LMFDB - Group of Dirichlet characters of modulus 4067

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4067)

pari: g = idealstar(,4067,2)

Character group

sage: G.order() pari: g.no
Order	=	3444
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{1722}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4067}(2159,\cdot)$, $\chi_{4067}(2990,\cdot)$

First 32 of 3444 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{4067}(1,\cdot)$	4067.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4067}(2,\cdot)$	4067.be	1722	yes	$-1$	$1$	$e\left(\frac{185}{1722}\right)$	$e\left(\frac{428}{861}\right)$	$e\left(\frac{185}{861}\right)$	$e\left(\frac{485}{1722}\right)$	$e\left(\frac{347}{574}\right)$	$e\left(\frac{185}{574}\right)$	$e\left(\frac{856}{861}\right)$	$e\left(\frac{335}{861}\right)$	$e\left(\frac{47}{861}\right)$	$e\left(\frac{613}{861}\right)$
$\chi_{4067}(3,\cdot)$	4067.bd	1722	yes	$-1$	$1$	$e\left(\frac{428}{861}\right)$	$e\left(\frac{419}{1722}\right)$	$e\left(\frac{856}{861}\right)$	$e\left(\frac{685}{1722}\right)$	$e\left(\frac{425}{574}\right)$	$e\left(\frac{141}{287}\right)$	$e\left(\frac{419}{861}\right)$	$e\left(\frac{1541}{1722}\right)$	$e\left(\frac{22}{861}\right)$	$e\left(\frac{409}{1722}\right)$
$\chi_{4067}(4,\cdot)$	4067.bc	861	yes	$1$	$1$	$e\left(\frac{185}{861}\right)$	$e\left(\frac{856}{861}\right)$	$e\left(\frac{370}{861}\right)$	$e\left(\frac{485}{861}\right)$	$e\left(\frac{60}{287}\right)$	$e\left(\frac{185}{287}\right)$	$e\left(\frac{851}{861}\right)$	$e\left(\frac{670}{861}\right)$	$e\left(\frac{94}{861}\right)$	$e\left(\frac{365}{861}\right)$
$\chi_{4067}(5,\cdot)$	4067.bf	1722	yes	$1$	$1$	$e\left(\frac{485}{1722}\right)$	$e\left(\frac{685}{1722}\right)$	$e\left(\frac{485}{861}\right)$	$e\left(\frac{787}{861}\right)$	$e\left(\frac{195}{287}\right)$	$e\left(\frac{485}{574}\right)$	$e\left(\frac{685}{861}\right)$	$e\left(\frac{337}{1722}\right)$	$e\left(\frac{449}{861}\right)$	$e\left(\frac{1655}{1722}\right)$
$\chi_{4067}(6,\cdot)$	4067.z	574	yes	$1$	$1$	$e\left(\frac{347}{574}\right)$	$e\left(\frac{425}{574}\right)$	$e\left(\frac{60}{287}\right)$	$e\left(\frac{195}{287}\right)$	$e\left(\frac{99}{287}\right)$	$e\left(\frac{467}{574}\right)$	$e\left(\frac{138}{287}\right)$	$e\left(\frac{163}{574}\right)$	$e\left(\frac{23}{287}\right)$	$e\left(\frac{545}{574}\right)$
$\chi_{4067}(8,\cdot)$	4067.ba	574	yes	$-1$	$1$	$e\left(\frac{185}{574}\right)$	$e\left(\frac{141}{287}\right)$	$e\left(\frac{185}{287}\right)$	$e\left(\frac{485}{574}\right)$	$e\left(\frac{467}{574}\right)$	$e\left(\frac{555}{574}\right)$	$e\left(\frac{282}{287}\right)$	$e\left(\frac{48}{287}\right)$	$e\left(\frac{47}{287}\right)$	$e\left(\frac{39}{287}\right)$
$\chi_{4067}(9,\cdot)$	4067.bc	861	yes	$1$	$1$	$e\left(\frac{856}{861}\right)$	$e\left(\frac{419}{861}\right)$	$e\left(\frac{851}{861}\right)$	$e\left(\frac{685}{861}\right)$	$e\left(\frac{138}{287}\right)$	$e\left(\frac{282}{287}\right)$	$e\left(\frac{838}{861}\right)$	$e\left(\frac{680}{861}\right)$	$e\left(\frac{44}{861}\right)$	$e\left(\frac{409}{861}\right)$
