LMFDB - Group of Dirichlet characters of modulus 6982

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6982)

pari: g = idealstar(,6982,2)

Character group

sage: G.order() pari: g.no
Order	=	3490
sage: H.invariants() pari: g.cyc
Structure	=	$C_{3490}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6982}(3493,\cdot)$

First 32 of 3490 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{6982}(1,\cdot)$	6982.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6982}(3,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{1582}{1745}\right)$	$e\left(\frac{236}{1745}\right)$	$e\left(\frac{198}{1745}\right)$	$e\left(\frac{1419}{1745}\right)$	$e\left(\frac{1421}{1745}\right)$	$e\left(\frac{80}{349}\right)$	$e\left(\frac{73}{1745}\right)$	$e\left(\frac{229}{1745}\right)$	$e\left(\frac{1276}{1745}\right)$	$e\left(\frac{7}{349}\right)$
$\chi_{6982}(5,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{236}{1745}\right)$	$e\left(\frac{33}{1745}\right)$	$e\left(\frac{634}{1745}\right)$	$e\left(\frac{472}{1745}\right)$	$e\left(\frac{73}{1745}\right)$	$e\left(\frac{94}{349}\right)$	$e\left(\frac{269}{1745}\right)$	$e\left(\frac{557}{1745}\right)$	$e\left(\frac{208}{1745}\right)$	$e\left(\frac{174}{349}\right)$
$\chi_{6982}(7,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{198}{1745}\right)$	$e\left(\frac{634}{1745}\right)$	$e\left(\frac{177}{1745}\right)$	$e\left(\frac{396}{1745}\right)$	$e\left(\frac{1614}{1745}\right)$	$e\left(\frac{209}{349}\right)$	$e\left(\frac{832}{1745}\right)$	$e\left(\frac{1606}{1745}\right)$	$e\left(\frac{559}{1745}\right)$	$e\left(\frac{75}{349}\right)$
$\chi_{6982}(9,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{1419}{1745}\right)$	$e\left(\frac{472}{1745}\right)$	$e\left(\frac{396}{1745}\right)$	$e\left(\frac{1093}{1745}\right)$	$e\left(\frac{1097}{1745}\right)$	$e\left(\frac{160}{349}\right)$	$e\left(\frac{146}{1745}\right)$	$e\left(\frac{458}{1745}\right)$	$e\left(\frac{807}{1745}\right)$	$e\left(\frac{14}{349}\right)$
$\chi_{6982}(11,\cdot)$	6982.h	3490	no	$-1$	$1$	$e\left(\frac{1421}{1745}\right)$	$e\left(\frac{73}{1745}\right)$	$e\left(\frac{1614}{1745}\right)$	$e\left(\frac{1097}{1745}\right)$	$e\left(\frac{2491}{3490}\right)$	$e\left(\frac{363}{698}\right)$	$e\left(\frac{1494}{1745}\right)$	$e\left(\frac{3469}{3490}\right)$	$e\left(\frac{513}{1745}\right)$	$e\left(\frac{258}{349}\right)$
$\chi_{6982}(13,\cdot)$	6982.f	698	no	$-1$	$1$	$e\left(\frac{80}{349}\right)$	$e\left(\frac{94}{349}\right)$	$e\left(\frac{209}{349}\right)$	$e\left(\frac{160}{349}\right)$	$e\left(\frac{363}{698}\right)$	$e\left(\frac{573}{698}\right)$	$e\left(\frac{174}{349}\right)$	$e\left(\frac{561}{698}\right)$	$e\left(\frac{106}{349}\right)$	$e\left(\frac{289}{349}\right)$
$\chi_{6982}(15,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{73}{1745}\right)$	$e\left(\frac{269}{1745}\right)$	$e\left(\frac{832}{1745}\right)$	$e\left(\frac{146}{1745}\right)$	$e\left(\frac{1494}{1745}\right)$	$e\left(\frac{174}{349}\right)$	$e\left(\frac{342}{1745}\right)$	$e\left(\frac{786}{1745}\right)$	$e\left(\frac{1484}{1745}\right)$	$e\left(\frac{181}{349}\right)$
