LMFDB - Group of Dirichlet characters of modulus 8019

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8019)

pari: g = idealstar(,8019,2)

Character group

sage: G.order() pari: g.no
Order	=	4860
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2430}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8019}(5105,\cdot)$, $\chi_{8019}(2917,\cdot)$

First 32 of 4860 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{8019}(1,\cdot)$	8019.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8019}(2,\cdot)$	8019.bu	2430	yes	$1$	$1$	$e\left(\frac{124}{1215}\right)$	$e\left(\frac{248}{1215}\right)$	$e\left(\frac{1087}{2430}\right)$	$e\left(\frac{1241}{2430}\right)$	$e\left(\frac{124}{405}\right)$	$e\left(\frac{89}{162}\right)$	$e\left(\frac{1903}{2430}\right)$	$e\left(\frac{1489}{2430}\right)$	$e\left(\frac{496}{1215}\right)$	$e\left(\frac{392}{405}\right)$
$\chi_{8019}(4,\cdot)$	8019.bs	1215	yes	$1$	$1$	$e\left(\frac{248}{1215}\right)$	$e\left(\frac{496}{1215}\right)$	$e\left(\frac{1087}{1215}\right)$	$e\left(\frac{26}{1215}\right)$	$e\left(\frac{248}{405}\right)$	$e\left(\frac{8}{81}\right)$	$e\left(\frac{688}{1215}\right)$	$e\left(\frac{274}{1215}\right)$	$e\left(\frac{992}{1215}\right)$	$e\left(\frac{379}{405}\right)$
$\chi_{8019}(5,\cdot)$	8019.bv	2430	yes	$-1$	$1$	$e\left(\frac{1087}{2430}\right)$	$e\left(\frac{1087}{1215}\right)$	$e\left(\frac{1673}{2430}\right)$	$e\left(\frac{542}{1215}\right)$	$e\left(\frac{277}{810}\right)$	$e\left(\frac{11}{81}\right)$	$e\left(\frac{136}{1215}\right)$	$e\left(\frac{2171}{2430}\right)$	$e\left(\frac{959}{1215}\right)$	$e\left(\frac{131}{810}\right)$
$\chi_{8019}(7,\cdot)$	8019.bt	2430	yes	$-1$	$1$	$e\left(\frac{1241}{2430}\right)$	$e\left(\frac{26}{1215}\right)$	$e\left(\frac{542}{1215}\right)$	$e\left(\frac{767}{2430}\right)$	$e\left(\frac{431}{810}\right)$	$e\left(\frac{155}{162}\right)$	$e\left(\frac{2071}{2430}\right)$	$e\left(\frac{1004}{1215}\right)$	$e\left(\frac{52}{1215}\right)$	$e\left(\frac{43}{810}\right)$
$\chi_{8019}(8,\cdot)$	8019.bq	810	no	$1$	$1$	$e\left(\frac{124}{405}\right)$	$e\left(\frac{248}{405}\right)$	$e\left(\frac{277}{810}\right)$	$e\left(\frac{431}{810}\right)$	$e\left(\frac{124}{135}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{283}{810}\right)$	$e\left(\frac{679}{810}\right)$	$e\left(\frac{91}{405}\right)$	$e\left(\frac{122}{135}\right)$
$\chi_{8019}(10,\cdot)$	8019.be	162	no	$-1$	$1$	$e\left(\frac{89}{162}\right)$	$e\left(\frac{8}{81}\right)$	$e\left(\frac{11}{81}\right)$	$e\left(\frac{155}{162}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{145}{162}\right)$	$e\left(\frac{41}{81}\right)$	$e\left(\frac{16}{81}\right)$	$e\left(\frac{7}{54}\right)$
$\chi_{8019}(13,\cdot)$	8019.bt	2430	yes	$-1$	$1$	$e\left(\frac{1903}{2430}\right)$	$e\left(\frac{688}{1215}\right)$	$e\left(\frac{136}{1215}\right)$	$e\left(\frac{2071}{2430}\right)$	$e\left(\frac{283}{810}\right)$	$e\left(\frac{145}{162}\right)$	$e\left(\frac{2183}{2430}\right)$	$e\left(\frac{772}{1215}\right)$	$e\left(\frac{161}{1215}\right)$	$e\left(\frac{359}{810}\right)$
