LMFDB - Group of Dirichlet characters of modulus 20433

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(20433)

gp:g = idealstar(,20433,2)

magma:G = FullDirichletGroup(20433);

Character group

Order	=	11592	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{6}\times C_{966}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{20433}(6812,\cdot)$, $\chi_{20433}(1669,\cdot)$, $\chi_{20433}(12790,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 11592 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character	Orbit	Order	Primitive	$-1$	$1$	$2$	$4$	$5$	$8$	$10$	$11$	$13$	$16$	$17$	$19$
$\chi_{20433}(1,\cdot)$	20433.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{20433}(2,\cdot)$	20433.gd	966	yes	$1$	$1$	$e\left(\frac{97}{161}\right)$	$e\left(\frac{33}{161}\right)$	$e\left(\frac{73}{966}\right)$	$e\left(\frac{130}{161}\right)$	$e\left(\frac{655}{966}\right)$	$e\left(\frac{785}{966}\right)$	$e\left(\frac{431}{483}\right)$	$e\left(\frac{66}{161}\right)$	$e\left(\frac{121}{161}\right)$	$e\left(\frac{5}{46}\right)$
$\chi_{20433}(4,\cdot)$	20433.fb	483	no	$1$	$1$	$e\left(\frac{33}{161}\right)$	$e\left(\frac{66}{161}\right)$	$e\left(\frac{73}{483}\right)$	$e\left(\frac{99}{161}\right)$	$e\left(\frac{172}{483}\right)$	$e\left(\frac{302}{483}\right)$	$e\left(\frac{379}{483}\right)$	$e\left(\frac{132}{161}\right)$	$e\left(\frac{81}{161}\right)$	$e\left(\frac{5}{23}\right)$
$\chi_{20433}(5,\cdot)$	20433.fz	966	yes	$1$	$1$	$e\left(\frac{73}{966}\right)$	$e\left(\frac{73}{483}\right)$	$e\left(\frac{19}{161}\right)$	$e\left(\frac{73}{322}\right)$	$e\left(\frac{187}{966}\right)$	$e\left(\frac{155}{322}\right)$	$e\left(\frac{647}{966}\right)$	$e\left(\frac{146}{483}\right)$	$e\left(\frac{214}{483}\right)$	$e\left(\frac{25}{138}\right)$
$\chi_{20433}(8,\cdot)$	20433.ev	322	yes	$1$	$1$	$e\left(\frac{130}{161}\right)$	$e\left(\frac{99}{161}\right)$	$e\left(\frac{73}{322}\right)$	$e\left(\frac{68}{161}\right)$	$e\left(\frac{11}{322}\right)$	$e\left(\frac{141}{322}\right)$	$e\left(\frac{109}{161}\right)$	$e\left(\frac{37}{161}\right)$	$e\left(\frac{41}{161}\right)$	$e\left(\frac{15}{46}\right)$
$\chi_{20433}(10,\cdot)$	20433.fv	966	no	$1$	$1$	$e\left(\frac{655}{966}\right)$	$e\left(\frac{172}{483}\right)$	$e\left(\frac{187}{966}\right)$	$e\left(\frac{11}{322}\right)$	$e\left(\frac{421}{483}\right)$	$e\left(\frac{142}{483}\right)$	$e\left(\frac{181}{322}\right)$	$e\left(\frac{344}{483}\right)$	$e\left(\frac{94}{483}\right)$	$e\left(\frac{20}{69}\right)$
$\chi_{20433}(11,\cdot)$	20433.fp	966	yes	$-1$	$1$	$e\left(\frac{785}{966}\right)$	$e\left(\frac{302}{483}\right)$	$e\left(\frac{155}{322}\right)$	$e\left(\frac{141}{322}\right)$	$e\left(\frac{142}{483}\right)$	$e\left(\frac{145}{322}\right)$	$e\left(\frac{326}{483}\right)$	$e\left(\frac{121}{483}\right)$	$e\left(\frac{229}{966}\right)$	$e\left(\frac{64}{69}\right)$
$\chi_{20433}(13,\cdot)$	20433.fk	966	no	$-1$	$1$	$e\left(\frac{431}{483}\right)$	$e\left(\frac{379}{483}\right)$	$e\left(\frac{647}{966}\right)$	$e\left(\frac{109}{161}\right)$	$e\left(\frac{181}{322}\right)$	$e\left(\frac{326}{483}\right)$	$e\left(\frac{589}{966}\right)$	$e\left(\frac{275}{483}\right)$	$e\left(\frac{257}{966}\right)$	$e\left(\frac{109}{138}\right)$
