LMFDB - Group of Dirichlet characters of modulus 141

Show commands: PariGP / SageMath

sage: H = DirichletGroup(141)

pari: g = idealstar(,141,2)

Character group

sage: G.order() pari: g.no
Order	=	92
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{46}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{141}(95,\cdot)$, $\chi_{141}(52,\cdot)$

First 32 of 92 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{141}(1,\cdot)$	141.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{141}(2,\cdot)$	141.h	46	yes	$-1$	$1$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{4}{23}\right)$
$\chi_{141}(4,\cdot)$	141.e	23	no	$1$	$1$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{8}{23}\right)$
$\chi_{141}(5,\cdot)$	141.g	46	yes	$1$	$1$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{13}{23}\right)$
$\chi_{141}(7,\cdot)$	141.e	23	no	$1$	$1$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{2}{23}\right)$
$\chi_{141}(8,\cdot)$	141.h	46	yes	$-1$	$1$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{12}{23}\right)$
$\chi_{141}(10,\cdot)$	141.f	46	no	$-1$	$1$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{17}{23}\right)$
$\chi_{141}(11,\cdot)$	141.g	46	yes	$1$	$1$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{22}{23}\right)$
$\chi_{141}(13,\cdot)$	141.f	46	no	$-1$	$1$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{31}{46}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{5}{23}\right)$
$\chi_{141}(14,\cdot)$	141.h	46	yes	$-1$	$1$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{6}{23}\right)$
$\chi_{141}(16,\cdot)$	141.e	23	no	$1$	$1$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{16}{23}\right)$
$\chi_{141}(17,\cdot)$	141.h	46	yes	$-1$	$1$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{1}{23}\right)$
$\chi_{141}(19,\cdot)$	141.f	46	no	$-1$	$1$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{10}{23}\right)$
$\chi_{141}(20,\cdot)$	141.g	46	yes	$1$	$1$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{21}{23}\right)$
$\chi_{141}(22,\cdot)$	141.f	46	no	$-1$	$1$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{3}{23}\right)$
$\chi_{141}(23,\cdot)$	141.g	46	yes	$1$	$1$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{19}{23}\right)$
$\chi_{141}(25,\cdot)$	141.e	23	no	$1$	$1$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{3}{23}\right)$
$\chi_{141}(26,\cdot)$	141.g	46	yes	$1$	$1$	$e\left(\frac{39}{46}\right)$	$e\left(\frac{16}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{43}{46}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{9}{23}\right)$
$\chi_{141}(28,\cdot)$	141.e	23	no	$1$	$1$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{10}{23}\right)$
$\chi_{141}(29,\cdot)$	141.g	46	yes	$1$	$1$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{25}{46}\right)$	$e\left(\frac{18}{23}\right)$
$\chi_{141}(31,\cdot)$	141.f	46	no	$-1$	$1$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{16}{23}\right)$
$\chi_{141}(32,\cdot)$	141.h	46	yes	$-1$	$1$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{20}{23}\right)$
$\chi_{141}(34,\cdot)$	141.e	23	no	$1$	$1$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{5}{23}\right)$
$\chi_{141}(35,\cdot)$	141.g	46	yes	$1$	$1$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{29}{46}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{41}{46}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{15}{23}\right)$
$\chi_{141}(37,\cdot)$	141.e	23	no	$1$	$1$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{17}{23}\right)$
$\chi_{141}(38,\cdot)$	141.g	46	yes	$1$	$1$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{20}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{21}{46}\right)$	$e\left(\frac{1}{46}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{14}{23}\right)$
$\chi_{141}(40,\cdot)$	141.f	46	no	$-1$	$1$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{33}{46}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{7}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{2}{23}\right)$
$\chi_{141}(41,\cdot)$	141.g	46	yes	$1$	$1$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{9}{46}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{37}{46}\right)$	$e\left(\frac{11}{23}\right)$
$\chi_{141}(43,\cdot)$	141.f	46	no	$-1$	$1$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{17}{46}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{8}{23}\right)$
$\chi_{141}(44,\cdot)$	141.g	46	yes	$1$	$1$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{45}{46}\right)$	$e\left(\frac{35}{46}\right)$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{13}{46}\right)$	$e\left(\frac{11}{46}\right)$	$e\left(\frac{7}{23}\right)$
$\chi_{141}(46,\cdot)$	141.d	2	no	$-1$	$1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$1$
$\chi_{141}(49,\cdot)$	141.e	23	no	$1$	$1$	$e\left(\frac{1}{23}\right)$	$e\left(\frac{2}{23}\right)$	$e\left(\frac{9}{23}\right)$	$e\left(\frac{12}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{7}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{4}{23}\right)$