$\chi_{4067}(10,\cdot)$	4067.bd	1722	yes	$-1$	$1$	$e\left(\frac{335}{861}\right)$	$e\left(\frac{1541}{1722}\right)$	$e\left(\frac{670}{861}\right)$	$e\left(\frac{337}{1722}\right)$	$e\left(\frac{163}{574}\right)$	$e\left(\frac{48}{287}\right)$	$e\left(\frac{680}{861}\right)$	$e\left(\frac{1007}{1722}\right)$	$e\left(\frac{496}{861}\right)$	$e\left(\frac{1159}{1722}\right)$
$\chi_{4067}(11,\cdot)$	4067.bc	861	yes	$1$	$1$	$e\left(\frac{47}{861}\right)$	$e\left(\frac{22}{861}\right)$	$e\left(\frac{94}{861}\right)$	$e\left(\frac{449}{861}\right)$	$e\left(\frac{23}{287}\right)$	$e\left(\frac{47}{287}\right)$	$e\left(\frac{44}{861}\right)$	$e\left(\frac{496}{861}\right)$	$e\left(\frac{103}{861}\right)$	$e\left(\frac{116}{861}\right)$
$\chi_{4067}(12,\cdot)$	4067.bd	1722	yes	$-1$	$1$	$e\left(\frac{613}{861}\right)$	$e\left(\frac{409}{1722}\right)$	$e\left(\frac{365}{861}\right)$	$e\left(\frac{1655}{1722}\right)$	$e\left(\frac{545}{574}\right)$	$e\left(\frac{39}{287}\right)$	$e\left(\frac{409}{861}\right)$	$e\left(\frac{1159}{1722}\right)$	$e\left(\frac{116}{861}\right)$	$e\left(\frac{1139}{1722}\right)$
$\chi_{4067}(13,\cdot)$	4067.z	574	yes	$1$	$1$	$e\left(\frac{211}{574}\right)$	$e\left(\frac{227}{574}\right)$	$e\left(\frac{211}{287}\right)$	$e\left(\frac{40}{287}\right)$	$e\left(\frac{219}{287}\right)$	$e\left(\frac{59}{574}\right)$	$e\left(\frac{227}{287}\right)$	$e\left(\frac{291}{574}\right)$	$e\left(\frac{277}{287}\right)$	$e\left(\frac{75}{574}\right)$
$\chi_{4067}(15,\cdot)$	4067.ba	574	yes	$-1$	$1$	$e\left(\frac{447}{574}\right)$	$e\left(\frac{184}{287}\right)$	$e\left(\frac{160}{287}\right)$	$e\left(\frac{179}{574}\right)$	$e\left(\frac{241}{574}\right)$	$e\left(\frac{193}{574}\right)$	$e\left(\frac{81}{287}\right)$	$e\left(\frac{26}{287}\right)$	$e\left(\frac{157}{287}\right)$	$e\left(\frac{57}{287}\right)$
$\chi_{4067}(16,\cdot)$	4067.bc	861	yes	$1$	$1$	$e\left(\frac{370}{861}\right)$	$e\left(\frac{851}{861}\right)$	$e\left(\frac{740}{861}\right)$	$e\left(\frac{109}{861}\right)$	$e\left(\frac{120}{287}\right)$	$e\left(\frac{83}{287}\right)$	$e\left(\frac{841}{861}\right)$	$e\left(\frac{479}{861}\right)$	$e\left(\frac{188}{861}\right)$	$e\left(\frac{730}{861}\right)$
$\chi_{4067}(17,\cdot)$	4067.bd	1722	yes	$-1$	$1$	$e\left(\frac{137}{861}\right)$	$e\left(\frac{1319}{1722}\right)$	$e\left(\frac{274}{861}\right)$	$e\left(\frac{1207}{1722}\right)$	$e\left(\frac{531}{574}\right)$	$e\left(\frac{137}{287}\right)$	$e\left(\frac{458}{861}\right)$	$e\left(\frac{1481}{1722}\right)$	$e\left(\frac{172}{861}\right)$	$e\left(\frac{145}{1722}\right)$
$\chi_{4067}(18,\cdot)$	4067.w	246	no	$-1$	$1$	$e\left(\frac{25}{246}\right)$	$e\left(\frac{121}{123}\right)$	$e\left(\frac{25}{123}\right)$	$e\left(\frac{19}{246}\right)$	$e\left(\frac{7}{82}\right)$	$e\left(\frac{25}{82}\right)$	$e\left(\frac{119}{123}\right)$	$e\left(\frac{22}{123}\right)$	$e\left(\frac{13}{123}\right)$	$e\left(\frac{23}{123}\right)$
