LMFDB - Group of Dirichlet characters of modulus 247

sage:H = DirichletGroup(247)

pari:g = idealstar(,247,2)

Character group

sage:G.order() pari:g.no
Order	=	216
sage:H.invariants() pari:g.cyc
Structure	=	$C_{6}\times C_{36}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{247}(210,\cdot)$, $\chi_{247}(40,\cdot)$

First 32 of 216 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{247}(1,\cdot)$	247.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{247}(2,\cdot)$	247.br	36	yes	$1$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{36}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{7}{9}\right)$	$i$
$\chi_{247}(3,\cdot)$	247.bp	18	yes	$-1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{18}\right)$	$1$
$\chi_{247}(4,\cdot)$	247.bi	18	yes	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{9}\right)$	$-1$
$\chi_{247}(5,\cdot)$	247.bv	36	yes	$-1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{247}(6,\cdot)$	247.bu	36	yes	$-1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{35}{36}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{18}\right)$	$i$
$\chi_{247}(7,\cdot)$	247.bg	12	yes	$-1$	$1$	$i$	$1$	$-1$	$e\left(\frac{7}{12}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$-i$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{247}(8,\cdot)$	247.be	12	yes	$1$	$1$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$-i$	$i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$-i$
$\chi_{247}(9,\cdot)$	247.y	9	yes	$1$	$1$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{9}\right)$	$1$
$\chi_{247}(10,\cdot)$	247.bm	18	yes	$-1$	$1$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{247}(11,\cdot)$	247.bg	12	yes	$-1$	$1$	$i$	$1$	$-1$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{5}{12}\right)$	$-i$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{247}(12,\cdot)$	247.n	6	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$
$\chi_{247}(14,\cdot)$	247.bk	18	no	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{247}(15,\cdot)$	247.bq	36	yes	$1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{247}(16,\cdot)$	247.y	9	yes	$1$	$1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$1$
$\chi_{247}(17,\cdot)$	247.bo	18	yes	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{247}(18,\cdot)$	247.i	4	yes	$1$	$1$	$i$	$-1$	$-1$	$-i$	$-i$	$i$	$-i$	$1$	$1$	$i$
$\chi_{247}(20,\cdot)$	247.bc	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{247}(21,\cdot)$	247.bs	36	yes	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{12}\right)$
$\chi_{247}(22,\cdot)$	247.bj	18	yes	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{247}(23,\cdot)$	247.bo	18	yes	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{247}(24,\cdot)$	247.bu	36	yes	$-1$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{13}{36}\right)$	$-i$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{18}\right)$	$-i$
$\chi_{247}(25,\cdot)$	247.bn	18	yes	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{247}(27,\cdot)$	247.t	6	no	$-1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$
$\chi_{247}(28,\cdot)$	247.bt	36	yes	$-1$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{247}(29,\cdot)$	247.bj	18	yes	$-1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{247}(30,\cdot)$	247.r	6	yes	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$
$\chi_{247}(31,\cdot)$	247.be	12	yes	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$i$	$-i$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$i$
$\chi_{247}(32,\cdot)$	247.br	36	yes	$1$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{35}{36}\right)$	$i$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{8}{9}\right)$	$i$
$\chi_{247}(33,\cdot)$	247.bq	36	yes	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{247}(34,\cdot)$	247.bs	36	yes	$1$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{247}(35,\cdot)$	247.w	9	yes	$1$	$1$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$247$
Structure	\(C_{6}\times C_{36}\)
Order	$216$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{247}(1,\cdot)\)	247.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{247}(2,\cdot)\)	247.br	36	yes	\(1\)	\(1\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(i\)
\(\chi_{247}(3,\cdot)\)	247.bp	18	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(1\)
\(\chi_{247}(4,\cdot)\)	247.bi	18	yes	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(-1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(-1\)
\(\chi_{247}(5,\cdot)\)	247.bv	36	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{247}(6,\cdot)\)	247.bu	36	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(i\)
\(\chi_{247}(7,\cdot)\)	247.bg	12	yes	\(-1\)	\(1\)	\(i\)	\(1\)	\(-1\)	\(e\left(\frac{7}{12}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{247}(8,\cdot)\)	247.be	12	yes	\(1\)	\(1\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)
\(\chi_{247}(9,\cdot)\)	247.y	9	yes	\(1\)	\(1\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(1\)
\(\chi_{247}(10,\cdot)\)	247.bm	18	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{247}(11,\cdot)\)	247.bg	12	yes	\(-1\)	\(1\)	\(i\)	\(1\)	\(-1\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{5}{12}\right)\)	\(-i\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{247}(12,\cdot)\)	247.n	6	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)
\(\chi_{247}(14,\cdot)\)	247.bk	18	no	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{247}(15,\cdot)\)	247.bq	36	yes	\(1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{247}(16,\cdot)\)	247.y	9	yes	\(1\)	\(1\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(1\)
\(\chi_{247}(17,\cdot)\)	247.bo	18	yes	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{247}(18,\cdot)\)	247.i	4	yes	\(1\)	\(1\)	\(i\)	\(-1\)	\(-1\)	\(-i\)	\(-i\)	\(i\)	\(-i\)	\(1\)	\(1\)	\(i\)
\(\chi_{247}(20,\cdot)\)	247.bc	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{247}(21,\cdot)\)	247.bs	36	yes	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)
\(\chi_{247}(22,\cdot)\)	247.bj	18	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{247}(23,\cdot)\)	247.bo	18	yes	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{247}(24,\cdot)\)	247.bu	36	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(-i\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(-i\)
\(\chi_{247}(25,\cdot)\)	247.bn	18	yes	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{247}(27,\cdot)\)	247.t	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)
\(\chi_{247}(28,\cdot)\)	247.bt	36	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{247}(29,\cdot)\)	247.bj	18	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{247}(30,\cdot)\)	247.r	6	yes	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{247}(31,\cdot)\)	247.be	12	yes	\(1\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(i\)
\(\chi_{247}(32,\cdot)\)	247.br	36	yes	\(1\)	\(1\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(i\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(i\)
\(\chi_{247}(33,\cdot)\)	247.bq	36	yes	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{247}(34,\cdot)\)	247.bs	36	yes	\(1\)	\(1\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{247}(35,\cdot)\)	247.w	9	yes	\(1\)	\(1\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)

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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.