}\right)$	$e\left(\frac{351}{722}\right)$	$e\left(\frac{1085}{2166}\right)$	$e\left(\frac{493}{4332}\right)$	$e\left(\frac{1325}{2166}\right)$	$e\left(\frac{3307}{4332}\right)$
$\chi_{987696}(85,\cdot)$	987696.vh	12996	yes	$1$	$1$	$e\left(\frac{6229}{12996}\right)$	$e\left(\frac{103}{722}\right)$	$e\left(\frac{1523}{4332}\right)$	$e\left(\frac{3767}{12996}\right)$	$e\left(\frac{1480}{3249}\right)$	$e\left(\frac{3313}{6498}\right)$	$e\left(\frac{6229}{6498}\right)$	$e\left(\frac{5711}{12996}\right)$	$e\left(\frac{652}{1083}\right)$	$e\left(\frac{8083}{12996}\right)$
$\chi_{987696}(89,\cdot)$	987696.ue	6498	no	$1$	$1$	$e\left(\frac{2227}{3249}\right)$	$e\left(\frac{449}{1083}\right)$	$e\left(\frac{433}{1083}\right)$	$e\left(\frac{728}{3249}\right)$	$e\left(\frac{2561}{6498}\right)$	$e\left(\frac{5365}{6498}\right)$	$e\left(\frac{1205}{3249}\right)$	$e\left(\frac{4081}{6498}\right)$	$e\left(\frac{1057}{2166}\right)$	$e\left(\frac{325}{3249}\right)$
$\chi_{987696}(91,\cdot)$	987696.vt	12996	no	$1$	$1$	$e\left(\frac{8677}{12996}\right)$	$e\left(\frac{632}{1083}\right)$	$e\left(\frac{3217}{4332}\right)$	$e\left(\frac{2765}{12996}\right)$	$e\left(\frac{2485}{3249}\right)$	$e\left(\frac{83}{3249}\right)$	$e\left(\frac{2179}{6498}\right)$	$e\left(\frac{4829}{12996}\right)$	$e\left(\frac{563}{1083}\right)$	$e\left(\frac{3265}{12996}\right)$
$\chi_{987696}(97,\cdot)$	987696.vc	6498	no	$-1$	$1$	$e\left(\frac{2540}{3249}\right)$	$e\left(\frac{241}{361}\right)$	$e\left(\frac{1051}{1083}\right)$	$e\left(\frac{1559}{6498}\right)$	$e\left(\frac{554}{3249}\right)$	$e\left(\frac{2137}{3249}\right)$	$e\left(\frac{1831}{3249}\right)$	$e\left(\frac{3521}{6498}\right)$	$e\left(\frac{1255}{2166}\right)$	$e\left(\frac{1460}{3249}\right)$
$\chi_{987696}(101,\cdot)$	987696.vr	12996	yes	$-1$	$1$	$e\left(\frac{11971}{12996}\right)$	$e\left(\frac{1835}{2166}\right)$	$e\left(\frac{443}{1444}\right)$	$e\left(\frac{5255}{12996}\right)$	$e\left(\frac{3263}{6498}\right)$	$e\left(\frac{287}{3249}\right)$	$e\left(\frac{5473}{6498}\right)$	$e\left(\frac{1301}{12996}\right)$	$e\left(\frac{69}{361}\right)$	$e\left(\frac{9985}{12996}\right)$

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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	$987696$
Structure	\(C_{2}\times C_{2}\times C_{6}\times C_{12996}\)
