LMFDB - Group of Dirichlet characters of modulus 160499

Show commands: PariGP / SageMath

sage: H = DirichletGroup(160499)

pari: g = idealstar(,160499,2)

Character group

sage: G.order() pari: g.no
Order	=	160498
sage: H.invariants() pari: g.cyc
Structure	=	$C_{160498}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{160499}(2,\cdot)$

First 32 of 160498 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{160499}(1,\cdot)$	160499.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{160499}(2,\cdot)$	160499.h	160498	yes	$-1$	$1$	$e\left(\frac{1}{160498}\right)$	$e\left(\frac{18528}{80249}\right)$	$e\left(\frac{1}{80249}\right)$	$e\left(\frac{658}{80249}\right)$	$e\left(\frac{37057}{160498}\right)$	$e\left(\frac{79258}{80249}\right)$	$e\left(\frac{3}{160498}\right)$	$e\left(\frac{37056}{80249}\right)$	$e\left(\frac{1317}{160498}\right)$	$e\left(\frac{114255}{160498}\right)$
$\chi_{160499}(3,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{18528}{80249}\right)$	$e\left(\frac{43373}{80249}\right)$	$e\left(\frac{37056}{80249}\right)$	$e\left(\frac{67401}{80249}\right)$	$e\left(\frac{61901}{80249}\right)$	$e\left(\frac{31546}{80249}\right)$	$e\left(\frac{55584}{80249}\right)$	$e\left(\frac{6497}{80249}\right)$	$e\left(\frac{5680}{80249}\right)$	$e\left(\frac{28269}{80249}\right)$
$\chi_{160499}(4,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{1}{80249}\right)$	$e\left(\frac{37056}{80249}\right)$	$e\left(\frac{2}{80249}\right)$	$e\left(\frac{1316}{80249}\right)$	$e\left(\frac{37057}{80249}\right)$	$e\left(\frac{78267}{80249}\right)$	$e\left(\frac{3}{80249}\right)$	$e\left(\frac{74112}{80249}\right)$	$e\left(\frac{1317}{80249}\right)$	$e\left(\frac{34006}{80249}\right)$
$\chi_{160499}(5,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{658}{80249}\right)$	$e\left(\frac{67401}{80249}\right)$	$e\left(\frac{1316}{80249}\right)$	$e\left(\frac{63438}{80249}\right)$	$e\left(\frac{68059}{80249}\right)$	$e\left(\frac{60077}{80249}\right)$	$e\left(\frac{1974}{80249}\right)$	$e\left(\frac{54553}{80249}\right)$	$e\left(\frac{64096}{80249}\right)$	$e\left(\frac{66726}{80249}\right)$
$\chi_{160499}(6,\cdot)$	160499.h	160498	yes	$-1$	$1$	$e\left(\frac{37057}{160498}\right)$	$e\left(\frac{61901}{80249}\right)$	$e\left(\frac{37057}{80249}\right)$	$e\left(\frac{68059}{80249}\right)$	$e\left(\frac{361}{160498}\right)$	$e\left(\frac{30555}{80249}\right)$	$e\left(\frac{111171}{160498}\right)$	$e\left(\frac{43553}{80249}\right)$	$e\left(\frac{12677}{160498}\right)$	$e\left(\frac{10295}{160498}\right)$
$\chi_{160499}(7,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{79258}{80249}\right)$	$e\left(\frac{31546}{80249}\right)$	$e\left(\frac{78267}{80249}\right)$	$e\left(\frac{60077}{80249}\right)$	$e\left(\frac{30555}{80249}\right)$	$e\left(\frac{38186}{80249}\right)$	$e\left(\frac{77276}{80249}\right)$	$e\left(\frac{63092}{80249}\right)$	$e\left(\frac{59086}{80249}\right)$	$e\left(\frac{4634}{80249}\right)$
$\chi_{160499}(8,\cdot)$	160499.h	160498	yes	$-1$	$1$	$e\left(\frac{3}{160498}\right)$	$e\left(\frac{55584}{80249}\right)$	$e\left(\frac{3}{80249}\right)$	$e\left(\frac{1974}{80249}\right)$	$e\left(\frac{111171}{160498}\right)$	$e\left(\frac{77276}{80249}\right)$	$e\left(\frac{9}{160498}\right)$	$e\left(\frac{30919}{80249}\right)$	$e\left(\frac{3951}{160498}\right)$	$e\left(\frac{21769}{160498}\right)$
