LMFDB - Group of Dirichlet characters of modulus 109744

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(109744)

gp:g = idealstar(,109744,2)

magma:G = FullDirichletGroup(109744);

Character group

Order	=	51984	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{12996}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{109744}(68591,\cdot)$, $\chi_{109744}(82309,\cdot)$, $\chi_{109744}(89169,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 51984 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$21$	$23$
$\chi_{109744}(1,\cdot)$	109744.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{109744}(3,\cdot)$	109744.ec	12996	yes	$1$	$1$	$e\left(\frac{9401}{12996}\right)$	$e\left(\frac{1739}{12996}\right)$	$e\left(\frac{568}{1083}\right)$	$e\left(\frac{2903}{6498}\right)$	$e\left(\frac{3467}{4332}\right)$	$e\left(\frac{319}{12996}\right)$	$e\left(\frac{2785}{3249}\right)$	$e\left(\frac{1685}{3249}\right)$	$e\left(\frac{3221}{12996}\right)$	$e\left(\frac{1939}{3249}\right)$
$\chi_{109744}(5,\cdot)$	109744.ea	12996	yes	$1$	$1$	$e\left(\frac{1739}{12996}\right)$	$e\left(\frac{5561}{12996}\right)$	$e\left(\frac{1283}{2166}\right)$	$e\left(\frac{1739}{6498}\right)$	$e\left(\frac{2723}{4332}\right)$	$e\left(\frac{979}{12996}\right)$	$e\left(\frac{1825}{3249}\right)$	$e\left(\frac{1250}{3249}\right)$	$e\left(\frac{9437}{12996}\right)$	$e\left(\frac{3947}{6498}\right)$
$\chi_{109744}(7,\cdot)$	109744.dm	2166	no	$-1$	$1$	$e\left(\frac{568}{1083}\right)$	$e\left(\frac{1283}{2166}\right)$	$e\left(\frac{543}{722}\right)$	$e\left(\frac{53}{1083}\right)$	$e\left(\frac{337}{361}\right)$	$e\left(\frac{1801}{2166}\right)$	$e\left(\frac{253}{2166}\right)$	$e\left(\frac{235}{1083}\right)$	$e\left(\frac{599}{2166}\right)$	$e\left(\frac{859}{2166}\right)$
$\chi_{109744}(9,\cdot)$	109744.du	6498	no	$1$	$1$	$e\left(\frac{2903}{6498}\right)$	$e\left(\frac{1739}{6498}\right)$	$e\left(\frac{53}{1083}\right)$	$e\left(\frac{2903}{3249}\right)$	$e\left(\frac{1301}{2166}\right)$	$e\left(\frac{319}{6498}\right)$	$e\left(\frac{2321}{3249}\right)$	$e\left(\frac{121}{3249}\right)$	$e\left(\frac{3221}{6498}\right)$	$e\left(\frac{629}{3249}\right)$
$\chi_{109744}(11,\cdot)$	109744.dp	4332	yes	$-1$	$1$	$e\left(\frac{3467}{4332}\right)$	$e\left(\frac{2723}{4332}\right)$	$e\left(\frac{337}{361}\right)$	$e\left(\frac{1301}{2166}\right)$	$e\left(\frac{1267}{1444}\right)$	$e\left(\frac{3505}{4332}\right)$	$e\left(\frac{929}{2166}\right)$	$e\left(\frac{422}{1083}\right)$	$e\left(\frac{3179}{4332}\right)$	$e\left(\frac{1057}{1083}\right)$
$\chi_{109744}(13,\cdot)$	109744.ed	12996	yes	$-1$	$1$	$e\left(\frac{319}{12996}\right)$	$e\left(\frac{979}{12996}\right)$	$e\left(\frac{1801}{2166}\right)$	$e\left(\frac{319}{6498}\right)$	$e\left(\frac{3505}{4332}\right)$	$e\left(\frac{4955}{12996}\right)$	$e\left(\frac{649}{6498}\right)$	$e\left(\frac{1780}{3249}\right)$	$e\left(\frac{11125}{12996}\right)$	$e\left(\frac{4087}{6498}\right)$
$\chi_{109744}(15,\cdot)$	109744.dw	6498	no	$1$	$1$	$e\left(\frac{2785}{3249}\right)$	$e\left(\frac{1825}{3249}\right)$	$e\left(\frac{253}{2166}\right)$	$e\left(\frac{2321}{3249}\right)$	$e\left(\frac{929}{2166}\right)$	$e\left(\frac{649}{6498}\right)$	$e\left(\frac{1361}{3249}\right)$	$e\left(\frac{2935}{3249}\right)$	$e\left(\frac{6329}{6498}\right)$	$e\left(\frac{1327}{6498}\right)$
