LMFDB - Group of Dirichlet characters of modulus 531

Show commands: PariGP / SageMath

sage: H = DirichletGroup(531)

pari: g = idealstar(,531,2)

Character group

sage: G.order() pari: g.no
Order	=	348
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{174}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{531}(119,\cdot)$, $\chi_{531}(415,\cdot)$

First 32 of 348 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{531}(1,\cdot)$	531.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{531}(2,\cdot)$	531.p	174	yes	$1$	$1$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{163}{174}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{19}{174}\right)$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{64}{87}\right)$
$\chi_{531}(4,\cdot)$	531.m	87	yes	$1$	$1$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{41}{87}\right)$
$\chi_{531}(5,\cdot)$	531.n	174	yes	$-1$	$1$	$e\left(\frac{163}{174}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{137}{174}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{73}{174}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{23}{174}\right)$	$e\left(\frac{65}{87}\right)$
$\chi_{531}(7,\cdot)$	531.m	87	yes	$1$	$1$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{79}{87}\right)$
$\chi_{531}(8,\cdot)$	531.j	58	no	$1$	$1$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{3}{29}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{6}{29}\right)$
$\chi_{531}(10,\cdot)$	531.k	58	no	$-1$	$1$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{21}{29}\right)$	$e\left(\frac{5}{29}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{14}{29}\right)$
$\chi_{531}(11,\cdot)$	531.p	174	yes	$1$	$1$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{73}{174}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{127}{174}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{34}{87}\right)$
$\chi_{531}(13,\cdot)$	531.o	174	yes	$-1$	$1$	$e\left(\frac{19}{174}\right)$	$e\left(\frac{19}{87}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{127}{174}\right)$	$e\left(\frac{101}{174}\right)$	$e\left(\frac{71}{174}\right)$	$e\left(\frac{38}{87}\right)$
$\chi_{531}(14,\cdot)$	531.p	174	yes	$1$	$1$	$e\left(\frac{14}{87}\right)$	$e\left(\frac{28}{87}\right)$	$e\left(\frac{23}{174}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{71}{174}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{56}{87}\right)$
$\chi_{531}(16,\cdot)$	531.m	87	yes	$1$	$1$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{82}{87}\right)$
$\chi_{531}(17,\cdot)$	531.l	58	no	$-1$	$1$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{22}{29}\right)$
$\chi_{531}(19,\cdot)$	531.i	29	no	$1$	$1$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{23}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{18}{29}\right)$
$\chi_{531}(20,\cdot)$	531.n	174	yes	$-1$	$1$	$e\left(\frac{53}{174}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{115}{174}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{107}{174}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{79}{174}\right)$	$e\left(\frac{19}{87}\right)$
$\chi_{531}(22,\cdot)$	531.m	87	yes	$1$	$1$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{35}{87}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{11}{87}\right)$
$\chi_{531}(23,\cdot)$	531.p	174	yes	$1$	$1$	$e\left(\frac{8}{87}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{125}{174}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{47}{58}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{53}{174}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{32}{87}\right)$
$\chi_{531}(25,\cdot)$	531.m	87	yes	$1$	$1$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{43}{87}\right)$
$\chi_{531}(26,\cdot)$	531.l	58	no	$-1$	$1$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{17}{29}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{5}{29}\right)$
$\chi_{531}(28,\cdot)$	531.i	29	no	$1$	$1$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{1}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{11}{29}\right)$
