LMFDB - Group of Dirichlet characters of modulus 1632

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(1632)

gp:g = idealstar(,1632,2)

magma:G = FullDirichletGroup(1632);

Character group

Order	=	512	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{8}\times C_{16}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{1632}(511,\cdot)$, $\chi_{1632}(613,\cdot)$, $\chi_{1632}(545,\cdot)$, $\chi_{1632}(1057,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 512 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	$-1$	$1$	$5$	$7$	$11$	$13$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{1632}(1,\cdot)$	1632.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1632}(5,\cdot)$	1632.dw	16	yes	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1632}(7,\cdot)$	1632.dm	16	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{16}\right)$	$i$
$\chi_{1632}(11,\cdot)$	1632.ej	16	yes	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1632}(13,\cdot)$	1632.bv	8	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$i$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$
$\chi_{1632}(19,\cdot)$	1632.da	8	no	$-1$	$1$	$i$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{1632}(23,\cdot)$	1632.ep	16	no	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{16}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{15}{16}\right)$	$i$
$\chi_{1632}(25,\cdot)$	1632.cf	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$-1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$
$\chi_{1632}(29,\cdot)$	1632.el	16	yes	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1632}(31,\cdot)$	1632.du	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-1$
$\chi_{1632}(35,\cdot)$	1632.cj	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$-i$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$
$\chi_{1632}(37,\cdot)$	1632.dx	16	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1632}(41,\cdot)$	1632.en	16	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{16}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-i$
$\chi_{1632}(43,\cdot)$	1632.bw	8	no	$-1$	$1$	$i$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1632}(47,\cdot)$	1632.y	4	no	$1$	$1$	$i$	$i$	$i$	$-1$	$-1$	$-i$	$-1$	$i$	$-i$	$-1$
$\chi_{1632}(49,\cdot)$	1632.cu	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$-i$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$
$\chi_{1632}(53,\cdot)$	1632.bo	8	yes	$-1$	$1$	$-1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1632}(55,\cdot)$	1632.q	4	no	$-1$	$1$	$-1$	$i$	$-1$	$i$	$i$	$i$	$1$	$1$	$i$	$-i$
$\chi_{1632}(59,\cdot)$	1632.db	8	yes	$1$	$1$	$-i$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1632}(61,\cdot)$	1632.dx	16	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{1632}(65,\cdot)$	1632.dt	16	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-1$
$\chi_{1632}(67,\cdot)$	1632.cp	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$-i$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$
$\chi_{1632}(71,\cdot)$	1632.ep	16	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{16}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$
$\chi_{1632}(73,\cdot)$	1632.dk	16	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{15}{16}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{16}\right)$	$i$
$\chi_{1632}(77,\cdot)$	1632.di	8	yes	$-1$	$1$	$1$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{1632}(79,\cdot)$	1632.ef	16	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{16}\right)$	$1$
$\chi_{1632}(83,\cdot)$	1632.db	8	yes	$1$	$1$	$i$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1632}(89,\cdot)$	1632.t	4	no	$-1$	$1$	$-1$	$-i$	$1$	$-i$	$i$	$i$	$1$	$1$	$-i$	$i$
$\chi_{1632}(91,\cdot)$	1632.dp	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1632}(95,\cdot)$	1632.eh	16	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{16}\right)$	$1$
$\chi_{1632}(97,\cdot)$	1632.ee	16	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$	$1$
$\chi_{1632}(101,\cdot)$	1632.cl	8	yes	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$i$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$

Click here to search among the remaining 480 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 $\F_{q}$
Belyi maps

Modulus	$1632$
Structure	\(C_{2}\times C_{2}\times C_{8}\times C_{16}\)
Order	$512$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{1632}(1,\cdot)\)	1632.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1632}(5,\cdot)\)	1632.dw	16	yes	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1632}(7,\cdot)\)	1632.dm	16	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)
\(\chi_{1632}(11,\cdot)\)	1632.ej	16	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1632}(13,\cdot)\)	1632.bv	8	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1632}(19,\cdot)\)	1632.da	8	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{1632}(23,\cdot)\)	1632.ep	16	no	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(i\)
\(\chi_{1632}(25,\cdot)\)	1632.cf	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)
\(\chi_{1632}(29,\cdot)\)	1632.el	16	yes	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1632}(31,\cdot)\)	1632.du	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)
\(\chi_{1632}(35,\cdot)\)	1632.cj	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{1632}(37,\cdot)\)	1632.dx	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1632}(41,\cdot)\)	1632.en	16	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)
\(\chi_{1632}(43,\cdot)\)	1632.bw	8	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1632}(47,\cdot)\)	1632.y	4	no	\(1\)	\(1\)	\(i\)	\(i\)	\(i\)	\(-1\)	\(-1\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(-1\)
\(\chi_{1632}(49,\cdot)\)	1632.cu	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)
\(\chi_{1632}(53,\cdot)\)	1632.bo	8	yes	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1632}(55,\cdot)\)	1632.q	4	no	\(-1\)	\(1\)	\(-1\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(i\)	\(1\)	\(1\)	\(i\)	\(-i\)
\(\chi_{1632}(59,\cdot)\)	1632.db	8	yes	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1632}(61,\cdot)\)	1632.dx	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{1632}(65,\cdot)\)	1632.dt	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)
\(\chi_{1632}(67,\cdot)\)	1632.cp	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1632}(71,\cdot)\)	1632.ep	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)
\(\chi_{1632}(73,\cdot)\)	1632.dk	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)
\(\chi_{1632}(77,\cdot)\)	1632.di	8	yes	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{1632}(79,\cdot)\)	1632.ef	16	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(1\)
\(\chi_{1632}(83,\cdot)\)	1632.db	8	yes	\(1\)	\(1\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1632}(89,\cdot)\)	1632.t	4	no	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(-i\)	\(i\)	\(i\)	\(1\)	\(1\)	\(-i\)	\(i\)
\(\chi_{1632}(91,\cdot)\)	1632.dp	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1632}(95,\cdot)\)	1632.eh	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)
\(\chi_{1632}(97,\cdot)\)	1632.ee	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(1\)
\(\chi_{1632}(101,\cdot)\)	1632.cl	8	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Downloads

Learn more

Character group

First 32 of 512 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.