$\chi_{109744}(17,\cdot)$	109744.do	3249	no	$1$	$1$	$e\left(\frac{1685}{3249}\right)$	$e\left(\frac{1250}{3249}\right)$	$e\left(\frac{235}{1083}\right)$	$e\left(\frac{121}{3249}\right)$	$e\left(\frac{422}{1083}\right)$	$e\left(\frac{1780}{3249}\right)$	$e\left(\frac{2935}{3249}\right)$	$e\left(\frac{230}{3249}\right)$	$e\left(\frac{2390}{3249}\right)$	$e\left(\frac{766}{3249}\right)$
$\chi_{109744}(21,\cdot)$	109744.ed	12996	yes	$-1$	$1$	$e\left(\frac{3221}{12996}\right)$	$e\left(\frac{9437}{12996}\right)$	$e\left(\frac{599}{2166}\right)$	$e\left(\frac{3221}{6498}\right)$	$e\left(\frac{3179}{4332}\right)$	$e\left(\frac{11125}{12996}\right)$	$e\left(\frac{6329}{6498}\right)$	$e\left(\frac{2390}{3249}\right)$	$e\left(\frac{6815}{12996}\right)$	$e\left(\frac{6455}{6498}\right)$
$\chi_{109744}(23,\cdot)$	109744.dt	6498	no	$-1$	$1$	$e\left(\frac{1939}{3249}\right)$	$e\left(\frac{3947}{6498}\right)$	$e\left(\frac{859}{2166}\right)$	$e\left(\frac{629}{3249}\right)$	$e\left(\frac{1057}{1083}\right)$	$e\left(\frac{4087}{6498}\right)$	$e\left(\frac{1327}{6498}\right)$	$e\left(\frac{766}{3249}\right)$	$e\left(\frac{6455}{6498}\right)$	$e\left(\frac{5413}{6498}\right)$
$\chi_{109744}(25,\cdot)$	109744.du	6498	no	$1$	$1$	$e\left(\frac{1739}{6498}\right)$	$e\left(\frac{5561}{6498}\right)$	$e\left(\frac{200}{1083}\right)$	$e\left(\frac{1739}{3249}\right)$	$e\left(\frac{557}{2166}\right)$	$e\left(\frac{979}{6498}\right)$	$e\left(\frac{401}{3249}\right)$	$e\left(\frac{2500}{3249}\right)$	$e\left(\frac{2939}{6498}\right)$	$e\left(\frac{698}{3249}\right)$
$\chi_{109744}(27,\cdot)$	109744.dr	4332	yes	$1$	$1$	$e\left(\frac{737}{4332}\right)$	$e\left(\frac{1739}{4332}\right)$	$e\left(\frac{207}{361}\right)$	$e\left(\frac{737}{2166}\right)$	$e\left(\frac{579}{1444}\right)$	$e\left(\frac{319}{4332}\right)$	$e\left(\frac{619}{1083}\right)$	$e\left(\frac{602}{1083}\right)$	$e\left(\frac{3221}{4332}\right)$	$e\left(\frac{856}{1083}\right)$
$\chi_{109744}(29,\cdot)$	109744.ed	12996	yes	$-1$	$1$	$e\left(\frac{2503}{12996}\right)$	$e\left(\frac{12163}{12996}\right)$	$e\left(\frac{565}{2166}\right)$	$e\left(\frac{2503}{6498}\right)$	$e\left(\frac{301}{4332}\right)$	$e\left(\frac{1439}{12996}\right)$	$e\left(\frac{835}{6498}\right)$	$e\left(\frac{553}{3249}\right)$	$e\left(\frac{5893}{12996}\right)$	$e\left(\frac{943}{6498}\right)$
$\chi_{109744}(31,\cdot)$	109744.dl	2166	no	$1$	$1$	$e\left(\frac{835}{1083}\right)$	$e\left(\frac{658}{1083}\right)$	$e\left(\frac{129}{722}\right)$	$e\left(\frac{587}{1083}\right)$	$e\left(\frac{565}{722}\right)$	$e\left(\frac{739}{2166}\right)$	$e\left(\frac{410}{1083}\right)$	$e\left(\frac{355}{1083}\right)$	$e\left(\frac{2057}{2166}\right)$	$e\left(\frac{2035}{2166}\right)$
$\chi_{109744}(33,\cdot)$	109744.dv	6498	no	$-1$	$1$	$e\left(\frac{3403}{6498}\right)$	$e\left(\frac{2477}{3249}\right)$	$e\left(\frac{496}{1083}\right)$	$e\left(\frac{154}{3249}\right)$	$e\left(\frac{734}{1083}\right)$	$e\left(\frac{5417}{6498}\right)$	$e\left(\frac{1859}{6498}\right)$	$e\left(\frac{2951}{3249}\right)$	$e\left(\frac{6379}{6498}\right)$	$e\left(\frac{1861}{3249}\right)$
