LMFDB - Group of Dirichlet characters of modulus 8043

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8043)

pari: g = idealstar(,8043,2)

Character group

sage: G.order() pari: g.no
Order	=	4584
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{1146}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8043}(5363,\cdot)$, $\chi_{8043}(2299,\cdot)$, $\chi_{8043}(6133,\cdot)$

First 32 of 4584 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{8043}(1,\cdot)$	8043.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8043}(2,\cdot)$	8043.z	1146	yes	$-1$	$1$	$e\left(\frac{197}{1146}\right)$	$e\left(\frac{197}{573}\right)$	$e\left(\frac{593}{1146}\right)$	$e\left(\frac{197}{382}\right)$	$e\left(\frac{395}{573}\right)$	$e\left(\frac{37}{1146}\right)$	$e\left(\frac{26}{191}\right)$	$e\left(\frac{394}{573}\right)$	$e\left(\frac{637}{1146}\right)$	$e\left(\frac{154}{573}\right)$
$\chi_{8043}(4,\cdot)$	8043.y	573	no	$1$	$1$	$e\left(\frac{197}{573}\right)$	$e\left(\frac{394}{573}\right)$	$e\left(\frac{20}{573}\right)$	$e\left(\frac{6}{191}\right)$	$e\left(\frac{217}{573}\right)$	$e\left(\frac{37}{573}\right)$	$e\left(\frac{52}{191}\right)$	$e\left(\frac{215}{573}\right)$	$e\left(\frac{64}{573}\right)$	$e\left(\frac{308}{573}\right)$
$\chi_{8043}(5,\cdot)$	8043.ba	1146	yes	$-1$	$1$	$e\left(\frac{593}{1146}\right)$	$e\left(\frac{20}{573}\right)$	$e\left(\frac{767}{1146}\right)$	$e\left(\frac{211}{382}\right)$	$e\left(\frac{107}{573}\right)$	$e\left(\frac{380}{573}\right)$	$e\left(\frac{23}{191}\right)$	$e\left(\frac{40}{573}\right)$	$e\left(\frac{425}{573}\right)$	$e\left(\frac{581}{1146}\right)$
$\chi_{8043}(8,\cdot)$	8043.x	382	no	$-1$	$1$	$e\left(\frac{197}{382}\right)$	$e\left(\frac{6}{191}\right)$	$e\left(\frac{211}{382}\right)$	$e\left(\frac{209}{382}\right)$	$e\left(\frac{13}{191}\right)$	$e\left(\frac{37}{382}\right)$	$e\left(\frac{78}{191}\right)$	$e\left(\frac{12}{191}\right)$	$e\left(\frac{255}{382}\right)$	$e\left(\frac{154}{191}\right)$
$\chi_{8043}(10,\cdot)$	8043.bf	1146	no	$1$	$1$	$e\left(\frac{395}{573}\right)$	$e\left(\frac{217}{573}\right)$	$e\left(\frac{107}{573}\right)$	$e\left(\frac{13}{191}\right)$	$e\left(\frac{502}{573}\right)$	$e\left(\frac{797}{1146}\right)$	$e\left(\frac{49}{191}\right)$	$e\left(\frac{434}{573}\right)$	$e\left(\frac{341}{1146}\right)$	$e\left(\frac{889}{1146}\right)$
$\chi_{8043}(11,\cdot)$	8043.bc	1146	yes	$1$	$1$	$e\left(\frac{37}{1146}\right)$	$e\left(\frac{37}{573}\right)$	$e\left(\frac{380}{573}\right)$	$e\left(\frac{37}{382}\right)$	$e\left(\frac{797}{1146}\right)$	$e\left(\frac{130}{573}\right)$	$e\left(\frac{257}{382}\right)$	$e\left(\frac{74}{573}\right)$	$e\left(\frac{713}{1146}\right)$	$e\left(\frac{122}{573}\right)$
$\chi_{8043}(13,\cdot)$	8043.r	382	no	$1$	$1$	$e\left(\frac{26}{191}\right)$	$e\left(\frac{52}{191}\right)$	$e\left(\frac{23}{191}\right)$	$e\left(\frac{78}{191}\right)$	$e\left(\frac{49}{191}\right)$	$e\left(\frac{257}{382}\right)$	$e\left(\frac{103}{191}\right)$	$e\left(\frac{104}{191}\right)$	$e\left(\frac{109}{382}\right)$	$e\left(\frac{59}{382}\right)$
