LMFDB - Group of Dirichlet characters of modulus 9600

Show commands: PariGP / SageMath

sage: H = DirichletGroup(9600)

pari: g = idealstar(,9600,2)

Character group

sage: G.order() pari: g.no
Order	=	2560
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{160}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{9600}(4351,\cdot)$, $\chi_{9600}(901,\cdot)$, $\chi_{9600}(6401,\cdot)$, $\chi_{9600}(5377,\cdot)$

First 32 of 2560 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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{9600}(1,\cdot)$	9600.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{9600}(7,\cdot)$	9600.di	16	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{9600}(11,\cdot)$	9600.go	160	yes	$1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{93}{160}\right)$	$e\left(\frac{7}{160}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{159}{160}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{131}{160}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{97}{160}\right)$	$e\left(\frac{31}{80}\right)$
$\chi_{9600}(13,\cdot)$	9600.gt	160	no	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{160}\right)$	$e\left(\frac{13}{160}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{141}{160}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{89}{160}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{43}{160}\right)$	$e\left(\frac{69}{80}\right)$
$\chi_{9600}(17,\cdot)$	9600.fm	40	no	$1$	$1$	$1$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{9600}(19,\cdot)$	9600.gj	160	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{159}{160}\right)$	$e\left(\frac{141}{160}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{37}{160}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{33}{160}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{11}{160}\right)$	$e\left(\frac{13}{80}\right)$
$\chi_{9600}(23,\cdot)$	9600.ga	80	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{37}{80}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{33}{40}\right)$
$\chi_{9600}(29,\cdot)$	9600.gn	160	yes	$-1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{131}{160}\right)$	$e\left(\frac{89}{160}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{33}{160}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{77}{160}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{159}{160}\right)$	$e\left(\frac{17}{80}\right)$
$\chi_{9600}(31,\cdot)$	9600.ee	20	no	$-1$	$1$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{10}\right)$
$\chi_{9600}(37,\cdot)$	9600.gt	160	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{97}{160}\right)$	$e\left(\frac{43}{160}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{11}{160}\right)$	$e\left(\frac{71}{80}\right)$	$e\left(\frac{159}{160}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{93}{160}\right)$	$e\left(\frac{19}{80}\right)$
$\chi_{9600}(41,\cdot)$	9600.fy	80	no	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{69}{80}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{80}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{17}{80}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{17}{40}\right)$
$\chi_{9600}(43,\cdot)$	9600.ew	32	no	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{31}{32}\right)$	$-i$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{3}{16}\right)$
$\chi_{9600}(47,\cdot)$	9600.ez	40	no	$-1$	$1$	$-1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{9600}(49,\cdot)$	9600.bz	8	no	$1$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$i$	$e\left(\frac{7}{8}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$-i$
$\chi_{9600}(53,\cdot)$	9600.ge	160	yes	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{61}{160}\right)$	$e\left(\frac{159}{160}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{143}{160}\right)$	$e\left(\frac{43}{80}\right)$	$e\left(\frac{67}{160}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{160}\right)$	$e\left(\frac{47}{80}\right)$