$\chi_{8019}(14,\cdot)$	8019.bv	2430	yes	$-1$	$1$	$e\left(\frac{1489}{2430}\right)$	$e\left(\frac{274}{1215}\right)$	$e\left(\frac{2171}{2430}\right)$	$e\left(\frac{1004}{1215}\right)$	$e\left(\frac{679}{810}\right)$	$e\left(\frac{41}{81}\right)$	$e\left(\frac{772}{1215}\right)$	$e\left(\frac{1067}{2430}\right)$	$e\left(\frac{548}{1215}\right)$	$e\left(\frac{17}{810}\right)$
$\chi_{8019}(16,\cdot)$	8019.bs	1215	yes	$1$	$1$	$e\left(\frac{496}{1215}\right)$	$e\left(\frac{992}{1215}\right)$	$e\left(\frac{959}{1215}\right)$	$e\left(\frac{52}{1215}\right)$	$e\left(\frac{91}{405}\right)$	$e\left(\frac{16}{81}\right)$	$e\left(\frac{161}{1215}\right)$	$e\left(\frac{548}{1215}\right)$	$e\left(\frac{769}{1215}\right)$	$e\left(\frac{353}{405}\right)$
$\chi_{8019}(17,\cdot)$	8019.bq	810	no	$1$	$1$	$e\left(\frac{392}{405}\right)$	$e\left(\frac{379}{405}\right)$	$e\left(\frac{131}{810}\right)$	$e\left(\frac{43}{810}\right)$	$e\left(\frac{122}{135}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{359}{810}\right)$	$e\left(\frac{17}{810}\right)$	$e\left(\frac{353}{405}\right)$	$e\left(\frac{46}{135}\right)$
$\chi_{8019}(19,\cdot)$	8019.br	810	no	$-1$	$1$	$e\left(\frac{773}{810}\right)$	$e\left(\frac{368}{405}\right)$	$e\left(\frac{101}{405}\right)$	$e\left(\frac{731}{810}\right)$	$e\left(\frac{233}{270}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{433}{810}\right)$	$e\left(\frac{347}{405}\right)$	$e\left(\frac{331}{405}\right)$	$e\left(\frac{79}{270}\right)$
$\chi_{8019}(20,\cdot)$	8019.bv	2430	yes	$-1$	$1$	$e\left(\frac{1583}{2430}\right)$	$e\left(\frac{368}{1215}\right)$	$e\left(\frac{1417}{2430}\right)$	$e\left(\frac{568}{1215}\right)$	$e\left(\frac{773}{810}\right)$	$e\left(\frac{19}{81}\right)$	$e\left(\frac{824}{1215}\right)$	$e\left(\frac{289}{2430}\right)$	$e\left(\frac{736}{1215}\right)$	$e\left(\frac{79}{810}\right)$
$\chi_{8019}(23,\cdot)$	8019.bm	486	no	$-1$	$1$	$e\left(\frac{389}{486}\right)$	$e\left(\frac{146}{243}\right)$	$e\left(\frac{199}{486}\right)$	$e\left(\frac{88}{243}\right)$	$e\left(\frac{65}{162}\right)$	$e\left(\frac{17}{81}\right)$	$e\left(\frac{179}{243}\right)$	$e\left(\frac{79}{486}\right)$	$e\left(\frac{49}{243}\right)$	$e\left(\frac{67}{162}\right)$
$\chi_{8019}(25,\cdot)$	8019.bs	1215	yes	$1$	$1$	$e\left(\frac{1087}{1215}\right)$	$e\left(\frac{959}{1215}\right)$	$e\left(\frac{458}{1215}\right)$	$e\left(\frac{1084}{1215}\right)$	$e\left(\frac{277}{405}\right)$	$e\left(\frac{22}{81}\right)$	$e\left(\frac{272}{1215}\right)$	$e\left(\frac{956}{1215}\right)$	$e\left(\frac{703}{1215}\right)$	$e\left(\frac{131}{405}\right)$
$\chi_{8019}(26,\cdot)$	8019.bj	270	no	$-1$	$1$	$e\left(\frac{239}{270}\right)$	$e\left(\frac{104}{135}\right)$	$e\left(\frac{151}{270}\right)$	$e\left(\frac{49}{135}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{92}{135}\right)$	$e\left(\frac{67}{270}\right)$	$e\left(\frac{73}{135}\right)$	$e\left(\frac{37}{90}\right)$