$\chi_{8043}(16,\cdot)$	8043.y	573	no	$1$	$1$	$e\left(\frac{394}{573}\right)$	$e\left(\frac{215}{573}\right)$	$e\left(\frac{40}{573}\right)$	$e\left(\frac{12}{191}\right)$	$e\left(\frac{434}{573}\right)$	$e\left(\frac{74}{573}\right)$	$e\left(\frac{104}{191}\right)$	$e\left(\frac{430}{573}\right)$	$e\left(\frac{128}{573}\right)$	$e\left(\frac{43}{573}\right)$
$\chi_{8043}(17,\cdot)$	8043.bb	1146	yes	$1$	$1$	$e\left(\frac{637}{1146}\right)$	$e\left(\frac{64}{573}\right)$	$e\left(\frac{425}{573}\right)$	$e\left(\frac{255}{382}\right)$	$e\left(\frac{341}{1146}\right)$	$e\left(\frac{713}{1146}\right)$	$e\left(\frac{109}{382}\right)$	$e\left(\frac{128}{573}\right)$	$e\left(\frac{214}{573}\right)$	$e\left(\frac{1057}{1146}\right)$
$\chi_{8043}(19,\cdot)$	8043.be	1146	no	$-1$	$1$	$e\left(\frac{154}{573}\right)$	$e\left(\frac{308}{573}\right)$	$e\left(\frac{581}{1146}\right)$	$e\left(\frac{154}{191}\right)$	$e\left(\frac{889}{1146}\right)$	$e\left(\frac{122}{573}\right)$	$e\left(\frac{59}{382}\right)$	$e\left(\frac{43}{573}\right)$	$e\left(\frac{1057}{1146}\right)$	$e\left(\frac{467}{1146}\right)$
$\chi_{8043}(20,\cdot)$	8043.w	382	yes	$-1$	$1$	$e\left(\frac{329}{382}\right)$	$e\left(\frac{138}{191}\right)$	$e\left(\frac{269}{382}\right)$	$e\left(\frac{223}{382}\right)$	$e\left(\frac{108}{191}\right)$	$e\left(\frac{139}{191}\right)$	$e\left(\frac{75}{191}\right)$	$e\left(\frac{85}{191}\right)$	$e\left(\frac{163}{191}\right)$	$e\left(\frac{17}{382}\right)$
$\chi_{8043}(22,\cdot)$	8043.t	382	no	$-1$	$1$	$e\left(\frac{39}{191}\right)$	$e\left(\frac{78}{191}\right)$	$e\left(\frac{69}{382}\right)$	$e\left(\frac{117}{191}\right)$	$e\left(\frac{147}{382}\right)$	$e\left(\frac{99}{382}\right)$	$e\left(\frac{309}{382}\right)$	$e\left(\frac{156}{191}\right)$	$e\left(\frac{34}{191}\right)$	$e\left(\frac{92}{191}\right)$
$\chi_{8043}(23,\cdot)$	8043.z	1146	yes	$-1$	$1$	$e\left(\frac{527}{1146}\right)$	$e\left(\frac{527}{573}\right)$	$e\left(\frac{929}{1146}\right)$	$e\left(\frac{145}{382}\right)$	$e\left(\frac{155}{573}\right)$	$e\left(\frac{1117}{1146}\right)$	$e\left(\frac{119}{191}\right)$	$e\left(\frac{481}{573}\right)$	$e\left(\frac{337}{1146}\right)$	$e\left(\frac{220}{573}\right)$
$\chi_{8043}(25,\cdot)$	8043.y	573	no	$1$	$1$	$e\left(\frac{20}{573}\right)$	$e\left(\frac{40}{573}\right)$	$e\left(\frac{194}{573}\right)$	$e\left(\frac{20}{191}\right)$	$e\left(\frac{214}{573}\right)$	$e\left(\frac{187}{573}\right)$	$e\left(\frac{46}{191}\right)$	$e\left(\frac{80}{573}\right)$	$e\left(\frac{277}{573}\right)$	$e\left(\frac{8}{573}\right)$
$\chi_{8043}(26,\cdot)$	8043.ba	1146	yes	$-1$	$1$	$e\left(\frac{353}{1146}\right)$	$e\left(\frac{353}{573}\right)$	$e\left(\frac{731}{1146}\right)$	$e\left(\frac{353}{382}\right)$	$e\left(\frac{542}{573}\right)$	$e\left(\frac{404}{573}\right)$	$e\left(\frac{129}{191}\right)$	$e\left(\frac{133}{573}\right)$	$e\left(\frac{482}{573}\right)$	$e\left(\frac{485}{1146}\right)$