$\chi_{9600}(59,\cdot)$	9600.gl	160	yes	$1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{57}{160}\right)$	$e\left(\frac{43}{160}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{51}{160}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{39}{160}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{93}{160}\right)$	$e\left(\frac{19}{80}\right)$
$\chi_{9600}(61,\cdot)$	9600.gk	160	no	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{43}{160}\right)$	$e\left(\frac{17}{160}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{9}{160}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{101}{160}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{160}\right)$	$e\left(\frac{1}{80}\right)$
$\chi_{9600}(67,\cdot)$	9600.gf	160	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{59}{160}\right)$	$e\left(\frac{41}{160}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{137}{160}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{53}{160}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{111}{160}\right)$	$e\left(\frac{33}{80}\right)$
$\chi_{9600}(71,\cdot)$	9600.fu	80	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{79}{80}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{11}{40}\right)$
$\chi_{9600}(73,\cdot)$	9600.fr	80	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{53}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{33}{40}\right)$
$\chi_{9600}(77,\cdot)$	9600.ge	160	yes	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{103}{160}\right)$	$e\left(\frac{77}{160}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{29}{160}\right)$	$e\left(\frac{49}{80}\right)$	$e\left(\frac{121}{160}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{107}{160}\right)$	$e\left(\frac{61}{80}\right)$
$\chi_{9600}(79,\cdot)$	9600.ff	40	no	$-1$	$1$	$i$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{9600}(83,\cdot)$	9600.gs	160	yes	$-1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{159}{160}\right)$	$e\left(\frac{21}{160}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{37}{160}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{113}{160}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{131}{160}\right)$	$e\left(\frac{53}{80}\right)$
$\chi_{9600}(89,\cdot)$	9600.fw	80	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{80}\right)$	$e\left(\frac{11}{80}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{23}{80}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{23}{40}\right)$
$\chi_{9600}(91,\cdot)$	9600.gm	160	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{17}{160}\right)$	$e\left(\frac{83}{160}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{11}{160}\right)$	$e\left(\frac{51}{80}\right)$	$e\left(\frac{79}{160}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{53}{160}\right)$	$e\left(\frac{19}{80}\right)$
$\chi_{9600}(97,\cdot)$	9600.dx	20	no	$-1$	$1$	$-i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{9600}(101,\cdot)$	9600.es	32	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{32}\right)$	$i$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{15}{16}\right)$
$\chi_{9600}(103,\cdot)$	9600.gb	80	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{33}{80}\right)$	$e\left(\frac{47}{80}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{80}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{57}{80}\right)$	$e\left(\frac{11}{40}\right)$
$\chi_{9600}(107,\cdot)$	9600.ej	32	no	$-1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{31}{32}\right)$	$-i$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{11}{16}\right)$
$\chi_{9600}(109,\cdot)$	9600.gp	160	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{47}{160}\right)$	$e\left(\frac{13}{160}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{21}{160}\right)$	$e\left(\frac{61}{80}\right)$	$e\left(\frac{129}{160}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{43}{160}\right)$	$e\left(\frac{29}{80}\right)$
$\chi_{9600}(113,\cdot)$	9600.fm	40	no	$1$	$1$	$1$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{9600}(119,\cdot)$	9600.fs	80	no	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{27}{80}\right)$	$e\left(\frac{73}{80}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{63}{80}\right)$	$e\left(\frac{29}{40}\right)$

