LMFDB - Group of Dirichlet characters of modulus 800

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(800)

gp:g = idealstar(,800,2)

magma:G = FullDirichletGroup(800);

Character group

Order	=	320	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{4}\times C_{40}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{800}(351,\cdot)$, $\chi_{800}(101,\cdot)$, $\chi_{800}(577,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 320 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{800}(1,\cdot)$	800.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{800}(3,\cdot)$	800.cd	40	yes	$1$	$1$	$e\left(\frac{3}{40}\right)$	$1$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{40}\right)$
$\chi_{800}(7,\cdot)$	800.s	4	no	$1$	$1$	$1$	$i$	$1$	$-i$	$-1$	$i$	$-i$	$i$	$-i$	$1$
$\chi_{800}(9,\cdot)$	800.bt	20	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{800}(11,\cdot)$	800.cb	40	yes	$-1$	$1$	$e\left(\frac{39}{40}\right)$	$-i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{37}{40}\right)$
$\chi_{800}(13,\cdot)$	800.bw	40	yes	$-1$	$1$	$e\left(\frac{11}{40}\right)$	$-1$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{23}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{33}{40}\right)$
$\chi_{800}(17,\cdot)$	800.br	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{800}(19,\cdot)$	800.bz	40	yes	$-1$	$1$	$e\left(\frac{17}{40}\right)$	$-i$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{11}{40}\right)$
$\chi_{800}(21,\cdot)$	800.ca	40	yes	$1$	$1$	$e\left(\frac{3}{40}\right)$	$i$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{9}{40}\right)$
$\chi_{800}(23,\cdot)$	800.bl	20	no	$1$	$1$	$e\left(\frac{3}{5}\right)$	$-i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{800}(27,\cdot)$	800.cd	40	yes	$1$	$1$	$e\left(\frac{9}{40}\right)$	$1$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{40}\right)$	$e\left(\frac{9}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{27}{40}\right)$
$\chi_{800}(29,\cdot)$	800.by	40	yes	$1$	$1$	$e\left(\frac{33}{40}\right)$	$i$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{21}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{19}{40}\right)$
$\chi_{800}(31,\cdot)$	800.bh	10	no	$-1$	$1$	$e\left(\frac{3}{10}\right)$	$-1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{9}{10}\right)$
$\chi_{800}(33,\cdot)$	800.bo	20	no	$-1$	$1$	$e\left(\frac{1}{20}\right)$	$-i$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{20}\right)$
$\chi_{800}(37,\cdot)$	800.bw	40	yes	$-1$	$1$	$e\left(\frac{21}{40}\right)$	$-1$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{40}\right)$
$\chi_{800}(39,\cdot)$	800.bn	20	no	$-1$	$1$	$e\left(\frac{7}{20}\right)$	$-1$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{20}\right)$
$\chi_{800}(41,\cdot)$	800.bm	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$-1$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{800}(43,\cdot)$	800.v	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$-1$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{7}{8}\right)$
$\chi_{800}(47,\cdot)$	800.bp	20	no	$1$	$1$	$e\left(\frac{19}{20}\right)$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{20}\right)$
$\chi_{800}(49,\cdot)$	800.f	2	no	$1$	$1$	$1$	$-1$	$1$	$-1$	$1$	$-1$	$-1$	$-1$	$-1$	$1$
$\chi_{800}(51,\cdot)$	800.x	8	no	$-1$	$1$	$e\left(\frac{1}{8}\right)$	$i$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$e\left(\frac{3}{8}\right)$
$\chi_{800}(53,\cdot)$	800.cc	40	yes	$-1$	$1$	$e\left(\frac{13}{40}\right)$	$1$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{29}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{39}{40}\right)$
$\chi_{800}(57,\cdot)$	800.i	4	no	$-1$	$1$	$-1$	$-i$	$1$	$i$	$-1$	$i$	$i$	$i$	$i$	$-1$
$\chi_{800}(59,\cdot)$	800.bz	40	yes	$-1$	$1$	$e\left(\frac{31}{40}\right)$	$i$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{40}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{13}{40}\right)$
$\chi_{800}(61,\cdot)$	800.ca	40	yes	$1$	$1$	$e\left(\frac{29}{40}\right)$	$-i$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{19}{40}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{40}\right)$
$\chi_{800}(63,\cdot)$	800.bq	20	no	$1$	$1$	$e\left(\frac{3}{20}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{20}\right)$
$\chi_{800}(67,\cdot)$	800.bx	40	yes	$1$	$1$	$e\left(\frac{7}{40}\right)$	$-1$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{31}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{33}{40}\right)$	$e\left(\frac{27}{40}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{21}{40}\right)$
$\chi_{800}(69,\cdot)$	800.by	40	yes	$1$	$1$	$e\left(\frac{27}{40}\right)$	$-i$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{40}\right)$
$\chi_{800}(71,\cdot)$	800.bs	20	no	$-1$	$1$	$e\left(\frac{9}{20}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{800}(73,\cdot)$	800.bv	20	no	$-1$	$1$	$e\left(\frac{1}{10}\right)$	$i$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{3}{10}\right)$
$\chi_{800}(77,\cdot)$	800.cc	40	yes	$-1$	$1$	$e\left(\frac{39}{40}\right)$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{7}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{40}\right)$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{37}{40}\right)$
$\chi_{800}(79,\cdot)$	800.bi	10	no	$-1$	$1$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{10}\right)$