$\chi_{8019}(28,\cdot)$	8019.bk	270	no	$-1$	$1$	$e\left(\frac{193}{270}\right)$	$e\left(\frac{58}{135}\right)$	$e\left(\frac{46}{135}\right)$	$e\left(\frac{91}{270}\right)$	$e\left(\frac{13}{90}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{113}{270}\right)$	$e\left(\frac{7}{135}\right)$	$e\left(\frac{116}{135}\right)$	$e\left(\frac{89}{90}\right)$
$\chi_{8019}(29,\cdot)$	8019.bu	2430	yes	$1$	$1$	$e\left(\frac{133}{1215}\right)$	$e\left(\frac{266}{1215}\right)$	$e\left(\frac{529}{2430}\right)$	$e\left(\frac{557}{2430}\right)$	$e\left(\frac{133}{405}\right)$	$e\left(\frac{53}{162}\right)$	$e\left(\frac{1561}{2430}\right)$	$e\left(\frac{823}{2430}\right)$	$e\left(\frac{532}{1215}\right)$	$e\left(\frac{329}{405}\right)$
$\chi_{8019}(31,\cdot)$	8019.bs	1215	yes	$1$	$1$	$e\left(\frac{374}{1215}\right)$	$e\left(\frac{748}{1215}\right)$	$e\left(\frac{826}{1215}\right)$	$e\left(\frac{98}{1215}\right)$	$e\left(\frac{374}{405}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{724}{1215}\right)$	$e\left(\frac{472}{1215}\right)$	$e\left(\frac{281}{1215}\right)$	$e\left(\frac{307}{405}\right)$
$\chi_{8019}(32,\cdot)$	8019.bo	486	yes	$1$	$1$	$e\left(\frac{124}{243}\right)$	$e\left(\frac{5}{243}\right)$	$e\left(\frac{115}{486}\right)$	$e\left(\frac{269}{486}\right)$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{121}{162}\right)$	$e\left(\frac{445}{486}\right)$	$e\left(\frac{31}{486}\right)$	$e\left(\frac{10}{243}\right)$	$e\left(\frac{68}{81}\right)$
$\chi_{8019}(34,\cdot)$	8019.bh	243	no	$1$	$1$	$e\left(\frac{17}{243}\right)$	$e\left(\frac{34}{243}\right)$	$e\left(\frac{148}{243}\right)$	$e\left(\frac{137}{243}\right)$	$e\left(\frac{17}{81}\right)$	$e\left(\frac{55}{81}\right)$	$e\left(\frac{55}{243}\right)$	$e\left(\frac{154}{243}\right)$	$e\left(\frac{68}{243}\right)$	$e\left(\frac{25}{81}\right)$
$\chi_{8019}(35,\cdot)$	8019.bq	810	no	$1$	$1$	$e\left(\frac{388}{405}\right)$	$e\left(\frac{371}{405}\right)$	$e\left(\frac{109}{810}\right)$	$e\left(\frac{617}{810}\right)$	$e\left(\frac{118}{135}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{781}{810}\right)$	$e\left(\frac{583}{810}\right)$	$e\left(\frac{337}{405}\right)$	$e\left(\frac{29}{135}\right)$
$\chi_{8019}(37,\cdot)$	8019.bl	405	no	$1$	$1$	$e\left(\frac{296}{405}\right)$	$e\left(\frac{187}{405}\right)$	$e\left(\frac{4}{405}\right)$	$e\left(\frac{227}{405}\right)$	$e\left(\frac{26}{135}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{181}{405}\right)$	$e\left(\frac{118}{405}\right)$	$e\left(\frac{374}{405}\right)$	$e\left(\frac{43}{135}\right)$
$\chi_{8019}(38,\cdot)$	8019.bv	2430	yes	$-1$	$1$	$e\left(\frac{137}{2430}\right)$	$e\left(\frac{137}{1215}\right)$	$e\left(\frac{1693}{2430}\right)$	$e\left(\frac{502}{1215}\right)$	$e\left(\frac{137}{810}\right)$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{386}{1215}\right)$	$e\left(\frac{1141}{2430}\right)$	$e\left(\frac{274}{1215}\right)$	$e\left(\frac{211}{810}\right)$
$\chi_{8019}(40,\cdot)$	8019.bt	2430	yes	$-1$	$1$	$e\left(\frac{1831}{2430}\right)$	$e\left(\frac{616}{1215}\right)$	$e\left(\frac{37}{1215}\right)$	$e\left(\frac{2377}{2430}\right)$	$e\left(\frac{211}{810}\right)$	$e\left(\frac{127}{162}\right)$	$e\left(\frac{1121}{2430}\right)$	$e\left(\frac{889}{1215}\right)$	$e\left(\frac{17}{1215}\right)$	$e\left(\frac{53}{810}\right)$