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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	$9600$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{160}\)
Order	$2560$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{9600}(1,\cdot)\)	9600.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{9600}(7,\cdot)\)	9600.di	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{9600}(11,\cdot)\)	9600.go	160	yes	\(1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{93}{160}\right)\)	\(e\left(\frac{7}{160}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{159}{160}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{131}{160}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{97}{160}\right)\)	\(e\left(\frac{31}{80}\right)\)
\(\chi_{9600}(13,\cdot)\)	9600.gt	160	no	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{160}\right)\)	\(e\left(\frac{13}{160}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{141}{160}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{89}{160}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{43}{160}\right)\)	\(e\left(\frac{69}{80}\right)\)
\(\chi_{9600}(17,\cdot)\)	9600.fm	40	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{9600}(19,\cdot)\)	9600.gj	160	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{159}{160}\right)\)	\(e\left(\frac{141}{160}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{37}{160}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{33}{160}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{11}{160}\right)\)	\(e\left(\frac{13}{80}\right)\)
\(\chi_{9600}(23,\cdot)\)	9600.ga	80	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{37}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)
\(\chi_{9600}(29,\cdot)\)	9600.gn	160	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{131}{160}\right)\)	\(e\left(\frac{89}{160}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{33}{160}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{77}{160}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{159}{160}\right)\)	\(e\left(\frac{17}{80}\right)\)
\(\chi_{9600}(31,\cdot)\)	9600.ee	20	no	\(-1\)	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{9600}(37,\cdot)\)	9600.gt	160	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{97}{160}\right)\)	\(e\left(\frac{43}{160}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{11}{160}\right)\)	\(e\left(\frac{71}{80}\right)\)	\(e\left(\frac{159}{160}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{93}{160}\right)\)	\(e\left(\frac{19}{80}\right)\)
\(\chi_{9600}(41,\cdot)\)	9600.fy	80	no	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{69}{80}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{17}{80}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)
\(\chi_{9600}(43,\cdot)\)	9600.ew	32	no	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(-i\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{3}{16}\right)\)
\(\chi_{9600}(47,\cdot)\)	9600.ez	40	no	\(-1\)	\(1\)	\(-1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{9600}(49,\cdot)\)	9600.bz	8	no	\(1\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)
\(\chi_{9600}(53,\cdot)\)	9600.ge	160	yes	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{61}{160}\right)\)	\(e\left(\frac{159}{160}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{143}{160}\right)\)	\(e\left(\frac{43}{80}\right)\)	\(e\left(\frac{67}{160}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{160}\right)\)	\(e\left(\frac{47}{80}\right)\)
\(\chi_{9600}(59,\cdot)\)	9600.gl	160	yes	\(1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{57}{160}\right)\)	\(e\left(\frac{43}{160}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{51}{160}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{39}{160}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{93}{160}\right)\)	\(e\left(\frac{19}{80}\right)\)
\(\chi_{9600}(61,\cdot)\)	9600.gk	160	no	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{43}{160}\right)\)	\(e\left(\frac{17}{160}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{9}{160}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{101}{160}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{160}\right)\)	\(e\left(\frac{1}{80}\right)\)
\(\chi_{9600}(67,\cdot)\)	9600.gf	160	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{59}{160}\right)\)	\(e\left(\frac{41}{160}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{137}{160}\right)\)	\(e\left(\frac{77}{80}\right)\)	\(e\left(\frac{53}{160}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{111}{160}\right)\)	\(e\left(\frac{33}{80}\right)\)
\(\chi_{9600}(71,\cdot)\)	9600.fu	80	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{79}{80}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)
\(\chi_{9600}(73,\cdot)\)	9600.fr	80	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{53}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{33}{40}\right)\)
\(\chi_{9600}(77,\cdot)\)	9600.ge	160	yes	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{103}{160}\right)\)	\(e\left(\frac{77}{160}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{29}{160}\right)\)	\(e\left(\frac{49}{80}\right)\)	\(e\left(\frac{121}{160}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{107}{160}\right)\)	\(e\left(\frac{61}{80}\right)\)
\(\chi_{9600}(79,\cdot)\)	9600.ff	40	no	\(-1\)	\(1\)	\(i\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{9600}(83,\cdot)\)	9600.gs	160	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{159}{160}\right)\)	\(e\left(\frac{21}{160}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{37}{160}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{113}{160}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{131}{160}\right)\)	\(e\left(\frac{53}{80}\right)\)
\(\chi_{9600}(89,\cdot)\)	9600.fw	80	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{80}\right)\)	\(e\left(\frac{11}{80}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{23}{80}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{23}{40}\right)\)
\(\chi_{9600}(91,\cdot)\)	9600.gm	160	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{17}{160}\right)\)	\(e\left(\frac{83}{160}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{11}{160}\right)\)	\(e\left(\frac{51}{80}\right)\)	\(e\left(\frac{79}{160}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{53}{160}\right)\)	\(e\left(\frac{19}{80}\right)\)
\(\chi_{9600}(97,\cdot)\)	9600.dx	20	no	\(-1\)	\(1\)	\(-i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{9600}(101,\cdot)\)	9600.es	32	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(i\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{15}{16}\right)\)
\(\chi_{9600}(103,\cdot)\)	9600.gb	80	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{33}{80}\right)\)	\(e\left(\frac{47}{80}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{31}{80}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{11}{40}\right)\)
\(\chi_{9600}(107,\cdot)\)	9600.ej	32	no	\(-1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(-i\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{11}{16}\right)\)
\(\chi_{9600}(109,\cdot)\)	9600.gp	160	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{47}{160}\right)\)	\(e\left(\frac{13}{160}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{21}{160}\right)\)	\(e\left(\frac{61}{80}\right)\)	\(e\left(\frac{129}{160}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{43}{160}\right)\)	\(e\left(\frac{29}{80}\right)\)
\(\chi_{9600}(113,\cdot)\)	9600.fm	40	no	\(1\)	\(1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{9600}(119,\cdot)\)	9600.fs	80	no	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{73}{80}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{80}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{29}{80}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{63}{80}\right)\)	\(e\left(\frac{29}{40}\right)\)

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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.