LMFDB - Group of Dirichlet characters of modulus 549261

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(549261)

gp:g = idealstar(,549261,2)

magma:G = FullDirichletGroup(549261);

Character group

Order	=	366120	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{6}\times C_{61020}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{549261}(47468,\cdot)$, $\chi_{549261}(501796,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 366120 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{549261}(1,\cdot)$	549261.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{549261}(2,\cdot)$	549261.jy	61020	yes	$1$	$1$	$e\left(\frac{1139}{61020}\right)$	$e\left(\frac{1139}{30510}\right)$	$e\left(\frac{13189}{15255}\right)$	$e\left(\frac{43613}{61020}\right)$	$e\left(\frac{1139}{20340}\right)$	$e\left(\frac{3593}{4068}\right)$	$e\left(\frac{7637}{15255}\right)$	$e\left(\frac{58747}{61020}\right)$	$e\left(\frac{11188}{15255}\right)$	$e\left(\frac{1139}{15255}\right)$
$\chi_{549261}(4,\cdot)$	549261.jx	30510	yes	$1$	$1$	$e\left(\frac{1139}{30510}\right)$	$e\left(\frac{1139}{15255}\right)$	$e\left(\frac{11123}{15255}\right)$	$e\left(\frac{13103}{30510}\right)$	$e\left(\frac{1139}{10170}\right)$	$e\left(\frac{1559}{2034}\right)$	$e\left(\frac{19}{15255}\right)$	$e\left(\frac{28237}{30510}\right)$	$e\left(\frac{7121}{15255}\right)$	$e\left(\frac{2278}{15255}\right)$
$\chi_{549261}(5,\cdot)$	549261.jt	30510	yes	$-1$	$1$	$e\left(\frac{13189}{15255}\right)$	$e\left(\frac{11123}{15255}\right)$	$e\left(\frac{9787}{30510}\right)$	$e\left(\frac{7481}{30510}\right)$	$e\left(\frac{3019}{5085}\right)$	$e\left(\frac{377}{2034}\right)$	$e\left(\frac{13001}{30510}\right)$	$e\left(\frac{1009}{30510}\right)$	$e\left(\frac{3349}{30510}\right)$	$e\left(\frac{6991}{15255}\right)$
$\chi_{549261}(7,\cdot)$	549261.ka	61020	yes	$-1$	$1$	$e\left(\frac{43613}{61020}\right)$	$e\left(\frac{13103}{30510}\right)$	$e\left(\frac{7481}{30510}\right)$	$e\left(\frac{51581}{61020}\right)$	$e\left(\frac{2933}{20340}\right)$	$e\left(\frac{3905}{4068}\right)$	$e\left(\frac{4183}{30510}\right)$	$e\left(\frac{24139}{61020}\right)$	$e\left(\frac{17087}{30510}\right)$	$e\left(\frac{13103}{15255}\right)$
$\chi_{549261}(8,\cdot)$	549261.jm	20340	no	$1$	$1$	$e\left(\frac{1139}{20340}\right)$	$e\left(\frac{1139}{10170}\right)$	$e\left(\frac{3019}{5085}\right)$	$e\left(\frac{2933}{20340}\right)$	$e\left(\frac{1139}{6780}\right)$	$e\left(\frac{881}{1356}\right)$	$e\left(\frac{2552}{5085}\right)$	$e\left(\frac{18067}{20340}\right)$	$e\left(\frac{1018}{5085}\right)$	$e\left(\frac{1139}{5085}\right)$
$\chi_{549261}(10,\cdot)$	549261.hv	4068	no	$-1$	$1$	$e\left(\frac{3593}{4068}\right)$	$e\left(\frac{1559}{2034}\right)$	$e\left(\frac{377}{2034}\right)$	$e\left(\frac{3905}{4068}\right)$	$e\left(\frac{881}{1356}\right)$	$e\left(\frac{31}{452}\right)$	$e\left(\frac{1885}{2034}\right)$	$e\left(\frac{4051}{4068}\right)$	$e\left(\frac{1715}{2034}\right)$	$e\left(\frac{542}{1017}\right)$
$\chi_{549261}(11,\cdot)$	549261.jq	30510	yes	$-1$	$1$	$e\left(\frac{7637}{15255}\right)$	$e\left(\frac{19}{15255}\right)$	$e\left(\frac{13001}{30510}\right)$	$e\left(\frac{4183}{30510}\right)$	$e\left(\frac{2552}{5085}\right)$	$e\left(\frac{1885}{2034}\right)$	$e\left(\frac{1273}{30510}\right)$	$e\left(\frac{7757}{30510}\right)$	$e\left(\frac{19457}{30510}\right)$	$e\left(\frac{38}{15255}\right)$
