LMFDB - Group of Dirichlet characters of modulus 393129

Show commands: PariGP / SageMath

sage: H = DirichletGroup(393129)

pari: g = idealstar(,393129,2)

Character group

sage: G.order() pari: g.no
Order	=	225720
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{18810}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{393129}(305768,\cdot)$, $\chi_{393129}(152704,\cdot)$, $\chi_{393129}(327790,\cdot)$

First 32 of 225720 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{393129}(1,\cdot)$	393129.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{393129}(2,\cdot)$	393129.to	18810	yes	$-1$	$1$	$e\left(\frac{3361}{18810}\right)$	$e\left(\frac{3361}{9405}\right)$	$e\left(\frac{3469}{18810}\right)$	$e\left(\frac{353}{2090}\right)$	$e\left(\frac{3361}{6270}\right)$	$e\left(\frac{683}{1881}\right)$	$e\left(\frac{2008}{9405}\right)$	$e\left(\frac{3269}{9405}\right)$	$e\left(\frac{6722}{9405}\right)$	$e\left(\frac{5702}{9405}\right)$
$\chi_{393129}(4,\cdot)$	393129.su	9405	yes	$1$	$1$	$e\left(\frac{3361}{9405}\right)$	$e\left(\frac{6722}{9405}\right)$	$e\left(\frac{3469}{9405}\right)$	$e\left(\frac{353}{1045}\right)$	$e\left(\frac{226}{3135}\right)$	$e\left(\frac{1366}{1881}\right)$	$e\left(\frac{4016}{9405}\right)$	$e\left(\frac{6538}{9405}\right)$	$e\left(\frac{4039}{9405}\right)$	$e\left(\frac{1999}{9405}\right)$
$\chi_{393129}(5,\cdot)$	393129.tj	18810	yes	$-1$	$1$	$e\left(\frac{3469}{18810}\right)$	$e\left(\frac{3469}{9405}\right)$	$e\left(\frac{6181}{18810}\right)$	$e\left(\frac{2498}{3135}\right)$	$e\left(\frac{3469}{6270}\right)$	$e\left(\frac{965}{1881}\right)$	$e\left(\frac{7462}{9405}\right)$	$e\left(\frac{18457}{18810}\right)$	$e\left(\frac{6938}{9405}\right)$	$e\left(\frac{14551}{18810}\right)$
$\chi_{393129}(7,\cdot)$	393129.ss	6270	yes	$-1$	$1$	$e\left(\frac{353}{2090}\right)$	$e\left(\frac{353}{1045}\right)$	$e\left(\frac{2498}{3135}\right)$	$e\left(\frac{5653}{6270}\right)$	$e\left(\frac{1059}{2090}\right)$	$e\left(\frac{1211}{1254}\right)$	$e\left(\frac{123}{2090}\right)$	$e\left(\frac{221}{3135}\right)$	$e\left(\frac{706}{1045}\right)$	$e\left(\frac{1511}{6270}\right)$
$\chi_{393129}(8,\cdot)$	393129.sa	6270	no	$-1$	$1$	$e\left(\frac{3361}{6270}\right)$	$e\left(\frac{226}{3135}\right)$	$e\left(\frac{3469}{6270}\right)$	$e\left(\frac{1059}{2090}\right)$	$e\left(\frac{1271}{2090}\right)$	$e\left(\frac{56}{627}\right)$	$e\left(\frac{2008}{3135}\right)$	$e\left(\frac{134}{3135}\right)$	$e\left(\frac{452}{3135}\right)$	$e\left(\frac{2567}{3135}\right)$
$\chi_{393129}(10,\cdot)$	393129.rk	3762	no	$1$	$1$	$e\left(\frac{683}{1881}\right)$	$e\left(\frac{1366}{1881}\right)$	$e\left(\frac{965}{1881}\right)$	$e\left(\frac{1211}{1254}\right)$	$e\left(\frac{56}{627}\right)$	$e\left(\frac{1648}{1881}\right)$	$e\left(\frac{13}{1881}\right)$	$e\left(\frac{1237}{3762}\right)$	$e\left(\frac{851}{1881}\right)$	$e\left(\frac{1429}{3762}\right)$
$\chi_{393129}(13,\cdot)$	393129.tr	18810	yes	$1$	$1$	$e\left(\frac{2008}{9405}\right)$	$e\left(\frac{4016}{9405}\right)$	$e\left(\frac{7462}{9405}\right)$	$e\left(\frac{123}{2090}\right)$	$e\left(\frac{2008}{3135}\right)$	$e\left(\frac{13}{1881}\right)$	$e\left(\frac{8438}{9405}\right)$	$e\left(\frac{5123}{18810}\right)$	$e\left(\frac{8032}{9405}\right)$	$e\left(\frac{7529}{18810}\right)$
