LMFDB - Group of Dirichlet characters of modulus 6043

Show commands: PariGP / SageMath

sage: H = DirichletGroup(6043)

pari: g = idealstar(,6043,2)

Character group

sage: G.order() pari: g.no
Order	=	6042
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6042}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{6043}(5,\cdot)$

First 32 of 6042 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{6043}(1,\cdot)$	6043.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{6043}(2,\cdot)$	6043.l	318	yes	$-1$	$1$	$e\left(\frac{247}{318}\right)$	$e\left(\frac{49}{106}\right)$	$e\left(\frac{88}{159}\right)$	$e\left(\frac{91}{318}\right)$	$e\left(\frac{38}{159}\right)$	$e\left(\frac{5}{318}\right)$	$e\left(\frac{35}{106}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{10}{159}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{6043}(3,\cdot)$	6043.n	2014	yes	$-1$	$1$	$e\left(\frac{49}{106}\right)$	$e\left(\frac{1345}{2014}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{979}{2014}\right)$	$e\left(\frac{131}{1007}\right)$	$e\left(\frac{345}{2014}\right)$	$e\left(\frac{41}{106}\right)$	$e\left(\frac{338}{1007}\right)$	$e\left(\frac{955}{1007}\right)$	$e\left(\frac{33}{38}\right)$
$\chi_{6043}(4,\cdot)$	6043.k	159	yes	$1$	$1$	$e\left(\frac{88}{159}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{17}{159}\right)$	$e\left(\frac{91}{159}\right)$	$e\left(\frac{76}{159}\right)$	$e\left(\frac{5}{159}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{20}{159}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{6043}(5,\cdot)$	6043.p	6042	yes	$-1$	$1$	$e\left(\frac{91}{318}\right)$	$e\left(\frac{979}{2014}\right)$	$e\left(\frac{91}{159}\right)$	$e\left(\frac{1}{6042}\right)$	$e\left(\frac{2333}{3021}\right)$	$e\left(\frac{671}{6042}\right)$	$e\left(\frac{91}{106}\right)$	$e\left(\frac{979}{1007}\right)$	$e\left(\frac{865}{3021}\right)$	$e\left(\frac{47}{114}\right)$
$\chi_{6043}(6,\cdot)$	6043.o	3021	yes	$1$	$1$	$e\left(\frac{38}{159}\right)$	$e\left(\frac{131}{1007}\right)$	$e\left(\frac{76}{159}\right)$	$e\left(\frac{2333}{3021}\right)$	$e\left(\frac{1115}{3021}\right)$	$e\left(\frac{565}{3021}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{262}{1007}\right)$	$e\left(\frac{34}{3021}\right)$	$e\left(\frac{40}{57}\right)$
$\chi_{6043}(7,\cdot)$	6043.p	6042	yes	$-1$	$1$	$e\left(\frac{5}{318}\right)$	$e\left(\frac{345}{2014}\right)$	$e\left(\frac{5}{159}\right)$	$e\left(\frac{671}{6042}\right)$	$e\left(\frac{565}{3021}\right)$	$e\left(\frac{3133}{6042}\right)$	$e\left(\frac{5}{106}\right)$	$e\left(\frac{345}{1007}\right)$	$e\left(\frac{383}{3021}\right)$	$e\left(\frac{73}{114}\right)$
$\chi_{6043}(8,\cdot)$	6043.i	106	yes	$-1$	$1$	$e\left(\frac{35}{106}\right)$	$e\left(\frac{41}{106}\right)$	$e\left(\frac{35}{53}\right)$	$e\left(\frac{91}{106}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{5}{106}\right)$	$e\left(\frac{105}{106}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{10}{53}\right)$	$-1$
