LMFDB - Group of Dirichlet characters of modulus 931

sage:H = DirichletGroup(931)

pari:g = idealstar(,931,2)

Character group

sage:G.order() pari:g.no
Order	=	756
sage:H.invariants() pari:g.cyc
Structure	=	$C_{6}\times C_{126}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{931}(248,\cdot)$, $\chi_{931}(344,\cdot)$

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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{931}(1,\cdot)$	931.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{931}(2,\cdot)$	931.ce	126	yes	$-1$	$1$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$
$\chi_{931}(3,\cdot)$	931.ci	126	yes	$1$	$1$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{931}(4,\cdot)$	931.ca	63	yes	$1$	$1$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{931}(5,\cdot)$	931.cj	126	yes	$-1$	$1$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{931}(6,\cdot)$	931.cl	126	yes	$-1$	$1$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{31}{126}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{31}{42}\right)$
$\chi_{931}(8,\cdot)$	931.br	42	yes	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{14}\right)$
$\chi_{931}(9,\cdot)$	931.cb	63	yes	$1$	$1$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{52}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{931}(10,\cdot)$	931.cd	126	yes	$1$	$1$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{5}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{931}(11,\cdot)$	931.bk	21	yes	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{931}(12,\cdot)$	931.bz	42	yes	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{931}(13,\cdot)$	931.ch	126	yes	$1$	$1$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{13}{126}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{59}{63}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{931}(15,\cdot)$	931.cf	126	yes	$-1$	$1$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{83}{126}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{53}{63}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{85}{126}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{42}\right)$
$\chi_{931}(16,\cdot)$	931.ca	63	yes	$1$	$1$	$e\left(\frac{38}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{46}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{931}(17,\cdot)$	931.ck	126	yes	$-1$	$1$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{103}{126}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{107}{126}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{37}{42}\right)$
$\chi_{931}(18,\cdot)$	931.r	6	no	$-1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{931}(20,\cdot)$	931.y	14	no	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{931}(22,\cdot)$	931.cf	126	yes	$-1$	$1$	$e\left(\frac{73}{126}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{8}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{58}{63}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{42}\right)$
$\chi_{931}(23,\cdot)$	931.cb	63	yes	$1$	$1$	$e\left(\frac{40}{63}\right)$	$e\left(\frac{22}{63}\right)$	$e\left(\frac{17}{63}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{44}{63}\right)$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{931}(24,\cdot)$	931.ck	126	yes	$-1$	$1$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{55}{126}\right)$	$e\left(\frac{37}{63}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{29}{126}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{55}{63}\right)$	$e\left(\frac{71}{126}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{42}\right)$
$\chi_{931}(25,\cdot)$	931.ca	63	yes	$1$	$1$	$e\left(\frac{43}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{931}(26,\cdot)$	931.bo	42	yes	$-1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{19}{42}\right)$
$\chi_{931}(27,\cdot)$	931.bs	42	yes	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{931}(29,\cdot)$	931.cf	126	yes	$-1$	$1$	$e\left(\frac{11}{126}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{50}{63}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{79}{126}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{37}{42}\right)$
$\chi_{931}(30,\cdot)$	931.g	3	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{931}(31,\cdot)$	931.s	6	no	$1$	$1$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{931}(32,\cdot)$	931.ce	126	yes	$-1$	$1$	$e\left(\frac{95}{126}\right)$	$e\left(\frac{89}{126}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{13}{63}\right)$	$e\left(\frac{29}{63}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{26}{63}\right)$	$e\left(\frac{121}{126}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$
$\chi_{931}(33,\cdot)$	931.cd	126	yes	$1$	$1$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{2}{63}\right)$	$e\left(\frac{34}{63}\right)$	$e\left(\frac{67}{126}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{4}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{931}(34,\cdot)$	931.ch	126	yes	$1$	$1$	$e\left(\frac{23}{126}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{23}{63}\right)$	$e\left(\frac{125}{126}\right)$	$e\left(\frac{43}{126}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{20}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{931}(36,\cdot)$	931.cc	63	yes	$1$	$1$	$e\left(\frac{62}{63}\right)$	$e\left(\frac{32}{63}\right)$	$e\left(\frac{61}{63}\right)$	$e\left(\frac{11}{63}\right)$	$e\left(\frac{31}{63}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{63}\right)$	$e\left(\frac{10}{63}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{931}(37,\cdot)$	931.bq	42	yes	$-1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{37}{42}\right)$
$\chi_{931}(39,\cdot)$	931.bm	21	no	$1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{21}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$931$