$\chi_{109744}(35,\cdot)$	109744.eb	12996	yes	$-1$	$1$	$e\left(\frac{8555}{12996}\right)$	$e\left(\frac{263}{12996}\right)$	$e\left(\frac{373}{1083}\right)$	$e\left(\frac{2057}{6498}\right)$	$e\left(\frac{2435}{4332}\right)$	$e\left(\frac{11785}{12996}\right)$	$e\left(\frac{4409}{6498}\right)$	$e\left(\frac{1955}{3249}\right)$	$e\left(\frac{35}{12996}\right)$	$e\left(\frac{13}{3249}\right)$
$\chi_{109744}(37,\cdot)$	109744.df	1444	yes	$-1$	$1$	$e\left(\frac{117}{1444}\right)$	$e\left(\frac{857}{1444}\right)$	$e\left(\frac{85}{722}\right)$	$e\left(\frac{117}{722}\right)$	$e\left(\frac{697}{1444}\right)$	$e\left(\frac{1333}{1444}\right)$	$e\left(\frac{487}{722}\right)$	$e\left(\frac{147}{361}\right)$	$e\left(\frac{287}{1444}\right)$	$e\left(\frac{141}{722}\right)$
$\chi_{109744}(39,\cdot)$	109744.cz	722	no	$-1$	$1$	$e\left(\frac{270}{361}\right)$	$e\left(\frac{151}{722}\right)$	$e\left(\frac{257}{722}\right)$	$e\left(\frac{179}{361}\right)$	$e\left(\frac{220}{361}\right)$	$e\left(\frac{293}{722}\right)$	$e\left(\frac{691}{722}\right)$	$e\left(\frac{24}{361}\right)$	$e\left(\frac{75}{722}\right)$	$e\left(\frac{163}{722}\right)$
$\chi_{109744}(41,\cdot)$	109744.dy	6498	no	$-1$	$1$	$e\left(\frac{2861}{3249}\right)$	$e\left(\frac{5797}{6498}\right)$	$e\left(\frac{820}{1083}\right)$	$e\left(\frac{2473}{3249}\right)$	$e\left(\frac{1309}{2166}\right)$	$e\left(\frac{2386}{3249}\right)$	$e\left(\frac{5021}{6498}\right)$	$e\left(\frac{1586}{3249}\right)$	$e\left(\frac{2072}{3249}\right)$	$e\left(\frac{1129}{3249}\right)$
$\chi_{109744}(43,\cdot)$	109744.eb	12996	yes	$-1$	$1$	$e\left(\frac{3341}{12996}\right)$	$e\left(\frac{8909}{12996}\right)$	$e\left(\frac{331}{1083}\right)$	$e\left(\frac{3341}{6498}\right)$	$e\left(\frac{1313}{4332}\right)$	$e\left(\frac{4291}{12996}\right)$	$e\left(\frac{6125}{6498}\right)$	$e\left(\frac{1430}{3249}\right)$	$e\left(\frac{7313}{12996}\right)$	$e\left(\frac{1231}{3249}\right)$
$\chi_{109744}(45,\cdot)$	109744.ds	4332	yes	$1$	$1$	$e\left(\frac{2515}{4332}\right)$	$e\left(\frac{3013}{4332}\right)$	$e\left(\frac{463}{722}\right)$	$e\left(\frac{349}{2166}\right)$	$e\left(\frac{331}{1444}\right)$	$e\left(\frac{539}{4332}\right)$	$e\left(\frac{299}{1083}\right)$	$e\left(\frac{457}{1083}\right)$	$e\left(\frac{961}{4332}\right)$	$e\left(\frac{1735}{2166}\right)$
$\chi_{109744}(47,\cdot)$	109744.dz	6498	no	$-1$	$1$	$e\left(\frac{1733}{6498}\right)$	$e\left(\frac{1819}{3249}\right)$	$e\left(\frac{1585}{2166}\right)$	$e\left(\frac{1733}{3249}\right)$	$e\left(\frac{1625}{2166}\right)$	$e\left(\frac{173}{3249}\right)$	$e\left(\frac{5371}{6498}\right)$	$e\left(\frac{2596}{3249}\right)$	$e\left(\frac{3244}{3249}\right)$	$e\left(\frac{6019}{6498}\right)$
$\chi_{109744}(49,\cdot)$	109744.dc	1083	no	$1$	$1$	$e\left(\frac{53}{1083}\right)$	$e\left(\frac{200}{1083}\right)$	$e\left(\frac{182}{361}\right)$	$e\left(\frac{106}{1083}\right)$	$e\left(\frac{313}{361}\right)$	$e\left(\frac{718}{1083}\right)$	$e\left(\frac{253}{1083}\right)$	$e\left(\frac{470}{1083}\right)$	$e\left(\frac{599}{1083}\right)$	$e\left(\frac{859}{1083}\right)$