$\chi_{4067}(19,\cdot)$	4067.v	246	no	$1$	$1$	$e\left(\frac{59}{246}\right)$	$e\left(\frac{25}{246}\right)$	$e\left(\frac{59}{123}\right)$	$e\left(\frac{79}{123}\right)$	$e\left(\frac{14}{41}\right)$	$e\left(\frac{59}{82}\right)$	$e\left(\frac{25}{123}\right)$	$e\left(\frac{217}{246}\right)$	$e\left(\frac{11}{123}\right)$	$e\left(\frac{143}{246}\right)$
$\chi_{4067}(20,\cdot)$	4067.z	574	yes	$1$	$1$	$e\left(\frac{285}{574}\right)$	$e\left(\frac{225}{574}\right)$	$e\left(\frac{285}{287}\right)$	$e\left(\frac{137}{287}\right)$	$e\left(\frac{255}{287}\right)$	$e\left(\frac{281}{574}\right)$	$e\left(\frac{225}{287}\right)$	$e\left(\frac{559}{574}\right)$	$e\left(\frac{181}{287}\right)$	$e\left(\frac{221}{574}\right)$
$\chi_{4067}(22,\cdot)$	4067.ba	574	yes	$-1$	$1$	$e\left(\frac{93}{574}\right)$	$e\left(\frac{150}{287}\right)$	$e\left(\frac{93}{287}\right)$	$e\left(\frac{461}{574}\right)$	$e\left(\frac{393}{574}\right)$	$e\left(\frac{279}{574}\right)$	$e\left(\frac{13}{287}\right)$	$e\left(\frac{277}{287}\right)$	$e\left(\frac{50}{287}\right)$	$e\left(\frac{243}{287}\right)$
$\chi_{4067}(23,\cdot)$	4067.bc	861	yes	$1$	$1$	$e\left(\frac{220}{861}\right)$	$e\left(\frac{506}{861}\right)$	$e\left(\frac{440}{861}\right)$	$e\left(\frac{856}{861}\right)$	$e\left(\frac{242}{287}\right)$	$e\left(\frac{220}{287}\right)$	$e\left(\frac{151}{861}\right)$	$e\left(\frac{215}{861}\right)$	$e\left(\frac{647}{861}\right)$	$e\left(\frac{85}{861}\right)$
$\chi_{4067}(24,\cdot)$	4067.bf	1722	yes	$1$	$1$	$e\left(\frac{1411}{1722}\right)$	$e\left(\frac{1265}{1722}\right)$	$e\left(\frac{550}{861}\right)$	$e\left(\frac{209}{861}\right)$	$e\left(\frac{159}{287}\right)$	$e\left(\frac{263}{574}\right)$	$e\left(\frac{404}{861}\right)$	$e\left(\frac{107}{1722}\right)$	$e\left(\frac{163}{861}\right)$	$e\left(\frac{643}{1722}\right)$
$\chi_{4067}(25,\cdot)$	4067.bc	861	yes	$1$	$1$	$e\left(\frac{485}{861}\right)$	$e\left(\frac{685}{861}\right)$	$e\left(\frac{109}{861}\right)$	$e\left(\frac{713}{861}\right)$	$e\left(\frac{103}{287}\right)$	$e\left(\frac{198}{287}\right)$	$e\left(\frac{509}{861}\right)$	$e\left(\frac{337}{861}\right)$	$e\left(\frac{37}{861}\right)$	$e\left(\frac{794}{861}\right)$
$\chi_{4067}(26,\cdot)$	4067.bd	1722	yes	$-1$	$1$	$e\left(\frac{409}{861}\right)$	$e\left(\frac{1537}{1722}\right)$	$e\left(\frac{818}{861}\right)$	$e\left(\frac{725}{1722}\right)$	$e\left(\frac{211}{574}\right)$	$e\left(\frac{122}{287}\right)$	$e\left(\frac{676}{861}\right)$	$e\left(\frac{1543}{1722}\right)$	$e\left(\frac{17}{861}\right)$	$e\left(\frac{1451}{1722}\right)$
$\chi_{4067}(27,\cdot)$	4067.bb	574	yes	$-1$	$1$	$e\left(\frac{141}{287}\right)$	$e\left(\frac{419}{574}\right)$	$e\left(\frac{282}{287}\right)$	$e\left(\frac{111}{574}\right)$	$e\left(\frac{127}{574}\right)$	$e\left(\frac{136}{287}\right)$	$e\left(\frac{132}{287}\right)$	$e\left(\frac{393}{574}\right)$	$e\left(\frac{22}{287}\right)$	$e\left(\frac{409}{574}\right)$
$\chi_{4067}(29,\cdot)$	4067.y	287	yes	$1$	$1$	$e\left(\frac{83}{287}\right)$	$e\left(\frac{277}{287}\right)$	$e\left(\frac{166}{287}\right)$	$e\left(\frac{109}{287}\right)$	$e\left(\frac{73}{287}\right)$	$e\left(\frac{249}{287}\right)$	$e\left(\frac{267}{287}\right)$	$e\left(\frac{192}{287}\right)$	$e\left(\frac{188}{287}\right)$	$e\left(\frac{156}{287}\right)$