$\chi_{20433}(16,\cdot)$	20433.fb	483	no	$1$	$1$	$e\left(\frac{66}{161}\right)$	$e\left(\frac{132}{161}\right)$	$e\left(\frac{146}{483}\right)$	$e\left(\frac{37}{161}\right)$	$e\left(\frac{344}{483}\right)$	$e\left(\frac{121}{483}\right)$	$e\left(\frac{275}{483}\right)$	$e\left(\frac{103}{161}\right)$	$e\left(\frac{1}{161}\right)$	$e\left(\frac{10}{23}\right)$
$\chi_{20433}(17,\cdot)$	20433.gb	966	yes	$-1$	$1$	$e\left(\frac{121}{161}\right)$	$e\left(\frac{81}{161}\right)$	$e\left(\frac{214}{483}\right)$	$e\left(\frac{41}{161}\right)$	$e\left(\frac{94}{483}\right)$	$e\left(\frac{229}{966}\right)$	$e\left(\frac{257}{966}\right)$	$e\left(\frac{1}{161}\right)$	$e\left(\frac{111}{322}\right)$	$e\left(\frac{3}{23}\right)$
$\chi_{20433}(19,\cdot)$	20433.en	138	no	$1$	$1$	$e\left(\frac{5}{46}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{25}{138}\right)$	$e\left(\frac{15}{46}\right)$	$e\left(\frac{20}{69}\right)$	$e\left(\frac{64}{69}\right)$	$e\left(\frac{109}{138}\right)$	$e\left(\frac{10}{23}\right)$	$e\left(\frac{3}{23}\right)$	$e\left(\frac{3}{23}\right)$
$\chi_{20433}(20,\cdot)$	20433.fs	966	yes	$1$	$1$	$e\left(\frac{271}{966}\right)$	$e\left(\frac{271}{483}\right)$	$e\left(\frac{130}{483}\right)$	$e\left(\frac{271}{322}\right)$	$e\left(\frac{177}{322}\right)$	$e\left(\frac{103}{966}\right)$	$e\left(\frac{439}{966}\right)$	$e\left(\frac{59}{483}\right)$	$e\left(\frac{457}{483}\right)$	$e\left(\frac{55}{138}\right)$
$\chi_{20433}(22,\cdot)$	20433.fr	966	no	$-1$	$1$	$e\left(\frac{401}{966}\right)$	$e\left(\frac{401}{483}\right)$	$e\left(\frac{269}{483}\right)$	$e\left(\frac{79}{322}\right)$	$e\left(\frac{313}{322}\right)$	$e\left(\frac{127}{483}\right)$	$e\left(\frac{274}{483}\right)$	$e\left(\frac{319}{483}\right)$	$e\left(\frac{955}{966}\right)$	$e\left(\frac{5}{138}\right)$
$\chi_{20433}(23,\cdot)$	20433.fn	966	yes	$1$	$1$	$e\left(\frac{106}{483}\right)$	$e\left(\frac{212}{483}\right)$	$e\left(\frac{545}{966}\right)$	$e\left(\frac{106}{161}\right)$	$e\left(\frac{757}{966}\right)$	$e\left(\frac{541}{966}\right)$	$e\left(\frac{61}{161}\right)$	$e\left(\frac{424}{483}\right)$	$e\left(\frac{26}{483}\right)$	$e\left(\frac{83}{138}\right)$
$\chi_{20433}(25,\cdot)$	20433.fa	483	no	$1$	$1$	$e\left(\frac{73}{483}\right)$	$e\left(\frac{146}{483}\right)$	$e\left(\frac{38}{161}\right)$	$e\left(\frac{73}{161}\right)$	$e\left(\frac{187}{483}\right)$	$e\left(\frac{155}{161}\right)$	$e\left(\frac{164}{483}\right)$	$e\left(\frac{292}{483}\right)$	$e\left(\frac{428}{483}\right)$	$e\left(\frac{25}{69}\right)$
$\chi_{20433}(26,\cdot)$	20433.fo	966	yes	$-1$	$1$	$e\left(\frac{239}{483}\right)$	$e\left(\frac{478}{483}\right)$	$e\left(\frac{120}{161}\right)$	$e\left(\frac{78}{161}\right)$	$e\left(\frac{116}{483}\right)$	$e\left(\frac{157}{322}\right)$	$e\left(\frac{485}{966}\right)$	$e\left(\frac{473}{483}\right)$	$e\left(\frac{17}{966}\right)$	$e\left(\frac{62}{69}\right)$
$\chi_{20433}(29,\cdot)$	20433.fy	966	yes	$-1$	$1$	$e\left(\frac{313}{966}\right)$	$e\left(\frac{313}{483}\right)$	$e\left(\frac{491}{966}\right)$	$e\left(\frac{313}{322}\right)$	$e\left(\frac{134}{161}\right)$	$e\left(\frac{397}{966}\right)$	$e\left(\frac{356}{483}\right)$	$e\left(\frac{143}{483}\right)$	$e\left(\frac{95}{966}\right)$	$e\left(\frac{38}{69}\right)$
