LMFDB - Group of Dirichlet characters of modulus 859

Show commands: PariGP / SageMath

sage: H = DirichletGroup(859)

pari: g = idealstar(,859,2)

Character group

sage: G.order() pari: g.no
Order	=	858
sage: H.invariants() pari: g.cyc
Structure	=	$C_{858}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{859}(2,\cdot)$

First 32 of 858 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{859}(1,\cdot)$	859.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{859}(2,\cdot)$	859.p	858	yes	$-1$	$1$	$e\left(\frac{1}{858}\right)$	$e\left(\frac{119}{858}\right)$	$e\left(\frac{1}{429}\right)$	$e\left(\frac{181}{429}\right)$	$e\left(\frac{20}{143}\right)$	$e\left(\frac{317}{429}\right)$	$e\left(\frac{1}{286}\right)$	$e\left(\frac{119}{429}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{129}{286}\right)$
$\chi_{859}(3,\cdot)$	859.p	858	yes	$-1$	$1$	$e\left(\frac{119}{858}\right)$	$e\left(\frac{433}{858}\right)$	$e\left(\frac{119}{429}\right)$	$e\left(\frac{89}{429}\right)$	$e\left(\frac{92}{143}\right)$	$e\left(\frac{400}{429}\right)$	$e\left(\frac{119}{286}\right)$	$e\left(\frac{4}{429}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{193}{286}\right)$
$\chi_{859}(4,\cdot)$	859.o	429	yes	$1$	$1$	$e\left(\frac{1}{429}\right)$	$e\left(\frac{119}{429}\right)$	$e\left(\frac{2}{429}\right)$	$e\left(\frac{362}{429}\right)$	$e\left(\frac{40}{143}\right)$	$e\left(\frac{205}{429}\right)$	$e\left(\frac{1}{143}\right)$	$e\left(\frac{238}{429}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{129}{143}\right)$
$\chi_{859}(5,\cdot)$	859.o	429	yes	$1$	$1$	$e\left(\frac{181}{429}\right)$	$e\left(\frac{89}{429}\right)$	$e\left(\frac{362}{429}\right)$	$e\left(\frac{314}{429}\right)$	$e\left(\frac{90}{143}\right)$	$e\left(\frac{211}{429}\right)$	$e\left(\frac{38}{143}\right)$	$e\left(\frac{178}{429}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{40}{143}\right)$
$\chi_{859}(6,\cdot)$	859.m	143	yes	$1$	$1$	$e\left(\frac{20}{143}\right)$	$e\left(\frac{92}{143}\right)$	$e\left(\frac{40}{143}\right)$	$e\left(\frac{90}{143}\right)$	$e\left(\frac{112}{143}\right)$	$e\left(\frac{96}{143}\right)$	$e\left(\frac{60}{143}\right)$	$e\left(\frac{41}{143}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{18}{143}\right)$
$\chi_{859}(7,\cdot)$	859.o	429	yes	$1$	$1$	$e\left(\frac{317}{429}\right)$	$e\left(\frac{400}{429}\right)$	$e\left(\frac{205}{429}\right)$	$e\left(\frac{211}{429}\right)$	$e\left(\frac{96}{143}\right)$	$e\left(\frac{206}{429}\right)$	$e\left(\frac{31}{143}\right)$	$e\left(\frac{371}{429}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{138}{143}\right)$
$\chi_{859}(8,\cdot)$	859.n	286	yes	$-1$	$1$	$e\left(\frac{1}{286}\right)$	$e\left(\frac{119}{286}\right)$	$e\left(\frac{1}{143}\right)$	$e\left(\frac{38}{143}\right)$	$e\left(\frac{60}{143}\right)$	$e\left(\frac{31}{143}\right)$	$e\left(\frac{3}{286}\right)$	$e\left(\frac{119}{143}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{101}{286}\right)$