$\chi_{531}(29,\cdot)$	531.n	174	yes	$-1$	$1$	$e\left(\frac{113}{174}\right)$	$e\left(\frac{26}{87}\right)$	$e\left(\frac{127}{174}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{41}{174}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{1}{174}\right)$	$e\left(\frac{52}{87}\right)$
$\chi_{531}(31,\cdot)$	531.o	174	yes	$-1$	$1$	$e\left(\frac{31}{174}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{64}{87}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{31}{58}\right)$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{79}{174}\right)$	$e\left(\frac{119}{174}\right)$	$e\left(\frac{125}{174}\right)$	$e\left(\frac{62}{87}\right)$
$\chi_{531}(32,\cdot)$	531.p	174	yes	$1$	$1$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{119}{174}\right)$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{22}{29}\right)$	$e\left(\frac{35}{58}\right)$	$e\left(\frac{86}{87}\right)$	$e\left(\frac{95}{174}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{59}{87}\right)$
$\chi_{531}(34,\cdot)$	531.o	174	yes	$-1$	$1$	$e\left(\frac{65}{174}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{7}{58}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{59}{174}\right)$	$e\left(\frac{25}{174}\right)$	$e\left(\frac{133}{174}\right)$	$e\left(\frac{43}{87}\right)$
$\chi_{531}(35,\cdot)$	531.l	58	no	$-1$	$1$	$e\left(\frac{53}{58}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{13}{29}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{21}{58}\right)$	$e\left(\frac{19}{29}\right)$
$\chi_{531}(37,\cdot)$	531.k	58	no	$-1$	$1$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{49}{58}\right)$	$e\left(\frac{37}{58}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{39}{58}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{23}{29}\right)$
$\chi_{531}(38,\cdot)$	531.p	174	yes	$1$	$1$	$e\left(\frac{73}{87}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{151}{174}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{103}{174}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{31}{87}\right)$
$\chi_{531}(40,\cdot)$	531.o	174	yes	$-1$	$1$	$e\left(\frac{85}{174}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{52}{87}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{27}{58}\right)$	$e\left(\frac{5}{58}\right)$	$e\left(\frac{37}{174}\right)$	$e\left(\frac{113}{174}\right)$	$e\left(\frac{107}{174}\right)$	$e\left(\frac{83}{87}\right)$
$\chi_{531}(41,\cdot)$	531.n	174	yes	$-1$	$1$	$e\left(\frac{13}{174}\right)$	$e\left(\frac{13}{87}\right)$	$e\left(\frac{107}{174}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{13}{58}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{151}{174}\right)$	$e\left(\frac{46}{87}\right)$	$e\left(\frac{131}{174}\right)$	$e\left(\frac{26}{87}\right)$
$\chi_{531}(43,\cdot)$	531.o	174	yes	$-1$	$1$	$e\left(\frac{41}{174}\right)$	$e\left(\frac{41}{87}\right)$	$e\left(\frac{65}{87}\right)$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{41}{58}\right)$	$e\left(\frac{57}{58}\right)$	$e\left(\frac{155}{174}\right)$	$e\left(\frac{163}{174}\right)$	$e\left(\frac{25}{174}\right)$	$e\left(\frac{82}{87}\right)$
$\chi_{531}(44,\cdot)$	531.j	58	no	$1$	$1$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{17}{58}\right)$	$e\left(\frac{11}{29}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{4}{29}\right)$	$e\left(\frac{55}{58}\right)$	$e\left(\frac{10}{29}\right)$	$e\left(\frac{25}{29}\right)$
$\chi_{531}(46,\cdot)$	531.i	29	no	$1$	$1$	$e\left(\frac{8}{29}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{28}{29}\right)$	$e\left(\frac{24}{29}\right)$	$e\left(\frac{27}{29}\right)$	$e\left(\frac{26}{29}\right)$	$e\left(\frac{12}{29}\right)$	$e\left(\frac{7}{29}\right)$	$e\left(\frac{3}{29}\right)$
$\chi_{531}(47,\cdot)$	531.p	174	yes	$1$	$1$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{37}{174}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{20}{29}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{7}{87}\right)$	$e\left(\frac{31}{174}\right)$	$e\left(\frac{32}{87}\right)$	$e\left(\frac{22}{87}\right)$

