LMFDB - Group of Dirichlet characters of modulus 1037

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1037)

pari: g = idealstar(,1037,2)

Character group

sage: G.order() pari: g.no
Order	=	960
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4}\times C_{240}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1037}(428,\cdot)$, $\chi_{1037}(307,\cdot)$

First 32 of 960 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1037}(1,\cdot)$	1037.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1037}(2,\cdot)$	1037.cp	120	yes	$-1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1037}(3,\cdot)$	1037.cl	80	yes	$-1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{1037}(4,\cdot)$	1037.ch	60	yes	$1$	$1$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{60}\right)$	$-i$
$\chi_{1037}(5,\cdot)$	1037.cq	240	yes	$-1$	$1$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{151}{240}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{1037}(6,\cdot)$	1037.cr	240	yes	$1$	$1$	$e\left(\frac{29}{120}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{61}{240}\right)$	$e\left(\frac{211}{240}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{119}{240}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{1037}(7,\cdot)$	1037.cs	240	yes	$1$	$1$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{97}{240}\right)$	$e\left(\frac{7}{240}\right)$	$e\left(\frac{139}{240}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{1037}(8,\cdot)$	1037.bu	40	yes	$-1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{1037}(9,\cdot)$	1037.bv	40	yes	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1037}(10,\cdot)$	1037.cr	240	yes	$1$	$1$	$e\left(\frac{1}{120}\right)$	$e\left(\frac{39}{80}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{119}{240}\right)$	$e\left(\frac{203}{240}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{91}{240}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{1037}(11,\cdot)$	1037.bf	16	yes	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$-i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1037}(12,\cdot)$	1037.ct	240	yes	$-1$	$1$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{1}{60}\right)$	$e\left(\frac{239}{240}\right)$	$e\left(\frac{29}{240}\right)$	$e\left(\frac{113}{240}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{1037}(13,\cdot)$	1037.bb	12	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$-1$	$-1$	$e\left(\frac{1}{12}\right)$	$-i$
$\chi_{1037}(14,\cdot)$	1037.cb	48	yes	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{1037}(15,\cdot)$	1037.co	120	yes	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{17}{120}\right)$	$e\left(\frac{107}{120}\right)$	$e\left(\frac{119}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1037}(16,\cdot)$	1037.bt	30	yes	$1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{30}\right)$	$-1$
$\chi_{1037}(18,\cdot)$	1037.cg	60	no	$-1$	$1$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{59}{60}\right)$	$i$
$\chi_{1037}(19,\cdot)$	1037.cn	120	yes	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{19}{120}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{71}{120}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1037}(20,\cdot)$	1037.ci	80	yes	$-1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{1037}(21,\cdot)$	1037.y	12	yes	$-1$	$1$	$e\left(\frac{5}{12}\right)$	$i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$-1$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{1037}(22,\cdot)$	1037.ct	240	yes	$-1$	$1$	$e\left(\frac{77}{120}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{103}{240}\right)$	$e\left(\frac{133}{240}\right)$	$e\left(\frac{121}{240}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{17}{240}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{1037}(23,\cdot)$	1037.cj	80	yes	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1037}(24,\cdot)$	1037.cj	80	yes	$1$	$1$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{59}{80}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{1037}(25,\cdot)$	1037.co	120	yes	$1$	$1$	$e\left(\frac{29}{60}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{31}{120}\right)$	$e\left(\frac{61}{120}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{89}{120}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1037}(26,\cdot)$	1037.cm	120	yes	$-1$	$1$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{79}{120}\right)$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{120}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{1037}(27,\cdot)$	1037.cl	80	yes	$-1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1037}(28,\cdot)$	1037.ck	80	yes	$1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{41}{80}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1037}(29,\cdot)$	1037.ca	48	yes	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{1037}(30,\cdot)$	1037.cf	60	yes	$-1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{15}\right)$	$1$
$\chi_{1037}(31,\cdot)$	1037.cs	240	yes	$1$	$1$	$e\left(\frac{103}{120}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{107}{240}\right)$	$e\left(\frac{77}{240}\right)$	$e\left(\frac{89}{240}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{73}{240}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{1037}(32,\cdot)$	1037.bn	24	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{24}\right)$	$1$	$-i$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1037}(33,\cdot)$	1037.bi	20	yes	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$-i$