$\chi_{859}(9,\cdot)$	859.o	429	yes	$1$	$1$	$e\left(\frac{119}{429}\right)$	$e\left(\frac{4}{429}\right)$	$e\left(\frac{238}{429}\right)$	$e\left(\frac{178}{429}\right)$	$e\left(\frac{41}{143}\right)$	$e\left(\frac{371}{429}\right)$	$e\left(\frac{119}{143}\right)$	$e\left(\frac{8}{429}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{50}{143}\right)$
$\chi_{859}(10,\cdot)$	859.h	26	yes	$-1$	$1$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{11}{13}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{859}(11,\cdot)$	859.n	286	yes	$-1$	$1$	$e\left(\frac{129}{286}\right)$	$e\left(\frac{193}{286}\right)$	$e\left(\frac{129}{143}\right)$	$e\left(\frac{40}{143}\right)$	$e\left(\frac{18}{143}\right)$	$e\left(\frac{138}{143}\right)$	$e\left(\frac{101}{286}\right)$	$e\left(\frac{50}{143}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{159}{286}\right)$
$\chi_{859}(12,\cdot)$	859.l	78	yes	$-1$	$1$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{11}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{16}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{859}(13,\cdot)$	859.e	11	yes	$1$	$1$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{4}{11}\right)$	$1$	$e\left(\frac{9}{11}\right)$
$\chi_{859}(14,\cdot)$	859.p	858	yes	$-1$	$1$	$e\left(\frac{635}{858}\right)$	$e\left(\frac{61}{858}\right)$	$e\left(\frac{206}{429}\right)$	$e\left(\frac{392}{429}\right)$	$e\left(\frac{116}{143}\right)$	$e\left(\frac{94}{429}\right)$	$e\left(\frac{63}{286}\right)$	$e\left(\frac{61}{429}\right)$	$e\left(\frac{17}{26}\right)$	$e\left(\frac{119}{286}\right)$
$\chi_{859}(15,\cdot)$	859.k	66	yes	$-1$	$1$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{31}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{14}{33}\right)$	$-1$	$e\left(\frac{21}{22}\right)$
$\chi_{859}(16,\cdot)$	859.o	429	yes	$1$	$1$	$e\left(\frac{2}{429}\right)$	$e\left(\frac{238}{429}\right)$	$e\left(\frac{4}{429}\right)$	$e\left(\frac{295}{429}\right)$	$e\left(\frac{80}{143}\right)$	$e\left(\frac{410}{429}\right)$	$e\left(\frac{2}{143}\right)$	$e\left(\frac{47}{429}\right)$	$e\left(\frac{9}{13}\right)$	$e\left(\frac{115}{143}\right)$
$\chi_{859}(17,\cdot)$	859.o	429	yes	$1$	$1$	$e\left(\frac{400}{429}\right)$	$e\left(\frac{410}{429}\right)$	$e\left(\frac{371}{429}\right)$	$e\left(\frac{227}{429}\right)$	$e\left(\frac{127}{143}\right)$	$e\left(\frac{61}{429}\right)$	$e\left(\frac{114}{143}\right)$	$e\left(\frac{391}{429}\right)$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{120}{143}\right)$
$\chi_{859}(18,\cdot)$	859.p	858	yes	$-1$	$1$	$e\left(\frac{239}{858}\right)$	$e\left(\frac{127}{858}\right)$	$e\left(\frac{239}{429}\right)$	$e\left(\frac{359}{429}\right)$	$e\left(\frac{61}{143}\right)$	$e\left(\frac{259}{429}\right)$	$e\left(\frac{239}{286}\right)$	$e\left(\frac{127}{429}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{229}{286}\right)$
$\chi_{859}(19,\cdot)$	859.k	66	yes	$-1$	$1$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{4}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{4}{33}\right)$	$-1$	$e\left(\frac{17}{22}\right)$
