LMFDB - Group of Dirichlet characters of modulus 1667

sage:H = DirichletGroup(1667)

pari:g = idealstar(,1667,2)

Character group

sage:G.order() pari:g.no
Order	=	1666
sage:H.invariants() pari:g.cyc
Structure	=	$C_{1666}$
sage:H.gens() pari:g.gen
Generators	=	$\chi_{1667}(2,\cdot)$

First 32 of 1666 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1667}(1,\cdot)$	1667.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1667}(2,\cdot)$	1667.l	1666	yes	$-1$	$1$	$e\left(\frac{1}{1666}\right)$	$e\left(\frac{607}{833}\right)$	$e\left(\frac{1}{833}\right)$	$e\left(\frac{1457}{1666}\right)$	$e\left(\frac{1215}{1666}\right)$	$e\left(\frac{1031}{1666}\right)$	$e\left(\frac{3}{1666}\right)$	$e\left(\frac{381}{833}\right)$	$e\left(\frac{729}{833}\right)$	$e\left(\frac{236}{833}\right)$
$\chi_{1667}(3,\cdot)$	1667.k	833	yes	$1$	$1$	$e\left(\frac{607}{833}\right)$	$e\left(\frac{526}{833}\right)$	$e\left(\frac{381}{833}\right)$	$e\left(\frac{586}{833}\right)$	$e\left(\frac{300}{833}\right)$	$e\left(\frac{234}{833}\right)$	$e\left(\frac{155}{833}\right)$	$e\left(\frac{219}{833}\right)$	$e\left(\frac{360}{833}\right)$	$e\left(\frac{785}{833}\right)$
$\chi_{1667}(4,\cdot)$	1667.k	833	yes	$1$	$1$	$e\left(\frac{1}{833}\right)$	$e\left(\frac{381}{833}\right)$	$e\left(\frac{2}{833}\right)$	$e\left(\frac{624}{833}\right)$	$e\left(\frac{382}{833}\right)$	$e\left(\frac{198}{833}\right)$	$e\left(\frac{3}{833}\right)$	$e\left(\frac{762}{833}\right)$	$e\left(\frac{625}{833}\right)$	$e\left(\frac{472}{833}\right)$
$\chi_{1667}(5,\cdot)$	1667.l	1666	yes	$-1$	$1$	$e\left(\frac{1457}{1666}\right)$	$e\left(\frac{586}{833}\right)$	$e\left(\frac{624}{833}\right)$	$e\left(\frac{365}{1666}\right)$	$e\left(\frac{963}{1666}\right)$	$e\left(\frac{1101}{1666}\right)$	$e\left(\frac{1039}{1666}\right)$	$e\left(\frac{339}{833}\right)$	$e\left(\frac{78}{833}\right)$	$e\left(\frac{656}{833}\right)$
$\chi_{1667}(6,\cdot)$	1667.l	1666	yes	$-1$	$1$	$e\left(\frac{1215}{1666}\right)$	$e\left(\frac{300}{833}\right)$	$e\left(\frac{382}{833}\right)$	$e\left(\frac{963}{1666}\right)$	$e\left(\frac{149}{1666}\right)$	$e\left(\frac{1499}{1666}\right)$	$e\left(\frac{313}{1666}\right)$	$e\left(\frac{600}{833}\right)$	$e\left(\frac{256}{833}\right)$	$e\left(\frac{188}{833}\right)$
$\chi_{1667}(7,\cdot)$	1667.l	1666	yes	$-1$	$1$	$e\left(\frac{1031}{1666}\right)$	$e\left(\frac{234}{833}\right)$	$e\left(\frac{198}{833}\right)$	$e\left(\frac{1101}{1666}\right)$	$e\left(\frac{1499}{1666}\right)$	$e\left(\frac{53}{1666}\right)$	$e\left(\frac{1427}{1666}\right)$	$e\left(\frac{468}{833}\right)$	$e\left(\frac{233}{833}\right)$	$e\left(\frac{80}{833}\right)$
$\chi_{1667}(8,\cdot)$	1667.l	1666	yes	$-1$	$1$	$e\left(\frac{3}{1666}\right)$	$e\left(\frac{155}{833}\right)$	$e\left(\frac{3}{833}\right)$	$e\left(\frac{1039}{1666}\right)$	$e\left(\frac{313}{1666}\right)$	$e\left(\frac{1427}{1666}\right)$	$e\left(\frac{9}{1666}\right)$	$e\left(\frac{310}{833}\right)$	$e\left(\frac{521}{833}\right)$	$e\left(\frac{708}{833}\right)$