$\chi_{8043}(29,\cdot)$	8043.x	382	no	$-1$	$1$	$e\left(\frac{127}{382}\right)$	$e\left(\frac{127}{191}\right)$	$e\left(\frac{105}{382}\right)$	$e\left(\frac{381}{382}\right)$	$e\left(\frac{116}{191}\right)$	$e\left(\frac{51}{382}\right)$	$e\left(\frac{123}{191}\right)$	$e\left(\frac{63}{191}\right)$	$e\left(\frac{145}{382}\right)$	$e\left(\frac{140}{191}\right)$
$\chi_{8043}(31,\cdot)$	8043.be	1146	no	$-1$	$1$	$e\left(\frac{320}{573}\right)$	$e\left(\frac{67}{573}\right)$	$e\left(\frac{1051}{1146}\right)$	$e\left(\frac{129}{191}\right)$	$e\left(\frac{545}{1146}\right)$	$e\left(\frac{127}{573}\right)$	$e\left(\frac{135}{382}\right)$	$e\left(\frac{134}{573}\right)$	$e\left(\frac{269}{1146}\right)$	$e\left(\frac{829}{1146}\right)$
$\chi_{8043}(32,\cdot)$	8043.z	1146	yes	$-1$	$1$	$e\left(\frac{985}{1146}\right)$	$e\left(\frac{412}{573}\right)$	$e\left(\frac{673}{1146}\right)$	$e\left(\frac{221}{382}\right)$	$e\left(\frac{256}{573}\right)$	$e\left(\frac{185}{1146}\right)$	$e\left(\frac{130}{191}\right)$	$e\left(\frac{251}{573}\right)$	$e\left(\frac{893}{1146}\right)$	$e\left(\frac{197}{573}\right)$
$\chi_{8043}(34,\cdot)$	8043.s	382	no	$-1$	$1$	$e\left(\frac{139}{191}\right)$	$e\left(\frac{87}{191}\right)$	$e\left(\frac{99}{382}\right)$	$e\left(\frac{35}{191}\right)$	$e\left(\frac{377}{382}\right)$	$e\left(\frac{125}{191}\right)$	$e\left(\frac{161}{382}\right)$	$e\left(\frac{174}{191}\right)$	$e\left(\frac{355}{382}\right)$	$e\left(\frac{73}{382}\right)$
$\chi_{8043}(37,\cdot)$	8043.bd	1146	no	$-1$	$1$	$e\left(\frac{256}{573}\right)$	$e\left(\frac{512}{573}\right)$	$e\left(\frac{497}{1146}\right)$	$e\left(\frac{65}{191}\right)$	$e\left(\frac{1009}{1146}\right)$	$e\left(\frac{547}{1146}\right)$	$e\left(\frac{299}{382}\right)$	$e\left(\frac{451}{573}\right)$	$e\left(\frac{566}{573}\right)$	$e\left(\frac{217}{573}\right)$
$\chi_{8043}(38,\cdot)$	8043.bb	1146	yes	$1$	$1$	$e\left(\frac{505}{1146}\right)$	$e\left(\frac{505}{573}\right)$	$e\left(\frac{14}{573}\right)$	$e\left(\frac{123}{382}\right)$	$e\left(\frac{533}{1146}\right)$	$e\left(\frac{281}{1146}\right)$	$e\left(\frac{111}{382}\right)$	$e\left(\frac{437}{573}\right)$	$e\left(\frac{274}{573}\right)$	$e\left(\frac{775}{1146}\right)$
$\chi_{8043}(40,\cdot)$	8043.bf	1146	no	$1$	$1$	$e\left(\frac{19}{573}\right)$	$e\left(\frac{38}{573}\right)$	$e\left(\frac{127}{573}\right)$	$e\left(\frac{19}{191}\right)$	$e\left(\frac{146}{573}\right)$	$e\left(\frac{871}{1146}\right)$	$e\left(\frac{101}{191}\right)$	$e\left(\frac{76}{573}\right)$	$e\left(\frac{469}{1146}\right)$	$e\left(\frac{359}{1146}\right)$
$\chi_{8043}(41,\cdot)$	8043.w	382	yes	$-1$	$1$	$e\left(\frac{13}{382}\right)$	$e\left(\frac{13}{191}\right)$	$e\left(\frac{107}{382}\right)$	$e\left(\frac{39}{382}\right)$	$e\left(\frac{60}{191}\right)$	$e\left(\frac{56}{191}\right)$	$e\left(\frac{169}{191}\right)$	$e\left(\frac{26}{191}\right)$	$e\left(\frac{133}{191}\right)$	$e\left(\frac{349}{382}\right)$
$\chi_{8043}(43,\cdot)$	8043.q	191	no	$1$	$1$	$e\left(\frac{16}{191}\right)$	$e\left(\frac{32}{191}\right)$	$e\left(\frac{117}{191}\right)$	$e\left(\frac{48}{191}\right)$	$e\left(\frac{133}{191}\right)$	$e\left(\frac{35}{191}\right)$	$e\left(\frac{34}{191}\right)$	$e\left(\frac{64}{191}\right)$	$e\left(\frac{107}{191}\right)$	$e\left(\frac{121}{191}\right)$
