LMFDB - Group of Dirichlet characters of modulus 64

Show commands: PariGP / SageMath

sage: H = DirichletGroup(64)

pari: g = idealstar(,64,2)

Character group

sage: G.order() pari: g.no
Order	=	32
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{16}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{64}(63,\cdot)$, $\chi_{64}(5,\cdot)$

First 32 of 32 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{64}(1,\cdot)$	64.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{64}(3,\cdot)$	64.j	16	yes	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{64}(5,\cdot)$	64.i	16	yes	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$-i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{64}(7,\cdot)$	64.h	8	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{64}(9,\cdot)$	64.g	8	no	$1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{64}(11,\cdot)$	64.j	16	yes	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-i$	$-i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{64}(13,\cdot)$	64.i	16	yes	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{64}(15,\cdot)$	64.f	4	no	$-1$	$1$	$i$	$i$	$1$	$-1$	$-i$	$-i$	$-1$	$1$	$i$	$i$
$\chi_{64}(17,\cdot)$	64.e	4	no	$1$	$1$	$i$	$-i$	$-1$	$-1$	$-i$	$i$	$1$	$1$	$i$	$-i$
$\chi_{64}(19,\cdot)$	64.j	16	yes	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$	$i$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{64}(21,\cdot)$	64.i	16	yes	$1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$-i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{64}(23,\cdot)$	64.h	8	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{64}(25,\cdot)$	64.g	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{64}(27,\cdot)$	64.j	16	yes	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-i$	$-i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{64}(29,\cdot)$	64.i	16	yes	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{64}(31,\cdot)$	64.d	2	no	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$
$\chi_{64}(33,\cdot)$	64.b	2	no	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$	$1$	$1$	$-1$	$-1$
$\chi_{64}(35,\cdot)$	64.j	16	yes	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$i$	$i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{64}(37,\cdot)$	64.i	16	yes	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$-i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{64}(39,\cdot)$	64.h	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{64}(41,\cdot)$	64.g	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{64}(43,\cdot)$	64.j	16	yes	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-i$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$
$\chi_{64}(45,\cdot)$	64.i	16	yes	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{64}(47,\cdot)$	64.f	4	no	$-1$	$1$	$-i$	$-i$	$1$	$-1$	$i$	$i$	$-1$	$1$	$-i$	$-i$
$\chi_{64}(49,\cdot)$	64.e	4	no	$1$	$1$	$-i$	$i$	$-1$	$-1$	$i$	$-i$	$1$	$1$	$-i$	$i$
$\chi_{64}(51,\cdot)$	64.j	16	yes	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$i$	$i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{64}(53,\cdot)$	64.i	16	yes	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{64}(55,\cdot)$	64.h	8	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{64}(57,\cdot)$	64.g	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{64}(59,\cdot)$	64.j	16	yes	$-1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$	$-i$	$-i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{64}(61,\cdot)$	64.i	16	yes	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-i$	$i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{64}(63,\cdot)$	64.c	2	no	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$

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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	$64$
Structure	\(C_{2}\times C_{16}\)
Order	$32$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{64}(1,\cdot)\)	64.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{64}(3,\cdot)\)	64.j	16	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{64}(5,\cdot)\)	64.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{64}(7,\cdot)\)	64.h	8	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{64}(9,\cdot)\)	64.g	8	no	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{64}(11,\cdot)\)	64.j	16	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{64}(13,\cdot)\)	64.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{64}(15,\cdot)\)	64.f	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(i\)
\(\chi_{64}(17,\cdot)\)	64.e	4	no	\(1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(i\)	\(1\)	\(1\)	\(i\)	\(-i\)
\(\chi_{64}(19,\cdot)\)	64.j	16	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(i\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{64}(21,\cdot)\)	64.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{64}(23,\cdot)\)	64.h	8	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{64}(25,\cdot)\)	64.g	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{64}(27,\cdot)\)	64.j	16	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{64}(29,\cdot)\)	64.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{64}(31,\cdot)\)	64.d	2	no	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)
\(\chi_{64}(33,\cdot)\)	64.b	2	no	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{64}(35,\cdot)\)	64.j	16	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(i\)	\(i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{64}(37,\cdot)\)	64.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{64}(39,\cdot)\)	64.h	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{64}(41,\cdot)\)	64.g	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{64}(43,\cdot)\)	64.j	16	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{64}(45,\cdot)\)	64.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{64}(47,\cdot)\)	64.f	4	no	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(-1\)	\(i\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(-i\)
\(\chi_{64}(49,\cdot)\)	64.e	4	no	\(1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(1\)	\(1\)	\(-i\)	\(i\)
\(\chi_{64}(51,\cdot)\)	64.j	16	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(i\)	\(i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{64}(53,\cdot)\)	64.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{64}(55,\cdot)\)	64.h	8	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{64}(57,\cdot)\)	64.g	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{64}(59,\cdot)\)	64.j	16	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{64}(61,\cdot)\)	64.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{64}(63,\cdot)\)	64.c	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)

Introduction

L-functions

Modular forms

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Fields

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Character group

First 32 of 32 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.