LMFDB - Group of Dirichlet characters of modulus 8037

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8037)

pari: g = idealstar(,8037,2)

Character group

sage: G.order() pari: g.no
Order	=	4968
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{6}\times C_{414}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8037}(4466,\cdot)$, $\chi_{8037}(1693,\cdot)$, $\chi_{8037}(7525,\cdot)$

First 32 of 4968 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{8037}(1,\cdot)$	8037.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8037}(2,\cdot)$	8037.ei	414	yes	$1$	$1$	$e\left(\frac{55}{207}\right)$	$e\left(\frac{110}{207}\right)$	$e\left(\frac{47}{414}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{157}{414}\right)$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{379}{414}\right)$	$e\left(\frac{163}{207}\right)$	$e\left(\frac{13}{207}\right)$
$\chi_{8037}(4,\cdot)$	8037.ea	207	yes	$1$	$1$	$e\left(\frac{110}{207}\right)$	$e\left(\frac{13}{207}\right)$	$e\left(\frac{47}{207}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{157}{207}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{172}{207}\right)$	$e\left(\frac{119}{207}\right)$	$e\left(\frac{26}{207}\right)$
$\chi_{8037}(5,\cdot)$	8037.ek	414	yes	$1$	$1$	$e\left(\frac{47}{414}\right)$	$e\left(\frac{47}{207}\right)$	$e\left(\frac{85}{207}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{217}{414}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{145}{414}\right)$	$e\left(\frac{197}{414}\right)$	$e\left(\frac{94}{207}\right)$
$\chi_{8037}(7,\cdot)$	8037.cu	69	yes	$1$	$1$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{2}{23}\right)$
$\chi_{8037}(8,\cdot)$	8037.do	138	no	$1$	$1$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{41}{69}\right)$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{19}{138}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{103}{138}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{13}{69}\right)$
$\chi_{8037}(10,\cdot)$	8037.en	414	no	$1$	$1$	$e\left(\frac{157}{414}\right)$	$e\left(\frac{157}{207}\right)$	$e\left(\frac{217}{414}\right)$	$e\left(\frac{61}{69}\right)$	$e\left(\frac{19}{138}\right)$	$e\left(\frac{187}{207}\right)$	$e\left(\frac{31}{138}\right)$	$e\left(\frac{55}{207}\right)$	$e\left(\frac{109}{414}\right)$	$e\left(\frac{107}{207}\right)$
$\chi_{8037}(11,\cdot)$	8037.db	138	yes	$1$	$1$	$e\left(\frac{79}{138}\right)$	$e\left(\frac{10}{69}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{37}{69}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{31}{138}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{20}{69}\right)$
$\chi_{8037}(13,\cdot)$	8037.ee	414	yes	$1$	$1$	$e\left(\frac{379}{414}\right)$	$e\left(\frac{172}{207}\right)$	$e\left(\frac{145}{414}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{103}{138}\right)$	$e\left(\frac{55}{207}\right)$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{142}{207}\right)$	$e\left(\frac{235}{414}\right)$	$e\left(\frac{137}{207}\right)$
$\chi_{8037}(14,\cdot)$	8037.ex	414	yes	$1$	$1$	$e\left(\frac{163}{207}\right)$	$e\left(\frac{119}{207}\right)$	$e\left(\frac{197}{414}\right)$	$e\left(\frac{31}{69}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{109}{414}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{235}{414}\right)$	$e\left(\frac{49}{207}\right)$	$e\left(\frac{31}{207}\right)$
$\chi_{8037}(16,\cdot)$	8037.ea	207	yes	$1$	$1$	$e\left(\frac{13}{207}\right)$	$e\left(\frac{26}{207}\right)$	$e\left(\frac{94}{207}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{107}{207}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{137}{207}\right)$	$e\left(\frac{31}{207}\right)$	$e\left(\frac{52}{207}\right)$