$\chi_{6043}(9,\cdot)$	6043.m	1007	yes	$1$	$1$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{338}{1007}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{979}{1007}\right)$	$e\left(\frac{262}{1007}\right)$	$e\left(\frac{345}{1007}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{676}{1007}\right)$	$e\left(\frac{903}{1007}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{6043}(10,\cdot)$	6043.o	3021	yes	$1$	$1$	$e\left(\frac{10}{159}\right)$	$e\left(\frac{955}{1007}\right)$	$e\left(\frac{20}{159}\right)$	$e\left(\frac{865}{3021}\right)$	$e\left(\frac{34}{3021}\right)$	$e\left(\frac{383}{3021}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{903}{1007}\right)$	$e\left(\frac{1055}{3021}\right)$	$e\left(\frac{14}{57}\right)$
$\chi_{6043}(11,\cdot)$	6043.j	114	yes	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{33}{38}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{47}{114}\right)$	$e\left(\frac{40}{57}\right)$	$e\left(\frac{73}{114}\right)$	$-1$	$e\left(\frac{14}{19}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{113}{114}\right)$
$\chi_{6043}(12,\cdot)$	6043.p	6042	yes	$-1$	$1$	$e\left(\frac{5}{318}\right)$	$e\left(\frac{1193}{2014}\right)$	$e\left(\frac{5}{159}\right)$	$e\left(\frac{353}{6042}\right)$	$e\left(\frac{1837}{3021}\right)$	$e\left(\frac{1225}{6042}\right)$	$e\left(\frac{5}{106}\right)$	$e\left(\frac{186}{1007}\right)$	$e\left(\frac{224}{3021}\right)$	$e\left(\frac{61}{114}\right)$
$\chi_{6043}(13,\cdot)$	6043.p	6042	yes	$-1$	$1$	$e\left(\frac{101}{318}\right)$	$e\left(\frac{79}{2014}\right)$	$e\left(\frac{101}{159}\right)$	$e\left(\frac{4205}{6042}\right)$	$e\left(\frac{1078}{3021}\right)$	$e\left(\frac{5983}{6042}\right)$	$e\left(\frac{101}{106}\right)$	$e\left(\frac{79}{1007}\right)$	$e\left(\frac{41}{3021}\right)$	$e\left(\frac{73}{114}\right)$
$\chi_{6043}(14,\cdot)$	6043.m	1007	yes	$1$	$1$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{638}{1007}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{400}{1007}\right)$	$e\left(\frac{429}{1007}\right)$	$e\left(\frac{538}{1007}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{269}{1007}\right)$	$e\left(\frac{191}{1007}\right)$	$e\left(\frac{9}{19}\right)$
$\chi_{6043}(15,\cdot)$	6043.o	3021	yes	$1$	$1$	$e\left(\frac{119}{159}\right)$	$e\left(\frac{155}{1007}\right)$	$e\left(\frac{79}{159}\right)$	$e\left(\frac{1469}{3021}\right)$	$e\left(\frac{2726}{3021}\right)$	$e\left(\frac{853}{3021}\right)$	$e\left(\frac{13}{53}\right)$	$e\left(\frac{310}{1007}\right)$	$e\left(\frac{709}{3021}\right)$	$e\left(\frac{16}{57}\right)$
$\chi_{6043}(16,\cdot)$	6043.k	159	yes	$1$	$1$	$e\left(\frac{17}{159}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{34}{159}\right)$	$e\left(\frac{23}{159}\right)$	$e\left(\frac{152}{159}\right)$	$e\left(\frac{10}{159}\right)$	$e\left(\frac{17}{53}\right)$	$e\left(\frac{37}{53}\right)$	$e\left(\frac{40}{159}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{6043}(17,\cdot)$	6043.o	3021	yes	$1$	$1$	$e\left(\frac{49}{159}\right)$	$e\left(\frac{837}{1007}\right)$	$e\left(\frac{98}{159}\right)$	$e\left(\frac{2092}{3021}\right)$	$e\left(\frac{421}{3021}\right)$	$e\left(\frac{1988}{3021}\right)$	$e\left(\frac{49}{53}\right)$	$e\left(\frac{667}{1007}\right)$	$e\left(\frac{2}{3021}\right)$	$e\left(\frac{56}{57}\right)$
