LMFDB - Group of Dirichlet characters of modulus 51

Show commands: PariGP / SageMath

sage: H = DirichletGroup(51)

pari: g = idealstar(,51,2)

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	=	$\chi_{51}(35,\cdot)$, $\chi_{51}(37,\cdot)$

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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{51}(1,\cdot)$	51.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{51}(2,\cdot)$	51.g	8	yes	$-1$	$1$	$-i$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$1$
$\chi_{51}(4,\cdot)$	51.e	4	no	$1$	$1$	$-1$	$1$	$-i$	$i$	$-1$	$i$	$i$	$1$	$-i$	$1$
$\chi_{51}(5,\cdot)$	51.i	16	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{5}{16}\right)$	$-1$
$\chi_{51}(7,\cdot)$	51.j	16	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$-1$
$\chi_{51}(8,\cdot)$	51.g	8	yes	$-1$	$1$	$i$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$1$
$\chi_{51}(10,\cdot)$	51.j	16	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{11}{16}\right)$	$-1$
$\chi_{51}(11,\cdot)$	51.i	16	yes	$1$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{7}{16}\right)$	$-1$
$\chi_{51}(13,\cdot)$	51.e	4	no	$1$	$1$	$-1$	$1$	$i$	$-i$	$-1$	$-i$	$-i$	$1$	$i$	$1$
$\chi_{51}(14,\cdot)$	51.i	16	yes	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$-1$
$\chi_{51}(16,\cdot)$	51.d	2	no	$1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$-1$	$-1$	$1$	$-1$	$1$
$\chi_{51}(19,\cdot)$	51.h	8	no	$1$	$1$	$i$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$1$
$\chi_{51}(20,\cdot)$	51.i	16	yes	$1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$e\left(\frac{1}{16}\right)$	$-1$
$\chi_{51}(22,\cdot)$	51.j	16	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$e\left(\frac{13}{16}\right)$	$-1$
$\chi_{51}(23,\cdot)$	51.i	16	yes	$1$	$1$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$e\left(\frac{15}{16}\right)$	$-1$
$\chi_{51}(25,\cdot)$	51.h	8	no	$1$	$1$	$-i$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$
$\chi_{51}(26,\cdot)$	51.g	8	yes	$-1$	$1$	$i$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$1$
$\chi_{51}(28,\cdot)$	51.j	16	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$e\left(\frac{15}{16}\right)$	$-1$
$\chi_{51}(29,\cdot)$	51.i	16	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$e\left(\frac{13}{16}\right)$	$-1$
$\chi_{51}(31,\cdot)$	51.j	16	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{15}{16}\right)$	$i$	$e\left(\frac{1}{16}\right)$	$-1$
$\chi_{51}(32,\cdot)$	51.g	8	yes	$-1$	$1$	$-i$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$1$
$\chi_{51}(35,\cdot)$	51.b	2	no	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$1$
$\chi_{51}(37,\cdot)$	51.j	16	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$-1$
$\chi_{51}(38,\cdot)$	51.f	4	yes	$-1$	$1$	$1$	$1$	$i$	$i$	$1$	$i$	$-i$	$1$	$i$	$1$
$\chi_{51}(40,\cdot)$	51.j	16	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{7}{16}\right)$	$-1$
$\chi_{51}(41,\cdot)$	51.i	16	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{11}{16}\right)$	$-1$
$\chi_{51}(43,\cdot)$	51.h	8	no	$1$	$1$	$-i$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{1}{8}\right)$	$1$
$\chi_{51}(44,\cdot)$	51.i	16	yes	$1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{16}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$-1$
$\chi_{51}(46,\cdot)$	51.j	16	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$e\left(\frac{5}{16}\right)$	$-1$
$\chi_{51}(47,\cdot)$	51.f	4	yes	$-1$	$1$	$1$	$1$	$-i$	$-i$	$1$	$-i$	$i$	$1$	$-i$	$1$
$\chi_{51}(49,\cdot)$	51.h	8	no	$1$	$1$	$i$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$1$
$\chi_{51}(50,\cdot)$	51.c	2	yes	$-1$	$1$	$-1$	$1$	$1$	$-1$	$-1$	$-1$	$1$	$1$	$1$	$1$

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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	$51$
Structure	\(C_{2}\times C_{16}\)
Order	$32$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{51}(1,\cdot)\)	51.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{51}(2,\cdot)\)	51.g	8	yes	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)
\(\chi_{51}(4,\cdot)\)	51.e	4	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(1\)	\(-i\)	\(1\)
\(\chi_{51}(5,\cdot)\)	51.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)
\(\chi_{51}(7,\cdot)\)	51.j	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)
\(\chi_{51}(8,\cdot)\)	51.g	8	yes	\(-1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(1\)
\(\chi_{51}(10,\cdot)\)	51.j	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)
\(\chi_{51}(11,\cdot)\)	51.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)
\(\chi_{51}(13,\cdot)\)	51.e	4	no	\(1\)	\(1\)	\(-1\)	\(1\)	\(i\)	\(-i\)	\(-1\)	\(-i\)	\(-i\)	\(1\)	\(i\)	\(1\)
\(\chi_{51}(14,\cdot)\)	51.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)
\(\chi_{51}(16,\cdot)\)	51.d	2	no	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{51}(19,\cdot)\)	51.h	8	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(1\)
\(\chi_{51}(20,\cdot)\)	51.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(i\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)
\(\chi_{51}(22,\cdot)\)	51.j	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)
\(\chi_{51}(23,\cdot)\)	51.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)
\(\chi_{51}(25,\cdot)\)	51.h	8	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)
\(\chi_{51}(26,\cdot)\)	51.g	8	yes	\(-1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)
\(\chi_{51}(28,\cdot)\)	51.j	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(-1\)
\(\chi_{51}(29,\cdot)\)	51.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)	\(e\left(\frac{13}{16}\right)\)	\(-1\)
\(\chi_{51}(31,\cdot)\)	51.j	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(i\)	\(e\left(\frac{1}{16}\right)\)	\(-1\)
\(\chi_{51}(32,\cdot)\)	51.g	8	yes	\(-1\)	\(1\)	\(-i\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(1\)
\(\chi_{51}(35,\cdot)\)	51.b	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)
\(\chi_{51}(37,\cdot)\)	51.j	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(-1\)
\(\chi_{51}(38,\cdot)\)	51.f	4	yes	\(-1\)	\(1\)	\(1\)	\(1\)	\(i\)	\(i\)	\(1\)	\(i\)	\(-i\)	\(1\)	\(i\)	\(1\)
\(\chi_{51}(40,\cdot)\)	51.j	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)
\(\chi_{51}(41,\cdot)\)	51.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{11}{16}\right)\)	\(-1\)
\(\chi_{51}(43,\cdot)\)	51.h	8	no	\(1\)	\(1\)	\(-i\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(1\)
\(\chi_{51}(44,\cdot)\)	51.i	16	yes	\(1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)
\(\chi_{51}(46,\cdot)\)	51.j	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)
\(\chi_{51}(47,\cdot)\)	51.f	4	yes	\(-1\)	\(1\)	\(1\)	\(1\)	\(-i\)	\(-i\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(-i\)	\(1\)
\(\chi_{51}(49,\cdot)\)	51.h	8	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)
\(\chi_{51}(50,\cdot)\)	51.c	2	yes	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.