$\chi_{6982}(17,\cdot)$	6982.h	3490	no	$-1$	$1$	$e\left(\frac{229}{1745}\right)$	$e\left(\frac{557}{1745}\right)$	$e\left(\frac{1606}{1745}\right)$	$e\left(\frac{458}{1745}\right)$	$e\left(\frac{3469}{3490}\right)$	$e\left(\frac{561}{698}\right)$	$e\left(\frac{786}{1745}\right)$	$e\left(\frac{31}{3490}\right)$	$e\left(\frac{1237}{1745}\right)$	$e\left(\frac{18}{349}\right)$
$\chi_{6982}(19,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{1276}{1745}\right)$	$e\left(\frac{208}{1745}\right)$	$e\left(\frac{559}{1745}\right)$	$e\left(\frac{807}{1745}\right)$	$e\left(\frac{513}{1745}\right)$	$e\left(\frac{106}{349}\right)$	$e\left(\frac{1484}{1745}\right)$	$e\left(\frac{1237}{1745}\right)$	$e\left(\frac{888}{1745}\right)$	$e\left(\frac{18}{349}\right)$
$\chi_{6982}(21,\cdot)$	6982.e	349	no	$1$	$1$	$e\left(\frac{7}{349}\right)$	$e\left(\frac{174}{349}\right)$	$e\left(\frac{75}{349}\right)$	$e\left(\frac{14}{349}\right)$	$e\left(\frac{258}{349}\right)$	$e\left(\frac{289}{349}\right)$	$e\left(\frac{181}{349}\right)$	$e\left(\frac{18}{349}\right)$	$e\left(\frac{18}{349}\right)$	$e\left(\frac{82}{349}\right)$
$\chi_{6982}(23,\cdot)$	6982.h	3490	no	$-1$	$1$	$e\left(\frac{808}{1745}\right)$	$e\left(\frac{1089}{1745}\right)$	$e\left(\frac{1727}{1745}\right)$	$e\left(\frac{1616}{1745}\right)$	$e\left(\frac{3073}{3490}\right)$	$e\left(\frac{271}{698}\right)$	$e\left(\frac{152}{1745}\right)$	$e\left(\frac{117}{3490}\right)$	$e\left(\frac{1629}{1745}\right)$	$e\left(\frac{158}{349}\right)$
$\chi_{6982}(25,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{472}{1745}\right)$	$e\left(\frac{66}{1745}\right)$	$e\left(\frac{1268}{1745}\right)$	$e\left(\frac{944}{1745}\right)$	$e\left(\frac{146}{1745}\right)$	$e\left(\frac{188}{349}\right)$	$e\left(\frac{538}{1745}\right)$	$e\left(\frac{1114}{1745}\right)$	$e\left(\frac{416}{1745}\right)$	$e\left(\frac{348}{349}\right)$
$\chi_{6982}(27,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{1256}{1745}\right)$	$e\left(\frac{708}{1745}\right)$	$e\left(\frac{594}{1745}\right)$	$e\left(\frac{767}{1745}\right)$	$e\left(\frac{773}{1745}\right)$	$e\left(\frac{240}{349}\right)$	$e\left(\frac{219}{1745}\right)$	$e\left(\frac{687}{1745}\right)$	$e\left(\frac{338}{1745}\right)$	$e\left(\frac{21}{349}\right)$
$\chi_{6982}(29,\cdot)$	6982.h	3490	no	$-1$	$1$	$e\left(\frac{1451}{1745}\right)$	$e\left(\frac{1068}{1745}\right)$	$e\left(\frac{689}{1745}\right)$	$e\left(\frac{1157}{1745}\right)$	$e\left(\frac{1711}{3490}\right)$	$e\left(\frac{659}{698}\right)$	$e\left(\frac{774}{1745}\right)$	$e\left(\frac{1629}{3490}\right)$	$e\left(\frac{1338}{1745}\right)$	$e\left(\frac{79}{349}\right)$
$\chi_{6982}(31,\cdot)$	6982.h	3490	no	$-1$	$1$	$e\left(\frac{52}{1745}\right)$	$e\left(\frac{96}{1745}\right)$	$e\left(\frac{258}{1745}\right)$	$e\left(\frac{104}{1745}\right)$	$e\left(\frac{2487}{3490}\right)$	$e\left(\frac{71}{698}\right)$	$e\left(\frac{148}{1745}\right)$	$e\left(\frac{1813}{3490}\right)$	$e\left(\frac{1081}{1745}\right)$	$e\left(\frac{62}{349}\right)$
