LMFDB - Group of Dirichlet characters of modulus 1011

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1011)

pari: g = idealstar(,1011,2)

Character group

sage: G.order() pari: g.no
Order	=	672
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{336}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1011}(338,\cdot)$, $\chi_{1011}(10,\cdot)$

First 32 of 672 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	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{1011}(1,\cdot)$	1011.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1011}(2,\cdot)$	1011.ba	42	yes	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{1011}(4,\cdot)$	1011.u	21	no	$1$	$1$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{8}{21}\right)$
$\chi_{1011}(5,\cdot)$	1011.bj	112	yes	$1$	$1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{3}{7}\right)$
$\chi_{1011}(7,\cdot)$	1011.be	56	no	$1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{27}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{1011}(8,\cdot)$	1011.r	14	yes	$-1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{1011}(10,\cdot)$	1011.bn	336	no	$-1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{11}{112}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{336}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{1011}(11,\cdot)$	1011.bj	112	yes	$1$	$1$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{47}{56}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{57}{112}\right)$	$e\left(\frac{59}{112}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{1011}(13,\cdot)$	1011.u	21	no	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{19}{21}\right)$
$\chi_{1011}(14,\cdot)$	1011.bk	168	yes	$-1$	$1$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{143}{168}\right)$	$e\left(\frac{3}{56}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{79}{84}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{1011}(16,\cdot)$	1011.u	21	no	$1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{1011}(17,\cdot)$	1011.bj	112	yes	$1$	$1$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{43}{112}\right)$	$e\left(\frac{29}{56}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{3}{112}\right)$	$e\left(\frac{9}{112}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{4}{7}\right)$
$\chi_{1011}(19,\cdot)$	1011.bn	336	no	$-1$	$1$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{79}{112}\right)$	$e\left(\frac{9}{56}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{109}{336}\right)$	$e\left(\frac{53}{112}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{131}{168}\right)$	$e\left(\frac{10}{21}\right)$
$\chi_{1011}(20,\cdot)$	1011.bm	336	yes	$1$	$1$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{51}{112}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{305}{336}\right)$	$e\left(\frac{81}{112}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{168}\right)$	$e\left(\frac{17}{21}\right)$
$\chi_{1011}(22,\cdot)$	1011.bn	336	no	$-1$	$1$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{73}{112}\right)$	$e\left(\frac{31}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{139}{336}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{53}{168}\right)$	$e\left(\frac{1}{21}\right)$
$\chi_{1011}(23,\cdot)$	1011.bm	336	yes	$1$	$1$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{111}{112}\right)$	$e\left(\frac{41}{56}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{229}{336}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{1011}(25,\cdot)$	1011.be	56	no	$1$	$1$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{27}{56}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{6}{7}\right)$
$\chi_{1011}(26,\cdot)$	1011.ba	42	yes	$-1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{1011}(28,\cdot)$	1011.bl	168	no	$1$	$1$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{53}{56}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{127}{168}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{17}{84}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{1011}(29,\cdot)$	1011.bm	336	yes	$1$	$1$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{257}{336}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{43}{168}\right)$	$e\left(\frac{2}{21}\right)$
$\chi_{1011}(31,\cdot)$	1011.bn	336	no	$-1$	$1$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{103}{112}\right)$	$e\left(\frac{33}{56}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{101}{336}\right)$	$e\left(\frac{45}{112}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{163}{168}\right)$	$e\left(\frac{11}{21}\right)$
$\chi_{1011}(32,\cdot)$	1011.ba	42	yes	$-1$	$1$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{1011}(34,\cdot)$	1011.bn	336	no	$-1$	$1$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{83}{112}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{313}{336}\right)$	$e\left(\frac{33}{112}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{71}{168}\right)$	$e\left(\frac{16}{21}\right)$
$\chi_{1011}(35,\cdot)$	1011.bj	112	yes	$1$	$1$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{109}{112}\right)$	$e\left(\frac{11}{56}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{112}\right)$	$e\left(\frac{15}{112}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{1011}(37,\cdot)$	1011.bh	84	no	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{15}{28}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{9}{28}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{13}{21}\right)$
$\chi_{1011}(38,\cdot)$	1011.bd	48	yes	$1$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{7}{8}\right)$	$-1$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{1011}(40,\cdot)$	1011.t	16	no	$-1$	$1$	$1$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{3}{8}\right)$	$1$	$e\left(\frac{13}{16}\right)$	$e\left(\frac{15}{16}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$1$
$\chi_{1011}(41,\cdot)$	1011.bg	84	yes	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{55}{84}\right)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{4}{21}\right)$
$\chi_{1011}(43,\cdot)$	1011.be	56	no	$1$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{37}{56}\right)$	$e\left(\frac{23}{28}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{13}{56}\right)$	$e\left(\frac{39}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{2}{7}\right)$
$\chi_{1011}(44,\cdot)$	1011.bm	336	yes	$1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{1}{112}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{107}{336}\right)$	$e\left(\frac{107}{112}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{97}{168}\right)$	$e\left(\frac{5}{21}\right)$
$\chi_{1011}(46,\cdot)$	1011.bn	336	no	$-1$	$1$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{39}{112}\right)$	$e\left(\frac{25}{56}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{197}{336}\right)$	$e\left(\frac{29}{112}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{115}{168}\right)$	$e\left(\frac{20}{21}\right)$
$\chi_{1011}(47,\cdot)$	1011.bf	56	yes	$-1$	$1$	$e\left(\frac{13}{14}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{19}{56}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{15}{56}\right)$	$e\left(\frac{17}{56}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{5}{7}\right)$