$\chi_{8043}(44,\cdot)$	8043.bc	1146	yes	$1$	$1$	$e\left(\frac{431}{1146}\right)$	$e\left(\frac{431}{573}\right)$	$e\left(\frac{400}{573}\right)$	$e\left(\frac{49}{382}\right)$	$e\left(\frac{85}{1146}\right)$	$e\left(\frac{167}{573}\right)$	$e\left(\frac{361}{382}\right)$	$e\left(\frac{289}{573}\right)$	$e\left(\frac{841}{1146}\right)$	$e\left(\frac{430}{573}\right)$
$\chi_{8043}(46,\cdot)$	8043.y	573	no	$1$	$1$	$e\left(\frac{362}{573}\right)$	$e\left(\frac{151}{573}\right)$	$e\left(\frac{188}{573}\right)$	$e\left(\frac{171}{191}\right)$	$e\left(\frac{550}{573}\right)$	$e\left(\frac{4}{573}\right)$	$e\left(\frac{145}{191}\right)$	$e\left(\frac{302}{573}\right)$	$e\left(\frac{487}{573}\right)$	$e\left(\frac{374}{573}\right)$
$\chi_{8043}(47,\cdot)$	8043.ba	1146	yes	$-1$	$1$	$e\left(\frac{695}{1146}\right)$	$e\left(\frac{122}{573}\right)$	$e\left(\frac{725}{1146}\right)$	$e\left(\frac{313}{382}\right)$	$e\left(\frac{137}{573}\right)$	$e\left(\frac{26}{573}\right)$	$e\left(\frac{83}{191}\right)$	$e\left(\frac{244}{573}\right)$	$e\left(\frac{14}{573}\right)$	$e\left(\frac{851}{1146}\right)$
$\chi_{8043}(50,\cdot)$	8043.x	382	no	$-1$	$1$	$e\left(\frac{79}{382}\right)$	$e\left(\frac{79}{191}\right)$	$e\left(\frac{327}{382}\right)$	$e\left(\frac{237}{382}\right)$	$e\left(\frac{12}{191}\right)$	$e\left(\frac{137}{382}\right)$	$e\left(\frac{72}{191}\right)$	$e\left(\frac{158}{191}\right)$	$e\left(\frac{15}{382}\right)$	$e\left(\frac{54}{191}\right)$
$\chi_{8043}(52,\cdot)$	8043.bf	1146	no	$1$	$1$	$e\left(\frac{275}{573}\right)$	$e\left(\frac{550}{573}\right)$	$e\left(\frac{89}{573}\right)$	$e\left(\frac{84}{191}\right)$	$e\left(\frac{364}{573}\right)$	$e\left(\frac{845}{1146}\right)$	$e\left(\frac{155}{191}\right)$	$e\left(\frac{527}{573}\right)$	$e\left(\frac{455}{1146}\right)$	$e\left(\frac{793}{1146}\right)$
$\chi_{8043}(53,\cdot)$	8043.bc	1146	yes	$1$	$1$	$e\left(\frac{403}{1146}\right)$	$e\left(\frac{403}{573}\right)$	$e\left(\frac{35}{573}\right)$	$e\left(\frac{21}{382}\right)$	$e\left(\frac{473}{1146}\right)$	$e\left(\frac{208}{573}\right)$	$e\left(\frac{373}{382}\right)$	$e\left(\frac{233}{573}\right)$	$e\left(\frac{797}{1146}\right)$	$e\left(\frac{539}{573}\right)$
$\chi_{8043}(55,\cdot)$	8043.s	382	no	$-1$	$1$	$e\left(\frac{105}{191}\right)$	$e\left(\frac{19}{191}\right)$	$e\left(\frac{127}{382}\right)$	$e\left(\frac{124}{191}\right)$	$e\left(\frac{337}{382}\right)$	$e\left(\frac{170}{191}\right)$	$e\left(\frac{303}{382}\right)$	$e\left(\frac{38}{191}\right)$	$e\left(\frac{139}{382}\right)$	$e\left(\frac{275}{382}\right)$

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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	$8043$
Structure	\(C_{2}\times C_{2}\times C_{1146}\)