$\chi_{6982}(33,\cdot)$	6982.h	3490	no	$-1$	$1$	$e\left(\frac{1258}{1745}\right)$	$e\left(\frac{309}{1745}\right)$	$e\left(\frac{67}{1745}\right)$	$e\left(\frac{771}{1745}\right)$	$e\left(\frac{1843}{3490}\right)$	$e\left(\frac{523}{698}\right)$	$e\left(\frac{1567}{1745}\right)$	$e\left(\frac{437}{3490}\right)$	$e\left(\frac{44}{1745}\right)$	$e\left(\frac{265}{349}\right)$
$\chi_{6982}(35,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{434}{1745}\right)$	$e\left(\frac{667}{1745}\right)$	$e\left(\frac{811}{1745}\right)$	$e\left(\frac{868}{1745}\right)$	$e\left(\frac{1687}{1745}\right)$	$e\left(\frac{303}{349}\right)$	$e\left(\frac{1101}{1745}\right)$	$e\left(\frac{418}{1745}\right)$	$e\left(\frac{767}{1745}\right)$	$e\left(\frac{249}{349}\right)$
$\chi_{6982}(37,\cdot)$	6982.h	3490	no	$-1$	$1$	$e\left(\frac{1712}{1745}\right)$	$e\left(\frac{476}{1745}\right)$	$e\left(\frac{843}{1745}\right)$	$e\left(\frac{1679}{1745}\right)$	$e\left(\frac{1207}{3490}\right)$	$e\left(\frac{163}{698}\right)$	$e\left(\frac{443}{1745}\right)$	$e\left(\frac{2373}{3490}\right)$	$e\left(\frac{1361}{1745}\right)$	$e\left(\frac{162}{349}\right)$
$\chi_{6982}(39,\cdot)$	6982.h	3490	no	$-1$	$1$	$e\left(\frac{237}{1745}\right)$	$e\left(\frac{706}{1745}\right)$	$e\left(\frac{1243}{1745}\right)$	$e\left(\frac{474}{1745}\right)$	$e\left(\frac{1167}{3490}\right)$	$e\left(\frac{35}{698}\right)$	$e\left(\frac{943}{1745}\right)$	$e\left(\frac{3263}{3490}\right)$	$e\left(\frac{61}{1745}\right)$	$e\left(\frac{296}{349}\right)$
$\chi_{6982}(41,\cdot)$	6982.h	3490	no	$-1$	$1$	$e\left(\frac{501}{1745}\right)$	$e\left(\frac{388}{1745}\right)$	$e\left(\frac{1479}{1745}\right)$	$e\left(\frac{1002}{1745}\right)$	$e\left(\frac{1981}{3490}\right)$	$e\left(\frac{127}{698}\right)$	$e\left(\frac{889}{1745}\right)$	$e\left(\frac{1729}{3490}\right)$	$e\left(\frac{1388}{1745}\right)$	$e\left(\frac{47}{349}\right)$
$\chi_{6982}(43,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{549}{1745}\right)$	$e\left(\frac{1282}{1745}\right)$	$e\left(\frac{1046}{1745}\right)$	$e\left(\frac{1098}{1745}\right)$	$e\left(\frac{192}{1745}\right)$	$e\left(\frac{56}{349}\right)$	$e\left(\frac{86}{1745}\right)$	$e\left(\frac{963}{1745}\right)$	$e\left(\frac{1312}{1745}\right)$	$e\left(\frac{319}{349}\right)$
$\chi_{6982}(45,\cdot)$	6982.e	349	no	$1$	$1$	$e\left(\frac{331}{349}\right)$	$e\left(\frac{101}{349}\right)$	$e\left(\frac{206}{349}\right)$	$e\left(\frac{313}{349}\right)$	$e\left(\frac{234}{349}\right)$	$e\left(\frac{254}{349}\right)$	$e\left(\frac{83}{349}\right)$	$e\left(\frac{203}{349}\right)$	$e\left(\frac{203}{349}\right)$	$e\left(\frac{188}{349}\right)$
$\chi_{6982}(47,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{1049}{1745}\right)$	$e\left(\frac{997}{1745}\right)$	$e\left(\frac{171}{1745}\right)$	$e\left(\frac{353}{1745}\right)$	$e\left(\frac{672}{1745}\right)$	$e\left(\frac{196}{349}\right)$	$e\left(\frac{301}{1745}\right)$	$e\left(\frac{753}{1745}\right)$	$e\left(\frac{1102}{1745}\right)$	$e\left(\frac{244}{349}\right)$
$\chi_{6982}(49,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{396}{1745}\right)$	$e\left(\frac{1268}{1745}\right)$	$e\left(\frac{354}{1745}\right)$	$e\left(\frac{792}{1745}\right)$	$e\left(\frac{1483}{1745}\right)$	$e\left(\frac{69}{349}\right)$	$e\left(\frac{1664}{1745}\right)$	$e\left(\frac{1467}{1745}\right)$	$e\left(\frac{1118}{1745}\right)$	$e\left(\frac{150}{349}\right)$