$\chi_{6043}(18,\cdot)$	6043.p	6042	yes	$-1$	$1$	$e\left(\frac{223}{318}\right)$	$e\left(\frac{1607}{2014}\right)$	$e\left(\frac{64}{159}\right)$	$e\left(\frac{1561}{6042}\right)$	$e\left(\frac{1508}{3021}\right)$	$e\left(\frac{2165}{6042}\right)$	$e\left(\frac{11}{106}\right)$	$e\left(\frac{600}{1007}\right)$	$e\left(\frac{2899}{3021}\right)$	$e\left(\frac{65}{114}\right)$
$\chi_{6043}(19,\cdot)$	6043.p	6042	yes	$-1$	$1$	$e\left(\frac{305}{318}\right)$	$e\left(\frac{905}{2014}\right)$	$e\left(\frac{146}{159}\right)$	$e\left(\frac{4679}{6042}\right)$	$e\left(\frac{1234}{3021}\right)$	$e\left(\frac{3811}{6042}\right)$	$e\left(\frac{93}{106}\right)$	$e\left(\frac{905}{1007}\right)$	$e\left(\frac{2216}{3021}\right)$	$e\left(\frac{7}{114}\right)$
$\chi_{6043}(20,\cdot)$	6043.n	2014	yes	$-1$	$1$	$e\left(\frac{89}{106}\right)$	$e\left(\frac{827}{2014}\right)$	$e\left(\frac{36}{53}\right)$	$e\left(\frac{1153}{2014}\right)$	$e\left(\frac{252}{1007}\right)$	$e\left(\frac{287}{2014}\right)$	$e\left(\frac{55}{106}\right)$	$e\left(\frac{827}{1007}\right)$	$e\left(\frac{415}{1007}\right)$	$e\left(\frac{3}{38}\right)$
$\chi_{6043}(21,\cdot)$	6043.o	3021	yes	$1$	$1$	$e\left(\frac{76}{159}\right)$	$e\left(\frac{845}{1007}\right)$	$e\left(\frac{152}{159}\right)$	$e\left(\frac{1804}{3021}\right)$	$e\left(\frac{958}{3021}\right)$	$e\left(\frac{2084}{3021}\right)$	$e\left(\frac{23}{53}\right)$	$e\left(\frac{683}{1007}\right)$	$e\left(\frac{227}{3021}\right)$	$e\left(\frac{29}{57}\right)$
$\chi_{6043}(22,\cdot)$	6043.o	3021	yes	$1$	$1$	$e\left(\frac{97}{159}\right)$	$e\left(\frac{333}{1007}\right)$	$e\left(\frac{35}{159}\right)$	$e\left(\frac{2110}{3021}\right)$	$e\left(\frac{2842}{3021}\right)$	$e\left(\frac{1982}{3021}\right)$	$e\left(\frac{44}{53}\right)$	$e\left(\frac{666}{1007}\right)$	$e\left(\frac{932}{3021}\right)$	$e\left(\frac{47}{57}\right)$
$\chi_{6043}(23,\cdot)$	6043.m	1007	yes	$1$	$1$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{561}{1007}\right)$	$e\left(\frac{30}{53}\right)$	$e\left(\frac{317}{1007}\right)$	$e\left(\frac{846}{1007}\right)$	$e\left(\frac{230}{1007}\right)$	$e\left(\frac{45}{53}\right)$	$e\left(\frac{115}{1007}\right)$	$e\left(\frac{602}{1007}\right)$	$e\left(\frac{3}{19}\right)$
$\chi_{6043}(24,\cdot)$	6043.m	1007	yes	$1$	$1$	$e\left(\frac{42}{53}\right)$	$e\left(\frac{55}{1007}\right)$	$e\left(\frac{31}{53}\right)$	$e\left(\frac{347}{1007}\right)$	$e\left(\frac{853}{1007}\right)$	$e\left(\frac{220}{1007}\right)$	$e\left(\frac{20}{53}\right)$	$e\left(\frac{110}{1007}\right)$	$e\left(\frac{138}{1007}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{6043}(25,\cdot)$	6043.o	3021	yes	$1$	$1$	$e\left(\frac{91}{159}\right)$	$e\left(\frac{979}{1007}\right)$	$e\left(\frac{23}{159}\right)$	$e\left(\frac{1}{3021}\right)$	$e\left(\frac{1645}{3021}\right)$	$e\left(\frac{671}{3021}\right)$	$e\left(\frac{38}{53}\right)$	$e\left(\frac{951}{1007}\right)$	$e\left(\frac{1730}{3021}\right)$	$e\left(\frac{47}{57}\right)$