$\chi_{393129}(14,\cdot)$	393129.tm	18810	yes	$1$	$1$	$e\left(\frac{3269}{9405}\right)$	$e\left(\frac{6538}{9405}\right)$	$e\left(\frac{18457}{18810}\right)$	$e\left(\frac{221}{3135}\right)$	$e\left(\frac{134}{3135}\right)$	$e\left(\frac{1237}{3762}\right)$	$e\left(\frac{5123}{18810}\right)$	$e\left(\frac{3932}{9405}\right)$	$e\left(\frac{3671}{9405}\right)$	$e\left(\frac{15937}{18810}\right)$
$\chi_{393129}(16,\cdot)$	393129.su	9405	yes	$1$	$1$	$e\left(\frac{6722}{9405}\right)$	$e\left(\frac{4039}{9405}\right)$	$e\left(\frac{6938}{9405}\right)$	$e\left(\frac{706}{1045}\right)$	$e\left(\frac{452}{3135}\right)$	$e\left(\frac{851}{1881}\right)$	$e\left(\frac{8032}{9405}\right)$	$e\left(\frac{3671}{9405}\right)$	$e\left(\frac{8078}{9405}\right)$	$e\left(\frac{3998}{9405}\right)$
$\chi_{393129}(17,\cdot)$	393129.th	18810	no	$1$	$1$	$e\left(\frac{5702}{9405}\right)$	$e\left(\frac{1999}{9405}\right)$	$e\left(\frac{14551}{18810}\right)$	$e\left(\frac{1511}{6270}\right)$	$e\left(\frac{2567}{3135}\right)$	$e\left(\frac{1429}{3762}\right)$	$e\left(\frac{7529}{18810}\right)$	$e\left(\frac{15937}{18810}\right)$	$e\left(\frac{3998}{9405}\right)$	$e\left(\frac{6323}{9405}\right)$
$\chi_{393129}(20,\cdot)$	393129.rz	6270	yes	$-1$	$1$	$e\left(\frac{3397}{6270}\right)$	$e\left(\frac{262}{3135}\right)$	$e\left(\frac{4373}{6270}\right)$	$e\left(\frac{422}{3135}\right)$	$e\left(\frac{1307}{2090}\right)$	$e\left(\frac{50}{209}\right)$	$e\left(\frac{691}{3135}\right)$	$e\left(\frac{4241}{6270}\right)$	$e\left(\frac{524}{3135}\right)$	$e\left(\frac{2061}{2090}\right)$
$\chi_{393129}(23,\cdot)$	393129.rr	3762	yes	$-1$	$1$	$e\left(\frac{3373}{3762}\right)$	$e\left(\frac{1492}{1881}\right)$	$e\left(\frac{1123}{3762}\right)$	$e\left(\frac{172}{209}\right)$	$e\left(\frac{865}{1254}\right)$	$e\left(\frac{367}{1881}\right)$	$e\left(\frac{733}{1881}\right)$	$e\left(\frac{2707}{3762}\right)$	$e\left(\frac{1103}{1881}\right)$	$e\left(\frac{607}{3762}\right)$
$\chi_{393129}(25,\cdot)$	393129.sw	9405	yes	$1$	$1$	$e\left(\frac{3469}{9405}\right)$	$e\left(\frac{6938}{9405}\right)$	$e\left(\frac{6181}{9405}\right)$	$e\left(\frac{1861}{3135}\right)$	$e\left(\frac{334}{3135}\right)$	$e\left(\frac{49}{1881}\right)$	$e\left(\frac{5519}{9405}\right)$	$e\left(\frac{9052}{9405}\right)$	$e\left(\frac{4471}{9405}\right)$	$e\left(\frac{5146}{9405}\right)$
$\chi_{393129}(26,\cdot)$	393129.rx	6270	no	$-1$	$1$	$e\left(\frac{2459}{6270}\right)$	$e\left(\frac{2459}{3135}\right)$	$e\left(\frac{6131}{6270}\right)$	$e\left(\frac{238}{1045}\right)$	$e\left(\frac{369}{2090}\right)$	$e\left(\frac{232}{627}\right)$	$e\left(\frac{347}{3135}\right)$	$e\left(\frac{3887}{6270}\right)$	$e\left(\frac{1783}{3135}\right)$	$e\left(\frac{41}{6270}\right)$
$\chi_{393129}(28,\cdot)$	393129.oh	990	no	$-1$	$1$	$e\left(\frac{521}{990}\right)$	$e\left(\frac{26}{495}\right)$	$e\left(\frac{82}{495}\right)$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{191}{330}\right)$	$e\left(\frac{137}{198}\right)$	$e\left(\frac{481}{990}\right)$	$e\left(\frac{379}{495}\right)$	$e\left(\frac{52}{495}\right)$	$e\left(\frac{449}{990}\right)$