$\chi_{6982}(51,\cdot)$	6982.h	3490	no	$-1$	$1$	$e\left(\frac{66}{1745}\right)$	$e\left(\frac{793}{1745}\right)$	$e\left(\frac{59}{1745}\right)$	$e\left(\frac{132}{1745}\right)$	$e\left(\frac{2821}{3490}\right)$	$e\left(\frac{23}{698}\right)$	$e\left(\frac{859}{1745}\right)$	$e\left(\frac{489}{3490}\right)$	$e\left(\frac{768}{1745}\right)$	$e\left(\frac{25}{349}\right)$
$\chi_{6982}(53,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{1301}{1745}\right)$	$e\left(\frac{1328}{1745}\right)$	$e\left(\frac{79}{1745}\right)$	$e\left(\frac{857}{1745}\right)$	$e\left(\frac{188}{1745}\right)$	$e\left(\frac{113}{349}\right)$	$e\left(\frac{884}{1745}\right)$	$e\left(\frac{1052}{1745}\right)$	$e\left(\frac{703}{1745}\right)$	$e\left(\frac{276}{349}\right)$
$\chi_{6982}(55,\cdot)$	6982.h	3490	no	$-1$	$1$	$e\left(\frac{1657}{1745}\right)$	$e\left(\frac{106}{1745}\right)$	$e\left(\frac{503}{1745}\right)$	$e\left(\frac{1569}{1745}\right)$	$e\left(\frac{2637}{3490}\right)$	$e\left(\frac{551}{698}\right)$	$e\left(\frac{18}{1745}\right)$	$e\left(\frac{1093}{3490}\right)$	$e\left(\frac{721}{1745}\right)$	$e\left(\frac{83}{349}\right)$
$\chi_{6982}(57,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{1113}{1745}\right)$	$e\left(\frac{444}{1745}\right)$	$e\left(\frac{757}{1745}\right)$	$e\left(\frac{481}{1745}\right)$	$e\left(\frac{189}{1745}\right)$	$e\left(\frac{186}{349}\right)$	$e\left(\frac{1557}{1745}\right)$	$e\left(\frac{1466}{1745}\right)$	$e\left(\frac{419}{1745}\right)$	$e\left(\frac{25}{349}\right)$
$\chi_{6982}(59,\cdot)$	6982.e	349	no	$1$	$1$	$e\left(\frac{311}{349}\right)$	$e\left(\frac{252}{349}\right)$	$e\left(\frac{241}{349}\right)$	$e\left(\frac{273}{349}\right)$	$e\left(\frac{145}{349}\right)$	$e\left(\frac{226}{349}\right)$	$e\left(\frac{214}{349}\right)$	$e\left(\frac{2}{349}\right)$	$e\left(\frac{2}{349}\right)$	$e\left(\frac{203}{349}\right)$
$\chi_{6982}(61,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{214}{1745}\right)$	$e\left(\frac{932}{1745}\right)$	$e\left(\frac{1196}{1745}\right)$	$e\left(\frac{428}{1745}\right)$	$e\left(\frac{1057}{1745}\right)$	$e\left(\frac{32}{349}\right)$	$e\left(\frac{1146}{1745}\right)$	$e\left(\frac{1348}{1745}\right)$	$e\left(\frac{1697}{1745}\right)$	$e\left(\frac{282}{349}\right)$
$\chi_{6982}(63,\cdot)$	6982.g	1745	no	$1$	$1$	$e\left(\frac{1617}{1745}\right)$	$e\left(\frac{1106}{1745}\right)$	$e\left(\frac{573}{1745}\right)$	$e\left(\frac{1489}{1745}\right)$	$e\left(\frac{966}{1745}\right)$	$e\left(\frac{20}{349}\right)$	$e\left(\frac{978}{1745}\right)$	$e\left(\frac{319}{1745}\right)$	$e\left(\frac{1366}{1745}\right)$	$e\left(\frac{89}{349}\right)$

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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	$6982$
Structure	\(C_{3490}\)