$\chi_{859}(20,\cdot)$	859.i	33	yes	$1$	$1$	$e\left(\frac{14}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{32}{33}\right)$	$1$	$e\left(\frac{2}{11}\right)$
$\chi_{859}(21,\cdot)$	859.n	286	yes	$-1$	$1$	$e\left(\frac{251}{286}\right)$	$e\left(\frac{125}{286}\right)$	$e\left(\frac{108}{143}\right)$	$e\left(\frac{100}{143}\right)$	$e\left(\frac{45}{143}\right)$	$e\left(\frac{59}{143}\right)$	$e\left(\frac{181}{286}\right)$	$e\left(\frac{125}{143}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{183}{286}\right)$
$\chi_{859}(22,\cdot)$	859.o	429	yes	$1$	$1$	$e\left(\frac{194}{429}\right)$	$e\left(\frac{349}{429}\right)$	$e\left(\frac{388}{429}\right)$	$e\left(\frac{301}{429}\right)$	$e\left(\frac{38}{143}\right)$	$e\left(\frac{302}{429}\right)$	$e\left(\frac{51}{143}\right)$	$e\left(\frac{269}{429}\right)$	$e\left(\frac{2}{13}\right)$	$e\left(\frac{1}{143}\right)$
$\chi_{859}(23,\cdot)$	859.l	78	yes	$-1$	$1$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{10}{13}\right)$	$e\left(\frac{22}{39}\right)$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{1}{39}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{19}{26}\right)$
$\chi_{859}(24,\cdot)$	859.o	429	yes	$1$	$1$	$e\left(\frac{61}{429}\right)$	$e\left(\frac{395}{429}\right)$	$e\left(\frac{122}{429}\right)$	$e\left(\frac{203}{429}\right)$	$e\left(\frac{9}{143}\right)$	$e\left(\frac{64}{429}\right)$	$e\left(\frac{61}{143}\right)$	$e\left(\frac{361}{429}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{4}{143}\right)$
$\chi_{859}(25,\cdot)$	859.o	429	yes	$1$	$1$	$e\left(\frac{362}{429}\right)$	$e\left(\frac{178}{429}\right)$	$e\left(\frac{295}{429}\right)$	$e\left(\frac{199}{429}\right)$	$e\left(\frac{37}{143}\right)$	$e\left(\frac{422}{429}\right)$	$e\left(\frac{76}{143}\right)$	$e\left(\frac{356}{429}\right)$	$e\left(\frac{4}{13}\right)$	$e\left(\frac{80}{143}\right)$
$\chi_{859}(26,\cdot)$	859.l	78	yes	$-1$	$1$	$e\left(\frac{71}{78}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{20}{39}\right)$	$e\left(\frac{3}{13}\right)$	$e\left(\frac{4}{39}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{7}{26}\right)$
$\chi_{859}(27,\cdot)$	859.n	286	yes	$-1$	$1$	$e\left(\frac{119}{286}\right)$	$e\left(\frac{147}{286}\right)$	$e\left(\frac{119}{143}\right)$	$e\left(\frac{89}{143}\right)$	$e\left(\frac{133}{143}\right)$	$e\left(\frac{114}{143}\right)$	$e\left(\frac{71}{286}\right)$	$e\left(\frac{4}{143}\right)$	$e\left(\frac{1}{26}\right)$	$e\left(\frac{7}{286}\right)$
$\chi_{859}(28,\cdot)$	859.m	143	yes	$1$	$1$	$e\left(\frac{106}{143}\right)$	$e\left(\frac{30}{143}\right)$	$e\left(\frac{69}{143}\right)$	$e\left(\frac{48}{143}\right)$	$e\left(\frac{136}{143}\right)$	$e\left(\frac{137}{143}\right)$	$e\left(\frac{32}{143}\right)$	$e\left(\frac{60}{143}\right)$	$e\left(\frac{1}{13}\right)$	$e\left(\frac{124}{143}\right)$
