LMFDB - Group of Dirichlet characters of modulus 143

Show commands: PariGP / SageMath

sage: H = DirichletGroup(143)

pari: g = idealstar(,143,2)

Character group

sage: G.order() pari: g.no
Order	=	120
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{60}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{143}(79,\cdot)$, $\chi_{143}(67,\cdot)$

First 32 of 120 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{143}(1,\cdot)$	143.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{143}(2,\cdot)$	143.w	60	yes	$1$	$1$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{143}(3,\cdot)$	143.q	15	yes	$1$	$1$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{143}(4,\cdot)$	143.u	30	yes	$1$	$1$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{143}(5,\cdot)$	143.r	20	yes	$-1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$-1$	$-1$
$\chi_{143}(6,\cdot)$	143.w	60	yes	$1$	$1$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{60}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{143}(7,\cdot)$	143.w	60	yes	$1$	$1$	$e\left(\frac{37}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{53}{60}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{143}(8,\cdot)$	143.s	20	yes	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$-1$
$\chi_{143}(9,\cdot)$	143.q	15	yes	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{143}(10,\cdot)$	143.i	6	yes	$-1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$1$
$\chi_{143}(12,\cdot)$	143.b	2	no	$1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$
$\chi_{143}(14,\cdot)$	143.h	5	no	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$1$
$\chi_{143}(15,\cdot)$	143.x	60	yes	$-1$	$1$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{6}\right)$	$-1$
$\chi_{143}(16,\cdot)$	143.q	15	yes	$1$	$1$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{143}(17,\cdot)$	143.v	30	yes	$-1$	$1$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{1}{6}\right)$	$1$
$\chi_{143}(18,\cdot)$	143.s	20	yes	$1$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$1$	$-1$
$\chi_{143}(19,\cdot)$	143.w	60	yes	$1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{143}(20,\cdot)$	143.x	60	yes	$-1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{6}\right)$	$-1$
$\chi_{143}(21,\cdot)$	143.g	4	yes	$1$	$1$	$-i$	$1$	$-1$	$i$	$-i$	$i$	$i$	$1$	$1$	$-1$
$\chi_{143}(23,\cdot)$	143.j	6	no	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{143}(24,\cdot)$	143.w	60	yes	$1$	$1$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{143}(25,\cdot)$	143.n	10	yes	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$1$
$\chi_{143}(27,\cdot)$	143.h	5	no	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{2}{5}\right)$	$1$	$1$
$\chi_{143}(28,\cdot)$	143.w	60	yes	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{13}{60}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{1}{3}\right)$	$-1$
$\chi_{143}(29,\cdot)$	143.t	30	yes	$-1$	$1$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{6}\right)$	$1$
$\chi_{143}(30,\cdot)$	143.v	30	yes	$-1$	$1$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{1}{6}\right)$	$1$
$\chi_{143}(31,\cdot)$	143.r	20	yes	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$-1$
$\chi_{143}(32,\cdot)$	143.o	12	yes	$1$	$1$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{12}\right)$	$-i$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$
$\chi_{143}(34,\cdot)$	143.f	4	no	$-1$	$1$	$i$	$1$	$-1$	$i$	$i$	$-i$	$-i$	$1$	$-1$	$-1$
$\chi_{143}(35,\cdot)$	143.t	30	yes	$-1$	$1$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{6}\right)$	$1$
$\chi_{143}(36,\cdot)$	143.u	30	yes	$1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{3}\right)$	$1$
$\chi_{143}(37,\cdot)$	143.x	60	yes	$-1$	$1$	$e\left(\frac{47}{60}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{49}{60}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

Click here to search among the remaining 88 characters.

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	$143$
Structure	\(C_{2}\times C_{60}\)
Order	$120$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(12\)
\(\chi_{143}(1,\cdot)\)	143.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{143}(2,\cdot)\)	143.w	60	yes	\(1\)	\(1\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{143}(3,\cdot)\)	143.q	15	yes	\(1\)	\(1\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{143}(4,\cdot)\)	143.u	30	yes	\(1\)	\(1\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{143}(5,\cdot)\)	143.r	20	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(-1\)	\(-1\)
\(\chi_{143}(6,\cdot)\)	143.w	60	yes	\(1\)	\(1\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{60}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{143}(7,\cdot)\)	143.w	60	yes	\(1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{143}(8,\cdot)\)	143.s	20	yes	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(-1\)
\(\chi_{143}(9,\cdot)\)	143.q	15	yes	\(1\)	\(1\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{143}(10,\cdot)\)	143.i	6	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)
\(\chi_{143}(12,\cdot)\)	143.b	2	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)
\(\chi_{143}(14,\cdot)\)	143.h	5	no	\(1\)	\(1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(1\)
\(\chi_{143}(15,\cdot)\)	143.x	60	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{60}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)
\(\chi_{143}(16,\cdot)\)	143.q	15	yes	\(1\)	\(1\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{143}(17,\cdot)\)	143.v	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)
\(\chi_{143}(18,\cdot)\)	143.s	20	yes	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(1\)	\(-1\)
\(\chi_{143}(19,\cdot)\)	143.w	60	yes	\(1\)	\(1\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{143}(20,\cdot)\)	143.x	60	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{17}{60}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)
\(\chi_{143}(21,\cdot)\)	143.g	4	yes	\(1\)	\(1\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(-i\)	\(i\)	\(i\)	\(1\)	\(1\)	\(-1\)
\(\chi_{143}(23,\cdot)\)	143.j	6	no	\(1\)	\(1\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{143}(24,\cdot)\)	143.w	60	yes	\(1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{143}(25,\cdot)\)	143.n	10	yes	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(1\)	\(1\)
\(\chi_{143}(27,\cdot)\)	143.h	5	no	\(1\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(1\)	\(1\)
\(\chi_{143}(28,\cdot)\)	143.w	60	yes	\(1\)	\(1\)	\(e\left(\frac{59}{60}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{31}{60}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(-1\)
\(\chi_{143}(29,\cdot)\)	143.t	30	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{30}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(1\)
\(\chi_{143}(30,\cdot)\)	143.v	30	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)
\(\chi_{143}(31,\cdot)\)	143.r	20	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(-1\)
\(\chi_{143}(32,\cdot)\)	143.o	12	yes	\(1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-i\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(-i\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(-1\)
\(\chi_{143}(34,\cdot)\)	143.f	4	no	\(-1\)	\(1\)	\(i\)	\(1\)	\(-1\)	\(i\)	\(i\)	\(-i\)	\(-i\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{143}(35,\cdot)\)	143.t	30	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{8}{15}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{1}{30}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(1\)
\(\chi_{143}(36,\cdot)\)	143.u	30	yes	\(1\)	\(1\)	\(e\left(\frac{19}{30}\right)\)	\(e\left(\frac{11}{15}\right)\)	\(e\left(\frac{4}{15}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{15}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(1\)
\(\chi_{143}(37,\cdot)\)	143.x	60	yes	\(-1\)	\(1\)	\(e\left(\frac{47}{60}\right)\)	\(e\left(\frac{14}{15}\right)\)	\(e\left(\frac{17}{30}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{43}{60}\right)\)	\(e\left(\frac{49}{60}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{15}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 120 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.