LMFDB - Group of Dirichlet characters of modulus 137

Show commands: PariGP / SageMath

sage: H = DirichletGroup(137)

pari: g = idealstar(,137,2)

Character group

sage: G.order() pari: g.no
Order	=	136
sage: H.invariants() pari: g.cyc
Structure	=	$C_{136}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{137}(3,\cdot)$

First 32 of 136 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{137}(1,\cdot)$	137.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{137}(2,\cdot)$	137.g	68	yes	$1$	$1$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{5}{34}\right)$	$i$	$e\left(\frac{33}{34}\right)$
$\chi_{137}(3,\cdot)$	137.h	136	yes	$-1$	$1$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{1}{136}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{75}{136}\right)$	$e\left(\frac{11}{136}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{61}{68}\right)$
$\chi_{137}(4,\cdot)$	137.f	34	yes	$1$	$1$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{5}{17}\right)$	$-1$	$e\left(\frac{16}{17}\right)$
$\chi_{137}(5,\cdot)$	137.h	136	yes	$-1$	$1$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{75}{136}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{19}{68}\right)$
$\chi_{137}(6,\cdot)$	137.h	136	yes	$-1$	$1$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{11}{136}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{9}{136}\right)$	$e\left(\frac{121}{136}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{59}{68}\right)$
$\chi_{137}(7,\cdot)$	137.g	68	yes	$1$	$1$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{21}{34}\right)$	$i$	$e\left(\frac{23}{34}\right)$
$\chi_{137}(8,\cdot)$	137.g	68	yes	$1$	$1$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{15}{34}\right)$	$-i$	$e\left(\frac{31}{34}\right)$
$\chi_{137}(9,\cdot)$	137.g	68	yes	$1$	$1$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{1}{34}\right)$	$i$	$e\left(\frac{27}{34}\right)$
$\chi_{137}(10,\cdot)$	137.d	8	yes	$-1$	$1$	$i$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$-i$	$i$	$e\left(\frac{1}{8}\right)$	$i$
$\chi_{137}(11,\cdot)$	137.g	68	yes	$1$	$1$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{61}{68}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{59}{68}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{27}{34}\right)$	$i$	$e\left(\frac{15}{34}\right)$
$\chi_{137}(12,\cdot)$	137.h	136	yes	$-1$	$1$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{21}{136}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{79}{136}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{57}{68}\right)$
$\chi_{137}(13,\cdot)$	137.h	136	yes	$-1$	$1$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{107}{136}\right)$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{29}{68}\right)$
$\chi_{137}(14,\cdot)$	137.f	34	yes	$1$	$1$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{13}{17}\right)$	$-1$	$e\left(\frac{11}{17}\right)$
$\chi_{137}(15,\cdot)$	137.f	34	yes	$1$	$1$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{2}{17}\right)$	$-1$	$e\left(\frac{3}{17}\right)$
$\chi_{137}(16,\cdot)$	137.e	17	yes	$1$	$1$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{10}{17}\right)$	$1$	$e\left(\frac{15}{17}\right)$
$\chi_{137}(17,\cdot)$	137.g	68	yes	$1$	$1$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{19}{34}\right)$	$-i$	$e\left(\frac{3}{34}\right)$
$\chi_{137}(18,\cdot)$	137.f	34	yes	$1$	$1$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{3}{17}\right)$	$-1$	$e\left(\frac{13}{17}\right)$