$\chi_{160499}(9,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{37056}{80249}\right)$	$e\left(\frac{6497}{80249}\right)$	$e\left(\frac{74112}{80249}\right)$	$e\left(\frac{54553}{80249}\right)$	$e\left(\frac{43553}{80249}\right)$	$e\left(\frac{63092}{80249}\right)$	$e\left(\frac{30919}{80249}\right)$	$e\left(\frac{12994}{80249}\right)$	$e\left(\frac{11360}{80249}\right)$	$e\left(\frac{56538}{80249}\right)$
$\chi_{160499}(10,\cdot)$	160499.h	160498	yes	$-1$	$1$	$e\left(\frac{1317}{160498}\right)$	$e\left(\frac{5680}{80249}\right)$	$e\left(\frac{1317}{80249}\right)$	$e\left(\frac{64096}{80249}\right)$	$e\left(\frac{12677}{160498}\right)$	$e\left(\frac{59086}{80249}\right)$	$e\left(\frac{3951}{160498}\right)$	$e\left(\frac{11360}{80249}\right)$	$e\left(\frac{129509}{160498}\right)$	$e\left(\frac{87209}{160498}\right)$
$\chi_{160499}(11,\cdot)$	160499.h	160498	yes	$-1$	$1$	$e\left(\frac{114255}{160498}\right)$	$e\left(\frac{28269}{80249}\right)$	$e\left(\frac{34006}{80249}\right)$	$e\left(\frac{66726}{80249}\right)$	$e\left(\frac{10295}{160498}\right)$	$e\left(\frac{4634}{80249}\right)$	$e\left(\frac{21769}{160498}\right)$	$e\left(\frac{56538}{80249}\right)$	$e\left(\frac{87209}{160498}\right)$	$e\left(\frac{100195}{160498}\right)$
$\chi_{160499}(12,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{18529}{80249}\right)$	$e\left(\frac{180}{80249}\right)$	$e\left(\frac{37058}{80249}\right)$	$e\left(\frac{68717}{80249}\right)$	$e\left(\frac{18709}{80249}\right)$	$e\left(\frac{29564}{80249}\right)$	$e\left(\frac{55587}{80249}\right)$	$e\left(\frac{360}{80249}\right)$	$e\left(\frac{6997}{80249}\right)$	$e\left(\frac{62275}{80249}\right)$
$\chi_{160499}(13,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{47481}{80249}\right)$	$e\left(\frac{76860}{80249}\right)$	$e\left(\frac{14713}{80249}\right)$	$e\left(\frac{51274}{80249}\right)$	$e\left(\frac{44092}{80249}\right)$	$e\left(\frac{24735}{80249}\right)$	$e\left(\frac{62194}{80249}\right)$	$e\left(\frac{73471}{80249}\right)$	$e\left(\frac{18506}{80249}\right)$	$e\left(\frac{29006}{80249}\right)$
$\chi_{160499}(14,\cdot)$	160499.h	160498	yes	$-1$	$1$	$e\left(\frac{158517}{160498}\right)$	$e\left(\frac{50074}{80249}\right)$	$e\left(\frac{78268}{80249}\right)$	$e\left(\frac{60735}{80249}\right)$	$e\left(\frac{98167}{160498}\right)$	$e\left(\frac{37195}{80249}\right)$	$e\left(\frac{154555}{160498}\right)$	$e\left(\frac{19899}{80249}\right)$	$e\left(\frac{119489}{160498}\right)$	$e\left(\frac{123523}{160498}\right)$
$\chi_{160499}(15,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{19186}{80249}\right)$	$e\left(\frac{30525}{80249}\right)$	$e\left(\frac{38372}{80249}\right)$	$e\left(\frac{50590}{80249}\right)$	$e\left(\frac{49711}{80249}\right)$	$e\left(\frac{11374}{80249}\right)$	$e\left(\frac{57558}{80249}\right)$	$e\left(\frac{61050}{80249}\right)$	$e\left(\frac{69776}{80249}\right)$	$e\left(\frac{14746}{80249}\right)$
$\chi_{160499}(16,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{2}{80249}\right)$	$e\left(\frac{74112}{80249}\right)$	$e\left(\frac{4}{80249}\right)$	$e\left(\frac{2632}{80249}\right)$	$e\left(\frac{74114}{80249}\right)$	$e\left(\frac{76285}{80249}\right)$	$e\left(\frac{6}{80249}\right)$	$e\left(\frac{67975}{80249}\right)$	$e\left(\frac{2634}{80249}\right)$	$e\left(\frac{68012}{80249}\right)$
