LMFDB - Group of Dirichlet characters of modulus 8011

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8011)

pari: g = idealstar(,8011,2)

Character group

sage: G.order() pari: g.no
Order	=	8010
sage: H.invariants() pari: g.cyc
Structure	=	$C_{8010}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8011}(14,\cdot)$

First 32 of 8010 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{8011}(1,\cdot)$	8011.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8011}(2,\cdot)$	8011.v	2670	yes	$-1$	$1$	$e\left(\frac{441}{890}\right)$	$e\left(\frac{99}{890}\right)$	$e\left(\frac{441}{445}\right)$	$e\left(\frac{348}{445}\right)$	$e\left(\frac{54}{89}\right)$	$e\left(\frac{1019}{1335}\right)$	$e\left(\frac{433}{890}\right)$	$e\left(\frac{99}{445}\right)$	$e\left(\frac{247}{890}\right)$	$e\left(\frac{729}{890}\right)$
$\chi_{8011}(3,\cdot)$	8011.v	2670	yes	$-1$	$1$	$e\left(\frac{99}{890}\right)$	$e\left(\frac{331}{890}\right)$	$e\left(\frac{99}{445}\right)$	$e\left(\frac{287}{445}\right)$	$e\left(\frac{43}{89}\right)$	$e\left(\frac{256}{1335}\right)$	$e\left(\frac{297}{890}\right)$	$e\left(\frac{331}{445}\right)$	$e\left(\frac{673}{890}\right)$	$e\left(\frac{91}{890}\right)$
$\chi_{8011}(4,\cdot)$	8011.t	1335	yes	$1$	$1$	$e\left(\frac{441}{445}\right)$	$e\left(\frac{99}{445}\right)$	$e\left(\frac{437}{445}\right)$	$e\left(\frac{251}{445}\right)$	$e\left(\frac{19}{89}\right)$	$e\left(\frac{703}{1335}\right)$	$e\left(\frac{433}{445}\right)$	$e\left(\frac{198}{445}\right)$	$e\left(\frac{247}{445}\right)$	$e\left(\frac{284}{445}\right)$
$\chi_{8011}(5,\cdot)$	8011.p	445	yes	$1$	$1$	$e\left(\frac{348}{445}\right)$	$e\left(\frac{287}{445}\right)$	$e\left(\frac{251}{445}\right)$	$e\left(\frac{413}{445}\right)$	$e\left(\frac{38}{89}\right)$	$e\left(\frac{83}{445}\right)$	$e\left(\frac{154}{445}\right)$	$e\left(\frac{129}{445}\right)$	$e\left(\frac{316}{445}\right)$	$e\left(\frac{212}{445}\right)$
$\chi_{8011}(6,\cdot)$	8011.l	89	yes	$1$	$1$	$e\left(\frac{54}{89}\right)$	$e\left(\frac{43}{89}\right)$	$e\left(\frac{19}{89}\right)$	$e\left(\frac{38}{89}\right)$	$e\left(\frac{8}{89}\right)$	$e\left(\frac{85}{89}\right)$	$e\left(\frac{73}{89}\right)$	$e\left(\frac{86}{89}\right)$	$e\left(\frac{3}{89}\right)$	$e\left(\frac{82}{89}\right)$
$\chi_{8011}(7,\cdot)$	8011.w	4005	yes	$1$	$1$	$e\left(\frac{1019}{1335}\right)$	$e\left(\frac{256}{1335}\right)$	$e\left(\frac{703}{1335}\right)$	$e\left(\frac{83}{445}\right)$	$e\left(\frac{85}{89}\right)$	$e\left(\frac{3917}{4005}\right)$	$e\left(\frac{129}{445}\right)$	$e\left(\frac{512}{1335}\right)$	$e\left(\frac{1268}{1335}\right)$	$e\left(\frac{62}{445}\right)$
$\chi_{8011}(8,\cdot)$	8011.s	890	yes	$-1$	$1$	$e\left(\frac{433}{890}\right)$	$e\left(\frac{297}{890}\right)$	$e\left(\frac{433}{445}\right)$	$e\left(\frac{154}{445}\right)$	$e\left(\frac{73}{89}\right)$	$e\left(\frac{129}{445}\right)$	$e\left(\frac{409}{890}\right)$	$e\left(\frac{297}{445}\right)$	$e\left(\frac{741}{890}\right)$	$e\left(\frac{407}{890}\right)$