$\chi_{6043}(26,\cdot)$	6043.m	1007	yes	$1$	$1$	$e\left(\frac{5}{53}\right)$	$e\left(\frac{505}{1007}\right)$	$e\left(\frac{10}{53}\right)$	$e\left(\frac{989}{1007}\right)$	$e\left(\frac{600}{1007}\right)$	$e\left(\frac{6}{1007}\right)$	$e\left(\frac{15}{53}\right)$	$e\left(\frac{3}{1007}\right)$	$e\left(\frac{77}{1007}\right)$	$e\left(\frac{9}{19}\right)$
$\chi_{6043}(27,\cdot)$	6043.n	2014	yes	$-1$	$1$	$e\left(\frac{41}{106}\right)$	$e\left(\frac{7}{2014}\right)$	$e\left(\frac{41}{53}\right)$	$e\left(\frac{923}{2014}\right)$	$e\left(\frac{393}{1007}\right)$	$e\left(\frac{1035}{2014}\right)$	$e\left(\frac{17}{106}\right)$	$e\left(\frac{7}{1007}\right)$	$e\left(\frac{851}{1007}\right)$	$e\left(\frac{23}{38}\right)$
$\chi_{6043}(28,\cdot)$	6043.p	6042	yes	$-1$	$1$	$e\left(\frac{181}{318}\right)$	$e\left(\frac{193}{2014}\right)$	$e\left(\frac{22}{159}\right)$	$e\left(\frac{4129}{6042}\right)$	$e\left(\frac{2009}{3021}\right)$	$e\left(\frac{3323}{6042}\right)$	$e\left(\frac{75}{106}\right)$	$e\left(\frac{193}{1007}\right)$	$e\left(\frac{763}{3021}\right)$	$e\left(\frac{35}{114}\right)$
$\chi_{6043}(29,\cdot)$	6043.p	6042	yes	$-1$	$1$	$e\left(\frac{289}{318}\right)$	$e\left(\frac{967}{2014}\right)$	$e\left(\frac{130}{159}\right)$	$e\left(\frac{433}{6042}\right)$	$e\left(\frac{1175}{3021}\right)$	$e\left(\frac{527}{6042}\right)$	$e\left(\frac{77}{106}\right)$	$e\left(\frac{967}{1007}\right)$	$e\left(\frac{2962}{3021}\right)$	$e\left(\frac{59}{114}\right)$
$\chi_{6043}(30,\cdot)$	6043.p	6042	yes	$-1$	$1$	$e\left(\frac{167}{318}\right)$	$e\left(\frac{1241}{2014}\right)$	$e\left(\frac{8}{159}\right)$	$e\left(\frac{4667}{6042}\right)$	$e\left(\frac{427}{3021}\right)$	$e\left(\frac{1801}{6042}\right)$	$e\left(\frac{61}{106}\right)$	$e\left(\frac{234}{1007}\right)$	$e\left(\frac{899}{3021}\right)$	$e\left(\frac{13}{114}\right)$
$\chi_{6043}(31,\cdot)$	6043.o	3021	yes	$1$	$1$	$e\left(\frac{113}{159}\right)$	$e\left(\frac{271}{1007}\right)$	$e\left(\frac{67}{159}\right)$	$e\left(\frac{314}{3021}\right)$	$e\left(\frac{2960}{3021}\right)$	$e\left(\frac{2245}{3021}\right)$	$e\left(\frac{7}{53}\right)$	$e\left(\frac{542}{1007}\right)$	$e\left(\frac{2461}{3021}\right)$	$e\left(\frac{52}{57}\right)$
$\chi_{6043}(32,\cdot)$	6043.l	318	yes	$-1$	$1$	$e\left(\frac{281}{318}\right)$	$e\left(\frac{33}{106}\right)$	$e\left(\frac{122}{159}\right)$	$e\left(\frac{137}{318}\right)$	$e\left(\frac{31}{159}\right)$	$e\left(\frac{25}{318}\right)$	$e\left(\frac{69}{106}\right)$	$e\left(\frac{33}{53}\right)$	$e\left(\frac{50}{159}\right)$	$e\left(\frac{1}{6}\right)$

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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	$6043$
Structure	\(C_{6042}\)