$\chi_{549261}(13,\cdot)$	549261.jz	61020	yes	$-1$	$1$	$e\left(\frac{58747}{61020}\right)$	$e\left(\frac{28237}{30510}\right)$	$e\left(\frac{1009}{30510}\right)$	$e\left(\frac{24139}{61020}\right)$	$e\left(\frac{18067}{20340}\right)$	$e\left(\frac{4051}{4068}\right)$	$e\left(\frac{7757}{30510}\right)$	$e\left(\frac{14081}{61020}\right)$	$e\left(\frac{10933}{30510}\right)$	$e\left(\frac{12982}{15255}\right)$
$\chi_{549261}(14,\cdot)$	549261.jv	30510	yes	$-1$	$1$	$e\left(\frac{11188}{15255}\right)$	$e\left(\frac{7121}{15255}\right)$	$e\left(\frac{3349}{30510}\right)$	$e\left(\frac{17087}{30510}\right)$	$e\left(\frac{1018}{5085}\right)$	$e\left(\frac{1715}{2034}\right)$	$e\left(\frac{19457}{30510}\right)$	$e\left(\frac{10933}{30510}\right)$	$e\left(\frac{8953}{30510}\right)$	$e\left(\frac{14242}{15255}\right)$
$\chi_{549261}(16,\cdot)$	549261.ji	15255	yes	$1$	$1$	$e\left(\frac{1139}{15255}\right)$	$e\left(\frac{2278}{15255}\right)$	$e\left(\frac{6991}{15255}\right)$	$e\left(\frac{13103}{15255}\right)$	$e\left(\frac{1139}{5085}\right)$	$e\left(\frac{542}{1017}\right)$	$e\left(\frac{38}{15255}\right)$	$e\left(\frac{12982}{15255}\right)$	$e\left(\frac{14242}{15255}\right)$	$e\left(\frac{4556}{15255}\right)$
$\chi_{549261}(17,\cdot)$	549261.ix	10170	no	$-1$	$1$	$e\left(\frac{3947}{10170}\right)$	$e\left(\frac{3947}{5085}\right)$	$e\left(\frac{8413}{10170}\right)$	$e\left(\frac{517}{5085}\right)$	$e\left(\frac{557}{3390}\right)$	$e\left(\frac{73}{339}\right)$	$e\left(\frac{29}{10170}\right)$	$e\left(\frac{1073}{5085}\right)$	$e\left(\frac{4981}{10170}\right)$	$e\left(\frac{2809}{5085}\right)$
$\chi_{549261}(19,\cdot)$	549261.ga	1017	no	$1$	$1$	$e\left(\frac{553}{1017}\right)$	$e\left(\frac{89}{1017}\right)$	$e\left(\frac{20}{1017}\right)$	$e\left(\frac{82}{1017}\right)$	$e\left(\frac{214}{339}\right)$	$e\left(\frac{191}{339}\right)$	$e\left(\frac{439}{1017}\right)$	$e\left(\frac{959}{1017}\right)$	$e\left(\frac{635}{1017}\right)$	$e\left(\frac{178}{1017}\right)$
$\chi_{549261}(20,\cdot)$	549261.ju	30510	yes	$-1$	$1$	$e\left(\frac{27517}{30510}\right)$	$e\left(\frac{12262}{15255}\right)$	$e\left(\frac{1523}{30510}\right)$	$e\left(\frac{10292}{15255}\right)$	$e\left(\frac{7177}{10170}\right)$	$e\left(\frac{968}{1017}\right)$	$e\left(\frac{13039}{30510}\right)$	$e\left(\frac{14623}{15255}\right)$	$e\left(\frac{17591}{30510}\right)$	$e\left(\frac{9269}{15255}\right)$
$\chi_{549261}(22,\cdot)$	549261.kd	61020	yes	$-1$	$1$	$e\left(\frac{31687}{61020}\right)$	$e\left(\frac{1177}{30510}\right)$	$e\left(\frac{8869}{30510}\right)$	$e\left(\frac{51979}{61020}\right)$	$e\left(\frac{11347}{20340}\right)$	$e\left(\frac{3295}{4068}\right)$	$e\left(\frac{16547}{30510}\right)$	$e\left(\frac{13241}{61020}\right)$	$e\left(\frac{11323}{30510}\right)$	$e\left(\frac{1177}{15255}\right)$
$\chi_{549261}(23,\cdot)$	549261.jy	61020	yes	$1$	$1$	$e\left(\frac{22681}{61020}\right)$	$e\left(\frac{22681}{30510}\right)$	$e\left(\frac{4571}{15255}\right)$	$e\left(\frac{52387}{61020}\right)$	$e\left(\frac{2341}{20340}\right)$	$e\left(\frac{2731}{4068}\right)$	$e\left(\frac{9973}{15255}\right)$	$e\left(\frac{28133}{61020}\right)$	$e\left(\frac{3512}{15255}\right)$	$e\left(\frac{7426}{15255}\right)$