$\chi_{859}(29,\cdot)$	859.p	858	yes	$-1$	$1$	$e\left(\frac{763}{858}\right)$	$e\left(\frac{707}{858}\right)$	$e\left(\frac{334}{429}\right)$	$e\left(\frac{394}{429}\right)$	$e\left(\frac{102}{143}\right)$	$e\left(\frac{344}{429}\right)$	$e\left(\frac{191}{286}\right)$	$e\left(\frac{278}{429}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{43}{286}\right)$
$\chi_{859}(30,\cdot)$	859.o	429	yes	$1$	$1$	$e\left(\frac{241}{429}\right)$	$e\left(\frac{365}{429}\right)$	$e\left(\frac{53}{429}\right)$	$e\left(\frac{155}{429}\right)$	$e\left(\frac{59}{143}\right)$	$e\left(\frac{70}{429}\right)$	$e\left(\frac{98}{143}\right)$	$e\left(\frac{301}{429}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{58}{143}\right)$
$\chi_{859}(31,\cdot)$	859.o	429	yes	$1$	$1$	$e\left(\frac{230}{429}\right)$	$e\left(\frac{343}{429}\right)$	$e\left(\frac{31}{429}\right)$	$e\left(\frac{34}{429}\right)$	$e\left(\frac{48}{143}\right)$	$e\left(\frac{389}{429}\right)$	$e\left(\frac{87}{143}\right)$	$e\left(\frac{257}{429}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{69}{143}\right)$
$\chi_{859}(32,\cdot)$	859.p	858	yes	$-1$	$1$	$e\left(\frac{5}{858}\right)$	$e\left(\frac{595}{858}\right)$	$e\left(\frac{5}{429}\right)$	$e\left(\frac{47}{429}\right)$	$e\left(\frac{100}{143}\right)$	$e\left(\frac{298}{429}\right)$	$e\left(\frac{5}{286}\right)$	$e\left(\frac{166}{429}\right)$	$e\left(\frac{3}{26}\right)$	$e\left(\frac{73}{286}\right)$

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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	$859$
Structure	\(C_{858}\)
Order	$858$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{859}(1,\cdot)\)	859.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{859}(2,\cdot)\)	859.p	858	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{858}\right)\)	\(e\left(\frac{119}{858}\right)\)	\(e\left(\frac{1}{429}\right)\)	\(e\left(\frac{181}{429}\right)\)	\(e\left(\frac{20}{143}\right)\)	\(e\left(\frac{317}{429}\right)\)	\(e\left(\frac{1}{286}\right)\)	\(e\left(\frac{119}{429}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{129}{286}\right)\)
\(\chi_{859}(3,\cdot)\)	859.p	858	yes	\(-1\)	\(1\)	\(e\left(\frac{119}{858}\right)\)	\(e\left(\frac{433}{858}\right)\)	\(e\left(\frac{119}{429}\right)\)	\(e\left(\frac{89}{429}\right)\)	\(e\left(\frac{92}{143}\right)\)	\(e\left(\frac{400}{429}\right)\)	\(e\left(\frac{119}{286}\right)\)	\(e\left(\frac{4}{429}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{193}{286}\right)\)
\(\chi_{859}(4,\cdot)\)	859.o	429	yes	\(1\)	\(1\)	\(e\left(\frac{1}{429}\right)\)	\(e\left(\frac{119}{429}\right)\)	\(e\left(\frac{2}{429}\right)\)	\(e\left(\frac{362}{429}\right)\)	\(e\left(\frac{40}{143}\right)\)	\(e\left(\frac{205}{429}\right)\)	\(e\left(\frac{1}{143}\right)\)	\(e\left(\frac{238}{429}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{129}{143}\right)\)
\(\chi_{859}(5,\cdot)\)	859.o	429	yes	\(1\)	\(1\)	\(e\left(\frac{181}{429}\right)\)	\(e\left(\frac{89}{429}\right)\)	\(e\left(\frac{362}{429}\right)\)	\(e\left(\frac{314}{429}\right)\)	\(e\left(\frac{90}{143}\right)\)	\(e\left(\frac{211}{429}\right)\)	\(e\left(\frac{38}{143}\right)\)	\(e\left(\frac{178}{429}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{40}{143}\right)\)