$\chi_{8037}(17,\cdot)$	8037.em	414	no	$-1$	$1$	$e\left(\frac{131}{414}\right)$	$e\left(\frac{131}{207}\right)$	$e\left(\frac{305}{414}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{131}{138}\right)$	$e\left(\frac{11}{207}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{125}{207}\right)$	$e\left(\frac{323}{414}\right)$	$e\left(\frac{55}{207}\right)$
$\chi_{8037}(20,\cdot)$	8037.dk	138	no	$1$	$1$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{55}{69}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{7}{138}\right)$	$e\left(\frac{40}{69}\right)$
$\chi_{8037}(22,\cdot)$	8037.er	414	yes	$1$	$1$	$e\left(\frac{347}{414}\right)$	$e\left(\frac{140}{207}\right)$	$e\left(\frac{317}{414}\right)$	$e\left(\frac{4}{69}\right)$	$e\left(\frac{71}{138}\right)$	$e\left(\frac{125}{207}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{53}{207}\right)$	$e\left(\frac{371}{414}\right)$	$e\left(\frac{73}{207}\right)$
$\chi_{8037}(23,\cdot)$	8037.ef	414	yes	$1$	$1$	$e\left(\frac{373}{414}\right)$	$e\left(\frac{166}{207}\right)$	$e\left(\frac{11}{207}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{97}{138}\right)$	$e\left(\frac{395}{414}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{173}{414}\right)$	$e\left(\frac{157}{414}\right)$	$e\left(\frac{125}{207}\right)$
$\chi_{8037}(25,\cdot)$	8037.eb	207	yes	$1$	$1$	$e\left(\frac{47}{207}\right)$	$e\left(\frac{94}{207}\right)$	$e\left(\frac{170}{207}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{10}{207}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{145}{207}\right)$	$e\left(\frac{197}{207}\right)$	$e\left(\frac{188}{207}\right)$
$\chi_{8037}(26,\cdot)$	8037.dh	138	no	$1$	$1$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{25}{69}\right)$	$e\left(\frac{32}{69}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{89}{138}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{83}{138}\right)$	$e\left(\frac{49}{138}\right)$	$e\left(\frac{50}{69}\right)$
$\chi_{8037}(28,\cdot)$	8037.ec	207	no	$1$	$1$	$e\left(\frac{11}{207}\right)$	$e\left(\frac{22}{207}\right)$	$e\left(\frac{122}{207}\right)$	$e\left(\frac{67}{69}\right)$	$e\left(\frac{11}{69}\right)$	$e\left(\frac{133}{207}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{100}{207}\right)$	$e\left(\frac{5}{207}\right)$	$e\left(\frac{44}{207}\right)$
$\chi_{8037}(29,\cdot)$	8037.es	414	yes	$-1$	$1$	$e\left(\frac{167}{207}\right)$	$e\left(\frac{127}{207}\right)$	$e\left(\frac{146}{207}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{106}{207}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{88}{207}\right)$	$e\left(\frac{101}{207}\right)$	$e\left(\frac{47}{207}\right)$
$\chi_{8037}(31,\cdot)$	8037.dm	138	yes	$1$	$1$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{47}{69}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{29}{69}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{28}{69}\right)$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{38}{69}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{25}{69}\right)$
$\chi_{8037}(32,\cdot)$	8037.ei	414	yes	$1$	$1$	$e\left(\frac{68}{207}\right)$	$e\left(\frac{136}{207}\right)$	$e\left(\frac{235}{414}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{371}{414}\right)$	$e\left(\frac{119}{138}\right)$	$e\left(\frac{239}{414}\right)$	$e\left(\frac{194}{207}\right)$	$e\left(\frac{65}{207}\right)$