$\chi_{8019}(41,\cdot)$	8019.bu	2430	yes	$1$	$1$	$e\left(\frac{902}{1215}\right)$	$e\left(\frac{589}{1215}\right)$	$e\left(\frac{911}{2430}\right)$	$e\left(\frac{973}{2430}\right)$	$e\left(\frac{92}{405}\right)$	$e\left(\frac{19}{162}\right)$	$e\left(\frac{419}{2430}\right)$	$e\left(\frac{347}{2430}\right)$	$e\left(\frac{1178}{1215}\right)$	$e\left(\frac{121}{405}\right)$
$\chi_{8019}(43,\cdot)$	8019.bn	486	yes	$-1$	$1$	$e\left(\frac{211}{486}\right)$	$e\left(\frac{211}{243}\right)$	$e\left(\frac{118}{243}\right)$	$e\left(\frac{271}{486}\right)$	$e\left(\frac{49}{162}\right)$	$e\left(\frac{149}{162}\right)$	$e\left(\frac{311}{486}\right)$	$e\left(\frac{241}{243}\right)$	$e\left(\frac{179}{243}\right)$	$e\left(\frac{53}{162}\right)$
$\chi_{8019}(46,\cdot)$	8019.br	810	no	$-1$	$1$	$e\left(\frac{731}{810}\right)$	$e\left(\frac{326}{405}\right)$	$e\left(\frac{347}{405}\right)$	$e\left(\frac{707}{810}\right)$	$e\left(\frac{191}{270}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{421}{810}\right)$	$e\left(\frac{314}{405}\right)$	$e\left(\frac{247}{405}\right)$	$e\left(\frac{103}{270}\right)$
$\chi_{8019}(47,\cdot)$	8019.bv	2430	yes	$-1$	$1$	$e\left(\frac{1439}{2430}\right)$	$e\left(\frac{224}{1215}\right)$	$e\left(\frac{1021}{2430}\right)$	$e\left(\frac{874}{1215}\right)$	$e\left(\frac{629}{810}\right)$	$e\left(\frac{1}{81}\right)$	$e\left(\frac{977}{1215}\right)$	$e\left(\frac{757}{2430}\right)$	$e\left(\frac{448}{1215}\right)$	$e\left(\frac{277}{810}\right)$
$\chi_{8019}(49,\cdot)$	8019.bs	1215	yes	$1$	$1$	$e\left(\frac{26}{1215}\right)$	$e\left(\frac{52}{1215}\right)$	$e\left(\frac{1084}{1215}\right)$	$e\left(\frac{767}{1215}\right)$	$e\left(\frac{26}{405}\right)$	$e\left(\frac{74}{81}\right)$	$e\left(\frac{856}{1215}\right)$	$e\left(\frac{793}{1215}\right)$	$e\left(\frac{104}{1215}\right)$	$e\left(\frac{43}{405}\right)$
$\chi_{8019}(50,\cdot)$	8019.bu	2430	yes	$1$	$1$	$e\left(\frac{1211}{1215}\right)$	$e\left(\frac{1207}{1215}\right)$	$e\left(\frac{2003}{2430}\right)$	$e\left(\frac{979}{2430}\right)$	$e\left(\frac{401}{405}\right)$	$e\left(\frac{133}{162}\right)$	$e\left(\frac{17}{2430}\right)$	$e\left(\frac{971}{2430}\right)$	$e\left(\frac{1199}{1215}\right)$	$e\left(\frac{118}{405}\right)$
$\chi_{8019}(52,\cdot)$	8019.bt	2430	yes	$-1$	$1$	$e\left(\frac{2399}{2430}\right)$	$e\left(\frac{1184}{1215}\right)$	$e\left(\frac{8}{1215}\right)$	$e\left(\frac{2123}{2430}\right)$	$e\left(\frac{779}{810}\right)$	$e\left(\frac{161}{162}\right)$	$e\left(\frac{1129}{2430}\right)$	$e\left(\frac{1046}{1215}\right)$	$e\left(\frac{1153}{1215}\right)$	$e\left(\frac{307}{810}\right)$

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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	$8019$
Structure	\(C_{2}\times C_{2430}\)
