LMFDB - Group of Dirichlet characters of modulus 512

Show commands: PariGP / SageMath

sage: H = DirichletGroup(512)

pari: g = idealstar(,512,2)

Character group

sage: G.order() pari: g.no
Order	=	256
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{128}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{512}(511,\cdot)$, $\chi_{512}(5,\cdot)$

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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{512}(1,\cdot)$	512.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{512}(3,\cdot)$	512.p	128	yes	$-1$	$1$	$e\left(\frac{9}{128}\right)$	$e\left(\frac{35}{128}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{95}{128}\right)$	$e\left(\frac{45}{128}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{101}{128}\right)$	$e\left(\frac{103}{128}\right)$
$\chi_{512}(5,\cdot)$	512.o	128	yes	$1$	$1$	$e\left(\frac{35}{128}\right)$	$e\left(\frac{1}{128}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{85}{128}\right)$	$e\left(\frac{111}{128}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{23}{128}\right)$	$e\left(\frac{109}{128}\right)$
$\chi_{512}(7,\cdot)$	512.n	64	no	$-1$	$1$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{1}{64}\right)$
$\chi_{512}(9,\cdot)$	512.m	64	no	$1$	$1$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{39}{64}\right)$
$\chi_{512}(11,\cdot)$	512.p	128	yes	$-1$	$1$	$e\left(\frac{95}{128}\right)$	$e\left(\frac{85}{128}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{121}{128}\right)$	$e\left(\frac{91}{128}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{99}{128}\right)$	$e\left(\frac{49}{128}\right)$
$\chi_{512}(13,\cdot)$	512.o	128	yes	$1$	$1$	$e\left(\frac{45}{128}\right)$	$e\left(\frac{111}{128}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{91}{128}\right)$	$e\left(\frac{33}{128}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{121}{128}\right)$	$e\left(\frac{67}{128}\right)$
$\chi_{512}(15,\cdot)$	512.l	32	no	$-1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{21}{32}\right)$
$\chi_{512}(17,\cdot)$	512.k	32	no	$1$	$1$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{27}{32}\right)$
$\chi_{512}(19,\cdot)$	512.p	128	yes	$-1$	$1$	$e\left(\frac{101}{128}\right)$	$e\left(\frac{23}{128}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{99}{128}\right)$	$e\left(\frac{121}{128}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{81}{128}\right)$	$e\left(\frac{75}{128}\right)$
$\chi_{512}(21,\cdot)$	512.o	128	yes	$1$	$1$	$e\left(\frac{103}{128}\right)$	$e\left(\frac{109}{128}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{49}{128}\right)$	$e\left(\frac{67}{128}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{75}{128}\right)$	$e\left(\frac{105}{128}\right)$
$\chi_{512}(23,\cdot)$	512.n	64	no	$-1$	$1$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{59}{64}\right)$
$\chi_{512}(25,\cdot)$	512.m	64	no	$1$	$1$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{45}{64}\right)$
$\chi_{512}(27,\cdot)$	512.p	128	yes	$-1$	$1$	$e\left(\frac{27}{128}\right)$	$e\left(\frac{105}{128}\right)$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{29}{128}\right)$	$e\left(\frac{7}{128}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{47}{128}\right)$	$e\left(\frac{53}{128}\right)$
$\chi_{512}(29,\cdot)$	512.o	128	yes	$1$	$1$	$e\left(\frac{81}{128}\right)$	$e\left(\frac{123}{128}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{87}{128}\right)$	$e\left(\frac{85}{128}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{13}{128}\right)$	$e\left(\frac{95}{128}\right)$
