LMFDB - Group of Dirichlet characters of modulus 8673

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8673)

pari: g = idealstar(,8673,2)

Character group

sage: G.order() pari: g.no
Order	=	4872
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{1218}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8673}(5783,\cdot)$, $\chi_{8673}(6373,\cdot)$, $\chi_{8673}(8380,\cdot)$

First 32 of 4872 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{8673}(1,\cdot)$	8673.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8673}(2,\cdot)$	8673.ch	1218	yes	$1$	$1$	$e\left(\frac{373}{609}\right)$	$e\left(\frac{137}{609}\right)$	$e\left(\frac{677}{1218}\right)$	$e\left(\frac{170}{203}\right)$	$e\left(\frac{205}{1218}\right)$	$e\left(\frac{422}{609}\right)$	$e\left(\frac{83}{406}\right)$	$e\left(\frac{274}{609}\right)$	$e\left(\frac{811}{1218}\right)$	$e\left(\frac{28}{87}\right)$
$\chi_{8673}(4,\cdot)$	8673.ce	609	no	$1$	$1$	$e\left(\frac{137}{609}\right)$	$e\left(\frac{274}{609}\right)$	$e\left(\frac{68}{609}\right)$	$e\left(\frac{137}{203}\right)$	$e\left(\frac{205}{609}\right)$	$e\left(\frac{235}{609}\right)$	$e\left(\frac{83}{203}\right)$	$e\left(\frac{548}{609}\right)$	$e\left(\frac{202}{609}\right)$	$e\left(\frac{56}{87}\right)$
$\chi_{8673}(5,\cdot)$	8673.ci	1218	yes	$1$	$1$	$e\left(\frac{677}{1218}\right)$	$e\left(\frac{68}{609}\right)$	$e\left(\frac{88}{609}\right)$	$e\left(\frac{271}{406}\right)$	$e\left(\frac{853}{1218}\right)$	$e\left(\frac{859}{1218}\right)$	$e\left(\frac{179}{406}\right)$	$e\left(\frac{136}{609}\right)$	$e\left(\frac{548}{609}\right)$	$e\left(\frac{17}{174}\right)$
$\chi_{8673}(8,\cdot)$	8673.cb	406	yes	$1$	$1$	$e\left(\frac{170}{203}\right)$	$e\left(\frac{137}{203}\right)$	$e\left(\frac{271}{406}\right)$	$e\left(\frac{104}{203}\right)$	$e\left(\frac{205}{406}\right)$	$e\left(\frac{16}{203}\right)$	$e\left(\frac{249}{406}\right)$	$e\left(\frac{71}{203}\right)$	$e\left(\frac{405}{406}\right)$	$e\left(\frac{28}{29}\right)$
$\chi_{8673}(10,\cdot)$	8673.ck	1218	no	$1$	$1$	$e\left(\frac{205}{1218}\right)$	$e\left(\frac{205}{609}\right)$	$e\left(\frac{853}{1218}\right)$	$e\left(\frac{205}{406}\right)$	$e\left(\frac{529}{609}\right)$	$e\left(\frac{485}{1218}\right)$	$e\left(\frac{131}{203}\right)$	$e\left(\frac{410}{609}\right)$	$e\left(\frac{689}{1218}\right)$	$e\left(\frac{73}{174}\right)$
$\chi_{8673}(11,\cdot)$	8673.ch	1218	yes	$1$	$1$	$e\left(\frac{422}{609}\right)$	$e\left(\frac{235}{609}\right)$	$e\left(\frac{859}{1218}\right)$	$e\left(\frac{16}{203}\right)$	$e\left(\frac{485}{1218}\right)$	$e\left(\frac{226}{609}\right)$	$e\left(\frac{335}{406}\right)$	$e\left(\frac{470}{609}\right)$	$e\left(\frac{671}{1218}\right)$	$e\left(\frac{62}{87}\right)$
$\chi_{8673}(13,\cdot)$	8673.by	406	no	$1$	$1$	$e\left(\frac{83}{406}\right)$	$e\left(\frac{83}{203}\right)$	$e\left(\frac{179}{406}\right)$	$e\left(\frac{249}{406}\right)$	$e\left(\frac{131}{203}\right)$	$e\left(\frac{335}{406}\right)$	$e\left(\frac{171}{203}\right)$	$e\left(\frac{166}{203}\right)$	$e\left(\frac{275}{406}\right)$	$e\left(\frac{57}{58}\right)$