$\chi_{549261}(25,\cdot)$	549261.jh	15255	yes	$1$	$1$	$e\left(\frac{11123}{15255}\right)$	$e\left(\frac{6991}{15255}\right)$	$e\left(\frac{9787}{15255}\right)$	$e\left(\frac{7481}{15255}\right)$	$e\left(\frac{953}{5085}\right)$	$e\left(\frac{377}{1017}\right)$	$e\left(\frac{13001}{15255}\right)$	$e\left(\frac{1009}{15255}\right)$	$e\left(\frac{3349}{15255}\right)$	$e\left(\frac{13982}{15255}\right)$
$\chi_{549261}(26,\cdot)$	549261.hg	3390	no	$-1$	$1$	$e\left(\frac{1109}{1130}\right)$	$e\left(\frac{544}{565}\right)$	$e\left(\frac{3043}{3390}\right)$	$e\left(\frac{187}{1695}\right)$	$e\left(\frac{1067}{1130}\right)$	$e\left(\frac{298}{339}\right)$	$e\left(\frac{853}{1130}\right)$	$e\left(\frac{328}{1695}\right)$	$e\left(\frac{311}{3390}\right)$	$e\left(\frac{523}{565}\right)$
$\chi_{549261}(28,\cdot)$	549261.il	6780	no	$-1$	$1$	$e\left(\frac{5099}{6780}\right)$	$e\left(\frac{1709}{3390}\right)$	$e\left(\frac{1101}{1130}\right)$	$e\left(\frac{621}{2260}\right)$	$e\left(\frac{579}{2260}\right)$	$e\left(\frac{985}{1356}\right)$	$e\left(\frac{469}{3390}\right)$	$e\left(\frac{2177}{6780}\right)$	$e\left(\frac{91}{3390}\right)$	$e\left(\frac{14}{1695}\right)$
$\chi_{549261}(29,\cdot)$	549261.jt	30510	yes	$-1$	$1$	$e\left(\frac{143}{15255}\right)$	$e\left(\frac{286}{15255}\right)$	$e\left(\frac{27359}{30510}\right)$	$e\left(\frac{20947}{30510}\right)$	$e\left(\frac{143}{5085}\right)$	$e\left(\frac{1843}{2034}\right)$	$e\left(\frac{3907}{30510}\right)$	$e\left(\frac{29783}{30510}\right)$	$e\left(\frac{21233}{30510}\right)$	$e\left(\frac{572}{15255}\right)$
$\chi_{549261}(31,\cdot)$	549261.ka	61020	yes	$-1$	$1$	$e\left(\frac{38809}{61020}\right)$	$e\left(\frac{8299}{30510}\right)$	$e\left(\frac{15703}{30510}\right)$	$e\left(\frac{32353}{61020}\right)$	$e\left(\frac{18469}{20340}\right)$	$e\left(\frac{613}{4068}\right)$	$e\left(\frac{26309}{30510}\right)$	$e\left(\frac{3707}{61020}\right)$	$e\left(\frac{5071}{30510}\right)$	$e\left(\frac{8299}{15255}\right)$
$\chi_{549261}(32,\cdot)$	549261.jf	12204	yes	$1$	$1$	$e\left(\frac{1139}{12204}\right)$	$e\left(\frac{1139}{6102}\right)$	$e\left(\frac{985}{3051}\right)$	$e\left(\frac{7001}{12204}\right)$	$e\left(\frac{1139}{4068}\right)$	$e\left(\frac{1693}{4068}\right)$	$e\left(\frac{1535}{3051}\right)$	$e\left(\frac{9931}{12204}\right)$	$e\left(\frac{2035}{3051}\right)$	$e\left(\frac{1139}{3051}\right)$
$\chi_{549261}(34,\cdot)$	549261.kd	61020	yes	$-1$	$1$	$e\left(\frac{24821}{61020}\right)$	$e\left(\frac{24821}{30510}\right)$	$e\left(\frac{21107}{30510}\right)$	$e\left(\frac{49817}{61020}\right)$	$e\left(\frac{4481}{20340}\right)$	$e\left(\frac{401}{4068}\right)$	$e\left(\frac{15361}{30510}\right)$	$e\left(\frac{10603}{61020}\right)$	$e\left(\frac{6809}{30510}\right)$	$e\left(\frac{9566}{15255}\right)$
$\chi_{549261}(35,\cdot)$	549261.jm	20340	no	$1$	$1$	$e\left(\frac{11783}{20340}\right)$	$e\left(\frac{1613}{10170}\right)$	$e\left(\frac{2878}{5085}\right)$	$e\left(\frac{1841}{20340}\right)$	$e\left(\frac{5003}{6780}\right)$	$e\left(\frac{197}{1356}\right)$	$e\left(\frac{2864}{5085}\right)$	$e\left(\frac{8719}{20340}\right)$	$e\left(\frac{3406}{5085}\right)$	$e\left(\frac{1613}{5085}\right)$