$\chi_{4067}(30,\cdot)$	4067.u	123	no	$1$	$1$	$e\left(\frac{109}{123}\right)$	$e\left(\frac{17}{123}\right)$	$e\left(\frac{95}{123}\right)$	$e\left(\frac{73}{123}\right)$	$e\left(\frac{1}{41}\right)$	$e\left(\frac{27}{41}\right)$	$e\left(\frac{34}{123}\right)$	$e\left(\frac{59}{123}\right)$	$e\left(\frac{74}{123}\right)$	$e\left(\frac{112}{123}\right)$
$\chi_{4067}(31,\cdot)$	4067.x	246	no	$-1$	$1$	$e\left(\frac{98}{123}\right)$	$e\left(\frac{131}{246}\right)$	$e\left(\frac{73}{123}\right)$	$e\left(\frac{85}{246}\right)$	$e\left(\frac{27}{82}\right)$	$e\left(\frac{16}{41}\right)$	$e\left(\frac{8}{123}\right)$	$e\left(\frac{35}{246}\right)$	$e\left(\frac{97}{123}\right)$	$e\left(\frac{31}{246}\right)$
$\chi_{4067}(32,\cdot)$	4067.be	1722	yes	$-1$	$1$	$e\left(\frac{925}{1722}\right)$	$e\left(\frac{418}{861}\right)$	$e\left(\frac{64}{861}\right)$	$e\left(\frac{703}{1722}\right)$	$e\left(\frac{13}{574}\right)$	$e\left(\frac{351}{574}\right)$	$e\left(\frac{836}{861}\right)$	$e\left(\frac{814}{861}\right)$	$e\left(\frac{235}{861}\right)$	$e\left(\frac{482}{861}\right)$
$\chi_{4067}(33,\cdot)$	4067.bd	1722	yes	$-1$	$1$	$e\left(\frac{475}{861}\right)$	$e\left(\frac{463}{1722}\right)$	$e\left(\frac{89}{861}\right)$	$e\left(\frac{1583}{1722}\right)$	$e\left(\frac{471}{574}\right)$	$e\left(\frac{188}{287}\right)$	$e\left(\frac{463}{861}\right)$	$e\left(\frac{811}{1722}\right)$	$e\left(\frac{125}{861}\right)$	$e\left(\frac{641}{1722}\right)$
$\chi_{4067}(34,\cdot)$	4067.z	574	yes	$1$	$1$	$e\left(\frac{153}{574}\right)$	$e\left(\frac{151}{574}\right)$	$e\left(\frac{153}{287}\right)$	$e\left(\frac{282}{287}\right)$	$e\left(\frac{152}{287}\right)$	$e\left(\frac{459}{574}\right)$	$e\left(\frac{151}{287}\right)$	$e\left(\frac{143}{574}\right)$	$e\left(\frac{73}{287}\right)$	$e\left(\frac{457}{574}\right)$
$\chi_{4067}(36,\cdot)$	4067.y	287	yes	$1$	$1$	$e\left(\frac{60}{287}\right)$	$e\left(\frac{138}{287}\right)$	$e\left(\frac{120}{287}\right)$	$e\left(\frac{103}{287}\right)$	$e\left(\frac{198}{287}\right)$	$e\left(\frac{180}{287}\right)$	$e\left(\frac{276}{287}\right)$	$e\left(\frac{163}{287}\right)$	$e\left(\frac{46}{287}\right)$	$e\left(\frac{258}{287}\right)$
$\chi_{4067}(37,\cdot)$	4067.bc	861	yes	$1$	$1$	$e\left(\frac{46}{861}\right)$	$e\left(\frac{278}{861}\right)$	$e\left(\frac{92}{861}\right)$	$e\left(\frac{586}{861}\right)$	$e\left(\frac{108}{287}\right)$	$e\left(\frac{46}{287}\right)$	$e\left(\frac{556}{861}\right)$	$e\left(\frac{632}{861}\right)$	$e\left(\frac{284}{861}\right)$	$e\left(\frac{370}{861}\right)$

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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	$4067$
Structure	\(C_{2}\times C_{1722}\)
