LMFDB - Group of Dirichlet characters of modulus 87

Show commands: PariGP / SageMath

sage: H = DirichletGroup(87)

pari: g = idealstar(,87,2)

Character group

sage: G.order() pari: g.no
Order	=	56
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{28}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{87}(59,\cdot)$, $\chi_{87}(31,\cdot)$

First 32 of 56 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{87}(1,\cdot)$	87.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{87}(2,\cdot)$	87.k	28	yes	$1$	$1$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{87}(4,\cdot)$	87.i	14	no	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{87}(5,\cdot)$	87.h	14	yes	$-1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{87}(7,\cdot)$	87.g	7	no	$1$	$1$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{87}(8,\cdot)$	87.k	28	yes	$1$	$1$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{87}(10,\cdot)$	87.l	28	no	$-1$	$1$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{87}(11,\cdot)$	87.k	28	yes	$1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{87}(13,\cdot)$	87.i	14	no	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{87}(14,\cdot)$	87.k	28	yes	$1$	$1$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{87}(16,\cdot)$	87.g	7	no	$1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{87}(17,\cdot)$	87.f	4	yes	$1$	$1$	$i$	$-1$	$1$	$1$	$-i$	$i$	$i$	$-1$	$i$	$1$
$\chi_{87}(19,\cdot)$	87.l	28	no	$-1$	$1$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{87}(20,\cdot)$	87.j	14	yes	$-1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{87}(22,\cdot)$	87.i	14	no	$1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{87}(23,\cdot)$	87.j	14	yes	$-1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{87}(25,\cdot)$	87.g	7	no	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{87}(26,\cdot)$	87.k	28	yes	$1$	$1$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{87}(28,\cdot)$	87.c	2	no	$1$	$1$	$-1$	$1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$-1$	$1$
$\chi_{87}(31,\cdot)$	87.l	28	no	$-1$	$1$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{87}(32,\cdot)$	87.k	28	yes	$1$	$1$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{5}{7}\right)$
$\chi_{87}(34,\cdot)$	87.i	14	no	$1$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{1}{7}\right)$
$\chi_{87}(35,\cdot)$	87.h	14	yes	$-1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{87}(37,\cdot)$	87.l	28	no	$-1$	$1$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{87}(38,\cdot)$	87.h	14	yes	$-1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{87}(40,\cdot)$	87.l	28	no	$-1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{87}(41,\cdot)$	87.f	4	yes	$1$	$1$	$-i$	$-1$	$1$	$1$	$i$	$-i$	$-i$	$-1$	$-i$	$1$
$\chi_{87}(43,\cdot)$	87.l	28	no	$-1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{87}(44,\cdot)$	87.k	28	yes	$1$	$1$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{87}(46,\cdot)$	87.e	4	no	$-1$	$1$	$-i$	$-1$	$-1$	$1$	$i$	$i$	$-i$	$-1$	$-i$	$1$
$\chi_{87}(47,\cdot)$	87.k	28	yes	$1$	$1$	$e\left(\frac{25}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{28}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{17}{28}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{87}(49,\cdot)$	87.g	7	no	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$

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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	$87$
Structure	\(C_{2}\times C_{28}\)
Order	$56$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{87}(1,\cdot)\)	87.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{87}(2,\cdot)\)	87.k	28	yes	\(1\)	\(1\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{87}(4,\cdot)\)	87.i	14	no	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{87}(5,\cdot)\)	87.h	14	yes	\(-1\)	\(1\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{87}(7,\cdot)\)	87.g	7	no	\(1\)	\(1\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{87}(8,\cdot)\)	87.k	28	yes	\(1\)	\(1\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{87}(10,\cdot)\)	87.l	28	no	\(-1\)	\(1\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{87}(11,\cdot)\)	87.k	28	yes	\(1\)	\(1\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{87}(13,\cdot)\)	87.i	14	no	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{87}(14,\cdot)\)	87.k	28	yes	\(1\)	\(1\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{87}(16,\cdot)\)	87.g	7	no	\(1\)	\(1\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{87}(17,\cdot)\)	87.f	4	yes	\(1\)	\(1\)	\(i\)	\(-1\)	\(1\)	\(1\)	\(-i\)	\(i\)	\(i\)	\(-1\)	\(i\)	\(1\)
\(\chi_{87}(19,\cdot)\)	87.l	28	no	\(-1\)	\(1\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{87}(20,\cdot)\)	87.j	14	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{87}(22,\cdot)\)	87.i	14	no	\(1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{87}(23,\cdot)\)	87.j	14	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{87}(25,\cdot)\)	87.g	7	no	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{87}(26,\cdot)\)	87.k	28	yes	\(1\)	\(1\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{87}(28,\cdot)\)	87.c	2	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{87}(31,\cdot)\)	87.l	28	no	\(-1\)	\(1\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{87}(32,\cdot)\)	87.k	28	yes	\(1\)	\(1\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)
\(\chi_{87}(34,\cdot)\)	87.i	14	no	\(1\)	\(1\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)
\(\chi_{87}(35,\cdot)\)	87.h	14	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{87}(37,\cdot)\)	87.l	28	no	\(-1\)	\(1\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{87}(38,\cdot)\)	87.h	14	yes	\(-1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{87}(40,\cdot)\)	87.l	28	no	\(-1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{87}(41,\cdot)\)	87.f	4	yes	\(1\)	\(1\)	\(-i\)	\(-1\)	\(1\)	\(1\)	\(i\)	\(-i\)	\(-i\)	\(-1\)	\(-i\)	\(1\)
\(\chi_{87}(43,\cdot)\)	87.l	28	no	\(-1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{87}(44,\cdot)\)	87.k	28	yes	\(1\)	\(1\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{87}(46,\cdot)\)	87.e	4	no	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(1\)	\(i\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(1\)
\(\chi_{87}(47,\cdot)\)	87.k	28	yes	\(1\)	\(1\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{1}{28}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{87}(49,\cdot)\)	87.g	7	no	\(1\)	\(1\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)

Introduction

L-functions

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Character group

First 32 of 56 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.