$\chi_{8673}(16,\cdot)$	8673.ce	609	no	$1$	$1$	$e\left(\frac{274}{609}\right)$	$e\left(\frac{548}{609}\right)$	$e\left(\frac{136}{609}\right)$	$e\left(\frac{71}{203}\right)$	$e\left(\frac{410}{609}\right)$	$e\left(\frac{470}{609}\right)$	$e\left(\frac{166}{203}\right)$	$e\left(\frac{487}{609}\right)$	$e\left(\frac{404}{609}\right)$	$e\left(\frac{25}{87}\right)$
$\chi_{8673}(17,\cdot)$	8673.ci	1218	yes	$1$	$1$	$e\left(\frac{811}{1218}\right)$	$e\left(\frac{202}{609}\right)$	$e\left(\frac{548}{609}\right)$	$e\left(\frac{405}{406}\right)$	$e\left(\frac{689}{1218}\right)$	$e\left(\frac{671}{1218}\right)$	$e\left(\frac{275}{406}\right)$	$e\left(\frac{404}{609}\right)$	$e\left(\frac{589}{609}\right)$	$e\left(\frac{7}{174}\right)$
$\chi_{8673}(19,\cdot)$	8673.bt	174	no	$-1$	$1$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{17}{174}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{73}{174}\right)$	$e\left(\frac{62}{87}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{7}{174}\right)$	$e\left(\frac{11}{174}\right)$
$\chi_{8673}(20,\cdot)$	8673.ca	406	yes	$1$	$1$	$e\left(\frac{317}{406}\right)$	$e\left(\frac{114}{203}\right)$	$e\left(\frac{52}{203}\right)$	$e\left(\frac{139}{406}\right)$	$e\left(\frac{15}{406}\right)$	$e\left(\frac{37}{406}\right)$	$e\left(\frac{345}{406}\right)$	$e\left(\frac{25}{203}\right)$	$e\left(\frac{47}{203}\right)$	$e\left(\frac{43}{58}\right)$
$\chi_{8673}(22,\cdot)$	8673.bw	203	no	$1$	$1$	$e\left(\frac{62}{203}\right)$	$e\left(\frac{124}{203}\right)$	$e\left(\frac{53}{203}\right)$	$e\left(\frac{186}{203}\right)$	$e\left(\frac{115}{203}\right)$	$e\left(\frac{13}{203}\right)$	$e\left(\frac{6}{203}\right)$	$e\left(\frac{45}{203}\right)$	$e\left(\frac{44}{203}\right)$	$e\left(\frac{1}{29}\right)$
$\chi_{8673}(23,\cdot)$	8673.ch	1218	yes	$1$	$1$	$e\left(\frac{172}{609}\right)$	$e\left(\frac{344}{609}\right)$	$e\left(\frac{353}{1218}\right)$	$e\left(\frac{172}{203}\right)$	$e\left(\frac{697}{1218}\right)$	$e\left(\frac{95}{609}\right)$	$e\left(\frac{201}{406}\right)$	$e\left(\frac{79}{609}\right)$	$e\left(\frac{565}{1218}\right)$	$e\left(\frac{43}{87}\right)$
$\chi_{8673}(25,\cdot)$	8673.ce	609	no	$1$	$1$	$e\left(\frac{68}{609}\right)$	$e\left(\frac{136}{609}\right)$	$e\left(\frac{176}{609}\right)$	$e\left(\frac{68}{203}\right)$	$e\left(\frac{244}{609}\right)$	$e\left(\frac{250}{609}\right)$	$e\left(\frac{179}{203}\right)$	$e\left(\frac{272}{609}\right)$	$e\left(\frac{487}{609}\right)$	$e\left(\frac{17}{87}\right)$
$\chi_{8673}(26,\cdot)$	8673.ci	1218	yes	$1$	$1$	$e\left(\frac{995}{1218}\right)$	$e\left(\frac{386}{609}\right)$	$e\left(\frac{607}{609}\right)$	$e\left(\frac{183}{406}\right)$	$e\left(\frac{991}{1218}\right)$	$e\left(\frac{631}{1218}\right)$	$e\left(\frac{19}{406}\right)$	$e\left(\frac{163}{609}\right)$	$e\left(\frac{209}{609}\right)$	$e\left(\frac{53}{174}\right)$