$\chi_{109744}(51,\cdot)$	109744.ec	12996	yes	$1$	$1$	$e\left(\frac{3145}{12996}\right)$	$e\left(\frac{6739}{12996}\right)$	$e\left(\frac{803}{1083}\right)$	$e\left(\frac{3145}{6498}\right)$	$e\left(\frac{823}{4332}\right)$	$e\left(\frac{7439}{12996}\right)$	$e\left(\frac{2471}{3249}\right)$	$e\left(\frac{1915}{3249}\right)$	$e\left(\frac{12781}{12996}\right)$	$e\left(\frac{2705}{3249}\right)$
$\chi_{109744}(53,\cdot)$	109744.ed	12996	yes	$-1$	$1$	$e\left(\frac{10933}{12996}\right)$	$e\left(\frac{7561}{12996}\right)$	$e\left(\frac{1471}{2166}\right)$	$e\left(\frac{4435}{6498}\right)$	$e\left(\frac{799}{4332}\right)$	$e\left(\frac{10325}{12996}\right)$	$e\left(\frac{2749}{6498}\right)$	$e\left(\frac{1342}{3249}\right)$	$e\left(\frac{6763}{12996}\right)$	$e\left(\frac{661}{6498}\right)$
$\chi_{109744}(55,\cdot)$	109744.dt	6498	no	$-1$	$1$	$e\left(\frac{3035}{3249}\right)$	$e\left(\frac{367}{6498}\right)$	$e\left(\frac{1139}{2166}\right)$	$e\left(\frac{2821}{3249}\right)$	$e\left(\frac{548}{1083}\right)$	$e\left(\frac{5747}{6498}\right)$	$e\left(\frac{6437}{6498}\right)$	$e\left(\frac{2516}{3249}\right)$	$e\left(\frac{2989}{6498}\right)$	$e\left(\frac{3791}{6498}\right)$
$\chi_{109744}(59,\cdot)$	109744.ec	12996	yes	$1$	$1$	$e\left(\frac{1583}{12996}\right)$	$e\left(\frac{1049}{12996}\right)$	$e\left(\frac{763}{1083}\right)$	$e\left(\frac{1583}{6498}\right)$	$e\left(\frac{2333}{4332}\right)$	$e\left(\frac{10513}{12996}\right)$	$e\left(\frac{658}{3249}\right)$	$e\left(\frac{2498}{3249}\right)$	$e\left(\frac{10739}{12996}\right)$	$e\left(\frac{2782}{3249}\right)$
$\chi_{109744}(61,\cdot)$	109744.ea	12996	yes	$1$	$1$	$e\left(\frac{781}{12996}\right)$	$e\left(\frac{9343}{12996}\right)$	$e\left(\frac{1123}{2166}\right)$	$e\left(\frac{781}{6498}\right)$	$e\left(\frac{3577}{4332}\right)$	$e\left(\frac{4961}{12996}\right)$	$e\left(\frac{2531}{3249}\right)$	$e\left(\frac{1333}{3249}\right)$	$e\left(\frac{7519}{12996}\right)$	$e\left(\frac{6421}{6498}\right)$
$\chi_{109744}(63,\cdot)$	109744.dz	6498	no	$-1$	$1$	$e\left(\frac{6311}{6498}\right)$	$e\left(\frac{2794}{3249}\right)$	$e\left(\frac{1735}{2166}\right)$	$e\left(\frac{3062}{3249}\right)$	$e\left(\frac{1157}{2166}\right)$	$e\left(\frac{2861}{3249}\right)$	$e\left(\frac{5401}{6498}\right)$	$e\left(\frac{826}{3249}\right)$	$e\left(\frac{2509}{3249}\right)$	$e\left(\frac{3835}{6498}\right)$
$\chi_{109744}(65,\cdot)$	109744.dn	2166	no	$-1$	$1$	$e\left(\frac{343}{2166}\right)$	$e\left(\frac{545}{1083}\right)$	$e\left(\frac{153}{361}\right)$	$e\left(\frac{343}{1083}\right)$	$e\left(\frac{158}{361}\right)$	$e\left(\frac{989}{2166}\right)$	$e\left(\frac{1433}{2166}\right)$	$e\left(\frac{1010}{1083}\right)$	$e\left(\frac{1261}{2166}\right)$	$e\left(\frac{256}{1083}\right)$
$\chi_{109744}(67,\cdot)$	109744.ec	12996	yes	$1$	$1$	$e\left(\frac{6553}{12996}\right)$	$e\left(\frac{7339}{12996}\right)$	$e\left(\frac{398}{1083}\right)$	$e\left(\frac{55}{6498}\right)$	$e\left(\frac{679}{4332}\right)$	$e\left(\frac{3095}{12996}\right)$	$e\left(\frac{224}{3249}\right)$	$e\left(\frac{643}{3249}\right)$	$e\left(\frac{11329}{12996}\right)$	$e\left(\frac{2537}{3249}\right)$

Click here to search among the remaining 51952 characters.

