LMFDB - Group of Dirichlet characters of modulus 145

Show commands: PariGP / SageMath

sage: H = DirichletGroup(145)

pari: g = idealstar(,145,2)

Character group

sage: G.order() pari: g.no
Order	=	112
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4}\times C_{28}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{145}(117,\cdot)$, $\chi_{145}(31,\cdot)$

First 32 of 112 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	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{145}(1,\cdot)$	145.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{145}(2,\cdot)$	145.o	28	yes	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{25}{28}\right)$	$-1$	$e\left(\frac{11}{28}\right)$
$\chi_{145}(3,\cdot)$	145.t	28	yes	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{28}\right)$	$1$	$e\left(\frac{13}{28}\right)$
$\chi_{145}(4,\cdot)$	145.l	14	yes	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{14}\right)$	$1$	$e\left(\frac{11}{14}\right)$
$\chi_{145}(6,\cdot)$	145.m	14	no	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{14}\right)$	$-1$	$e\left(\frac{6}{7}\right)$
$\chi_{145}(7,\cdot)$	145.p	28	yes	$-1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$i$	$e\left(\frac{13}{28}\right)$
$\chi_{145}(8,\cdot)$	145.o	28	yes	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{19}{28}\right)$	$-1$	$e\left(\frac{5}{28}\right)$
$\chi_{145}(9,\cdot)$	145.l	14	yes	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{14}\right)$	$1$	$e\left(\frac{13}{14}\right)$
$\chi_{145}(11,\cdot)$	145.r	28	no	$-1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{9}{28}\right)$	$i$	$e\left(\frac{1}{14}\right)$
$\chi_{145}(12,\cdot)$	145.e	4	yes	$1$	$1$	$-1$	$1$	$1$	$-1$	$i$	$-1$	$1$	$i$	$1$	$i$
$\chi_{145}(13,\cdot)$	145.q	28	yes	$-1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{1}{14}\right)$	$i$	$e\left(\frac{23}{28}\right)$
$\chi_{145}(14,\cdot)$	145.s	28	yes	$-1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{17}{28}\right)$	$-i$	$e\left(\frac{6}{7}\right)$
$\chi_{145}(16,\cdot)$	145.k	7	no	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$1$	$e\left(\frac{4}{7}\right)$
$\chi_{145}(17,\cdot)$	145.j	4	yes	$1$	$1$	$1$	$-1$	$1$	$-1$	$i$	$1$	$1$	$-i$	$-1$	$i$
$\chi_{145}(18,\cdot)$	145.o	28	yes	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{23}{28}\right)$	$-1$	$e\left(\frac{9}{28}\right)$
$\chi_{145}(19,\cdot)$	145.s	28	yes	$-1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{28}\right)$	$-i$	$e\left(\frac{2}{7}\right)$
$\chi_{145}(21,\cdot)$	145.r	28	no	$-1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{28}\right)$	$i$	$e\left(\frac{13}{14}\right)$
$\chi_{145}(22,\cdot)$	145.q	28	yes	$-1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{14}\right)$	$-i$	$e\left(\frac{13}{28}\right)$
$\chi_{145}(23,\cdot)$	145.p	28	yes	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$-i$	$e\left(\frac{3}{28}\right)$
$\chi_{145}(24,\cdot)$	145.n	14	yes	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$-1$	$e\left(\frac{9}{14}\right)$
$\chi_{145}(26,\cdot)$	145.r	28	no	$-1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{27}{28}\right)$	$-i$	$e\left(\frac{3}{14}\right)$
$\chi_{145}(27,\cdot)$	145.t	28	yes	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{28}\right)$	$1$	$e\left(\frac{11}{28}\right)$
$\chi_{145}(28,\cdot)$	145.h	4	yes	$-1$	$1$	$i$	$-i$	$-1$	$1$	$-i$	$-i$	$-1$	$-1$	$i$	$i$
$\chi_{145}(31,\cdot)$	145.r	28	no	$-1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{25}{28}\right)$	$i$	$e\left(\frac{9}{14}\right)$
$\chi_{145}(32,\cdot)$	145.o	28	yes	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{28}\right)$	$-1$	$e\left(\frac{27}{28}\right)$
$\chi_{145}(33,\cdot)$	145.q	28	yes	$-1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{14}\right)$	$i$	$e\left(\frac{15}{28}\right)$
$\chi_{145}(34,\cdot)$	145.l	14	yes	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{9}{14}\right)$	$1$	$e\left(\frac{9}{14}\right)$
$\chi_{145}(36,\cdot)$	145.k	7	no	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$1$	$e\left(\frac{5}{7}\right)$
$\chi_{145}(37,\cdot)$	145.t	28	yes	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{19}{28}\right)$	$1$	$e\left(\frac{19}{28}\right)$
$\chi_{145}(38,\cdot)$	145.q	28	yes	$-1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{13}{14}\right)$	$i$	$e\left(\frac{19}{28}\right)$
$\chi_{145}(39,\cdot)$	145.s	28	yes	$-1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{15}{28}\right)$	$i$	$e\left(\frac{2}{7}\right)$
$\chi_{145}(41,\cdot)$	145.g	4	no	$-1$	$1$	$i$	$i$	$-1$	$-1$	$1$	$-i$	$-1$	$i$	$-i$	$-1$

