LMFDB - Group of Dirichlet characters of modulus 1137

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1137)

pari: g = idealstar(,1137,2)

Character group

sage: G.order() pari: g.no
Order	=	756
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{378}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1137}(380,\cdot)$, $\chi_{1137}(760,\cdot)$

First 32 of 756 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{1137}(1,\cdot)$	1137.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1137}(2,\cdot)$	1137.be	378	yes	$1$	$1$	$e\left(\frac{95}{189}\right)$	$e\left(\frac{1}{189}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{155}{378}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{145}{378}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{313}{378}\right)$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{2}{189}\right)$
$\chi_{1137}(4,\cdot)$	1137.bc	189	no	$1$	$1$	$e\left(\frac{1}{189}\right)$	$e\left(\frac{2}{189}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{155}{189}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{145}{189}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{124}{189}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{4}{189}\right)$
$\chi_{1137}(5,\cdot)$	1137.t	42	yes	$-1$	$1$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{1137}(7,\cdot)$	1137.bf	378	no	$-1$	$1$	$e\left(\frac{155}{378}\right)$	$e\left(\frac{155}{189}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{211}{378}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{173}{378}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{131}{378}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{121}{189}\right)$
$\chi_{1137}(8,\cdot)$	1137.bb	126	yes	$1$	$1$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{2}{63}\right)$
$\chi_{1137}(10,\cdot)$	1137.bf	378	no	$-1$	$1$	$e\left(\frac{145}{378}\right)$	$e\left(\frac{145}{189}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{173}{378}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{235}{378}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{25}{378}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{101}{189}\right)$
$\chi_{1137}(11,\cdot)$	1137.x	54	yes	$1$	$1$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{8}{27}\right)$
$\chi_{1137}(13,\cdot)$	1137.bf	378	no	$-1$	$1$	$e\left(\frac{313}{378}\right)$	$e\left(\frac{124}{189}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{131}{378}\right)$	$e\left(\frac{61}{126}\right)$	$e\left(\frac{25}{378}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{67}{378}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{59}{189}\right)$
$\chi_{1137}(14,\cdot)$	1137.ba	126	yes	$-1$	$1$	$e\left(\frac{115}{126}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{41}{63}\right)$
$\chi_{1137}(16,\cdot)$	1137.bc	189	no	$1$	$1$	$e\left(\frac{2}{189}\right)$	$e\left(\frac{4}{189}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{121}{189}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{101}{189}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{59}{189}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{8}{189}\right)$
$\chi_{1137}(17,\cdot)$	1137.be	378	yes	$1$	$1$	$e\left(\frac{152}{189}\right)$	$e\left(\frac{115}{189}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{59}{378}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{43}{378}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{85}{378}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{41}{189}\right)$
$\chi_{1137}(19,\cdot)$	1137.bc	189	no	$1$	$1$	$e\left(\frac{116}{189}\right)$	$e\left(\frac{43}{189}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{25}{189}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{188}{189}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{20}{189}\right)$	$e\left(\frac{47}{63}\right)$	$e\left(\frac{86}{189}\right)$
$\chi_{1137}(20,\cdot)$	1137.bd	378	yes	$-1$	$1$	$e\left(\frac{335}{378}\right)$	$e\left(\frac{146}{189}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{164}{189}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{1}{189}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{169}{189}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{103}{189}\right)$
$\chi_{1137}(22,\cdot)$	1137.bc	189	no	$1$	$1$	$e\left(\frac{109}{189}\right)$	$e\left(\frac{29}{189}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{74}{189}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{118}{189}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{97}{189}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{58}{189}\right)$
$\chi_{1137}(23,\cdot)$	1137.ba	126	yes	$-1$	$1$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{16}{63}\right)$
$\chi_{1137}(25,\cdot)$	1137.q	21	no	$1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{1137}(26,\cdot)$	1137.bd	378	yes	$-1$	$1$	$e\left(\frac{125}{378}\right)$	$e\left(\frac{125}{189}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{143}{189}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{85}{189}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{1}{189}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{61}{189}\right)$
$\chi_{1137}(28,\cdot)$	1137.bf	378	no	$-1$	$1$	$e\left(\frac{157}{378}\right)$	$e\left(\frac{157}{189}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{143}{378}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{85}{378}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{1}{378}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{125}{189}\right)$
$\chi_{1137}(29,\cdot)$	1137.bb	126	yes	$1$	$1$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{44}{63}\right)$
$\chi_{1137}(31,\cdot)$	1137.bf	378	no	$-1$	$1$	$e\left(\frac{205}{378}\right)$	$e\left(\frac{16}{189}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{23}{378}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{241}{378}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{283}{378}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{32}{189}\right)$
$\chi_{1137}(32,\cdot)$	1137.be	378	yes	$1$	$1$	$e\left(\frac{97}{189}\right)$	$e\left(\frac{5}{189}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{19}{378}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{347}{378}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{53}{378}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{10}{189}\right)$
$\chi_{1137}(34,\cdot)$	1137.bc	189	no	$1$	$1$	$e\left(\frac{58}{189}\right)$	$e\left(\frac{116}{189}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{107}{189}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{94}{189}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{10}{189}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{43}{189}\right)$
$\chi_{1137}(35,\cdot)$	1137.be	378	yes	$1$	$1$	$e\left(\frac{55}{189}\right)$	$e\left(\frac{110}{189}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{229}{378}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{263}{378}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{221}{378}\right)$	$e\left(\frac{113}{126}\right)$	$e\left(\frac{31}{189}\right)$
$\chi_{1137}(37,\cdot)$	1137.y	63	no	$1$	$1$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{23}{63}\right)$
$\chi_{1137}(38,\cdot)$	1137.be	378	yes	$1$	$1$	$e\left(\frac{22}{189}\right)$	$e\left(\frac{44}{189}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{205}{378}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{143}{378}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{353}{378}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{88}{189}\right)$
$\chi_{1137}(40,\cdot)$	1137.p	18	no	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{9}\right)$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1137}(41,\cdot)$	1137.ba	126	yes	$-1$	$1$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{40}{63}\right)$
$\chi_{1137}(43,\cdot)$	1137.bf	378	no	$-1$	$1$	$e\left(\frac{107}{378}\right)$	$e\left(\frac{107}{189}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{331}{378}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{17}{378}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{227}{378}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{25}{189}\right)$
$\chi_{1137}(44,\cdot)$	1137.bb	126	yes	$1$	$1$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{126}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{20}{63}\right)$
$\chi_{1137}(46,\cdot)$	1137.bf	378	no	$-1$	$1$	$e\left(\frac{25}{378}\right)$	$e\left(\frac{25}{189}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{95}{378}\right)$	$e\left(\frac{25}{126}\right)$	$e\left(\frac{223}{378}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{265}{378}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{50}{189}\right)$
$\chi_{1137}(47,\cdot)$	1137.be	378	yes	$1$	$1$	$e\left(\frac{67}{189}\right)$	$e\left(\frac{134}{189}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{169}{378}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{341}{378}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{173}{378}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{79}{189}\right)$