Order	$6042$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{6043}(1,\cdot)\)	6043.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{6043}(2,\cdot)\)	6043.l	318	yes	\(-1\)	\(1\)	\(e\left(\frac{247}{318}\right)\)	\(e\left(\frac{49}{106}\right)\)	\(e\left(\frac{88}{159}\right)\)	\(e\left(\frac{91}{318}\right)\)	\(e\left(\frac{38}{159}\right)\)	\(e\left(\frac{5}{318}\right)\)	\(e\left(\frac{35}{106}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{10}{159}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{6043}(3,\cdot)\)	6043.n	2014	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{106}\right)\)	\(e\left(\frac{1345}{2014}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{979}{2014}\right)\)	\(e\left(\frac{131}{1007}\right)\)	\(e\left(\frac{345}{2014}\right)\)	\(e\left(\frac{41}{106}\right)\)	\(e\left(\frac{338}{1007}\right)\)	\(e\left(\frac{955}{1007}\right)\)	\(e\left(\frac{33}{38}\right)\)
\(\chi_{6043}(4,\cdot)\)	6043.k	159	yes	\(1\)	\(1\)	\(e\left(\frac{88}{159}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{17}{159}\right)\)	\(e\left(\frac{91}{159}\right)\)	\(e\left(\frac{76}{159}\right)\)	\(e\left(\frac{5}{159}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{20}{159}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{6043}(5,\cdot)\)	6043.p	6042	yes	\(-1\)	\(1\)	\(e\left(\frac{91}{318}\right)\)	\(e\left(\frac{979}{2014}\right)\)	\(e\left(\frac{91}{159}\right)\)	\(e\left(\frac{1}{6042}\right)\)	\(e\left(\frac{2333}{3021}\right)\)	\(e\left(\frac{671}{6042}\right)\)	\(e\left(\frac{91}{106}\right)\)	\(e\left(\frac{979}{1007}\right)\)	\(e\left(\frac{865}{3021}\right)\)	\(e\left(\frac{47}{114}\right)\)
\(\chi_{6043}(6,\cdot)\)	6043.o	3021	yes	\(1\)	\(1\)	\(e\left(\frac{38}{159}\right)\)	\(e\left(\frac{131}{1007}\right)\)	\(e\left(\frac{76}{159}\right)\)	\(e\left(\frac{2333}{3021}\right)\)	\(e\left(\frac{1115}{3021}\right)\)	\(e\left(\frac{565}{3021}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{262}{1007}\right)\)	\(e\left(\frac{34}{3021}\right)\)	\(e\left(\frac{40}{57}\right)\)
\(\chi_{6043}(7,\cdot)\)	6043.p	6042	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{318}\right)\)	\(e\left(\frac{345}{2014}\right)\)	\(e\left(\frac{5}{159}\right)\)	\(e\left(\frac{671}{6042}\right)\)	\(e\left(\frac{565}{3021}\right)\)	\(e\left(\frac{3133}{6042}\right)\)	\(e\left(\frac{5}{106}\right)\)	\(e\left(\frac{345}{1007}\right)\)	\(e\left(\frac{383}{3021}\right)\)	\(e\left(\frac{73}{114}\right)\)
\(\chi_{6043}(8,\cdot)\)	6043.i	106	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{106}\right)\)	\(e\left(\frac{41}{106}\right)\)	\(e\left(\frac{35}{53}\right)\)	\(e\left(\frac{91}{106}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{5}{106}\right)\)	\(e\left(\frac{105}{106}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(-1\)
\(\chi_{6043}(9,\cdot)\)	6043.m	1007	yes	\(1\)	\(1\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{338}{1007}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{979}{1007}\right)\)	\(e\left(\frac{262}{1007}\right)\)	\(e\left(\frac{345}{1007}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{676}{1007}\right)\)	\(e\left(\frac{903}{1007}\right)\)	\(e\left(\frac{14}{19}\right)\)