Order	$311904$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{987696}(1,\cdot)\)	987696.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{987696}(5,\cdot)\)	987696.vr	12996	yes	\(-1\)	\(1\)	\(e\left(\frac{7727}{12996}\right)\)	\(e\left(\frac{2005}{2166}\right)\)	\(e\left(\frac{667}{1444}\right)\)	\(e\left(\frac{9643}{12996}\right)\)	\(e\left(\frac{5749}{6498}\right)\)	\(e\left(\frac{2515}{3249}\right)\)	\(e\left(\frac{1229}{6498}\right)\)	\(e\left(\frac{9997}{12996}\right)\)	\(e\left(\frac{99}{361}\right)\)	\(e\left(\frac{6761}{12996}\right)\)
\(\chi_{987696}(7,\cdot)\)	987696.qy	2166	no	\(-1\)	\(1\)	\(e\left(\frac{2005}{2166}\right)\)	\(e\left(\frac{907}{2166}\right)\)	\(e\left(\frac{650}{1083}\right)\)	\(e\left(\frac{119}{722}\right)\)	\(e\left(\frac{235}{1083}\right)\)	\(e\left(\frac{527}{722}\right)\)	\(e\left(\frac{922}{1083}\right)\)	\(e\left(\frac{2009}{2166}\right)\)	\(e\left(\frac{1109}{2166}\right)\)	\(e\left(\frac{373}{1083}\right)\)
\(\chi_{987696}(11,\cdot)\)	987696.sq	4332	yes	\(1\)	\(1\)	\(e\left(\frac{667}{1444}\right)\)	\(e\left(\frac{650}{1083}\right)\)	\(e\left(\frac{191}{4332}\right)\)	\(e\left(\frac{617}{4332}\right)\)	\(e\left(\frac{1927}{2166}\right)\)	\(e\left(\frac{1753}{2166}\right)\)	\(e\left(\frac{667}{722}\right)\)	\(e\left(\frac{341}{1444}\right)\)	\(e\left(\frac{251}{2166}\right)\)	\(e\left(\frac{269}{4332}\right)\)
\(\chi_{987696}(13,\cdot)\)	987696.wb	12996	yes	\(-1\)	\(1\)	\(e\left(\frac{9643}{12996}\right)\)	\(e\left(\frac{119}{722}\right)\)	\(e\left(\frac{617}{4332}\right)\)	\(e\left(\frac{623}{12996}\right)\)	\(e\left(\frac{1780}{3249}\right)\)	\(e\left(\frac{1921}{6498}\right)\)	\(e\left(\frac{3145}{6498}\right)\)	\(e\left(\frac{5771}{12996}\right)\)	\(e\left(\frac{17}{2166}\right)\)	\(e\left(\frac{11785}{12996}\right)\)
\(\chi_{987696}(17,\cdot)\)	987696.tz	6498	no	\(-1\)	\(1\)	\(e\left(\frac{5749}{6498}\right)\)	\(e\left(\frac{235}{1083}\right)\)	\(e\left(\frac{1927}{2166}\right)\)	\(e\left(\frac{1780}{3249}\right)\)	\(e\left(\frac{3709}{6498}\right)\)	\(e\left(\frac{4781}{6498}\right)\)	\(e\left(\frac{2500}{3249}\right)\)	\(e\left(\frac{4355}{6498}\right)\)	\(e\left(\frac{355}{1083}\right)\)	\(e\left(\frac{661}{6498}\right)\)
\(\chi_{987696}(23,\cdot)\)	987696.tt	6498	no	\(1\)	\(1\)	\(e\left(\frac{2515}{3249}\right)\)	\(e\left(\frac{527}{722}\right)\)	\(e\left(\frac{1753}{2166}\right)\)	\(e\left(\frac{1921}{6498}\right)\)	\(e\left(\frac{4781}{6498}\right)\)	\(e\left(\frac{3248}{3249}\right)\)	\(e\left(\frac{1781}{3249}\right)\)	\(e\left(\frac{3179}{3249}\right)\)	\(e\left(\frac{1313}{2166}\right)\)	\(e\left(\frac{3275}{6498}\right)\)