Order	$3444$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{4067}(1,\cdot)\)	4067.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4067}(2,\cdot)\)	4067.be	1722	yes	\(-1\)	\(1\)	\(e\left(\frac{185}{1722}\right)\)	\(e\left(\frac{428}{861}\right)\)	\(e\left(\frac{185}{861}\right)\)	\(e\left(\frac{485}{1722}\right)\)	\(e\left(\frac{347}{574}\right)\)	\(e\left(\frac{185}{574}\right)\)	\(e\left(\frac{856}{861}\right)\)	\(e\left(\frac{335}{861}\right)\)	\(e\left(\frac{47}{861}\right)\)	\(e\left(\frac{613}{861}\right)\)
\(\chi_{4067}(3,\cdot)\)	4067.bd	1722	yes	\(-1\)	\(1\)	\(e\left(\frac{428}{861}\right)\)	\(e\left(\frac{419}{1722}\right)\)	\(e\left(\frac{856}{861}\right)\)	\(e\left(\frac{685}{1722}\right)\)	\(e\left(\frac{425}{574}\right)\)	\(e\left(\frac{141}{287}\right)\)	\(e\left(\frac{419}{861}\right)\)	\(e\left(\frac{1541}{1722}\right)\)	\(e\left(\frac{22}{861}\right)\)	\(e\left(\frac{409}{1722}\right)\)
\(\chi_{4067}(4,\cdot)\)	4067.bc	861	yes	\(1\)	\(1\)	\(e\left(\frac{185}{861}\right)\)	\(e\left(\frac{856}{861}\right)\)	\(e\left(\frac{370}{861}\right)\)	\(e\left(\frac{485}{861}\right)\)	\(e\left(\frac{60}{287}\right)\)	\(e\left(\frac{185}{287}\right)\)	\(e\left(\frac{851}{861}\right)\)	\(e\left(\frac{670}{861}\right)\)	\(e\left(\frac{94}{861}\right)\)	\(e\left(\frac{365}{861}\right)\)
\(\chi_{4067}(5,\cdot)\)	4067.bf	1722	yes	\(1\)	\(1\)	\(e\left(\frac{485}{1722}\right)\)	\(e\left(\frac{685}{1722}\right)\)	\(e\left(\frac{485}{861}\right)\)	\(e\left(\frac{787}{861}\right)\)	\(e\left(\frac{195}{287}\right)\)	\(e\left(\frac{485}{574}\right)\)	\(e\left(\frac{685}{861}\right)\)	\(e\left(\frac{337}{1722}\right)\)	\(e\left(\frac{449}{861}\right)\)	\(e\left(\frac{1655}{1722}\right)\)
\(\chi_{4067}(6,\cdot)\)	4067.z	574	yes	\(1\)	\(1\)	\(e\left(\frac{347}{574}\right)\)	\(e\left(\frac{425}{574}\right)\)	\(e\left(\frac{60}{287}\right)\)	\(e\left(\frac{195}{287}\right)\)	\(e\left(\frac{99}{287}\right)\)	\(e\left(\frac{467}{574}\right)\)	\(e\left(\frac{138}{287}\right)\)	\(e\left(\frac{163}{574}\right)\)	\(e\left(\frac{23}{287}\right)\)	\(e\left(\frac{545}{574}\right)\)
\(\chi_{4067}(8,\cdot)\)	4067.ba	574	yes	\(-1\)	\(1\)	\(e\left(\frac{185}{574}\right)\)	\(e\left(\frac{141}{287}\right)\)	\(e\left(\frac{185}{287}\right)\)	\(e\left(\frac{485}{574}\right)\)	\(e\left(\frac{467}{574}\right)\)	\(e\left(\frac{555}{574}\right)\)	\(e\left(\frac{282}{287}\right)\)	\(e\left(\frac{48}{287}\right)\)	\(e\left(\frac{47}{287}\right)\)	\(e\left(\frac{39}{287}\right)\)
\(\chi_{4067}(9,\cdot)\)	4067.bc	861	yes	\(1\)	\(1\)	\(e\left(\frac{856}{861}\right)\)	\(e\left(\frac{419}{861}\right)\)	\(e\left(\frac{851}{861}\right)\)	\(e\left(\frac{685}{861}\right)\)	\(e\left(\frac{138}{287}\right)\)	\(e\left(\frac{282}{287}\right)\)	\(e\left(\frac{838}{861}\right)\)	\(e\left(\frac{680}{861}\right)\)	\(e\left(\frac{44}{861}\right)\)	\(e\left(\frac{409}{861}\right)\)
\(\chi_{4067}(10,\cdot)\)	4067.bd	1722	yes	\(-1\)	\(1\)	\(e\left(\frac{335}{861}\right)\)	\(e\left(\frac{1541}{1722}\right)\)	\(e\left(\frac{670}{861}\right)\)	\(e\left(\frac{337}{1722}\right)\)	\(e\left(\frac{163}{574}\right)\)	\(e\left(\frac{48}{287}\right)\)	\(e\left(\frac{680}{861}\right)\)	\(e\left(\frac{1007}{1722}\right)\)	\(e\left(\frac{496}{861}\right)\)	\(e\left(\frac{1159}{1722}\right)\)