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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	$141$
Structure	\(C_{2}\times C_{46}\)
Order	$92$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{141}(1,\cdot)\)	141.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{141}(2,\cdot)\)	141.h	46	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{4}{23}\right)\)
\(\chi_{141}(4,\cdot)\)	141.e	23	no	\(1\)	\(1\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)
\(\chi_{141}(5,\cdot)\)	141.g	46	yes	\(1\)	\(1\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{13}{23}\right)\)
\(\chi_{141}(7,\cdot)\)	141.e	23	no	\(1\)	\(1\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)
\(\chi_{141}(8,\cdot)\)	141.h	46	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{12}{23}\right)\)
\(\chi_{141}(10,\cdot)\)	141.f	46	no	\(-1\)	\(1\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)
\(\chi_{141}(11,\cdot)\)	141.g	46	yes	\(1\)	\(1\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{22}{23}\right)\)
\(\chi_{141}(13,\cdot)\)	141.f	46	no	\(-1\)	\(1\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{31}{46}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)
\(\chi_{141}(14,\cdot)\)	141.h	46	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{6}{23}\right)\)
\(\chi_{141}(16,\cdot)\)	141.e	23	no	\(1\)	\(1\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)
\(\chi_{141}(17,\cdot)\)	141.h	46	yes	\(-1\)	\(1\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{1}{23}\right)\)
\(\chi_{141}(19,\cdot)\)	141.f	46	no	\(-1\)	\(1\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)
\(\chi_{141}(20,\cdot)\)	141.g	46	yes	\(1\)	\(1\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{21}{23}\right)\)
\(\chi_{141}(22,\cdot)\)	141.f	46	no	\(-1\)	\(1\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)
\(\chi_{141}(23,\cdot)\)	141.g	46	yes	\(1\)	\(1\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{19}{23}\right)\)
\(\chi_{141}(25,\cdot)\)	141.e	23	no	\(1\)	\(1\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)
\(\chi_{141}(26,\cdot)\)	141.g	46	yes	\(1\)	\(1\)	\(e\left(\frac{39}{46}\right)\)	\(e\left(\frac{16}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{43}{46}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{9}{23}\right)\)
\(\chi_{141}(28,\cdot)\)	141.e	23	no	\(1\)	\(1\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)
\(\chi_{141}(29,\cdot)\)	141.g	46	yes	\(1\)	\(1\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{25}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)
\(\chi_{141}(31,\cdot)\)	141.f	46	no	\(-1\)	\(1\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{16}{23}\right)\)
\(\chi_{141}(32,\cdot)\)	141.h	46	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{20}{23}\right)\)
\(\chi_{141}(34,\cdot)\)	141.e	23	no	\(1\)	\(1\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{14}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)
\(\chi_{141}(35,\cdot)\)	141.g	46	yes	\(1\)	\(1\)	\(e\left(\frac{19}{46}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{29}{46}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{41}{46}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)
\(\chi_{141}(37,\cdot)\)	141.e	23	no	\(1\)	\(1\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)
\(\chi_{141}(38,\cdot)\)	141.g	46	yes	\(1\)	\(1\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{20}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{21}{46}\right)\)	\(e\left(\frac{1}{46}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{14}{23}\right)\)
\(\chi_{141}(40,\cdot)\)	141.f	46	no	\(-1\)	\(1\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{33}{46}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{7}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)
\(\chi_{141}(41,\cdot)\)	141.g	46	yes	\(1\)	\(1\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{19}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{9}{46}\right)\)	\(e\left(\frac{18}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{37}{46}\right)\)	\(e\left(\frac{11}{23}\right)\)
\(\chi_{141}(43,\cdot)\)	141.f	46	no	\(-1\)	\(1\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{17}{46}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{8}{23}\right)\)
\(\chi_{141}(44,\cdot)\)	141.g	46	yes	\(1\)	\(1\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{15}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{21}{23}\right)\)	\(e\left(\frac{45}{46}\right)\)	\(e\left(\frac{35}{46}\right)\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{13}{46}\right)\)	\(e\left(\frac{11}{46}\right)\)	\(e\left(\frac{7}{23}\right)\)
\(\chi_{141}(46,\cdot)\)	141.d	2	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)
\(\chi_{141}(49,\cdot)\)	141.e	23	no	\(1\)	\(1\)	\(e\left(\frac{1}{23}\right)\)	\(e\left(\frac{2}{23}\right)\)	\(e\left(\frac{9}{23}\right)\)	\(e\left(\frac{12}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{7}{23}\right)\)	\(e\left(\frac{13}{23}\right)\)	\(e\left(\frac{4}{23}\right)\)

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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.