\(\chi_{859}(6,\cdot)\)	859.m	143	yes	\(1\)	\(1\)	\(e\left(\frac{20}{143}\right)\)	\(e\left(\frac{92}{143}\right)\)	\(e\left(\frac{40}{143}\right)\)	\(e\left(\frac{90}{143}\right)\)	\(e\left(\frac{112}{143}\right)\)	\(e\left(\frac{96}{143}\right)\)	\(e\left(\frac{60}{143}\right)\)	\(e\left(\frac{41}{143}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{18}{143}\right)\)
\(\chi_{859}(7,\cdot)\)	859.o	429	yes	\(1\)	\(1\)	\(e\left(\frac{317}{429}\right)\)	\(e\left(\frac{400}{429}\right)\)	\(e\left(\frac{205}{429}\right)\)	\(e\left(\frac{211}{429}\right)\)	\(e\left(\frac{96}{143}\right)\)	\(e\left(\frac{206}{429}\right)\)	\(e\left(\frac{31}{143}\right)\)	\(e\left(\frac{371}{429}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{138}{143}\right)\)
\(\chi_{859}(8,\cdot)\)	859.n	286	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{286}\right)\)	\(e\left(\frac{119}{286}\right)\)	\(e\left(\frac{1}{143}\right)\)	\(e\left(\frac{38}{143}\right)\)	\(e\left(\frac{60}{143}\right)\)	\(e\left(\frac{31}{143}\right)\)	\(e\left(\frac{3}{286}\right)\)	\(e\left(\frac{119}{143}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{101}{286}\right)\)
\(\chi_{859}(9,\cdot)\)	859.o	429	yes	\(1\)	\(1\)	\(e\left(\frac{119}{429}\right)\)	\(e\left(\frac{4}{429}\right)\)	\(e\left(\frac{238}{429}\right)\)	\(e\left(\frac{178}{429}\right)\)	\(e\left(\frac{41}{143}\right)\)	\(e\left(\frac{371}{429}\right)\)	\(e\left(\frac{119}{143}\right)\)	\(e\left(\frac{8}{429}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{50}{143}\right)\)
\(\chi_{859}(10,\cdot)\)	859.h	26	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{859}(11,\cdot)\)	859.n	286	yes	\(-1\)	\(1\)	\(e\left(\frac{129}{286}\right)\)	\(e\left(\frac{193}{286}\right)\)	\(e\left(\frac{129}{143}\right)\)	\(e\left(\frac{40}{143}\right)\)	\(e\left(\frac{18}{143}\right)\)	\(e\left(\frac{138}{143}\right)\)	\(e\left(\frac{101}{286}\right)\)	\(e\left(\frac{50}{143}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{159}{286}\right)\)
\(\chi_{859}(12,\cdot)\)	859.l	78	yes	\(-1\)	\(1\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{11}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{16}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{859}(13,\cdot)\)	859.e	11	yes	\(1\)	\(1\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(1\)	\(e\left(\frac{9}{11}\right)\)
\(\chi_{859}(14,\cdot)\)	859.p	858	yes	\(-1\)	\(1\)	\(e\left(\frac{635}{858}\right)\)	\(e\left(\frac{61}{858}\right)\)	\(e\left(\frac{206}{429}\right)\)	\(e\left(\frac{392}{429}\right)\)	\(e\left(\frac{116}{143}\right)\)	\(e\left(\frac{94}{429}\right)\)	\(e\left(\frac{63}{286}\right)\)	\(e\left(\frac{61}{429}\right)\)	\(e\left(\frac{17}{26}\right)\)	\(e\left(\frac{119}{286}\right)\)
\(\chi_{859}(15,\cdot)\)	859.k	66	yes	\(-1\)	\(1\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{14}{33}\right)\)	\(-1\)	\(e\left(\frac{21}{22}\right)\)