$\chi_{8673}(29,\cdot)$	8673.bx	406	yes	$-1$	$1$	$e\left(\frac{51}{406}\right)$	$e\left(\frac{51}{203}\right)$	$e\left(\frac{335}{406}\right)$	$e\left(\frac{153}{406}\right)$	$e\left(\frac{193}{203}\right)$	$e\left(\frac{289}{406}\right)$	$e\left(\frac{176}{203}\right)$	$e\left(\frac{102}{203}\right)$	$e\left(\frac{213}{406}\right)$	$e\left(\frac{10}{29}\right)$
$\chi_{8673}(31,\cdot)$	8673.bp	174	no	$1$	$1$	$e\left(\frac{31}{174}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{157}{174}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{137}{174}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{62}{87}\right)$	$e\left(\frac{167}{174}\right)$	$e\left(\frac{163}{174}\right)$
$\chi_{8673}(32,\cdot)$	8673.ch	1218	yes	$1$	$1$	$e\left(\frac{38}{609}\right)$	$e\left(\frac{76}{609}\right)$	$e\left(\frac{949}{1218}\right)$	$e\left(\frac{38}{203}\right)$	$e\left(\frac{1025}{1218}\right)$	$e\left(\frac{283}{609}\right)$	$e\left(\frac{9}{406}\right)$	$e\left(\frac{152}{609}\right)$	$e\left(\frac{401}{1218}\right)$	$e\left(\frac{53}{87}\right)$
$\chi_{8673}(34,\cdot)$	8673.by	406	no	$1$	$1$	$e\left(\frac{113}{406}\right)$	$e\left(\frac{113}{203}\right)$	$e\left(\frac{185}{406}\right)$	$e\left(\frac{339}{406}\right)$	$e\left(\frac{149}{203}\right)$	$e\left(\frac{99}{406}\right)$	$e\left(\frac{179}{203}\right)$	$e\left(\frac{23}{203}\right)$	$e\left(\frac{257}{406}\right)$	$e\left(\frac{21}{58}\right)$
$\chi_{8673}(37,\cdot)$	8673.cj	1218	no	$-1$	$1$	$e\left(\frac{923}{1218}\right)$	$e\left(\frac{314}{609}\right)$	$e\left(\frac{478}{609}\right)$	$e\left(\frac{111}{406}\right)$	$e\left(\frac{661}{1218}\right)$	$e\left(\frac{223}{1218}\right)$	$e\left(\frac{331}{406}\right)$	$e\left(\frac{19}{609}\right)$	$e\left(\frac{596}{609}\right)$	$e\left(\frac{61}{87}\right)$
$\chi_{8673}(38,\cdot)$	8673.cf	1218	yes	$-1$	$1$	$e\left(\frac{569}{609}\right)$	$e\left(\frac{529}{609}\right)$	$e\left(\frac{398}{609}\right)$	$e\left(\frac{163}{203}\right)$	$e\left(\frac{358}{609}\right)$	$e\left(\frac{247}{609}\right)$	$e\left(\frac{38}{203}\right)$	$e\left(\frac{449}{609}\right)$	$e\left(\frac{430}{609}\right)$	$e\left(\frac{67}{174}\right)$
$\chi_{8673}(40,\cdot)$	8673.ck	1218	no	$1$	$1$	$e\left(\frac{479}{1218}\right)$	$e\left(\frac{479}{609}\right)$	$e\left(\frac{989}{1218}\right)$	$e\left(\frac{73}{406}\right)$	$e\left(\frac{125}{609}\right)$	$e\left(\frac{955}{1218}\right)$	$e\left(\frac{11}{203}\right)$	$e\left(\frac{349}{609}\right)$	$e\left(\frac{1093}{1218}\right)$	$e\left(\frac{11}{174}\right)$
$\chi_{8673}(41,\cdot)$	8673.ca	406	yes	$1$	$1$	$e\left(\frac{11}{406}\right)$	$e\left(\frac{11}{203}\right)$	$e\left(\frac{62}{203}\right)$	$e\left(\frac{33}{406}\right)$	$e\left(\frac{135}{406}\right)$	$e\left(\frac{333}{406}\right)$	$e\left(\frac{263}{406}\right)$	$e\left(\frac{22}{203}\right)$	$e\left(\frac{17}{203}\right)$	$e\left(\frac{39}{58}\right)$