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	$109744$
Structure	\(C_{2}\times C_{2}\times C_{12996}\)
Order	$51984$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)
\(\chi_{109744}(1,\cdot)\)	109744.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{109744}(3,\cdot)\)	109744.ec	12996	yes	\(1\)	\(1\)	\(e\left(\frac{9401}{12996}\right)\)	\(e\left(\frac{1739}{12996}\right)\)	\(e\left(\frac{568}{1083}\right)\)	\(e\left(\frac{2903}{6498}\right)\)	\(e\left(\frac{3467}{4332}\right)\)	\(e\left(\frac{319}{12996}\right)\)	\(e\left(\frac{2785}{3249}\right)\)	\(e\left(\frac{1685}{3249}\right)\)	\(e\left(\frac{3221}{12996}\right)\)	\(e\left(\frac{1939}{3249}\right)\)
\(\chi_{109744}(5,\cdot)\)	109744.ea	12996	yes	\(1\)	\(1\)	\(e\left(\frac{1739}{12996}\right)\)	\(e\left(\frac{5561}{12996}\right)\)	\(e\left(\frac{1283}{2166}\right)\)	\(e\left(\frac{1739}{6498}\right)\)	\(e\left(\frac{2723}{4332}\right)\)	\(e\left(\frac{979}{12996}\right)\)	\(e\left(\frac{1825}{3249}\right)\)	\(e\left(\frac{1250}{3249}\right)\)	\(e\left(\frac{9437}{12996}\right)\)	\(e\left(\frac{3947}{6498}\right)\)
\(\chi_{109744}(7,\cdot)\)	109744.dm	2166	no	\(-1\)	\(1\)	\(e\left(\frac{568}{1083}\right)\)	\(e\left(\frac{1283}{2166}\right)\)	\(e\left(\frac{543}{722}\right)\)	\(e\left(\frac{53}{1083}\right)\)	\(e\left(\frac{337}{361}\right)\)	\(e\left(\frac{1801}{2166}\right)\)	\(e\left(\frac{253}{2166}\right)\)	\(e\left(\frac{235}{1083}\right)\)	\(e\left(\frac{599}{2166}\right)\)	\(e\left(\frac{859}{2166}\right)\)
\(\chi_{109744}(9,\cdot)\)	109744.du	6498	no	\(1\)	\(1\)	\(e\left(\frac{2903}{6498}\right)\)	\(e\left(\frac{1739}{6498}\right)\)	\(e\left(\frac{53}{1083}\right)\)	\(e\left(\frac{2903}{3249}\right)\)	\(e\left(\frac{1301}{2166}\right)\)	\(e\left(\frac{319}{6498}\right)\)	\(e\left(\frac{2321}{3249}\right)\)	\(e\left(\frac{121}{3249}\right)\)	\(e\left(\frac{3221}{6498}\right)\)	\(e\left(\frac{629}{3249}\right)\)
\(\chi_{109744}(11,\cdot)\)	109744.dp	4332	yes	\(-1\)	\(1\)	\(e\left(\frac{3467}{4332}\right)\)	\(e\left(\frac{2723}{4332}\right)\)	\(e\left(\frac{337}{361}\right)\)	\(e\left(\frac{1301}{2166}\right)\)	\(e\left(\frac{1267}{1444}\right)\)	\(e\left(\frac{3505}{4332}\right)\)	\(e\left(\frac{929}{2166}\right)\)	\(e\left(\frac{422}{1083}\right)\)	\(e\left(\frac{3179}{4332}\right)\)	\(e\left(\frac{1057}{1083}\right)\)
\(\chi_{109744}(13,\cdot)\)	109744.ed	12996	yes	\(-1\)	\(1\)	\(e\left(\frac{319}{12996}\right)\)	\(e\left(\frac{979}{12996}\right)\)	\(e\left(\frac{1801}{2166}\right)\)	\(e\left(\frac{319}{6498}\right)\)	\(e\left(\frac{3505}{4332}\right)\)	\(e\left(\frac{4955}{12996}\right)\)	\(e\left(\frac{649}{6498}\right)\)	\(e\left(\frac{1780}{3249}\right)\)	\(e\left(\frac{11125}{12996}\right)\)	\(e\left(\frac{4087}{6498}\right)\)
\(\chi_{109744}(15,\cdot)\)	109744.dw	6498	no	\(1\)	\(1\)	\(e\left(\frac{2785}{3249}\right)\)	\(e\left(\frac{1825}{3249}\right)\)	\(e\left(\frac{253}{2166}\right)\)	\(e\left(\frac{2321}{3249}\right)\)	\(e\left(\frac{929}{2166}\right)\)	\(e\left(\frac{649}{6498}\right)\)	\(e\left(\frac{1361}{3249}\right)\)	\(e\left(\frac{2935}{3249}\right)\)	\(e\left(\frac{6329}{6498}\right)\)	\(e\left(\frac{1327}{6498}\right)\)