$\chi_{8037}(34,\cdot)$	8037.el	414	yes	$-1$	$1$	$e\left(\frac{241}{414}\right)$	$e\left(\frac{34}{207}\right)$	$e\left(\frac{176}{207}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{103}{138}\right)$	$e\left(\frac{179}{414}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{215}{414}\right)$	$e\left(\frac{235}{414}\right)$	$e\left(\frac{68}{207}\right)$
$\chi_{8037}(35,\cdot)$	8037.eo	414	no	$1$	$1$	$e\left(\frac{263}{414}\right)$	$e\left(\frac{56}{207}\right)$	$e\left(\frac{160}{207}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{125}{138}\right)$	$e\left(\frac{169}{414}\right)$	$e\left(\frac{13}{69}\right)$	$e\left(\frac{1}{414}\right)$	$e\left(\frac{383}{414}\right)$	$e\left(\frac{112}{207}\right)$
$\chi_{8037}(37,\cdot)$	8037.cq	46	no	$-1$	$1$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{17}{23}\right)$
$\chi_{8037}(40,\cdot)$	8037.er	414	yes	$1$	$1$	$e\left(\frac{377}{414}\right)$	$e\left(\frac{170}{207}\right)$	$e\left(\frac{311}{414}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{101}{138}\right)$	$e\left(\frac{137}{207}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{20}{207}\right)$	$e\left(\frac{347}{414}\right)$	$e\left(\frac{133}{207}\right)$
$\chi_{8037}(41,\cdot)$	8037.es	414	yes	$-1$	$1$	$e\left(\frac{88}{207}\right)$	$e\left(\frac{176}{207}\right)$	$e\left(\frac{10}{207}\right)$	$e\left(\frac{7}{69}\right)$	$e\left(\frac{19}{69}\right)$	$e\left(\frac{98}{207}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{179}{207}\right)$	$e\left(\frac{109}{207}\right)$	$e\left(\frac{145}{207}\right)$
$\chi_{8037}(43,\cdot)$	8037.eh	414	yes	$-1$	$1$	$e\left(\frac{133}{207}\right)$	$e\left(\frac{59}{207}\right)$	$e\left(\frac{347}{414}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{199}{414}\right)$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{367}{414}\right)$	$e\left(\frac{142}{207}\right)$	$e\left(\frac{118}{207}\right)$
$\chi_{8037}(44,\cdot)$	8037.eo	414	no	$1$	$1$	$e\left(\frac{43}{414}\right)$	$e\left(\frac{43}{207}\right)$	$e\left(\frac{182}{207}\right)$	$e\left(\frac{40}{69}\right)$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{407}{414}\right)$	$e\left(\frac{26}{69}\right)$	$e\left(\frac{71}{414}\right)$	$e\left(\frac{283}{414}\right)$	$e\left(\frac{86}{207}\right)$
$\chi_{8037}(46,\cdot)$	8037.bh	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{8037}(49,\cdot)$	8037.cu	69	yes	$1$	$1$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{50}{69}\right)$	$e\left(\frac{59}{69}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{53}{69}\right)$	$e\left(\frac{5}{69}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{62}{69}\right)$	$e\left(\frac{4}{23}\right)$
$\chi_{8037}(50,\cdot)$	8037.du	138	yes	$1$	$1$	$e\left(\frac{34}{69}\right)$	$e\left(\frac{68}{69}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{17}{69}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{59}{138}\right)$	$e\left(\frac{121}{138}\right)$	$e\left(\frac{85}{138}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{67}{69}\right)$
$\chi_{8037}(52,\cdot)$	8037.ee	414	yes	$1$	$1$	$e\left(\frac{185}{414}\right)$	$e\left(\frac{185}{207}\right)$	$e\left(\frac{239}{414}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{47}{138}\right)$	$e\left(\frac{5}{207}\right)$	$e\left(\frac{67}{138}\right)$	$e\left(\frac{107}{207}\right)$	$e\left(\frac{59}{414}\right)$	$e\left(\frac{163}{207}\right)$

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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	$8037$
Structure	\(C_{2}\times C_{6}\times C_{414}\)