$\chi_{8011}(9,\cdot)$	8011.t	1335	yes	$1$	$1$	$e\left(\frac{99}{445}\right)$	$e\left(\frac{331}{445}\right)$	$e\left(\frac{198}{445}\right)$	$e\left(\frac{129}{445}\right)$	$e\left(\frac{86}{89}\right)$	$e\left(\frac{512}{1335}\right)$	$e\left(\frac{297}{445}\right)$	$e\left(\frac{217}{445}\right)$	$e\left(\frac{228}{445}\right)$	$e\left(\frac{91}{445}\right)$
$\chi_{8011}(10,\cdot)$	8011.v	2670	yes	$-1$	$1$	$e\left(\frac{247}{890}\right)$	$e\left(\frac{673}{890}\right)$	$e\left(\frac{247}{445}\right)$	$e\left(\frac{316}{445}\right)$	$e\left(\frac{3}{89}\right)$	$e\left(\frac{1268}{1335}\right)$	$e\left(\frac{741}{890}\right)$	$e\left(\frac{228}{445}\right)$	$e\left(\frac{879}{890}\right)$	$e\left(\frac{263}{890}\right)$
$\chi_{8011}(11,\cdot)$	8011.s	890	yes	$-1$	$1$	$e\left(\frac{729}{890}\right)$	$e\left(\frac{91}{890}\right)$	$e\left(\frac{284}{445}\right)$	$e\left(\frac{212}{445}\right)$	$e\left(\frac{82}{89}\right)$	$e\left(\frac{62}{445}\right)$	$e\left(\frac{407}{890}\right)$	$e\left(\frac{91}{445}\right)$	$e\left(\frac{263}{890}\right)$	$e\left(\frac{751}{890}\right)$
$\chi_{8011}(12,\cdot)$	8011.v	2670	yes	$-1$	$1$	$e\left(\frac{91}{890}\right)$	$e\left(\frac{529}{890}\right)$	$e\left(\frac{91}{445}\right)$	$e\left(\frac{93}{445}\right)$	$e\left(\frac{62}{89}\right)$	$e\left(\frac{959}{1335}\right)$	$e\left(\frac{273}{890}\right)$	$e\left(\frac{84}{445}\right)$	$e\left(\frac{277}{890}\right)$	$e\left(\frac{659}{890}\right)$
$\chi_{8011}(13,\cdot)$	8011.w	4005	yes	$1$	$1$	$e\left(\frac{724}{1335}\right)$	$e\left(\frac{326}{1335}\right)$	$e\left(\frac{113}{1335}\right)$	$e\left(\frac{283}{445}\right)$	$e\left(\frac{70}{89}\right)$	$e\left(\frac{3142}{4005}\right)$	$e\left(\frac{279}{445}\right)$	$e\left(\frac{652}{1335}\right)$	$e\left(\frac{238}{1335}\right)$	$e\left(\frac{72}{445}\right)$
$\chi_{8011}(14,\cdot)$	8011.x	8010	yes	$-1$	$1$	$e\left(\frac{691}{2670}\right)$	$e\left(\frac{809}{2670}\right)$	$e\left(\frac{691}{1335}\right)$	$e\left(\frac{431}{445}\right)$	$e\left(\frac{50}{89}\right)$	$e\left(\frac{2969}{4005}\right)$	$e\left(\frac{691}{890}\right)$	$e\left(\frac{809}{1335}\right)$	$e\left(\frac{607}{2670}\right)$	$e\left(\frac{853}{890}\right)$
$\chi_{8011}(15,\cdot)$	8011.q	534	yes	$-1$	$1$	$e\left(\frac{159}{178}\right)$	$e\left(\frac{3}{178}\right)$	$e\left(\frac{70}{89}\right)$	$e\left(\frac{51}{89}\right)$	$e\left(\frac{81}{89}\right)$	$e\left(\frac{101}{267}\right)$	$e\left(\frac{121}{178}\right)$	$e\left(\frac{3}{89}\right)$	$e\left(\frac{83}{178}\right)$	$e\left(\frac{103}{178}\right)$
$\chi_{8011}(16,\cdot)$	8011.t	1335	yes	$1$	$1$	$e\left(\frac{437}{445}\right)$	$e\left(\frac{198}{445}\right)$	$e\left(\frac{429}{445}\right)$	$e\left(\frac{57}{445}\right)$	$e\left(\frac{38}{89}\right)$	$e\left(\frac{71}{1335}\right)$	$e\left(\frac{421}{445}\right)$	$e\left(\frac{396}{445}\right)$	$e\left(\frac{49}{445}\right)$	$e\left(\frac{123}{445}\right)$
