LMFDB - Group of Dirichlet characters of modulus 1020

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(1020)

gp:g = idealstar(,1020,2)

magma:G = FullDirichletGroup(1020);

Character group

Order	=	256	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{4}\times C_{16}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{1020}(511,\cdot)$, $\chi_{1020}(341,\cdot)$, $\chi_{1020}(817,\cdot)$, $\chi_{1020}(241,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 256 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	$-1$	$1$	$7$	$11$	$13$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{1020}(1,\cdot)$	1020.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1020}(7,\cdot)$	1020.ce	16	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1020}(11,\cdot)$	1020.co	16	no	$-1$	$1$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1020}(13,\cdot)$	1020.t	4	no	$-1$	$1$	$-1$	$-i$	$i$	$1$	$1$	$-i$	$i$	$1$	$-i$	$-i$
$\chi_{1020}(19,\cdot)$	1020.cb	8	no	$-1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$-i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$
$\chi_{1020}(23,\cdot)$	1020.cr	16	yes	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{16}\right)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1020}(29,\cdot)$	1020.cp	16	no	$1$	$1$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{1020}(31,\cdot)$	1020.cn	16	no	$1$	$1$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1020}(37,\cdot)$	1020.cq	16	no	$1$	$1$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{16}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1020}(41,\cdot)$	1020.ck	16	no	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1020}(43,\cdot)$	1020.by	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$-i$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$
$\chi_{1020}(47,\cdot)$	1020.q	4	yes	$-1$	$1$	$-1$	$-i$	$-i$	$-1$	$-1$	$i$	$-i$	$-1$	$i$	$-i$
$\chi_{1020}(49,\cdot)$	1020.cc	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$1$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$i$
$\chi_{1020}(53,\cdot)$	1020.bz	8	no	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$-i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$1$
$\chi_{1020}(59,\cdot)$	1020.cd	8	yes	$1$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$
$\chi_{1020}(61,\cdot)$	1020.cj	16	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1020}(67,\cdot)$	1020.bj	4	no	$1$	$1$	$i$	$1$	$-i$	$1$	$-i$	$1$	$1$	$-i$	$-1$	$i$
$\chi_{1020}(71,\cdot)$	1020.co	16	no	$-1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{16}\right)$	$i$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{8}\right)$
$\chi_{1020}(73,\cdot)$	1020.cg	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{16}\right)$	$-1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1020}(77,\cdot)$	1020.bz	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$i$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$1$
$\chi_{1020}(79,\cdot)$	1020.ci	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{9}{16}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1020}(83,\cdot)$	1020.bu	8	yes	$-1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$	$i$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-1$
$\chi_{1020}(89,\cdot)$	1020.z	4	no	$-1$	$1$	$-i$	$-i$	$-1$	$-1$	$i$	$i$	$-i$	$i$	$-i$	$1$
$\chi_{1020}(91,\cdot)$	1020.cn	16	no	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{1}{16}\right)$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1020}(97,\cdot)$	1020.cq	16	no	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{11}{16}\right)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{8}\right)$
$\chi_{1020}(101,\cdot)$	1020.i	2	no	$-1$	$1$	$-1$	$1$	$1$	$1$	$1$	$1$	$-1$	$-1$	$1$	$1$
$\chi_{1020}(103,\cdot)$	1020.w	4	no	$1$	$1$	$i$	$-1$	$i$	$1$	$-i$	$-1$	$-1$	$-i$	$1$	$-i$
$\chi_{1020}(107,\cdot)$	1020.cr	16	yes	$1$	$1$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{16}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1020}(109,\cdot)$	1020.cm	16	no	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{13}{16}\right)$	$i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{7}{8}\right)$
$\chi_{1020}(113,\cdot)$	1020.ct	16	no	$-1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{9}{16}\right)$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{1}{8}\right)$
$\chi_{1020}(121,\cdot)$	1020.bp	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$-1$	$i$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{5}{8}\right)$	$-i$
$\chi_{1020}(127,\cdot)$	1020.bt	8	no	$1$	$1$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{7}{8}\right)$	$i$	$-i$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{7}{8}\right)$	$-1$