$\chi_{1667}(9,\cdot)$	1667.k	833	yes	$1$	$1$	$e\left(\frac{381}{833}\right)$	$e\left(\frac{219}{833}\right)$	$e\left(\frac{762}{833}\right)$	$e\left(\frac{339}{833}\right)$	$e\left(\frac{600}{833}\right)$	$e\left(\frac{468}{833}\right)$	$e\left(\frac{310}{833}\right)$	$e\left(\frac{438}{833}\right)$	$e\left(\frac{720}{833}\right)$	$e\left(\frac{737}{833}\right)$
$\chi_{1667}(10,\cdot)$	1667.k	833	yes	$1$	$1$	$e\left(\frac{729}{833}\right)$	$e\left(\frac{360}{833}\right)$	$e\left(\frac{625}{833}\right)$	$e\left(\frac{78}{833}\right)$	$e\left(\frac{256}{833}\right)$	$e\left(\frac{233}{833}\right)$	$e\left(\frac{521}{833}\right)$	$e\left(\frac{720}{833}\right)$	$e\left(\frac{807}{833}\right)$	$e\left(\frac{59}{833}\right)$
$\chi_{1667}(11,\cdot)$	1667.k	833	yes	$1$	$1$	$e\left(\frac{236}{833}\right)$	$e\left(\frac{785}{833}\right)$	$e\left(\frac{472}{833}\right)$	$e\left(\frac{656}{833}\right)$	$e\left(\frac{188}{833}\right)$	$e\left(\frac{80}{833}\right)$	$e\left(\frac{708}{833}\right)$	$e\left(\frac{737}{833}\right)$	$e\left(\frac{59}{833}\right)$	$e\left(\frac{603}{833}\right)$
$\chi_{1667}(12,\cdot)$	1667.k	833	yes	$1$	$1$	$e\left(\frac{608}{833}\right)$	$e\left(\frac{74}{833}\right)$	$e\left(\frac{383}{833}\right)$	$e\left(\frac{377}{833}\right)$	$e\left(\frac{682}{833}\right)$	$e\left(\frac{432}{833}\right)$	$e\left(\frac{158}{833}\right)$	$e\left(\frac{148}{833}\right)$	$e\left(\frac{152}{833}\right)$	$e\left(\frac{424}{833}\right)$
$\chi_{1667}(13,\cdot)$	1667.g	49	yes	$1$	$1$	$e\left(\frac{11}{49}\right)$	$e\left(\frac{26}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{4}{49}\right)$	$e\left(\frac{37}{49}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{33}{49}\right)$	$e\left(\frac{3}{49}\right)$	$e\left(\frac{15}{49}\right)$	$e\left(\frac{47}{49}\right)$
$\chi_{1667}(14,\cdot)$	1667.k	833	yes	$1$	$1$	$e\left(\frac{516}{833}\right)$	$e\left(\frac{8}{833}\right)$	$e\left(\frac{199}{833}\right)$	$e\left(\frac{446}{833}\right)$	$e\left(\frac{524}{833}\right)$	$e\left(\frac{542}{833}\right)$	$e\left(\frac{715}{833}\right)$	$e\left(\frac{16}{833}\right)$	$e\left(\frac{129}{833}\right)$	$e\left(\frac{316}{833}\right)$
$\chi_{1667}(15,\cdot)$	1667.l	1666	yes	$-1$	$1$	$e\left(\frac{1005}{1666}\right)$	$e\left(\frac{279}{833}\right)$	$e\left(\frac{172}{833}\right)$	$e\left(\frac{1537}{1666}\right)$	$e\left(\frac{1563}{1666}\right)$	$e\left(\frac{1569}{1666}\right)$	$e\left(\frac{1349}{1666}\right)$	$e\left(\frac{558}{833}\right)$	$e\left(\frac{438}{833}\right)$	$e\left(\frac{608}{833}\right)$
$\chi_{1667}(16,\cdot)$	1667.k	833	yes	$1$	$1$	$e\left(\frac{2}{833}\right)$	$e\left(\frac{762}{833}\right)$	$e\left(\frac{4}{833}\right)$	$e\left(\frac{415}{833}\right)$	$e\left(\frac{764}{833}\right)$	$e\left(\frac{396}{833}\right)$	$e\left(\frac{6}{833}\right)$	$e\left(\frac{691}{833}\right)$	$e\left(\frac{417}{833}\right)$	$e\left(\frac{111}{833}\right)$
$\chi_{1667}(17,\cdot)$	1667.k	833	yes	$1$	$1$	$e\left(\frac{218}{833}\right)$	$e\left(\frac{591}{833}\right)$	$e\left(\frac{436}{833}\right)$	$e\left(\frac{253}{833}\right)$	$e\left(\frac{809}{833}\right)$	$e\left(\frac{681}{833}\right)$	$e\left(\frac{654}{833}\right)$	$e\left(\frac{349}{833}\right)$	$e\left(\frac{471}{833}\right)$	$e\left(\frac{437}{833}\right)$