Order	$4860$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\(\chi_{8019}(1,\cdot)\)	8019.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8019}(2,\cdot)\)	8019.bu	2430	yes	\(1\)	\(1\)	\(e\left(\frac{124}{1215}\right)\)	\(e\left(\frac{248}{1215}\right)\)	\(e\left(\frac{1087}{2430}\right)\)	\(e\left(\frac{1241}{2430}\right)\)	\(e\left(\frac{124}{405}\right)\)	\(e\left(\frac{89}{162}\right)\)	\(e\left(\frac{1903}{2430}\right)\)	\(e\left(\frac{1489}{2430}\right)\)	\(e\left(\frac{496}{1215}\right)\)	\(e\left(\frac{392}{405}\right)\)
\(\chi_{8019}(4,\cdot)\)	8019.bs	1215	yes	\(1\)	\(1\)	\(e\left(\frac{248}{1215}\right)\)	\(e\left(\frac{496}{1215}\right)\)	\(e\left(\frac{1087}{1215}\right)\)	\(e\left(\frac{26}{1215}\right)\)	\(e\left(\frac{248}{405}\right)\)	\(e\left(\frac{8}{81}\right)\)	\(e\left(\frac{688}{1215}\right)\)	\(e\left(\frac{274}{1215}\right)\)	\(e\left(\frac{992}{1215}\right)\)	\(e\left(\frac{379}{405}\right)\)
\(\chi_{8019}(5,\cdot)\)	8019.bv	2430	yes	\(-1\)	\(1\)	\(e\left(\frac{1087}{2430}\right)\)	\(e\left(\frac{1087}{1215}\right)\)	\(e\left(\frac{1673}{2430}\right)\)	\(e\left(\frac{542}{1215}\right)\)	\(e\left(\frac{277}{810}\right)\)	\(e\left(\frac{11}{81}\right)\)	\(e\left(\frac{136}{1215}\right)\)	\(e\left(\frac{2171}{2430}\right)\)	\(e\left(\frac{959}{1215}\right)\)	\(e\left(\frac{131}{810}\right)\)
\(\chi_{8019}(7,\cdot)\)	8019.bt	2430	yes	\(-1\)	\(1\)	\(e\left(\frac{1241}{2430}\right)\)	\(e\left(\frac{26}{1215}\right)\)	\(e\left(\frac{542}{1215}\right)\)	\(e\left(\frac{767}{2430}\right)\)	\(e\left(\frac{431}{810}\right)\)	\(e\left(\frac{155}{162}\right)\)	\(e\left(\frac{2071}{2430}\right)\)	\(e\left(\frac{1004}{1215}\right)\)	\(e\left(\frac{52}{1215}\right)\)	\(e\left(\frac{43}{810}\right)\)
\(\chi_{8019}(8,\cdot)\)	8019.bq	810	no	\(1\)	\(1\)	\(e\left(\frac{124}{405}\right)\)	\(e\left(\frac{248}{405}\right)\)	\(e\left(\frac{277}{810}\right)\)	\(e\left(\frac{431}{810}\right)\)	\(e\left(\frac{124}{135}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{283}{810}\right)\)	\(e\left(\frac{679}{810}\right)\)	\(e\left(\frac{91}{405}\right)\)	\(e\left(\frac{122}{135}\right)\)
\(\chi_{8019}(10,\cdot)\)	8019.be	162	no	\(-1\)	\(1\)	\(e\left(\frac{89}{162}\right)\)	\(e\left(\frac{8}{81}\right)\)	\(e\left(\frac{11}{81}\right)\)	\(e\left(\frac{155}{162}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{145}{162}\right)\)	\(e\left(\frac{41}{81}\right)\)	\(e\left(\frac{16}{81}\right)\)	\(e\left(\frac{7}{54}\right)\)
\(\chi_{8019}(13,\cdot)\)	8019.bt	2430	yes	\(-1\)	\(1\)	\(e\left(\frac{1903}{2430}\right)\)	\(e\left(\frac{688}{1215}\right)\)	\(e\left(\frac{136}{1215}\right)\)	\(e\left(\frac{2071}{2430}\right)\)	\(e\left(\frac{283}{810}\right)\)	\(e\left(\frac{145}{162}\right)\)	\(e\left(\frac{2183}{2430}\right)\)	\(e\left(\frac{772}{1215}\right)\)	\(e\left(\frac{161}{1215}\right)\)	\(e\left(\frac{359}{810}\right)\)
\(\chi_{8019}(14,\cdot)\)	8019.bv	2430	yes	\(-1\)	\(1\)	\(e\left(\frac{1489}{2430}\right)\)	\(e\left(\frac{274}{1215}\right)\)	\(e\left(\frac{2171}{2430}\right)\)	\(e\left(\frac{1004}{1215}\right)\)	\(e\left(\frac{679}{810}\right)\)	\(e\left(\frac{41}{81}\right)\)	\(e\left(\frac{772}{1215}\right)\)	\(e\left(\frac{1067}{2430}\right)\)	\(e\left(\frac{548}{1215}\right)\)	\(e\left(\frac{17}{810}\right)\)