$\chi_{512}(31,\cdot)$	512.j	16	no	$-1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$	$-i$	$-i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$
$\chi_{512}(33,\cdot)$	512.i	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{512}(35,\cdot)$	512.p	128	yes	$-1$	$1$	$e\left(\frac{1}{128}\right)$	$e\left(\frac{75}{128}\right)$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{39}{128}\right)$	$e\left(\frac{5}{128}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{125}{128}\right)$	$e\left(\frac{111}{128}\right)$
$\chi_{512}(37,\cdot)$	512.o	128	yes	$1$	$1$	$e\left(\frac{107}{128}\right)$	$e\left(\frac{25}{128}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{77}{128}\right)$	$e\left(\frac{87}{128}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{63}{128}\right)$	$e\left(\frac{37}{128}\right)$
$\chi_{512}(39,\cdot)$	512.n	64	no	$-1$	$1$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{21}{64}\right)$
$\chi_{512}(41,\cdot)$	512.m	64	no	$1$	$1$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{19}{64}\right)$
$\chi_{512}(43,\cdot)$	512.p	128	yes	$-1$	$1$	$e\left(\frac{23}{128}\right)$	$e\left(\frac{61}{128}\right)$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{1}{128}\right)$	$e\left(\frac{115}{128}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{59}{128}\right)$	$e\left(\frac{121}{128}\right)$
$\chi_{512}(45,\cdot)$	512.o	128	yes	$1$	$1$	$e\left(\frac{53}{128}\right)$	$e\left(\frac{71}{128}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{19}{128}\right)$	$e\left(\frac{73}{128}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{97}{128}\right)$	$e\left(\frac{59}{128}\right)$
$\chi_{512}(47,\cdot)$	512.l	32	no	$-1$	$1$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{15}{32}\right)$
$\chi_{512}(49,\cdot)$	512.k	32	no	$1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{1}{32}\right)$
$\chi_{512}(51,\cdot)$	512.p	128	yes	$-1$	$1$	$e\left(\frac{93}{128}\right)$	$e\left(\frac{63}{128}\right)$	$e\left(\frac{59}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{43}{128}\right)$	$e\left(\frac{81}{128}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{105}{128}\right)$	$e\left(\frac{83}{128}\right)$
$\chi_{512}(53,\cdot)$	512.o	128	yes	$1$	$1$	$e\left(\frac{47}{128}\right)$	$e\left(\frac{5}{128}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{41}{128}\right)$	$e\left(\frac{43}{128}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{115}{128}\right)$	$e\left(\frac{33}{128}\right)$
$\chi_{512}(55,\cdot)$	512.n	64	no	$-1$	$1$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{39}{64}\right)$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{15}{64}\right)$
$\chi_{512}(57,\cdot)$	512.m	64	no	$1$	$1$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{25}{64}\right)$
$\chi_{512}(59,\cdot)$	512.p	128	yes	$-1$	$1$	$e\left(\frac{83}{128}\right)$	$e\left(\frac{81}{128}\right)$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{37}{128}\right)$	$e\left(\frac{31}{128}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{7}{128}\right)$	$e\left(\frac{125}{128}\right)$
$\chi_{512}(61,\cdot)$	512.o	128	yes	$1$	$1$	$e\left(\frac{89}{128}\right)$	$e\left(\frac{83}{128}\right)$	$e\left(\frac{63}{64}\right)$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{15}{128}\right)$	$e\left(\frac{125}{128}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{117}{128}\right)$	$e\left(\frac{87}{128}\right)$
$\chi_{512}(63,\cdot)$	512.h	8	no	$-1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-i$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$