$\chi_{393129}(29,\cdot)$	393129.tb	18810	yes	$-1$	$1$	$e\left(\frac{6977}{18810}\right)$	$e\left(\frac{6977}{9405}\right)$	$e\left(\frac{15083}{18810}\right)$	$e\left(\frac{1283}{6270}\right)$	$e\left(\frac{707}{6270}\right)$	$e\left(\frac{325}{1881}\right)$	$e\left(\frac{2786}{9405}\right)$	$e\left(\frac{5413}{9405}\right)$	$e\left(\frac{4549}{9405}\right)$	$e\left(\frac{2884}{9405}\right)$
$\chi_{393129}(31,\cdot)$	393129.rw	6270	yes	$-1$	$1$	$e\left(\frac{7}{6270}\right)$	$e\left(\frac{7}{3135}\right)$	$e\left(\frac{68}{1045}\right)$	$e\left(\frac{2197}{3135}\right)$	$e\left(\frac{7}{2090}\right)$	$e\left(\frac{83}{1254}\right)$	$e\left(\frac{707}{6270}\right)$	$e\left(\frac{1467}{2090}\right)$	$e\left(\frac{14}{3135}\right)$	$e\left(\frac{1684}{3135}\right)$
$\chi_{393129}(32,\cdot)$	393129.ra	3762	yes	$-1$	$1$	$e\left(\frac{3361}{3762}\right)$	$e\left(\frac{1480}{1881}\right)$	$e\left(\frac{3469}{3762}\right)$	$e\left(\frac{353}{418}\right)$	$e\left(\frac{853}{1254}\right)$	$e\left(\frac{1534}{1881}\right)$	$e\left(\frac{127}{1881}\right)$	$e\left(\frac{1388}{1881}\right)$	$e\left(\frac{1079}{1881}\right)$	$e\left(\frac{59}{1881}\right)$
$\chi_{393129}(34,\cdot)$	393129.re	3762	yes	$-1$	$1$	$e\left(\frac{2953}{3762}\right)$	$e\left(\frac{1072}{1881}\right)$	$e\left(\frac{1802}{1881}\right)$	$e\left(\frac{257}{627}\right)$	$e\left(\frac{445}{1254}\right)$	$e\left(\frac{2795}{3762}\right)$	$e\left(\frac{2309}{3762}\right)$	$e\left(\frac{733}{3762}\right)$	$e\left(\frac{263}{1881}\right)$	$e\left(\frac{524}{1881}\right)$
$\chi_{393129}(35,\cdot)$	393129.th	18810	no	$1$	$1$	$e\left(\frac{3323}{9405}\right)$	$e\left(\frac{6646}{9405}\right)$	$e\left(\frac{2359}{18810}\right)$	$e\left(\frac{4379}{6270}\right)$	$e\left(\frac{188}{3135}\right)$	$e\left(\frac{1801}{3762}\right)$	$e\left(\frac{16031}{18810}\right)$	$e\left(\frac{973}{18810}\right)$	$e\left(\frac{3887}{9405}\right)$	$e\left(\frac{137}{9405}\right)$
$\chi_{393129}(37,\cdot)$	393129.qp	2090	no	$-1$	$1$	$e\left(\frac{1073}{2090}\right)$	$e\left(\frac{28}{1045}\right)$	$e\left(\frac{816}{1045}\right)$	$e\left(\frac{428}{1045}\right)$	$e\left(\frac{1129}{2090}\right)$	$e\left(\frac{123}{418}\right)$	$e\left(\frac{1783}{2090}\right)$	$e\left(\frac{1929}{2090}\right)$	$e\left(\frac{56}{1045}\right)$	$e\left(\frac{466}{1045}\right)$
$\chi_{393129}(40,\cdot)$	393129.pz	1710	no	$1$	$1$	$e\left(\frac{616}{855}\right)$	$e\left(\frac{377}{855}\right)$	$e\left(\frac{754}{855}\right)$	$e\left(\frac{173}{570}\right)$	$e\left(\frac{46}{285}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{371}{855}\right)$	$e\left(\frac{41}{1710}\right)$	$e\left(\frac{754}{855}\right)$	$e\left(\frac{1013}{1710}\right)$
$\chi_{393129}(41,\cdot)$	393129.tb	18810	yes	$-1$	$1$	$e\left(\frac{4483}{18810}\right)$	$e\left(\frac{4483}{9405}\right)$	$e\left(\frac{1687}{18810}\right)$	$e\left(\frac{1147}{6270}\right)$	$e\left(\frac{4483}{6270}\right)$	$e\left(\frac{617}{1881}\right)$	$e\left(\frac{2239}{9405}\right)$	$e\left(\frac{3962}{9405}\right)$	$e\left(\frac{8966}{9405}\right)$	$e\left(\frac{191}{9405}\right)$
$\chi_{393129}(43,\cdot)$	393129.qz	3762	yes	$-1$	$1$	$e\left(\frac{173}{3762}\right)$	$e\left(\frac{173}{1881}\right)$	$e\left(\frac{802}{1881}\right)$	$e\left(\frac{27}{418}\right)$	$e\left(\frac{173}{1254}\right)$	$e\left(\frac{1777}{3762}\right)$	$e\left(\frac{1171}{3762}\right)$	$e\left(\frac{208}{1881}\right)$	$e\left(\frac{346}{1881}\right)$	$e\left(\frac{1877}{3762}\right)$