$\chi_{20433}(31,\cdot)$	20433.dp	138	no	$-1$	$1$	$e\left(\frac{17}{23}\right)$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{101}{138}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{65}{138}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{65}{138}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{27}{46}\right)$	$e\left(\frac{27}{46}\right)$
$\chi_{20433}(32,\cdot)$	20433.gd	966	yes	$1$	$1$	$e\left(\frac{2}{161}\right)$	$e\left(\frac{4}{161}\right)$	$e\left(\frac{365}{966}\right)$	$e\left(\frac{6}{161}\right)$	$e\left(\frac{377}{966}\right)$	$e\left(\frac{61}{966}\right)$	$e\left(\frac{223}{483}\right)$	$e\left(\frac{8}{161}\right)$	$e\left(\frac{122}{161}\right)$	$e\left(\frac{25}{46}\right)$
$\chi_{20433}(34,\cdot)$	20433.ew	322	no	$-1$	$1$	$e\left(\frac{57}{161}\right)$	$e\left(\frac{114}{161}\right)$	$e\left(\frac{167}{322}\right)$	$e\left(\frac{10}{161}\right)$	$e\left(\frac{281}{322}\right)$	$e\left(\frac{8}{161}\right)$	$e\left(\frac{51}{322}\right)$	$e\left(\frac{67}{161}\right)$	$e\left(\frac{31}{322}\right)$	$e\left(\frac{11}{46}\right)$
$\chi_{20433}(37,\cdot)$	20433.fa	483	no	$1$	$1$	$e\left(\frac{188}{483}\right)$	$e\left(\frac{376}{483}\right)$	$e\left(\frac{153}{161}\right)$	$e\left(\frac{27}{161}\right)$	$e\left(\frac{164}{483}\right)$	$e\left(\frac{86}{161}\right)$	$e\left(\frac{118}{483}\right)$	$e\left(\frac{269}{483}\right)$	$e\left(\frac{37}{483}\right)$	$e\left(\frac{2}{69}\right)$
$\chi_{20433}(38,\cdot)$	20433.fd	966	yes	$1$	$1$	$e\left(\frac{229}{322}\right)$	$e\left(\frac{68}{161}\right)$	$e\left(\frac{124}{483}\right)$	$e\left(\frac{43}{322}\right)$	$e\left(\frac{935}{966}\right)$	$e\left(\frac{715}{966}\right)$	$e\left(\frac{659}{966}\right)$	$e\left(\frac{136}{161}\right)$	$e\left(\frac{142}{161}\right)$	$e\left(\frac{11}{46}\right)$
$\chi_{20433}(40,\cdot)$	20433.fq	966	no	$1$	$1$	$e\left(\frac{853}{966}\right)$	$e\left(\frac{370}{483}\right)$	$e\left(\frac{111}{322}\right)$	$e\left(\frac{209}{322}\right)$	$e\left(\frac{110}{483}\right)$	$e\left(\frac{148}{161}\right)$	$e\left(\frac{335}{966}\right)$	$e\left(\frac{257}{483}\right)$	$e\left(\frac{337}{483}\right)$	$e\left(\frac{35}{69}\right)$
$\chi_{20433}(41,\cdot)$	20433.fs	966	yes	$1$	$1$	$e\left(\frac{17}{966}\right)$	$e\left(\frac{17}{483}\right)$	$e\left(\frac{386}{483}\right)$	$e\left(\frac{17}{322}\right)$	$e\left(\frac{263}{322}\right)$	$e\left(\frac{395}{966}\right)$	$e\left(\frac{605}{966}\right)$	$e\left(\frac{34}{483}\right)$	$e\left(\frac{116}{483}\right)$	$e\left(\frac{89}{138}\right)$
$\chi_{20433}(43,\cdot)$	20433.cn	42	no	$-1$	$1$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{20433}(44,\cdot)$	20433.fw	966	yes	$-1$	$1$	$e\left(\frac{17}{966}\right)$	$e\left(\frac{17}{483}\right)$	$e\left(\frac{611}{966}\right)$	$e\left(\frac{17}{322}\right)$	$e\left(\frac{314}{483}\right)$	$e\left(\frac{73}{966}\right)$	$e\left(\frac{74}{161}\right)$	$e\left(\frac{34}{483}\right)$	$e\left(\frac{715}{966}\right)$	$e\left(\frac{10}{69}\right)$
