LMFDB - Group of Dirichlet characters of modulus 1000

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(1000)

gp:g = idealstar(,1000,2)

magma:G = FullDirichletGroup(1000);

Character group

Order	=	400	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{100}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{1000}(751,\cdot)$, $\chi_{1000}(501,\cdot)$, $\chi_{1000}(377,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 400 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	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{1000}(1,\cdot)$	1000.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1000}(3,\cdot)$	1000.bh	100	yes	$1$	$1$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{47}{100}\right)$
$\chi_{1000}(7,\cdot)$	1000.w	20	no	$1$	$1$	$e\left(\frac{9}{20}\right)$	$-i$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{7}{20}\right)$
$\chi_{1000}(9,\cdot)$	1000.be	50	no	$1$	$1$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{47}{50}\right)$
$\chi_{1000}(11,\cdot)$	1000.bc	50	yes	$-1$	$1$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{24}{25}\right)$
$\chi_{1000}(13,\cdot)$	1000.bj	100	yes	$-1$	$1$	$e\left(\frac{23}{100}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{71}{100}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{69}{100}\right)$
$\chi_{1000}(17,\cdot)$	1000.bg	100	no	$-1$	$1$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{33}{100}\right)$
$\chi_{1000}(19,\cdot)$	1000.ba	50	yes	$-1$	$1$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{39}{50}\right)$
$\chi_{1000}(21,\cdot)$	1000.bb	50	yes	$1$	$1$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{41}{50}\right)$
$\chi_{1000}(23,\cdot)$	1000.bi	100	no	$1$	$1$	$e\left(\frac{67}{100}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{9}{100}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{13}{25}\right)$	$e\left(\frac{11}{100}\right)$	$e\left(\frac{1}{100}\right)$
$\chi_{1000}(27,\cdot)$	1000.bh	100	yes	$1$	$1$	$e\left(\frac{47}{100}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{69}{100}\right)$	$e\left(\frac{33}{100}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{1}{100}\right)$	$e\left(\frac{41}{100}\right)$
$\chi_{1000}(29,\cdot)$	1000.bd	50	yes	$1$	$1$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{17}{25}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{33}{50}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{13}{25}\right)$
$\chi_{1000}(31,\cdot)$	1000.bf	50	no	$-1$	$1$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{29}{50}\right)$
$\chi_{1000}(33,\cdot)$	1000.bg	100	no	$-1$	$1$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{59}{100}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{73}{100}\right)$	$e\left(\frac{43}{100}\right)$
$\chi_{1000}(37,\cdot)$	1000.bj	100	yes	$-1$	$1$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{17}{100}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{9}{50}\right)$	$e\left(\frac{99}{100}\right)$	$e\left(\frac{59}{100}\right)$
$\chi_{1000}(39,\cdot)$	1000.z	50	no	$-1$	$1$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{47}{50}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{4}{25}\right)$
$\chi_{1000}(41,\cdot)$	1000.y	25	no	$1$	$1$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{16}{25}\right)$	$e\left(\frac{6}{25}\right)$
$\chi_{1000}(43,\cdot)$	1000.v	20	no	$1$	$1$	$e\left(\frac{13}{20}\right)$	$i$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{20}\right)$
$\chi_{1000}(47,\cdot)$	1000.bi	100	no	$1$	$1$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{83}{100}\right)$	$e\left(\frac{81}{100}\right)$	$e\left(\frac{24}{25}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{87}{100}\right)$
$\chi_{1000}(49,\cdot)$	1000.q	10	no	$1$	$1$	$e\left(\frac{9}{10}\right)$	$-1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$
$\chi_{1000}(51,\cdot)$	1000.n	10	no	$-1$	$1$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{4}{5}\right)$
$\chi_{1000}(53,\cdot)$	1000.bj	100	yes	$-1$	$1$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{63}{100}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{7}{50}\right)$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{57}{100}\right)$
$\chi_{1000}(57,\cdot)$	1000.l	4	no	$-1$	$1$	$-i$	$i$	$-1$	$1$	$-i$	$i$	$-1$	$1$	$-i$	$i$
$\chi_{1000}(59,\cdot)$	1000.ba	50	yes	$-1$	$1$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{19}{25}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{3}{25}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{1}{25}\right)$	$e\left(\frac{7}{50}\right)$
$\chi_{1000}(61,\cdot)$	1000.bb	50	yes	$1$	$1$	$e\left(\frac{21}{50}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{21}{25}\right)$	$e\left(\frac{3}{50}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{29}{50}\right)$	$e\left(\frac{1}{50}\right)$	$e\left(\frac{9}{25}\right)$	$e\left(\frac{13}{50}\right)$
$\chi_{1000}(63,\cdot)$	1000.bi	100	no	$1$	$1$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{61}{100}\right)$	$e\left(\frac{27}{100}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{19}{100}\right)$	$e\left(\frac{29}{100}\right)$
$\chi_{1000}(67,\cdot)$	1000.bh	100	yes	$1$	$1$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{22}{25}\right)$	$e\left(\frac{57}{100}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{73}{100}\right)$
$\chi_{1000}(69,\cdot)$	1000.bd	50	yes	$1$	$1$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{8}{25}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{17}{50}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{39}{50}\right)$	$e\left(\frac{12}{25}\right)$
$\chi_{1000}(71,\cdot)$	1000.bf	50	no	$-1$	$1$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{11}{50}\right)$	$e\left(\frac{2}{25}\right)$	$e\left(\frac{14}{25}\right)$	$e\left(\frac{23}{50}\right)$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{31}{50}\right)$
$\chi_{1000}(73,\cdot)$	1000.bg	100	no	$-1$	$1$	$e\left(\frac{37}{100}\right)$	$e\left(\frac{7}{20}\right)$	$e\left(\frac{37}{50}\right)$	$e\left(\frac{4}{25}\right)$	$e\left(\frac{49}{100}\right)$	$e\left(\frac{43}{100}\right)$	$e\left(\frac{19}{50}\right)$	$e\left(\frac{18}{25}\right)$	$e\left(\frac{21}{100}\right)$	$e\left(\frac{11}{100}\right)$
$\chi_{1000}(77,\cdot)$	1000.bj	100	yes	$-1$	$1$	$e\left(\frac{77}{100}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{27}{50}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{29}{100}\right)$	$e\left(\frac{53}{100}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{31}{50}\right)$	$e\left(\frac{91}{100}\right)$	$e\left(\frac{31}{100}\right)$
$\chi_{1000}(79,\cdot)$	1000.z	50	no	$-1$	$1$	$e\left(\frac{6}{25}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{12}{25}\right)$	$e\left(\frac{41}{50}\right)$	$e\left(\frac{49}{50}\right)$	$e\left(\frac{43}{50}\right)$	$e\left(\frac{13}{50}\right)$	$e\left(\frac{11}{25}\right)$	$e\left(\frac{23}{25}\right)$	$e\left(\frac{18}{25}\right)$

