LMFDB - Group of Dirichlet characters of modulus 768

Show commands: PariGP / SageMath

sage: H = DirichletGroup(768)

pari: g = idealstar(,768,2)

Character group

sage: G.order() pari: g.no
Order	=	256
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{64}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{768}(511,\cdot)$, $\chi_{768}(517,\cdot)$, $\chi_{768}(257,\cdot)$

First 32 of 256 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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{768}(1,\cdot)$	768.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{768}(5,\cdot)$	768.y	64	yes	$-1$	$1$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{768}(7,\cdot)$	768.u	32	no	$-1$	$1$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{32}\right)$	$-i$
$\chi_{768}(11,\cdot)$	768.ba	64	yes	$1$	$1$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{768}(13,\cdot)$	768.z	64	no	$1$	$1$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{768}(17,\cdot)$	768.q	16	no	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$-1$
$\chi_{768}(19,\cdot)$	768.bb	64	no	$-1$	$1$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{768}(23,\cdot)$	768.w	32	no	$1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{32}\right)$	$i$
$\chi_{768}(25,\cdot)$	768.v	32	no	$1$	$1$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{27}{32}\right)$	$i$
$\chi_{768}(29,\cdot)$	768.y	64	yes	$-1$	$1$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{768}(31,\cdot)$	768.m	8	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$i$	$i$	$e\left(\frac{3}{8}\right)$	$-1$
$\chi_{768}(35,\cdot)$	768.ba	64	yes	$1$	$1$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{768}(37,\cdot)$	768.z	64	no	$1$	$1$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{768}(41,\cdot)$	768.x	32	no	$-1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{21}{32}\right)$	$-i$
$\chi_{768}(43,\cdot)$	768.bb	64	no	$-1$	$1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{768}(47,\cdot)$	768.s	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{16}\right)$	$1$
$\chi_{768}(49,\cdot)$	768.r	16	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{16}\right)$	$-1$
$\chi_{768}(53,\cdot)$	768.y	64	yes	$-1$	$1$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{768}(55,\cdot)$	768.u	32	no	$-1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{9}{32}\right)$	$i$
$\chi_{768}(59,\cdot)$	768.ba	64	yes	$1$	$1$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{768}(61,\cdot)$	768.z	64	no	$1$	$1$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{768}(65,\cdot)$	768.i	4	no	$-1$	$1$	$i$	$-1$	$i$	$i$	$-1$	$i$	$1$	$-1$	$-i$	$1$
$\chi_{768}(67,\cdot)$	768.bb	64	no	$-1$	$1$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{768}(71,\cdot)$	768.w	32	no	$1$	$1$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{32}\right)$	$-i$
$\chi_{768}(73,\cdot)$	768.v	32	no	$1$	$1$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{25}{32}\right)$	$-i$
$\chi_{768}(77,\cdot)$	768.y	64	yes	$-1$	$1$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{768}(79,\cdot)$	768.t	16	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$1$
$\chi_{768}(83,\cdot)$	768.ba	64	yes	$1$	$1$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{768}(85,\cdot)$	768.z	64	no	$1$	$1$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{768}(89,\cdot)$	768.x	32	no	$-1$	$1$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{19}{32}\right)$	$i$
$\chi_{768}(91,\cdot)$	768.bb	64	no	$-1$	$1$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{768}(95,\cdot)$	768.o	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$-i$	$e\left(\frac{5}{8}\right)$	$-1$

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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	$768$
Structure	\(C_{2}\times C_{2}\times C_{64}\)
Order	$256$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{768}(1,\cdot)\)	768.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{768}(5,\cdot)\)	768.y	64	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{768}(7,\cdot)\)	768.u	32	no	\(-1\)	\(1\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(-i\)
\(\chi_{768}(11,\cdot)\)	768.ba	64	yes	\(1\)	\(1\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{768}(13,\cdot)\)	768.z	64	no	\(1\)	\(1\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{768}(17,\cdot)\)	768.q	16	no	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)
\(\chi_{768}(19,\cdot)\)	768.bb	64	no	\(-1\)	\(1\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{768}(23,\cdot)\)	768.w	32	no	\(1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(i\)
\(\chi_{768}(25,\cdot)\)	768.v	32	no	\(1\)	\(1\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(i\)
\(\chi_{768}(29,\cdot)\)	768.y	64	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{768}(31,\cdot)\)	768.m	8	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(-1\)
\(\chi_{768}(35,\cdot)\)	768.ba	64	yes	\(1\)	\(1\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{768}(37,\cdot)\)	768.z	64	no	\(1\)	\(1\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{768}(41,\cdot)\)	768.x	32	no	\(-1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(-i\)
\(\chi_{768}(43,\cdot)\)	768.bb	64	no	\(-1\)	\(1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{768}(47,\cdot)\)	768.s	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(1\)
\(\chi_{768}(49,\cdot)\)	768.r	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-1\)
\(\chi_{768}(53,\cdot)\)	768.y	64	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{768}(55,\cdot)\)	768.u	32	no	\(-1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(i\)
\(\chi_{768}(59,\cdot)\)	768.ba	64	yes	\(1\)	\(1\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{768}(61,\cdot)\)	768.z	64	no	\(1\)	\(1\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{768}(65,\cdot)\)	768.i	4	no	\(-1\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(-1\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(1\)
\(\chi_{768}(67,\cdot)\)	768.bb	64	no	\(-1\)	\(1\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{768}(71,\cdot)\)	768.w	32	no	\(1\)	\(1\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(-i\)
\(\chi_{768}(73,\cdot)\)	768.v	32	no	\(1\)	\(1\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(-i\)
\(\chi_{768}(77,\cdot)\)	768.y	64	yes	\(-1\)	\(1\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{768}(79,\cdot)\)	768.t	16	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)
\(\chi_{768}(83,\cdot)\)	768.ba	64	yes	\(1\)	\(1\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{768}(85,\cdot)\)	768.z	64	no	\(1\)	\(1\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{768}(89,\cdot)\)	768.x	32	no	\(-1\)	\(1\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(i\)
\(\chi_{768}(91,\cdot)\)	768.bb	64	no	\(-1\)	\(1\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{768}(95,\cdot)\)	768.o	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)

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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.