$\chi_{8673}(43,\cdot)$	8673.bz	406	no	$-1$	$1$	$e\left(\frac{115}{406}\right)$	$e\left(\frac{115}{203}\right)$	$e\left(\frac{113}{203}\right)$	$e\left(\frac{345}{406}\right)$	$e\left(\frac{341}{406}\right)$	$e\left(\frac{381}{406}\right)$	$e\left(\frac{129}{406}\right)$	$e\left(\frac{27}{203}\right)$	$e\left(\frac{67}{203}\right)$	$e\left(\frac{18}{29}\right)$
$\chi_{8673}(44,\cdot)$	8673.ch	1218	yes	$1$	$1$	$e\left(\frac{559}{609}\right)$	$e\left(\frac{509}{609}\right)$	$e\left(\frac{995}{1218}\right)$	$e\left(\frac{153}{203}\right)$	$e\left(\frac{895}{1218}\right)$	$e\left(\frac{461}{609}\right)$	$e\left(\frac{95}{406}\right)$	$e\left(\frac{409}{609}\right)$	$e\left(\frac{1075}{1218}\right)$	$e\left(\frac{31}{87}\right)$
$\chi_{8673}(46,\cdot)$	8673.ce	609	no	$1$	$1$	$e\left(\frac{545}{609}\right)$	$e\left(\frac{481}{609}\right)$	$e\left(\frac{515}{609}\right)$	$e\left(\frac{139}{203}\right)$	$e\left(\frac{451}{609}\right)$	$e\left(\frac{517}{609}\right)$	$e\left(\frac{142}{203}\right)$	$e\left(\frac{353}{609}\right)$	$e\left(\frac{79}{609}\right)$	$e\left(\frac{71}{87}\right)$
$\chi_{8673}(47,\cdot)$	8673.cf	1218	yes	$-1$	$1$	$e\left(\frac{604}{609}\right)$	$e\left(\frac{599}{609}\right)$	$e\left(\frac{202}{609}\right)$	$e\left(\frac{198}{203}\right)$	$e\left(\frac{197}{609}\right)$	$e\left(\frac{107}{609}\right)$	$e\left(\frac{157}{203}\right)$	$e\left(\frac{589}{609}\right)$	$e\left(\frac{206}{609}\right)$	$e\left(\frac{41}{174}\right)$
$\chi_{8673}(50,\cdot)$	8673.bi	58	no	$1$	$1$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{15}{29}\right)$
$\chi_{8673}(52,\cdot)$	8673.ck	1218	no	$1$	$1$	$e\left(\frac{523}{1218}\right)$	$e\left(\frac{523}{609}\right)$	$e\left(\frac{673}{1218}\right)$	$e\left(\frac{117}{406}\right)$	$e\left(\frac{598}{609}\right)$	$e\left(\frac{257}{1218}\right)$	$e\left(\frac{51}{203}\right)$	$e\left(\frac{437}{609}\right)$	$e\left(\frac{11}{1218}\right)$	$e\left(\frac{109}{174}\right)$
$\chi_{8673}(53,\cdot)$	8673.cl	1218	yes	$-1$	$1$	$e\left(\frac{85}{1218}\right)$	$e\left(\frac{85}{609}\right)$	$e\left(\frac{829}{1218}\right)$	$e\left(\frac{85}{406}\right)$	$e\left(\frac{457}{609}\right)$	$e\left(\frac{617}{1218}\right)$	$e\left(\frac{188}{203}\right)$	$e\left(\frac{170}{609}\right)$	$e\left(\frac{761}{1218}\right)$	$e\left(\frac{65}{87}\right)$
$\chi_{8673}(55,\cdot)$	8673.by	406	no	$1$	$1$	$e\left(\frac{101}{406}\right)$	$e\left(\frac{101}{203}\right)$	$e\left(\frac{345}{406}\right)$	$e\left(\frac{303}{406}\right)$	$e\left(\frac{20}{203}\right)$	$e\left(\frac{31}{406}\right)$	$e\left(\frac{54}{203}\right)$	$e\left(\frac{202}{203}\right)$	$e\left(\frac{183}{406}\right)$	$e\left(\frac{47}{58}\right)$

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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	$8673$
Structure	\(C_{2}\times C_{2}\times C_{1218}\)