Click here to search among the remaining 368 characters.

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	$1000$
Structure	\(C_{2}\times C_{2}\times C_{100}\)
Order	$400$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(7\)	\(9\)	\(11\)	\(13\)	\(17\)	\(19\)	\(21\)	\(23\)	\(27\)
\(\chi_{1000}(1,\cdot)\)	1000.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1000}(3,\cdot)\)	1000.bh	100	yes	\(1\)	\(1\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{9}{20}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{47}{100}\right)\)
\(\chi_{1000}(7,\cdot)\)	1000.w	20	no	\(1\)	\(1\)	\(e\left(\frac{9}{20}\right)\)	\(-i\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)
\(\chi_{1000}(9,\cdot)\)	1000.be	50	no	\(1\)	\(1\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{47}{50}\right)\)
\(\chi_{1000}(11,\cdot)\)	1000.bc	50	yes	\(-1\)	\(1\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)
\(\chi_{1000}(13,\cdot)\)	1000.bj	100	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{100}\right)\)	\(e\left(\frac{3}{20}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{71}{100}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{69}{100}\right)\)
\(\chi_{1000}(17,\cdot)\)	1000.bg	100	no	\(-1\)	\(1\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{33}{100}\right)\)
\(\chi_{1000}(19,\cdot)\)	1000.ba	50	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{39}{50}\right)\)
\(\chi_{1000}(21,\cdot)\)	1000.bb	50	yes	\(1\)	\(1\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)
\(\chi_{1000}(23,\cdot)\)	1000.bi	100	no	\(1\)	\(1\)	\(e\left(\frac{67}{100}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{9}{100}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{13}{25}\right)\)	\(e\left(\frac{11}{100}\right)\)	\(e\left(\frac{1}{100}\right)\)
\(\chi_{1000}(27,\cdot)\)	1000.bh	100	yes	\(1\)	\(1\)	\(e\left(\frac{47}{100}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{69}{100}\right)\)	\(e\left(\frac{33}{100}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{1}{100}\right)\)	\(e\left(\frac{41}{100}\right)\)
\(\chi_{1000}(29,\cdot)\)	1000.bd	50	yes	\(1\)	\(1\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{17}{25}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{33}{50}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{13}{25}\right)\)
\(\chi_{1000}(31,\cdot)\)	1000.bf	50	no	\(-1\)	\(1\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{29}{50}\right)\)
\(\chi_{1000}(33,\cdot)\)	1000.bg	100	no	\(-1\)	\(1\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{59}{100}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{73}{100}\right)\)	\(e\left(\frac{43}{100}\right)\)
\(\chi_{1000}(37,\cdot)\)	1000.bj	100	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{17}{100}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{9}{50}\right)\)	\(e\left(\frac{99}{100}\right)\)	\(e\left(\frac{59}{100}\right)\)
\(\chi_{1000}(39,\cdot)\)	1000.z	50	no	\(-1\)	\(1\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{47}{50}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)
\(\chi_{1000}(41,\cdot)\)	1000.y	25	no	\(1\)	\(1\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{16}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)
\(\chi_{1000}(43,\cdot)\)	1000.v	20	no	\(1\)	\(1\)	\(e\left(\frac{13}{20}\right)\)	\(i\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{20}\right)\)
\(\chi_{1000}(47,\cdot)\)	1000.bi	100	no	\(1\)	\(1\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{83}{100}\right)\)	\(e\left(\frac{81}{100}\right)\)	\(e\left(\frac{24}{25}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{87}{100}\right)\)