$\chi_{1667}(18,\cdot)$	1667.j	238	yes	$-1$	$1$	$e\left(\frac{109}{238}\right)$	$e\left(\frac{118}{119}\right)$	$e\left(\frac{109}{119}\right)$	$e\left(\frac{67}{238}\right)$	$e\left(\frac{107}{238}\right)$	$e\left(\frac{43}{238}\right)$	$e\left(\frac{89}{238}\right)$	$e\left(\frac{117}{119}\right)$	$e\left(\frac{88}{119}\right)$	$e\left(\frac{20}{119}\right)$
$\chi_{1667}(19,\cdot)$	1667.k	833	yes	$1$	$1$	$e\left(\frac{491}{833}\right)$	$e\left(\frac{479}{833}\right)$	$e\left(\frac{149}{833}\right)$	$e\left(\frac{673}{833}\right)$	$e\left(\frac{137}{833}\right)$	$e\left(\frac{590}{833}\right)$	$e\left(\frac{640}{833}\right)$	$e\left(\frac{125}{833}\right)$	$e\left(\frac{331}{833}\right)$	$e\left(\frac{178}{833}\right)$
$\chi_{1667}(20,\cdot)$	1667.l	1666	yes	$-1$	$1$	$e\left(\frac{1459}{1666}\right)$	$e\left(\frac{134}{833}\right)$	$e\left(\frac{626}{833}\right)$	$e\left(\frac{1613}{1666}\right)$	$e\left(\frac{61}{1666}\right)$	$e\left(\frac{1497}{1666}\right)$	$e\left(\frac{1045}{1666}\right)$	$e\left(\frac{268}{833}\right)$	$e\left(\frac{703}{833}\right)$	$e\left(\frac{295}{833}\right)$
$\chi_{1667}(21,\cdot)$	1667.l	1666	yes	$-1$	$1$	$e\left(\frac{579}{1666}\right)$	$e\left(\frac{760}{833}\right)$	$e\left(\frac{579}{833}\right)$	$e\left(\frac{607}{1666}\right)$	$e\left(\frac{433}{1666}\right)$	$e\left(\frac{521}{1666}\right)$	$e\left(\frac{71}{1666}\right)$	$e\left(\frac{687}{833}\right)$	$e\left(\frac{593}{833}\right)$	$e\left(\frac{32}{833}\right)$
$\chi_{1667}(22,\cdot)$	1667.l	1666	yes	$-1$	$1$	$e\left(\frac{473}{1666}\right)$	$e\left(\frac{559}{833}\right)$	$e\left(\frac{473}{833}\right)$	$e\left(\frac{1103}{1666}\right)$	$e\left(\frac{1591}{1666}\right)$	$e\left(\frac{1191}{1666}\right)$	$e\left(\frac{1419}{1666}\right)$	$e\left(\frac{285}{833}\right)$	$e\left(\frac{788}{833}\right)$	$e\left(\frac{6}{833}\right)$
$\chi_{1667}(23,\cdot)$	1667.k	833	yes	$1$	$1$	$e\left(\frac{270}{833}\right)$	$e\left(\frac{411}{833}\right)$	$e\left(\frac{540}{833}\right)$	$e\left(\frac{214}{833}\right)$	$e\left(\frac{681}{833}\right)$	$e\left(\frac{148}{833}\right)$	$e\left(\frac{810}{833}\right)$	$e\left(\frac{822}{833}\right)$	$e\left(\frac{484}{833}\right)$	$e\left(\frac{824}{833}\right)$
$\chi_{1667}(24,\cdot)$	1667.l	1666	yes	$-1$	$1$	$e\left(\frac{1217}{1666}\right)$	$e\left(\frac{681}{833}\right)$	$e\left(\frac{384}{833}\right)$	$e\left(\frac{545}{1666}\right)$	$e\left(\frac{913}{1666}\right)$	$e\left(\frac{229}{1666}\right)$	$e\left(\frac{319}{1666}\right)$	$e\left(\frac{529}{833}\right)$	$e\left(\frac{48}{833}\right)$	$e\left(\frac{660}{833}\right)$
$\chi_{1667}(25,\cdot)$	1667.k	833	yes	$1$	$1$	$e\left(\frac{624}{833}\right)$	$e\left(\frac{339}{833}\right)$	$e\left(\frac{415}{833}\right)$	$e\left(\frac{365}{833}\right)$	$e\left(\frac{130}{833}\right)$	$e\left(\frac{268}{833}\right)$	$e\left(\frac{206}{833}\right)$	$e\left(\frac{678}{833}\right)$	$e\left(\frac{156}{833}\right)$	$e\left(\frac{479}{833}\right)$