Order	$4968$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{8037}(1,\cdot)\)	8037.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8037}(2,\cdot)\)	8037.ei	414	yes	\(1\)	\(1\)	\(e\left(\frac{55}{207}\right)\)	\(e\left(\frac{110}{207}\right)\)	\(e\left(\frac{47}{414}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{157}{414}\right)\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{379}{414}\right)\)	\(e\left(\frac{163}{207}\right)\)	\(e\left(\frac{13}{207}\right)\)
\(\chi_{8037}(4,\cdot)\)	8037.ea	207	yes	\(1\)	\(1\)	\(e\left(\frac{110}{207}\right)\)	\(e\left(\frac{13}{207}\right)\)	\(e\left(\frac{47}{207}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{157}{207}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{172}{207}\right)\)	\(e\left(\frac{119}{207}\right)\)	\(e\left(\frac{26}{207}\right)\)
\(\chi_{8037}(5,\cdot)\)	8037.ek	414	yes	\(1\)	\(1\)	\(e\left(\frac{47}{414}\right)\)	\(e\left(\frac{47}{207}\right)\)	\(e\left(\frac{85}{207}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{217}{414}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{145}{414}\right)\)	\(e\left(\frac{197}{414}\right)\)	\(e\left(\frac{94}{207}\right)\)
\(\chi_{8037}(7,\cdot)\)	8037.cu	69	yes	\(1\)	\(1\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{2}{23}\right)\)
\(\chi_{8037}(8,\cdot)\)	8037.do	138	no	\(1\)	\(1\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{41}{69}\right)\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{19}{138}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{103}{138}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{13}{69}\right)\)
\(\chi_{8037}(10,\cdot)\)	8037.en	414	no	\(1\)	\(1\)	\(e\left(\frac{157}{414}\right)\)	\(e\left(\frac{157}{207}\right)\)	\(e\left(\frac{217}{414}\right)\)	\(e\left(\frac{61}{69}\right)\)	\(e\left(\frac{19}{138}\right)\)	\(e\left(\frac{187}{207}\right)\)	\(e\left(\frac{31}{138}\right)\)	\(e\left(\frac{55}{207}\right)\)	\(e\left(\frac{109}{414}\right)\)	\(e\left(\frac{107}{207}\right)\)
\(\chi_{8037}(11,\cdot)\)	8037.db	138	yes	\(1\)	\(1\)	\(e\left(\frac{79}{138}\right)\)	\(e\left(\frac{10}{69}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{37}{69}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{31}{138}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{20}{69}\right)\)
\(\chi_{8037}(13,\cdot)\)	8037.ee	414	yes	\(1\)	\(1\)	\(e\left(\frac{379}{414}\right)\)	\(e\left(\frac{172}{207}\right)\)	\(e\left(\frac{145}{414}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{103}{138}\right)\)	\(e\left(\frac{55}{207}\right)\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{142}{207}\right)\)	\(e\left(\frac{235}{414}\right)\)	\(e\left(\frac{137}{207}\right)\)
\(\chi_{8037}(14,\cdot)\)	8037.ex	414	yes	\(1\)	\(1\)	\(e\left(\frac{163}{207}\right)\)	\(e\left(\frac{119}{207}\right)\)	\(e\left(\frac{197}{414}\right)\)	\(e\left(\frac{31}{69}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{109}{414}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{235}{414}\right)\)	\(e\left(\frac{49}{207}\right)\)	\(e\left(\frac{31}{207}\right)\)
\(\chi_{8037}(16,\cdot)\)	8037.ea	207	yes	\(1\)	\(1\)	\(e\left(\frac{13}{207}\right)\)	\(e\left(\frac{26}{207}\right)\)	\(e\left(\frac{94}{207}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{107}{207}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{137}{207}\right)\)	\(e\left(\frac{31}{207}\right)\)	\(e\left(\frac{52}{207}\right)\)