\(\chi_{8019}(16,\cdot)\)	8019.bs	1215	yes	\(1\)	\(1\)	\(e\left(\frac{496}{1215}\right)\)	\(e\left(\frac{992}{1215}\right)\)	\(e\left(\frac{959}{1215}\right)\)	\(e\left(\frac{52}{1215}\right)\)	\(e\left(\frac{91}{405}\right)\)	\(e\left(\frac{16}{81}\right)\)	\(e\left(\frac{161}{1215}\right)\)	\(e\left(\frac{548}{1215}\right)\)	\(e\left(\frac{769}{1215}\right)\)	\(e\left(\frac{353}{405}\right)\)
\(\chi_{8019}(17,\cdot)\)	8019.bq	810	no	\(1\)	\(1\)	\(e\left(\frac{392}{405}\right)\)	\(e\left(\frac{379}{405}\right)\)	\(e\left(\frac{131}{810}\right)\)	\(e\left(\frac{43}{810}\right)\)	\(e\left(\frac{122}{135}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{359}{810}\right)\)	\(e\left(\frac{17}{810}\right)\)	\(e\left(\frac{353}{405}\right)\)	\(e\left(\frac{46}{135}\right)\)
\(\chi_{8019}(19,\cdot)\)	8019.br	810	no	\(-1\)	\(1\)	\(e\left(\frac{773}{810}\right)\)	\(e\left(\frac{368}{405}\right)\)	\(e\left(\frac{101}{405}\right)\)	\(e\left(\frac{731}{810}\right)\)	\(e\left(\frac{233}{270}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{433}{810}\right)\)	\(e\left(\frac{347}{405}\right)\)	\(e\left(\frac{331}{405}\right)\)	\(e\left(\frac{79}{270}\right)\)
\(\chi_{8019}(20,\cdot)\)	8019.bv	2430	yes	\(-1\)	\(1\)	\(e\left(\frac{1583}{2430}\right)\)	\(e\left(\frac{368}{1215}\right)\)	\(e\left(\frac{1417}{2430}\right)\)	\(e\left(\frac{568}{1215}\right)\)	\(e\left(\frac{773}{810}\right)\)	\(e\left(\frac{19}{81}\right)\)	\(e\left(\frac{824}{1215}\right)\)	\(e\left(\frac{289}{2430}\right)\)	\(e\left(\frac{736}{1215}\right)\)	\(e\left(\frac{79}{810}\right)\)
\(\chi_{8019}(23,\cdot)\)	8019.bm	486	no	\(-1\)	\(1\)	\(e\left(\frac{389}{486}\right)\)	\(e\left(\frac{146}{243}\right)\)	\(e\left(\frac{199}{486}\right)\)	\(e\left(\frac{88}{243}\right)\)	\(e\left(\frac{65}{162}\right)\)	\(e\left(\frac{17}{81}\right)\)	\(e\left(\frac{179}{243}\right)\)	\(e\left(\frac{79}{486}\right)\)	\(e\left(\frac{49}{243}\right)\)	\(e\left(\frac{67}{162}\right)\)
\(\chi_{8019}(25,\cdot)\)	8019.bs	1215	yes	\(1\)	\(1\)	\(e\left(\frac{1087}{1215}\right)\)	\(e\left(\frac{959}{1215}\right)\)	\(e\left(\frac{458}{1215}\right)\)	\(e\left(\frac{1084}{1215}\right)\)	\(e\left(\frac{277}{405}\right)\)	\(e\left(\frac{22}{81}\right)\)	\(e\left(\frac{272}{1215}\right)\)	\(e\left(\frac{956}{1215}\right)\)	\(e\left(\frac{703}{1215}\right)\)	\(e\left(\frac{131}{405}\right)\)
\(\chi_{8019}(26,\cdot)\)	8019.bj	270	no	\(-1\)	\(1\)	\(e\left(\frac{239}{270}\right)\)	\(e\left(\frac{104}{135}\right)\)	\(e\left(\frac{151}{270}\right)\)	\(e\left(\frac{49}{135}\right)\)	\(e\left(\frac{59}{90}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{92}{135}\right)\)	\(e\left(\frac{67}{270}\right)\)	\(e\left(\frac{73}{135}\right)\)	\(e\left(\frac{37}{90}\right)\)
\(\chi_{8019}(28,\cdot)\)	8019.bk	270	no	\(-1\)	\(1\)	\(e\left(\frac{193}{270}\right)\)	\(e\left(\frac{58}{135}\right)\)	\(e\left(\frac{46}{135}\right)\)	\(e\left(\frac{91}{270}\right)\)	\(e\left(\frac{13}{90}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{113}{270}\right)\)	\(e\left(\frac{7}{135}\right)\)	\(e\left(\frac{116}{135}\right)\)	\(e\left(\frac{89}{90}\right)\)