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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	$1137$
Structure	\(C_{2}\times C_{378}\)
Order	$756$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{1137}(1,\cdot)\)	1137.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1137}(2,\cdot)\)	1137.be	378	yes	\(1\)	\(1\)	\(e\left(\frac{95}{189}\right)\)	\(e\left(\frac{1}{189}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{155}{378}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{145}{378}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{313}{378}\right)\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{2}{189}\right)\)
\(\chi_{1137}(4,\cdot)\)	1137.bc	189	no	\(1\)	\(1\)	\(e\left(\frac{1}{189}\right)\)	\(e\left(\frac{2}{189}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{155}{189}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{145}{189}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{124}{189}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{4}{189}\right)\)
\(\chi_{1137}(5,\cdot)\)	1137.t	42	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{1137}(7,\cdot)\)	1137.bf	378	no	\(-1\)	\(1\)	\(e\left(\frac{155}{378}\right)\)	\(e\left(\frac{155}{189}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{211}{378}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{173}{378}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{131}{378}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{121}{189}\right)\)
\(\chi_{1137}(8,\cdot)\)	1137.bb	126	yes	\(1\)	\(1\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{2}{63}\right)\)
\(\chi_{1137}(10,\cdot)\)	1137.bf	378	no	\(-1\)	\(1\)	\(e\left(\frac{145}{378}\right)\)	\(e\left(\frac{145}{189}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{173}{378}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{235}{378}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{25}{378}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{101}{189}\right)\)
\(\chi_{1137}(11,\cdot)\)	1137.x	54	yes	\(1\)	\(1\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{8}{27}\right)\)
\(\chi_{1137}(13,\cdot)\)	1137.bf	378	no	\(-1\)	\(1\)	\(e\left(\frac{313}{378}\right)\)	\(e\left(\frac{124}{189}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{131}{378}\right)\)	\(e\left(\frac{61}{126}\right)\)	\(e\left(\frac{25}{378}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{67}{378}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{59}{189}\right)\)
\(\chi_{1137}(14,\cdot)\)	1137.ba	126	yes	\(-1\)	\(1\)	\(e\left(\frac{115}{126}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{41}{63}\right)\)
\(\chi_{1137}(16,\cdot)\)	1137.bc	189	no	\(1\)	\(1\)	\(e\left(\frac{2}{189}\right)\)	\(e\left(\frac{4}{189}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{121}{189}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{101}{189}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{59}{189}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{8}{189}\right)\)
\(\chi_{1137}(17,\cdot)\)	1137.be	378	yes	\(1\)	\(1\)	\(e\left(\frac{152}{189}\right)\)	\(e\left(\frac{115}{189}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{59}{378}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{43}{378}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{85}{378}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{41}{189}\right)\)
\(\chi_{1137}(19,\cdot)\)	1137.bc	189	no	\(1\)	\(1\)	\(e\left(\frac{116}{189}\right)\)	\(e\left(\frac{43}{189}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{25}{189}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{188}{189}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{20}{189}\right)\)	\(e\left(\frac{47}{63}\right)\)	\(e\left(\frac{86}{189}\right)\)
\(\chi_{1137}(20,\cdot)\)	1137.bd	378	yes	\(-1\)	\(1\)	\(e\left(\frac{335}{378}\right)\)	\(e\left(\frac{146}{189}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{164}{189}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{1}{189}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{169}{189}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{103}{189}\right)\)
\(\chi_{1137}(22,\cdot)\)	1137.bc	189	no	\(1\)	\(1\)	\(e\left(\frac{109}{189}\right)\)	\(e\left(\frac{29}{189}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{74}{189}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{118}{189}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{97}{189}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{58}{189}\right)\)
\(\chi_{1137}(23,\cdot)\)	1137.ba	126	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{16}{63}\right)\)