$\chi_{160499}(17,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{49572}{80249}\right)$	$e\left(\frac{40422}{80249}\right)$	$e\left(\frac{18895}{80249}\right)$	$e\left(\frac{74564}{80249}\right)$	$e\left(\frac{9745}{80249}\right)$	$e\left(\frac{53321}{80249}\right)$	$e\left(\frac{68467}{80249}\right)$	$e\left(\frac{595}{80249}\right)$	$e\left(\frac{43887}{80249}\right)$	$e\left(\frac{34938}{80249}\right)$
$\chi_{160499}(18,\cdot)$	160499.f	12346	yes	$-1$	$1$	$e\left(\frac{5701}{12346}\right)$	$e\left(\frac{1925}{6173}\right)$	$e\left(\frac{5701}{6173}\right)$	$e\left(\frac{4247}{6173}\right)$	$e\left(\frac{9551}{12346}\right)$	$e\left(\frac{4777}{6173}\right)$	$e\left(\frac{4757}{12346}\right)$	$e\left(\frac{3850}{6173}\right)$	$e\left(\frac{1849}{12346}\right)$	$e\left(\frac{5141}{12346}\right)$
$\chi_{160499}(19,\cdot)$	160499.h	160498	yes	$-1$	$1$	$e\left(\frac{104141}{160498}\right)$	$e\left(\frac{17492}{80249}\right)$	$e\left(\frac{23892}{80249}\right)$	$e\left(\frac{72381}{80249}\right)$	$e\left(\frac{139125}{160498}\right)$	$e\left(\frac{76732}{80249}\right)$	$e\left(\frac{151925}{160498}\right)$	$e\left(\frac{34984}{80249}\right)$	$e\left(\frac{88405}{160498}\right)$	$e\left(\frac{110725}{160498}\right)$
$\chi_{160499}(20,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{659}{80249}\right)$	$e\left(\frac{24208}{80249}\right)$	$e\left(\frac{1318}{80249}\right)$	$e\left(\frac{64754}{80249}\right)$	$e\left(\frac{24867}{80249}\right)$	$e\left(\frac{58095}{80249}\right)$	$e\left(\frac{1977}{80249}\right)$	$e\left(\frac{48416}{80249}\right)$	$e\left(\frac{65413}{80249}\right)$	$e\left(\frac{20483}{80249}\right)$
$\chi_{160499}(21,\cdot)$	160499.e	6173	yes	$1$	$1$	$e\left(\frac{1349}{6173}\right)$	$e\left(\frac{5763}{6173}\right)$	$e\left(\frac{2698}{6173}\right)$	$e\left(\frac{3633}{6173}\right)$	$e\left(\frac{939}{6173}\right)$	$e\left(\frac{5364}{6173}\right)$	$e\left(\frac{4047}{6173}\right)$	$e\left(\frac{5353}{6173}\right)$	$e\left(\frac{4982}{6173}\right)$	$e\left(\frac{2531}{6173}\right)$
$\chi_{160499}(22,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{57128}{80249}\right)$	$e\left(\frac{46797}{80249}\right)$	$e\left(\frac{34007}{80249}\right)$	$e\left(\frac{67384}{80249}\right)$	$e\left(\frac{23676}{80249}\right)$	$e\left(\frac{3643}{80249}\right)$	$e\left(\frac{10886}{80249}\right)$	$e\left(\frac{13345}{80249}\right)$	$e\left(\frac{44263}{80249}\right)$	$e\left(\frac{26976}{80249}\right)$
$\chi_{160499}(23,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{26361}{80249}\right)$	$e\left(\frac{42388}{80249}\right)$	$e\left(\frac{52722}{80249}\right)$	$e\left(\frac{23508}{80249}\right)$	$e\left(\frac{68749}{80249}\right)$	$e\left(\frac{74846}{80249}\right)$	$e\left(\frac{79083}{80249}\right)$	$e\left(\frac{4527}{80249}\right)$	$e\left(\frac{49869}{80249}\right)$	$e\left(\frac{50836}{80249}\right)$
$\chi_{160499}(24,\cdot)$	160499.h	160498	yes	$-1$	$1$	$e\left(\frac{37059}{160498}\right)$	$e\left(\frac{18708}{80249}\right)$	$e\left(\frac{37059}{80249}\right)$	$e\left(\frac{69375}{80249}\right)$	$e\left(\frac{74475}{160498}\right)$	$e\left(\frac{28573}{80249}\right)$	$e\left(\frac{111177}{160498}\right)$	$e\left(\frac{37416}{80249}\right)$	$e\left(\frac{15311}{160498}\right)$	$e\left(\frac{78307}{160498}\right)$
$\chi_{160499}(25,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{1316}{80249}\right)$	$e\left(\frac{54553}{80249}\right)$	$e\left(\frac{2632}{80249}\right)$	$e\left(\frac{46627}{80249}\right)$	$e\left(\frac{55869}{80249}\right)$	$e\left(\frac{39905}{80249}\right)$	$e\left(\frac{3948}{80249}\right)$	$e\left(\frac{28857}{80249}\right)$	$e\left(\frac{47943}{80249}\right)$	$e\left(\frac{53203}{80249}\right)$