Order	$3490$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{6982}(1,\cdot)\)	6982.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6982}(3,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{1582}{1745}\right)\)	\(e\left(\frac{236}{1745}\right)\)	\(e\left(\frac{198}{1745}\right)\)	\(e\left(\frac{1419}{1745}\right)\)	\(e\left(\frac{1421}{1745}\right)\)	\(e\left(\frac{80}{349}\right)\)	\(e\left(\frac{73}{1745}\right)\)	\(e\left(\frac{229}{1745}\right)\)	\(e\left(\frac{1276}{1745}\right)\)	\(e\left(\frac{7}{349}\right)\)
\(\chi_{6982}(5,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{236}{1745}\right)\)	\(e\left(\frac{33}{1745}\right)\)	\(e\left(\frac{634}{1745}\right)\)	\(e\left(\frac{472}{1745}\right)\)	\(e\left(\frac{73}{1745}\right)\)	\(e\left(\frac{94}{349}\right)\)	\(e\left(\frac{269}{1745}\right)\)	\(e\left(\frac{557}{1745}\right)\)	\(e\left(\frac{208}{1745}\right)\)	\(e\left(\frac{174}{349}\right)\)
\(\chi_{6982}(7,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{198}{1745}\right)\)	\(e\left(\frac{634}{1745}\right)\)	\(e\left(\frac{177}{1745}\right)\)	\(e\left(\frac{396}{1745}\right)\)	\(e\left(\frac{1614}{1745}\right)\)	\(e\left(\frac{209}{349}\right)\)	\(e\left(\frac{832}{1745}\right)\)	\(e\left(\frac{1606}{1745}\right)\)	\(e\left(\frac{559}{1745}\right)\)	\(e\left(\frac{75}{349}\right)\)
\(\chi_{6982}(9,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{1419}{1745}\right)\)	\(e\left(\frac{472}{1745}\right)\)	\(e\left(\frac{396}{1745}\right)\)	\(e\left(\frac{1093}{1745}\right)\)	\(e\left(\frac{1097}{1745}\right)\)	\(e\left(\frac{160}{349}\right)\)	\(e\left(\frac{146}{1745}\right)\)	\(e\left(\frac{458}{1745}\right)\)	\(e\left(\frac{807}{1745}\right)\)	\(e\left(\frac{14}{349}\right)\)
\(\chi_{6982}(11,\cdot)\)	6982.h	3490	no	\(-1\)	\(1\)	\(e\left(\frac{1421}{1745}\right)\)	\(e\left(\frac{73}{1745}\right)\)	\(e\left(\frac{1614}{1745}\right)\)	\(e\left(\frac{1097}{1745}\right)\)	\(e\left(\frac{2491}{3490}\right)\)	\(e\left(\frac{363}{698}\right)\)	\(e\left(\frac{1494}{1745}\right)\)	\(e\left(\frac{3469}{3490}\right)\)	\(e\left(\frac{513}{1745}\right)\)	\(e\left(\frac{258}{349}\right)\)
\(\chi_{6982}(13,\cdot)\)	6982.f	698	no	\(-1\)	\(1\)	\(e\left(\frac{80}{349}\right)\)	\(e\left(\frac{94}{349}\right)\)	\(e\left(\frac{209}{349}\right)\)	\(e\left(\frac{160}{349}\right)\)	\(e\left(\frac{363}{698}\right)\)	\(e\left(\frac{573}{698}\right)\)	\(e\left(\frac{174}{349}\right)\)	\(e\left(\frac{561}{698}\right)\)	\(e\left(\frac{106}{349}\right)\)	\(e\left(\frac{289}{349}\right)\)
\(\chi_{6982}(15,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{73}{1745}\right)\)	\(e\left(\frac{269}{1745}\right)\)	\(e\left(\frac{832}{1745}\right)\)	\(e\left(\frac{146}{1745}\right)\)	\(e\left(\frac{1494}{1745}\right)\)	\(e\left(\frac{174}{349}\right)\)	\(e\left(\frac{342}{1745}\right)\)	\(e\left(\frac{786}{1745}\right)\)	\(e\left(\frac{1484}{1745}\right)\)	\(e\left(\frac{181}{349}\right)\)
\(\chi_{6982}(17,\cdot)\)	6982.h	3490	no	\(-1\)	\(1\)	\(e\left(\frac{229}{1745}\right)\)	\(e\left(\frac{557}{1745}\right)\)	\(e\left(\frac{1606}{1745}\right)\)	\(e\left(\frac{458}{1745}\right)\)	\(e\left(\frac{3469}{3490}\right)\)	\(e\left(\frac{561}{698}\right)\)	\(e\left(\frac{786}{1745}\right)\)	\(e\left(\frac{31}{3490}\right)\)	\(e\left(\frac{1237}{1745}\right)\)	\(e\left(\frac{18}{349}\right)\)
