LMFDB - Group of Dirichlet characters of modulus 147

Show commands: PariGP / SageMath

sage: H = DirichletGroup(147)

pari: g = idealstar(,147,2)

Character group

sage: G.order() pari: g.no
Order	=	84
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{42}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{147}(50,\cdot)$, $\chi_{147}(52,\cdot)$

First 32 of 84 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	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{147}(1,\cdot)$	147.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{147}(2,\cdot)$	147.n	42	yes	$-1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{147}(4,\cdot)$	147.m	21	no	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{147}(5,\cdot)$	147.o	42	yes	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{147}(8,\cdot)$	147.l	14	yes	$-1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$1$
$\chi_{147}(10,\cdot)$	147.p	42	no	$-1$	$1$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{147}(11,\cdot)$	147.n	42	yes	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{147}(13,\cdot)$	147.j	14	no	$-1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$	$-1$
$\chi_{147}(16,\cdot)$	147.m	21	no	$1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{147}(17,\cdot)$	147.o	42	yes	$1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{147}(19,\cdot)$	147.f	6	no	$-1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{147}(20,\cdot)$	147.k	14	yes	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$-1$
$\chi_{147}(22,\cdot)$	147.i	7	no	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$1$
$\chi_{147}(23,\cdot)$	147.n	42	yes	$-1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{147}(25,\cdot)$	147.m	21	no	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{147}(26,\cdot)$	147.o	42	yes	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{147}(29,\cdot)$	147.l	14	yes	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$1$
$\chi_{147}(31,\cdot)$	147.f	6	no	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{147}(32,\cdot)$	147.n	42	yes	$-1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{147}(34,\cdot)$	147.j	14	no	$-1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{14}\right)$	$-1$
$\chi_{147}(37,\cdot)$	147.m	21	no	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{147}(38,\cdot)$	147.o	42	yes	$1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{147}(40,\cdot)$	147.p	42	no	$-1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{147}(41,\cdot)$	147.k	14	yes	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$-1$
$\chi_{147}(43,\cdot)$	147.i	7	no	$1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$1$
$\chi_{147}(44,\cdot)$	147.n	42	yes	$-1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{42}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{147}(46,\cdot)$	147.m	21	no	$1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{147}(47,\cdot)$	147.o	42	yes	$1$	$1$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{1}{6}\right)$
$\chi_{147}(50,\cdot)$	147.b	2	no	$-1$	$1$	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$1$	$-1$	$1$
$\chi_{147}(52,\cdot)$	147.p	42	no	$-1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{147}(53,\cdot)$	147.n	42	yes	$-1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{1}{3}\right)$
$\chi_{147}(55,\cdot)$	147.j	14	no	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$-1$

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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	$147$
Structure	\(C_{2}\times C_{42}\)
Order	$84$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{147}(1,\cdot)\)	147.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{147}(2,\cdot)\)	147.n	42	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{147}(4,\cdot)\)	147.m	21	no	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{147}(5,\cdot)\)	147.o	42	yes	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{147}(8,\cdot)\)	147.l	14	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(1\)
\(\chi_{147}(10,\cdot)\)	147.p	42	no	\(-1\)	\(1\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{147}(11,\cdot)\)	147.n	42	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{147}(13,\cdot)\)	147.j	14	no	\(-1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(-1\)
\(\chi_{147}(16,\cdot)\)	147.m	21	no	\(1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{147}(17,\cdot)\)	147.o	42	yes	\(1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{147}(19,\cdot)\)	147.f	6	no	\(-1\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{147}(20,\cdot)\)	147.k	14	yes	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(-1\)
\(\chi_{147}(22,\cdot)\)	147.i	7	no	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(1\)
\(\chi_{147}(23,\cdot)\)	147.n	42	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{147}(25,\cdot)\)	147.m	21	no	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{147}(26,\cdot)\)	147.o	42	yes	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{147}(29,\cdot)\)	147.l	14	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(1\)
\(\chi_{147}(31,\cdot)\)	147.f	6	no	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{147}(32,\cdot)\)	147.n	42	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{147}(34,\cdot)\)	147.j	14	no	\(-1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-1\)
\(\chi_{147}(37,\cdot)\)	147.m	21	no	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{147}(38,\cdot)\)	147.o	42	yes	\(1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{147}(40,\cdot)\)	147.p	42	no	\(-1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{147}(41,\cdot)\)	147.k	14	yes	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(-1\)
\(\chi_{147}(43,\cdot)\)	147.i	7	no	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)
\(\chi_{147}(44,\cdot)\)	147.n	42	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{147}(46,\cdot)\)	147.m	21	no	\(1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{147}(47,\cdot)\)	147.o	42	yes	\(1\)	\(1\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{1}{6}\right)\)
\(\chi_{147}(50,\cdot)\)	147.b	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{147}(52,\cdot)\)	147.p	42	no	\(-1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{25}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{147}(53,\cdot)\)	147.n	42	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{147}(55,\cdot)\)	147.j	14	no	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(-1\)

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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.