\(\chi_{6043}(10,\cdot)\)	6043.o	3021	yes	\(1\)	\(1\)	\(e\left(\frac{10}{159}\right)\)	\(e\left(\frac{955}{1007}\right)\)	\(e\left(\frac{20}{159}\right)\)	\(e\left(\frac{865}{3021}\right)\)	\(e\left(\frac{34}{3021}\right)\)	\(e\left(\frac{383}{3021}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{903}{1007}\right)\)	\(e\left(\frac{1055}{3021}\right)\)	\(e\left(\frac{14}{57}\right)\)
\(\chi_{6043}(11,\cdot)\)	6043.j	114	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{33}{38}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{47}{114}\right)\)	\(e\left(\frac{40}{57}\right)\)	\(e\left(\frac{73}{114}\right)\)	\(-1\)	\(e\left(\frac{14}{19}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{113}{114}\right)\)
\(\chi_{6043}(12,\cdot)\)	6043.p	6042	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{318}\right)\)	\(e\left(\frac{1193}{2014}\right)\)	\(e\left(\frac{5}{159}\right)\)	\(e\left(\frac{353}{6042}\right)\)	\(e\left(\frac{1837}{3021}\right)\)	\(e\left(\frac{1225}{6042}\right)\)	\(e\left(\frac{5}{106}\right)\)	\(e\left(\frac{186}{1007}\right)\)	\(e\left(\frac{224}{3021}\right)\)	\(e\left(\frac{61}{114}\right)\)
\(\chi_{6043}(13,\cdot)\)	6043.p	6042	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{318}\right)\)	\(e\left(\frac{79}{2014}\right)\)	\(e\left(\frac{101}{159}\right)\)	\(e\left(\frac{4205}{6042}\right)\)	\(e\left(\frac{1078}{3021}\right)\)	\(e\left(\frac{5983}{6042}\right)\)	\(e\left(\frac{101}{106}\right)\)	\(e\left(\frac{79}{1007}\right)\)	\(e\left(\frac{41}{3021}\right)\)	\(e\left(\frac{73}{114}\right)\)
\(\chi_{6043}(14,\cdot)\)	6043.m	1007	yes	\(1\)	\(1\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{638}{1007}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{400}{1007}\right)\)	\(e\left(\frac{429}{1007}\right)\)	\(e\left(\frac{538}{1007}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{269}{1007}\right)\)	\(e\left(\frac{191}{1007}\right)\)	\(e\left(\frac{9}{19}\right)\)
\(\chi_{6043}(15,\cdot)\)	6043.o	3021	yes	\(1\)	\(1\)	\(e\left(\frac{119}{159}\right)\)	\(e\left(\frac{155}{1007}\right)\)	\(e\left(\frac{79}{159}\right)\)	\(e\left(\frac{1469}{3021}\right)\)	\(e\left(\frac{2726}{3021}\right)\)	\(e\left(\frac{853}{3021}\right)\)	\(e\left(\frac{13}{53}\right)\)	\(e\left(\frac{310}{1007}\right)\)	\(e\left(\frac{709}{3021}\right)\)	\(e\left(\frac{16}{57}\right)\)
\(\chi_{6043}(16,\cdot)\)	6043.k	159	yes	\(1\)	\(1\)	\(e\left(\frac{17}{159}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{34}{159}\right)\)	\(e\left(\frac{23}{159}\right)\)	\(e\left(\frac{152}{159}\right)\)	\(e\left(\frac{10}{159}\right)\)	\(e\left(\frac{17}{53}\right)\)	\(e\left(\frac{37}{53}\right)\)	\(e\left(\frac{40}{159}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{6043}(17,\cdot)\)	6043.o	3021	yes	\(1\)	\(1\)	\(e\left(\frac{49}{159}\right)\)	\(e\left(\frac{837}{1007}\right)\)	\(e\left(\frac{98}{159}\right)\)	\(e\left(\frac{2092}{3021}\right)\)	\(e\left(\frac{421}{3021}\right)\)	\(e\left(\frac{1988}{3021}\right)\)	\(e\left(\frac{49}{53}\right)\)	\(e\left(\frac{667}{1007}\right)\)	\(e\left(\frac{2}{3021}\right)\)	\(e\left(\frac{56}{57}\right)\)