$\chi_{393129}(46,\cdot)$	393129.sn	6270	no	$1$	$1$	$e\left(\frac{236}{3135}\right)$	$e\left(\frac{472}{3135}\right)$	$e\left(\frac{1514}{3135}\right)$	$e\left(\frac{2073}{2090}\right)$	$e\left(\frac{236}{1045}\right)$	$e\left(\frac{350}{627}\right)$	$e\left(\frac{1891}{3135}\right)$	$e\left(\frac{421}{6270}\right)$	$e\left(\frac{944}{3135}\right)$	$e\left(\frac{4813}{6270}\right)$
$\chi_{393129}(47,\cdot)$	393129.tj	18810	yes	$-1$	$1$	$e\left(\frac{2513}{18810}\right)$	$e\left(\frac{2513}{9405}\right)$	$e\left(\frac{7487}{18810}\right)$	$e\left(\frac{961}{3135}\right)$	$e\left(\frac{2513}{6270}\right)$	$e\left(\frac{1000}{1881}\right)$	$e\left(\frac{3074}{9405}\right)$	$e\left(\frac{8279}{18810}\right)$	$e\left(\frac{5026}{9405}\right)$	$e\left(\frac{6317}{18810}\right)$
$\chi_{393129}(49,\cdot)$	393129.qt	3135	yes	$1$	$1$	$e\left(\frac{353}{1045}\right)$	$e\left(\frac{706}{1045}\right)$	$e\left(\frac{1861}{3135}\right)$	$e\left(\frac{2518}{3135}\right)$	$e\left(\frac{14}{1045}\right)$	$e\left(\frac{584}{627}\right)$	$e\left(\frac{123}{1045}\right)$	$e\left(\frac{442}{3135}\right)$	$e\left(\frac{367}{1045}\right)$	$e\left(\frac{1511}{3135}\right)$
$\chi_{393129}(50,\cdot)$	393129.sf	6270	yes	$-1$	$1$	$e\left(\frac{3433}{6270}\right)$	$e\left(\frac{298}{3135}\right)$	$e\left(\frac{1759}{2090}\right)$	$e\left(\frac{4781}{6270}\right)$	$e\left(\frac{1343}{2090}\right)$	$e\left(\frac{244}{627}\right)$	$e\left(\frac{2509}{3135}\right)$	$e\left(\frac{324}{1045}\right)$	$e\left(\frac{596}{3135}\right)$	$e\left(\frac{481}{3135}\right)$
$\chi_{393129}(52,\cdot)$	393129.tr	18810	yes	$1$	$1$	$e\left(\frac{5369}{9405}\right)$	$e\left(\frac{1333}{9405}\right)$	$e\left(\frac{1526}{9405}\right)$	$e\left(\frac{829}{2090}\right)$	$e\left(\frac{2234}{3135}\right)$	$e\left(\frac{1379}{1881}\right)$	$e\left(\frac{3049}{9405}\right)$	$e\left(\frac{18199}{18810}\right)$	$e\left(\frac{2666}{9405}\right)$	$e\left(\frac{11527}{18810}\right)$
$\chi_{393129}(53,\cdot)$	393129.tn	18810	no	$1$	$1$	$e\left(\frac{6643}{9405}\right)$	$e\left(\frac{3881}{9405}\right)$	$e\left(\frac{2129}{18810}\right)$	$e\left(\frac{467}{3135}\right)$	$e\left(\frac{373}{3135}\right)$	$e\left(\frac{3083}{3762}\right)$	$e\left(\frac{3241}{18810}\right)$	$e\left(\frac{8044}{9405}\right)$	$e\left(\frac{7762}{9405}\right)$	$e\left(\frac{10649}{18810}\right)$
$\chi_{393129}(56,\cdot)$	393129.ov	1254	yes	$1$	$1$	$e\left(\frac{442}{627}\right)$	$e\left(\frac{257}{627}\right)$	$e\left(\frac{439}{1254}\right)$	$e\left(\frac{256}{627}\right)$	$e\left(\frac{24}{209}\right)$	$e\left(\frac{23}{418}\right)$	$e\left(\frac{877}{1254}\right)$	$e\left(\frac{71}{627}\right)$	$e\left(\frac{514}{627}\right)$	$e\left(\frac{25}{418}\right)$

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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	$393129$
Structure	\(C_{2}\times C_{6}\times C_{18810}\)