\(\chi_{109744}(17,\cdot)\)	109744.do	3249	no	\(1\)	\(1\)	\(e\left(\frac{1685}{3249}\right)\)	\(e\left(\frac{1250}{3249}\right)\)	\(e\left(\frac{235}{1083}\right)\)	\(e\left(\frac{121}{3249}\right)\)	\(e\left(\frac{422}{1083}\right)\)	\(e\left(\frac{1780}{3249}\right)\)	\(e\left(\frac{2935}{3249}\right)\)	\(e\left(\frac{230}{3249}\right)\)	\(e\left(\frac{2390}{3249}\right)\)	\(e\left(\frac{766}{3249}\right)\)
\(\chi_{109744}(21,\cdot)\)	109744.ed	12996	yes	\(-1\)	\(1\)	\(e\left(\frac{3221}{12996}\right)\)	\(e\left(\frac{9437}{12996}\right)\)	\(e\left(\frac{599}{2166}\right)\)	\(e\left(\frac{3221}{6498}\right)\)	\(e\left(\frac{3179}{4332}\right)\)	\(e\left(\frac{11125}{12996}\right)\)	\(e\left(\frac{6329}{6498}\right)\)	\(e\left(\frac{2390}{3249}\right)\)	\(e\left(\frac{6815}{12996}\right)\)	\(e\left(\frac{6455}{6498}\right)\)
\(\chi_{109744}(23,\cdot)\)	109744.dt	6498	no	\(-1\)	\(1\)	\(e\left(\frac{1939}{3249}\right)\)	\(e\left(\frac{3947}{6498}\right)\)	\(e\left(\frac{859}{2166}\right)\)	\(e\left(\frac{629}{3249}\right)\)	\(e\left(\frac{1057}{1083}\right)\)	\(e\left(\frac{4087}{6498}\right)\)	\(e\left(\frac{1327}{6498}\right)\)	\(e\left(\frac{766}{3249}\right)\)	\(e\left(\frac{6455}{6498}\right)\)	\(e\left(\frac{5413}{6498}\right)\)
\(\chi_{109744}(25,\cdot)\)	109744.du	6498	no	\(1\)	\(1\)	\(e\left(\frac{1739}{6498}\right)\)	\(e\left(\frac{5561}{6498}\right)\)	\(e\left(\frac{200}{1083}\right)\)	\(e\left(\frac{1739}{3249}\right)\)	\(e\left(\frac{557}{2166}\right)\)	\(e\left(\frac{979}{6498}\right)\)	\(e\left(\frac{401}{3249}\right)\)	\(e\left(\frac{2500}{3249}\right)\)	\(e\left(\frac{2939}{6498}\right)\)	\(e\left(\frac{698}{3249}\right)\)
\(\chi_{109744}(27,\cdot)\)	109744.dr	4332	yes	\(1\)	\(1\)	\(e\left(\frac{737}{4332}\right)\)	\(e\left(\frac{1739}{4332}\right)\)	\(e\left(\frac{207}{361}\right)\)	\(e\left(\frac{737}{2166}\right)\)	\(e\left(\frac{579}{1444}\right)\)	\(e\left(\frac{319}{4332}\right)\)	\(e\left(\frac{619}{1083}\right)\)	\(e\left(\frac{602}{1083}\right)\)	\(e\left(\frac{3221}{4332}\right)\)	\(e\left(\frac{856}{1083}\right)\)
\(\chi_{109744}(29,\cdot)\)	109744.ed	12996	yes	\(-1\)	\(1\)	\(e\left(\frac{2503}{12996}\right)\)	\(e\left(\frac{12163}{12996}\right)\)	\(e\left(\frac{565}{2166}\right)\)	\(e\left(\frac{2503}{6498}\right)\)	\(e\left(\frac{301}{4332}\right)\)	\(e\left(\frac{1439}{12996}\right)\)	\(e\left(\frac{835}{6498}\right)\)	\(e\left(\frac{553}{3249}\right)\)	\(e\left(\frac{5893}{12996}\right)\)	\(e\left(\frac{943}{6498}\right)\)
\(\chi_{109744}(31,\cdot)\)	109744.dl	2166	no	\(1\)	\(1\)	\(e\left(\frac{835}{1083}\right)\)	\(e\left(\frac{658}{1083}\right)\)	\(e\left(\frac{129}{722}\right)\)	\(e\left(\frac{587}{1083}\right)\)	\(e\left(\frac{565}{722}\right)\)	\(e\left(\frac{739}{2166}\right)\)	\(e\left(\frac{410}{1083}\right)\)	\(e\left(\frac{355}{1083}\right)\)	\(e\left(\frac{2057}{2166}\right)\)	\(e\left(\frac{2035}{2166}\right)\)
\(\chi_{109744}(33,\cdot)\)	109744.dv	6498	no	\(-1\)	\(1\)	\(e\left(\frac{3403}{6498}\right)\)	\(e\left(\frac{2477}{3249}\right)\)	\(e\left(\frac{496}{1083}\right)\)	\(e\left(\frac{154}{3249}\right)\)	\(e\left(\frac{734}{1083}\right)\)	\(e\left(\frac{5417}{6498}\right)\)	\(e\left(\frac{1859}{6498}\right)\)	\(e\left(\frac{2951}{3249}\right)\)	\(e\left(\frac{6379}{6498}\right)\)	\(e\left(\frac{1861}{3249}\right)\)