$\chi_{8011}(17,\cdot)$	8011.w	4005	yes	$1$	$1$	$e\left(\frac{461}{1335}\right)$	$e\left(\frac{49}{1335}\right)$	$e\left(\frac{922}{1335}\right)$	$e\left(\frac{407}{445}\right)$	$e\left(\frac{34}{89}\right)$	$e\left(\frac{2528}{4005}\right)$	$e\left(\frac{16}{445}\right)$	$e\left(\frac{98}{1335}\right)$	$e\left(\frac{347}{1335}\right)$	$e\left(\frac{363}{445}\right)$
$\chi_{8011}(18,\cdot)$	8011.v	2670	yes	$-1$	$1$	$e\left(\frac{639}{890}\right)$	$e\left(\frac{761}{890}\right)$	$e\left(\frac{194}{445}\right)$	$e\left(\frac{32}{445}\right)$	$e\left(\frac{51}{89}\right)$	$e\left(\frac{196}{1335}\right)$	$e\left(\frac{137}{890}\right)$	$e\left(\frac{316}{445}\right)$	$e\left(\frac{703}{890}\right)$	$e\left(\frac{21}{890}\right)$
$\chi_{8011}(19,\cdot)$	8011.r	801	yes	$1$	$1$	$e\left(\frac{17}{267}\right)$	$e\left(\frac{91}{267}\right)$	$e\left(\frac{34}{267}\right)$	$e\left(\frac{82}{89}\right)$	$e\left(\frac{36}{89}\right)$	$e\left(\frac{461}{801}\right)$	$e\left(\frac{17}{89}\right)$	$e\left(\frac{182}{267}\right)$	$e\left(\frac{263}{267}\right)$	$e\left(\frac{13}{89}\right)$
$\chi_{8011}(20,\cdot)$	8011.t	1335	yes	$1$	$1$	$e\left(\frac{344}{445}\right)$	$e\left(\frac{386}{445}\right)$	$e\left(\frac{243}{445}\right)$	$e\left(\frac{219}{445}\right)$	$e\left(\frac{57}{89}\right)$	$e\left(\frac{952}{1335}\right)$	$e\left(\frac{142}{445}\right)$	$e\left(\frac{327}{445}\right)$	$e\left(\frac{118}{445}\right)$	$e\left(\frac{51}{445}\right)$
$\chi_{8011}(21,\cdot)$	8011.u	1602	yes	$-1$	$1$	$e\left(\frac{467}{534}\right)$	$e\left(\frac{301}{534}\right)$	$e\left(\frac{200}{267}\right)$	$e\left(\frac{74}{89}\right)$	$e\left(\frac{39}{89}\right)$	$e\left(\frac{136}{801}\right)$	$e\left(\frac{111}{178}\right)$	$e\left(\frac{34}{267}\right)$	$e\left(\frac{377}{534}\right)$	$e\left(\frac{43}{178}\right)$
$\chi_{8011}(22,\cdot)$	8011.o	267	yes	$1$	$1$	$e\left(\frac{28}{89}\right)$	$e\left(\frac{19}{89}\right)$	$e\left(\frac{56}{89}\right)$	$e\left(\frac{23}{89}\right)$	$e\left(\frac{47}{89}\right)$	$e\left(\frac{241}{267}\right)$	$e\left(\frac{84}{89}\right)$	$e\left(\frac{38}{89}\right)$	$e\left(\frac{51}{89}\right)$	$e\left(\frac{59}{89}\right)$
$\chi_{8011}(23,\cdot)$	8011.w	4005	yes	$1$	$1$	$e\left(\frac{1109}{1335}\right)$	$e\left(\frac{31}{1335}\right)$	$e\left(\frac{883}{1335}\right)$	$e\left(\frac{203}{445}\right)$	$e\left(\frac{76}{89}\right)$	$e\left(\frac{3452}{4005}\right)$	$e\left(\frac{219}{445}\right)$	$e\left(\frac{62}{1335}\right)$	$e\left(\frac{383}{1335}\right)$	$e\left(\frac{157}{445}\right)$
$\chi_{8011}(24,\cdot)$	8011.t	1335	yes	$1$	$1$	$e\left(\frac{266}{445}\right)$	$e\left(\frac{314}{445}\right)$	$e\left(\frac{87}{445}\right)$	$e\left(\frac{441}{445}\right)$	$e\left(\frac{27}{89}\right)$	$e\left(\frac{643}{1335}\right)$	$e\left(\frac{353}{445}\right)$	$e\left(\frac{183}{445}\right)$	$e\left(\frac{262}{445}\right)$	$e\left(\frac{249}{445}\right)$
$\chi_{8011}(25,\cdot)$	8011.p	445	yes	$1$	$1$	$e\left(\frac{251}{445}\right)$	$e\left(\frac{129}{445}\right)$	$e\left(\frac{57}{445}\right)$	$e\left(\frac{381}{445}\right)$	$e\left(\frac{76}{89}\right)$	$e\left(\frac{166}{445}\right)$	$e\left(\frac{308}{445}\right)$	$e\left(\frac{258}{445}\right)$	$e\left(\frac{187}{445}\right)$	$e\left(\frac{424}{445}\right)$