Order	$225720$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\(\chi_{393129}(1,\cdot)\)	393129.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{393129}(2,\cdot)\)	393129.to	18810	yes	\(-1\)	\(1\)	\(e\left(\frac{3361}{18810}\right)\)	\(e\left(\frac{3361}{9405}\right)\)	\(e\left(\frac{3469}{18810}\right)\)	\(e\left(\frac{353}{2090}\right)\)	\(e\left(\frac{3361}{6270}\right)\)	\(e\left(\frac{683}{1881}\right)\)	\(e\left(\frac{2008}{9405}\right)\)	\(e\left(\frac{3269}{9405}\right)\)	\(e\left(\frac{6722}{9405}\right)\)	\(e\left(\frac{5702}{9405}\right)\)
\(\chi_{393129}(4,\cdot)\)	393129.su	9405	yes	\(1\)	\(1\)	\(e\left(\frac{3361}{9405}\right)\)	\(e\left(\frac{6722}{9405}\right)\)	\(e\left(\frac{3469}{9405}\right)\)	\(e\left(\frac{353}{1045}\right)\)	\(e\left(\frac{226}{3135}\right)\)	\(e\left(\frac{1366}{1881}\right)\)	\(e\left(\frac{4016}{9405}\right)\)	\(e\left(\frac{6538}{9405}\right)\)	\(e\left(\frac{4039}{9405}\right)\)	\(e\left(\frac{1999}{9405}\right)\)
\(\chi_{393129}(5,\cdot)\)	393129.tj	18810	yes	\(-1\)	\(1\)	\(e\left(\frac{3469}{18810}\right)\)	\(e\left(\frac{3469}{9405}\right)\)	\(e\left(\frac{6181}{18810}\right)\)	\(e\left(\frac{2498}{3135}\right)\)	\(e\left(\frac{3469}{6270}\right)\)	\(e\left(\frac{965}{1881}\right)\)	\(e\left(\frac{7462}{9405}\right)\)	\(e\left(\frac{18457}{18810}\right)\)	\(e\left(\frac{6938}{9405}\right)\)	\(e\left(\frac{14551}{18810}\right)\)
\(\chi_{393129}(7,\cdot)\)	393129.ss	6270	yes	\(-1\)	\(1\)	\(e\left(\frac{353}{2090}\right)\)	\(e\left(\frac{353}{1045}\right)\)	\(e\left(\frac{2498}{3135}\right)\)	\(e\left(\frac{5653}{6270}\right)\)	\(e\left(\frac{1059}{2090}\right)\)	\(e\left(\frac{1211}{1254}\right)\)	\(e\left(\frac{123}{2090}\right)\)	\(e\left(\frac{221}{3135}\right)\)	\(e\left(\frac{706}{1045}\right)\)	\(e\left(\frac{1511}{6270}\right)\)
\(\chi_{393129}(8,\cdot)\)	393129.sa	6270	no	\(-1\)	\(1\)	\(e\left(\frac{3361}{6270}\right)\)	\(e\left(\frac{226}{3135}\right)\)	\(e\left(\frac{3469}{6270}\right)\)	\(e\left(\frac{1059}{2090}\right)\)	\(e\left(\frac{1271}{2090}\right)\)	\(e\left(\frac{56}{627}\right)\)	\(e\left(\frac{2008}{3135}\right)\)	\(e\left(\frac{134}{3135}\right)\)	\(e\left(\frac{452}{3135}\right)\)	\(e\left(\frac{2567}{3135}\right)\)
\(\chi_{393129}(10,\cdot)\)	393129.rk	3762	no	\(1\)	\(1\)	\(e\left(\frac{683}{1881}\right)\)	\(e\left(\frac{1366}{1881}\right)\)	\(e\left(\frac{965}{1881}\right)\)	\(e\left(\frac{1211}{1254}\right)\)	\(e\left(\frac{56}{627}\right)\)	\(e\left(\frac{1648}{1881}\right)\)	\(e\left(\frac{13}{1881}\right)\)	\(e\left(\frac{1237}{3762}\right)\)	\(e\left(\frac{851}{1881}\right)\)	\(e\left(\frac{1429}{3762}\right)\)
\(\chi_{393129}(13,\cdot)\)	393129.tr	18810	yes	\(1\)	\(1\)	\(e\left(\frac{2008}{9405}\right)\)	\(e\left(\frac{4016}{9405}\right)\)	\(e\left(\frac{7462}{9405}\right)\)	\(e\left(\frac{123}{2090}\right)\)	\(e\left(\frac{2008}{3135}\right)\)	\(e\left(\frac{13}{1881}\right)\)	\(e\left(\frac{8438}{9405}\right)\)	\(e\left(\frac{5123}{18810}\right)\)	\(e\left(\frac{8032}{9405}\right)\)	\(e\left(\frac{7529}{18810}\right)\)
\(\chi_{393129}(14,\cdot)\)	393129.tm	18810	yes	\(1\)	\(1\)	\(e\left(\frac{3269}{9405}\right)\)	\(e\left(\frac{6538}{9405}\right)\)	\(e\left(\frac{18457}{18810}\right)\)	\(e\left(\frac{221}{3135}\right)\)	\(e\left(\frac{134}{3135}\right)\)	\(e\left(\frac{1237}{3762}\right)\)	\(e\left(\frac{5123}{18810}\right)\)	\(e\left(\frac{3932}{9405}\right)\)	\(e\left(\frac{3671}{9405}\right)\)	\(e\left(\frac{15937}{18810}\right)\)