\(\chi_{8037}(17,\cdot)\)	8037.em	414	no	\(-1\)	\(1\)	\(e\left(\frac{131}{414}\right)\)	\(e\left(\frac{131}{207}\right)\)	\(e\left(\frac{305}{414}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{131}{138}\right)\)	\(e\left(\frac{11}{207}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{125}{207}\right)\)	\(e\left(\frac{323}{414}\right)\)	\(e\left(\frac{55}{207}\right)\)
\(\chi_{8037}(20,\cdot)\)	8037.dk	138	no	\(1\)	\(1\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{55}{69}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{7}{138}\right)\)	\(e\left(\frac{40}{69}\right)\)
\(\chi_{8037}(22,\cdot)\)	8037.er	414	yes	\(1\)	\(1\)	\(e\left(\frac{347}{414}\right)\)	\(e\left(\frac{140}{207}\right)\)	\(e\left(\frac{317}{414}\right)\)	\(e\left(\frac{4}{69}\right)\)	\(e\left(\frac{71}{138}\right)\)	\(e\left(\frac{125}{207}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{53}{207}\right)\)	\(e\left(\frac{371}{414}\right)\)	\(e\left(\frac{73}{207}\right)\)
\(\chi_{8037}(23,\cdot)\)	8037.ef	414	yes	\(1\)	\(1\)	\(e\left(\frac{373}{414}\right)\)	\(e\left(\frac{166}{207}\right)\)	\(e\left(\frac{11}{207}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{97}{138}\right)\)	\(e\left(\frac{395}{414}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{173}{414}\right)\)	\(e\left(\frac{157}{414}\right)\)	\(e\left(\frac{125}{207}\right)\)
\(\chi_{8037}(25,\cdot)\)	8037.eb	207	yes	\(1\)	\(1\)	\(e\left(\frac{47}{207}\right)\)	\(e\left(\frac{94}{207}\right)\)	\(e\left(\frac{170}{207}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{10}{207}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{145}{207}\right)\)	\(e\left(\frac{197}{207}\right)\)	\(e\left(\frac{188}{207}\right)\)
\(\chi_{8037}(26,\cdot)\)	8037.dh	138	no	\(1\)	\(1\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{25}{69}\right)\)	\(e\left(\frac{32}{69}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{89}{138}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{83}{138}\right)\)	\(e\left(\frac{49}{138}\right)\)	\(e\left(\frac{50}{69}\right)\)
\(\chi_{8037}(28,\cdot)\)	8037.ec	207	no	\(1\)	\(1\)	\(e\left(\frac{11}{207}\right)\)	\(e\left(\frac{22}{207}\right)\)	\(e\left(\frac{122}{207}\right)\)	\(e\left(\frac{67}{69}\right)\)	\(e\left(\frac{11}{69}\right)\)	\(e\left(\frac{133}{207}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{100}{207}\right)\)	\(e\left(\frac{5}{207}\right)\)	\(e\left(\frac{44}{207}\right)\)
\(\chi_{8037}(29,\cdot)\)	8037.es	414	yes	\(-1\)	\(1\)	\(e\left(\frac{167}{207}\right)\)	\(e\left(\frac{127}{207}\right)\)	\(e\left(\frac{146}{207}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{106}{207}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{88}{207}\right)\)	\(e\left(\frac{101}{207}\right)\)	\(e\left(\frac{47}{207}\right)\)
\(\chi_{8037}(31,\cdot)\)	8037.dm	138	yes	\(1\)	\(1\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{47}{69}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{29}{69}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{28}{69}\right)\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{38}{69}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{25}{69}\right)\)
\(\chi_{8037}(32,\cdot)\)	8037.ei	414	yes	\(1\)	\(1\)	\(e\left(\frac{68}{207}\right)\)	\(e\left(\frac{136}{207}\right)\)	\(e\left(\frac{235}{414}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{371}{414}\right)\)	\(e\left(\frac{119}{138}\right)\)	\(e\left(\frac{239}{414}\right)\)	\(e\left(\frac{194}{207}\right)\)	\(e\left(\frac{65}{207}\right)\)