\(\chi_{8019}(29,\cdot)\)	8019.bu	2430	yes	\(1\)	\(1\)	\(e\left(\frac{133}{1215}\right)\)	\(e\left(\frac{266}{1215}\right)\)	\(e\left(\frac{529}{2430}\right)\)	\(e\left(\frac{557}{2430}\right)\)	\(e\left(\frac{133}{405}\right)\)	\(e\left(\frac{53}{162}\right)\)	\(e\left(\frac{1561}{2430}\right)\)	\(e\left(\frac{823}{2430}\right)\)	\(e\left(\frac{532}{1215}\right)\)	\(e\left(\frac{329}{405}\right)\)
\(\chi_{8019}(31,\cdot)\)	8019.bs	1215	yes	\(1\)	\(1\)	\(e\left(\frac{374}{1215}\right)\)	\(e\left(\frac{748}{1215}\right)\)	\(e\left(\frac{826}{1215}\right)\)	\(e\left(\frac{98}{1215}\right)\)	\(e\left(\frac{374}{405}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{724}{1215}\right)\)	\(e\left(\frac{472}{1215}\right)\)	\(e\left(\frac{281}{1215}\right)\)	\(e\left(\frac{307}{405}\right)\)
\(\chi_{8019}(32,\cdot)\)	8019.bo	486	yes	\(1\)	\(1\)	\(e\left(\frac{124}{243}\right)\)	\(e\left(\frac{5}{243}\right)\)	\(e\left(\frac{115}{486}\right)\)	\(e\left(\frac{269}{486}\right)\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{121}{162}\right)\)	\(e\left(\frac{445}{486}\right)\)	\(e\left(\frac{31}{486}\right)\)	\(e\left(\frac{10}{243}\right)\)	\(e\left(\frac{68}{81}\right)\)
\(\chi_{8019}(34,\cdot)\)	8019.bh	243	no	\(1\)	\(1\)	\(e\left(\frac{17}{243}\right)\)	\(e\left(\frac{34}{243}\right)\)	\(e\left(\frac{148}{243}\right)\)	\(e\left(\frac{137}{243}\right)\)	\(e\left(\frac{17}{81}\right)\)	\(e\left(\frac{55}{81}\right)\)	\(e\left(\frac{55}{243}\right)\)	\(e\left(\frac{154}{243}\right)\)	\(e\left(\frac{68}{243}\right)\)	\(e\left(\frac{25}{81}\right)\)
\(\chi_{8019}(35,\cdot)\)	8019.bq	810	no	\(1\)	\(1\)	\(e\left(\frac{388}{405}\right)\)	\(e\left(\frac{371}{405}\right)\)	\(e\left(\frac{109}{810}\right)\)	\(e\left(\frac{617}{810}\right)\)	\(e\left(\frac{118}{135}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{781}{810}\right)\)	\(e\left(\frac{583}{810}\right)\)	\(e\left(\frac{337}{405}\right)\)	\(e\left(\frac{29}{135}\right)\)
\(\chi_{8019}(37,\cdot)\)	8019.bl	405	no	\(1\)	\(1\)	\(e\left(\frac{296}{405}\right)\)	\(e\left(\frac{187}{405}\right)\)	\(e\left(\frac{4}{405}\right)\)	\(e\left(\frac{227}{405}\right)\)	\(e\left(\frac{26}{135}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{181}{405}\right)\)	\(e\left(\frac{118}{405}\right)\)	\(e\left(\frac{374}{405}\right)\)	\(e\left(\frac{43}{135}\right)\)
\(\chi_{8019}(38,\cdot)\)	8019.bv	2430	yes	\(-1\)	\(1\)	\(e\left(\frac{137}{2430}\right)\)	\(e\left(\frac{137}{1215}\right)\)	\(e\left(\frac{1693}{2430}\right)\)	\(e\left(\frac{502}{1215}\right)\)	\(e\left(\frac{137}{810}\right)\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{386}{1215}\right)\)	\(e\left(\frac{1141}{2430}\right)\)	\(e\left(\frac{274}{1215}\right)\)	\(e\left(\frac{211}{810}\right)\)
\(\chi_{8019}(40,\cdot)\)	8019.bt	2430	yes	\(-1\)	\(1\)	\(e\left(\frac{1831}{2430}\right)\)	\(e\left(\frac{616}{1215}\right)\)	\(e\left(\frac{37}{1215}\right)\)	\(e\left(\frac{2377}{2430}\right)\)	\(e\left(\frac{211}{810}\right)\)	\(e\left(\frac{127}{162}\right)\)	\(e\left(\frac{1121}{2430}\right)\)	\(e\left(\frac{889}{1215}\right)\)	\(e\left(\frac{17}{1215}\right)\)	\(e\left(\frac{53}{810}\right)\)