\(\chi_{393129}(16,\cdot)\)	393129.su	9405	yes	\(1\)	\(1\)	\(e\left(\frac{6722}{9405}\right)\)	\(e\left(\frac{4039}{9405}\right)\)	\(e\left(\frac{6938}{9405}\right)\)	\(e\left(\frac{706}{1045}\right)\)	\(e\left(\frac{452}{3135}\right)\)	\(e\left(\frac{851}{1881}\right)\)	\(e\left(\frac{8032}{9405}\right)\)	\(e\left(\frac{3671}{9405}\right)\)	\(e\left(\frac{8078}{9405}\right)\)	\(e\left(\frac{3998}{9405}\right)\)
\(\chi_{393129}(17,\cdot)\)	393129.th	18810	no	\(1\)	\(1\)	\(e\left(\frac{5702}{9405}\right)\)	\(e\left(\frac{1999}{9405}\right)\)	\(e\left(\frac{14551}{18810}\right)\)	\(e\left(\frac{1511}{6270}\right)\)	\(e\left(\frac{2567}{3135}\right)\)	\(e\left(\frac{1429}{3762}\right)\)	\(e\left(\frac{7529}{18810}\right)\)	\(e\left(\frac{15937}{18810}\right)\)	\(e\left(\frac{3998}{9405}\right)\)	\(e\left(\frac{6323}{9405}\right)\)
\(\chi_{393129}(20,\cdot)\)	393129.rz	6270	yes	\(-1\)	\(1\)	\(e\left(\frac{3397}{6270}\right)\)	\(e\left(\frac{262}{3135}\right)\)	\(e\left(\frac{4373}{6270}\right)\)	\(e\left(\frac{422}{3135}\right)\)	\(e\left(\frac{1307}{2090}\right)\)	\(e\left(\frac{50}{209}\right)\)	\(e\left(\frac{691}{3135}\right)\)	\(e\left(\frac{4241}{6270}\right)\)	\(e\left(\frac{524}{3135}\right)\)	\(e\left(\frac{2061}{2090}\right)\)
\(\chi_{393129}(23,\cdot)\)	393129.rr	3762	yes	\(-1\)	\(1\)	\(e\left(\frac{3373}{3762}\right)\)	\(e\left(\frac{1492}{1881}\right)\)	\(e\left(\frac{1123}{3762}\right)\)	\(e\left(\frac{172}{209}\right)\)	\(e\left(\frac{865}{1254}\right)\)	\(e\left(\frac{367}{1881}\right)\)	\(e\left(\frac{733}{1881}\right)\)	\(e\left(\frac{2707}{3762}\right)\)	\(e\left(\frac{1103}{1881}\right)\)	\(e\left(\frac{607}{3762}\right)\)
\(\chi_{393129}(25,\cdot)\)	393129.sw	9405	yes	\(1\)	\(1\)	\(e\left(\frac{3469}{9405}\right)\)	\(e\left(\frac{6938}{9405}\right)\)	\(e\left(\frac{6181}{9405}\right)\)	\(e\left(\frac{1861}{3135}\right)\)	\(e\left(\frac{334}{3135}\right)\)	\(e\left(\frac{49}{1881}\right)\)	\(e\left(\frac{5519}{9405}\right)\)	\(e\left(\frac{9052}{9405}\right)\)	\(e\left(\frac{4471}{9405}\right)\)	\(e\left(\frac{5146}{9405}\right)\)
\(\chi_{393129}(26,\cdot)\)	393129.rx	6270	no	\(-1\)	\(1\)	\(e\left(\frac{2459}{6270}\right)\)	\(e\left(\frac{2459}{3135}\right)\)	\(e\left(\frac{6131}{6270}\right)\)	\(e\left(\frac{238}{1045}\right)\)	\(e\left(\frac{369}{2090}\right)\)	\(e\left(\frac{232}{627}\right)\)	\(e\left(\frac{347}{3135}\right)\)	\(e\left(\frac{3887}{6270}\right)\)	\(e\left(\frac{1783}{3135}\right)\)	\(e\left(\frac{41}{6270}\right)\)
\(\chi_{393129}(28,\cdot)\)	393129.oh	990	no	\(-1\)	\(1\)	\(e\left(\frac{521}{990}\right)\)	\(e\left(\frac{26}{495}\right)\)	\(e\left(\frac{82}{495}\right)\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{191}{330}\right)\)	\(e\left(\frac{137}{198}\right)\)	\(e\left(\frac{481}{990}\right)\)	\(e\left(\frac{379}{495}\right)\)	\(e\left(\frac{52}{495}\right)\)	\(e\left(\frac{449}{990}\right)\)
\(\chi_{393129}(29,\cdot)\)	393129.tb	18810	yes	\(-1\)	\(1\)	\(e\left(\frac{6977}{18810}\right)\)	\(e\left(\frac{6977}{9405}\right)\)	\(e\left(\frac{15083}{18810}\right)\)	\(e\left(\frac{1283}{6270}\right)\)	\(e\left(\frac{707}{6270}\right)\)	\(e\left(\frac{325}{1881}\right)\)	\(e\left(\frac{2786}{9405}\right)\)	\(e\left(\frac{5413}{9405}\right)\)	\(e\left(\frac{4549}{9405}\right)\)	\(e\left(\frac{2884}{9405}\right)\)