$\chi_{8011}(26,\cdot)$	8011.x	8010	yes	$-1$	$1$	$e\left(\frac{101}{2670}\right)$	$e\left(\frac{949}{2670}\right)$	$e\left(\frac{101}{1335}\right)$	$e\left(\frac{186}{445}\right)$	$e\left(\frac{35}{89}\right)$	$e\left(\frac{2194}{4005}\right)$	$e\left(\frac{101}{890}\right)$	$e\left(\frac{949}{1335}\right)$	$e\left(\frac{1217}{2670}\right)$	$e\left(\frac{873}{890}\right)$
$\chi_{8011}(27,\cdot)$	8011.s	890	yes	$-1$	$1$	$e\left(\frac{297}{890}\right)$	$e\left(\frac{103}{890}\right)$	$e\left(\frac{297}{445}\right)$	$e\left(\frac{416}{445}\right)$	$e\left(\frac{40}{89}\right)$	$e\left(\frac{256}{445}\right)$	$e\left(\frac{1}{890}\right)$	$e\left(\frac{103}{445}\right)$	$e\left(\frac{239}{890}\right)$	$e\left(\frac{273}{890}\right)$
$\chi_{8011}(28,\cdot)$	8011.w	4005	yes	$1$	$1$	$e\left(\frac{1007}{1335}\right)$	$e\left(\frac{553}{1335}\right)$	$e\left(\frac{679}{1335}\right)$	$e\left(\frac{334}{445}\right)$	$e\left(\frac{15}{89}\right)$	$e\left(\frac{2021}{4005}\right)$	$e\left(\frac{117}{445}\right)$	$e\left(\frac{1106}{1335}\right)$	$e\left(\frac{674}{1335}\right)$	$e\left(\frac{346}{445}\right)$
$\chi_{8011}(29,\cdot)$	8011.p	445	yes	$1$	$1$	$e\left(\frac{147}{445}\right)$	$e\left(\frac{33}{445}\right)$	$e\left(\frac{294}{445}\right)$	$e\left(\frac{232}{445}\right)$	$e\left(\frac{36}{89}\right)$	$e\left(\frac{177}{445}\right)$	$e\left(\frac{441}{445}\right)$	$e\left(\frac{66}{445}\right)$	$e\left(\frac{379}{445}\right)$	$e\left(\frac{243}{445}\right)$
$\chi_{8011}(30,\cdot)$	8011.p	445	yes	$1$	$1$	$e\left(\frac{173}{445}\right)$	$e\left(\frac{57}{445}\right)$	$e\left(\frac{346}{445}\right)$	$e\left(\frac{158}{445}\right)$	$e\left(\frac{46}{89}\right)$	$e\left(\frac{63}{445}\right)$	$e\left(\frac{74}{445}\right)$	$e\left(\frac{114}{445}\right)$	$e\left(\frac{331}{445}\right)$	$e\left(\frac{177}{445}\right)$
$\chi_{8011}(31,\cdot)$	8011.p	445	yes	$1$	$1$	$e\left(\frac{94}{445}\right)$	$e\left(\frac{121}{445}\right)$	$e\left(\frac{188}{445}\right)$	$e\left(\frac{109}{445}\right)$	$e\left(\frac{43}{89}\right)$	$e\left(\frac{204}{445}\right)$	$e\left(\frac{282}{445}\right)$	$e\left(\frac{242}{445}\right)$	$e\left(\frac{203}{445}\right)$	$e\left(\frac{1}{445}\right)$
$\chi_{8011}(32,\cdot)$	8011.q	534	yes	$-1$	$1$	$e\left(\frac{85}{178}\right)$	$e\left(\frac{99}{178}\right)$	$e\left(\frac{85}{89}\right)$	$e\left(\frac{81}{89}\right)$	$e\left(\frac{3}{89}\right)$	$e\left(\frac{218}{267}\right)$	$e\left(\frac{77}{178}\right)$	$e\left(\frac{10}{89}\right)$	$e\left(\frac{69}{178}\right)$	$e\left(\frac{17}{178}\right)$

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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	$8011$
Structure	\(C_{8010}\)