\(\chi_{6982}(19,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{1276}{1745}\right)\)	\(e\left(\frac{208}{1745}\right)\)	\(e\left(\frac{559}{1745}\right)\)	\(e\left(\frac{807}{1745}\right)\)	\(e\left(\frac{513}{1745}\right)\)	\(e\left(\frac{106}{349}\right)\)	\(e\left(\frac{1484}{1745}\right)\)	\(e\left(\frac{1237}{1745}\right)\)	\(e\left(\frac{888}{1745}\right)\)	\(e\left(\frac{18}{349}\right)\)
\(\chi_{6982}(21,\cdot)\)	6982.e	349	no	\(1\)	\(1\)	\(e\left(\frac{7}{349}\right)\)	\(e\left(\frac{174}{349}\right)\)	\(e\left(\frac{75}{349}\right)\)	\(e\left(\frac{14}{349}\right)\)	\(e\left(\frac{258}{349}\right)\)	\(e\left(\frac{289}{349}\right)\)	\(e\left(\frac{181}{349}\right)\)	\(e\left(\frac{18}{349}\right)\)	\(e\left(\frac{18}{349}\right)\)	\(e\left(\frac{82}{349}\right)\)
\(\chi_{6982}(23,\cdot)\)	6982.h	3490	no	\(-1\)	\(1\)	\(e\left(\frac{808}{1745}\right)\)	\(e\left(\frac{1089}{1745}\right)\)	\(e\left(\frac{1727}{1745}\right)\)	\(e\left(\frac{1616}{1745}\right)\)	\(e\left(\frac{3073}{3490}\right)\)	\(e\left(\frac{271}{698}\right)\)	\(e\left(\frac{152}{1745}\right)\)	\(e\left(\frac{117}{3490}\right)\)	\(e\left(\frac{1629}{1745}\right)\)	\(e\left(\frac{158}{349}\right)\)
\(\chi_{6982}(25,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{472}{1745}\right)\)	\(e\left(\frac{66}{1745}\right)\)	\(e\left(\frac{1268}{1745}\right)\)	\(e\left(\frac{944}{1745}\right)\)	\(e\left(\frac{146}{1745}\right)\)	\(e\left(\frac{188}{349}\right)\)	\(e\left(\frac{538}{1745}\right)\)	\(e\left(\frac{1114}{1745}\right)\)	\(e\left(\frac{416}{1745}\right)\)	\(e\left(\frac{348}{349}\right)\)
\(\chi_{6982}(27,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{1256}{1745}\right)\)	\(e\left(\frac{708}{1745}\right)\)	\(e\left(\frac{594}{1745}\right)\)	\(e\left(\frac{767}{1745}\right)\)	\(e\left(\frac{773}{1745}\right)\)	\(e\left(\frac{240}{349}\right)\)	\(e\left(\frac{219}{1745}\right)\)	\(e\left(\frac{687}{1745}\right)\)	\(e\left(\frac{338}{1745}\right)\)	\(e\left(\frac{21}{349}\right)\)
\(\chi_{6982}(29,\cdot)\)	6982.h	3490	no	\(-1\)	\(1\)	\(e\left(\frac{1451}{1745}\right)\)	\(e\left(\frac{1068}{1745}\right)\)	\(e\left(\frac{689}{1745}\right)\)	\(e\left(\frac{1157}{1745}\right)\)	\(e\left(\frac{1711}{3490}\right)\)	\(e\left(\frac{659}{698}\right)\)	\(e\left(\frac{774}{1745}\right)\)	\(e\left(\frac{1629}{3490}\right)\)	\(e\left(\frac{1338}{1745}\right)\)	\(e\left(\frac{79}{349}\right)\)
\(\chi_{6982}(31,\cdot)\)	6982.h	3490	no	\(-1\)	\(1\)	\(e\left(\frac{52}{1745}\right)\)	\(e\left(\frac{96}{1745}\right)\)	\(e\left(\frac{258}{1745}\right)\)	\(e\left(\frac{104}{1745}\right)\)	\(e\left(\frac{2487}{3490}\right)\)	\(e\left(\frac{71}{698}\right)\)	\(e\left(\frac{148}{1745}\right)\)	\(e\left(\frac{1813}{3490}\right)\)	\(e\left(\frac{1081}{1745}\right)\)	\(e\left(\frac{62}{349}\right)\)
\(\chi_{6982}(33,\cdot)\)	6982.h	3490	no	\(-1\)	\(1\)	\(e\left(\frac{1258}{1745}\right)\)	\(e\left(\frac{309}{1745}\right)\)	\(e\left(\frac{67}{1745}\right)\)	\(e\left(\frac{771}{1745}\right)\)	\(e\left(\frac{1843}{3490}\right)\)	\(e\left(\frac{523}{698}\right)\)	\(e\left(\frac{1567}{1745}\right)\)	\(e\left(\frac{437}{3490}\right)\)	\(e\left(\frac{44}{1745}\right)\)	\(e\left(\frac{265}{349}\right)\)