\(\chi_{859}(16,\cdot)\)	859.o	429	yes	\(1\)	\(1\)	\(e\left(\frac{2}{429}\right)\)	\(e\left(\frac{238}{429}\right)\)	\(e\left(\frac{4}{429}\right)\)	\(e\left(\frac{295}{429}\right)\)	\(e\left(\frac{80}{143}\right)\)	\(e\left(\frac{410}{429}\right)\)	\(e\left(\frac{2}{143}\right)\)	\(e\left(\frac{47}{429}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{115}{143}\right)\)
\(\chi_{859}(17,\cdot)\)	859.o	429	yes	\(1\)	\(1\)	\(e\left(\frac{400}{429}\right)\)	\(e\left(\frac{410}{429}\right)\)	\(e\left(\frac{371}{429}\right)\)	\(e\left(\frac{227}{429}\right)\)	\(e\left(\frac{127}{143}\right)\)	\(e\left(\frac{61}{429}\right)\)	\(e\left(\frac{114}{143}\right)\)	\(e\left(\frac{391}{429}\right)\)	\(e\left(\frac{6}{13}\right)\)	\(e\left(\frac{120}{143}\right)\)
\(\chi_{859}(18,\cdot)\)	859.p	858	yes	\(-1\)	\(1\)	\(e\left(\frac{239}{858}\right)\)	\(e\left(\frac{127}{858}\right)\)	\(e\left(\frac{239}{429}\right)\)	\(e\left(\frac{359}{429}\right)\)	\(e\left(\frac{61}{143}\right)\)	\(e\left(\frac{259}{429}\right)\)	\(e\left(\frac{239}{286}\right)\)	\(e\left(\frac{127}{429}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{229}{286}\right)\)
\(\chi_{859}(19,\cdot)\)	859.k	66	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(-1\)	\(e\left(\frac{17}{22}\right)\)
\(\chi_{859}(20,\cdot)\)	859.i	33	yes	\(1\)	\(1\)	\(e\left(\frac{14}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(1\)	\(e\left(\frac{2}{11}\right)\)
\(\chi_{859}(21,\cdot)\)	859.n	286	yes	\(-1\)	\(1\)	\(e\left(\frac{251}{286}\right)\)	\(e\left(\frac{125}{286}\right)\)	\(e\left(\frac{108}{143}\right)\)	\(e\left(\frac{100}{143}\right)\)	\(e\left(\frac{45}{143}\right)\)	\(e\left(\frac{59}{143}\right)\)	\(e\left(\frac{181}{286}\right)\)	\(e\left(\frac{125}{143}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{183}{286}\right)\)
\(\chi_{859}(22,\cdot)\)	859.o	429	yes	\(1\)	\(1\)	\(e\left(\frac{194}{429}\right)\)	\(e\left(\frac{349}{429}\right)\)	\(e\left(\frac{388}{429}\right)\)	\(e\left(\frac{301}{429}\right)\)	\(e\left(\frac{38}{143}\right)\)	\(e\left(\frac{302}{429}\right)\)	\(e\left(\frac{51}{143}\right)\)	\(e\left(\frac{269}{429}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{1}{143}\right)\)
\(\chi_{859}(23,\cdot)\)	859.l	78	yes	\(-1\)	\(1\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{10}{13}\right)\)	\(e\left(\frac{22}{39}\right)\)	\(e\left(\frac{7}{26}\right)\)	\(e\left(\frac{1}{39}\right)\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{19}{26}\right)\)
\(\chi_{859}(24,\cdot)\)	859.o	429	yes	\(1\)	\(1\)	\(e\left(\frac{61}{429}\right)\)	\(e\left(\frac{395}{429}\right)\)	\(e\left(\frac{122}{429}\right)\)	\(e\left(\frac{203}{429}\right)\)	\(e\left(\frac{9}{143}\right)\)	\(e\left(\frac{64}{429}\right)\)	\(e\left(\frac{61}{143}\right)\)	\(e\left(\frac{361}{429}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{4}{143}\right)\)