\(\chi_{987696}(25,\cdot)\)	987696.ui	6498	no	\(1\)	\(1\)	\(e\left(\frac{1229}{6498}\right)\)	\(e\left(\frac{922}{1083}\right)\)	\(e\left(\frac{667}{722}\right)\)	\(e\left(\frac{3145}{6498}\right)\)	\(e\left(\frac{2500}{3249}\right)\)	\(e\left(\frac{1781}{3249}\right)\)	\(e\left(\frac{1229}{3249}\right)\)	\(e\left(\frac{3499}{6498}\right)\)	\(e\left(\frac{198}{361}\right)\)	\(e\left(\frac{263}{6498}\right)\)
\(\chi_{987696}(29,\cdot)\)	987696.vs	12996	yes	\(1\)	\(1\)	\(e\left(\frac{9997}{12996}\right)\)	\(e\left(\frac{2009}{2166}\right)\)	\(e\left(\frac{341}{1444}\right)\)	\(e\left(\frac{5771}{12996}\right)\)	\(e\left(\frac{4355}{6498}\right)\)	\(e\left(\frac{3179}{3249}\right)\)	\(e\left(\frac{3499}{6498}\right)\)	\(e\left(\frac{5309}{12996}\right)\)	\(e\left(\frac{433}{722}\right)\)	\(e\left(\frac{9055}{12996}\right)\)
\(\chi_{987696}(31,\cdot)\)	987696.ro	2166	no	\(1\)	\(1\)	\(e\left(\frac{99}{361}\right)\)	\(e\left(\frac{1109}{2166}\right)\)	\(e\left(\frac{251}{2166}\right)\)	\(e\left(\frac{17}{2166}\right)\)	\(e\left(\frac{355}{1083}\right)\)	\(e\left(\frac{1313}{2166}\right)\)	\(e\left(\frac{198}{361}\right)\)	\(e\left(\frac{433}{722}\right)\)	\(e\left(\frac{35}{1083}\right)\)	\(e\left(\frac{1703}{2166}\right)\)
\(\chi_{987696}(35,\cdot)\)	987696.vj	12996	no	\(1\)	\(1\)	\(e\left(\frac{6761}{12996}\right)\)	\(e\left(\frac{373}{1083}\right)\)	\(e\left(\frac{269}{4332}\right)\)	\(e\left(\frac{11785}{12996}\right)\)	\(e\left(\frac{661}{6498}\right)\)	\(e\left(\frac{3275}{6498}\right)\)	\(e\left(\frac{263}{6498}\right)\)	\(e\left(\frac{9055}{12996}\right)\)	\(e\left(\frac{1703}{2166}\right)\)	\(e\left(\frac{11237}{12996}\right)\)
\(\chi_{987696}(37,\cdot)\)	987696.ps	1444	no	\(-1\)	\(1\)	\(e\left(\frac{857}{1444}\right)\)	\(e\left(\frac{85}{722}\right)\)	\(e\left(\frac{697}{1444}\right)\)	\(e\left(\frac{1333}{1444}\right)\)	\(e\left(\frac{147}{361}\right)\)	\(e\left(\frac{141}{722}\right)\)	\(e\left(\frac{135}{722}\right)\)	\(e\left(\frac{1329}{1444}\right)\)	\(e\left(\frac{451}{722}\right)\)	\(e\left(\frac{1027}{1444}\right)\)
\(\chi_{987696}(41,\cdot)\)	987696.tx	6498	no	\(1\)	\(1\)	\(e\left(\frac{191}{3249}\right)\)	\(e\left(\frac{98}{1083}\right)\)	\(e\left(\frac{158}{361}\right)\)	\(e\left(\frac{1303}{3249}\right)\)	\(e\left(\frac{6421}{6498}\right)\)	\(e\left(\frac{3341}{6498}\right)\)	\(e\left(\frac{382}{3249}\right)\)	\(e\left(\frac{5357}{6498}\right)\)	\(e\left(\frac{685}{722}\right)\)	\(e\left(\frac{485}{3249}\right)\)
\(\chi_{987696}(43,\cdot)\)	987696.vq	12996	yes	\(-1\)	\(1\)	\(e\left(\frac{245}{12996}\right)\)	\(e\left(\frac{351}{361}\right)\)	\(e\left(\frac{4201}{4332}\right)\)	\(e\left(\frac{8623}{12996}\right)\)	\(e\left(\frac{1430}{3249}\right)\)	\(e\left(\frac{2314}{3249}\right)\)	\(e\left(\frac{245}{6498}\right)\)	\(e\left(\frac{7867}{12996}\right)\)	\(e\left(\frac{1699}{2166}\right)\)	\(e\left(\frac{12881}{12996}\right)\)