Order	$4584$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{8043}(1,\cdot)\)	8043.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8043}(2,\cdot)\)	8043.z	1146	yes	\(-1\)	\(1\)	\(e\left(\frac{197}{1146}\right)\)	\(e\left(\frac{197}{573}\right)\)	\(e\left(\frac{593}{1146}\right)\)	\(e\left(\frac{197}{382}\right)\)	\(e\left(\frac{395}{573}\right)\)	\(e\left(\frac{37}{1146}\right)\)	\(e\left(\frac{26}{191}\right)\)	\(e\left(\frac{394}{573}\right)\)	\(e\left(\frac{637}{1146}\right)\)	\(e\left(\frac{154}{573}\right)\)
\(\chi_{8043}(4,\cdot)\)	8043.y	573	no	\(1\)	\(1\)	\(e\left(\frac{197}{573}\right)\)	\(e\left(\frac{394}{573}\right)\)	\(e\left(\frac{20}{573}\right)\)	\(e\left(\frac{6}{191}\right)\)	\(e\left(\frac{217}{573}\right)\)	\(e\left(\frac{37}{573}\right)\)	\(e\left(\frac{52}{191}\right)\)	\(e\left(\frac{215}{573}\right)\)	\(e\left(\frac{64}{573}\right)\)	\(e\left(\frac{308}{573}\right)\)
\(\chi_{8043}(5,\cdot)\)	8043.ba	1146	yes	\(-1\)	\(1\)	\(e\left(\frac{593}{1146}\right)\)	\(e\left(\frac{20}{573}\right)\)	\(e\left(\frac{767}{1146}\right)\)	\(e\left(\frac{211}{382}\right)\)	\(e\left(\frac{107}{573}\right)\)	\(e\left(\frac{380}{573}\right)\)	\(e\left(\frac{23}{191}\right)\)	\(e\left(\frac{40}{573}\right)\)	\(e\left(\frac{425}{573}\right)\)	\(e\left(\frac{581}{1146}\right)\)
\(\chi_{8043}(8,\cdot)\)	8043.x	382	no	\(-1\)	\(1\)	\(e\left(\frac{197}{382}\right)\)	\(e\left(\frac{6}{191}\right)\)	\(e\left(\frac{211}{382}\right)\)	\(e\left(\frac{209}{382}\right)\)	\(e\left(\frac{13}{191}\right)\)	\(e\left(\frac{37}{382}\right)\)	\(e\left(\frac{78}{191}\right)\)	\(e\left(\frac{12}{191}\right)\)	\(e\left(\frac{255}{382}\right)\)	\(e\left(\frac{154}{191}\right)\)
\(\chi_{8043}(10,\cdot)\)	8043.bf	1146	no	\(1\)	\(1\)	\(e\left(\frac{395}{573}\right)\)	\(e\left(\frac{217}{573}\right)\)	\(e\left(\frac{107}{573}\right)\)	\(e\left(\frac{13}{191}\right)\)	\(e\left(\frac{502}{573}\right)\)	\(e\left(\frac{797}{1146}\right)\)	\(e\left(\frac{49}{191}\right)\)	\(e\left(\frac{434}{573}\right)\)	\(e\left(\frac{341}{1146}\right)\)	\(e\left(\frac{889}{1146}\right)\)
\(\chi_{8043}(11,\cdot)\)	8043.bc	1146	yes	\(1\)	\(1\)	\(e\left(\frac{37}{1146}\right)\)	\(e\left(\frac{37}{573}\right)\)	\(e\left(\frac{380}{573}\right)\)	\(e\left(\frac{37}{382}\right)\)	\(e\left(\frac{797}{1146}\right)\)	\(e\left(\frac{130}{573}\right)\)	\(e\left(\frac{257}{382}\right)\)	\(e\left(\frac{74}{573}\right)\)	\(e\left(\frac{713}{1146}\right)\)	\(e\left(\frac{122}{573}\right)\)
\(\chi_{8043}(13,\cdot)\)	8043.r	382	no	\(1\)	\(1\)	\(e\left(\frac{26}{191}\right)\)	\(e\left(\frac{52}{191}\right)\)	\(e\left(\frac{23}{191}\right)\)	\(e\left(\frac{78}{191}\right)\)	\(e\left(\frac{49}{191}\right)\)	\(e\left(\frac{257}{382}\right)\)	\(e\left(\frac{103}{191}\right)\)	\(e\left(\frac{104}{191}\right)\)	\(e\left(\frac{109}{382}\right)\)	\(e\left(\frac{59}{382}\right)\)
\(\chi_{8043}(16,\cdot)\)	8043.y	573	no	\(1\)	\(1\)	\(e\left(\frac{394}{573}\right)\)	\(e\left(\frac{215}{573}\right)\)	\(e\left(\frac{40}{573}\right)\)	\(e\left(\frac{12}{191}\right)\)	\(e\left(\frac{434}{573}\right)\)	\(e\left(\frac{74}{573}\right)\)	\(e\left(\frac{104}{191}\right)\)	\(e\left(\frac{430}{573}\right)\)	\(e\left(\frac{128}{573}\right)\)	\(e\left(\frac{43}{573}\right)\)