$\chi_{1667}(26,\cdot)$	1667.l	1666	yes	$-1$	$1$	$e\left(\frac{375}{1666}\right)$	$e\left(\frac{216}{833}\right)$	$e\left(\frac{375}{833}\right)$	$e\left(\frac{1593}{1666}\right)$	$e\left(\frac{807}{1666}\right)$	$e\left(\frac{113}{1666}\right)$	$e\left(\frac{1125}{1666}\right)$	$e\left(\frac{432}{833}\right)$	$e\left(\frac{151}{833}\right)$	$e\left(\frac{202}{833}\right)$
$\chi_{1667}(27,\cdot)$	1667.k	833	yes	$1$	$1$	$e\left(\frac{155}{833}\right)$	$e\left(\frac{745}{833}\right)$	$e\left(\frac{310}{833}\right)$	$e\left(\frac{92}{833}\right)$	$e\left(\frac{67}{833}\right)$	$e\left(\frac{702}{833}\right)$	$e\left(\frac{465}{833}\right)$	$e\left(\frac{657}{833}\right)$	$e\left(\frac{247}{833}\right)$	$e\left(\frac{689}{833}\right)$
$\chi_{1667}(28,\cdot)$	1667.l	1666	yes	$-1$	$1$	$e\left(\frac{1033}{1666}\right)$	$e\left(\frac{615}{833}\right)$	$e\left(\frac{200}{833}\right)$	$e\left(\frac{683}{1666}\right)$	$e\left(\frac{597}{1666}\right)$	$e\left(\frac{449}{1666}\right)$	$e\left(\frac{1433}{1666}\right)$	$e\left(\frac{397}{833}\right)$	$e\left(\frac{25}{833}\right)$	$e\left(\frac{552}{833}\right)$
$\chi_{1667}(29,\cdot)$	1667.l	1666	yes	$-1$	$1$	$e\left(\frac{1335}{1666}\right)$	$e\left(\frac{669}{833}\right)$	$e\left(\frac{502}{833}\right)$	$e\left(\frac{873}{1666}\right)$	$e\left(\frac{1007}{1666}\right)$	$e\left(\frac{269}{1666}\right)$	$e\left(\frac{673}{1666}\right)$	$e\left(\frac{505}{833}\right)$	$e\left(\frac{271}{833}\right)$	$e\left(\frac{186}{833}\right)$
$\chi_{1667}(30,\cdot)$	1667.k	833	yes	$1$	$1$	$e\left(\frac{503}{833}\right)$	$e\left(\frac{53}{833}\right)$	$e\left(\frac{173}{833}\right)$	$e\left(\frac{664}{833}\right)$	$e\left(\frac{556}{833}\right)$	$e\left(\frac{467}{833}\right)$	$e\left(\frac{676}{833}\right)$	$e\left(\frac{106}{833}\right)$	$e\left(\frac{334}{833}\right)$	$e\left(\frac{11}{833}\right)$
$\chi_{1667}(31,\cdot)$	1667.k	833	yes	$1$	$1$	$e\left(\frac{360}{833}\right)$	$e\left(\frac{548}{833}\right)$	$e\left(\frac{720}{833}\right)$	$e\left(\frac{563}{833}\right)$	$e\left(\frac{75}{833}\right)$	$e\left(\frac{475}{833}\right)$	$e\left(\frac{247}{833}\right)$	$e\left(\frac{263}{833}\right)$	$e\left(\frac{90}{833}\right)$	$e\left(\frac{821}{833}\right)$
$\chi_{1667}(32,\cdot)$	1667.l	1666	yes	$-1$	$1$	$e\left(\frac{5}{1666}\right)$	$e\left(\frac{536}{833}\right)$	$e\left(\frac{5}{833}\right)$	$e\left(\frac{621}{1666}\right)$	$e\left(\frac{1077}{1666}\right)$	$e\left(\frac{157}{1666}\right)$	$e\left(\frac{15}{1666}\right)$	$e\left(\frac{239}{833}\right)$	$e\left(\frac{313}{833}\right)$	$e\left(\frac{347}{833}\right)$

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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	$1667$
Structure	\(C_{1666}\)