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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	$531$
Structure	\(C_{2}\times C_{174}\)
Order	$348$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{531}(1,\cdot)\)	531.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{531}(2,\cdot)\)	531.p	174	yes	\(1\)	\(1\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{163}{174}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{19}{174}\right)\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{64}{87}\right)\)
\(\chi_{531}(4,\cdot)\)	531.m	87	yes	\(1\)	\(1\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{41}{87}\right)\)
\(\chi_{531}(5,\cdot)\)	531.n	174	yes	\(-1\)	\(1\)	\(e\left(\frac{163}{174}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{137}{174}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{73}{174}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{23}{174}\right)\)	\(e\left(\frac{65}{87}\right)\)
\(\chi_{531}(7,\cdot)\)	531.m	87	yes	\(1\)	\(1\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{79}{87}\right)\)
\(\chi_{531}(8,\cdot)\)	531.j	58	no	\(1\)	\(1\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)
\(\chi_{531}(10,\cdot)\)	531.k	58	no	\(-1\)	\(1\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{21}{29}\right)\)	\(e\left(\frac{5}{29}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{14}{29}\right)\)
\(\chi_{531}(11,\cdot)\)	531.p	174	yes	\(1\)	\(1\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{73}{174}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{127}{174}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{34}{87}\right)\)
\(\chi_{531}(13,\cdot)\)	531.o	174	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{174}\right)\)	\(e\left(\frac{19}{87}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{127}{174}\right)\)	\(e\left(\frac{101}{174}\right)\)	\(e\left(\frac{71}{174}\right)\)	\(e\left(\frac{38}{87}\right)\)
\(\chi_{531}(14,\cdot)\)	531.p	174	yes	\(1\)	\(1\)	\(e\left(\frac{14}{87}\right)\)	\(e\left(\frac{28}{87}\right)\)	\(e\left(\frac{23}{174}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{71}{174}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)
\(\chi_{531}(16,\cdot)\)	531.m	87	yes	\(1\)	\(1\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{82}{87}\right)\)
\(\chi_{531}(17,\cdot)\)	531.l	58	no	\(-1\)	\(1\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{22}{29}\right)\)
\(\chi_{531}(19,\cdot)\)	531.i	29	no	\(1\)	\(1\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{23}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{18}{29}\right)\)
\(\chi_{531}(20,\cdot)\)	531.n	174	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{174}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{115}{174}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{107}{174}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{79}{174}\right)\)	\(e\left(\frac{19}{87}\right)\)
\(\chi_{531}(22,\cdot)\)	531.m	87	yes	\(1\)	\(1\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{35}{87}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{11}{87}\right)\)
\(\chi_{531}(23,\cdot)\)	531.p	174	yes	\(1\)	\(1\)	\(e\left(\frac{8}{87}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{125}{174}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{47}{58}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{53}{174}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{32}{87}\right)\)
\(\chi_{531}(25,\cdot)\)	531.m	87	yes	\(1\)	\(1\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{43}{87}\right)\)
\(\chi_{531}(26,\cdot)\)	531.l	58	no	\(-1\)	\(1\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{17}{29}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{5}{29}\right)\)
\(\chi_{531}(28,\cdot)\)	531.i	29	no	\(1\)	\(1\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{1}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{11}{29}\right)\)
\(\chi_{531}(29,\cdot)\)	531.n	174	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{174}\right)\)	\(e\left(\frac{26}{87}\right)\)	\(e\left(\frac{127}{174}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{41}{174}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{1}{174}\right)\)	\(e\left(\frac{52}{87}\right)\)
\(\chi_{531}(31,\cdot)\)	531.o	174	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{174}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{64}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{31}{58}\right)\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{79}{174}\right)\)	\(e\left(\frac{119}{174}\right)\)	\(e\left(\frac{125}{174}\right)\)	\(e\left(\frac{62}{87}\right)\)
\(\chi_{531}(32,\cdot)\)	531.p	174	yes	\(1\)	\(1\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{119}{174}\right)\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{22}{29}\right)\)	\(e\left(\frac{35}{58}\right)\)	\(e\left(\frac{86}{87}\right)\)	\(e\left(\frac{95}{174}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{59}{87}\right)\)
\(\chi_{531}(34,\cdot)\)	531.o	174	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{174}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{7}{58}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{59}{174}\right)\)	\(e\left(\frac{25}{174}\right)\)	\(e\left(\frac{133}{174}\right)\)	\(e\left(\frac{43}{87}\right)\)
\(\chi_{531}(35,\cdot)\)	531.l	58	no	\(-1\)	\(1\)	\(e\left(\frac{53}{58}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{13}{29}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{21}{58}\right)\)	\(e\left(\frac{19}{29}\right)\)
\(\chi_{531}(37,\cdot)\)	531.k	58	no	\(-1\)	\(1\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{49}{58}\right)\)	\(e\left(\frac{37}{58}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{39}{58}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{23}{29}\right)\)
\(\chi_{531}(38,\cdot)\)	531.p	174	yes	\(1\)	\(1\)	\(e\left(\frac{73}{87}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{151}{174}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{103}{174}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{31}{87}\right)\)
\(\chi_{531}(40,\cdot)\)	531.o	174	yes	\(-1\)	\(1\)	\(e\left(\frac{85}{174}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{52}{87}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{27}{58}\right)\)	\(e\left(\frac{5}{58}\right)\)	\(e\left(\frac{37}{174}\right)\)	\(e\left(\frac{113}{174}\right)\)	\(e\left(\frac{107}{174}\right)\)	\(e\left(\frac{83}{87}\right)\)
\(\chi_{531}(41,\cdot)\)	531.n	174	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{174}\right)\)	\(e\left(\frac{13}{87}\right)\)	\(e\left(\frac{107}{174}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{13}{58}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{151}{174}\right)\)	\(e\left(\frac{46}{87}\right)\)	\(e\left(\frac{131}{174}\right)\)	\(e\left(\frac{26}{87}\right)\)
\(\chi_{531}(43,\cdot)\)	531.o	174	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{174}\right)\)	\(e\left(\frac{41}{87}\right)\)	\(e\left(\frac{65}{87}\right)\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{41}{58}\right)\)	\(e\left(\frac{57}{58}\right)\)	\(e\left(\frac{155}{174}\right)\)	\(e\left(\frac{163}{174}\right)\)	\(e\left(\frac{25}{174}\right)\)	\(e\left(\frac{82}{87}\right)\)
\(\chi_{531}(44,\cdot)\)	531.j	58	no	\(1\)	\(1\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{17}{58}\right)\)	\(e\left(\frac{11}{29}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{4}{29}\right)\)	\(e\left(\frac{55}{58}\right)\)	\(e\left(\frac{10}{29}\right)\)	\(e\left(\frac{25}{29}\right)\)
\(\chi_{531}(46,\cdot)\)	531.i	29	no	\(1\)	\(1\)	\(e\left(\frac{8}{29}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{28}{29}\right)\)	\(e\left(\frac{24}{29}\right)\)	\(e\left(\frac{27}{29}\right)\)	\(e\left(\frac{26}{29}\right)\)	\(e\left(\frac{12}{29}\right)\)	\(e\left(\frac{7}{29}\right)\)	\(e\left(\frac{3}{29}\right)\)
\(\chi_{531}(47,\cdot)\)	531.p	174	yes	\(1\)	\(1\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{37}{174}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{7}{87}\right)\)	\(e\left(\frac{31}{174}\right)\)	\(e\left(\frac{32}{87}\right)\)	\(e\left(\frac{22}{87}\right)\)

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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.