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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	$512$
Structure	\(C_{2}\times C_{128}\)
Order	$256$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{512}(1,\cdot)\)	512.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{512}(3,\cdot)\)	512.p	128	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{128}\right)\)	\(e\left(\frac{35}{128}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{95}{128}\right)\)	\(e\left(\frac{45}{128}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{101}{128}\right)\)	\(e\left(\frac{103}{128}\right)\)
\(\chi_{512}(5,\cdot)\)	512.o	128	yes	\(1\)	\(1\)	\(e\left(\frac{35}{128}\right)\)	\(e\left(\frac{1}{128}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{85}{128}\right)\)	\(e\left(\frac{111}{128}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{23}{128}\right)\)	\(e\left(\frac{109}{128}\right)\)
\(\chi_{512}(7,\cdot)\)	512.n	64	no	\(-1\)	\(1\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{1}{64}\right)\)
\(\chi_{512}(9,\cdot)\)	512.m	64	no	\(1\)	\(1\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)
\(\chi_{512}(11,\cdot)\)	512.p	128	yes	\(-1\)	\(1\)	\(e\left(\frac{95}{128}\right)\)	\(e\left(\frac{85}{128}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{121}{128}\right)\)	\(e\left(\frac{91}{128}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{99}{128}\right)\)	\(e\left(\frac{49}{128}\right)\)
\(\chi_{512}(13,\cdot)\)	512.o	128	yes	\(1\)	\(1\)	\(e\left(\frac{45}{128}\right)\)	\(e\left(\frac{111}{128}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{91}{128}\right)\)	\(e\left(\frac{33}{128}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{121}{128}\right)\)	\(e\left(\frac{67}{128}\right)\)
\(\chi_{512}(15,\cdot)\)	512.l	32	no	\(-1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)
\(\chi_{512}(17,\cdot)\)	512.k	32	no	\(1\)	\(1\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)
\(\chi_{512}(19,\cdot)\)	512.p	128	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{128}\right)\)	\(e\left(\frac{23}{128}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{99}{128}\right)\)	\(e\left(\frac{121}{128}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{81}{128}\right)\)	\(e\left(\frac{75}{128}\right)\)
\(\chi_{512}(21,\cdot)\)	512.o	128	yes	\(1\)	\(1\)	\(e\left(\frac{103}{128}\right)\)	\(e\left(\frac{109}{128}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{49}{128}\right)\)	\(e\left(\frac{67}{128}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{75}{128}\right)\)	\(e\left(\frac{105}{128}\right)\)
\(\chi_{512}(23,\cdot)\)	512.n	64	no	\(-1\)	\(1\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{59}{64}\right)\)
\(\chi_{512}(25,\cdot)\)	512.m	64	no	\(1\)	\(1\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{45}{64}\right)\)
\(\chi_{512}(27,\cdot)\)	512.p	128	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{128}\right)\)	\(e\left(\frac{105}{128}\right)\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{29}{128}\right)\)	\(e\left(\frac{7}{128}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{47}{128}\right)\)	\(e\left(\frac{53}{128}\right)\)
\(\chi_{512}(29,\cdot)\)	512.o	128	yes	\(1\)	\(1\)	\(e\left(\frac{81}{128}\right)\)	\(e\left(\frac{123}{128}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{87}{128}\right)\)	\(e\left(\frac{85}{128}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{13}{128}\right)\)	\(e\left(\frac{95}{128}\right)\)
\(\chi_{512}(31,\cdot)\)	512.j	16	no	\(-1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)
\(\chi_{512}(33,\cdot)\)	512.i	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{512}(35,\cdot)\)	512.p	128	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{128}\right)\)	\(e\left(\frac{75}{128}\right)\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{39}{128}\right)\)	\(e\left(\frac{5}{128}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{125}{128}\right)\)	\(e\left(\frac{111}{128}\right)\)
\(\chi_{512}(37,\cdot)\)	512.o	128	yes	\(1\)	\(1\)	\(e\left(\frac{107}{128}\right)\)	\(e\left(\frac{25}{128}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{77}{128}\right)\)	\(e\left(\frac{87}{128}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{63}{128}\right)\)	\(e\left(\frac{37}{128}\right)\)
\(\chi_{512}(39,\cdot)\)	512.n	64	no	\(-1\)	\(1\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{21}{64}\right)\)
\(\chi_{512}(41,\cdot)\)	512.m	64	no	\(1\)	\(1\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)
\(\chi_{512}(43,\cdot)\)	512.p	128	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{128}\right)\)	\(e\left(\frac{61}{128}\right)\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{1}{128}\right)\)	\(e\left(\frac{115}{128}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{59}{128}\right)\)	\(e\left(\frac{121}{128}\right)\)
\(\chi_{512}(45,\cdot)\)	512.o	128	yes	\(1\)	\(1\)	\(e\left(\frac{53}{128}\right)\)	\(e\left(\frac{71}{128}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{19}{128}\right)\)	\(e\left(\frac{73}{128}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{97}{128}\right)\)	\(e\left(\frac{59}{128}\right)\)
\(\chi_{512}(47,\cdot)\)	512.l	32	no	\(-1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)
\(\chi_{512}(49,\cdot)\)	512.k	32	no	\(1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)
\(\chi_{512}(51,\cdot)\)	512.p	128	yes	\(-1\)	\(1\)	\(e\left(\frac{93}{128}\right)\)	\(e\left(\frac{63}{128}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{43}{128}\right)\)	\(e\left(\frac{81}{128}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{105}{128}\right)\)	\(e\left(\frac{83}{128}\right)\)
\(\chi_{512}(53,\cdot)\)	512.o	128	yes	\(1\)	\(1\)	\(e\left(\frac{47}{128}\right)\)	\(e\left(\frac{5}{128}\right)\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{41}{128}\right)\)	\(e\left(\frac{43}{128}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{115}{128}\right)\)	\(e\left(\frac{33}{128}\right)\)
\(\chi_{512}(55,\cdot)\)	512.n	64	no	\(-1\)	\(1\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{39}{64}\right)\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{15}{64}\right)\)
\(\chi_{512}(57,\cdot)\)	512.m	64	no	\(1\)	\(1\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)
\(\chi_{512}(59,\cdot)\)	512.p	128	yes	\(-1\)	\(1\)	\(e\left(\frac{83}{128}\right)\)	\(e\left(\frac{81}{128}\right)\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{37}{128}\right)\)	\(e\left(\frac{31}{128}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{7}{128}\right)\)	\(e\left(\frac{125}{128}\right)\)
\(\chi_{512}(61,\cdot)\)	512.o	128	yes	\(1\)	\(1\)	\(e\left(\frac{89}{128}\right)\)	\(e\left(\frac{83}{128}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{15}{128}\right)\)	\(e\left(\frac{125}{128}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{117}{128}\right)\)	\(e\left(\frac{87}{128}\right)\)
\(\chi_{512}(63,\cdot)\)	512.h	8	no	\(-1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)

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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.