\(\chi_{987696}(47,\cdot)\)	987696.uj	6498	no	\(1\)	\(1\)	\(e\left(\frac{2555}{6498}\right)\)	\(e\left(\frac{863}{2166}\right)\)	\(e\left(\frac{331}{361}\right)\)	\(e\left(\frac{1256}{3249}\right)\)	\(e\left(\frac{1943}{6498}\right)\)	\(e\left(\frac{2468}{3249}\right)\)	\(e\left(\frac{2555}{3249}\right)\)	\(e\left(\frac{2209}{6498}\right)\)	\(e\left(\frac{71}{722}\right)\)	\(e\left(\frac{2572}{3249}\right)\)
\(\chi_{987696}(49,\cdot)\)	987696.pl	1083	no	\(1\)	\(1\)	\(e\left(\frac{922}{1083}\right)\)	\(e\left(\frac{907}{1083}\right)\)	\(e\left(\frac{217}{1083}\right)\)	\(e\left(\frac{119}{361}\right)\)	\(e\left(\frac{470}{1083}\right)\)	\(e\left(\frac{166}{361}\right)\)	\(e\left(\frac{761}{1083}\right)\)	\(e\left(\frac{926}{1083}\right)\)	\(e\left(\frac{26}{1083}\right)\)	\(e\left(\frac{746}{1083}\right)\)
\(\chi_{987696}(53,\cdot)\)	987696.vw	12996	no	\(1\)	\(1\)	\(e\left(\frac{1063}{12996}\right)\)	\(e\left(\frac{1471}{2166}\right)\)	\(e\left(\frac{2965}{4332}\right)\)	\(e\left(\frac{10325}{12996}\right)\)	\(e\left(\frac{5933}{6498}\right)\)	\(e\left(\frac{1955}{3249}\right)\)	\(e\left(\frac{1063}{6498}\right)\)	\(e\left(\frac{2651}{12996}\right)\)	\(e\left(\frac{517}{2166}\right)\)	\(e\left(\frac{9889}{12996}\right)\)
\(\chi_{987696}(55,\cdot)\)	987696.ty	6498	no	\(-1\)	\(1\)	\(e\left(\frac{367}{6498}\right)\)	\(e\left(\frac{1139}{2166}\right)\)	\(e\left(\frac{548}{1083}\right)\)	\(e\left(\frac{5747}{6498}\right)\)	\(e\left(\frac{2516}{3249}\right)\)	\(e\left(\frac{3791}{6498}\right)\)	\(e\left(\frac{367}{3249}\right)\)	\(e\left(\frac{35}{6498}\right)\)	\(e\left(\frac{845}{2166}\right)\)	\(e\left(\frac{1892}{3249}\right)\)
\(\chi_{987696}(59,\cdot)\)	987696.wd	12996	yes	\(-1\)	\(1\)	\(e\left(\frac{3215}{12996}\right)\)	\(e\left(\frac{41}{1083}\right)\)	\(e\left(\frac{537}{1444}\right)\)	\(e\left(\frac{6181}{12996}\right)\)	\(e\left(\frac{1747}{6498}\right)\)	\(e\left(\frac{149}{6498}\right)\)	\(e\left(\frac{3215}{6498}\right)\)	\(e\left(\frac{8947}{12996}\right)\)	\(e\left(\frac{333}{361}\right)\)	\(e\left(\frac{3707}{12996}\right)\)
\(\chi_{987696}(61,\cdot)\)	987696.vl	12996	yes	\(1\)	\(1\)	\(e\left(\frac{679}{12996}\right)\)	\(e\left(\frac{401}{2166}\right)\)	\(e\left(\frac{711}{1444}\right)\)	\(e\left(\frac{9293}{12996}\right)\)	\(e\left(\frac{1333}{3249}\right)\)	\(e\left(\frac{2089}{6498}\right)\)	\(e\left(\frac{679}{6498}\right)\)	\(e\left(\frac{5465}{12996}\right)\)	\(e\left(\frac{92}{361}\right)\)	\(e\left(\frac{3085}{12996}\right)\)