\(\chi_{8037}(34,\cdot)\)	8037.el	414	yes	\(-1\)	\(1\)	\(e\left(\frac{241}{414}\right)\)	\(e\left(\frac{34}{207}\right)\)	\(e\left(\frac{176}{207}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{103}{138}\right)\)	\(e\left(\frac{179}{414}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{215}{414}\right)\)	\(e\left(\frac{235}{414}\right)\)	\(e\left(\frac{68}{207}\right)\)
\(\chi_{8037}(35,\cdot)\)	8037.eo	414	no	\(1\)	\(1\)	\(e\left(\frac{263}{414}\right)\)	\(e\left(\frac{56}{207}\right)\)	\(e\left(\frac{160}{207}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{125}{138}\right)\)	\(e\left(\frac{169}{414}\right)\)	\(e\left(\frac{13}{69}\right)\)	\(e\left(\frac{1}{414}\right)\)	\(e\left(\frac{383}{414}\right)\)	\(e\left(\frac{112}{207}\right)\)
\(\chi_{8037}(37,\cdot)\)	8037.cq	46	no	\(-1\)	\(1\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{17}{23}\right)\)
\(\chi_{8037}(40,\cdot)\)	8037.er	414	yes	\(1\)	\(1\)	\(e\left(\frac{377}{414}\right)\)	\(e\left(\frac{170}{207}\right)\)	\(e\left(\frac{311}{414}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{101}{138}\right)\)	\(e\left(\frac{137}{207}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{20}{207}\right)\)	\(e\left(\frac{347}{414}\right)\)	\(e\left(\frac{133}{207}\right)\)
\(\chi_{8037}(41,\cdot)\)	8037.es	414	yes	\(-1\)	\(1\)	\(e\left(\frac{88}{207}\right)\)	\(e\left(\frac{176}{207}\right)\)	\(e\left(\frac{10}{207}\right)\)	\(e\left(\frac{7}{69}\right)\)	\(e\left(\frac{19}{69}\right)\)	\(e\left(\frac{98}{207}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{179}{207}\right)\)	\(e\left(\frac{109}{207}\right)\)	\(e\left(\frac{145}{207}\right)\)
\(\chi_{8037}(43,\cdot)\)	8037.eh	414	yes	\(-1\)	\(1\)	\(e\left(\frac{133}{207}\right)\)	\(e\left(\frac{59}{207}\right)\)	\(e\left(\frac{347}{414}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{199}{414}\right)\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{367}{414}\right)\)	\(e\left(\frac{142}{207}\right)\)	\(e\left(\frac{118}{207}\right)\)
\(\chi_{8037}(44,\cdot)\)	8037.eo	414	no	\(1\)	\(1\)	\(e\left(\frac{43}{414}\right)\)	\(e\left(\frac{43}{207}\right)\)	\(e\left(\frac{182}{207}\right)\)	\(e\left(\frac{40}{69}\right)\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{407}{414}\right)\)	\(e\left(\frac{26}{69}\right)\)	\(e\left(\frac{71}{414}\right)\)	\(e\left(\frac{283}{414}\right)\)	\(e\left(\frac{86}{207}\right)\)
\(\chi_{8037}(46,\cdot)\)	8037.bh	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{8037}(49,\cdot)\)	8037.cu	69	yes	\(1\)	\(1\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{50}{69}\right)\)	\(e\left(\frac{59}{69}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{53}{69}\right)\)	\(e\left(\frac{5}{69}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{62}{69}\right)\)	\(e\left(\frac{4}{23}\right)\)
\(\chi_{8037}(50,\cdot)\)	8037.du	138	yes	\(1\)	\(1\)	\(e\left(\frac{34}{69}\right)\)	\(e\left(\frac{68}{69}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{17}{69}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{59}{138}\right)\)	\(e\left(\frac{121}{138}\right)\)	\(e\left(\frac{85}{138}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{67}{69}\right)\)
\(\chi_{8037}(52,\cdot)\)	8037.ee	414	yes	\(1\)	\(1\)	\(e\left(\frac{185}{414}\right)\)	\(e\left(\frac{185}{207}\right)\)	\(e\left(\frac{239}{414}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{47}{138}\right)\)	\(e\left(\frac{5}{207}\right)\)	\(e\left(\frac{67}{138}\right)\)	\(e\left(\frac{107}{207}\right)\)	\(e\left(\frac{59}{414}\right)\)	\(e\left(\frac{163}{207}\right)\)

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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.