$\chi_{549261}(37,\cdot)$	549261.iv	10170	no	$1$	$1$	$e\left(\frac{599}{10170}\right)$	$e\left(\frac{599}{5085}\right)$	$e\left(\frac{4793}{5085}\right)$	$e\left(\frac{10013}{10170}\right)$	$e\left(\frac{599}{3390}\right)$	$e\left(\frac{1}{678}\right)$	$e\left(\frac{2269}{5085}\right)$	$e\left(\frac{8677}{10170}\right)$	$e\left(\frac{221}{5085}\right)$	$e\left(\frac{1198}{5085}\right)$
$\chi_{549261}(38,\cdot)$	549261.jy	61020	yes	$1$	$1$	$e\left(\frac{34319}{61020}\right)$	$e\left(\frac{3809}{30510}\right)$	$e\left(\frac{13489}{15255}\right)$	$e\left(\frac{48533}{61020}\right)$	$e\left(\frac{13979}{20340}\right)$	$e\left(\frac{1817}{4068}\right)$	$e\left(\frac{14222}{15255}\right)$	$e\left(\frac{55267}{61020}\right)$	$e\left(\frac{5458}{15255}\right)$	$e\left(\frac{3809}{15255}\right)$
$\chi_{549261}(40,\cdot)$	549261.ka	61020	yes	$-1$	$1$	$e\left(\frac{56173}{61020}\right)$	$e\left(\frac{25663}{30510}\right)$	$e\left(\frac{27901}{30510}\right)$	$e\left(\frac{23761}{61020}\right)$	$e\left(\frac{15493}{20340}\right)$	$e\left(\frac{3397}{4068}\right)$	$e\left(\frac{28313}{30510}\right)$	$e\left(\frac{56219}{61020}\right)$	$e\left(\frac{9457}{30510}\right)$	$e\left(\frac{10408}{15255}\right)$
$\chi_{549261}(41,\cdot)$	549261.jv	30510	yes	$-1$	$1$	$e\left(\frac{9667}{15255}\right)$	$e\left(\frac{4079}{15255}\right)$	$e\left(\frac{7741}{30510}\right)$	$e\left(\frac{923}{30510}\right)$	$e\left(\frac{4582}{5085}\right)$	$e\left(\frac{1805}{2034}\right)$	$e\left(\frac{29213}{30510}\right)$	$e\left(\frac{637}{30510}\right)$	$e\left(\frac{20257}{30510}\right)$	$e\left(\frac{8158}{15255}\right)$
$\chi_{549261}(43,\cdot)$	549261.jd	12204	yes	$-1$	$1$	$e\left(\frac{6439}{12204}\right)$	$e\left(\frac{337}{6102}\right)$	$e\left(\frac{5275}{6102}\right)$	$e\left(\frac{6643}{12204}\right)$	$e\left(\frac{2371}{4068}\right)$	$e\left(\frac{1595}{4068}\right)$	$e\left(\frac{611}{6102}\right)$	$e\left(\frac{1949}{12204}\right)$	$e\left(\frac{439}{6102}\right)$	$e\left(\frac{337}{3051}\right)$
$\chi_{549261}(44,\cdot)$	549261.ix	10170	no	$-1$	$1$	$e\left(\frac{5471}{10170}\right)$	$e\left(\frac{386}{5085}\right)$	$e\left(\frac{1579}{10170}\right)$	$e\left(\frac{2881}{5085}\right)$	$e\left(\frac{2081}{3390}\right)$	$e\left(\frac{235}{339}\right)$	$e\left(\frac{437}{10170}\right)$	$e\left(\frac{914}{5085}\right)$	$e\left(\frac{1063}{10170}\right)$	$e\left(\frac{772}{5085}\right)$
$\chi_{549261}(46,\cdot)$	549261.ga	1017	no	$1$	$1$	$e\left(\frac{397}{1017}\right)$	$e\left(\frac{794}{1017}\right)$	$e\left(\frac{167}{1017}\right)$	$e\left(\frac{583}{1017}\right)$	$e\left(\frac{58}{339}\right)$	$e\left(\frac{188}{339}\right)$	$e\left(\frac{157}{1017}\right)$	$e\left(\frac{431}{1017}\right)$	$e\left(\frac{980}{1017}\right)$	$e\left(\frac{571}{1017}\right)$
$\chi_{549261}(47,\cdot)$	549261.jy	61020	yes	$1$	$1$	$e\left(\frac{8783}{61020}\right)$	$e\left(\frac{8783}{30510}\right)$	$e\left(\frac{8083}{15255}\right)$	$e\left(\frac{40421}{61020}\right)$	$e\left(\frac{8783}{20340}\right)$	$e\left(\frac{2741}{4068}\right)$	$e\left(\frac{13634}{15255}\right)$	$e\left(\frac{3259}{61020}\right)$	$e\left(\frac{12301}{15255}\right)$	$e\left(\frac{8783}{15255}\right)$

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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	$549261$
Structure	\(C_{6}\times C_{61020}\)