\(\chi_{6982}(35,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{434}{1745}\right)\)	\(e\left(\frac{667}{1745}\right)\)	\(e\left(\frac{811}{1745}\right)\)	\(e\left(\frac{868}{1745}\right)\)	\(e\left(\frac{1687}{1745}\right)\)	\(e\left(\frac{303}{349}\right)\)	\(e\left(\frac{1101}{1745}\right)\)	\(e\left(\frac{418}{1745}\right)\)	\(e\left(\frac{767}{1745}\right)\)	\(e\left(\frac{249}{349}\right)\)
\(\chi_{6982}(37,\cdot)\)	6982.h	3490	no	\(-1\)	\(1\)	\(e\left(\frac{1712}{1745}\right)\)	\(e\left(\frac{476}{1745}\right)\)	\(e\left(\frac{843}{1745}\right)\)	\(e\left(\frac{1679}{1745}\right)\)	\(e\left(\frac{1207}{3490}\right)\)	\(e\left(\frac{163}{698}\right)\)	\(e\left(\frac{443}{1745}\right)\)	\(e\left(\frac{2373}{3490}\right)\)	\(e\left(\frac{1361}{1745}\right)\)	\(e\left(\frac{162}{349}\right)\)
\(\chi_{6982}(39,\cdot)\)	6982.h	3490	no	\(-1\)	\(1\)	\(e\left(\frac{237}{1745}\right)\)	\(e\left(\frac{706}{1745}\right)\)	\(e\left(\frac{1243}{1745}\right)\)	\(e\left(\frac{474}{1745}\right)\)	\(e\left(\frac{1167}{3490}\right)\)	\(e\left(\frac{35}{698}\right)\)	\(e\left(\frac{943}{1745}\right)\)	\(e\left(\frac{3263}{3490}\right)\)	\(e\left(\frac{61}{1745}\right)\)	\(e\left(\frac{296}{349}\right)\)
\(\chi_{6982}(41,\cdot)\)	6982.h	3490	no	\(-1\)	\(1\)	\(e\left(\frac{501}{1745}\right)\)	\(e\left(\frac{388}{1745}\right)\)	\(e\left(\frac{1479}{1745}\right)\)	\(e\left(\frac{1002}{1745}\right)\)	\(e\left(\frac{1981}{3490}\right)\)	\(e\left(\frac{127}{698}\right)\)	\(e\left(\frac{889}{1745}\right)\)	\(e\left(\frac{1729}{3490}\right)\)	\(e\left(\frac{1388}{1745}\right)\)	\(e\left(\frac{47}{349}\right)\)
\(\chi_{6982}(43,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{549}{1745}\right)\)	\(e\left(\frac{1282}{1745}\right)\)	\(e\left(\frac{1046}{1745}\right)\)	\(e\left(\frac{1098}{1745}\right)\)	\(e\left(\frac{192}{1745}\right)\)	\(e\left(\frac{56}{349}\right)\)	\(e\left(\frac{86}{1745}\right)\)	\(e\left(\frac{963}{1745}\right)\)	\(e\left(\frac{1312}{1745}\right)\)	\(e\left(\frac{319}{349}\right)\)
\(\chi_{6982}(45,\cdot)\)	6982.e	349	no	\(1\)	\(1\)	\(e\left(\frac{331}{349}\right)\)	\(e\left(\frac{101}{349}\right)\)	\(e\left(\frac{206}{349}\right)\)	\(e\left(\frac{313}{349}\right)\)	\(e\left(\frac{234}{349}\right)\)	\(e\left(\frac{254}{349}\right)\)	\(e\left(\frac{83}{349}\right)\)	\(e\left(\frac{203}{349}\right)\)	\(e\left(\frac{203}{349}\right)\)	\(e\left(\frac{188}{349}\right)\)
\(\chi_{6982}(47,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{1049}{1745}\right)\)	\(e\left(\frac{997}{1745}\right)\)	\(e\left(\frac{171}{1745}\right)\)	\(e\left(\frac{353}{1745}\right)\)	\(e\left(\frac{672}{1745}\right)\)	\(e\left(\frac{196}{349}\right)\)	\(e\left(\frac{301}{1745}\right)\)	\(e\left(\frac{753}{1745}\right)\)	\(e\left(\frac{1102}{1745}\right)\)	\(e\left(\frac{244}{349}\right)\)
\(\chi_{6982}(49,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{396}{1745}\right)\)	\(e\left(\frac{1268}{1745}\right)\)	\(e\left(\frac{354}{1745}\right)\)	\(e\left(\frac{792}{1745}\right)\)	\(e\left(\frac{1483}{1745}\right)\)	\(e\left(\frac{69}{349}\right)\)	\(e\left(\frac{1664}{1745}\right)\)	\(e\left(\frac{1467}{1745}\right)\)	\(e\left(\frac{1118}{1745}\right)\)	\(e\left(\frac{150}{349}\right)\)