\(\chi_{6043}(18,\cdot)\)	6043.p	6042	yes	\(-1\)	\(1\)	\(e\left(\frac{223}{318}\right)\)	\(e\left(\frac{1607}{2014}\right)\)	\(e\left(\frac{64}{159}\right)\)	\(e\left(\frac{1561}{6042}\right)\)	\(e\left(\frac{1508}{3021}\right)\)	\(e\left(\frac{2165}{6042}\right)\)	\(e\left(\frac{11}{106}\right)\)	\(e\left(\frac{600}{1007}\right)\)	\(e\left(\frac{2899}{3021}\right)\)	\(e\left(\frac{65}{114}\right)\)
\(\chi_{6043}(19,\cdot)\)	6043.p	6042	yes	\(-1\)	\(1\)	\(e\left(\frac{305}{318}\right)\)	\(e\left(\frac{905}{2014}\right)\)	\(e\left(\frac{146}{159}\right)\)	\(e\left(\frac{4679}{6042}\right)\)	\(e\left(\frac{1234}{3021}\right)\)	\(e\left(\frac{3811}{6042}\right)\)	\(e\left(\frac{93}{106}\right)\)	\(e\left(\frac{905}{1007}\right)\)	\(e\left(\frac{2216}{3021}\right)\)	\(e\left(\frac{7}{114}\right)\)
\(\chi_{6043}(20,\cdot)\)	6043.n	2014	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{106}\right)\)	\(e\left(\frac{827}{2014}\right)\)	\(e\left(\frac{36}{53}\right)\)	\(e\left(\frac{1153}{2014}\right)\)	\(e\left(\frac{252}{1007}\right)\)	\(e\left(\frac{287}{2014}\right)\)	\(e\left(\frac{55}{106}\right)\)	\(e\left(\frac{827}{1007}\right)\)	\(e\left(\frac{415}{1007}\right)\)	\(e\left(\frac{3}{38}\right)\)
\(\chi_{6043}(21,\cdot)\)	6043.o	3021	yes	\(1\)	\(1\)	\(e\left(\frac{76}{159}\right)\)	\(e\left(\frac{845}{1007}\right)\)	\(e\left(\frac{152}{159}\right)\)	\(e\left(\frac{1804}{3021}\right)\)	\(e\left(\frac{958}{3021}\right)\)	\(e\left(\frac{2084}{3021}\right)\)	\(e\left(\frac{23}{53}\right)\)	\(e\left(\frac{683}{1007}\right)\)	\(e\left(\frac{227}{3021}\right)\)	\(e\left(\frac{29}{57}\right)\)
\(\chi_{6043}(22,\cdot)\)	6043.o	3021	yes	\(1\)	\(1\)	\(e\left(\frac{97}{159}\right)\)	\(e\left(\frac{333}{1007}\right)\)	\(e\left(\frac{35}{159}\right)\)	\(e\left(\frac{2110}{3021}\right)\)	\(e\left(\frac{2842}{3021}\right)\)	\(e\left(\frac{1982}{3021}\right)\)	\(e\left(\frac{44}{53}\right)\)	\(e\left(\frac{666}{1007}\right)\)	\(e\left(\frac{932}{3021}\right)\)	\(e\left(\frac{47}{57}\right)\)
\(\chi_{6043}(23,\cdot)\)	6043.m	1007	yes	\(1\)	\(1\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{561}{1007}\right)\)	\(e\left(\frac{30}{53}\right)\)	\(e\left(\frac{317}{1007}\right)\)	\(e\left(\frac{846}{1007}\right)\)	\(e\left(\frac{230}{1007}\right)\)	\(e\left(\frac{45}{53}\right)\)	\(e\left(\frac{115}{1007}\right)\)	\(e\left(\frac{602}{1007}\right)\)	\(e\left(\frac{3}{19}\right)\)
\(\chi_{6043}(24,\cdot)\)	6043.m	1007	yes	\(1\)	\(1\)	\(e\left(\frac{42}{53}\right)\)	\(e\left(\frac{55}{1007}\right)\)	\(e\left(\frac{31}{53}\right)\)	\(e\left(\frac{347}{1007}\right)\)	\(e\left(\frac{853}{1007}\right)\)	\(e\left(\frac{220}{1007}\right)\)	\(e\left(\frac{20}{53}\right)\)	\(e\left(\frac{110}{1007}\right)\)	\(e\left(\frac{138}{1007}\right)\)	\(e\left(\frac{7}{19}\right)\)
\(\chi_{6043}(25,\cdot)\)	6043.o	3021	yes	\(1\)	\(1\)	\(e\left(\frac{91}{159}\right)\)	\(e\left(\frac{979}{1007}\right)\)	\(e\left(\frac{23}{159}\right)\)	\(e\left(\frac{1}{3021}\right)\)	\(e\left(\frac{1645}{3021}\right)\)	\(e\left(\frac{671}{3021}\right)\)	\(e\left(\frac{38}{53}\right)\)	\(e\left(\frac{951}{1007}\right)\)	\(e\left(\frac{1730}{3021}\right)\)	\(e\left(\frac{47}{57}\right)\)