\(\chi_{393129}(31,\cdot)\)	393129.rw	6270	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{6270}\right)\)	\(e\left(\frac{7}{3135}\right)\)	\(e\left(\frac{68}{1045}\right)\)	\(e\left(\frac{2197}{3135}\right)\)	\(e\left(\frac{7}{2090}\right)\)	\(e\left(\frac{83}{1254}\right)\)	\(e\left(\frac{707}{6270}\right)\)	\(e\left(\frac{1467}{2090}\right)\)	\(e\left(\frac{14}{3135}\right)\)	\(e\left(\frac{1684}{3135}\right)\)
\(\chi_{393129}(32,\cdot)\)	393129.ra	3762	yes	\(-1\)	\(1\)	\(e\left(\frac{3361}{3762}\right)\)	\(e\left(\frac{1480}{1881}\right)\)	\(e\left(\frac{3469}{3762}\right)\)	\(e\left(\frac{353}{418}\right)\)	\(e\left(\frac{853}{1254}\right)\)	\(e\left(\frac{1534}{1881}\right)\)	\(e\left(\frac{127}{1881}\right)\)	\(e\left(\frac{1388}{1881}\right)\)	\(e\left(\frac{1079}{1881}\right)\)	\(e\left(\frac{59}{1881}\right)\)
\(\chi_{393129}(34,\cdot)\)	393129.re	3762	yes	\(-1\)	\(1\)	\(e\left(\frac{2953}{3762}\right)\)	\(e\left(\frac{1072}{1881}\right)\)	\(e\left(\frac{1802}{1881}\right)\)	\(e\left(\frac{257}{627}\right)\)	\(e\left(\frac{445}{1254}\right)\)	\(e\left(\frac{2795}{3762}\right)\)	\(e\left(\frac{2309}{3762}\right)\)	\(e\left(\frac{733}{3762}\right)\)	\(e\left(\frac{263}{1881}\right)\)	\(e\left(\frac{524}{1881}\right)\)
\(\chi_{393129}(35,\cdot)\)	393129.th	18810	no	\(1\)	\(1\)	\(e\left(\frac{3323}{9405}\right)\)	\(e\left(\frac{6646}{9405}\right)\)	\(e\left(\frac{2359}{18810}\right)\)	\(e\left(\frac{4379}{6270}\right)\)	\(e\left(\frac{188}{3135}\right)\)	\(e\left(\frac{1801}{3762}\right)\)	\(e\left(\frac{16031}{18810}\right)\)	\(e\left(\frac{973}{18810}\right)\)	\(e\left(\frac{3887}{9405}\right)\)	\(e\left(\frac{137}{9405}\right)\)
\(\chi_{393129}(37,\cdot)\)	393129.qp	2090	no	\(-1\)	\(1\)	\(e\left(\frac{1073}{2090}\right)\)	\(e\left(\frac{28}{1045}\right)\)	\(e\left(\frac{816}{1045}\right)\)	\(e\left(\frac{428}{1045}\right)\)	\(e\left(\frac{1129}{2090}\right)\)	\(e\left(\frac{123}{418}\right)\)	\(e\left(\frac{1783}{2090}\right)\)	\(e\left(\frac{1929}{2090}\right)\)	\(e\left(\frac{56}{1045}\right)\)	\(e\left(\frac{466}{1045}\right)\)
\(\chi_{393129}(40,\cdot)\)	393129.pz	1710	no	\(1\)	\(1\)	\(e\left(\frac{616}{855}\right)\)	\(e\left(\frac{377}{855}\right)\)	\(e\left(\frac{754}{855}\right)\)	\(e\left(\frac{173}{570}\right)\)	\(e\left(\frac{46}{285}\right)\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{371}{855}\right)\)	\(e\left(\frac{41}{1710}\right)\)	\(e\left(\frac{754}{855}\right)\)	\(e\left(\frac{1013}{1710}\right)\)
\(\chi_{393129}(41,\cdot)\)	393129.tb	18810	yes	\(-1\)	\(1\)	\(e\left(\frac{4483}{18810}\right)\)	\(e\left(\frac{4483}{9405}\right)\)	\(e\left(\frac{1687}{18810}\right)\)	\(e\left(\frac{1147}{6270}\right)\)	\(e\left(\frac{4483}{6270}\right)\)	\(e\left(\frac{617}{1881}\right)\)	\(e\left(\frac{2239}{9405}\right)\)	\(e\left(\frac{3962}{9405}\right)\)	\(e\left(\frac{8966}{9405}\right)\)	\(e\left(\frac{191}{9405}\right)\)