\(\chi_{6982}(51,\cdot)\)	6982.h	3490	no	\(-1\)	\(1\)	\(e\left(\frac{66}{1745}\right)\)	\(e\left(\frac{793}{1745}\right)\)	\(e\left(\frac{59}{1745}\right)\)	\(e\left(\frac{132}{1745}\right)\)	\(e\left(\frac{2821}{3490}\right)\)	\(e\left(\frac{23}{698}\right)\)	\(e\left(\frac{859}{1745}\right)\)	\(e\left(\frac{489}{3490}\right)\)	\(e\left(\frac{768}{1745}\right)\)	\(e\left(\frac{25}{349}\right)\)
\(\chi_{6982}(53,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{1301}{1745}\right)\)	\(e\left(\frac{1328}{1745}\right)\)	\(e\left(\frac{79}{1745}\right)\)	\(e\left(\frac{857}{1745}\right)\)	\(e\left(\frac{188}{1745}\right)\)	\(e\left(\frac{113}{349}\right)\)	\(e\left(\frac{884}{1745}\right)\)	\(e\left(\frac{1052}{1745}\right)\)	\(e\left(\frac{703}{1745}\right)\)	\(e\left(\frac{276}{349}\right)\)
\(\chi_{6982}(55,\cdot)\)	6982.h	3490	no	\(-1\)	\(1\)	\(e\left(\frac{1657}{1745}\right)\)	\(e\left(\frac{106}{1745}\right)\)	\(e\left(\frac{503}{1745}\right)\)	\(e\left(\frac{1569}{1745}\right)\)	\(e\left(\frac{2637}{3490}\right)\)	\(e\left(\frac{551}{698}\right)\)	\(e\left(\frac{18}{1745}\right)\)	\(e\left(\frac{1093}{3490}\right)\)	\(e\left(\frac{721}{1745}\right)\)	\(e\left(\frac{83}{349}\right)\)
\(\chi_{6982}(57,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{1113}{1745}\right)\)	\(e\left(\frac{444}{1745}\right)\)	\(e\left(\frac{757}{1745}\right)\)	\(e\left(\frac{481}{1745}\right)\)	\(e\left(\frac{189}{1745}\right)\)	\(e\left(\frac{186}{349}\right)\)	\(e\left(\frac{1557}{1745}\right)\)	\(e\left(\frac{1466}{1745}\right)\)	\(e\left(\frac{419}{1745}\right)\)	\(e\left(\frac{25}{349}\right)\)
\(\chi_{6982}(59,\cdot)\)	6982.e	349	no	\(1\)	\(1\)	\(e\left(\frac{311}{349}\right)\)	\(e\left(\frac{252}{349}\right)\)	\(e\left(\frac{241}{349}\right)\)	\(e\left(\frac{273}{349}\right)\)	\(e\left(\frac{145}{349}\right)\)	\(e\left(\frac{226}{349}\right)\)	\(e\left(\frac{214}{349}\right)\)	\(e\left(\frac{2}{349}\right)\)	\(e\left(\frac{2}{349}\right)\)	\(e\left(\frac{203}{349}\right)\)
\(\chi_{6982}(61,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{214}{1745}\right)\)	\(e\left(\frac{932}{1745}\right)\)	\(e\left(\frac{1196}{1745}\right)\)	\(e\left(\frac{428}{1745}\right)\)	\(e\left(\frac{1057}{1745}\right)\)	\(e\left(\frac{32}{349}\right)\)	\(e\left(\frac{1146}{1745}\right)\)	\(e\left(\frac{1348}{1745}\right)\)	\(e\left(\frac{1697}{1745}\right)\)	\(e\left(\frac{282}{349}\right)\)
\(\chi_{6982}(63,\cdot)\)	6982.g	1745	no	\(1\)	\(1\)	\(e\left(\frac{1617}{1745}\right)\)	\(e\left(\frac{1106}{1745}\right)\)	\(e\left(\frac{573}{1745}\right)\)	\(e\left(\frac{1489}{1745}\right)\)	\(e\left(\frac{966}{1745}\right)\)	\(e\left(\frac{20}{349}\right)\)	\(e\left(\frac{978}{1745}\right)\)	\(e\left(\frac{319}{1745}\right)\)	\(e\left(\frac{1366}{1745}\right)\)	\(e\left(\frac{89}{349}\right)\)

Introduction

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First 32 of 3490 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.