\(\chi_{4067}(11,\cdot)\)	4067.bc	861	yes	\(1\)	\(1\)	\(e\left(\frac{47}{861}\right)\)	\(e\left(\frac{22}{861}\right)\)	\(e\left(\frac{94}{861}\right)\)	\(e\left(\frac{449}{861}\right)\)	\(e\left(\frac{23}{287}\right)\)	\(e\left(\frac{47}{287}\right)\)	\(e\left(\frac{44}{861}\right)\)	\(e\left(\frac{496}{861}\right)\)	\(e\left(\frac{103}{861}\right)\)	\(e\left(\frac{116}{861}\right)\)
\(\chi_{4067}(12,\cdot)\)	4067.bd	1722	yes	\(-1\)	\(1\)	\(e\left(\frac{613}{861}\right)\)	\(e\left(\frac{409}{1722}\right)\)	\(e\left(\frac{365}{861}\right)\)	\(e\left(\frac{1655}{1722}\right)\)	\(e\left(\frac{545}{574}\right)\)	\(e\left(\frac{39}{287}\right)\)	\(e\left(\frac{409}{861}\right)\)	\(e\left(\frac{1159}{1722}\right)\)	\(e\left(\frac{116}{861}\right)\)	\(e\left(\frac{1139}{1722}\right)\)
\(\chi_{4067}(13,\cdot)\)	4067.z	574	yes	\(1\)	\(1\)	\(e\left(\frac{211}{574}\right)\)	\(e\left(\frac{227}{574}\right)\)	\(e\left(\frac{211}{287}\right)\)	\(e\left(\frac{40}{287}\right)\)	\(e\left(\frac{219}{287}\right)\)	\(e\left(\frac{59}{574}\right)\)	\(e\left(\frac{227}{287}\right)\)	\(e\left(\frac{291}{574}\right)\)	\(e\left(\frac{277}{287}\right)\)	\(e\left(\frac{75}{574}\right)\)
\(\chi_{4067}(15,\cdot)\)	4067.ba	574	yes	\(-1\)	\(1\)	\(e\left(\frac{447}{574}\right)\)	\(e\left(\frac{184}{287}\right)\)	\(e\left(\frac{160}{287}\right)\)	\(e\left(\frac{179}{574}\right)\)	\(e\left(\frac{241}{574}\right)\)	\(e\left(\frac{193}{574}\right)\)	\(e\left(\frac{81}{287}\right)\)	\(e\left(\frac{26}{287}\right)\)	\(e\left(\frac{157}{287}\right)\)	\(e\left(\frac{57}{287}\right)\)
\(\chi_{4067}(16,\cdot)\)	4067.bc	861	yes	\(1\)	\(1\)	\(e\left(\frac{370}{861}\right)\)	\(e\left(\frac{851}{861}\right)\)	\(e\left(\frac{740}{861}\right)\)	\(e\left(\frac{109}{861}\right)\)	\(e\left(\frac{120}{287}\right)\)	\(e\left(\frac{83}{287}\right)\)	\(e\left(\frac{841}{861}\right)\)	\(e\left(\frac{479}{861}\right)\)	\(e\left(\frac{188}{861}\right)\)	\(e\left(\frac{730}{861}\right)\)
\(\chi_{4067}(17,\cdot)\)	4067.bd	1722	yes	\(-1\)	\(1\)	\(e\left(\frac{137}{861}\right)\)	\(e\left(\frac{1319}{1722}\right)\)	\(e\left(\frac{274}{861}\right)\)	\(e\left(\frac{1207}{1722}\right)\)	\(e\left(\frac{531}{574}\right)\)	\(e\left(\frac{137}{287}\right)\)	\(e\left(\frac{458}{861}\right)\)	\(e\left(\frac{1481}{1722}\right)\)	\(e\left(\frac{172}{861}\right)\)	\(e\left(\frac{145}{1722}\right)\)
\(\chi_{4067}(18,\cdot)\)	4067.w	246	no	\(-1\)	\(1\)	\(e\left(\frac{25}{246}\right)\)	\(e\left(\frac{121}{123}\right)\)	\(e\left(\frac{25}{123}\right)\)	\(e\left(\frac{19}{246}\right)\)	\(e\left(\frac{7}{82}\right)\)	\(e\left(\frac{25}{82}\right)\)	\(e\left(\frac{119}{123}\right)\)	\(e\left(\frac{22}{123}\right)\)	\(e\left(\frac{13}{123}\right)\)	\(e\left(\frac{23}{123}\right)\)
\(\chi_{4067}(19,\cdot)\)	4067.v	246	no	\(1\)	\(1\)	\(e\left(\frac{59}{246}\right)\)	\(e\left(\frac{25}{246}\right)\)	\(e\left(\frac{59}{123}\right)\)	\(e\left(\frac{79}{123}\right)\)	\(e\left(\frac{14}{41}\right)\)	\(e\left(\frac{59}{82}\right)\)	\(e\left(\frac{25}{123}\right)\)	\(e\left(\frac{217}{246}\right)\)	\(e\left(\frac{11}{123}\right)\)	\(e\left(\frac{143}{246}\right)\)