\(\chi_{6043}(26,\cdot)\)	6043.m	1007	yes	\(1\)	\(1\)	\(e\left(\frac{5}{53}\right)\)	\(e\left(\frac{505}{1007}\right)\)	\(e\left(\frac{10}{53}\right)\)	\(e\left(\frac{989}{1007}\right)\)	\(e\left(\frac{600}{1007}\right)\)	\(e\left(\frac{6}{1007}\right)\)	\(e\left(\frac{15}{53}\right)\)	\(e\left(\frac{3}{1007}\right)\)	\(e\left(\frac{77}{1007}\right)\)	\(e\left(\frac{9}{19}\right)\)
\(\chi_{6043}(27,\cdot)\)	6043.n	2014	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{106}\right)\)	\(e\left(\frac{7}{2014}\right)\)	\(e\left(\frac{41}{53}\right)\)	\(e\left(\frac{923}{2014}\right)\)	\(e\left(\frac{393}{1007}\right)\)	\(e\left(\frac{1035}{2014}\right)\)	\(e\left(\frac{17}{106}\right)\)	\(e\left(\frac{7}{1007}\right)\)	\(e\left(\frac{851}{1007}\right)\)	\(e\left(\frac{23}{38}\right)\)
\(\chi_{6043}(28,\cdot)\)	6043.p	6042	yes	\(-1\)	\(1\)	\(e\left(\frac{181}{318}\right)\)	\(e\left(\frac{193}{2014}\right)\)	\(e\left(\frac{22}{159}\right)\)	\(e\left(\frac{4129}{6042}\right)\)	\(e\left(\frac{2009}{3021}\right)\)	\(e\left(\frac{3323}{6042}\right)\)	\(e\left(\frac{75}{106}\right)\)	\(e\left(\frac{193}{1007}\right)\)	\(e\left(\frac{763}{3021}\right)\)	\(e\left(\frac{35}{114}\right)\)
\(\chi_{6043}(29,\cdot)\)	6043.p	6042	yes	\(-1\)	\(1\)	\(e\left(\frac{289}{318}\right)\)	\(e\left(\frac{967}{2014}\right)\)	\(e\left(\frac{130}{159}\right)\)	\(e\left(\frac{433}{6042}\right)\)	\(e\left(\frac{1175}{3021}\right)\)	\(e\left(\frac{527}{6042}\right)\)	\(e\left(\frac{77}{106}\right)\)	\(e\left(\frac{967}{1007}\right)\)	\(e\left(\frac{2962}{3021}\right)\)	\(e\left(\frac{59}{114}\right)\)
\(\chi_{6043}(30,\cdot)\)	6043.p	6042	yes	\(-1\)	\(1\)	\(e\left(\frac{167}{318}\right)\)	\(e\left(\frac{1241}{2014}\right)\)	\(e\left(\frac{8}{159}\right)\)	\(e\left(\frac{4667}{6042}\right)\)	\(e\left(\frac{427}{3021}\right)\)	\(e\left(\frac{1801}{6042}\right)\)	\(e\left(\frac{61}{106}\right)\)	\(e\left(\frac{234}{1007}\right)\)	\(e\left(\frac{899}{3021}\right)\)	\(e\left(\frac{13}{114}\right)\)
\(\chi_{6043}(31,\cdot)\)	6043.o	3021	yes	\(1\)	\(1\)	\(e\left(\frac{113}{159}\right)\)	\(e\left(\frac{271}{1007}\right)\)	\(e\left(\frac{67}{159}\right)\)	\(e\left(\frac{314}{3021}\right)\)	\(e\left(\frac{2960}{3021}\right)\)	\(e\left(\frac{2245}{3021}\right)\)	\(e\left(\frac{7}{53}\right)\)	\(e\left(\frac{542}{1007}\right)\)	\(e\left(\frac{2461}{3021}\right)\)	\(e\left(\frac{52}{57}\right)\)
\(\chi_{6043}(32,\cdot)\)	6043.l	318	yes	\(-1\)	\(1\)	\(e\left(\frac{281}{318}\right)\)	\(e\left(\frac{33}{106}\right)\)	\(e\left(\frac{122}{159}\right)\)	\(e\left(\frac{137}{318}\right)\)	\(e\left(\frac{31}{159}\right)\)	\(e\left(\frac{25}{318}\right)\)	\(e\left(\frac{69}{106}\right)\)	\(e\left(\frac{33}{53}\right)\)	\(e\left(\frac{50}{159}\right)\)	\(e\left(\frac{1}{6}\right)\)

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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.