Order	$8010$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{8011}(1,\cdot)\)	8011.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8011}(2,\cdot)\)	8011.v	2670	yes	\(-1\)	\(1\)	\(e\left(\frac{441}{890}\right)\)	\(e\left(\frac{99}{890}\right)\)	\(e\left(\frac{441}{445}\right)\)	\(e\left(\frac{348}{445}\right)\)	\(e\left(\frac{54}{89}\right)\)	\(e\left(\frac{1019}{1335}\right)\)	\(e\left(\frac{433}{890}\right)\)	\(e\left(\frac{99}{445}\right)\)	\(e\left(\frac{247}{890}\right)\)	\(e\left(\frac{729}{890}\right)\)
\(\chi_{8011}(3,\cdot)\)	8011.v	2670	yes	\(-1\)	\(1\)	\(e\left(\frac{99}{890}\right)\)	\(e\left(\frac{331}{890}\right)\)	\(e\left(\frac{99}{445}\right)\)	\(e\left(\frac{287}{445}\right)\)	\(e\left(\frac{43}{89}\right)\)	\(e\left(\frac{256}{1335}\right)\)	\(e\left(\frac{297}{890}\right)\)	\(e\left(\frac{331}{445}\right)\)	\(e\left(\frac{673}{890}\right)\)	\(e\left(\frac{91}{890}\right)\)
\(\chi_{8011}(4,\cdot)\)	8011.t	1335	yes	\(1\)	\(1\)	\(e\left(\frac{441}{445}\right)\)	\(e\left(\frac{99}{445}\right)\)	\(e\left(\frac{437}{445}\right)\)	\(e\left(\frac{251}{445}\right)\)	\(e\left(\frac{19}{89}\right)\)	\(e\left(\frac{703}{1335}\right)\)	\(e\left(\frac{433}{445}\right)\)	\(e\left(\frac{198}{445}\right)\)	\(e\left(\frac{247}{445}\right)\)	\(e\left(\frac{284}{445}\right)\)
\(\chi_{8011}(5,\cdot)\)	8011.p	445	yes	\(1\)	\(1\)	\(e\left(\frac{348}{445}\right)\)	\(e\left(\frac{287}{445}\right)\)	\(e\left(\frac{251}{445}\right)\)	\(e\left(\frac{413}{445}\right)\)	\(e\left(\frac{38}{89}\right)\)	\(e\left(\frac{83}{445}\right)\)	\(e\left(\frac{154}{445}\right)\)	\(e\left(\frac{129}{445}\right)\)	\(e\left(\frac{316}{445}\right)\)	\(e\left(\frac{212}{445}\right)\)
\(\chi_{8011}(6,\cdot)\)	8011.l	89	yes	\(1\)	\(1\)	\(e\left(\frac{54}{89}\right)\)	\(e\left(\frac{43}{89}\right)\)	\(e\left(\frac{19}{89}\right)\)	\(e\left(\frac{38}{89}\right)\)	\(e\left(\frac{8}{89}\right)\)	\(e\left(\frac{85}{89}\right)\)	\(e\left(\frac{73}{89}\right)\)	\(e\left(\frac{86}{89}\right)\)	\(e\left(\frac{3}{89}\right)\)	\(e\left(\frac{82}{89}\right)\)
\(\chi_{8011}(7,\cdot)\)	8011.w	4005	yes	\(1\)	\(1\)	\(e\left(\frac{1019}{1335}\right)\)	\(e\left(\frac{256}{1335}\right)\)	\(e\left(\frac{703}{1335}\right)\)	\(e\left(\frac{83}{445}\right)\)	\(e\left(\frac{85}{89}\right)\)	\(e\left(\frac{3917}{4005}\right)\)	\(e\left(\frac{129}{445}\right)\)	\(e\left(\frac{512}{1335}\right)\)	\(e\left(\frac{1268}{1335}\right)\)	\(e\left(\frac{62}{445}\right)\)
\(\chi_{8011}(8,\cdot)\)	8011.s	890	yes	\(-1\)	\(1\)	\(e\left(\frac{433}{890}\right)\)	\(e\left(\frac{297}{890}\right)\)	\(e\left(\frac{433}{445}\right)\)	\(e\left(\frac{154}{445}\right)\)	\(e\left(\frac{73}{89}\right)\)	\(e\left(\frac{129}{445}\right)\)	\(e\left(\frac{409}{890}\right)\)	\(e\left(\frac{297}{445}\right)\)	\(e\left(\frac{741}{890}\right)\)	\(e\left(\frac{407}{890}\right)\)
\(\chi_{8011}(9,\cdot)\)	8011.t	1335	yes	\(1\)	\(1\)	\(e\left(\frac{99}{445}\right)\)	\(e\left(\frac{331}{445}\right)\)	\(e\left(\frac{198}{445}\right)\)	\(e\left(\frac{129}{445}\right)\)	\(e\left(\frac{86}{89}\right)\)	\(e\left(\frac{512}{1335}\right)\)	\(e\left(\frac{297}{445}\right)\)	\(e\left(\frac{217}{445}\right)\)	\(e\left(\frac{228}{445}\right)\)	\(e\left(\frac{91}{445}\right)\)