$\chi_{137}(19,\cdot)$	137.g	68	yes	$1$	$1$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{23}{34}\right)$	$-i$	$e\left(\frac{9}{34}\right)$
$\chi_{137}(20,\cdot)$	137.h	136	yes	$-1$	$1$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{95}{136}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{53}{136}\right)$	$e\left(\frac{93}{136}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{27}{68}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{68}\right)$
$\chi_{137}(21,\cdot)$	137.h	136	yes	$-1$	$1$	$e\left(\frac{11}{68}\right)$	$e\left(\frac{43}{136}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{97}{136}\right)$	$e\left(\frac{65}{136}\right)$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{33}{68}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{39}{68}\right)$
$\chi_{137}(22,\cdot)$	137.f	34	yes	$1$	$1$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{16}{17}\right)$	$-1$	$e\left(\frac{7}{17}\right)$
$\chi_{137}(23,\cdot)$	137.h	136	yes	$-1$	$1$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{125}{136}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{127}{136}\right)$	$e\left(\frac{15}{136}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{68}\right)$
$\chi_{137}(24,\cdot)$	137.h	136	yes	$-1$	$1$	$e\left(\frac{19}{68}\right)$	$e\left(\frac{31}{136}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{13}{136}\right)$	$e\left(\frac{69}{136}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{55}{68}\right)$
$\chi_{137}(25,\cdot)$	137.g	68	yes	$1$	$1$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{9}{68}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{7}{34}\right)$	$-i$	$e\left(\frac{19}{34}\right)$
$\chi_{137}(26,\cdot)$	137.h	136	yes	$-1$	$1$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{41}{136}\right)$	$e\left(\frac{113}{136}\right)$	$e\left(\frac{55}{68}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{35}{68}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{27}{68}\right)$
$\chi_{137}(27,\cdot)$	137.h	136	yes	$-1$	$1$	$e\left(\frac{15}{68}\right)$	$e\left(\frac{3}{136}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{89}{136}\right)$	$e\left(\frac{33}{136}\right)$	$e\left(\frac{63}{68}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{47}{68}\right)$
$\chi_{137}(28,\cdot)$	137.g	68	yes	$1$	$1$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{13}{68}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{31}{34}\right)$	$-i$	$e\left(\frac{21}{34}\right)$
$\chi_{137}(29,\cdot)$	137.h	136	yes	$-1$	$1$	$e\left(\frac{47}{68}\right)$	$e\left(\frac{91}{136}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{25}{136}\right)$	$e\left(\frac{49}{136}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{23}{68}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{43}{68}\right)$
$\chi_{137}(30,\cdot)$	137.g	68	yes	$1$	$1$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{29}{68}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{9}{34}\right)$	$-i$	$e\left(\frac{5}{34}\right)$
$\chi_{137}(31,\cdot)$	137.h	136	yes	$-1$	$1$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{73}{136}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{35}{136}\right)$	$e\left(\frac{123}{136}\right)$	$e\left(\frac{37}{68}\right)$	$e\left(\frac{7}{68}\right)$	$e\left(\frac{5}{68}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{33}{68}\right)$
$\chi_{137}(32,\cdot)$	137.g	68	yes	$1$	$1$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{3}{68}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{1}{34}\right)$	$e\left(\frac{25}{34}\right)$	$i$	$e\left(\frac{29}{34}\right)$