\(\chi_{4067}(20,\cdot)\)	4067.z	574	yes	\(1\)	\(1\)	\(e\left(\frac{285}{574}\right)\)	\(e\left(\frac{225}{574}\right)\)	\(e\left(\frac{285}{287}\right)\)	\(e\left(\frac{137}{287}\right)\)	\(e\left(\frac{255}{287}\right)\)	\(e\left(\frac{281}{574}\right)\)	\(e\left(\frac{225}{287}\right)\)	\(e\left(\frac{559}{574}\right)\)	\(e\left(\frac{181}{287}\right)\)	\(e\left(\frac{221}{574}\right)\)
\(\chi_{4067}(22,\cdot)\)	4067.ba	574	yes	\(-1\)	\(1\)	\(e\left(\frac{93}{574}\right)\)	\(e\left(\frac{150}{287}\right)\)	\(e\left(\frac{93}{287}\right)\)	\(e\left(\frac{461}{574}\right)\)	\(e\left(\frac{393}{574}\right)\)	\(e\left(\frac{279}{574}\right)\)	\(e\left(\frac{13}{287}\right)\)	\(e\left(\frac{277}{287}\right)\)	\(e\left(\frac{50}{287}\right)\)	\(e\left(\frac{243}{287}\right)\)
\(\chi_{4067}(23,\cdot)\)	4067.bc	861	yes	\(1\)	\(1\)	\(e\left(\frac{220}{861}\right)\)	\(e\left(\frac{506}{861}\right)\)	\(e\left(\frac{440}{861}\right)\)	\(e\left(\frac{856}{861}\right)\)	\(e\left(\frac{242}{287}\right)\)	\(e\left(\frac{220}{287}\right)\)	\(e\left(\frac{151}{861}\right)\)	\(e\left(\frac{215}{861}\right)\)	\(e\left(\frac{647}{861}\right)\)	\(e\left(\frac{85}{861}\right)\)
\(\chi_{4067}(24,\cdot)\)	4067.bf	1722	yes	\(1\)	\(1\)	\(e\left(\frac{1411}{1722}\right)\)	\(e\left(\frac{1265}{1722}\right)\)	\(e\left(\frac{550}{861}\right)\)	\(e\left(\frac{209}{861}\right)\)	\(e\left(\frac{159}{287}\right)\)	\(e\left(\frac{263}{574}\right)\)	\(e\left(\frac{404}{861}\right)\)	\(e\left(\frac{107}{1722}\right)\)	\(e\left(\frac{163}{861}\right)\)	\(e\left(\frac{643}{1722}\right)\)
\(\chi_{4067}(25,\cdot)\)	4067.bc	861	yes	\(1\)	\(1\)	\(e\left(\frac{485}{861}\right)\)	\(e\left(\frac{685}{861}\right)\)	\(e\left(\frac{109}{861}\right)\)	\(e\left(\frac{713}{861}\right)\)	\(e\left(\frac{103}{287}\right)\)	\(e\left(\frac{198}{287}\right)\)	\(e\left(\frac{509}{861}\right)\)	\(e\left(\frac{337}{861}\right)\)	\(e\left(\frac{37}{861}\right)\)	\(e\left(\frac{794}{861}\right)\)
\(\chi_{4067}(26,\cdot)\)	4067.bd	1722	yes	\(-1\)	\(1\)	\(e\left(\frac{409}{861}\right)\)	\(e\left(\frac{1537}{1722}\right)\)	\(e\left(\frac{818}{861}\right)\)	\(e\left(\frac{725}{1722}\right)\)	\(e\left(\frac{211}{574}\right)\)	\(e\left(\frac{122}{287}\right)\)	\(e\left(\frac{676}{861}\right)\)	\(e\left(\frac{1543}{1722}\right)\)	\(e\left(\frac{17}{861}\right)\)	\(e\left(\frac{1451}{1722}\right)\)
\(\chi_{4067}(27,\cdot)\)	4067.bb	574	yes	\(-1\)	\(1\)	\(e\left(\frac{141}{287}\right)\)	\(e\left(\frac{419}{574}\right)\)	\(e\left(\frac{282}{287}\right)\)	\(e\left(\frac{111}{574}\right)\)	\(e\left(\frac{127}{574}\right)\)	\(e\left(\frac{136}{287}\right)\)	\(e\left(\frac{132}{287}\right)\)	\(e\left(\frac{393}{574}\right)\)	\(e\left(\frac{22}{287}\right)\)	\(e\left(\frac{409}{574}\right)\)