\(\chi_{8011}(10,\cdot)\)	8011.v	2670	yes	\(-1\)	\(1\)	\(e\left(\frac{247}{890}\right)\)	\(e\left(\frac{673}{890}\right)\)	\(e\left(\frac{247}{445}\right)\)	\(e\left(\frac{316}{445}\right)\)	\(e\left(\frac{3}{89}\right)\)	\(e\left(\frac{1268}{1335}\right)\)	\(e\left(\frac{741}{890}\right)\)	\(e\left(\frac{228}{445}\right)\)	\(e\left(\frac{879}{890}\right)\)	\(e\left(\frac{263}{890}\right)\)
\(\chi_{8011}(11,\cdot)\)	8011.s	890	yes	\(-1\)	\(1\)	\(e\left(\frac{729}{890}\right)\)	\(e\left(\frac{91}{890}\right)\)	\(e\left(\frac{284}{445}\right)\)	\(e\left(\frac{212}{445}\right)\)	\(e\left(\frac{82}{89}\right)\)	\(e\left(\frac{62}{445}\right)\)	\(e\left(\frac{407}{890}\right)\)	\(e\left(\frac{91}{445}\right)\)	\(e\left(\frac{263}{890}\right)\)	\(e\left(\frac{751}{890}\right)\)
\(\chi_{8011}(12,\cdot)\)	8011.v	2670	yes	\(-1\)	\(1\)	\(e\left(\frac{91}{890}\right)\)	\(e\left(\frac{529}{890}\right)\)	\(e\left(\frac{91}{445}\right)\)	\(e\left(\frac{93}{445}\right)\)	\(e\left(\frac{62}{89}\right)\)	\(e\left(\frac{959}{1335}\right)\)	\(e\left(\frac{273}{890}\right)\)	\(e\left(\frac{84}{445}\right)\)	\(e\left(\frac{277}{890}\right)\)	\(e\left(\frac{659}{890}\right)\)
\(\chi_{8011}(13,\cdot)\)	8011.w	4005	yes	\(1\)	\(1\)	\(e\left(\frac{724}{1335}\right)\)	\(e\left(\frac{326}{1335}\right)\)	\(e\left(\frac{113}{1335}\right)\)	\(e\left(\frac{283}{445}\right)\)	\(e\left(\frac{70}{89}\right)\)	\(e\left(\frac{3142}{4005}\right)\)	\(e\left(\frac{279}{445}\right)\)	\(e\left(\frac{652}{1335}\right)\)	\(e\left(\frac{238}{1335}\right)\)	\(e\left(\frac{72}{445}\right)\)
\(\chi_{8011}(14,\cdot)\)	8011.x	8010	yes	\(-1\)	\(1\)	\(e\left(\frac{691}{2670}\right)\)	\(e\left(\frac{809}{2670}\right)\)	\(e\left(\frac{691}{1335}\right)\)	\(e\left(\frac{431}{445}\right)\)	\(e\left(\frac{50}{89}\right)\)	\(e\left(\frac{2969}{4005}\right)\)	\(e\left(\frac{691}{890}\right)\)	\(e\left(\frac{809}{1335}\right)\)	\(e\left(\frac{607}{2670}\right)\)	\(e\left(\frac{853}{890}\right)\)
\(\chi_{8011}(15,\cdot)\)	8011.q	534	yes	\(-1\)	\(1\)	\(e\left(\frac{159}{178}\right)\)	\(e\left(\frac{3}{178}\right)\)	\(e\left(\frac{70}{89}\right)\)	\(e\left(\frac{51}{89}\right)\)	\(e\left(\frac{81}{89}\right)\)	\(e\left(\frac{101}{267}\right)\)	\(e\left(\frac{121}{178}\right)\)	\(e\left(\frac{3}{89}\right)\)	\(e\left(\frac{83}{178}\right)\)	\(e\left(\frac{103}{178}\right)\)
\(\chi_{8011}(16,\cdot)\)	8011.t	1335	yes	\(1\)	\(1\)	\(e\left(\frac{437}{445}\right)\)	\(e\left(\frac{198}{445}\right)\)	\(e\left(\frac{429}{445}\right)\)	\(e\left(\frac{57}{445}\right)\)	\(e\left(\frac{38}{89}\right)\)	\(e\left(\frac{71}{1335}\right)\)	\(e\left(\frac{421}{445}\right)\)	\(e\left(\frac{396}{445}\right)\)	\(e\left(\frac{49}{445}\right)\)	\(e\left(\frac{123}{445}\right)\)
\(\chi_{8011}(17,\cdot)\)	8011.w	4005	yes	\(1\)	\(1\)	\(e\left(\frac{461}{1335}\right)\)	\(e\left(\frac{49}{1335}\right)\)	\(e\left(\frac{922}{1335}\right)\)	\(e\left(\frac{407}{445}\right)\)	\(e\left(\frac{34}{89}\right)\)	\(e\left(\frac{2528}{4005}\right)\)	\(e\left(\frac{16}{445}\right)\)	\(e\left(\frac{98}{1335}\right)\)	\(e\left(\frac{347}{1335}\right)\)	\(e\left(\frac{363}{445}\right)\)
