LMFDB - Group of Dirichlet characters of modulus 192

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(192)

pari: g = idealstar(,192,2)

Character group

sage: G.order() pari: g.no
Order	=	64
sage: H.invariants() pari: g.cyc
Structure	=	$C_{16}\times C_{2}\times C_{2}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{192}(127,\cdot)$, $\chi_{192}(133,\cdot)$, $\chi_{192}(65,\cdot)$

First 32 of 64 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{192}(1,\cdot)$	192.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{192}(5,\cdot)$	192.q	16	yes	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$-1$
$\chi_{192}(7,\cdot)$	192.m	8	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$i$	$i$	$e\left(\frac{7}{8}\right)$	$-1$
$\chi_{192}(11,\cdot)$	192.s	16	yes	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$1$
$\chi_{192}(13,\cdot)$	192.r	16	no	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$-1$
$\chi_{192}(17,\cdot)$	192.i	4	no	$-1$	$1$	$i$	$-1$	$i$	$i$	$-1$	$i$	$1$	$-1$	$-i$	$1$
$\chi_{192}(19,\cdot)$	192.t	16	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$1$
$\chi_{192}(23,\cdot)$	192.o	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$
$\chi_{192}(25,\cdot)$	192.n	8	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$-i$	$i$	$e\left(\frac{3}{8}\right)$	$1$
$\chi_{192}(29,\cdot)$	192.q	16	yes	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$-1$
$\chi_{192}(31,\cdot)$	192.b	2	no	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$-1$	$-1$
$\chi_{192}(35,\cdot)$	192.s	16	yes	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$1$
$\chi_{192}(37,\cdot)$	192.r	16	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$-1$
$\chi_{192}(41,\cdot)$	192.p	8	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$1$
$\chi_{192}(43,\cdot)$	192.t	16	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$1$
$\chi_{192}(47,\cdot)$	192.k	4	no	$1$	$1$	$i$	$1$	$-i$	$i$	$-1$	$-i$	$-1$	$-1$	$-i$	$-1$
$\chi_{192}(49,\cdot)$	192.j	4	no	$1$	$1$	$i$	$-1$	$i$	$-i$	$1$	$-i$	$-1$	$-1$	$-i$	$1$
$\chi_{192}(53,\cdot)$	192.q	16	yes	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$-1$
$\chi_{192}(55,\cdot)$	192.m	8	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$-1$
$\chi_{192}(59,\cdot)$	192.s	16	yes	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$1$
$\chi_{192}(61,\cdot)$	192.r	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$-1$
$\chi_{192}(65,\cdot)$	192.e	2	no	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$
$\chi_{192}(67,\cdot)$	192.t	16	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$1$
$\chi_{192}(71,\cdot)$	192.o	8	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$i$	$e\left(\frac{3}{8}\right)$	$-1$
$\chi_{192}(73,\cdot)$	192.n	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$i$	$-i$	$e\left(\frac{1}{8}\right)$	$1$
$\chi_{192}(77,\cdot)$	192.q	16	yes	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$-1$
$\chi_{192}(79,\cdot)$	192.l	4	no	$-1$	$1$	$i$	$1$	$-i$	$-i$	$1$	$i$	$1$	$-1$	$-i$	$-1$
$\chi_{192}(83,\cdot)$	192.s	16	yes	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$1$
$\chi_{192}(85,\cdot)$	192.r	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$-1$
$\chi_{192}(89,\cdot)$	192.p	8	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$i$	$i$	$e\left(\frac{7}{8}\right)$	$1$
$\chi_{192}(91,\cdot)$	192.t	16	no	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$1$
$\chi_{192}(95,\cdot)$	192.f	2	no	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$	$-1$

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	$192$
Structure	\(C_{16}\times C_{2}\times C_{2}\)
Order	$64$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{192}(1,\cdot)\)	192.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{192}(5,\cdot)\)	192.q	16	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)
\(\chi_{192}(7,\cdot)\)	192.m	8	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)
\(\chi_{192}(11,\cdot)\)	192.s	16	yes	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)
\(\chi_{192}(13,\cdot)\)	192.r	16	no	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)
\(\chi_{192}(17,\cdot)\)	192.i	4	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(-1\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(1\)
\(\chi_{192}(19,\cdot)\)	192.t	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(1\)
\(\chi_{192}(23,\cdot)\)	192.o	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)
\(\chi_{192}(25,\cdot)\)	192.n	8	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(1\)
\(\chi_{192}(29,\cdot)\)	192.q	16	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)
\(\chi_{192}(31,\cdot)\)	192.b	2	no	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{192}(35,\cdot)\)	192.s	16	yes	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(1\)
\(\chi_{192}(37,\cdot)\)	192.r	16	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)
\(\chi_{192}(41,\cdot)\)	192.p	8	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(1\)
\(\chi_{192}(43,\cdot)\)	192.t	16	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)
\(\chi_{192}(47,\cdot)\)	192.k	4	no	\(1\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(-1\)
\(\chi_{192}(49,\cdot)\)	192.j	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(-i\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(1\)
\(\chi_{192}(53,\cdot)\)	192.q	16	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)
\(\chi_{192}(55,\cdot)\)	192.m	8	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)
\(\chi_{192}(59,\cdot)\)	192.s	16	yes	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)
\(\chi_{192}(61,\cdot)\)	192.r	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)
\(\chi_{192}(65,\cdot)\)	192.e	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{192}(67,\cdot)\)	192.t	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(1\)
\(\chi_{192}(71,\cdot)\)	192.o	8	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)
\(\chi_{192}(73,\cdot)\)	192.n	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(1\)
\(\chi_{192}(77,\cdot)\)	192.q	16	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)
\(\chi_{192}(79,\cdot)\)	192.l	4	no	\(-1\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(-1\)
\(\chi_{192}(83,\cdot)\)	192.s	16	yes	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(1\)
\(\chi_{192}(85,\cdot)\)	192.r	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)
\(\chi_{192}(89,\cdot)\)	192.p	8	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(1\)
\(\chi_{192}(91,\cdot)\)	192.t	16	no	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)
\(\chi_{192}(95,\cdot)\)	192.f	2	no	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Learn more

Character group

First 32 of 64 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.