LMFDB - Group of Dirichlet characters of modulus 1088

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1088)

pari: g = idealstar(,1088,2)

Character group

sage: G.order() pari: g.no
Order	=	512
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{16}\times C_{16}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1088}(511,\cdot)$, $\chi_{1088}(69,\cdot)$, $\chi_{1088}(513,\cdot)$

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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$19$	$21$	$23$
$\chi_{1088}(1,\cdot)$	1088.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1088}(3,\cdot)$	1088.bv	16	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{1}{16}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{1088}(5,\cdot)$	1088.bt	16	yes	$-1$	$1$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{16}\right)$	$1$	$-1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{1088}(7,\cdot)$	1088.cg	16	no	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{1088}(9,\cdot)$	1088.bp	8	no	$1$	$1$	$i$	$1$	$e\left(\frac{1}{8}\right)$	$-1$	$-i$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{1088}(11,\cdot)$	1088.bv	16	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{7}{16}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{1088}(13,\cdot)$	1088.cs	16	yes	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1088}(15,\cdot)$	1088.bf	8	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$i$	$-i$	$-1$	$-i$	$e\left(\frac{5}{8}\right)$
$\chi_{1088}(19,\cdot)$	1088.bw	16	yes	$-1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-i$
$\chi_{1088}(21,\cdot)$	1088.cs	16	yes	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1088}(23,\cdot)$	1088.cr	16	no	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1088}(25,\cdot)$	1088.bq	8	no	$1$	$1$	$1$	$i$	$e\left(\frac{1}{8}\right)$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{1088}(27,\cdot)$	1088.bv	16	yes	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{3}{16}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{1088}(29,\cdot)$	1088.ck	16	yes	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{13}{16}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1088}(31,\cdot)$	1088.cy	16	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{15}{16}\right)$
$\chi_{1088}(33,\cdot)$	1088.h	2	no	$1$	$1$	$1$	$1$	$-1$	$1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$
$\chi_{1088}(35,\cdot)$	1088.db	16	no	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{1088}(37,\cdot)$	1088.cb	16	yes	$-1$	$1$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1088}(39,\cdot)$	1088.cx	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{1088}(41,\cdot)$	1088.cw	16	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{1088}(43,\cdot)$	1088.di	16	yes	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$
$\chi_{1088}(45,\cdot)$	1088.bz	16	yes	$-1$	$1$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$-1$	$i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{1088}(47,\cdot)$	1088.t	4	no	$-1$	$1$	$1$	$1$	$-i$	$1$	$1$	$i$	$1$	$i$	$-i$	$-i$
$\chi_{1088}(49,\cdot)$	1088.bg	8	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$i$	$i$	$1$	$-i$	$e\left(\frac{1}{8}\right)$
$\chi_{1088}(53,\cdot)$	1088.ce	16	yes	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-1$
$\chi_{1088}(55,\cdot)$	1088.y	8	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$
$\chi_{1088}(57,\cdot)$	1088.ch	16	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{1088}(59,\cdot)$	1088.di	16	yes	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$
$\chi_{1088}(61,\cdot)$	1088.bz	16	yes	$-1$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$-1$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{1088}(63,\cdot)$	1088.cp	16	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{11}{16}\right)$
$\chi_{1088}(65,\cdot)$	1088.cz	16	no	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{7}{16}\right)$
$\chi_{1088}(67,\cdot)$	1088.cm	16	yes	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$

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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	$1088$
Structure	\(C_{2}\times C_{16}\times C_{16}\)
Order	$512$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(19\)	\(21\)	\(23\)
\(\chi_{1088}(1,\cdot)\)	1088.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1088}(3,\cdot)\)	1088.bv	16	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{16}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{1088}(5,\cdot)\)	1088.bt	16	yes	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{1088}(7,\cdot)\)	1088.cg	16	no	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{1088}(9,\cdot)\)	1088.bp	8	no	\(1\)	\(1\)	\(i\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{1088}(11,\cdot)\)	1088.bv	16	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{1088}(13,\cdot)\)	1088.cs	16	yes	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1088}(15,\cdot)\)	1088.bf	8	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1088}(19,\cdot)\)	1088.bw	16	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)
\(\chi_{1088}(21,\cdot)\)	1088.cs	16	yes	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1088}(23,\cdot)\)	1088.cr	16	no	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1088}(25,\cdot)\)	1088.bq	8	no	\(1\)	\(1\)	\(1\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{1088}(27,\cdot)\)	1088.bv	16	yes	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{1088}(29,\cdot)\)	1088.ck	16	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{13}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1088}(31,\cdot)\)	1088.cy	16	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1088}(33,\cdot)\)	1088.h	2	no	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)
\(\chi_{1088}(35,\cdot)\)	1088.db	16	no	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{1088}(37,\cdot)\)	1088.cb	16	yes	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1088}(39,\cdot)\)	1088.cx	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1088}(41,\cdot)\)	1088.cw	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{1088}(43,\cdot)\)	1088.di	16	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)
\(\chi_{1088}(45,\cdot)\)	1088.bz	16	yes	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{1088}(47,\cdot)\)	1088.t	4	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(-i\)	\(1\)	\(1\)	\(i\)	\(1\)	\(i\)	\(-i\)	\(-i\)
\(\chi_{1088}(49,\cdot)\)	1088.bg	8	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(i\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{1088}(53,\cdot)\)	1088.ce	16	yes	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)
\(\chi_{1088}(55,\cdot)\)	1088.y	8	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)
\(\chi_{1088}(57,\cdot)\)	1088.ch	16	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{1088}(59,\cdot)\)	1088.di	16	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)
\(\chi_{1088}(61,\cdot)\)	1088.bz	16	yes	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{1088}(63,\cdot)\)	1088.cp	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{1088}(65,\cdot)\)	1088.cz	16	no	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{1088}(67,\cdot)\)	1088.cm	16	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)

Introduction

L-functions

Modular forms

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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.