\(\chi_{8011}(18,\cdot)\)	8011.v	2670	yes	\(-1\)	\(1\)	\(e\left(\frac{639}{890}\right)\)	\(e\left(\frac{761}{890}\right)\)	\(e\left(\frac{194}{445}\right)\)	\(e\left(\frac{32}{445}\right)\)	\(e\left(\frac{51}{89}\right)\)	\(e\left(\frac{196}{1335}\right)\)	\(e\left(\frac{137}{890}\right)\)	\(e\left(\frac{316}{445}\right)\)	\(e\left(\frac{703}{890}\right)\)	\(e\left(\frac{21}{890}\right)\)
\(\chi_{8011}(19,\cdot)\)	8011.r	801	yes	\(1\)	\(1\)	\(e\left(\frac{17}{267}\right)\)	\(e\left(\frac{91}{267}\right)\)	\(e\left(\frac{34}{267}\right)\)	\(e\left(\frac{82}{89}\right)\)	\(e\left(\frac{36}{89}\right)\)	\(e\left(\frac{461}{801}\right)\)	\(e\left(\frac{17}{89}\right)\)	\(e\left(\frac{182}{267}\right)\)	\(e\left(\frac{263}{267}\right)\)	\(e\left(\frac{13}{89}\right)\)
\(\chi_{8011}(20,\cdot)\)	8011.t	1335	yes	\(1\)	\(1\)	\(e\left(\frac{344}{445}\right)\)	\(e\left(\frac{386}{445}\right)\)	\(e\left(\frac{243}{445}\right)\)	\(e\left(\frac{219}{445}\right)\)	\(e\left(\frac{57}{89}\right)\)	\(e\left(\frac{952}{1335}\right)\)	\(e\left(\frac{142}{445}\right)\)	\(e\left(\frac{327}{445}\right)\)	\(e\left(\frac{118}{445}\right)\)	\(e\left(\frac{51}{445}\right)\)
\(\chi_{8011}(21,\cdot)\)	8011.u	1602	yes	\(-1\)	\(1\)	\(e\left(\frac{467}{534}\right)\)	\(e\left(\frac{301}{534}\right)\)	\(e\left(\frac{200}{267}\right)\)	\(e\left(\frac{74}{89}\right)\)	\(e\left(\frac{39}{89}\right)\)	\(e\left(\frac{136}{801}\right)\)	\(e\left(\frac{111}{178}\right)\)	\(e\left(\frac{34}{267}\right)\)	\(e\left(\frac{377}{534}\right)\)	\(e\left(\frac{43}{178}\right)\)
\(\chi_{8011}(22,\cdot)\)	8011.o	267	yes	\(1\)	\(1\)	\(e\left(\frac{28}{89}\right)\)	\(e\left(\frac{19}{89}\right)\)	\(e\left(\frac{56}{89}\right)\)	\(e\left(\frac{23}{89}\right)\)	\(e\left(\frac{47}{89}\right)\)	\(e\left(\frac{241}{267}\right)\)	\(e\left(\frac{84}{89}\right)\)	\(e\left(\frac{38}{89}\right)\)	\(e\left(\frac{51}{89}\right)\)	\(e\left(\frac{59}{89}\right)\)
\(\chi_{8011}(23,\cdot)\)	8011.w	4005	yes	\(1\)	\(1\)	\(e\left(\frac{1109}{1335}\right)\)	\(e\left(\frac{31}{1335}\right)\)	\(e\left(\frac{883}{1335}\right)\)	\(e\left(\frac{203}{445}\right)\)	\(e\left(\frac{76}{89}\right)\)	\(e\left(\frac{3452}{4005}\right)\)	\(e\left(\frac{219}{445}\right)\)	\(e\left(\frac{62}{1335}\right)\)	\(e\left(\frac{383}{1335}\right)\)	\(e\left(\frac{157}{445}\right)\)
\(\chi_{8011}(24,\cdot)\)	8011.t	1335	yes	\(1\)	\(1\)	\(e\left(\frac{266}{445}\right)\)	\(e\left(\frac{314}{445}\right)\)	\(e\left(\frac{87}{445}\right)\)	\(e\left(\frac{441}{445}\right)\)	\(e\left(\frac{27}{89}\right)\)	\(e\left(\frac{643}{1335}\right)\)	\(e\left(\frac{353}{445}\right)\)	\(e\left(\frac{183}{445}\right)\)	\(e\left(\frac{262}{445}\right)\)	\(e\left(\frac{249}{445}\right)\)
\(\chi_{8011}(25,\cdot)\)	8011.p	445	yes	\(1\)	\(1\)	\(e\left(\frac{251}{445}\right)\)	\(e\left(\frac{129}{445}\right)\)	\(e\left(\frac{57}{445}\right)\)	\(e\left(\frac{381}{445}\right)\)	\(e\left(\frac{76}{89}\right)\)	\(e\left(\frac{166}{445}\right)\)	\(e\left(\frac{308}{445}\right)\)	\(e\left(\frac{258}{445}\right)\)	\(e\left(\frac{187}{445}\right)\)	\(e\left(\frac{424}{445}\right)\)