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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	$1011$
Structure	\(C_{2}\times C_{336}\)
Order	$672$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{1011}(1,\cdot)\)	1011.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1011}(2,\cdot)\)	1011.ba	42	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{1011}(4,\cdot)\)	1011.u	21	no	\(1\)	\(1\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)
\(\chi_{1011}(5,\cdot)\)	1011.bj	112	yes	\(1\)	\(1\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{3}{7}\right)\)
\(\chi_{1011}(7,\cdot)\)	1011.be	56	no	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{27}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{1011}(8,\cdot)\)	1011.r	14	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{1011}(10,\cdot)\)	1011.bn	336	no	\(-1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{11}{112}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{1}{336}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{1011}(11,\cdot)\)	1011.bj	112	yes	\(1\)	\(1\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{47}{56}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{57}{112}\right)\)	\(e\left(\frac{59}{112}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{1011}(13,\cdot)\)	1011.u	21	no	\(1\)	\(1\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{19}{21}\right)\)
\(\chi_{1011}(14,\cdot)\)	1011.bk	168	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{42}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{143}{168}\right)\)	\(e\left(\frac{3}{56}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{79}{84}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{1011}(16,\cdot)\)	1011.u	21	no	\(1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{1011}(17,\cdot)\)	1011.bj	112	yes	\(1\)	\(1\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{43}{112}\right)\)	\(e\left(\frac{29}{56}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{3}{112}\right)\)	\(e\left(\frac{9}{112}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)
\(\chi_{1011}(19,\cdot)\)	1011.bn	336	no	\(-1\)	\(1\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{79}{112}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{109}{336}\right)\)	\(e\left(\frac{53}{112}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{131}{168}\right)\)	\(e\left(\frac{10}{21}\right)\)
\(\chi_{1011}(20,\cdot)\)	1011.bm	336	yes	\(1\)	\(1\)	\(e\left(\frac{19}{42}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{51}{112}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{305}{336}\right)\)	\(e\left(\frac{81}{112}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{19}{168}\right)\)	\(e\left(\frac{17}{21}\right)\)
\(\chi_{1011}(22,\cdot)\)	1011.bn	336	no	\(-1\)	\(1\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{73}{112}\right)\)	\(e\left(\frac{31}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{139}{336}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{53}{168}\right)\)	\(e\left(\frac{1}{21}\right)\)
\(\chi_{1011}(23,\cdot)\)	1011.bm	336	yes	\(1\)	\(1\)	\(e\left(\frac{29}{42}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{111}{112}\right)\)	\(e\left(\frac{41}{56}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{229}{336}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{1011}(25,\cdot)\)	1011.be	56	no	\(1\)	\(1\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{27}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{6}{7}\right)\)
\(\chi_{1011}(26,\cdot)\)	1011.ba	42	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{20}{21}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{37}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{1011}(28,\cdot)\)	1011.bl	168	no	\(1\)	\(1\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{3}{7}\right)\)	\(e\left(\frac{127}{168}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{17}{84}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{1011}(29,\cdot)\)	1011.bm	336	yes	\(1\)	\(1\)	\(e\left(\frac{1}{42}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{257}{336}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{43}{168}\right)\)	\(e\left(\frac{2}{21}\right)\)