\(\chi_{8043}(17,\cdot)\)	8043.bb	1146	yes	\(1\)	\(1\)	\(e\left(\frac{637}{1146}\right)\)	\(e\left(\frac{64}{573}\right)\)	\(e\left(\frac{425}{573}\right)\)	\(e\left(\frac{255}{382}\right)\)	\(e\left(\frac{341}{1146}\right)\)	\(e\left(\frac{713}{1146}\right)\)	\(e\left(\frac{109}{382}\right)\)	\(e\left(\frac{128}{573}\right)\)	\(e\left(\frac{214}{573}\right)\)	\(e\left(\frac{1057}{1146}\right)\)
\(\chi_{8043}(19,\cdot)\)	8043.be	1146	no	\(-1\)	\(1\)	\(e\left(\frac{154}{573}\right)\)	\(e\left(\frac{308}{573}\right)\)	\(e\left(\frac{581}{1146}\right)\)	\(e\left(\frac{154}{191}\right)\)	\(e\left(\frac{889}{1146}\right)\)	\(e\left(\frac{122}{573}\right)\)	\(e\left(\frac{59}{382}\right)\)	\(e\left(\frac{43}{573}\right)\)	\(e\left(\frac{1057}{1146}\right)\)	\(e\left(\frac{467}{1146}\right)\)
\(\chi_{8043}(20,\cdot)\)	8043.w	382	yes	\(-1\)	\(1\)	\(e\left(\frac{329}{382}\right)\)	\(e\left(\frac{138}{191}\right)\)	\(e\left(\frac{269}{382}\right)\)	\(e\left(\frac{223}{382}\right)\)	\(e\left(\frac{108}{191}\right)\)	\(e\left(\frac{139}{191}\right)\)	\(e\left(\frac{75}{191}\right)\)	\(e\left(\frac{85}{191}\right)\)	\(e\left(\frac{163}{191}\right)\)	\(e\left(\frac{17}{382}\right)\)
\(\chi_{8043}(22,\cdot)\)	8043.t	382	no	\(-1\)	\(1\)	\(e\left(\frac{39}{191}\right)\)	\(e\left(\frac{78}{191}\right)\)	\(e\left(\frac{69}{382}\right)\)	\(e\left(\frac{117}{191}\right)\)	\(e\left(\frac{147}{382}\right)\)	\(e\left(\frac{99}{382}\right)\)	\(e\left(\frac{309}{382}\right)\)	\(e\left(\frac{156}{191}\right)\)	\(e\left(\frac{34}{191}\right)\)	\(e\left(\frac{92}{191}\right)\)
\(\chi_{8043}(23,\cdot)\)	8043.z	1146	yes	\(-1\)	\(1\)	\(e\left(\frac{527}{1146}\right)\)	\(e\left(\frac{527}{573}\right)\)	\(e\left(\frac{929}{1146}\right)\)	\(e\left(\frac{145}{382}\right)\)	\(e\left(\frac{155}{573}\right)\)	\(e\left(\frac{1117}{1146}\right)\)	\(e\left(\frac{119}{191}\right)\)	\(e\left(\frac{481}{573}\right)\)	\(e\left(\frac{337}{1146}\right)\)	\(e\left(\frac{220}{573}\right)\)
\(\chi_{8043}(25,\cdot)\)	8043.y	573	no	\(1\)	\(1\)	\(e\left(\frac{20}{573}\right)\)	\(e\left(\frac{40}{573}\right)\)	\(e\left(\frac{194}{573}\right)\)	\(e\left(\frac{20}{191}\right)\)	\(e\left(\frac{214}{573}\right)\)	\(e\left(\frac{187}{573}\right)\)	\(e\left(\frac{46}{191}\right)\)	\(e\left(\frac{80}{573}\right)\)	\(e\left(\frac{277}{573}\right)\)	\(e\left(\frac{8}{573}\right)\)
\(\chi_{8043}(26,\cdot)\)	8043.ba	1146	yes	\(-1\)	\(1\)	\(e\left(\frac{353}{1146}\right)\)	\(e\left(\frac{353}{573}\right)\)	\(e\left(\frac{731}{1146}\right)\)	\(e\left(\frac{353}{382}\right)\)	\(e\left(\frac{542}{573}\right)\)	\(e\left(\frac{404}{573}\right)\)	\(e\left(\frac{129}{191}\right)\)	\(e\left(\frac{133}{573}\right)\)	\(e\left(\frac{482}{573}\right)\)	\(e\left(\frac{485}{1146}\right)\)
\(\chi_{8043}(29,\cdot)\)	8043.x	382	no	\(-1\)	\(1\)	\(e\left(\frac{127}{382}\right)\)	\(e\left(\frac{127}{191}\right)\)	\(e\left(\frac{105}{382}\right)\)	\(e\left(\frac{381}{382}\right)\)	\(e\left(\frac{116}{191}\right)\)	\(e\left(\frac{51}{382}\right)\)	\(e\left(\frac{123}{191}\right)\)	\(e\left(\frac{63}{191}\right)\)	\(e\left(\frac{145}{382}\right)\)	\(e\left(\frac{140}{191}\right)\)