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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	$1037$
Structure	\(C_{4}\times C_{240}\)
Order	$960$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1037}(1,\cdot)\)	1037.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1037}(2,\cdot)\)	1037.cp	120	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1037}(3,\cdot)\)	1037.cl	80	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1037}(4,\cdot)\)	1037.ch	60	yes	\(1\)	\(1\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(-i\)
\(\chi_{1037}(5,\cdot)\)	1037.cq	240	yes	\(-1\)	\(1\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{151}{240}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{1037}(6,\cdot)\)	1037.cr	240	yes	\(1\)	\(1\)	\(e\left(\frac{29}{120}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{61}{240}\right)\)	\(e\left(\frac{211}{240}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{119}{240}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{1037}(7,\cdot)\)	1037.cs	240	yes	\(1\)	\(1\)	\(e\left(\frac{53}{120}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{97}{240}\right)\)	\(e\left(\frac{7}{240}\right)\)	\(e\left(\frac{139}{240}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{1037}(8,\cdot)\)	1037.bu	40	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{1037}(9,\cdot)\)	1037.bv	40	yes	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1037}(10,\cdot)\)	1037.cr	240	yes	\(1\)	\(1\)	\(e\left(\frac{1}{120}\right)\)	\(e\left(\frac{39}{80}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{119}{240}\right)\)	\(e\left(\frac{203}{240}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{91}{240}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{1037}(11,\cdot)\)	1037.bf	16	yes	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1037}(12,\cdot)\)	1037.ct	240	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{1}{60}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{29}{240}\right)\)	\(e\left(\frac{113}{240}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{1037}(13,\cdot)\)	1037.bb	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)
\(\chi_{1037}(14,\cdot)\)	1037.cb	48	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{1037}(15,\cdot)\)	1037.co	120	yes	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{17}{120}\right)\)	\(e\left(\frac{107}{120}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1037}(16,\cdot)\)	1037.bt	30	yes	\(1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(-1\)
\(\chi_{1037}(18,\cdot)\)	1037.cg	60	no	\(-1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(i\)
\(\chi_{1037}(19,\cdot)\)	1037.cn	120	yes	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{109}{120}\right)\)	\(e\left(\frac{19}{120}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1037}(20,\cdot)\)	1037.ci	80	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{1037}(21,\cdot)\)	1037.y	12	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{1037}(22,\cdot)\)	1037.ct	240	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{120}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{103}{240}\right)\)	\(e\left(\frac{133}{240}\right)\)	\(e\left(\frac{121}{240}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{17}{240}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{1037}(23,\cdot)\)	1037.cj	80	yes	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1037}(24,\cdot)\)	1037.cj	80	yes	\(1\)	\(1\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{1037}(25,\cdot)\)	1037.co	120	yes	\(1\)	\(1\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{31}{120}\right)\)	\(e\left(\frac{61}{120}\right)\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1037}(26,\cdot)\)	1037.cm	120	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{120}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{1037}(27,\cdot)\)	1037.cl	80	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1037}(28,\cdot)\)	1037.ck	80	yes	\(1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{41}{80}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1037}(29,\cdot)\)	1037.ca	48	yes	\(1\)	\(1\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{1037}(30,\cdot)\)	1037.cf	60	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(1\)
\(\chi_{1037}(31,\cdot)\)	1037.cs	240	yes	\(1\)	\(1\)	\(e\left(\frac{103}{120}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{107}{240}\right)\)	\(e\left(\frac{77}{240}\right)\)	\(e\left(\frac{89}{240}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{73}{240}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{1037}(32,\cdot)\)	1037.bn	24	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1037}(33,\cdot)\)	1037.bi	20	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(-i\)

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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.