LMFDB - Group of Dirichlet characters of modulus 1664

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(1664)

gp:g = idealstar(,1664,2)

magma:G = FullDirichletGroup(1664);

Character group

Order	=	768	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{96}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{1664}(1535,\cdot)$, $\chi_{1664}(261,\cdot)$, $\chi_{1664}(769,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 768 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{1664}(1,\cdot)$	1664.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1664}(3,\cdot)$	1664.df	96	yes	$-1$	$1$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{1664}(5,\cdot)$	1664.ct	32	yes	$-1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{1664}(7,\cdot)$	1664.cv	48	no	$1$	$1$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{24}\right)$
$\chi_{1664}(9,\cdot)$	1664.cx	48	no	$1$	$1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{24}\right)$
$\chi_{1664}(11,\cdot)$	1664.dj	96	yes	$1$	$1$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{25}{48}\right)$
$\chi_{1664}(15,\cdot)$	1664.cf	24	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{1664}(17,\cdot)$	1664.ch	24	no	$1$	$1$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{12}\right)$
$\chi_{1664}(19,\cdot)$	1664.dj	96	yes	$1$	$1$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{35}{48}\right)$
$\chi_{1664}(21,\cdot)$	1664.cm	32	yes	$-1$	$1$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{1664}(23,\cdot)$	1664.cw	48	no	$-1$	$1$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{1664}(25,\cdot)$	1664.cb	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{16}\right)$	$-i$	$-i$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1664}(27,\cdot)$	1664.cq	32	no	$-1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{7}{16}\right)$
$\chi_{1664}(29,\cdot)$	1664.dg	96	yes	$1$	$1$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{1664}(31,\cdot)$	1664.s	4	no	$1$	$1$	$i$	$1$	$i$	$-1$	$1$	$i$	$-1$	$1$	$-1$	$-1$
$\chi_{1664}(33,\cdot)$	1664.bt	12	no	$-1$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$
$\chi_{1664}(35,\cdot)$	1664.df	96	yes	$-1$	$1$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{1664}(37,\cdot)$	1664.dd	96	yes	$-1$	$1$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{1664}(41,\cdot)$	1664.da	48	no	$-1$	$1$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{23}{24}\right)$
$\chi_{1664}(43,\cdot)$	1664.dh	96	yes	$-1$	$1$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{41}{48}\right)$
$\chi_{1664}(45,\cdot)$	1664.dd	96	yes	$-1$	$1$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{11}{48}\right)$
$\chi_{1664}(47,\cdot)$	1664.bi	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$i$	$e\left(\frac{1}{8}\right)$	$i$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$
$\chi_{1664}(49,\cdot)$	1664.ch	24	no	$1$	$1$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{12}\right)$
$\chi_{1664}(51,\cdot)$	1664.co	32	yes	$-1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{1}{16}\right)$
$\chi_{1664}(53,\cdot)$	1664.cp	32	no	$1$	$1$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{1664}(55,\cdot)$	1664.cz	48	no	$-1$	$1$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{24}\right)$
$\chi_{1664}(57,\cdot)$	1664.cd	16	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{16}\right)$	$1$	$i$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1664}(59,\cdot)$	1664.dj	96	yes	$1$	$1$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{5}{48}\right)$
$\chi_{1664}(61,\cdot)$	1664.dg	96	yes	$1$	$1$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{1664}(63,\cdot)$	1664.bk	12	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{12}\right)$	$i$	$e\left(\frac{1}{3}\right)$
$\chi_{1664}(67,\cdot)$	1664.dj	96	yes	$1$	$1$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{31}{48}\right)$
$\chi_{1664}(69,\cdot)$	1664.de	96	yes	$1$	$1$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{5}{48}\right)$

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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 $\F_{q}$
Belyi maps

Modulus	$1664$
Structure	\(C_{2}\times C_{4}\times C_{96}\)
Order	$768$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{1664}(1,\cdot)\)	1664.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1664}(3,\cdot)\)	1664.df	96	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{1664}(5,\cdot)\)	1664.ct	32	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{1664}(7,\cdot)\)	1664.cv	48	no	\(1\)	\(1\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{24}\right)\)
\(\chi_{1664}(9,\cdot)\)	1664.cx	48	no	\(1\)	\(1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{24}\right)\)
\(\chi_{1664}(11,\cdot)\)	1664.dj	96	yes	\(1\)	\(1\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{25}{48}\right)\)
\(\chi_{1664}(15,\cdot)\)	1664.cf	24	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1664}(17,\cdot)\)	1664.ch	24	no	\(1\)	\(1\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{12}\right)\)
\(\chi_{1664}(19,\cdot)\)	1664.dj	96	yes	\(1\)	\(1\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{35}{48}\right)\)
\(\chi_{1664}(21,\cdot)\)	1664.cm	32	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{1664}(23,\cdot)\)	1664.cw	48	no	\(-1\)	\(1\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{1664}(25,\cdot)\)	1664.cb	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1664}(27,\cdot)\)	1664.cq	32	no	\(-1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{1664}(29,\cdot)\)	1664.dg	96	yes	\(1\)	\(1\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{1664}(31,\cdot)\)	1664.s	4	no	\(1\)	\(1\)	\(i\)	\(1\)	\(i\)	\(-1\)	\(1\)	\(i\)	\(-1\)	\(1\)	\(-1\)	\(-1\)
\(\chi_{1664}(33,\cdot)\)	1664.bt	12	no	\(-1\)	\(1\)	\(e\left(\frac{11}{12}\right)\)	\(1\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(-1\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1664}(35,\cdot)\)	1664.df	96	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{1664}(37,\cdot)\)	1664.dd	96	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{1664}(41,\cdot)\)	1664.da	48	no	\(-1\)	\(1\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{23}{24}\right)\)
\(\chi_{1664}(43,\cdot)\)	1664.dh	96	yes	\(-1\)	\(1\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{41}{48}\right)\)
\(\chi_{1664}(45,\cdot)\)	1664.dd	96	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{11}{48}\right)\)
\(\chi_{1664}(47,\cdot)\)	1664.bi	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)
\(\chi_{1664}(49,\cdot)\)	1664.ch	24	no	\(1\)	\(1\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)
\(\chi_{1664}(51,\cdot)\)	1664.co	32	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{1}{16}\right)\)
\(\chi_{1664}(53,\cdot)\)	1664.cp	32	no	\(1\)	\(1\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{1664}(55,\cdot)\)	1664.cz	48	no	\(-1\)	\(1\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{1664}(57,\cdot)\)	1664.cd	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(1\)	\(i\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1664}(59,\cdot)\)	1664.dj	96	yes	\(1\)	\(1\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{5}{48}\right)\)
\(\chi_{1664}(61,\cdot)\)	1664.dg	96	yes	\(1\)	\(1\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{1664}(63,\cdot)\)	1664.bk	12	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(-i\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(i\)	\(e\left(\frac{1}{3}\right)\)
\(\chi_{1664}(67,\cdot)\)	1664.dj	96	yes	\(1\)	\(1\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{1664}(69,\cdot)\)	1664.de	96	yes	\(1\)	\(1\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{5}{48}\right)\)

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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.