Order	$1666$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1667}(1,\cdot)\)	1667.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1667}(2,\cdot)\)	1667.l	1666	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{1666}\right)\)	\(e\left(\frac{607}{833}\right)\)	\(e\left(\frac{1}{833}\right)\)	\(e\left(\frac{1457}{1666}\right)\)	\(e\left(\frac{1215}{1666}\right)\)	\(e\left(\frac{1031}{1666}\right)\)	\(e\left(\frac{3}{1666}\right)\)	\(e\left(\frac{381}{833}\right)\)	\(e\left(\frac{729}{833}\right)\)	\(e\left(\frac{236}{833}\right)\)
\(\chi_{1667}(3,\cdot)\)	1667.k	833	yes	\(1\)	\(1\)	\(e\left(\frac{607}{833}\right)\)	\(e\left(\frac{526}{833}\right)\)	\(e\left(\frac{381}{833}\right)\)	\(e\left(\frac{586}{833}\right)\)	\(e\left(\frac{300}{833}\right)\)	\(e\left(\frac{234}{833}\right)\)	\(e\left(\frac{155}{833}\right)\)	\(e\left(\frac{219}{833}\right)\)	\(e\left(\frac{360}{833}\right)\)	\(e\left(\frac{785}{833}\right)\)
\(\chi_{1667}(4,\cdot)\)	1667.k	833	yes	\(1\)	\(1\)	\(e\left(\frac{1}{833}\right)\)	\(e\left(\frac{381}{833}\right)\)	\(e\left(\frac{2}{833}\right)\)	\(e\left(\frac{624}{833}\right)\)	\(e\left(\frac{382}{833}\right)\)	\(e\left(\frac{198}{833}\right)\)	\(e\left(\frac{3}{833}\right)\)	\(e\left(\frac{762}{833}\right)\)	\(e\left(\frac{625}{833}\right)\)	\(e\left(\frac{472}{833}\right)\)
\(\chi_{1667}(5,\cdot)\)	1667.l	1666	yes	\(-1\)	\(1\)	\(e\left(\frac{1457}{1666}\right)\)	\(e\left(\frac{586}{833}\right)\)	\(e\left(\frac{624}{833}\right)\)	\(e\left(\frac{365}{1666}\right)\)	\(e\left(\frac{963}{1666}\right)\)	\(e\left(\frac{1101}{1666}\right)\)	\(e\left(\frac{1039}{1666}\right)\)	\(e\left(\frac{339}{833}\right)\)	\(e\left(\frac{78}{833}\right)\)	\(e\left(\frac{656}{833}\right)\)
\(\chi_{1667}(6,\cdot)\)	1667.l	1666	yes	\(-1\)	\(1\)	\(e\left(\frac{1215}{1666}\right)\)	\(e\left(\frac{300}{833}\right)\)	\(e\left(\frac{382}{833}\right)\)	\(e\left(\frac{963}{1666}\right)\)	\(e\left(\frac{149}{1666}\right)\)	\(e\left(\frac{1499}{1666}\right)\)	\(e\left(\frac{313}{1666}\right)\)	\(e\left(\frac{600}{833}\right)\)	\(e\left(\frac{256}{833}\right)\)	\(e\left(\frac{188}{833}\right)\)
\(\chi_{1667}(7,\cdot)\)	1667.l	1666	yes	\(-1\)	\(1\)	\(e\left(\frac{1031}{1666}\right)\)	\(e\left(\frac{234}{833}\right)\)	\(e\left(\frac{198}{833}\right)\)	\(e\left(\frac{1101}{1666}\right)\)	\(e\left(\frac{1499}{1666}\right)\)	\(e\left(\frac{53}{1666}\right)\)	\(e\left(\frac{1427}{1666}\right)\)	\(e\left(\frac{468}{833}\right)\)	\(e\left(\frac{233}{833}\right)\)	\(e\left(\frac{80}{833}\right)\)
\(\chi_{1667}(8,\cdot)\)	1667.l	1666	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{1666}\right)\)	\(e\left(\frac{155}{833}\right)\)	\(e\left(\frac{3}{833}\right)\)	\(e\left(\frac{1039}{1666}\right)\)	\(e\left(\frac{313}{1666}\right)\)	\(e\left(\frac{1427}{1666}\right)\)	\(e\left(\frac{9}{1666}\right)\)	\(e\left(\frac{310}{833}\right)\)	\(e\left(\frac{521}{833}\right)\)	\(e\left(\frac{708}{833}\right)\)
\(\chi_{1667}(9,\cdot)\)	1667.k	833	yes	\(1\)	\(1\)	\(e\left(\frac{381}{833}\right)\)	\(e\left(\frac{219}{833}\right)\)	\(e\left(\frac{762}{833}\right)\)	\(e\left(\frac{339}{833}\right)\)	\(e\left(\frac{600}{833}\right)\)	\(e\left(\frac{468}{833}\right)\)	\(e\left(\frac{310}{833}\right)\)	\(e\left(\frac{438}{833}\right)\)	\(e\left(\frac{720}{833}\right)\)	\(e\left(\frac{737}{833}\right)\)