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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	$800$
Structure	\(C_{2}\times C_{4}\times C_{40}\)
Order	$320$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{800}(1,\cdot)\)	800.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{800}(3,\cdot)\)	800.cd	40	yes	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{40}\right)\)
\(\chi_{800}(7,\cdot)\)	800.s	4	no	\(1\)	\(1\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(-1\)	\(i\)	\(-i\)	\(i\)	\(-i\)	\(1\)
\(\chi_{800}(9,\cdot)\)	800.bt	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{800}(11,\cdot)\)	800.cb	40	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(-i\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)
\(\chi_{800}(13,\cdot)\)	800.bw	40	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{40}\right)\)	\(-1\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{33}{40}\right)\)
\(\chi_{800}(17,\cdot)\)	800.br	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{800}(19,\cdot)\)	800.bz	40	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{40}\right)\)	\(-i\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)
\(\chi_{800}(21,\cdot)\)	800.ca	40	yes	\(1\)	\(1\)	\(e\left(\frac{3}{40}\right)\)	\(i\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{9}{40}\right)\)
\(\chi_{800}(23,\cdot)\)	800.bl	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(-i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{800}(27,\cdot)\)	800.cd	40	yes	\(1\)	\(1\)	\(e\left(\frac{9}{40}\right)\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{37}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{11}{40}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{27}{40}\right)\)
\(\chi_{800}(29,\cdot)\)	800.by	40	yes	\(1\)	\(1\)	\(e\left(\frac{33}{40}\right)\)	\(i\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{21}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{19}{40}\right)\)
\(\chi_{800}(31,\cdot)\)	800.bh	10	no	\(-1\)	\(1\)	\(e\left(\frac{3}{10}\right)\)	\(-1\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)
\(\chi_{800}(33,\cdot)\)	800.bo	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{20}\right)\)	\(-i\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)
\(\chi_{800}(37,\cdot)\)	800.bw	40	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{40}\right)\)	\(-1\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{23}{40}\right)\)
\(\chi_{800}(39,\cdot)\)	800.bn	20	no	\(-1\)	\(1\)	\(e\left(\frac{7}{20}\right)\)	\(-1\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)
\(\chi_{800}(41,\cdot)\)	800.bm	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(-1\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{800}(43,\cdot)\)	800.v	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{800}(47,\cdot)\)	800.bp	20	no	\(1\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(-i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{20}\right)\)
\(\chi_{800}(49,\cdot)\)	800.f	2	no	\(1\)	\(1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(1\)	\(-1\)	\(-1\)	\(-1\)	\(-1\)	\(1\)
\(\chi_{800}(51,\cdot)\)	800.x	8	no	\(-1\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{800}(53,\cdot)\)	800.cc	40	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{40}\right)\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{29}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{39}{40}\right)\)
\(\chi_{800}(57,\cdot)\)	800.i	4	no	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(i\)	\(i\)	\(i\)	\(-1\)
\(\chi_{800}(59,\cdot)\)	800.bz	40	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{40}\right)\)	\(i\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{13}{40}\right)\)
\(\chi_{800}(61,\cdot)\)	800.ca	40	yes	\(1\)	\(1\)	\(e\left(\frac{29}{40}\right)\)	\(-i\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{19}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)
\(\chi_{800}(63,\cdot)\)	800.bq	20	no	\(1\)	\(1\)	\(e\left(\frac{3}{20}\right)\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)
\(\chi_{800}(67,\cdot)\)	800.bx	40	yes	\(1\)	\(1\)	\(e\left(\frac{7}{40}\right)\)	\(-1\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{31}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{33}{40}\right)\)	\(e\left(\frac{27}{40}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{21}{40}\right)\)
\(\chi_{800}(69,\cdot)\)	800.by	40	yes	\(1\)	\(1\)	\(e\left(\frac{27}{40}\right)\)	\(-i\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)
\(\chi_{800}(71,\cdot)\)	800.bs	20	no	\(-1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{800}(73,\cdot)\)	800.bv	20	no	\(-1\)	\(1\)	\(e\left(\frac{1}{10}\right)\)	\(i\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{3}{10}\right)\)
\(\chi_{800}(77,\cdot)\)	800.cc	40	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{40}\right)\)	\(1\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{3}{40}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{39}{40}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{37}{40}\right)\)
\(\chi_{800}(79,\cdot)\)	800.bi	10	no	\(-1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)

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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.