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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	$137$
Structure	\(C_{136}\)
Order	$136$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{137}(1,\cdot)\)	137.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{137}(2,\cdot)\)	137.g	68	yes	\(1\)	\(1\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(i\)	\(e\left(\frac{33}{34}\right)\)
\(\chi_{137}(3,\cdot)\)	137.h	136	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{1}{136}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{75}{136}\right)\)	\(e\left(\frac{11}{136}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{61}{68}\right)\)
\(\chi_{137}(4,\cdot)\)	137.f	34	yes	\(1\)	\(1\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(-1\)	\(e\left(\frac{16}{17}\right)\)
\(\chi_{137}(5,\cdot)\)	137.h	136	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{75}{136}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{19}{68}\right)\)
\(\chi_{137}(6,\cdot)\)	137.h	136	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{11}{136}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{9}{136}\right)\)	\(e\left(\frac{121}{136}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{59}{68}\right)\)
\(\chi_{137}(7,\cdot)\)	137.g	68	yes	\(1\)	\(1\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(i\)	\(e\left(\frac{23}{34}\right)\)
\(\chi_{137}(8,\cdot)\)	137.g	68	yes	\(1\)	\(1\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(-i\)	\(e\left(\frac{31}{34}\right)\)
\(\chi_{137}(9,\cdot)\)	137.g	68	yes	\(1\)	\(1\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(i\)	\(e\left(\frac{27}{34}\right)\)
\(\chi_{137}(10,\cdot)\)	137.d	8	yes	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(-i\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(i\)
\(\chi_{137}(11,\cdot)\)	137.g	68	yes	\(1\)	\(1\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{61}{68}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{59}{68}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(i\)	\(e\left(\frac{15}{34}\right)\)
\(\chi_{137}(12,\cdot)\)	137.h	136	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{21}{136}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{79}{136}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{57}{68}\right)\)
\(\chi_{137}(13,\cdot)\)	137.h	136	yes	\(-1\)	\(1\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{107}{136}\right)\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{29}{68}\right)\)
\(\chi_{137}(14,\cdot)\)	137.f	34	yes	\(1\)	\(1\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(-1\)	\(e\left(\frac{11}{17}\right)\)
\(\chi_{137}(15,\cdot)\)	137.f	34	yes	\(1\)	\(1\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(-1\)	\(e\left(\frac{3}{17}\right)\)
\(\chi_{137}(16,\cdot)\)	137.e	17	yes	\(1\)	\(1\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(1\)	\(e\left(\frac{15}{17}\right)\)
\(\chi_{137}(17,\cdot)\)	137.g	68	yes	\(1\)	\(1\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(-i\)	\(e\left(\frac{3}{34}\right)\)
\(\chi_{137}(18,\cdot)\)	137.f	34	yes	\(1\)	\(1\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(-1\)	\(e\left(\frac{13}{17}\right)\)
\(\chi_{137}(19,\cdot)\)	137.g	68	yes	\(1\)	\(1\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(-i\)	\(e\left(\frac{9}{34}\right)\)
\(\chi_{137}(20,\cdot)\)	137.h	136	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{95}{136}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{53}{136}\right)\)	\(e\left(\frac{93}{136}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{27}{68}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{68}\right)\)
\(\chi_{137}(21,\cdot)\)	137.h	136	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{68}\right)\)	\(e\left(\frac{43}{136}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{97}{136}\right)\)	\(e\left(\frac{65}{136}\right)\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{33}{68}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{39}{68}\right)\)
\(\chi_{137}(22,\cdot)\)	137.f	34	yes	\(1\)	\(1\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(-1\)	\(e\left(\frac{7}{17}\right)\)
\(\chi_{137}(23,\cdot)\)	137.h	136	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{125}{136}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{127}{136}\right)\)	\(e\left(\frac{15}{136}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{68}\right)\)
\(\chi_{137}(24,\cdot)\)	137.h	136	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{68}\right)\)	\(e\left(\frac{31}{136}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{13}{136}\right)\)	\(e\left(\frac{69}{136}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{55}{68}\right)\)
\(\chi_{137}(25,\cdot)\)	137.g	68	yes	\(1\)	\(1\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{9}{68}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(-i\)	\(e\left(\frac{19}{34}\right)\)
\(\chi_{137}(26,\cdot)\)	137.h	136	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{41}{136}\right)\)	\(e\left(\frac{113}{136}\right)\)	\(e\left(\frac{55}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{35}{68}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{27}{68}\right)\)
\(\chi_{137}(27,\cdot)\)	137.h	136	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{68}\right)\)	\(e\left(\frac{3}{136}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{89}{136}\right)\)	\(e\left(\frac{33}{136}\right)\)	\(e\left(\frac{63}{68}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{47}{68}\right)\)
\(\chi_{137}(28,\cdot)\)	137.g	68	yes	\(1\)	\(1\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{13}{68}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(-i\)	\(e\left(\frac{21}{34}\right)\)
\(\chi_{137}(29,\cdot)\)	137.h	136	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{68}\right)\)	\(e\left(\frac{91}{136}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{25}{136}\right)\)	\(e\left(\frac{49}{136}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{23}{68}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{43}{68}\right)\)
\(\chi_{137}(30,\cdot)\)	137.g	68	yes	\(1\)	\(1\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{29}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(-i\)	\(e\left(\frac{5}{34}\right)\)
\(\chi_{137}(31,\cdot)\)	137.h	136	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{73}{136}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{35}{136}\right)\)	\(e\left(\frac{123}{136}\right)\)	\(e\left(\frac{37}{68}\right)\)	\(e\left(\frac{7}{68}\right)\)	\(e\left(\frac{5}{68}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{33}{68}\right)\)
\(\chi_{137}(32,\cdot)\)	137.g	68	yes	\(1\)	\(1\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{3}{68}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{1}{34}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(i\)	\(e\left(\frac{29}{34}\right)\)

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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.