\(\chi_{1667}(10,\cdot)\)	1667.k	833	yes	\(1\)	\(1\)	\(e\left(\frac{729}{833}\right)\)	\(e\left(\frac{360}{833}\right)\)	\(e\left(\frac{625}{833}\right)\)	\(e\left(\frac{78}{833}\right)\)	\(e\left(\frac{256}{833}\right)\)	\(e\left(\frac{233}{833}\right)\)	\(e\left(\frac{521}{833}\right)\)	\(e\left(\frac{720}{833}\right)\)	\(e\left(\frac{807}{833}\right)\)	\(e\left(\frac{59}{833}\right)\)
\(\chi_{1667}(11,\cdot)\)	1667.k	833	yes	\(1\)	\(1\)	\(e\left(\frac{236}{833}\right)\)	\(e\left(\frac{785}{833}\right)\)	\(e\left(\frac{472}{833}\right)\)	\(e\left(\frac{656}{833}\right)\)	\(e\left(\frac{188}{833}\right)\)	\(e\left(\frac{80}{833}\right)\)	\(e\left(\frac{708}{833}\right)\)	\(e\left(\frac{737}{833}\right)\)	\(e\left(\frac{59}{833}\right)\)	\(e\left(\frac{603}{833}\right)\)
\(\chi_{1667}(12,\cdot)\)	1667.k	833	yes	\(1\)	\(1\)	\(e\left(\frac{608}{833}\right)\)	\(e\left(\frac{74}{833}\right)\)	\(e\left(\frac{383}{833}\right)\)	\(e\left(\frac{377}{833}\right)\)	\(e\left(\frac{682}{833}\right)\)	\(e\left(\frac{432}{833}\right)\)	\(e\left(\frac{158}{833}\right)\)	\(e\left(\frac{148}{833}\right)\)	\(e\left(\frac{152}{833}\right)\)	\(e\left(\frac{424}{833}\right)\)
\(\chi_{1667}(13,\cdot)\)	1667.g	49	yes	\(1\)	\(1\)	\(e\left(\frac{11}{49}\right)\)	\(e\left(\frac{26}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{4}{49}\right)\)	\(e\left(\frac{37}{49}\right)\)	\(e\left(\frac{22}{49}\right)\)	\(e\left(\frac{33}{49}\right)\)	\(e\left(\frac{3}{49}\right)\)	\(e\left(\frac{15}{49}\right)\)	\(e\left(\frac{47}{49}\right)\)
\(\chi_{1667}(14,\cdot)\)	1667.k	833	yes	\(1\)	\(1\)	\(e\left(\frac{516}{833}\right)\)	\(e\left(\frac{8}{833}\right)\)	\(e\left(\frac{199}{833}\right)\)	\(e\left(\frac{446}{833}\right)\)	\(e\left(\frac{524}{833}\right)\)	\(e\left(\frac{542}{833}\right)\)	\(e\left(\frac{715}{833}\right)\)	\(e\left(\frac{16}{833}\right)\)	\(e\left(\frac{129}{833}\right)\)	\(e\left(\frac{316}{833}\right)\)
\(\chi_{1667}(15,\cdot)\)	1667.l	1666	yes	\(-1\)	\(1\)	\(e\left(\frac{1005}{1666}\right)\)	\(e\left(\frac{279}{833}\right)\)	\(e\left(\frac{172}{833}\right)\)	\(e\left(\frac{1537}{1666}\right)\)	\(e\left(\frac{1563}{1666}\right)\)	\(e\left(\frac{1569}{1666}\right)\)	\(e\left(\frac{1349}{1666}\right)\)	\(e\left(\frac{558}{833}\right)\)	\(e\left(\frac{438}{833}\right)\)	\(e\left(\frac{608}{833}\right)\)
\(\chi_{1667}(16,\cdot)\)	1667.k	833	yes	\(1\)	\(1\)	\(e\left(\frac{2}{833}\right)\)	\(e\left(\frac{762}{833}\right)\)	\(e\left(\frac{4}{833}\right)\)	\(e\left(\frac{415}{833}\right)\)	\(e\left(\frac{764}{833}\right)\)	\(e\left(\frac{396}{833}\right)\)	\(e\left(\frac{6}{833}\right)\)	\(e\left(\frac{691}{833}\right)\)	\(e\left(\frac{417}{833}\right)\)	\(e\left(\frac{111}{833}\right)\)
\(\chi_{1667}(17,\cdot)\)	1667.k	833	yes	\(1\)	\(1\)	\(e\left(\frac{218}{833}\right)\)	\(e\left(\frac{591}{833}\right)\)	\(e\left(\frac{436}{833}\right)\)	\(e\left(\frac{253}{833}\right)\)	\(e\left(\frac{809}{833}\right)\)	\(e\left(\frac{681}{833}\right)\)	\(e\left(\frac{654}{833}\right)\)	\(e\left(\frac{349}{833}\right)\)	\(e\left(\frac{471}{833}\right)\)	\(e\left(\frac{437}{833}\right)\)