Order	$366120$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{549261}(1,\cdot)\)	549261.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{549261}(2,\cdot)\)	549261.jy	61020	yes	\(1\)	\(1\)	\(e\left(\frac{1139}{61020}\right)\)	\(e\left(\frac{1139}{30510}\right)\)	\(e\left(\frac{13189}{15255}\right)\)	\(e\left(\frac{43613}{61020}\right)\)	\(e\left(\frac{1139}{20340}\right)\)	\(e\left(\frac{3593}{4068}\right)\)	\(e\left(\frac{7637}{15255}\right)\)	\(e\left(\frac{58747}{61020}\right)\)	\(e\left(\frac{11188}{15255}\right)\)	\(e\left(\frac{1139}{15255}\right)\)
\(\chi_{549261}(4,\cdot)\)	549261.jx	30510	yes	\(1\)	\(1\)	\(e\left(\frac{1139}{30510}\right)\)	\(e\left(\frac{1139}{15255}\right)\)	\(e\left(\frac{11123}{15255}\right)\)	\(e\left(\frac{13103}{30510}\right)\)	\(e\left(\frac{1139}{10170}\right)\)	\(e\left(\frac{1559}{2034}\right)\)	\(e\left(\frac{19}{15255}\right)\)	\(e\left(\frac{28237}{30510}\right)\)	\(e\left(\frac{7121}{15255}\right)\)	\(e\left(\frac{2278}{15255}\right)\)
\(\chi_{549261}(5,\cdot)\)	549261.jt	30510	yes	\(-1\)	\(1\)	\(e\left(\frac{13189}{15255}\right)\)	\(e\left(\frac{11123}{15255}\right)\)	\(e\left(\frac{9787}{30510}\right)\)	\(e\left(\frac{7481}{30510}\right)\)	\(e\left(\frac{3019}{5085}\right)\)	\(e\left(\frac{377}{2034}\right)\)	\(e\left(\frac{13001}{30510}\right)\)	\(e\left(\frac{1009}{30510}\right)\)	\(e\left(\frac{3349}{30510}\right)\)	\(e\left(\frac{6991}{15255}\right)\)
\(\chi_{549261}(7,\cdot)\)	549261.ka	61020	yes	\(-1\)	\(1\)	\(e\left(\frac{43613}{61020}\right)\)	\(e\left(\frac{13103}{30510}\right)\)	\(e\left(\frac{7481}{30510}\right)\)	\(e\left(\frac{51581}{61020}\right)\)	\(e\left(\frac{2933}{20340}\right)\)	\(e\left(\frac{3905}{4068}\right)\)	\(e\left(\frac{4183}{30510}\right)\)	\(e\left(\frac{24139}{61020}\right)\)	\(e\left(\frac{17087}{30510}\right)\)	\(e\left(\frac{13103}{15255}\right)\)
\(\chi_{549261}(8,\cdot)\)	549261.jm	20340	no	\(1\)	\(1\)	\(e\left(\frac{1139}{20340}\right)\)	\(e\left(\frac{1139}{10170}\right)\)	\(e\left(\frac{3019}{5085}\right)\)	\(e\left(\frac{2933}{20340}\right)\)	\(e\left(\frac{1139}{6780}\right)\)	\(e\left(\frac{881}{1356}\right)\)	\(e\left(\frac{2552}{5085}\right)\)	\(e\left(\frac{18067}{20340}\right)\)	\(e\left(\frac{1018}{5085}\right)\)	\(e\left(\frac{1139}{5085}\right)\)
\(\chi_{549261}(10,\cdot)\)	549261.hv	4068	no	\(-1\)	\(1\)	\(e\left(\frac{3593}{4068}\right)\)	\(e\left(\frac{1559}{2034}\right)\)	\(e\left(\frac{377}{2034}\right)\)	\(e\left(\frac{3905}{4068}\right)\)	\(e\left(\frac{881}{1356}\right)\)	\(e\left(\frac{31}{452}\right)\)	\(e\left(\frac{1885}{2034}\right)\)	\(e\left(\frac{4051}{4068}\right)\)	\(e\left(\frac{1715}{2034}\right)\)	\(e\left(\frac{542}{1017}\right)\)
\(\chi_{549261}(11,\cdot)\)	549261.jq	30510	yes	\(-1\)	\(1\)	\(e\left(\frac{7637}{15255}\right)\)	\(e\left(\frac{19}{15255}\right)\)	\(e\left(\frac{13001}{30510}\right)\)	\(e\left(\frac{4183}{30510}\right)\)	\(e\left(\frac{2552}{5085}\right)\)	\(e\left(\frac{1885}{2034}\right)\)	\(e\left(\frac{1273}{30510}\right)\)	\(e\left(\frac{7757}{30510}\right)\)	\(e\left(\frac{19457}{30510}\right)\)	\(e\left(\frac{38}{15255}\right)\)
\(\chi_{549261}(13,\cdot)\)	549261.jz	61020	yes	\(-1\)	\(1\)	\(e\left(\frac{58747}{61020}\right)\)	\(e\left(\frac{28237}{30510}\right)\)	\(e\left(\frac{1009}{30510}\right)\)	\(e\left(\frac{24139}{61020}\right)\)	\(e\left(\frac{18067}{20340}\right)\)	\(e\left(\frac{4051}{4068}\right)\)	\(e\left(\frac{7757}{30510}\right)\)	\(e\left(\frac{14081}{61020}\right)\)	\(e\left(\frac{10933}{30510}\right)\)	\(e\left(\frac{12982}{15255}\right)\)