\(\chi_{987696}(65,\cdot)\)	987696.ql	2166	no	\(1\)	\(1\)	\(e\left(\frac{243}{722}\right)\)	\(e\left(\frac{98}{1083}\right)\)	\(e\left(\frac{1309}{2166}\right)\)	\(e\left(\frac{1711}{2166}\right)\)	\(e\left(\frac{937}{2166}\right)\)	\(e\left(\frac{151}{2166}\right)\)	\(e\left(\frac{243}{361}\right)\)	\(e\left(\frac{77}{361}\right)\)	\(e\left(\frac{611}{2166}\right)\)	\(e\left(\frac{925}{2166}\right)\)
\(\chi_{987696}(67,\cdot)\)	987696.vu	12996	yes	\(1\)	\(1\)	\(e\left(\frac{3007}{12996}\right)\)	\(e\left(\frac{253}{361}\right)\)	\(e\left(\frac{2123}{4332}\right)\)	\(e\left(\frac{11759}{12996}\right)\)	\(e\left(\frac{643}{3249}\right)\)	\(e\left(\frac{1454}{3249}\right)\)	\(e\left(\frac{3007}{6498}\right)\)	\(e\left(\frac{995}{12996}\right)\)	\(e\left(\frac{655}{1083}\right)\)	\(e\left(\frac{12115}{12996}\right)\)
\(\chi_{987696}(71,\cdot)\)	987696.ud	6498	no	\(-1\)	\(1\)	\(e\left(\frac{614}{3249}\right)\)	\(e\left(\frac{1955}{2166}\right)\)	\(e\left(\frac{2059}{2166}\right)\)	\(e\left(\frac{1966}{3249}\right)\)	\(e\left(\frac{3319}{6498}\right)\)	\(e\left(\frac{2518}{3249}\right)\)	\(e\left(\frac{1228}{3249}\right)\)	\(e\left(\frac{2711}{6498}\right)\)	\(e\left(\frac{313}{1083}\right)\)	\(e\left(\frac{595}{6498}\right)\)
\(\chi_{987696}(73,\cdot)\)	987696.ub	6498	no	\(1\)	\(1\)	\(e\left(\frac{3583}{6498}\right)\)	\(e\left(\frac{235}{1083}\right)\)	\(e\left(\frac{1927}{2166}\right)\)	\(e\left(\frac{2477}{6498}\right)\)	\(e\left(\frac{2396}{3249}\right)\)	\(e\left(\frac{1849}{3249}\right)\)	\(e\left(\frac{334}{3249}\right)\)	\(e\left(\frac{23}{6498}\right)\)	\(e\left(\frac{355}{1083}\right)\)	\(e\left(\frac{4993}{6498}\right)\)
\(\chi_{987696}(77,\cdot)\)	987696.si	4332	yes	\(-1\)	\(1\)	\(e\left(\frac{1679}{4332}\right)\)	\(e\left(\frac{41}{2166}\right)\)	\(e\left(\frac{2791}{4332}\right)\)	\(e\left(\frac{1331}{4332}\right)\)	\(e\left(\frac{77}{722}\right)\)	\(e\left(\frac{584}{1083}\right)\)	\(e\left(\frac{1679}{2166}\right)\)	\(e\left(\frac{709}{4332}\right)\)	\(e\left(\frac{680}{1083}\right)\)	\(e\left(\frac{587}{1444}\right)\)
\(\chi_{987696}(79,\cdot)\)	987696.vf	6498	no	\(1\)	\(1\)	\(e\left(\frac{2042}{3249}\right)\)	\(e\left(\frac{151}{722}\right)\)	\(e\left(\frac{305}{2166}\right)\)	\(e\left(\frac{5651}{6498}\right)\)	\(e\left(\frac{1658}{3249}\right)\)	\(e\left(\frac{581}{6498}\right)\)	\(e\left(\frac{835}{3249}\right)\)	\(e\left(\frac{4931}{6498}\right)\)	\(e\left(\frac{707}{1083}\right)\)	\(e\left(\frac{5443}{6498}\right)\)