\(\chi_{1011}(31,\cdot)\)	1011.bn	336	no	\(-1\)	\(1\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{103}{112}\right)\)	\(e\left(\frac{33}{56}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{101}{336}\right)\)	\(e\left(\frac{45}{112}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{163}{168}\right)\)	\(e\left(\frac{11}{21}\right)\)
\(\chi_{1011}(32,\cdot)\)	1011.ba	42	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{1011}(34,\cdot)\)	1011.bn	336	no	\(-1\)	\(1\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{83}{112}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{313}{336}\right)\)	\(e\left(\frac{33}{112}\right)\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{71}{168}\right)\)	\(e\left(\frac{16}{21}\right)\)
\(\chi_{1011}(35,\cdot)\)	1011.bj	112	yes	\(1\)	\(1\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{109}{112}\right)\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{5}{112}\right)\)	\(e\left(\frac{15}{112}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{1011}(37,\cdot)\)	1011.bh	84	no	\(1\)	\(1\)	\(e\left(\frac{19}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{1}{14}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{37}{84}\right)\)	\(e\left(\frac{9}{28}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{41}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)
\(\chi_{1011}(38,\cdot)\)	1011.bd	48	yes	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{16}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(-1\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{11}{16}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{1011}(40,\cdot)\)	1011.t	16	no	\(-1\)	\(1\)	\(1\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(1\)	\(e\left(\frac{13}{16}\right)\)	\(e\left(\frac{15}{16}\right)\)	\(1\)	\(e\left(\frac{3}{8}\right)\)	\(1\)
\(\chi_{1011}(41,\cdot)\)	1011.bg	84	yes	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{3}{14}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{55}{84}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{16}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)
\(\chi_{1011}(43,\cdot)\)	1011.be	56	no	\(1\)	\(1\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{1}{7}\right)\)	\(e\left(\frac{37}{56}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{13}{56}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{2}{7}\right)\)
\(\chi_{1011}(44,\cdot)\)	1011.bm	336	yes	\(1\)	\(1\)	\(e\left(\frac{13}{42}\right)\)	\(e\left(\frac{13}{21}\right)\)	\(e\left(\frac{1}{112}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{107}{336}\right)\)	\(e\left(\frac{107}{112}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{97}{168}\right)\)	\(e\left(\frac{5}{21}\right)\)
\(\chi_{1011}(46,\cdot)\)	1011.bn	336	no	\(-1\)	\(1\)	\(e\left(\frac{5}{21}\right)\)	\(e\left(\frac{10}{21}\right)\)	\(e\left(\frac{39}{112}\right)\)	\(e\left(\frac{25}{56}\right)\)	\(e\left(\frac{5}{7}\right)\)	\(e\left(\frac{197}{336}\right)\)	\(e\left(\frac{29}{112}\right)\)	\(e\left(\frac{8}{21}\right)\)	\(e\left(\frac{115}{168}\right)\)	\(e\left(\frac{20}{21}\right)\)
\(\chi_{1011}(47,\cdot)\)	1011.bf	56	yes	\(-1\)	\(1\)	\(e\left(\frac{13}{14}\right)\)	\(e\left(\frac{6}{7}\right)\)	\(e\left(\frac{19}{56}\right)\)	\(e\left(\frac{5}{28}\right)\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{17}{56}\right)\)	\(e\left(\frac{2}{7}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{5}{7}\right)\)

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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.