Order	$4872$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{8673}(1,\cdot)\)	8673.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8673}(2,\cdot)\)	8673.ch	1218	yes	\(1\)	\(1\)	\(e\left(\frac{373}{609}\right)\)	\(e\left(\frac{137}{609}\right)\)	\(e\left(\frac{677}{1218}\right)\)	\(e\left(\frac{170}{203}\right)\)	\(e\left(\frac{205}{1218}\right)\)	\(e\left(\frac{422}{609}\right)\)	\(e\left(\frac{83}{406}\right)\)	\(e\left(\frac{274}{609}\right)\)	\(e\left(\frac{811}{1218}\right)\)	\(e\left(\frac{28}{87}\right)\)
\(\chi_{8673}(4,\cdot)\)	8673.ce	609	no	\(1\)	\(1\)	\(e\left(\frac{137}{609}\right)\)	\(e\left(\frac{274}{609}\right)\)	\(e\left(\frac{68}{609}\right)\)	\(e\left(\frac{137}{203}\right)\)	\(e\left(\frac{205}{609}\right)\)	\(e\left(\frac{235}{609}\right)\)	\(e\left(\frac{83}{203}\right)\)	\(e\left(\frac{548}{609}\right)\)	\(e\left(\frac{202}{609}\right)\)	\(e\left(\frac{56}{87}\right)\)
\(\chi_{8673}(5,\cdot)\)	8673.ci	1218	yes	\(1\)	\(1\)	\(e\left(\frac{677}{1218}\right)\)	\(e\left(\frac{68}{609}\right)\)	\(e\left(\frac{88}{609}\right)\)	\(e\left(\frac{271}{406}\right)\)	\(e\left(\frac{853}{1218}\right)\)	\(e\left(\frac{859}{1218}\right)\)	\(e\left(\frac{179}{406}\right)\)	\(e\left(\frac{136}{609}\right)\)	\(e\left(\frac{548}{609}\right)\)	\(e\left(\frac{17}{174}\right)\)
\(\chi_{8673}(8,\cdot)\)	8673.cb	406	yes	\(1\)	\(1\)	\(e\left(\frac{170}{203}\right)\)	\(e\left(\frac{137}{203}\right)\)	\(e\left(\frac{271}{406}\right)\)	\(e\left(\frac{104}{203}\right)\)	\(e\left(\frac{205}{406}\right)\)	\(e\left(\frac{16}{203}\right)\)	\(e\left(\frac{249}{406}\right)\)	\(e\left(\frac{71}{203}\right)\)	\(e\left(\frac{405}{406}\right)\)	\(e\left(\frac{28}{29}\right)\)
\(\chi_{8673}(10,\cdot)\)	8673.ck	1218	no	\(1\)	\(1\)	\(e\left(\frac{205}{1218}\right)\)	\(e\left(\frac{205}{609}\right)\)	\(e\left(\frac{853}{1218}\right)\)	\(e\left(\frac{205}{406}\right)\)	\(e\left(\frac{529}{609}\right)\)	\(e\left(\frac{485}{1218}\right)\)	\(e\left(\frac{131}{203}\right)\)	\(e\left(\frac{410}{609}\right)\)	\(e\left(\frac{689}{1218}\right)\)	\(e\left(\frac{73}{174}\right)\)
\(\chi_{8673}(11,\cdot)\)	8673.ch	1218	yes	\(1\)	\(1\)	\(e\left(\frac{422}{609}\right)\)	\(e\left(\frac{235}{609}\right)\)	\(e\left(\frac{859}{1218}\right)\)	\(e\left(\frac{16}{203}\right)\)	\(e\left(\frac{485}{1218}\right)\)	\(e\left(\frac{226}{609}\right)\)	\(e\left(\frac{335}{406}\right)\)	\(e\left(\frac{470}{609}\right)\)	\(e\left(\frac{671}{1218}\right)\)	\(e\left(\frac{62}{87}\right)\)
\(\chi_{8673}(13,\cdot)\)	8673.by	406	no	\(1\)	\(1\)	\(e\left(\frac{83}{406}\right)\)	\(e\left(\frac{83}{203}\right)\)	\(e\left(\frac{179}{406}\right)\)	\(e\left(\frac{249}{406}\right)\)	\(e\left(\frac{131}{203}\right)\)	\(e\left(\frac{335}{406}\right)\)	\(e\left(\frac{171}{203}\right)\)	\(e\left(\frac{166}{203}\right)\)	\(e\left(\frac{275}{406}\right)\)	\(e\left(\frac{57}{58}\right)\)
\(\chi_{8673}(16,\cdot)\)	8673.ce	609	no	\(1\)	\(1\)	\(e\left(\frac{274}{609}\right)\)	\(e\left(\frac{548}{609}\right)\)	\(e\left(\frac{136}{609}\right)\)	\(e\left(\frac{71}{203}\right)\)	\(e\left(\frac{410}{609}\right)\)	\(e\left(\frac{470}{609}\right)\)	\(e\left(\frac{166}{203}\right)\)	\(e\left(\frac{487}{609}\right)\)	\(e\left(\frac{404}{609}\right)\)	\(e\left(\frac{25}{87}\right)\)