\(\chi_{1667}(18,\cdot)\)	1667.j	238	yes	\(-1\)	\(1\)	\(e\left(\frac{109}{238}\right)\)	\(e\left(\frac{118}{119}\right)\)	\(e\left(\frac{109}{119}\right)\)	\(e\left(\frac{67}{238}\right)\)	\(e\left(\frac{107}{238}\right)\)	\(e\left(\frac{43}{238}\right)\)	\(e\left(\frac{89}{238}\right)\)	\(e\left(\frac{117}{119}\right)\)	\(e\left(\frac{88}{119}\right)\)	\(e\left(\frac{20}{119}\right)\)
\(\chi_{1667}(19,\cdot)\)	1667.k	833	yes	\(1\)	\(1\)	\(e\left(\frac{491}{833}\right)\)	\(e\left(\frac{479}{833}\right)\)	\(e\left(\frac{149}{833}\right)\)	\(e\left(\frac{673}{833}\right)\)	\(e\left(\frac{137}{833}\right)\)	\(e\left(\frac{590}{833}\right)\)	\(e\left(\frac{640}{833}\right)\)	\(e\left(\frac{125}{833}\right)\)	\(e\left(\frac{331}{833}\right)\)	\(e\left(\frac{178}{833}\right)\)
\(\chi_{1667}(20,\cdot)\)	1667.l	1666	yes	\(-1\)	\(1\)	\(e\left(\frac{1459}{1666}\right)\)	\(e\left(\frac{134}{833}\right)\)	\(e\left(\frac{626}{833}\right)\)	\(e\left(\frac{1613}{1666}\right)\)	\(e\left(\frac{61}{1666}\right)\)	\(e\left(\frac{1497}{1666}\right)\)	\(e\left(\frac{1045}{1666}\right)\)	\(e\left(\frac{268}{833}\right)\)	\(e\left(\frac{703}{833}\right)\)	\(e\left(\frac{295}{833}\right)\)
\(\chi_{1667}(21,\cdot)\)	1667.l	1666	yes	\(-1\)	\(1\)	\(e\left(\frac{579}{1666}\right)\)	\(e\left(\frac{760}{833}\right)\)	\(e\left(\frac{579}{833}\right)\)	\(e\left(\frac{607}{1666}\right)\)	\(e\left(\frac{433}{1666}\right)\)	\(e\left(\frac{521}{1666}\right)\)	\(e\left(\frac{71}{1666}\right)\)	\(e\left(\frac{687}{833}\right)\)	\(e\left(\frac{593}{833}\right)\)	\(e\left(\frac{32}{833}\right)\)
\(\chi_{1667}(22,\cdot)\)	1667.l	1666	yes	\(-1\)	\(1\)	\(e\left(\frac{473}{1666}\right)\)	\(e\left(\frac{559}{833}\right)\)	\(e\left(\frac{473}{833}\right)\)	\(e\left(\frac{1103}{1666}\right)\)	\(e\left(\frac{1591}{1666}\right)\)	\(e\left(\frac{1191}{1666}\right)\)	\(e\left(\frac{1419}{1666}\right)\)	\(e\left(\frac{285}{833}\right)\)	\(e\left(\frac{788}{833}\right)\)	\(e\left(\frac{6}{833}\right)\)
\(\chi_{1667}(23,\cdot)\)	1667.k	833	yes	\(1\)	\(1\)	\(e\left(\frac{270}{833}\right)\)	\(e\left(\frac{411}{833}\right)\)	\(e\left(\frac{540}{833}\right)\)	\(e\left(\frac{214}{833}\right)\)	\(e\left(\frac{681}{833}\right)\)	\(e\left(\frac{148}{833}\right)\)	\(e\left(\frac{810}{833}\right)\)	\(e\left(\frac{822}{833}\right)\)	\(e\left(\frac{484}{833}\right)\)	\(e\left(\frac{824}{833}\right)\)
\(\chi_{1667}(24,\cdot)\)	1667.l	1666	yes	\(-1\)	\(1\)	\(e\left(\frac{1217}{1666}\right)\)	\(e\left(\frac{681}{833}\right)\)	\(e\left(\frac{384}{833}\right)\)	\(e\left(\frac{545}{1666}\right)\)	\(e\left(\frac{913}{1666}\right)\)	\(e\left(\frac{229}{1666}\right)\)	\(e\left(\frac{319}{1666}\right)\)	\(e\left(\frac{529}{833}\right)\)	\(e\left(\frac{48}{833}\right)\)	\(e\left(\frac{660}{833}\right)\)
\(\chi_{1667}(25,\cdot)\)	1667.k	833	yes	\(1\)	\(1\)	\(e\left(\frac{624}{833}\right)\)	\(e\left(\frac{339}{833}\right)\)	\(e\left(\frac{415}{833}\right)\)	\(e\left(\frac{365}{833}\right)\)	\(e\left(\frac{130}{833}\right)\)	\(e\left(\frac{268}{833}\right)\)	\(e\left(\frac{206}{833}\right)\)	\(e\left(\frac{678}{833}\right)\)	\(e\left(\frac{156}{833}\right)\)	\(e\left(\frac{479}{833}\right)\)