\(\chi_{393129}(43,\cdot)\)	393129.qz	3762	yes	\(-1\)	\(1\)	\(e\left(\frac{173}{3762}\right)\)	\(e\left(\frac{173}{1881}\right)\)	\(e\left(\frac{802}{1881}\right)\)	\(e\left(\frac{27}{418}\right)\)	\(e\left(\frac{173}{1254}\right)\)	\(e\left(\frac{1777}{3762}\right)\)	\(e\left(\frac{1171}{3762}\right)\)	\(e\left(\frac{208}{1881}\right)\)	\(e\left(\frac{346}{1881}\right)\)	\(e\left(\frac{1877}{3762}\right)\)
\(\chi_{393129}(46,\cdot)\)	393129.sn	6270	no	\(1\)	\(1\)	\(e\left(\frac{236}{3135}\right)\)	\(e\left(\frac{472}{3135}\right)\)	\(e\left(\frac{1514}{3135}\right)\)	\(e\left(\frac{2073}{2090}\right)\)	\(e\left(\frac{236}{1045}\right)\)	\(e\left(\frac{350}{627}\right)\)	\(e\left(\frac{1891}{3135}\right)\)	\(e\left(\frac{421}{6270}\right)\)	\(e\left(\frac{944}{3135}\right)\)	\(e\left(\frac{4813}{6270}\right)\)
\(\chi_{393129}(47,\cdot)\)	393129.tj	18810	yes	\(-1\)	\(1\)	\(e\left(\frac{2513}{18810}\right)\)	\(e\left(\frac{2513}{9405}\right)\)	\(e\left(\frac{7487}{18810}\right)\)	\(e\left(\frac{961}{3135}\right)\)	\(e\left(\frac{2513}{6270}\right)\)	\(e\left(\frac{1000}{1881}\right)\)	\(e\left(\frac{3074}{9405}\right)\)	\(e\left(\frac{8279}{18810}\right)\)	\(e\left(\frac{5026}{9405}\right)\)	\(e\left(\frac{6317}{18810}\right)\)
\(\chi_{393129}(49,\cdot)\)	393129.qt	3135	yes	\(1\)	\(1\)	\(e\left(\frac{353}{1045}\right)\)	\(e\left(\frac{706}{1045}\right)\)	\(e\left(\frac{1861}{3135}\right)\)	\(e\left(\frac{2518}{3135}\right)\)	\(e\left(\frac{14}{1045}\right)\)	\(e\left(\frac{584}{627}\right)\)	\(e\left(\frac{123}{1045}\right)\)	\(e\left(\frac{442}{3135}\right)\)	\(e\left(\frac{367}{1045}\right)\)	\(e\left(\frac{1511}{3135}\right)\)
\(\chi_{393129}(50,\cdot)\)	393129.sf	6270	yes	\(-1\)	\(1\)	\(e\left(\frac{3433}{6270}\right)\)	\(e\left(\frac{298}{3135}\right)\)	\(e\left(\frac{1759}{2090}\right)\)	\(e\left(\frac{4781}{6270}\right)\)	\(e\left(\frac{1343}{2090}\right)\)	\(e\left(\frac{244}{627}\right)\)	\(e\left(\frac{2509}{3135}\right)\)	\(e\left(\frac{324}{1045}\right)\)	\(e\left(\frac{596}{3135}\right)\)	\(e\left(\frac{481}{3135}\right)\)
\(\chi_{393129}(52,\cdot)\)	393129.tr	18810	yes	\(1\)	\(1\)	\(e\left(\frac{5369}{9405}\right)\)	\(e\left(\frac{1333}{9405}\right)\)	\(e\left(\frac{1526}{9405}\right)\)	\(e\left(\frac{829}{2090}\right)\)	\(e\left(\frac{2234}{3135}\right)\)	\(e\left(\frac{1379}{1881}\right)\)	\(e\left(\frac{3049}{9405}\right)\)	\(e\left(\frac{18199}{18810}\right)\)	\(e\left(\frac{2666}{9405}\right)\)	\(e\left(\frac{11527}{18810}\right)\)
\(\chi_{393129}(53,\cdot)\)	393129.tn	18810	no	\(1\)	\(1\)	\(e\left(\frac{6643}{9405}\right)\)	\(e\left(\frac{3881}{9405}\right)\)	\(e\left(\frac{2129}{18810}\right)\)	\(e\left(\frac{467}{3135}\right)\)	\(e\left(\frac{373}{3135}\right)\)	\(e\left(\frac{3083}{3762}\right)\)	\(e\left(\frac{3241}{18810}\right)\)	\(e\left(\frac{8044}{9405}\right)\)	\(e\left(\frac{7762}{9405}\right)\)	\(e\left(\frac{10649}{18810}\right)\)
\(\chi_{393129}(56,\cdot)\)	393129.ov	1254	yes	\(1\)	\(1\)	\(e\left(\frac{442}{627}\right)\)	\(e\left(\frac{257}{627}\right)\)	\(e\left(\frac{439}{1254}\right)\)	\(e\left(\frac{256}{627}\right)\)	\(e\left(\frac{24}{209}\right)\)	\(e\left(\frac{23}{418}\right)\)	\(e\left(\frac{877}{1254}\right)\)	\(e\left(\frac{71}{627}\right)\)	\(e\left(\frac{514}{627}\right)\)	\(e\left(\frac{25}{418}\right)\)

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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.