\(\chi_{8673}(17,\cdot)\)	8673.ci	1218	yes	\(1\)	\(1\)	\(e\left(\frac{811}{1218}\right)\)	\(e\left(\frac{202}{609}\right)\)	\(e\left(\frac{548}{609}\right)\)	\(e\left(\frac{405}{406}\right)\)	\(e\left(\frac{689}{1218}\right)\)	\(e\left(\frac{671}{1218}\right)\)	\(e\left(\frac{275}{406}\right)\)	\(e\left(\frac{404}{609}\right)\)	\(e\left(\frac{589}{609}\right)\)	\(e\left(\frac{7}{174}\right)\)
\(\chi_{8673}(19,\cdot)\)	8673.bt	174	no	\(-1\)	\(1\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{17}{174}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{73}{174}\right)\)	\(e\left(\frac{62}{87}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{7}{174}\right)\)	\(e\left(\frac{11}{174}\right)\)
\(\chi_{8673}(20,\cdot)\)	8673.ca	406	yes	\(1\)	\(1\)	\(e\left(\frac{317}{406}\right)\)	\(e\left(\frac{114}{203}\right)\)	\(e\left(\frac{52}{203}\right)\)	\(e\left(\frac{139}{406}\right)\)	\(e\left(\frac{15}{406}\right)\)	\(e\left(\frac{37}{406}\right)\)	\(e\left(\frac{345}{406}\right)\)	\(e\left(\frac{25}{203}\right)\)	\(e\left(\frac{47}{203}\right)\)	\(e\left(\frac{43}{58}\right)\)
\(\chi_{8673}(22,\cdot)\)	8673.bw	203	no	\(1\)	\(1\)	\(e\left(\frac{62}{203}\right)\)	\(e\left(\frac{124}{203}\right)\)	\(e\left(\frac{53}{203}\right)\)	\(e\left(\frac{186}{203}\right)\)	\(e\left(\frac{115}{203}\right)\)	\(e\left(\frac{13}{203}\right)\)	\(e\left(\frac{6}{203}\right)\)	\(e\left(\frac{45}{203}\right)\)	\(e\left(\frac{44}{203}\right)\)	\(e\left(\frac{1}{29}\right)\)
\(\chi_{8673}(23,\cdot)\)	8673.ch	1218	yes	\(1\)	\(1\)	\(e\left(\frac{172}{609}\right)\)	\(e\left(\frac{344}{609}\right)\)	\(e\left(\frac{353}{1218}\right)\)	\(e\left(\frac{172}{203}\right)\)	\(e\left(\frac{697}{1218}\right)\)	\(e\left(\frac{95}{609}\right)\)	\(e\left(\frac{201}{406}\right)\)	\(e\left(\frac{79}{609}\right)\)	\(e\left(\frac{565}{1218}\right)\)	\(e\left(\frac{43}{87}\right)\)
\(\chi_{8673}(25,\cdot)\)	8673.ce	609	no	\(1\)	\(1\)	\(e\left(\frac{68}{609}\right)\)	\(e\left(\frac{136}{609}\right)\)	\(e\left(\frac{176}{609}\right)\)	\(e\left(\frac{68}{203}\right)\)	\(e\left(\frac{244}{609}\right)\)	\(e\left(\frac{250}{609}\right)\)	\(e\left(\frac{179}{203}\right)\)	\(e\left(\frac{272}{609}\right)\)	\(e\left(\frac{487}{609}\right)\)	\(e\left(\frac{17}{87}\right)\)
\(\chi_{8673}(26,\cdot)\)	8673.ci	1218	yes	\(1\)	\(1\)	\(e\left(\frac{995}{1218}\right)\)	\(e\left(\frac{386}{609}\right)\)	\(e\left(\frac{607}{609}\right)\)	\(e\left(\frac{183}{406}\right)\)	\(e\left(\frac{991}{1218}\right)\)	\(e\left(\frac{631}{1218}\right)\)	\(e\left(\frac{19}{406}\right)\)	\(e\left(\frac{163}{609}\right)\)	\(e\left(\frac{209}{609}\right)\)	\(e\left(\frac{53}{174}\right)\)