\(\chi_{8019}(41,\cdot)\)	8019.bu	2430	yes	\(1\)	\(1\)	\(e\left(\frac{902}{1215}\right)\)	\(e\left(\frac{589}{1215}\right)\)	\(e\left(\frac{911}{2430}\right)\)	\(e\left(\frac{973}{2430}\right)\)	\(e\left(\frac{92}{405}\right)\)	\(e\left(\frac{19}{162}\right)\)	\(e\left(\frac{419}{2430}\right)\)	\(e\left(\frac{347}{2430}\right)\)	\(e\left(\frac{1178}{1215}\right)\)	\(e\left(\frac{121}{405}\right)\)
\(\chi_{8019}(43,\cdot)\)	8019.bn	486	yes	\(-1\)	\(1\)	\(e\left(\frac{211}{486}\right)\)	\(e\left(\frac{211}{243}\right)\)	\(e\left(\frac{118}{243}\right)\)	\(e\left(\frac{271}{486}\right)\)	\(e\left(\frac{49}{162}\right)\)	\(e\left(\frac{149}{162}\right)\)	\(e\left(\frac{311}{486}\right)\)	\(e\left(\frac{241}{243}\right)\)	\(e\left(\frac{179}{243}\right)\)	\(e\left(\frac{53}{162}\right)\)
\(\chi_{8019}(46,\cdot)\)	8019.br	810	no	\(-1\)	\(1\)	\(e\left(\frac{731}{810}\right)\)	\(e\left(\frac{326}{405}\right)\)	\(e\left(\frac{347}{405}\right)\)	\(e\left(\frac{707}{810}\right)\)	\(e\left(\frac{191}{270}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{421}{810}\right)\)	\(e\left(\frac{314}{405}\right)\)	\(e\left(\frac{247}{405}\right)\)	\(e\left(\frac{103}{270}\right)\)
\(\chi_{8019}(47,\cdot)\)	8019.bv	2430	yes	\(-1\)	\(1\)	\(e\left(\frac{1439}{2430}\right)\)	\(e\left(\frac{224}{1215}\right)\)	\(e\left(\frac{1021}{2430}\right)\)	\(e\left(\frac{874}{1215}\right)\)	\(e\left(\frac{629}{810}\right)\)	\(e\left(\frac{1}{81}\right)\)	\(e\left(\frac{977}{1215}\right)\)	\(e\left(\frac{757}{2430}\right)\)	\(e\left(\frac{448}{1215}\right)\)	\(e\left(\frac{277}{810}\right)\)
\(\chi_{8019}(49,\cdot)\)	8019.bs	1215	yes	\(1\)	\(1\)	\(e\left(\frac{26}{1215}\right)\)	\(e\left(\frac{52}{1215}\right)\)	\(e\left(\frac{1084}{1215}\right)\)	\(e\left(\frac{767}{1215}\right)\)	\(e\left(\frac{26}{405}\right)\)	\(e\left(\frac{74}{81}\right)\)	\(e\left(\frac{856}{1215}\right)\)	\(e\left(\frac{793}{1215}\right)\)	\(e\left(\frac{104}{1215}\right)\)	\(e\left(\frac{43}{405}\right)\)
\(\chi_{8019}(50,\cdot)\)	8019.bu	2430	yes	\(1\)	\(1\)	\(e\left(\frac{1211}{1215}\right)\)	\(e\left(\frac{1207}{1215}\right)\)	\(e\left(\frac{2003}{2430}\right)\)	\(e\left(\frac{979}{2430}\right)\)	\(e\left(\frac{401}{405}\right)\)	\(e\left(\frac{133}{162}\right)\)	\(e\left(\frac{17}{2430}\right)\)	\(e\left(\frac{971}{2430}\right)\)	\(e\left(\frac{1199}{1215}\right)\)	\(e\left(\frac{118}{405}\right)\)
\(\chi_{8019}(52,\cdot)\)	8019.bt	2430	yes	\(-1\)	\(1\)	\(e\left(\frac{2399}{2430}\right)\)	\(e\left(\frac{1184}{1215}\right)\)	\(e\left(\frac{8}{1215}\right)\)	\(e\left(\frac{2123}{2430}\right)\)	\(e\left(\frac{779}{810}\right)\)	\(e\left(\frac{161}{162}\right)\)	\(e\left(\frac{1129}{2430}\right)\)	\(e\left(\frac{1046}{1215}\right)\)	\(e\left(\frac{1153}{1215}\right)\)	\(e\left(\frac{307}{810}\right)\)

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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.