$\chi_{160499}(26,\cdot)$	160499.h	160498	yes	$-1$	$1$	$e\left(\frac{94963}{160498}\right)$	$e\left(\frac{15139}{80249}\right)$	$e\left(\frac{14714}{80249}\right)$	$e\left(\frac{51932}{80249}\right)$	$e\left(\frac{125241}{160498}\right)$	$e\left(\frac{23744}{80249}\right)$	$e\left(\frac{124391}{160498}\right)$	$e\left(\frac{30278}{80249}\right)$	$e\left(\frac{38329}{160498}\right)$	$e\left(\frac{11769}{160498}\right)$
$\chi_{160499}(27,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{55584}{80249}\right)$	$e\left(\frac{49870}{80249}\right)$	$e\left(\frac{30919}{80249}\right)$	$e\left(\frac{41705}{80249}\right)$	$e\left(\frac{25205}{80249}\right)$	$e\left(\frac{14389}{80249}\right)$	$e\left(\frac{6254}{80249}\right)$	$e\left(\frac{19491}{80249}\right)$	$e\left(\frac{17040}{80249}\right)$	$e\left(\frac{4558}{80249}\right)$
$\chi_{160499}(28,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{79259}{80249}\right)$	$e\left(\frac{68602}{80249}\right)$	$e\left(\frac{78269}{80249}\right)$	$e\left(\frac{61393}{80249}\right)$	$e\left(\frac{67612}{80249}\right)$	$e\left(\frac{36204}{80249}\right)$	$e\left(\frac{77279}{80249}\right)$	$e\left(\frac{56955}{80249}\right)$	$e\left(\frac{60403}{80249}\right)$	$e\left(\frac{38640}{80249}\right)$
$\chi_{160499}(29,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{5883}{80249}\right)$	$e\left(\frac{44164}{80249}\right)$	$e\left(\frac{11766}{80249}\right)$	$e\left(\frac{38124}{80249}\right)$	$e\left(\frac{50047}{80249}\right)$	$e\left(\frac{56248}{80249}\right)$	$e\left(\frac{17649}{80249}\right)$	$e\left(\frac{8079}{80249}\right)$	$e\left(\frac{44007}{80249}\right)$	$e\left(\frac{76790}{80249}\right)$
$\chi_{160499}(30,\cdot)$	160499.h	160498	yes	$-1$	$1$	$e\left(\frac{38373}{160498}\right)$	$e\left(\frac{49053}{80249}\right)$	$e\left(\frac{38373}{80249}\right)$	$e\left(\frac{51248}{80249}\right)$	$e\left(\frac{136479}{160498}\right)$	$e\left(\frac{10383}{80249}\right)$	$e\left(\frac{115119}{160498}\right)$	$e\left(\frac{17857}{80249}\right)$	$e\left(\frac{140869}{160498}\right)$	$e\left(\frac{143747}{160498}\right)$
$\chi_{160499}(31,\cdot)$	160499.g	80249	yes	$1$	$1$	$e\left(\frac{24918}{80249}\right)$	$e\left(\frac{16414}{80249}\right)$	$e\left(\frac{49836}{80249}\right)$	$e\left(\frac{50496}{80249}\right)$	$e\left(\frac{41332}{80249}\right)$	$e\left(\frac{45908}{80249}\right)$	$e\left(\frac{74754}{80249}\right)$	$e\left(\frac{32828}{80249}\right)$	$e\left(\frac{75414}{80249}\right)$	$e\left(\frac{12317}{80249}\right)$
$\chi_{160499}(32,\cdot)$	160499.h	160498	yes	$-1$	$1$	$e\left(\frac{5}{160498}\right)$	$e\left(\frac{12391}{80249}\right)$	$e\left(\frac{5}{80249}\right)$	$e\left(\frac{3290}{80249}\right)$	$e\left(\frac{24787}{160498}\right)$	$e\left(\frac{75294}{80249}\right)$	$e\left(\frac{15}{160498}\right)$	$e\left(\frac{24782}{80249}\right)$	$e\left(\frac{6585}{160498}\right)$	$e\left(\frac{89781}{160498}\right)$

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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	$160499$
Structure	\(C_{160498}\)