\(\chi_{549261}(14,\cdot)\)	549261.jv	30510	yes	\(-1\)	\(1\)	\(e\left(\frac{11188}{15255}\right)\)	\(e\left(\frac{7121}{15255}\right)\)	\(e\left(\frac{3349}{30510}\right)\)	\(e\left(\frac{17087}{30510}\right)\)	\(e\left(\frac{1018}{5085}\right)\)	\(e\left(\frac{1715}{2034}\right)\)	\(e\left(\frac{19457}{30510}\right)\)	\(e\left(\frac{10933}{30510}\right)\)	\(e\left(\frac{8953}{30510}\right)\)	\(e\left(\frac{14242}{15255}\right)\)
\(\chi_{549261}(16,\cdot)\)	549261.ji	15255	yes	\(1\)	\(1\)	\(e\left(\frac{1139}{15255}\right)\)	\(e\left(\frac{2278}{15255}\right)\)	\(e\left(\frac{6991}{15255}\right)\)	\(e\left(\frac{13103}{15255}\right)\)	\(e\left(\frac{1139}{5085}\right)\)	\(e\left(\frac{542}{1017}\right)\)	\(e\left(\frac{38}{15255}\right)\)	\(e\left(\frac{12982}{15255}\right)\)	\(e\left(\frac{14242}{15255}\right)\)	\(e\left(\frac{4556}{15255}\right)\)
\(\chi_{549261}(17,\cdot)\)	549261.ix	10170	no	\(-1\)	\(1\)	\(e\left(\frac{3947}{10170}\right)\)	\(e\left(\frac{3947}{5085}\right)\)	\(e\left(\frac{8413}{10170}\right)\)	\(e\left(\frac{517}{5085}\right)\)	\(e\left(\frac{557}{3390}\right)\)	\(e\left(\frac{73}{339}\right)\)	\(e\left(\frac{29}{10170}\right)\)	\(e\left(\frac{1073}{5085}\right)\)	\(e\left(\frac{4981}{10170}\right)\)	\(e\left(\frac{2809}{5085}\right)\)
\(\chi_{549261}(19,\cdot)\)	549261.ga	1017	no	\(1\)	\(1\)	\(e\left(\frac{553}{1017}\right)\)	\(e\left(\frac{89}{1017}\right)\)	\(e\left(\frac{20}{1017}\right)\)	\(e\left(\frac{82}{1017}\right)\)	\(e\left(\frac{214}{339}\right)\)	\(e\left(\frac{191}{339}\right)\)	\(e\left(\frac{439}{1017}\right)\)	\(e\left(\frac{959}{1017}\right)\)	\(e\left(\frac{635}{1017}\right)\)	\(e\left(\frac{178}{1017}\right)\)
\(\chi_{549261}(20,\cdot)\)	549261.ju	30510	yes	\(-1\)	\(1\)	\(e\left(\frac{27517}{30510}\right)\)	\(e\left(\frac{12262}{15255}\right)\)	\(e\left(\frac{1523}{30510}\right)\)	\(e\left(\frac{10292}{15255}\right)\)	\(e\left(\frac{7177}{10170}\right)\)	\(e\left(\frac{968}{1017}\right)\)	\(e\left(\frac{13039}{30510}\right)\)	\(e\left(\frac{14623}{15255}\right)\)	\(e\left(\frac{17591}{30510}\right)\)	\(e\left(\frac{9269}{15255}\right)\)
\(\chi_{549261}(22,\cdot)\)	549261.kd	61020	yes	\(-1\)	\(1\)	\(e\left(\frac{31687}{61020}\right)\)	\(e\left(\frac{1177}{30510}\right)\)	\(e\left(\frac{8869}{30510}\right)\)	\(e\left(\frac{51979}{61020}\right)\)	\(e\left(\frac{11347}{20340}\right)\)	\(e\left(\frac{3295}{4068}\right)\)	\(e\left(\frac{16547}{30510}\right)\)	\(e\left(\frac{13241}{61020}\right)\)	\(e\left(\frac{11323}{30510}\right)\)	\(e\left(\frac{1177}{15255}\right)\)
\(\chi_{549261}(23,\cdot)\)	549261.jy	61020	yes	\(1\)	\(1\)	\(e\left(\frac{22681}{61020}\right)\)	\(e\left(\frac{22681}{30510}\right)\)	\(e\left(\frac{4571}{15255}\right)\)	\(e\left(\frac{52387}{61020}\right)\)	\(e\left(\frac{2341}{20340}\right)\)	\(e\left(\frac{2731}{4068}\right)\)	\(e\left(\frac{9973}{15255}\right)\)	\(e\left(\frac{28133}{61020}\right)\)	\(e\left(\frac{3512}{15255}\right)\)	\(e\left(\frac{7426}{15255}\right)\)
\(\chi_{549261}(25,\cdot)\)	549261.jh	15255	yes	\(1\)	\(1\)	\(e\left(\frac{11123}{15255}\right)\)	\(e\left(\frac{6991}{15255}\right)\)	\(e\left(\frac{9787}{15255}\right)\)	\(e\left(\frac{7481}{15255}\right)\)	\(e\left(\frac{953}{5085}\right)\)	\(e\left(\frac{377}{1017}\right)\)	\(e\left(\frac{13001}{15255}\right)\)	\(e\left(\frac{1009}{15255}\right)\)	\(e\left(\frac{3349}{15255}\right)\)	\(e\left(\frac{13982}{15255}\right)\)