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$1020$
Structure	\(C_{2}\times C_{2}\times C_{4}\times C_{16}\)
Order	$256$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)	\(43\)
\(\chi_{1020}(1,\cdot)\)	1020.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1020}(7,\cdot)\)	1020.ce	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1020}(11,\cdot)\)	1020.co	16	no	\(-1\)	\(1\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1020}(13,\cdot)\)	1020.t	4	no	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(i\)	\(1\)	\(1\)	\(-i\)	\(i\)	\(1\)	\(-i\)	\(-i\)
\(\chi_{1020}(19,\cdot)\)	1020.cb	8	no	\(-1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(-i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)
\(\chi_{1020}(23,\cdot)\)	1020.cr	16	yes	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(1\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1020}(29,\cdot)\)	1020.cp	16	no	\(1\)	\(1\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{1020}(31,\cdot)\)	1020.cn	16	no	\(1\)	\(1\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1020}(37,\cdot)\)	1020.cq	16	no	\(1\)	\(1\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1020}(41,\cdot)\)	1020.ck	16	no	\(1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1020}(43,\cdot)\)	1020.by	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)
\(\chi_{1020}(47,\cdot)\)	1020.q	4	yes	\(-1\)	\(1\)	\(-1\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(-i\)	\(-1\)	\(i\)	\(-i\)
\(\chi_{1020}(49,\cdot)\)	1020.cc	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(i\)
\(\chi_{1020}(53,\cdot)\)	1020.bz	8	no	\(1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(-i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(1\)
\(\chi_{1020}(59,\cdot)\)	1020.cd	8	yes	\(1\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)
\(\chi_{1020}(61,\cdot)\)	1020.cj	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1020}(67,\cdot)\)	1020.bj	4	no	\(1\)	\(1\)	\(i\)	\(1\)	\(-i\)	\(1\)	\(-i\)	\(1\)	\(1\)	\(-i\)	\(-1\)	\(i\)
\(\chi_{1020}(71,\cdot)\)	1020.co	16	no	\(-1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(i\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{8}\right)\)
\(\chi_{1020}(73,\cdot)\)	1020.cg	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(-1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1020}(77,\cdot)\)	1020.bz	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(i\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(1\)
\(\chi_{1020}(79,\cdot)\)	1020.ci	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1020}(83,\cdot)\)	1020.bu	8	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)	\(i\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-1\)
\(\chi_{1020}(89,\cdot)\)	1020.z	4	no	\(-1\)	\(1\)	\(-i\)	\(-i\)	\(-1\)	\(-1\)	\(i\)	\(i\)	\(-i\)	\(i\)	\(-i\)	\(1\)
\(\chi_{1020}(91,\cdot)\)	1020.cn	16	no	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1020}(97,\cdot)\)	1020.cq	16	no	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(1\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)
\(\chi_{1020}(101,\cdot)\)	1020.i	2	no	\(-1\)	\(1\)	\(-1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(-1\)	\(-1\)	\(1\)	\(1\)
\(\chi_{1020}(103,\cdot)\)	1020.w	4	no	\(1\)	\(1\)	\(i\)	\(-1\)	\(i\)	\(1\)	\(-i\)	\(-1\)	\(-1\)	\(-i\)	\(1\)	\(-i\)
\(\chi_{1020}(107,\cdot)\)	1020.cr	16	yes	\(1\)	\(1\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{16}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1020}(109,\cdot)\)	1020.cm	16	no	\(-1\)	\(1\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)
\(\chi_{1020}(113,\cdot)\)	1020.ct	16	no	\(-1\)	\(1\)	\(e\left(\frac{9}{16}\right)\)	\(e\left(\frac{9}{16}\right)\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{5}{16}\right)\)	\(e\left(\frac{1}{8}\right)\)
\(\chi_{1020}(121,\cdot)\)	1020.bp	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(-1\)	\(i\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(-i\)
\(\chi_{1020}(127,\cdot)\)	1020.bt	8	no	\(1\)	\(1\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(i\)	\(-i\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)

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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.