Order	$160498$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{160499}(1,\cdot)\)	160499.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{160499}(2,\cdot)\)	160499.h	160498	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{160498}\right)\)	\(e\left(\frac{18528}{80249}\right)\)	\(e\left(\frac{1}{80249}\right)\)	\(e\left(\frac{658}{80249}\right)\)	\(e\left(\frac{37057}{160498}\right)\)	\(e\left(\frac{79258}{80249}\right)\)	\(e\left(\frac{3}{160498}\right)\)	\(e\left(\frac{37056}{80249}\right)\)	\(e\left(\frac{1317}{160498}\right)\)	\(e\left(\frac{114255}{160498}\right)\)
\(\chi_{160499}(3,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{18528}{80249}\right)\)	\(e\left(\frac{43373}{80249}\right)\)	\(e\left(\frac{37056}{80249}\right)\)	\(e\left(\frac{67401}{80249}\right)\)	\(e\left(\frac{61901}{80249}\right)\)	\(e\left(\frac{31546}{80249}\right)\)	\(e\left(\frac{55584}{80249}\right)\)	\(e\left(\frac{6497}{80249}\right)\)	\(e\left(\frac{5680}{80249}\right)\)	\(e\left(\frac{28269}{80249}\right)\)
\(\chi_{160499}(4,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{1}{80249}\right)\)	\(e\left(\frac{37056}{80249}\right)\)	\(e\left(\frac{2}{80249}\right)\)	\(e\left(\frac{1316}{80249}\right)\)	\(e\left(\frac{37057}{80249}\right)\)	\(e\left(\frac{78267}{80249}\right)\)	\(e\left(\frac{3}{80249}\right)\)	\(e\left(\frac{74112}{80249}\right)\)	\(e\left(\frac{1317}{80249}\right)\)	\(e\left(\frac{34006}{80249}\right)\)
\(\chi_{160499}(5,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{658}{80249}\right)\)	\(e\left(\frac{67401}{80249}\right)\)	\(e\left(\frac{1316}{80249}\right)\)	\(e\left(\frac{63438}{80249}\right)\)	\(e\left(\frac{68059}{80249}\right)\)	\(e\left(\frac{60077}{80249}\right)\)	\(e\left(\frac{1974}{80249}\right)\)	\(e\left(\frac{54553}{80249}\right)\)	\(e\left(\frac{64096}{80249}\right)\)	\(e\left(\frac{66726}{80249}\right)\)
\(\chi_{160499}(6,\cdot)\)	160499.h	160498	yes	\(-1\)	\(1\)	\(e\left(\frac{37057}{160498}\right)\)	\(e\left(\frac{61901}{80249}\right)\)	\(e\left(\frac{37057}{80249}\right)\)	\(e\left(\frac{68059}{80249}\right)\)	\(e\left(\frac{361}{160498}\right)\)	\(e\left(\frac{30555}{80249}\right)\)	\(e\left(\frac{111171}{160498}\right)\)	\(e\left(\frac{43553}{80249}\right)\)	\(e\left(\frac{12677}{160498}\right)\)	\(e\left(\frac{10295}{160498}\right)\)
\(\chi_{160499}(7,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{79258}{80249}\right)\)	\(e\left(\frac{31546}{80249}\right)\)	\(e\left(\frac{78267}{80249}\right)\)	\(e\left(\frac{60077}{80249}\right)\)	\(e\left(\frac{30555}{80249}\right)\)	\(e\left(\frac{38186}{80249}\right)\)	\(e\left(\frac{77276}{80249}\right)\)	\(e\left(\frac{63092}{80249}\right)\)	\(e\left(\frac{59086}{80249}\right)\)	\(e\left(\frac{4634}{80249}\right)\)
\(\chi_{160499}(8,\cdot)\)	160499.h	160498	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{160498}\right)\)	\(e\left(\frac{55584}{80249}\right)\)	\(e\left(\frac{3}{80249}\right)\)	\(e\left(\frac{1974}{80249}\right)\)	\(e\left(\frac{111171}{160498}\right)\)	\(e\left(\frac{77276}{80249}\right)\)	\(e\left(\frac{9}{160498}\right)\)	\(e\left(\frac{30919}{80249}\right)\)	\(e\left(\frac{3951}{160498}\right)\)	\(e\left(\frac{21769}{160498}\right)\)
\(\chi_{160499}(9,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{37056}{80249}\right)\)	\(e\left(\frac{6497}{80249}\right)\)	\(e\left(\frac{74112}{80249}\right)\)	\(e\left(\frac{54553}{80249}\right)\)	\(e\left(\frac{43553}{80249}\right)\)	\(e\left(\frac{63092}{80249}\right)\)	\(e\left(\frac{30919}{80249}\right)\)	\(e\left(\frac{12994}{80249}\right)\)	\(e\left(\frac{11360}{80249}\right)\)	\(e\left(\frac{56538}{80249}\right)\)