\(\chi_{549261}(26,\cdot)\)	549261.hg	3390	no	\(-1\)	\(1\)	\(e\left(\frac{1109}{1130}\right)\)	\(e\left(\frac{544}{565}\right)\)	\(e\left(\frac{3043}{3390}\right)\)	\(e\left(\frac{187}{1695}\right)\)	\(e\left(\frac{1067}{1130}\right)\)	\(e\left(\frac{298}{339}\right)\)	\(e\left(\frac{853}{1130}\right)\)	\(e\left(\frac{328}{1695}\right)\)	\(e\left(\frac{311}{3390}\right)\)	\(e\left(\frac{523}{565}\right)\)
\(\chi_{549261}(28,\cdot)\)	549261.il	6780	no	\(-1\)	\(1\)	\(e\left(\frac{5099}{6780}\right)\)	\(e\left(\frac{1709}{3390}\right)\)	\(e\left(\frac{1101}{1130}\right)\)	\(e\left(\frac{621}{2260}\right)\)	\(e\left(\frac{579}{2260}\right)\)	\(e\left(\frac{985}{1356}\right)\)	\(e\left(\frac{469}{3390}\right)\)	\(e\left(\frac{2177}{6780}\right)\)	\(e\left(\frac{91}{3390}\right)\)	\(e\left(\frac{14}{1695}\right)\)
\(\chi_{549261}(29,\cdot)\)	549261.jt	30510	yes	\(-1\)	\(1\)	\(e\left(\frac{143}{15255}\right)\)	\(e\left(\frac{286}{15255}\right)\)	\(e\left(\frac{27359}{30510}\right)\)	\(e\left(\frac{20947}{30510}\right)\)	\(e\left(\frac{143}{5085}\right)\)	\(e\left(\frac{1843}{2034}\right)\)	\(e\left(\frac{3907}{30510}\right)\)	\(e\left(\frac{29783}{30510}\right)\)	\(e\left(\frac{21233}{30510}\right)\)	\(e\left(\frac{572}{15255}\right)\)
\(\chi_{549261}(31,\cdot)\)	549261.ka	61020	yes	\(-1\)	\(1\)	\(e\left(\frac{38809}{61020}\right)\)	\(e\left(\frac{8299}{30510}\right)\)	\(e\left(\frac{15703}{30510}\right)\)	\(e\left(\frac{32353}{61020}\right)\)	\(e\left(\frac{18469}{20340}\right)\)	\(e\left(\frac{613}{4068}\right)\)	\(e\left(\frac{26309}{30510}\right)\)	\(e\left(\frac{3707}{61020}\right)\)	\(e\left(\frac{5071}{30510}\right)\)	\(e\left(\frac{8299}{15255}\right)\)
\(\chi_{549261}(32,\cdot)\)	549261.jf	12204	yes	\(1\)	\(1\)	\(e\left(\frac{1139}{12204}\right)\)	\(e\left(\frac{1139}{6102}\right)\)	\(e\left(\frac{985}{3051}\right)\)	\(e\left(\frac{7001}{12204}\right)\)	\(e\left(\frac{1139}{4068}\right)\)	\(e\left(\frac{1693}{4068}\right)\)	\(e\left(\frac{1535}{3051}\right)\)	\(e\left(\frac{9931}{12204}\right)\)	\(e\left(\frac{2035}{3051}\right)\)	\(e\left(\frac{1139}{3051}\right)\)
\(\chi_{549261}(34,\cdot)\)	549261.kd	61020	yes	\(-1\)	\(1\)	\(e\left(\frac{24821}{61020}\right)\)	\(e\left(\frac{24821}{30510}\right)\)	\(e\left(\frac{21107}{30510}\right)\)	\(e\left(\frac{49817}{61020}\right)\)	\(e\left(\frac{4481}{20340}\right)\)	\(e\left(\frac{401}{4068}\right)\)	\(e\left(\frac{15361}{30510}\right)\)	\(e\left(\frac{10603}{61020}\right)\)	\(e\left(\frac{6809}{30510}\right)\)	\(e\left(\frac{9566}{15255}\right)\)
\(\chi_{549261}(35,\cdot)\)	549261.jm	20340	no	\(1\)	\(1\)	\(e\left(\frac{11783}{20340}\right)\)	\(e\left(\frac{1613}{10170}\right)\)	\(e\left(\frac{2878}{5085}\right)\)	\(e\left(\frac{1841}{20340}\right)\)	\(e\left(\frac{5003}{6780}\right)\)	\(e\left(\frac{197}{1356}\right)\)	\(e\left(\frac{2864}{5085}\right)\)	\(e\left(\frac{8719}{20340}\right)\)	\(e\left(\frac{3406}{5085}\right)\)	\(e\left(\frac{1613}{5085}\right)\)