\(\chi_{1000}(49,\cdot)\)	1000.q	10	no	\(1\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(-1\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)
\(\chi_{1000}(51,\cdot)\)	1000.n	10	no	\(-1\)	\(1\)	\(e\left(\frac{3}{5}\right)\)	\(-1\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{4}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{4}{5}\right)\)
\(\chi_{1000}(53,\cdot)\)	1000.bj	100	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{19}{20}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{63}{100}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{57}{100}\right)\)
\(\chi_{1000}(57,\cdot)\)	1000.l	4	no	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(i\)	\(-1\)	\(1\)	\(-i\)	\(i\)
\(\chi_{1000}(59,\cdot)\)	1000.ba	50	yes	\(-1\)	\(1\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{19}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{3}{25}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{1}{25}\right)\)	\(e\left(\frac{7}{50}\right)\)
\(\chi_{1000}(61,\cdot)\)	1000.bb	50	yes	\(1\)	\(1\)	\(e\left(\frac{21}{50}\right)\)	\(e\left(\frac{3}{5}\right)\)	\(e\left(\frac{21}{25}\right)\)	\(e\left(\frac{3}{50}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{29}{50}\right)\)	\(e\left(\frac{1}{50}\right)\)	\(e\left(\frac{9}{25}\right)\)	\(e\left(\frac{13}{50}\right)\)
\(\chi_{1000}(63,\cdot)\)	1000.bi	100	no	\(1\)	\(1\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{61}{100}\right)\)	\(e\left(\frac{27}{100}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{19}{100}\right)\)	\(e\left(\frac{29}{100}\right)\)
\(\chi_{1000}(67,\cdot)\)	1000.bh	100	yes	\(1\)	\(1\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{11}{20}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{22}{25}\right)\)	\(e\left(\frac{57}{100}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{73}{100}\right)\)
\(\chi_{1000}(69,\cdot)\)	1000.bd	50	yes	\(1\)	\(1\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{3}{10}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{8}{25}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{17}{50}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{39}{50}\right)\)	\(e\left(\frac{12}{25}\right)\)
\(\chi_{1000}(71,\cdot)\)	1000.bf	50	no	\(-1\)	\(1\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{11}{50}\right)\)	\(e\left(\frac{2}{25}\right)\)	\(e\left(\frac{14}{25}\right)\)	\(e\left(\frac{23}{50}\right)\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{31}{50}\right)\)
\(\chi_{1000}(73,\cdot)\)	1000.bg	100	no	\(-1\)	\(1\)	\(e\left(\frac{37}{100}\right)\)	\(e\left(\frac{7}{20}\right)\)	\(e\left(\frac{37}{50}\right)\)	\(e\left(\frac{4}{25}\right)\)	\(e\left(\frac{49}{100}\right)\)	\(e\left(\frac{43}{100}\right)\)	\(e\left(\frac{19}{50}\right)\)	\(e\left(\frac{18}{25}\right)\)	\(e\left(\frac{21}{100}\right)\)	\(e\left(\frac{11}{100}\right)\)
\(\chi_{1000}(77,\cdot)\)	1000.bj	100	yes	\(-1\)	\(1\)	\(e\left(\frac{77}{100}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{27}{50}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{29}{100}\right)\)	\(e\left(\frac{53}{100}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{31}{50}\right)\)	\(e\left(\frac{91}{100}\right)\)	\(e\left(\frac{31}{100}\right)\)
\(\chi_{1000}(79,\cdot)\)	1000.z	50	no	\(-1\)	\(1\)	\(e\left(\frac{6}{25}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{12}{25}\right)\)	\(e\left(\frac{41}{50}\right)\)	\(e\left(\frac{49}{50}\right)\)	\(e\left(\frac{43}{50}\right)\)	\(e\left(\frac{13}{50}\right)\)	\(e\left(\frac{11}{25}\right)\)	\(e\left(\frac{23}{25}\right)\)	\(e\left(\frac{18}{25}\right)\)

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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.