\(\chi_{8011}(26,\cdot)\)	8011.x	8010	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{2670}\right)\)	\(e\left(\frac{949}{2670}\right)\)	\(e\left(\frac{101}{1335}\right)\)	\(e\left(\frac{186}{445}\right)\)	\(e\left(\frac{35}{89}\right)\)	\(e\left(\frac{2194}{4005}\right)\)	\(e\left(\frac{101}{890}\right)\)	\(e\left(\frac{949}{1335}\right)\)	\(e\left(\frac{1217}{2670}\right)\)	\(e\left(\frac{873}{890}\right)\)
\(\chi_{8011}(27,\cdot)\)	8011.s	890	yes	\(-1\)	\(1\)	\(e\left(\frac{297}{890}\right)\)	\(e\left(\frac{103}{890}\right)\)	\(e\left(\frac{297}{445}\right)\)	\(e\left(\frac{416}{445}\right)\)	\(e\left(\frac{40}{89}\right)\)	\(e\left(\frac{256}{445}\right)\)	\(e\left(\frac{1}{890}\right)\)	\(e\left(\frac{103}{445}\right)\)	\(e\left(\frac{239}{890}\right)\)	\(e\left(\frac{273}{890}\right)\)
\(\chi_{8011}(28,\cdot)\)	8011.w	4005	yes	\(1\)	\(1\)	\(e\left(\frac{1007}{1335}\right)\)	\(e\left(\frac{553}{1335}\right)\)	\(e\left(\frac{679}{1335}\right)\)	\(e\left(\frac{334}{445}\right)\)	\(e\left(\frac{15}{89}\right)\)	\(e\left(\frac{2021}{4005}\right)\)	\(e\left(\frac{117}{445}\right)\)	\(e\left(\frac{1106}{1335}\right)\)	\(e\left(\frac{674}{1335}\right)\)	\(e\left(\frac{346}{445}\right)\)
\(\chi_{8011}(29,\cdot)\)	8011.p	445	yes	\(1\)	\(1\)	\(e\left(\frac{147}{445}\right)\)	\(e\left(\frac{33}{445}\right)\)	\(e\left(\frac{294}{445}\right)\)	\(e\left(\frac{232}{445}\right)\)	\(e\left(\frac{36}{89}\right)\)	\(e\left(\frac{177}{445}\right)\)	\(e\left(\frac{441}{445}\right)\)	\(e\left(\frac{66}{445}\right)\)	\(e\left(\frac{379}{445}\right)\)	\(e\left(\frac{243}{445}\right)\)
\(\chi_{8011}(30,\cdot)\)	8011.p	445	yes	\(1\)	\(1\)	\(e\left(\frac{173}{445}\right)\)	\(e\left(\frac{57}{445}\right)\)	\(e\left(\frac{346}{445}\right)\)	\(e\left(\frac{158}{445}\right)\)	\(e\left(\frac{46}{89}\right)\)	\(e\left(\frac{63}{445}\right)\)	\(e\left(\frac{74}{445}\right)\)	\(e\left(\frac{114}{445}\right)\)	\(e\left(\frac{331}{445}\right)\)	\(e\left(\frac{177}{445}\right)\)
\(\chi_{8011}(31,\cdot)\)	8011.p	445	yes	\(1\)	\(1\)	\(e\left(\frac{94}{445}\right)\)	\(e\left(\frac{121}{445}\right)\)	\(e\left(\frac{188}{445}\right)\)	\(e\left(\frac{109}{445}\right)\)	\(e\left(\frac{43}{89}\right)\)	\(e\left(\frac{204}{445}\right)\)	\(e\left(\frac{282}{445}\right)\)	\(e\left(\frac{242}{445}\right)\)	\(e\left(\frac{203}{445}\right)\)	\(e\left(\frac{1}{445}\right)\)
\(\chi_{8011}(32,\cdot)\)	8011.q	534	yes	\(-1\)	\(1\)	\(e\left(\frac{85}{178}\right)\)	\(e\left(\frac{99}{178}\right)\)	\(e\left(\frac{85}{89}\right)\)	\(e\left(\frac{81}{89}\right)\)	\(e\left(\frac{3}{89}\right)\)	\(e\left(\frac{218}{267}\right)\)	\(e\left(\frac{77}{178}\right)\)	\(e\left(\frac{10}{89}\right)\)	\(e\left(\frac{69}{178}\right)\)	\(e\left(\frac{17}{178}\right)\)

Introduction

L-functions

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Character group

First 32 of 8010 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.