LMFDB - Group of Dirichlet characters of modulus 256

Show commands: PariGP / SageMath

sage: H = DirichletGroup(256)

pari: g = idealstar(,256,2)

Character group

sage: G.order() pari: g.no
Order	=	128
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{64}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{256}(255,\cdot)$, $\chi_{256}(5,\cdot)$

First 32 of 128 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{256}(1,\cdot)$	256.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{256}(3,\cdot)$	256.n	64	yes	$-1$	$1$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{39}{64}\right)$
$\chi_{256}(5,\cdot)$	256.m	64	yes	$1$	$1$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{45}{64}\right)$
$\chi_{256}(7,\cdot)$	256.l	32	no	$-1$	$1$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{1}{32}\right)$
$\chi_{256}(9,\cdot)$	256.k	32	no	$1$	$1$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{7}{32}\right)$
$\chi_{256}(11,\cdot)$	256.n	64	yes	$-1$	$1$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{49}{64}\right)$
$\chi_{256}(13,\cdot)$	256.m	64	yes	$1$	$1$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{3}{64}\right)$
$\chi_{256}(15,\cdot)$	256.j	16	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$-i$	$-i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$
$\chi_{256}(17,\cdot)$	256.i	16	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$i$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{256}(19,\cdot)$	256.n	64	yes	$-1$	$1$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{11}{64}\right)$
$\chi_{256}(21,\cdot)$	256.m	64	yes	$1$	$1$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{41}{64}\right)$
$\chi_{256}(23,\cdot)$	256.l	32	no	$-1$	$1$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{27}{32}\right)$
$\chi_{256}(25,\cdot)$	256.k	32	no	$1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{13}{32}\right)$
$\chi_{256}(27,\cdot)$	256.n	64	yes	$-1$	$1$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{53}{64}\right)$
$\chi_{256}(29,\cdot)$	256.m	64	yes	$1$	$1$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{31}{64}\right)$
$\chi_{256}(31,\cdot)$	256.h	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{256}(33,\cdot)$	256.g	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$-1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{256}(35,\cdot)$	256.n	64	yes	$-1$	$1$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{47}{64}\right)$
$\chi_{256}(37,\cdot)$	256.m	64	yes	$1$	$1$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{37}{64}\right)$
$\chi_{256}(39,\cdot)$	256.l	32	no	$-1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{21}{32}\right)$
$\chi_{256}(41,\cdot)$	256.k	32	no	$1$	$1$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{19}{32}\right)$
$\chi_{256}(43,\cdot)$	256.n	64	yes	$-1$	$1$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{57}{64}\right)$
$\chi_{256}(45,\cdot)$	256.m	64	yes	$1$	$1$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{59}{64}\right)$
$\chi_{256}(47,\cdot)$	256.j	16	no	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$i$	$i$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{256}(49,\cdot)$	256.i	16	no	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$i$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{256}(51,\cdot)$	256.n	64	yes	$-1$	$1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{19}{64}\right)$
$\chi_{256}(53,\cdot)$	256.m	64	yes	$1$	$1$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{33}{64}\right)$
$\chi_{256}(55,\cdot)$	256.l	32	no	$-1$	$1$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{15}{32}\right)$
$\chi_{256}(57,\cdot)$	256.k	32	no	$1$	$1$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{25}{32}\right)$
$\chi_{256}(59,\cdot)$	256.n	64	yes	$-1$	$1$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{61}{64}\right)$
$\chi_{256}(61,\cdot)$	256.m	64	yes	$1$	$1$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{23}{64}\right)$
$\chi_{256}(63,\cdot)$	256.f	4	no	$-1$	$1$	$i$	$i$	$1$	$-1$	$-i$	$-i$	$-1$	$1$	$i$	$i$

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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	$256$
Structure	\(C_{2}\times C_{64}\)
Order	$128$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{256}(1,\cdot)\)	256.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{256}(3,\cdot)\)	256.n	64	yes	\(-1\)	\(1\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)
\(\chi_{256}(5,\cdot)\)	256.m	64	yes	\(1\)	\(1\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)
\(\chi_{256}(7,\cdot)\)	256.l	32	no	\(-1\)	\(1\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)
\(\chi_{256}(9,\cdot)\)	256.k	32	no	\(1\)	\(1\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)
\(\chi_{256}(11,\cdot)\)	256.n	64	yes	\(-1\)	\(1\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{49}{64}\right)\)
\(\chi_{256}(13,\cdot)\)	256.m	64	yes	\(1\)	\(1\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)
\(\chi_{256}(15,\cdot)\)	256.j	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)
\(\chi_{256}(17,\cdot)\)	256.i	16	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{256}(19,\cdot)\)	256.n	64	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{11}{64}\right)\)
\(\chi_{256}(21,\cdot)\)	256.m	64	yes	\(1\)	\(1\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)
\(\chi_{256}(23,\cdot)\)	256.l	32	no	\(-1\)	\(1\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)
\(\chi_{256}(25,\cdot)\)	256.k	32	no	\(1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)
\(\chi_{256}(27,\cdot)\)	256.n	64	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)
\(\chi_{256}(29,\cdot)\)	256.m	64	yes	\(1\)	\(1\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)
\(\chi_{256}(31,\cdot)\)	256.h	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{256}(33,\cdot)\)	256.g	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{256}(35,\cdot)\)	256.n	64	yes	\(-1\)	\(1\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)
\(\chi_{256}(37,\cdot)\)	256.m	64	yes	\(1\)	\(1\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{37}{64}\right)\)
\(\chi_{256}(39,\cdot)\)	256.l	32	no	\(-1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)
\(\chi_{256}(41,\cdot)\)	256.k	32	no	\(1\)	\(1\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)
\(\chi_{256}(43,\cdot)\)	256.n	64	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{57}{64}\right)\)
\(\chi_{256}(45,\cdot)\)	256.m	64	yes	\(1\)	\(1\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)
\(\chi_{256}(47,\cdot)\)	256.j	16	no	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(i\)	\(i\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{256}(49,\cdot)\)	256.i	16	no	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{256}(51,\cdot)\)	256.n	64	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)
\(\chi_{256}(53,\cdot)\)	256.m	64	yes	\(1\)	\(1\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{33}{64}\right)\)
\(\chi_{256}(55,\cdot)\)	256.l	32	no	\(-1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)
\(\chi_{256}(57,\cdot)\)	256.k	32	no	\(1\)	\(1\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)
\(\chi_{256}(59,\cdot)\)	256.n	64	yes	\(-1\)	\(1\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)
\(\chi_{256}(61,\cdot)\)	256.m	64	yes	\(1\)	\(1\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)
\(\chi_{256}(63,\cdot)\)	256.f	4	no	\(-1\)	\(1\)	\(i\)	\(i\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(1\)	\(i\)	\(i\)

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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.