Structure	\(C_{6}\times C_{126}\)
Order	$756$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{931}(1,\cdot)\)	931.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{931}(2,\cdot)\)	931.ce	126	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{931}(3,\cdot)\)	931.ci	126	yes	\(1\)	\(1\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{931}(4,\cdot)\)	931.ca	63	yes	\(1\)	\(1\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{931}(5,\cdot)\)	931.cj	126	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{931}(6,\cdot)\)	931.cl	126	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{31}{126}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)
\(\chi_{931}(8,\cdot)\)	931.br	42	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{931}(9,\cdot)\)	931.cb	63	yes	\(1\)	\(1\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{52}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{931}(10,\cdot)\)	931.cd	126	yes	\(1\)	\(1\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{5}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{931}(11,\cdot)\)	931.bk	21	yes	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{931}(12,\cdot)\)	931.bz	42	yes	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{931}(13,\cdot)\)	931.ch	126	yes	\(1\)	\(1\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{25}{63}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{13}{126}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{59}{63}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{931}(15,\cdot)\)	931.cf	126	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{83}{126}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{53}{63}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{85}{126}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)
\(\chi_{931}(16,\cdot)\)	931.ca	63	yes	\(1\)	\(1\)	\(e\left(\frac{38}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{46}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{931}(17,\cdot)\)	931.ck	126	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{103}{126}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{19}{126}\right)\)	\(e\left(\frac{107}{126}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)
\(\chi_{931}(18,\cdot)\)	931.r	6	no	\(-1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{931}(20,\cdot)\)	931.y	14	no	\(-1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{931}(22,\cdot)\)	931.cf	126	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{126}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{8}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{58}{63}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)
\(\chi_{931}(23,\cdot)\)	931.cb	63	yes	\(1\)	\(1\)	\(e\left(\frac{40}{63}\right)\)	\(e\left(\frac{22}{63}\right)\)	\(e\left(\frac{17}{63}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{44}{63}\right)\)	\(e\left(\frac{41}{63}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{931}(24,\cdot)\)	931.ck	126	yes	\(-1\)	\(1\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{55}{126}\right)\)	\(e\left(\frac{37}{63}\right)\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{29}{126}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{55}{63}\right)\)	\(e\left(\frac{71}{126}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)
\(\chi_{931}(25,\cdot)\)	931.ca	63	yes	\(1\)	\(1\)	\(e\left(\frac{43}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{931}(26,\cdot)\)	931.bo	42	yes	\(-1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)
\(\chi_{931}(27,\cdot)\)	931.bs	42	yes	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{931}(29,\cdot)\)	931.cf	126	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{126}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{50}{63}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{79}{126}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)
\(\chi_{931}(30,\cdot)\)	931.g	3	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{931}(31,\cdot)\)	931.s	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{931}(32,\cdot)\)	931.ce	126	yes	\(-1\)	\(1\)	\(e\left(\frac{95}{126}\right)\)	\(e\left(\frac{89}{126}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{13}{63}\right)\)	\(e\left(\frac{29}{63}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{26}{63}\right)\)	\(e\left(\frac{121}{126}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{931}(33,\cdot)\)	931.cd	126	yes	\(1\)	\(1\)	\(e\left(\frac{97}{126}\right)\)	\(e\left(\frac{2}{63}\right)\)	\(e\left(\frac{34}{63}\right)\)	\(e\left(\frac{67}{126}\right)\)	\(e\left(\frac{101}{126}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{4}{63}\right)\)	\(e\left(\frac{19}{63}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{931}(34,\cdot)\)	931.ch	126	yes	\(1\)	\(1\)	\(e\left(\frac{23}{126}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{23}{63}\right)\)	\(e\left(\frac{125}{126}\right)\)	\(e\left(\frac{43}{126}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{20}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{931}(36,\cdot)\)	931.cc	63	yes	\(1\)	\(1\)	\(e\left(\frac{62}{63}\right)\)	\(e\left(\frac{32}{63}\right)\)	\(e\left(\frac{61}{63}\right)\)	\(e\left(\frac{11}{63}\right)\)	\(e\left(\frac{31}{63}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{63}\right)\)	\(e\left(\frac{10}{63}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{931}(37,\cdot)\)	931.bq	42	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)
\(\chi_{931}(39,\cdot)\)	931.bm	21	no	\(1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)

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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.