\(\chi_{160499}(10,\cdot)\)	160499.h	160498	yes	\(-1\)	\(1\)	\(e\left(\frac{1317}{160498}\right)\)	\(e\left(\frac{5680}{80249}\right)\)	\(e\left(\frac{1317}{80249}\right)\)	\(e\left(\frac{64096}{80249}\right)\)	\(e\left(\frac{12677}{160498}\right)\)	\(e\left(\frac{59086}{80249}\right)\)	\(e\left(\frac{3951}{160498}\right)\)	\(e\left(\frac{11360}{80249}\right)\)	\(e\left(\frac{129509}{160498}\right)\)	\(e\left(\frac{87209}{160498}\right)\)
\(\chi_{160499}(11,\cdot)\)	160499.h	160498	yes	\(-1\)	\(1\)	\(e\left(\frac{114255}{160498}\right)\)	\(e\left(\frac{28269}{80249}\right)\)	\(e\left(\frac{34006}{80249}\right)\)	\(e\left(\frac{66726}{80249}\right)\)	\(e\left(\frac{10295}{160498}\right)\)	\(e\left(\frac{4634}{80249}\right)\)	\(e\left(\frac{21769}{160498}\right)\)	\(e\left(\frac{56538}{80249}\right)\)	\(e\left(\frac{87209}{160498}\right)\)	\(e\left(\frac{100195}{160498}\right)\)
\(\chi_{160499}(12,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{18529}{80249}\right)\)	\(e\left(\frac{180}{80249}\right)\)	\(e\left(\frac{37058}{80249}\right)\)	\(e\left(\frac{68717}{80249}\right)\)	\(e\left(\frac{18709}{80249}\right)\)	\(e\left(\frac{29564}{80249}\right)\)	\(e\left(\frac{55587}{80249}\right)\)	\(e\left(\frac{360}{80249}\right)\)	\(e\left(\frac{6997}{80249}\right)\)	\(e\left(\frac{62275}{80249}\right)\)
\(\chi_{160499}(13,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{47481}{80249}\right)\)	\(e\left(\frac{76860}{80249}\right)\)	\(e\left(\frac{14713}{80249}\right)\)	\(e\left(\frac{51274}{80249}\right)\)	\(e\left(\frac{44092}{80249}\right)\)	\(e\left(\frac{24735}{80249}\right)\)	\(e\left(\frac{62194}{80249}\right)\)	\(e\left(\frac{73471}{80249}\right)\)	\(e\left(\frac{18506}{80249}\right)\)	\(e\left(\frac{29006}{80249}\right)\)
\(\chi_{160499}(14,\cdot)\)	160499.h	160498	yes	\(-1\)	\(1\)	\(e\left(\frac{158517}{160498}\right)\)	\(e\left(\frac{50074}{80249}\right)\)	\(e\left(\frac{78268}{80249}\right)\)	\(e\left(\frac{60735}{80249}\right)\)	\(e\left(\frac{98167}{160498}\right)\)	\(e\left(\frac{37195}{80249}\right)\)	\(e\left(\frac{154555}{160498}\right)\)	\(e\left(\frac{19899}{80249}\right)\)	\(e\left(\frac{119489}{160498}\right)\)	\(e\left(\frac{123523}{160498}\right)\)
\(\chi_{160499}(15,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{19186}{80249}\right)\)	\(e\left(\frac{30525}{80249}\right)\)	\(e\left(\frac{38372}{80249}\right)\)	\(e\left(\frac{50590}{80249}\right)\)	\(e\left(\frac{49711}{80249}\right)\)	\(e\left(\frac{11374}{80249}\right)\)	\(e\left(\frac{57558}{80249}\right)\)	\(e\left(\frac{61050}{80249}\right)\)	\(e\left(\frac{69776}{80249}\right)\)	\(e\left(\frac{14746}{80249}\right)\)
\(\chi_{160499}(16,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{2}{80249}\right)\)	\(e\left(\frac{74112}{80249}\right)\)	\(e\left(\frac{4}{80249}\right)\)	\(e\left(\frac{2632}{80249}\right)\)	\(e\left(\frac{74114}{80249}\right)\)	\(e\left(\frac{76285}{80249}\right)\)	\(e\left(\frac{6}{80249}\right)\)	\(e\left(\frac{67975}{80249}\right)\)	\(e\left(\frac{2634}{80249}\right)\)	\(e\left(\frac{68012}{80249}\right)\)
\(\chi_{160499}(17,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{49572}{80249}\right)\)	\(e\left(\frac{40422}{80249}\right)\)	\(e\left(\frac{18895}{80249}\right)\)	\(e\left(\frac{74564}{80249}\right)\)	\(e\left(\frac{9745}{80249}\right)\)	\(e\left(\frac{53321}{80249}\right)\)	\(e\left(\frac{68467}{80249}\right)\)	\(e\left(\frac{595}{80249}\right)\)	\(e\left(\frac{43887}{80249}\right)\)	\(e\left(\frac{34938}{80249}\right)\)