\(\chi_{1667}(26,\cdot)\)	1667.l	1666	yes	\(-1\)	\(1\)	\(e\left(\frac{375}{1666}\right)\)	\(e\left(\frac{216}{833}\right)\)	\(e\left(\frac{375}{833}\right)\)	\(e\left(\frac{1593}{1666}\right)\)	\(e\left(\frac{807}{1666}\right)\)	\(e\left(\frac{113}{1666}\right)\)	\(e\left(\frac{1125}{1666}\right)\)	\(e\left(\frac{432}{833}\right)\)	\(e\left(\frac{151}{833}\right)\)	\(e\left(\frac{202}{833}\right)\)
\(\chi_{1667}(27,\cdot)\)	1667.k	833	yes	\(1\)	\(1\)	\(e\left(\frac{155}{833}\right)\)	\(e\left(\frac{745}{833}\right)\)	\(e\left(\frac{310}{833}\right)\)	\(e\left(\frac{92}{833}\right)\)	\(e\left(\frac{67}{833}\right)\)	\(e\left(\frac{702}{833}\right)\)	\(e\left(\frac{465}{833}\right)\)	\(e\left(\frac{657}{833}\right)\)	\(e\left(\frac{247}{833}\right)\)	\(e\left(\frac{689}{833}\right)\)
\(\chi_{1667}(28,\cdot)\)	1667.l	1666	yes	\(-1\)	\(1\)	\(e\left(\frac{1033}{1666}\right)\)	\(e\left(\frac{615}{833}\right)\)	\(e\left(\frac{200}{833}\right)\)	\(e\left(\frac{683}{1666}\right)\)	\(e\left(\frac{597}{1666}\right)\)	\(e\left(\frac{449}{1666}\right)\)	\(e\left(\frac{1433}{1666}\right)\)	\(e\left(\frac{397}{833}\right)\)	\(e\left(\frac{25}{833}\right)\)	\(e\left(\frac{552}{833}\right)\)
\(\chi_{1667}(29,\cdot)\)	1667.l	1666	yes	\(-1\)	\(1\)	\(e\left(\frac{1335}{1666}\right)\)	\(e\left(\frac{669}{833}\right)\)	\(e\left(\frac{502}{833}\right)\)	\(e\left(\frac{873}{1666}\right)\)	\(e\left(\frac{1007}{1666}\right)\)	\(e\left(\frac{269}{1666}\right)\)	\(e\left(\frac{673}{1666}\right)\)	\(e\left(\frac{505}{833}\right)\)	\(e\left(\frac{271}{833}\right)\)	\(e\left(\frac{186}{833}\right)\)
\(\chi_{1667}(30,\cdot)\)	1667.k	833	yes	\(1\)	\(1\)	\(e\left(\frac{503}{833}\right)\)	\(e\left(\frac{53}{833}\right)\)	\(e\left(\frac{173}{833}\right)\)	\(e\left(\frac{664}{833}\right)\)	\(e\left(\frac{556}{833}\right)\)	\(e\left(\frac{467}{833}\right)\)	\(e\left(\frac{676}{833}\right)\)	\(e\left(\frac{106}{833}\right)\)	\(e\left(\frac{334}{833}\right)\)	\(e\left(\frac{11}{833}\right)\)
\(\chi_{1667}(31,\cdot)\)	1667.k	833	yes	\(1\)	\(1\)	\(e\left(\frac{360}{833}\right)\)	\(e\left(\frac{548}{833}\right)\)	\(e\left(\frac{720}{833}\right)\)	\(e\left(\frac{563}{833}\right)\)	\(e\left(\frac{75}{833}\right)\)	\(e\left(\frac{475}{833}\right)\)	\(e\left(\frac{247}{833}\right)\)	\(e\left(\frac{263}{833}\right)\)	\(e\left(\frac{90}{833}\right)\)	\(e\left(\frac{821}{833}\right)\)
\(\chi_{1667}(32,\cdot)\)	1667.l	1666	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{1666}\right)\)	\(e\left(\frac{536}{833}\right)\)	\(e\left(\frac{5}{833}\right)\)	\(e\left(\frac{621}{1666}\right)\)	\(e\left(\frac{1077}{1666}\right)\)	\(e\left(\frac{157}{1666}\right)\)	\(e\left(\frac{15}{1666}\right)\)	\(e\left(\frac{239}{833}\right)\)	\(e\left(\frac{313}{833}\right)\)	\(e\left(\frac{347}{833}\right)\)

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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.