\(\chi_{109744}(35,\cdot)\)	109744.eb	12996	yes	\(-1\)	\(1\)	\(e\left(\frac{8555}{12996}\right)\)	\(e\left(\frac{263}{12996}\right)\)	\(e\left(\frac{373}{1083}\right)\)	\(e\left(\frac{2057}{6498}\right)\)	\(e\left(\frac{2435}{4332}\right)\)	\(e\left(\frac{11785}{12996}\right)\)	\(e\left(\frac{4409}{6498}\right)\)	\(e\left(\frac{1955}{3249}\right)\)	\(e\left(\frac{35}{12996}\right)\)	\(e\left(\frac{13}{3249}\right)\)
\(\chi_{109744}(37,\cdot)\)	109744.df	1444	yes	\(-1\)	\(1\)	\(e\left(\frac{117}{1444}\right)\)	\(e\left(\frac{857}{1444}\right)\)	\(e\left(\frac{85}{722}\right)\)	\(e\left(\frac{117}{722}\right)\)	\(e\left(\frac{697}{1444}\right)\)	\(e\left(\frac{1333}{1444}\right)\)	\(e\left(\frac{487}{722}\right)\)	\(e\left(\frac{147}{361}\right)\)	\(e\left(\frac{287}{1444}\right)\)	\(e\left(\frac{141}{722}\right)\)
\(\chi_{109744}(39,\cdot)\)	109744.cz	722	no	\(-1\)	\(1\)	\(e\left(\frac{270}{361}\right)\)	\(e\left(\frac{151}{722}\right)\)	\(e\left(\frac{257}{722}\right)\)	\(e\left(\frac{179}{361}\right)\)	\(e\left(\frac{220}{361}\right)\)	\(e\left(\frac{293}{722}\right)\)	\(e\left(\frac{691}{722}\right)\)	\(e\left(\frac{24}{361}\right)\)	\(e\left(\frac{75}{722}\right)\)	\(e\left(\frac{163}{722}\right)\)
\(\chi_{109744}(41,\cdot)\)	109744.dy	6498	no	\(-1\)	\(1\)	\(e\left(\frac{2861}{3249}\right)\)	\(e\left(\frac{5797}{6498}\right)\)	\(e\left(\frac{820}{1083}\right)\)	\(e\left(\frac{2473}{3249}\right)\)	\(e\left(\frac{1309}{2166}\right)\)	\(e\left(\frac{2386}{3249}\right)\)	\(e\left(\frac{5021}{6498}\right)\)	\(e\left(\frac{1586}{3249}\right)\)	\(e\left(\frac{2072}{3249}\right)\)	\(e\left(\frac{1129}{3249}\right)\)
\(\chi_{109744}(43,\cdot)\)	109744.eb	12996	yes	\(-1\)	\(1\)	\(e\left(\frac{3341}{12996}\right)\)	\(e\left(\frac{8909}{12996}\right)\)	\(e\left(\frac{331}{1083}\right)\)	\(e\left(\frac{3341}{6498}\right)\)	\(e\left(\frac{1313}{4332}\right)\)	\(e\left(\frac{4291}{12996}\right)\)	\(e\left(\frac{6125}{6498}\right)\)	\(e\left(\frac{1430}{3249}\right)\)	\(e\left(\frac{7313}{12996}\right)\)	\(e\left(\frac{1231}{3249}\right)\)
\(\chi_{109744}(45,\cdot)\)	109744.ds	4332	yes	\(1\)	\(1\)	\(e\left(\frac{2515}{4332}\right)\)	\(e\left(\frac{3013}{4332}\right)\)	\(e\left(\frac{463}{722}\right)\)	\(e\left(\frac{349}{2166}\right)\)	\(e\left(\frac{331}{1444}\right)\)	\(e\left(\frac{539}{4332}\right)\)	\(e\left(\frac{299}{1083}\right)\)	\(e\left(\frac{457}{1083}\right)\)	\(e\left(\frac{961}{4332}\right)\)	\(e\left(\frac{1735}{2166}\right)\)
\(\chi_{109744}(47,\cdot)\)	109744.dz	6498	no	\(-1\)	\(1\)	\(e\left(\frac{1733}{6498}\right)\)	\(e\left(\frac{1819}{3249}\right)\)	\(e\left(\frac{1585}{2166}\right)\)	\(e\left(\frac{1733}{3249}\right)\)	\(e\left(\frac{1625}{2166}\right)\)	\(e\left(\frac{173}{3249}\right)\)	\(e\left(\frac{5371}{6498}\right)\)	\(e\left(\frac{2596}{3249}\right)\)	\(e\left(\frac{3244}{3249}\right)\)	\(e\left(\frac{6019}{6498}\right)\)
\(\chi_{109744}(49,\cdot)\)	109744.dc	1083	no	\(1\)	\(1\)	\(e\left(\frac{53}{1083}\right)\)	\(e\left(\frac{200}{1083}\right)\)	\(e\left(\frac{182}{361}\right)\)	\(e\left(\frac{106}{1083}\right)\)	\(e\left(\frac{313}{361}\right)\)	\(e\left(\frac{718}{1083}\right)\)	\(e\left(\frac{253}{1083}\right)\)	\(e\left(\frac{470}{1083}\right)\)	\(e\left(\frac{599}{1083}\right)\)	\(e\left(\frac{859}{1083}\right)\)