\(\chi_{859}(25,\cdot)\)	859.o	429	yes	\(1\)	\(1\)	\(e\left(\frac{362}{429}\right)\)	\(e\left(\frac{178}{429}\right)\)	\(e\left(\frac{295}{429}\right)\)	\(e\left(\frac{199}{429}\right)\)	\(e\left(\frac{37}{143}\right)\)	\(e\left(\frac{422}{429}\right)\)	\(e\left(\frac{76}{143}\right)\)	\(e\left(\frac{356}{429}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{80}{143}\right)\)
\(\chi_{859}(26,\cdot)\)	859.l	78	yes	\(-1\)	\(1\)	\(e\left(\frac{71}{78}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{20}{39}\right)\)	\(e\left(\frac{3}{13}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{19}{26}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{11}{26}\right)\)	\(e\left(\frac{7}{26}\right)\)
\(\chi_{859}(27,\cdot)\)	859.n	286	yes	\(-1\)	\(1\)	\(e\left(\frac{119}{286}\right)\)	\(e\left(\frac{147}{286}\right)\)	\(e\left(\frac{119}{143}\right)\)	\(e\left(\frac{89}{143}\right)\)	\(e\left(\frac{133}{143}\right)\)	\(e\left(\frac{114}{143}\right)\)	\(e\left(\frac{71}{286}\right)\)	\(e\left(\frac{4}{143}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{7}{286}\right)\)
\(\chi_{859}(28,\cdot)\)	859.m	143	yes	\(1\)	\(1\)	\(e\left(\frac{106}{143}\right)\)	\(e\left(\frac{30}{143}\right)\)	\(e\left(\frac{69}{143}\right)\)	\(e\left(\frac{48}{143}\right)\)	\(e\left(\frac{136}{143}\right)\)	\(e\left(\frac{137}{143}\right)\)	\(e\left(\frac{32}{143}\right)\)	\(e\left(\frac{60}{143}\right)\)	\(e\left(\frac{1}{13}\right)\)	\(e\left(\frac{124}{143}\right)\)
\(\chi_{859}(29,\cdot)\)	859.p	858	yes	\(-1\)	\(1\)	\(e\left(\frac{763}{858}\right)\)	\(e\left(\frac{707}{858}\right)\)	\(e\left(\frac{334}{429}\right)\)	\(e\left(\frac{394}{429}\right)\)	\(e\left(\frac{102}{143}\right)\)	\(e\left(\frac{344}{429}\right)\)	\(e\left(\frac{191}{286}\right)\)	\(e\left(\frac{278}{429}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{43}{286}\right)\)
\(\chi_{859}(30,\cdot)\)	859.o	429	yes	\(1\)	\(1\)	\(e\left(\frac{241}{429}\right)\)	\(e\left(\frac{365}{429}\right)\)	\(e\left(\frac{53}{429}\right)\)	\(e\left(\frac{155}{429}\right)\)	\(e\left(\frac{59}{143}\right)\)	\(e\left(\frac{70}{429}\right)\)	\(e\left(\frac{98}{143}\right)\)	\(e\left(\frac{301}{429}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(e\left(\frac{58}{143}\right)\)
\(\chi_{859}(31,\cdot)\)	859.o	429	yes	\(1\)	\(1\)	\(e\left(\frac{230}{429}\right)\)	\(e\left(\frac{343}{429}\right)\)	\(e\left(\frac{31}{429}\right)\)	\(e\left(\frac{34}{429}\right)\)	\(e\left(\frac{48}{143}\right)\)	\(e\left(\frac{389}{429}\right)\)	\(e\left(\frac{87}{143}\right)\)	\(e\left(\frac{257}{429}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{69}{143}\right)\)
\(\chi_{859}(32,\cdot)\)	859.p	858	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{858}\right)\)	\(e\left(\frac{595}{858}\right)\)	\(e\left(\frac{5}{429}\right)\)	\(e\left(\frac{47}{429}\right)\)	\(e\left(\frac{100}{143}\right)\)	\(e\left(\frac{298}{429}\right)\)	\(e\left(\frac{5}{286}\right)\)	\(e\left(\frac{166}{429}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{73}{286}\right)\)

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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.