LMFDB - Group of Dirichlet characters of modulus 9984

sage:H = DirichletGroup(9984)

pari:g = idealstar(,9984,2)

Character group

sage:G.order() pari:g.no
Order	=	3072
sage:H.invariants() pari:g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{192}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{9984}(8191,\cdot)$, $\chi_{9984}(3589,\cdot)$, $\chi_{9984}(3329,\cdot)$, $\chi_{9984}(769,\cdot)$

First 32 of 3072 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	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{9984}(1,\cdot)$	9984.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{9984}(5,\cdot)$	9984.gn	64	yes	$1$	$1$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{43}{64}\right)$
$\chi_{9984}(7,\cdot)$	9984.hj	96	no	$1$	$1$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{85}{96}\right)$	$1$	$e\left(\frac{53}{96}\right)$
$\chi_{9984}(11,\cdot)$	9984.hs	192	yes	$-1$	$1$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{187}{192}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{185}{192}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{37}{192}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{53}{192}\right)$
$\chi_{9984}(17,\cdot)$	9984.ga	48	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{47}{48}\right)$	$1$	$e\left(\frac{31}{48}\right)$
$\chi_{9984}(19,\cdot)$	9984.ht	192	no	$1$	$1$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{185}{192}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{163}{192}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{167}{192}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{151}{192}\right)$
$\chi_{9984}(23,\cdot)$	9984.he	96	no	$1$	$1$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{71}{96}\right)$	$-i$	$e\left(\frac{7}{96}\right)$
$\chi_{9984}(25,\cdot)$	9984.fh	32	no	$1$	$1$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{27}{32}\right)$	$-i$	$e\left(\frac{11}{32}\right)$
$\chi_{9984}(29,\cdot)$	9984.hw	192	yes	$-1$	$1$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{37}{192}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{167}{192}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{43}{192}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{59}{192}\right)$
$\chi_{9984}(31,\cdot)$	9984.cs	8	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$-i$	$-i$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$
$\chi_{9984}(35,\cdot)$	9984.hp	192	yes	$1$	$1$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{53}{192}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{151}{192}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{59}{192}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{43}{192}\right)$
$\chi_{9984}(37,\cdot)$	9984.hl	192	no	$-1$	$1$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{55}{192}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{173}{192}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{73}{192}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{185}{192}\right)$
$\chi_{9984}(41,\cdot)$	9984.gw	96	no	$1$	$1$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{95}{96}\right)$	$-1$	$e\left(\frac{79}{96}\right)$
$\chi_{9984}(43,\cdot)$	9984.hn	192	no	$-1$	$1$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{131}{192}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{49}{192}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{173}{192}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{61}{192}\right)$
$\chi_{9984}(47,\cdot)$	9984.ed	16	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{16}\right)$	$i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$i$	$e\left(\frac{9}{16}\right)$
$\chi_{9984}(49,\cdot)$	9984.gc	48	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{37}{48}\right)$	$1$	$e\left(\frac{5}{48}\right)$
$\chi_{9984}(53,\cdot)$	9984.gh	64	no	$-1$	$1$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{23}{64}\right)$
$\chi_{9984}(55,\cdot)$	9984.hd	96	no	$-1$	$1$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{59}{96}\right)$	$i$	$e\left(\frac{91}{96}\right)$
$\chi_{9984}(59,\cdot)$	9984.hs	192	yes	$-1$	$1$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{191}{192}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{37}{192}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{161}{192}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{49}{192}\right)$
$\chi_{9984}(61,\cdot)$	9984.hv	192	no	$1$	$1$	$e\left(\frac{19}{64}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{173}{192}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{31}{192}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{35}{192}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{115}{192}\right)$
$\chi_{9984}(67,\cdot)$	9984.ht	192	no	$1$	$1$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{157}{192}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{47}{192}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{67}{192}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{179}{192}\right)$
$\chi_{9984}(71,\cdot)$	9984.gv	96	no	$-1$	$1$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{13}{96}\right)$	$-1$	$e\left(\frac{77}{96}\right)$
$\chi_{9984}(73,\cdot)$	9984.fm	32	no	$-1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{25}{32}\right)$	$1$	$e\left(\frac{9}{32}\right)$
$\chi_{9984}(77,\cdot)$	9984.gg	64	yes	$-1$	$1$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{41}{64}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{53}{64}\right)$
$\chi_{9984}(79,\cdot)$	9984.eg	16	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$-i$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$e\left(\frac{7}{16}\right)$
$\chi_{9984}(83,\cdot)$	9984.gl	64	yes	$-1$	$1$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{17}{64}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{29}{64}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{45}{64}\right)$
$\chi_{9984}(85,\cdot)$	9984.hl	192	no	$-1$	$1$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{179}{192}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{1}{192}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{77}{192}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{61}{192}\right)$
$\chi_{9984}(89,\cdot)$	9984.gw	96	no	$1$	$1$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{89}{96}\right)$	$-1$	$e\left(\frac{73}{96}\right)$
$\chi_{9984}(95,\cdot)$	9984.ep	24	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{7}{24}\right)$	$1$	$e\left(\frac{11}{24}\right)$
$\chi_{9984}(97,\cdot)$	9984.ev	24	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{13}{24}\right)$	$-i$	$e\left(\frac{5}{24}\right)$
$\chi_{9984}(101,\cdot)$	9984.hx	192	yes	$-1$	$1$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{55}{192}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{77}{192}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{25}{192}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{137}{192}\right)$
$\chi_{9984}(103,\cdot)$	9984.ff	32	no	$-1$	$1$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{11}{32}\right)$	$i$	$e\left(\frac{11}{32}\right)$

