LMFDB - Group of Dirichlet characters of modulus 8800

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(8800)

gp:g = idealstar(,8800,2)

magma:G = FullDirichletGroup(8800);

Character group

Order	=	3200	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{20}\times C_{40}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{8800}(2751,\cdot)$, $\chi_{8800}(3301,\cdot)$, $\chi_{8800}(4577,\cdot)$, $\chi_{8800}(5601,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 3200 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	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{8800}(1,\cdot)$	8800.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8800}(3,\cdot)$	8800.lu	40	yes	$1$	$1$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{3}{40}\right)$	$i$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{17}{40}\right)$
$\chi_{8800}(7,\cdot)$	8800.gh	20	no	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{17}{20}\right)$	$-i$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{8800}(9,\cdot)$	8800.hc	20	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{20}\right)$	$-1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{8800}(13,\cdot)$	8800.lz	40	yes	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{40}\right)$	$-i$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{9}{40}\right)$
$\chi_{8800}(17,\cdot)$	8800.hx	20	no	$1$	$1$	$i$	$e\left(\frac{11}{20}\right)$	$-1$	$-i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{20}\right)$	$-i$	$e\left(\frac{1}{10}\right)$
$\chi_{8800}(19,\cdot)$	8800.nh	40	yes	$1$	$1$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{21}{40}\right)$
$\chi_{8800}(21,\cdot)$	8800.ms	40	yes	$-1$	$1$	$e\left(\frac{3}{40}\right)$	$-i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{23}{40}\right)$
$\chi_{8800}(23,\cdot)$	8800.gq	20	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{8800}(27,\cdot)$	8800.lu	40	yes	$1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{40}\right)$	$-i$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{11}{40}\right)$
$\chi_{8800}(29,\cdot)$	8800.ny	40	yes	$-1$	$1$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{9}{40}\right)$
$\chi_{8800}(31,\cdot)$	8800.ew	10	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{10}\right)$	$1$
$\chi_{8800}(37,\cdot)$	8800.op	40	yes	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{10}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{27}{40}\right)$
$\chi_{8800}(39,\cdot)$	8800.hr	20	no	$1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{13}{20}\right)$
$\chi_{8800}(41,\cdot)$	8800.hn	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{20}\right)$	$-i$
$\chi_{8800}(43,\cdot)$	8800.cg	8	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$1$	$i$	$e\left(\frac{1}{8}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{8800}(47,\cdot)$	8800.jf	20	no	$1$	$1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{9}{20}\right)$	$i$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{8800}(49,\cdot)$	8800.dn	10	no	$1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{8800}(51,\cdot)$	8800.mz	40	no	$1$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{7}{8}\right)$	$-i$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{21}{40}\right)$
$\chi_{8800}(53,\cdot)$	8800.lr	40	yes	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{5}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{31}{40}\right)$
$\chi_{8800}(57,\cdot)$	8800.kq	20	no	$1$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{20}\right)$	$-i$	$i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{8800}(59,\cdot)$	8800.mw	40	yes	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{13}{20}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{40}\right)$
$\chi_{8800}(61,\cdot)$	8800.ob	40	yes	$-1$	$1$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{29}{40}\right)$	$1$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{1}{40}\right)$
$\chi_{8800}(63,\cdot)$	8800.id	20	no	$-1$	$1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{20}\right)$	$-1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{20}\right)$	$1$
$\chi_{8800}(67,\cdot)$	8800.ln	40	no	$1$	$1$	$e\left(\frac{7}{40}\right)$	$-1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{17}{40}\right)$
$\chi_{8800}(69,\cdot)$	8800.ne	40	yes	$1$	$1$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{31}{40}\right)$
$\chi_{8800}(71,\cdot)$	8800.hg	20	no	$-1$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{2}{5}\right)$	$i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{19}{20}\right)$	$-i$
$\chi_{8800}(73,\cdot)$	8800.kp	20	no	$1$	$1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{20}\right)$	$i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$i$
$\chi_{8800}(79,\cdot)$	8800.co	10	no	$1$	$1$	$-1$	$e\left(\frac{7}{10}\right)$	$1$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{2}{5}\right)$
$\chi_{8800}(81,\cdot)$	8800.eu	10	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{8800}(83,\cdot)$	8800.ok	40	yes	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{10}\right)$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{9}{40}\right)$
$\chi_{8800}(87,\cdot)$	8800.lb	20	no	$-1$	$1$	$e\left(\frac{9}{10}\right)$	$-i$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{13}{20}\right)$

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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	$8800$
Structure	\(C_{2}\times C_{2}\times C_{20}\times C_{40}\)
Order	$3200$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)	\(29\)
\(\chi_{8800}(1,\cdot)\)	8800.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8800}(3,\cdot)\)	8800.lu	40	yes	\(1\)	\(1\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(i\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)
\(\chi_{8800}(7,\cdot)\)	8800.gh	20	no	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{8800}(9,\cdot)\)	8800.hc	20	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{8800}(13,\cdot)\)	8800.lz	40	yes	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(-i\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)
\(\chi_{8800}(17,\cdot)\)	8800.hx	20	no	\(1\)	\(1\)	\(i\)	\(e\left(\frac{11}{20}\right)\)	\(-1\)	\(-i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)
\(\chi_{8800}(19,\cdot)\)	8800.nh	40	yes	\(1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)
\(\chi_{8800}(21,\cdot)\)	8800.ms	40	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(-i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)
\(\chi_{8800}(23,\cdot)\)	8800.gq	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{8800}(27,\cdot)\)	8800.lu	40	yes	\(1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(-i\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)
\(\chi_{8800}(29,\cdot)\)	8800.ny	40	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)
\(\chi_{8800}(31,\cdot)\)	8800.ew	10	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)
\(\chi_{8800}(37,\cdot)\)	8800.op	40	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{27}{40}\right)\)
\(\chi_{8800}(39,\cdot)\)	8800.hr	20	no	\(1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)
\(\chi_{8800}(41,\cdot)\)	8800.hn	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(-i\)
\(\chi_{8800}(43,\cdot)\)	8800.cg	8	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{8800}(47,\cdot)\)	8800.jf	20	no	\(1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(i\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{8800}(49,\cdot)\)	8800.dn	10	no	\(1\)	\(1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(-1\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{8800}(51,\cdot)\)	8800.mz	40	no	\(1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-i\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)
\(\chi_{8800}(53,\cdot)\)	8800.lr	40	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{31}{40}\right)\)
\(\chi_{8800}(57,\cdot)\)	8800.kq	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{8800}(59,\cdot)\)	8800.mw	40	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{40}\right)\)
\(\chi_{8800}(61,\cdot)\)	8800.ob	40	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)
\(\chi_{8800}(63,\cdot)\)	8800.id	20	no	\(-1\)	\(1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(-1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(1\)
\(\chi_{8800}(67,\cdot)\)	8800.ln	40	no	\(1\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(-1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)
\(\chi_{8800}(69,\cdot)\)	8800.ne	40	yes	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)
\(\chi_{8800}(71,\cdot)\)	8800.hg	20	no	\(-1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(-i\)
\(\chi_{8800}(73,\cdot)\)	8800.kp	20	no	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(i\)
\(\chi_{8800}(79,\cdot)\)	8800.co	10	no	\(1\)	\(1\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{8800}(81,\cdot)\)	8800.eu	10	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{8800}(83,\cdot)\)	8800.ok	40	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{9}{40}\right)\)
\(\chi_{8800}(87,\cdot)\)	8800.lb	20	no	\(-1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(-i\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)

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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.