\(\chi_{549261}(37,\cdot)\)	549261.iv	10170	no	\(1\)	\(1\)	\(e\left(\frac{599}{10170}\right)\)	\(e\left(\frac{599}{5085}\right)\)	\(e\left(\frac{4793}{5085}\right)\)	\(e\left(\frac{10013}{10170}\right)\)	\(e\left(\frac{599}{3390}\right)\)	\(e\left(\frac{1}{678}\right)\)	\(e\left(\frac{2269}{5085}\right)\)	\(e\left(\frac{8677}{10170}\right)\)	\(e\left(\frac{221}{5085}\right)\)	\(e\left(\frac{1198}{5085}\right)\)
\(\chi_{549261}(38,\cdot)\)	549261.jy	61020	yes	\(1\)	\(1\)	\(e\left(\frac{34319}{61020}\right)\)	\(e\left(\frac{3809}{30510}\right)\)	\(e\left(\frac{13489}{15255}\right)\)	\(e\left(\frac{48533}{61020}\right)\)	\(e\left(\frac{13979}{20340}\right)\)	\(e\left(\frac{1817}{4068}\right)\)	\(e\left(\frac{14222}{15255}\right)\)	\(e\left(\frac{55267}{61020}\right)\)	\(e\left(\frac{5458}{15255}\right)\)	\(e\left(\frac{3809}{15255}\right)\)
\(\chi_{549261}(40,\cdot)\)	549261.ka	61020	yes	\(-1\)	\(1\)	\(e\left(\frac{56173}{61020}\right)\)	\(e\left(\frac{25663}{30510}\right)\)	\(e\left(\frac{27901}{30510}\right)\)	\(e\left(\frac{23761}{61020}\right)\)	\(e\left(\frac{15493}{20340}\right)\)	\(e\left(\frac{3397}{4068}\right)\)	\(e\left(\frac{28313}{30510}\right)\)	\(e\left(\frac{56219}{61020}\right)\)	\(e\left(\frac{9457}{30510}\right)\)	\(e\left(\frac{10408}{15255}\right)\)
\(\chi_{549261}(41,\cdot)\)	549261.jv	30510	yes	\(-1\)	\(1\)	\(e\left(\frac{9667}{15255}\right)\)	\(e\left(\frac{4079}{15255}\right)\)	\(e\left(\frac{7741}{30510}\right)\)	\(e\left(\frac{923}{30510}\right)\)	\(e\left(\frac{4582}{5085}\right)\)	\(e\left(\frac{1805}{2034}\right)\)	\(e\left(\frac{29213}{30510}\right)\)	\(e\left(\frac{637}{30510}\right)\)	\(e\left(\frac{20257}{30510}\right)\)	\(e\left(\frac{8158}{15255}\right)\)
\(\chi_{549261}(43,\cdot)\)	549261.jd	12204	yes	\(-1\)	\(1\)	\(e\left(\frac{6439}{12204}\right)\)	\(e\left(\frac{337}{6102}\right)\)	\(e\left(\frac{5275}{6102}\right)\)	\(e\left(\frac{6643}{12204}\right)\)	\(e\left(\frac{2371}{4068}\right)\)	\(e\left(\frac{1595}{4068}\right)\)	\(e\left(\frac{611}{6102}\right)\)	\(e\left(\frac{1949}{12204}\right)\)	\(e\left(\frac{439}{6102}\right)\)	\(e\left(\frac{337}{3051}\right)\)
\(\chi_{549261}(44,\cdot)\)	549261.ix	10170	no	\(-1\)	\(1\)	\(e\left(\frac{5471}{10170}\right)\)	\(e\left(\frac{386}{5085}\right)\)	\(e\left(\frac{1579}{10170}\right)\)	\(e\left(\frac{2881}{5085}\right)\)	\(e\left(\frac{2081}{3390}\right)\)	\(e\left(\frac{235}{339}\right)\)	\(e\left(\frac{437}{10170}\right)\)	\(e\left(\frac{914}{5085}\right)\)	\(e\left(\frac{1063}{10170}\right)\)	\(e\left(\frac{772}{5085}\right)\)
\(\chi_{549261}(46,\cdot)\)	549261.ga	1017	no	\(1\)	\(1\)	\(e\left(\frac{397}{1017}\right)\)	\(e\left(\frac{794}{1017}\right)\)	\(e\left(\frac{167}{1017}\right)\)	\(e\left(\frac{583}{1017}\right)\)	\(e\left(\frac{58}{339}\right)\)	\(e\left(\frac{188}{339}\right)\)	\(e\left(\frac{157}{1017}\right)\)	\(e\left(\frac{431}{1017}\right)\)	\(e\left(\frac{980}{1017}\right)\)	\(e\left(\frac{571}{1017}\right)\)
\(\chi_{549261}(47,\cdot)\)	549261.jy	61020	yes	\(1\)	\(1\)	\(e\left(\frac{8783}{61020}\right)\)	\(e\left(\frac{8783}{30510}\right)\)	\(e\left(\frac{8083}{15255}\right)\)	\(e\left(\frac{40421}{61020}\right)\)	\(e\left(\frac{8783}{20340}\right)\)	\(e\left(\frac{2741}{4068}\right)\)	\(e\left(\frac{13634}{15255}\right)\)	\(e\left(\frac{3259}{61020}\right)\)	\(e\left(\frac{12301}{15255}\right)\)	\(e\left(\frac{8783}{15255}\right)\)

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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.