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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	$9984$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{192}\)
Order	$3072$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{9984}(1,\cdot)\)	9984.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{9984}(5,\cdot)\)	9984.gn	64	yes	\(1\)	\(1\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{43}{64}\right)\)
\(\chi_{9984}(7,\cdot)\)	9984.hj	96	no	\(1\)	\(1\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(1\)	\(e\left(\frac{53}{96}\right)\)
\(\chi_{9984}(11,\cdot)\)	9984.hs	192	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{187}{192}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{185}{192}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{37}{192}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{53}{192}\right)\)
\(\chi_{9984}(17,\cdot)\)	9984.ga	48	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(1\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{9984}(19,\cdot)\)	9984.ht	192	no	\(1\)	\(1\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{185}{192}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{163}{192}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{167}{192}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{151}{192}\right)\)
\(\chi_{9984}(23,\cdot)\)	9984.he	96	no	\(1\)	\(1\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(-i\)	\(e\left(\frac{7}{96}\right)\)
\(\chi_{9984}(25,\cdot)\)	9984.fh	32	no	\(1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(-i\)	\(e\left(\frac{11}{32}\right)\)
\(\chi_{9984}(29,\cdot)\)	9984.hw	192	yes	\(-1\)	\(1\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{37}{192}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{167}{192}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{43}{192}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{59}{192}\right)\)
\(\chi_{9984}(31,\cdot)\)	9984.cs	8	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{9984}(35,\cdot)\)	9984.hp	192	yes	\(1\)	\(1\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{53}{192}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{151}{192}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{59}{192}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{43}{192}\right)\)
\(\chi_{9984}(37,\cdot)\)	9984.hl	192	no	\(-1\)	\(1\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{55}{192}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{73}{192}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{185}{192}\right)\)
\(\chi_{9984}(41,\cdot)\)	9984.gw	96	no	\(1\)	\(1\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(-1\)	\(e\left(\frac{79}{96}\right)\)
\(\chi_{9984}(43,\cdot)\)	9984.hn	192	no	\(-1\)	\(1\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{131}{192}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{49}{192}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{61}{192}\right)\)
\(\chi_{9984}(47,\cdot)\)	9984.ed	16	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(i\)	\(e\left(\frac{9}{16}\right)\)
\(\chi_{9984}(49,\cdot)\)	9984.gc	48	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(1\)	\(e\left(\frac{5}{48}\right)\)
\(\chi_{9984}(53,\cdot)\)	9984.gh	64	no	\(-1\)	\(1\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{23}{64}\right)\)
\(\chi_{9984}(55,\cdot)\)	9984.hd	96	no	\(-1\)	\(1\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(i\)	\(e\left(\frac{91}{96}\right)\)
\(\chi_{9984}(59,\cdot)\)	9984.hs	192	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{191}{192}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{37}{192}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{161}{192}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{49}{192}\right)\)
\(\chi_{9984}(61,\cdot)\)	9984.hv	192	no	\(1\)	\(1\)	\(e\left(\frac{19}{64}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{31}{192}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{35}{192}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{115}{192}\right)\)
\(\chi_{9984}(67,\cdot)\)	9984.ht	192	no	\(1\)	\(1\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{157}{192}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{47}{192}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{67}{192}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{179}{192}\right)\)
\(\chi_{9984}(71,\cdot)\)	9984.gv	96	no	\(-1\)	\(1\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(-1\)	\(e\left(\frac{77}{96}\right)\)
\(\chi_{9984}(73,\cdot)\)	9984.fm	32	no	\(-1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(1\)	\(e\left(\frac{9}{32}\right)\)
\(\chi_{9984}(77,\cdot)\)	9984.gg	64	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{41}{64}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{53}{64}\right)\)
\(\chi_{9984}(79,\cdot)\)	9984.eg	16	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(-i\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)	\(e\left(\frac{7}{16}\right)\)
\(\chi_{9984}(83,\cdot)\)	9984.gl	64	yes	\(-1\)	\(1\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{17}{64}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{29}{64}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{45}{64}\right)\)
\(\chi_{9984}(85,\cdot)\)	9984.hl	192	no	\(-1\)	\(1\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{179}{192}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{1}{192}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{77}{192}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{61}{192}\right)\)
\(\chi_{9984}(89,\cdot)\)	9984.gw	96	no	\(1\)	\(1\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(-1\)	\(e\left(\frac{73}{96}\right)\)
\(\chi_{9984}(95,\cdot)\)	9984.ep	24	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{7}{24}\right)\)	\(1\)	\(e\left(\frac{11}{24}\right)\)
\(\chi_{9984}(97,\cdot)\)	9984.ev	24	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(-i\)	\(e\left(\frac{13}{24}\right)\)	\(-i\)	\(e\left(\frac{5}{24}\right)\)
\(\chi_{9984}(101,\cdot)\)	9984.hx	192	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{55}{192}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{77}{192}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{25}{192}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{137}{192}\right)\)
\(\chi_{9984}(103,\cdot)\)	9984.ff	32	no	\(-1\)	\(1\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(i\)	\(e\left(\frac{11}{32}\right)\)

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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.