\(\chi_{987696}(83,\cdot)\)	987696.sn	4332	yes	\(1\)	\(1\)	\(e\left(\frac{3251}{4332}\right)\)	\(e\left(\frac{14}{1083}\right)\)	\(e\left(\frac{1457}{4332}\right)\)	\(e\left(\frac{77}{1444}\right)\)	\(e\left(\frac{959}{2166}\right)\)	\(e\left(\frac{351}{722}\right)\)	\(e\left(\frac{1085}{2166}\right)\)	\(e\left(\frac{493}{4332}\right)\)	\(e\left(\frac{1325}{2166}\right)\)	\(e\left(\frac{3307}{4332}\right)\)
\(\chi_{987696}(85,\cdot)\)	987696.vh	12996	yes	\(1\)	\(1\)	\(e\left(\frac{6229}{12996}\right)\)	\(e\left(\frac{103}{722}\right)\)	\(e\left(\frac{1523}{4332}\right)\)	\(e\left(\frac{3767}{12996}\right)\)	\(e\left(\frac{1480}{3249}\right)\)	\(e\left(\frac{3313}{6498}\right)\)	\(e\left(\frac{6229}{6498}\right)\)	\(e\left(\frac{5711}{12996}\right)\)	\(e\left(\frac{652}{1083}\right)\)	\(e\left(\frac{8083}{12996}\right)\)
\(\chi_{987696}(89,\cdot)\)	987696.ue	6498	no	\(1\)	\(1\)	\(e\left(\frac{2227}{3249}\right)\)	\(e\left(\frac{449}{1083}\right)\)	\(e\left(\frac{433}{1083}\right)\)	\(e\left(\frac{728}{3249}\right)\)	\(e\left(\frac{2561}{6498}\right)\)	\(e\left(\frac{5365}{6498}\right)\)	\(e\left(\frac{1205}{3249}\right)\)	\(e\left(\frac{4081}{6498}\right)\)	\(e\left(\frac{1057}{2166}\right)\)	\(e\left(\frac{325}{3249}\right)\)
\(\chi_{987696}(91,\cdot)\)	987696.vt	12996	no	\(1\)	\(1\)	\(e\left(\frac{8677}{12996}\right)\)	\(e\left(\frac{632}{1083}\right)\)	\(e\left(\frac{3217}{4332}\right)\)	\(e\left(\frac{2765}{12996}\right)\)	\(e\left(\frac{2485}{3249}\right)\)	\(e\left(\frac{83}{3249}\right)\)	\(e\left(\frac{2179}{6498}\right)\)	\(e\left(\frac{4829}{12996}\right)\)	\(e\left(\frac{563}{1083}\right)\)	\(e\left(\frac{3265}{12996}\right)\)
\(\chi_{987696}(97,\cdot)\)	987696.vc	6498	no	\(-1\)	\(1\)	\(e\left(\frac{2540}{3249}\right)\)	\(e\left(\frac{241}{361}\right)\)	\(e\left(\frac{1051}{1083}\right)\)	\(e\left(\frac{1559}{6498}\right)\)	\(e\left(\frac{554}{3249}\right)\)	\(e\left(\frac{2137}{3249}\right)\)	\(e\left(\frac{1831}{3249}\right)\)	\(e\left(\frac{3521}{6498}\right)\)	\(e\left(\frac{1255}{2166}\right)\)	\(e\left(\frac{1460}{3249}\right)\)
\(\chi_{987696}(101,\cdot)\)	987696.vr	12996	yes	\(-1\)	\(1\)	\(e\left(\frac{11971}{12996}\right)\)	\(e\left(\frac{1835}{2166}\right)\)	\(e\left(\frac{443}{1444}\right)\)	\(e\left(\frac{5255}{12996}\right)\)	\(e\left(\frac{3263}{6498}\right)\)	\(e\left(\frac{287}{3249}\right)\)	\(e\left(\frac{5473}{6498}\right)\)	\(e\left(\frac{1301}{12996}\right)\)	\(e\left(\frac{69}{361}\right)\)	\(e\left(\frac{9985}{12996}\right)\)

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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.