LMFDB - Group of Dirichlet characters of modulus 703

Show commands: PariGP / SageMath

sage: H = DirichletGroup(703)

pari: g = idealstar(,703,2)

Character group

sage: G.order() pari: g.no
Order	=	648
sage: H.invariants() pari: g.cyc
Structure	=	$C_{18}\times C_{36}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{703}(667,\cdot)$, $\chi_{703}(39,\cdot)$

First 32 of 648 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{703}(1,\cdot)$	703.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{703}(2,\cdot)$	703.ds	36	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{2}{9}\right)$	$i$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{18}\right)$	$-1$
$\chi_{703}(3,\cdot)$	703.cs	18	yes	$-1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{703}(4,\cdot)$	703.cx	18	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{4}{9}\right)$	$-1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$1$
$\chi_{703}(5,\cdot)$	703.dw	36	yes	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{703}(6,\cdot)$	703.dg	36	yes	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{703}(7,\cdot)$	703.bb	9	yes	$1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$1$	$e\left(\frac{2}{3}\right)$
$\chi_{703}(8,\cdot)$	703.bj	12	yes	$1$	$1$	$i$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$
$\chi_{703}(9,\cdot)$	703.z	9	yes	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{703}(10,\cdot)$	703.ck	18	yes	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{703}(11,\cdot)$	703.k	6	yes	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{703}(12,\cdot)$	703.cb	18	yes	$-1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{703}(13,\cdot)$	703.du	36	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{4}{9}\right)$	$-i$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$-1$
$\chi_{703}(14,\cdot)$	703.df	36	yes	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{703}(15,\cdot)$	703.db	36	yes	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{703}(16,\cdot)$	703.w	9	yes	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{9}\right)$	$1$
$\chi_{703}(17,\cdot)$	703.de	36	yes	$-1$	$1$	$-i$	$e\left(\frac{5}{18}\right)$	$-1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{9}\right)$	$i$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$-1$
$\chi_{703}(18,\cdot)$	703.dm	36	yes	$1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{31}{36}\right)$	$-i$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{703}(20,\cdot)$	703.dk	36	no	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{35}{36}\right)$	$-i$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{703}(21,\cdot)$	703.bt	18	yes	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{8}{9}\right)$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{18}\right)$	$1$
$\chi_{703}(22,\cdot)$	703.ds	36	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{8}{9}\right)$	$-i$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{18}\right)$	$-1$
$\chi_{703}(23,\cdot)$	703.dp	36	yes	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{29}{36}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{703}(24,\cdot)$	703.da	36	yes	$-1$	$1$	$e\left(\frac{25}{36}\right)$	$-1$	$e\left(\frac{7}{18}\right)$	$-i$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{703}(25,\cdot)$	703.bw	18	yes	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{703}(26,\cdot)$	703.g	3	yes	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{703}(27,\cdot)$	703.m	6	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$1$
$\chi_{703}(28,\cdot)$	703.bw	18	yes	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{703}(29,\cdot)$	703.df	36	yes	$1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{703}(30,\cdot)$	703.cn	18	yes	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{703}(31,\cdot)$	703.bl	12	yes	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$1$	$i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$
$\chi_{703}(32,\cdot)$	703.ds	36	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{9}\right)$	$i$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{18}\right)$	$-1$
$\chi_{703}(33,\cdot)$	703.bv	18	yes	$-1$	$1$	$e\left(\frac{17}{18}\right)$	$-1$	$e\left(\frac{8}{9}\right)$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{3}\right)$

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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	$703$
Structure	\(C_{18}\times C_{36}\)
Order	$648$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{703}(1,\cdot)\)	703.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{703}(2,\cdot)\)	703.ds	36	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(i\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(-1\)
\(\chi_{703}(3,\cdot)\)	703.cs	18	yes	\(-1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{703}(4,\cdot)\)	703.cx	18	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(-1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(1\)
\(\chi_{703}(5,\cdot)\)	703.dw	36	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{703}(6,\cdot)\)	703.dg	36	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{703}(7,\cdot)\)	703.bb	9	yes	\(1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{703}(8,\cdot)\)	703.bj	12	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)
\(\chi_{703}(9,\cdot)\)	703.z	9	yes	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{703}(10,\cdot)\)	703.ck	18	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{703}(11,\cdot)\)	703.k	6	yes	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{703}(12,\cdot)\)	703.cb	18	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{703}(13,\cdot)\)	703.du	36	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(-i\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(-1\)
\(\chi_{703}(14,\cdot)\)	703.df	36	yes	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{703}(15,\cdot)\)	703.db	36	yes	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{703}(16,\cdot)\)	703.w	9	yes	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(1\)
\(\chi_{703}(17,\cdot)\)	703.de	36	yes	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{5}{18}\right)\)	\(-1\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(i\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(-1\)
\(\chi_{703}(18,\cdot)\)	703.dm	36	yes	\(1\)	\(1\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(-i\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{703}(20,\cdot)\)	703.dk	36	no	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(-i\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{703}(21,\cdot)\)	703.bt	18	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(1\)
\(\chi_{703}(22,\cdot)\)	703.ds	36	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(-i\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(-1\)
\(\chi_{703}(23,\cdot)\)	703.dp	36	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{703}(24,\cdot)\)	703.da	36	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(-1\)	\(e\left(\frac{7}{18}\right)\)	\(-i\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{703}(25,\cdot)\)	703.bw	18	yes	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{703}(26,\cdot)\)	703.g	3	yes	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{703}(27,\cdot)\)	703.m	6	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(1\)
\(\chi_{703}(28,\cdot)\)	703.bw	18	yes	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{703}(29,\cdot)\)	703.df	36	yes	\(1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{703}(30,\cdot)\)	703.cn	18	yes	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{703}(31,\cdot)\)	703.bl	12	yes	\(1\)	\(1\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(1\)	\(i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)
\(\chi_{703}(32,\cdot)\)	703.ds	36	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(i\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(-1\)
\(\chi_{703}(33,\cdot)\)	703.bv	18	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(-1\)	\(e\left(\frac{8}{9}\right)\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)

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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.