\(\chi_{4067}(29,\cdot)\)	4067.y	287	yes	\(1\)	\(1\)	\(e\left(\frac{83}{287}\right)\)	\(e\left(\frac{277}{287}\right)\)	\(e\left(\frac{166}{287}\right)\)	\(e\left(\frac{109}{287}\right)\)	\(e\left(\frac{73}{287}\right)\)	\(e\left(\frac{249}{287}\right)\)	\(e\left(\frac{267}{287}\right)\)	\(e\left(\frac{192}{287}\right)\)	\(e\left(\frac{188}{287}\right)\)	\(e\left(\frac{156}{287}\right)\)
\(\chi_{4067}(30,\cdot)\)	4067.u	123	no	\(1\)	\(1\)	\(e\left(\frac{109}{123}\right)\)	\(e\left(\frac{17}{123}\right)\)	\(e\left(\frac{95}{123}\right)\)	\(e\left(\frac{73}{123}\right)\)	\(e\left(\frac{1}{41}\right)\)	\(e\left(\frac{27}{41}\right)\)	\(e\left(\frac{34}{123}\right)\)	\(e\left(\frac{59}{123}\right)\)	\(e\left(\frac{74}{123}\right)\)	\(e\left(\frac{112}{123}\right)\)
\(\chi_{4067}(31,\cdot)\)	4067.x	246	no	\(-1\)	\(1\)	\(e\left(\frac{98}{123}\right)\)	\(e\left(\frac{131}{246}\right)\)	\(e\left(\frac{73}{123}\right)\)	\(e\left(\frac{85}{246}\right)\)	\(e\left(\frac{27}{82}\right)\)	\(e\left(\frac{16}{41}\right)\)	\(e\left(\frac{8}{123}\right)\)	\(e\left(\frac{35}{246}\right)\)	\(e\left(\frac{97}{123}\right)\)	\(e\left(\frac{31}{246}\right)\)
\(\chi_{4067}(32,\cdot)\)	4067.be	1722	yes	\(-1\)	\(1\)	\(e\left(\frac{925}{1722}\right)\)	\(e\left(\frac{418}{861}\right)\)	\(e\left(\frac{64}{861}\right)\)	\(e\left(\frac{703}{1722}\right)\)	\(e\left(\frac{13}{574}\right)\)	\(e\left(\frac{351}{574}\right)\)	\(e\left(\frac{836}{861}\right)\)	\(e\left(\frac{814}{861}\right)\)	\(e\left(\frac{235}{861}\right)\)	\(e\left(\frac{482}{861}\right)\)
\(\chi_{4067}(33,\cdot)\)	4067.bd	1722	yes	\(-1\)	\(1\)	\(e\left(\frac{475}{861}\right)\)	\(e\left(\frac{463}{1722}\right)\)	\(e\left(\frac{89}{861}\right)\)	\(e\left(\frac{1583}{1722}\right)\)	\(e\left(\frac{471}{574}\right)\)	\(e\left(\frac{188}{287}\right)\)	\(e\left(\frac{463}{861}\right)\)	\(e\left(\frac{811}{1722}\right)\)	\(e\left(\frac{125}{861}\right)\)	\(e\left(\frac{641}{1722}\right)\)
\(\chi_{4067}(34,\cdot)\)	4067.z	574	yes	\(1\)	\(1\)	\(e\left(\frac{153}{574}\right)\)	\(e\left(\frac{151}{574}\right)\)	\(e\left(\frac{153}{287}\right)\)	\(e\left(\frac{282}{287}\right)\)	\(e\left(\frac{152}{287}\right)\)	\(e\left(\frac{459}{574}\right)\)	\(e\left(\frac{151}{287}\right)\)	\(e\left(\frac{143}{574}\right)\)	\(e\left(\frac{73}{287}\right)\)	\(e\left(\frac{457}{574}\right)\)
\(\chi_{4067}(36,\cdot)\)	4067.y	287	yes	\(1\)	\(1\)	\(e\left(\frac{60}{287}\right)\)	\(e\left(\frac{138}{287}\right)\)	\(e\left(\frac{120}{287}\right)\)	\(e\left(\frac{103}{287}\right)\)	\(e\left(\frac{198}{287}\right)\)	\(e\left(\frac{180}{287}\right)\)	\(e\left(\frac{276}{287}\right)\)	\(e\left(\frac{163}{287}\right)\)	\(e\left(\frac{46}{287}\right)\)	\(e\left(\frac{258}{287}\right)\)
\(\chi_{4067}(37,\cdot)\)	4067.bc	861	yes	\(1\)	\(1\)	\(e\left(\frac{46}{861}\right)\)	\(e\left(\frac{278}{861}\right)\)	\(e\left(\frac{92}{861}\right)\)	\(e\left(\frac{586}{861}\right)\)	\(e\left(\frac{108}{287}\right)\)	\(e\left(\frac{46}{287}\right)\)	\(e\left(\frac{556}{861}\right)\)	\(e\left(\frac{632}{861}\right)\)	\(e\left(\frac{284}{861}\right)\)	\(e\left(\frac{370}{861}\right)\)

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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.