\(\chi_{160499}(18,\cdot)\)	160499.f	12346	yes	\(-1\)	\(1\)	\(e\left(\frac{5701}{12346}\right)\)	\(e\left(\frac{1925}{6173}\right)\)	\(e\left(\frac{5701}{6173}\right)\)	\(e\left(\frac{4247}{6173}\right)\)	\(e\left(\frac{9551}{12346}\right)\)	\(e\left(\frac{4777}{6173}\right)\)	\(e\left(\frac{4757}{12346}\right)\)	\(e\left(\frac{3850}{6173}\right)\)	\(e\left(\frac{1849}{12346}\right)\)	\(e\left(\frac{5141}{12346}\right)\)
\(\chi_{160499}(19,\cdot)\)	160499.h	160498	yes	\(-1\)	\(1\)	\(e\left(\frac{104141}{160498}\right)\)	\(e\left(\frac{17492}{80249}\right)\)	\(e\left(\frac{23892}{80249}\right)\)	\(e\left(\frac{72381}{80249}\right)\)	\(e\left(\frac{139125}{160498}\right)\)	\(e\left(\frac{76732}{80249}\right)\)	\(e\left(\frac{151925}{160498}\right)\)	\(e\left(\frac{34984}{80249}\right)\)	\(e\left(\frac{88405}{160498}\right)\)	\(e\left(\frac{110725}{160498}\right)\)
\(\chi_{160499}(20,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{659}{80249}\right)\)	\(e\left(\frac{24208}{80249}\right)\)	\(e\left(\frac{1318}{80249}\right)\)	\(e\left(\frac{64754}{80249}\right)\)	\(e\left(\frac{24867}{80249}\right)\)	\(e\left(\frac{58095}{80249}\right)\)	\(e\left(\frac{1977}{80249}\right)\)	\(e\left(\frac{48416}{80249}\right)\)	\(e\left(\frac{65413}{80249}\right)\)	\(e\left(\frac{20483}{80249}\right)\)
\(\chi_{160499}(21,\cdot)\)	160499.e	6173	yes	\(1\)	\(1\)	\(e\left(\frac{1349}{6173}\right)\)	\(e\left(\frac{5763}{6173}\right)\)	\(e\left(\frac{2698}{6173}\right)\)	\(e\left(\frac{3633}{6173}\right)\)	\(e\left(\frac{939}{6173}\right)\)	\(e\left(\frac{5364}{6173}\right)\)	\(e\left(\frac{4047}{6173}\right)\)	\(e\left(\frac{5353}{6173}\right)\)	\(e\left(\frac{4982}{6173}\right)\)	\(e\left(\frac{2531}{6173}\right)\)
\(\chi_{160499}(22,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{57128}{80249}\right)\)	\(e\left(\frac{46797}{80249}\right)\)	\(e\left(\frac{34007}{80249}\right)\)	\(e\left(\frac{67384}{80249}\right)\)	\(e\left(\frac{23676}{80249}\right)\)	\(e\left(\frac{3643}{80249}\right)\)	\(e\left(\frac{10886}{80249}\right)\)	\(e\left(\frac{13345}{80249}\right)\)	\(e\left(\frac{44263}{80249}\right)\)	\(e\left(\frac{26976}{80249}\right)\)
\(\chi_{160499}(23,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{26361}{80249}\right)\)	\(e\left(\frac{42388}{80249}\right)\)	\(e\left(\frac{52722}{80249}\right)\)	\(e\left(\frac{23508}{80249}\right)\)	\(e\left(\frac{68749}{80249}\right)\)	\(e\left(\frac{74846}{80249}\right)\)	\(e\left(\frac{79083}{80249}\right)\)	\(e\left(\frac{4527}{80249}\right)\)	\(e\left(\frac{49869}{80249}\right)\)	\(e\left(\frac{50836}{80249}\right)\)
\(\chi_{160499}(24,\cdot)\)	160499.h	160498	yes	\(-1\)	\(1\)	\(e\left(\frac{37059}{160498}\right)\)	\(e\left(\frac{18708}{80249}\right)\)	\(e\left(\frac{37059}{80249}\right)\)	\(e\left(\frac{69375}{80249}\right)\)	\(e\left(\frac{74475}{160498}\right)\)	\(e\left(\frac{28573}{80249}\right)\)	\(e\left(\frac{111177}{160498}\right)\)	\(e\left(\frac{37416}{80249}\right)\)	\(e\left(\frac{15311}{160498}\right)\)	\(e\left(\frac{78307}{160498}\right)\)
\(\chi_{160499}(25,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{1316}{80249}\right)\)	\(e\left(\frac{54553}{80249}\right)\)	\(e\left(\frac{2632}{80249}\right)\)	\(e\left(\frac{46627}{80249}\right)\)	\(e\left(\frac{55869}{80249}\right)\)	\(e\left(\frac{39905}{80249}\right)\)	\(e\left(\frac{3948}{80249}\right)\)	\(e\left(\frac{28857}{80249}\right)\)	\(e\left(\frac{47943}{80249}\right)\)	\(e\left(\frac{53203}{80249}\right)\)