\(\chi_{8043}(31,\cdot)\)	8043.be	1146	no	\(-1\)	\(1\)	\(e\left(\frac{320}{573}\right)\)	\(e\left(\frac{67}{573}\right)\)	\(e\left(\frac{1051}{1146}\right)\)	\(e\left(\frac{129}{191}\right)\)	\(e\left(\frac{545}{1146}\right)\)	\(e\left(\frac{127}{573}\right)\)	\(e\left(\frac{135}{382}\right)\)	\(e\left(\frac{134}{573}\right)\)	\(e\left(\frac{269}{1146}\right)\)	\(e\left(\frac{829}{1146}\right)\)
\(\chi_{8043}(32,\cdot)\)	8043.z	1146	yes	\(-1\)	\(1\)	\(e\left(\frac{985}{1146}\right)\)	\(e\left(\frac{412}{573}\right)\)	\(e\left(\frac{673}{1146}\right)\)	\(e\left(\frac{221}{382}\right)\)	\(e\left(\frac{256}{573}\right)\)	\(e\left(\frac{185}{1146}\right)\)	\(e\left(\frac{130}{191}\right)\)	\(e\left(\frac{251}{573}\right)\)	\(e\left(\frac{893}{1146}\right)\)	\(e\left(\frac{197}{573}\right)\)
\(\chi_{8043}(34,\cdot)\)	8043.s	382	no	\(-1\)	\(1\)	\(e\left(\frac{139}{191}\right)\)	\(e\left(\frac{87}{191}\right)\)	\(e\left(\frac{99}{382}\right)\)	\(e\left(\frac{35}{191}\right)\)	\(e\left(\frac{377}{382}\right)\)	\(e\left(\frac{125}{191}\right)\)	\(e\left(\frac{161}{382}\right)\)	\(e\left(\frac{174}{191}\right)\)	\(e\left(\frac{355}{382}\right)\)	\(e\left(\frac{73}{382}\right)\)
\(\chi_{8043}(37,\cdot)\)	8043.bd	1146	no	\(-1\)	\(1\)	\(e\left(\frac{256}{573}\right)\)	\(e\left(\frac{512}{573}\right)\)	\(e\left(\frac{497}{1146}\right)\)	\(e\left(\frac{65}{191}\right)\)	\(e\left(\frac{1009}{1146}\right)\)	\(e\left(\frac{547}{1146}\right)\)	\(e\left(\frac{299}{382}\right)\)	\(e\left(\frac{451}{573}\right)\)	\(e\left(\frac{566}{573}\right)\)	\(e\left(\frac{217}{573}\right)\)
\(\chi_{8043}(38,\cdot)\)	8043.bb	1146	yes	\(1\)	\(1\)	\(e\left(\frac{505}{1146}\right)\)	\(e\left(\frac{505}{573}\right)\)	\(e\left(\frac{14}{573}\right)\)	\(e\left(\frac{123}{382}\right)\)	\(e\left(\frac{533}{1146}\right)\)	\(e\left(\frac{281}{1146}\right)\)	\(e\left(\frac{111}{382}\right)\)	\(e\left(\frac{437}{573}\right)\)	\(e\left(\frac{274}{573}\right)\)	\(e\left(\frac{775}{1146}\right)\)
\(\chi_{8043}(40,\cdot)\)	8043.bf	1146	no	\(1\)	\(1\)	\(e\left(\frac{19}{573}\right)\)	\(e\left(\frac{38}{573}\right)\)	\(e\left(\frac{127}{573}\right)\)	\(e\left(\frac{19}{191}\right)\)	\(e\left(\frac{146}{573}\right)\)	\(e\left(\frac{871}{1146}\right)\)	\(e\left(\frac{101}{191}\right)\)	\(e\left(\frac{76}{573}\right)\)	\(e\left(\frac{469}{1146}\right)\)	\(e\left(\frac{359}{1146}\right)\)
\(\chi_{8043}(41,\cdot)\)	8043.w	382	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{382}\right)\)	\(e\left(\frac{13}{191}\right)\)	\(e\left(\frac{107}{382}\right)\)	\(e\left(\frac{39}{382}\right)\)	\(e\left(\frac{60}{191}\right)\)	\(e\left(\frac{56}{191}\right)\)	\(e\left(\frac{169}{191}\right)\)	\(e\left(\frac{26}{191}\right)\)	\(e\left(\frac{133}{191}\right)\)	\(e\left(\frac{349}{382}\right)\)
\(\chi_{8043}(43,\cdot)\)	8043.q	191	no	\(1\)	\(1\)	\(e\left(\frac{16}{191}\right)\)	\(e\left(\frac{32}{191}\right)\)	\(e\left(\frac{117}{191}\right)\)	\(e\left(\frac{48}{191}\right)\)	\(e\left(\frac{133}{191}\right)\)	\(e\left(\frac{35}{191}\right)\)	\(e\left(\frac{34}{191}\right)\)	\(e\left(\frac{64}{191}\right)\)	\(e\left(\frac{107}{191}\right)\)	\(e\left(\frac{121}{191}\right)\)