\(\chi_{109744}(51,\cdot)\)	109744.ec	12996	yes	\(1\)	\(1\)	\(e\left(\frac{3145}{12996}\right)\)	\(e\left(\frac{6739}{12996}\right)\)	\(e\left(\frac{803}{1083}\right)\)	\(e\left(\frac{3145}{6498}\right)\)	\(e\left(\frac{823}{4332}\right)\)	\(e\left(\frac{7439}{12996}\right)\)	\(e\left(\frac{2471}{3249}\right)\)	\(e\left(\frac{1915}{3249}\right)\)	\(e\left(\frac{12781}{12996}\right)\)	\(e\left(\frac{2705}{3249}\right)\)
\(\chi_{109744}(53,\cdot)\)	109744.ed	12996	yes	\(-1\)	\(1\)	\(e\left(\frac{10933}{12996}\right)\)	\(e\left(\frac{7561}{12996}\right)\)	\(e\left(\frac{1471}{2166}\right)\)	\(e\left(\frac{4435}{6498}\right)\)	\(e\left(\frac{799}{4332}\right)\)	\(e\left(\frac{10325}{12996}\right)\)	\(e\left(\frac{2749}{6498}\right)\)	\(e\left(\frac{1342}{3249}\right)\)	\(e\left(\frac{6763}{12996}\right)\)	\(e\left(\frac{661}{6498}\right)\)
\(\chi_{109744}(55,\cdot)\)	109744.dt	6498	no	\(-1\)	\(1\)	\(e\left(\frac{3035}{3249}\right)\)	\(e\left(\frac{367}{6498}\right)\)	\(e\left(\frac{1139}{2166}\right)\)	\(e\left(\frac{2821}{3249}\right)\)	\(e\left(\frac{548}{1083}\right)\)	\(e\left(\frac{5747}{6498}\right)\)	\(e\left(\frac{6437}{6498}\right)\)	\(e\left(\frac{2516}{3249}\right)\)	\(e\left(\frac{2989}{6498}\right)\)	\(e\left(\frac{3791}{6498}\right)\)
\(\chi_{109744}(59,\cdot)\)	109744.ec	12996	yes	\(1\)	\(1\)	\(e\left(\frac{1583}{12996}\right)\)	\(e\left(\frac{1049}{12996}\right)\)	\(e\left(\frac{763}{1083}\right)\)	\(e\left(\frac{1583}{6498}\right)\)	\(e\left(\frac{2333}{4332}\right)\)	\(e\left(\frac{10513}{12996}\right)\)	\(e\left(\frac{658}{3249}\right)\)	\(e\left(\frac{2498}{3249}\right)\)	\(e\left(\frac{10739}{12996}\right)\)	\(e\left(\frac{2782}{3249}\right)\)
\(\chi_{109744}(61,\cdot)\)	109744.ea	12996	yes	\(1\)	\(1\)	\(e\left(\frac{781}{12996}\right)\)	\(e\left(\frac{9343}{12996}\right)\)	\(e\left(\frac{1123}{2166}\right)\)	\(e\left(\frac{781}{6498}\right)\)	\(e\left(\frac{3577}{4332}\right)\)	\(e\left(\frac{4961}{12996}\right)\)	\(e\left(\frac{2531}{3249}\right)\)	\(e\left(\frac{1333}{3249}\right)\)	\(e\left(\frac{7519}{12996}\right)\)	\(e\left(\frac{6421}{6498}\right)\)
\(\chi_{109744}(63,\cdot)\)	109744.dz	6498	no	\(-1\)	\(1\)	\(e\left(\frac{6311}{6498}\right)\)	\(e\left(\frac{2794}{3249}\right)\)	\(e\left(\frac{1735}{2166}\right)\)	\(e\left(\frac{3062}{3249}\right)\)	\(e\left(\frac{1157}{2166}\right)\)	\(e\left(\frac{2861}{3249}\right)\)	\(e\left(\frac{5401}{6498}\right)\)	\(e\left(\frac{826}{3249}\right)\)	\(e\left(\frac{2509}{3249}\right)\)	\(e\left(\frac{3835}{6498}\right)\)
\(\chi_{109744}(65,\cdot)\)	109744.dn	2166	no	\(-1\)	\(1\)	\(e\left(\frac{343}{2166}\right)\)	\(e\left(\frac{545}{1083}\right)\)	\(e\left(\frac{153}{361}\right)\)	\(e\left(\frac{343}{1083}\right)\)	\(e\left(\frac{158}{361}\right)\)	\(e\left(\frac{989}{2166}\right)\)	\(e\left(\frac{1433}{2166}\right)\)	\(e\left(\frac{1010}{1083}\right)\)	\(e\left(\frac{1261}{2166}\right)\)	\(e\left(\frac{256}{1083}\right)\)
\(\chi_{109744}(67,\cdot)\)	109744.ec	12996	yes	\(1\)	\(1\)	\(e\left(\frac{6553}{12996}\right)\)	\(e\left(\frac{7339}{12996}\right)\)	\(e\left(\frac{398}{1083}\right)\)	\(e\left(\frac{55}{6498}\right)\)	\(e\left(\frac{679}{4332}\right)\)	\(e\left(\frac{3095}{12996}\right)\)	\(e\left(\frac{224}{3249}\right)\)	\(e\left(\frac{643}{3249}\right)\)	\(e\left(\frac{11329}{12996}\right)\)	\(e\left(\frac{2537}{3249}\right)\)

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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.