\(\chi_{1137}(25,\cdot)\)	1137.q	21	no	\(1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{1137}(26,\cdot)\)	1137.bd	378	yes	\(-1\)	\(1\)	\(e\left(\frac{125}{378}\right)\)	\(e\left(\frac{125}{189}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{143}{189}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{85}{189}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{1}{189}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{61}{189}\right)\)
\(\chi_{1137}(28,\cdot)\)	1137.bf	378	no	\(-1\)	\(1\)	\(e\left(\frac{157}{378}\right)\)	\(e\left(\frac{157}{189}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{143}{378}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{85}{378}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{1}{378}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{125}{189}\right)\)
\(\chi_{1137}(29,\cdot)\)	1137.bb	126	yes	\(1\)	\(1\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{44}{63}\right)\)
\(\chi_{1137}(31,\cdot)\)	1137.bf	378	no	\(-1\)	\(1\)	\(e\left(\frac{205}{378}\right)\)	\(e\left(\frac{16}{189}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{23}{378}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{241}{378}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{283}{378}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{32}{189}\right)\)
\(\chi_{1137}(32,\cdot)\)	1137.be	378	yes	\(1\)	\(1\)	\(e\left(\frac{97}{189}\right)\)	\(e\left(\frac{5}{189}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{19}{378}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{347}{378}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{53}{378}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{10}{189}\right)\)
\(\chi_{1137}(34,\cdot)\)	1137.bc	189	no	\(1\)	\(1\)	\(e\left(\frac{58}{189}\right)\)	\(e\left(\frac{116}{189}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{107}{189}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{94}{189}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{10}{189}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{43}{189}\right)\)
\(\chi_{1137}(35,\cdot)\)	1137.be	378	yes	\(1\)	\(1\)	\(e\left(\frac{55}{189}\right)\)	\(e\left(\frac{110}{189}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{229}{378}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{263}{378}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{221}{378}\right)\)	\(e\left(\frac{113}{126}\right)\)	\(e\left(\frac{31}{189}\right)\)
\(\chi_{1137}(37,\cdot)\)	1137.y	63	no	\(1\)	\(1\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{23}{63}\right)\)
\(\chi_{1137}(38,\cdot)\)	1137.be	378	yes	\(1\)	\(1\)	\(e\left(\frac{22}{189}\right)\)	\(e\left(\frac{44}{189}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{205}{378}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{143}{378}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{353}{378}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{88}{189}\right)\)
\(\chi_{1137}(40,\cdot)\)	1137.p	18	no	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1137}(41,\cdot)\)	1137.ba	126	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{40}{63}\right)\)
\(\chi_{1137}(43,\cdot)\)	1137.bf	378	no	\(-1\)	\(1\)	\(e\left(\frac{107}{378}\right)\)	\(e\left(\frac{107}{189}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{331}{378}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{17}{378}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{227}{378}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{25}{189}\right)\)
\(\chi_{1137}(44,\cdot)\)	1137.bb	126	yes	\(1\)	\(1\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{126}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{20}{63}\right)\)
\(\chi_{1137}(46,\cdot)\)	1137.bf	378	no	\(-1\)	\(1\)	\(e\left(\frac{25}{378}\right)\)	\(e\left(\frac{25}{189}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{95}{378}\right)\)	\(e\left(\frac{25}{126}\right)\)	\(e\left(\frac{223}{378}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{265}{378}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{50}{189}\right)\)
\(\chi_{1137}(47,\cdot)\)	1137.be	378	yes	\(1\)	\(1\)	\(e\left(\frac{67}{189}\right)\)	\(e\left(\frac{134}{189}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{169}{378}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{341}{378}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{173}{378}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{79}{189}\right)\)

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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.