Click here to search among the remaining 80 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	$145$
Structure	\(C_{4}\times C_{28}\)
Order	$112$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(6\)	\(7\)	\(8\)	\(9\)	\(11\)	\(12\)	\(13\)
\(\chi_{145}(1,\cdot)\)	145.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{145}(2,\cdot)\)	145.o	28	yes	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(-1\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{145}(3,\cdot)\)	145.t	28	yes	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(1\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{145}(4,\cdot)\)	145.l	14	yes	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(1\)	\(e\left(\frac{11}{14}\right)\)
\(\chi_{145}(6,\cdot)\)	145.m	14	no	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(-1\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{145}(7,\cdot)\)	145.p	28	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(i\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{145}(8,\cdot)\)	145.o	28	yes	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(-1\)	\(e\left(\frac{5}{28}\right)\)
\(\chi_{145}(9,\cdot)\)	145.l	14	yes	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(1\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{145}(11,\cdot)\)	145.r	28	no	\(-1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(i\)	\(e\left(\frac{1}{14}\right)\)
\(\chi_{145}(12,\cdot)\)	145.e	4	yes	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(i\)	\(-1\)	\(1\)	\(i\)	\(1\)	\(i\)
\(\chi_{145}(13,\cdot)\)	145.q	28	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(i\)	\(e\left(\frac{23}{28}\right)\)
\(\chi_{145}(14,\cdot)\)	145.s	28	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(-i\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{145}(16,\cdot)\)	145.k	7	no	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(1\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{145}(17,\cdot)\)	145.j	4	yes	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(i\)	\(1\)	\(1\)	\(-i\)	\(-1\)	\(i\)
\(\chi_{145}(18,\cdot)\)	145.o	28	yes	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(-1\)	\(e\left(\frac{9}{28}\right)\)
\(\chi_{145}(19,\cdot)\)	145.s	28	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(-i\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{145}(21,\cdot)\)	145.r	28	no	\(-1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(i\)	\(e\left(\frac{13}{14}\right)\)
\(\chi_{145}(22,\cdot)\)	145.q	28	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(-i\)	\(e\left(\frac{13}{28}\right)\)
\(\chi_{145}(23,\cdot)\)	145.p	28	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(-i\)	\(e\left(\frac{3}{28}\right)\)
\(\chi_{145}(24,\cdot)\)	145.n	14	yes	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(-1\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{145}(26,\cdot)\)	145.r	28	no	\(-1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(-i\)	\(e\left(\frac{3}{14}\right)\)
\(\chi_{145}(27,\cdot)\)	145.t	28	yes	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(1\)	\(e\left(\frac{11}{28}\right)\)
\(\chi_{145}(28,\cdot)\)	145.h	4	yes	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(i\)
\(\chi_{145}(31,\cdot)\)	145.r	28	no	\(-1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(i\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{145}(32,\cdot)\)	145.o	28	yes	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(-1\)	\(e\left(\frac{27}{28}\right)\)
\(\chi_{145}(33,\cdot)\)	145.q	28	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(i\)	\(e\left(\frac{15}{28}\right)\)
\(\chi_{145}(34,\cdot)\)	145.l	14	yes	\(1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(1\)	\(e\left(\frac{9}{14}\right)\)
\(\chi_{145}(36,\cdot)\)	145.k	7	no	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(1\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{145}(37,\cdot)\)	145.t	28	yes	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(1\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{145}(38,\cdot)\)	145.q	28	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(i\)	\(e\left(\frac{19}{28}\right)\)
\(\chi_{145}(39,\cdot)\)	145.s	28	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(i\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{145}(41,\cdot)\)	145.g	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(-1\)	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 112 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.