\(\chi_{160499}(26,\cdot)\)	160499.h	160498	yes	\(-1\)	\(1\)	\(e\left(\frac{94963}{160498}\right)\)	\(e\left(\frac{15139}{80249}\right)\)	\(e\left(\frac{14714}{80249}\right)\)	\(e\left(\frac{51932}{80249}\right)\)	\(e\left(\frac{125241}{160498}\right)\)	\(e\left(\frac{23744}{80249}\right)\)	\(e\left(\frac{124391}{160498}\right)\)	\(e\left(\frac{30278}{80249}\right)\)	\(e\left(\frac{38329}{160498}\right)\)	\(e\left(\frac{11769}{160498}\right)\)
\(\chi_{160499}(27,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{55584}{80249}\right)\)	\(e\left(\frac{49870}{80249}\right)\)	\(e\left(\frac{30919}{80249}\right)\)	\(e\left(\frac{41705}{80249}\right)\)	\(e\left(\frac{25205}{80249}\right)\)	\(e\left(\frac{14389}{80249}\right)\)	\(e\left(\frac{6254}{80249}\right)\)	\(e\left(\frac{19491}{80249}\right)\)	\(e\left(\frac{17040}{80249}\right)\)	\(e\left(\frac{4558}{80249}\right)\)
\(\chi_{160499}(28,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{79259}{80249}\right)\)	\(e\left(\frac{68602}{80249}\right)\)	\(e\left(\frac{78269}{80249}\right)\)	\(e\left(\frac{61393}{80249}\right)\)	\(e\left(\frac{67612}{80249}\right)\)	\(e\left(\frac{36204}{80249}\right)\)	\(e\left(\frac{77279}{80249}\right)\)	\(e\left(\frac{56955}{80249}\right)\)	\(e\left(\frac{60403}{80249}\right)\)	\(e\left(\frac{38640}{80249}\right)\)
\(\chi_{160499}(29,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{5883}{80249}\right)\)	\(e\left(\frac{44164}{80249}\right)\)	\(e\left(\frac{11766}{80249}\right)\)	\(e\left(\frac{38124}{80249}\right)\)	\(e\left(\frac{50047}{80249}\right)\)	\(e\left(\frac{56248}{80249}\right)\)	\(e\left(\frac{17649}{80249}\right)\)	\(e\left(\frac{8079}{80249}\right)\)	\(e\left(\frac{44007}{80249}\right)\)	\(e\left(\frac{76790}{80249}\right)\)
\(\chi_{160499}(30,\cdot)\)	160499.h	160498	yes	\(-1\)	\(1\)	\(e\left(\frac{38373}{160498}\right)\)	\(e\left(\frac{49053}{80249}\right)\)	\(e\left(\frac{38373}{80249}\right)\)	\(e\left(\frac{51248}{80249}\right)\)	\(e\left(\frac{136479}{160498}\right)\)	\(e\left(\frac{10383}{80249}\right)\)	\(e\left(\frac{115119}{160498}\right)\)	\(e\left(\frac{17857}{80249}\right)\)	\(e\left(\frac{140869}{160498}\right)\)	\(e\left(\frac{143747}{160498}\right)\)
\(\chi_{160499}(31,\cdot)\)	160499.g	80249	yes	\(1\)	\(1\)	\(e\left(\frac{24918}{80249}\right)\)	\(e\left(\frac{16414}{80249}\right)\)	\(e\left(\frac{49836}{80249}\right)\)	\(e\left(\frac{50496}{80249}\right)\)	\(e\left(\frac{41332}{80249}\right)\)	\(e\left(\frac{45908}{80249}\right)\)	\(e\left(\frac{74754}{80249}\right)\)	\(e\left(\frac{32828}{80249}\right)\)	\(e\left(\frac{75414}{80249}\right)\)	\(e\left(\frac{12317}{80249}\right)\)
\(\chi_{160499}(32,\cdot)\)	160499.h	160498	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{160498}\right)\)	\(e\left(\frac{12391}{80249}\right)\)	\(e\left(\frac{5}{80249}\right)\)	\(e\left(\frac{3290}{80249}\right)\)	\(e\left(\frac{24787}{160498}\right)\)	\(e\left(\frac{75294}{80249}\right)\)	\(e\left(\frac{15}{160498}\right)\)	\(e\left(\frac{24782}{80249}\right)\)	\(e\left(\frac{6585}{160498}\right)\)	\(e\left(\frac{89781}{160498}\right)\)

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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.