\(\chi_{8673}(29,\cdot)\)	8673.bx	406	yes	\(-1\)	\(1\)	\(e\left(\frac{51}{406}\right)\)	\(e\left(\frac{51}{203}\right)\)	\(e\left(\frac{335}{406}\right)\)	\(e\left(\frac{153}{406}\right)\)	\(e\left(\frac{193}{203}\right)\)	\(e\left(\frac{289}{406}\right)\)	\(e\left(\frac{176}{203}\right)\)	\(e\left(\frac{102}{203}\right)\)	\(e\left(\frac{213}{406}\right)\)	\(e\left(\frac{10}{29}\right)\)
\(\chi_{8673}(31,\cdot)\)	8673.bp	174	no	\(1\)	\(1\)	\(e\left(\frac{31}{174}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{157}{174}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{137}{174}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{62}{87}\right)\)	\(e\left(\frac{167}{174}\right)\)	\(e\left(\frac{163}{174}\right)\)
\(\chi_{8673}(32,\cdot)\)	8673.ch	1218	yes	\(1\)	\(1\)	\(e\left(\frac{38}{609}\right)\)	\(e\left(\frac{76}{609}\right)\)	\(e\left(\frac{949}{1218}\right)\)	\(e\left(\frac{38}{203}\right)\)	\(e\left(\frac{1025}{1218}\right)\)	\(e\left(\frac{283}{609}\right)\)	\(e\left(\frac{9}{406}\right)\)	\(e\left(\frac{152}{609}\right)\)	\(e\left(\frac{401}{1218}\right)\)	\(e\left(\frac{53}{87}\right)\)
\(\chi_{8673}(34,\cdot)\)	8673.by	406	no	\(1\)	\(1\)	\(e\left(\frac{113}{406}\right)\)	\(e\left(\frac{113}{203}\right)\)	\(e\left(\frac{185}{406}\right)\)	\(e\left(\frac{339}{406}\right)\)	\(e\left(\frac{149}{203}\right)\)	\(e\left(\frac{99}{406}\right)\)	\(e\left(\frac{179}{203}\right)\)	\(e\left(\frac{23}{203}\right)\)	\(e\left(\frac{257}{406}\right)\)	\(e\left(\frac{21}{58}\right)\)
\(\chi_{8673}(37,\cdot)\)	8673.cj	1218	no	\(-1\)	\(1\)	\(e\left(\frac{923}{1218}\right)\)	\(e\left(\frac{314}{609}\right)\)	\(e\left(\frac{478}{609}\right)\)	\(e\left(\frac{111}{406}\right)\)	\(e\left(\frac{661}{1218}\right)\)	\(e\left(\frac{223}{1218}\right)\)	\(e\left(\frac{331}{406}\right)\)	\(e\left(\frac{19}{609}\right)\)	\(e\left(\frac{596}{609}\right)\)	\(e\left(\frac{61}{87}\right)\)
\(\chi_{8673}(38,\cdot)\)	8673.cf	1218	yes	\(-1\)	\(1\)	\(e\left(\frac{569}{609}\right)\)	\(e\left(\frac{529}{609}\right)\)	\(e\left(\frac{398}{609}\right)\)	\(e\left(\frac{163}{203}\right)\)	\(e\left(\frac{358}{609}\right)\)	\(e\left(\frac{247}{609}\right)\)	\(e\left(\frac{38}{203}\right)\)	\(e\left(\frac{449}{609}\right)\)	\(e\left(\frac{430}{609}\right)\)	\(e\left(\frac{67}{174}\right)\)
\(\chi_{8673}(40,\cdot)\)	8673.ck	1218	no	\(1\)	\(1\)	\(e\left(\frac{479}{1218}\right)\)	\(e\left(\frac{479}{609}\right)\)	\(e\left(\frac{989}{1218}\right)\)	\(e\left(\frac{73}{406}\right)\)	\(e\left(\frac{125}{609}\right)\)	\(e\left(\frac{955}{1218}\right)\)	\(e\left(\frac{11}{203}\right)\)	\(e\left(\frac{349}{609}\right)\)	\(e\left(\frac{1093}{1218}\right)\)	\(e\left(\frac{11}{174}\right)\)
\(\chi_{8673}(41,\cdot)\)	8673.ca	406	yes	\(1\)	\(1\)	\(e\left(\frac{11}{406}\right)\)	\(e\left(\frac{11}{203}\right)\)	\(e\left(\frac{62}{203}\right)\)	\(e\left(\frac{33}{406}\right)\)	\(e\left(\frac{135}{406}\right)\)	\(e\left(\frac{333}{406}\right)\)	\(e\left(\frac{263}{406}\right)\)	\(e\left(\frac{22}{203}\right)\)	\(e\left(\frac{17}{203}\right)\)	\(e\left(\frac{39}{58}\right)\)