\(\chi_{8043}(44,\cdot)\)	8043.bc	1146	yes	\(1\)	\(1\)	\(e\left(\frac{431}{1146}\right)\)	\(e\left(\frac{431}{573}\right)\)	\(e\left(\frac{400}{573}\right)\)	\(e\left(\frac{49}{382}\right)\)	\(e\left(\frac{85}{1146}\right)\)	\(e\left(\frac{167}{573}\right)\)	\(e\left(\frac{361}{382}\right)\)	\(e\left(\frac{289}{573}\right)\)	\(e\left(\frac{841}{1146}\right)\)	\(e\left(\frac{430}{573}\right)\)
\(\chi_{8043}(46,\cdot)\)	8043.y	573	no	\(1\)	\(1\)	\(e\left(\frac{362}{573}\right)\)	\(e\left(\frac{151}{573}\right)\)	\(e\left(\frac{188}{573}\right)\)	\(e\left(\frac{171}{191}\right)\)	\(e\left(\frac{550}{573}\right)\)	\(e\left(\frac{4}{573}\right)\)	\(e\left(\frac{145}{191}\right)\)	\(e\left(\frac{302}{573}\right)\)	\(e\left(\frac{487}{573}\right)\)	\(e\left(\frac{374}{573}\right)\)
\(\chi_{8043}(47,\cdot)\)	8043.ba	1146	yes	\(-1\)	\(1\)	\(e\left(\frac{695}{1146}\right)\)	\(e\left(\frac{122}{573}\right)\)	\(e\left(\frac{725}{1146}\right)\)	\(e\left(\frac{313}{382}\right)\)	\(e\left(\frac{137}{573}\right)\)	\(e\left(\frac{26}{573}\right)\)	\(e\left(\frac{83}{191}\right)\)	\(e\left(\frac{244}{573}\right)\)	\(e\left(\frac{14}{573}\right)\)	\(e\left(\frac{851}{1146}\right)\)
\(\chi_{8043}(50,\cdot)\)	8043.x	382	no	\(-1\)	\(1\)	\(e\left(\frac{79}{382}\right)\)	\(e\left(\frac{79}{191}\right)\)	\(e\left(\frac{327}{382}\right)\)	\(e\left(\frac{237}{382}\right)\)	\(e\left(\frac{12}{191}\right)\)	\(e\left(\frac{137}{382}\right)\)	\(e\left(\frac{72}{191}\right)\)	\(e\left(\frac{158}{191}\right)\)	\(e\left(\frac{15}{382}\right)\)	\(e\left(\frac{54}{191}\right)\)
\(\chi_{8043}(52,\cdot)\)	8043.bf	1146	no	\(1\)	\(1\)	\(e\left(\frac{275}{573}\right)\)	\(e\left(\frac{550}{573}\right)\)	\(e\left(\frac{89}{573}\right)\)	\(e\left(\frac{84}{191}\right)\)	\(e\left(\frac{364}{573}\right)\)	\(e\left(\frac{845}{1146}\right)\)	\(e\left(\frac{155}{191}\right)\)	\(e\left(\frac{527}{573}\right)\)	\(e\left(\frac{455}{1146}\right)\)	\(e\left(\frac{793}{1146}\right)\)
\(\chi_{8043}(53,\cdot)\)	8043.bc	1146	yes	\(1\)	\(1\)	\(e\left(\frac{403}{1146}\right)\)	\(e\left(\frac{403}{573}\right)\)	\(e\left(\frac{35}{573}\right)\)	\(e\left(\frac{21}{382}\right)\)	\(e\left(\frac{473}{1146}\right)\)	\(e\left(\frac{208}{573}\right)\)	\(e\left(\frac{373}{382}\right)\)	\(e\left(\frac{233}{573}\right)\)	\(e\left(\frac{797}{1146}\right)\)	\(e\left(\frac{539}{573}\right)\)
\(\chi_{8043}(55,\cdot)\)	8043.s	382	no	\(-1\)	\(1\)	\(e\left(\frac{105}{191}\right)\)	\(e\left(\frac{19}{191}\right)\)	\(e\left(\frac{127}{382}\right)\)	\(e\left(\frac{124}{191}\right)\)	\(e\left(\frac{337}{382}\right)\)	\(e\left(\frac{170}{191}\right)\)	\(e\left(\frac{303}{382}\right)\)	\(e\left(\frac{38}{191}\right)\)	\(e\left(\frac{139}{382}\right)\)	\(e\left(\frac{275}{382}\right)\)

Introduction

L-functions

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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.