\(\chi_{8673}(43,\cdot)\)	8673.bz	406	no	\(-1\)	\(1\)	\(e\left(\frac{115}{406}\right)\)	\(e\left(\frac{115}{203}\right)\)	\(e\left(\frac{113}{203}\right)\)	\(e\left(\frac{345}{406}\right)\)	\(e\left(\frac{341}{406}\right)\)	\(e\left(\frac{381}{406}\right)\)	\(e\left(\frac{129}{406}\right)\)	\(e\left(\frac{27}{203}\right)\)	\(e\left(\frac{67}{203}\right)\)	\(e\left(\frac{18}{29}\right)\)
\(\chi_{8673}(44,\cdot)\)	8673.ch	1218	yes	\(1\)	\(1\)	\(e\left(\frac{559}{609}\right)\)	\(e\left(\frac{509}{609}\right)\)	\(e\left(\frac{995}{1218}\right)\)	\(e\left(\frac{153}{203}\right)\)	\(e\left(\frac{895}{1218}\right)\)	\(e\left(\frac{461}{609}\right)\)	\(e\left(\frac{95}{406}\right)\)	\(e\left(\frac{409}{609}\right)\)	\(e\left(\frac{1075}{1218}\right)\)	\(e\left(\frac{31}{87}\right)\)
\(\chi_{8673}(46,\cdot)\)	8673.ce	609	no	\(1\)	\(1\)	\(e\left(\frac{545}{609}\right)\)	\(e\left(\frac{481}{609}\right)\)	\(e\left(\frac{515}{609}\right)\)	\(e\left(\frac{139}{203}\right)\)	\(e\left(\frac{451}{609}\right)\)	\(e\left(\frac{517}{609}\right)\)	\(e\left(\frac{142}{203}\right)\)	\(e\left(\frac{353}{609}\right)\)	\(e\left(\frac{79}{609}\right)\)	\(e\left(\frac{71}{87}\right)\)
\(\chi_{8673}(47,\cdot)\)	8673.cf	1218	yes	\(-1\)	\(1\)	\(e\left(\frac{604}{609}\right)\)	\(e\left(\frac{599}{609}\right)\)	\(e\left(\frac{202}{609}\right)\)	\(e\left(\frac{198}{203}\right)\)	\(e\left(\frac{197}{609}\right)\)	\(e\left(\frac{107}{609}\right)\)	\(e\left(\frac{157}{203}\right)\)	\(e\left(\frac{589}{609}\right)\)	\(e\left(\frac{206}{609}\right)\)	\(e\left(\frac{41}{174}\right)\)
\(\chi_{8673}(50,\cdot)\)	8673.bi	58	no	\(1\)	\(1\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{15}{29}\right)\)
\(\chi_{8673}(52,\cdot)\)	8673.ck	1218	no	\(1\)	\(1\)	\(e\left(\frac{523}{1218}\right)\)	\(e\left(\frac{523}{609}\right)\)	\(e\left(\frac{673}{1218}\right)\)	\(e\left(\frac{117}{406}\right)\)	\(e\left(\frac{598}{609}\right)\)	\(e\left(\frac{257}{1218}\right)\)	\(e\left(\frac{51}{203}\right)\)	\(e\left(\frac{437}{609}\right)\)	\(e\left(\frac{11}{1218}\right)\)	\(e\left(\frac{109}{174}\right)\)
\(\chi_{8673}(53,\cdot)\)	8673.cl	1218	yes	\(-1\)	\(1\)	\(e\left(\frac{85}{1218}\right)\)	\(e\left(\frac{85}{609}\right)\)	\(e\left(\frac{829}{1218}\right)\)	\(e\left(\frac{85}{406}\right)\)	\(e\left(\frac{457}{609}\right)\)	\(e\left(\frac{617}{1218}\right)\)	\(e\left(\frac{188}{203}\right)\)	\(e\left(\frac{170}{609}\right)\)	\(e\left(\frac{761}{1218}\right)\)	\(e\left(\frac{65}{87}\right)\)
\(\chi_{8673}(55,\cdot)\)	8673.by	406	no	\(1\)	\(1\)	\(e\left(\frac{101}{406}\right)\)	\(e\left(\frac{101}{203}\right)\)	\(e\left(\frac{345}{406}\right)\)	\(e\left(\frac{303}{406}\right)\)	\(e\left(\frac{20}{203}\right)\)	\(e\left(\frac{31}{406}\right)\)	\(e\left(\frac{54}{203}\right)\)	\(e\left(\frac{202}{203}\right)\)	\(e\left(\frac{183}{406}\right)\)	\(e\left(\frac{47}{58}\right)\)

Introduction

L-functions

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Character group

First 32 of 4872 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.