$\chi_{20433}(46,\cdot)$	20433.fa	483	no	$1$	$1$	$e\left(\frac{397}{483}\right)$	$e\left(\frac{311}{483}\right)$	$e\left(\frac{103}{161}\right)$	$e\left(\frac{75}{161}\right)$	$e\left(\frac{223}{483}\right)$	$e\left(\frac{60}{161}\right)$	$e\left(\frac{131}{483}\right)$	$e\left(\frac{139}{483}\right)$	$e\left(\frac{389}{483}\right)$	$e\left(\frac{49}{69}\right)$
$\chi_{20433}(47,\cdot)$	20433.fz	966	yes	$1$	$1$	$e\left(\frac{295}{966}\right)$	$e\left(\frac{295}{483}\right)$	$e\left(\frac{4}{161}\right)$	$e\left(\frac{295}{322}\right)$	$e\left(\frac{319}{966}\right)$	$e\left(\frac{75}{322}\right)$	$e\left(\frac{365}{966}\right)$	$e\left(\frac{107}{483}\right)$	$e\left(\frac{223}{483}\right)$	$e\left(\frac{67}{138}\right)$
$\chi_{20433}(50,\cdot)$	20433.eg	138	no	$1$	$1$	$e\left(\frac{52}{69}\right)$	$e\left(\frac{35}{69}\right)$	$e\left(\frac{43}{138}\right)$	$e\left(\frac{6}{23}\right)$	$e\left(\frac{3}{46}\right)$	$e\left(\frac{107}{138}\right)$	$e\left(\frac{16}{69}\right)$	$e\left(\frac{1}{69}\right)$	$e\left(\frac{44}{69}\right)$	$e\left(\frac{65}{138}\right)$
$\chi_{20433}(52,\cdot)$	20433.fm	966	no	$-1$	$1$	$e\left(\frac{47}{483}\right)$	$e\left(\frac{94}{483}\right)$	$e\left(\frac{793}{966}\right)$	$e\left(\frac{47}{161}\right)$	$e\left(\frac{887}{966}\right)$	$e\left(\frac{145}{483}\right)$	$e\left(\frac{127}{322}\right)$	$e\left(\frac{188}{483}\right)$	$e\left(\frac{743}{966}\right)$	$e\left(\frac{1}{138}\right)$
$\chi_{20433}(53,\cdot)$	20433.gd	966	yes	$1$	$1$	$e\left(\frac{5}{161}\right)$	$e\left(\frac{10}{161}\right)$	$e\left(\frac{671}{966}\right)$	$e\left(\frac{15}{161}\right)$	$e\left(\frac{701}{966}\right)$	$e\left(\frac{877}{966}\right)$	$e\left(\frac{316}{483}\right)$	$e\left(\frac{20}{161}\right)$	$e\left(\frac{144}{161}\right)$	$e\left(\frac{5}{46}\right)$
$\chi_{20433}(55,\cdot)$	20433.ew	322	no	$-1$	$1$	$e\left(\frac{143}{161}\right)$	$e\left(\frac{125}{161}\right)$	$e\left(\frac{193}{322}\right)$	$e\left(\frac{107}{161}\right)$	$e\left(\frac{157}{322}\right)$	$e\left(\frac{150}{161}\right)$	$e\left(\frac{111}{322}\right)$	$e\left(\frac{89}{161}\right)$	$e\left(\frac{219}{322}\right)$	$e\left(\frac{5}{46}\right)$

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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	$20433$
Structure	\(C_{2}\times C_{6}\times C_{966}\)
Order	$11592$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(\chi_{20433}(1,\cdot)\)	20433.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{20433}(2,\cdot)\)	20433.gd	966	yes	\(1\)	\(1\)	\(e\left(\frac{97}{161}\right)\)	\(e\left(\frac{33}{161}\right)\)	\(e\left(\frac{73}{966}\right)\)	\(e\left(\frac{130}{161}\right)\)	\(e\left(\frac{655}{966}\right)\)	\(e\left(\frac{785}{966}\right)\)	\(e\left(\frac{431}{483}\right)\)	\(e\left(\frac{66}{161}\right)\)	\(e\left(\frac{121}{161}\right)\)	\(e\left(\frac{5}{46}\right)\)
\(\chi_{20433}(4,\cdot)\)	20433.fb	483	no	\(1\)	\(1\)	\(e\left(\frac{33}{161}\right)\)	\(e\left(\frac{66}{161}\right)\)	\(e\left(\frac{73}{483}\right)\)	\(e\left(\frac{99}{161}\right)\)	\(e\left(\frac{172}{483}\right)\)	\(e\left(\frac{302}{483}\right)\)	\(e\left(\frac{379}{483}\right)\)	\(e\left(\frac{132}{161}\right)\)	\(e\left(\frac{81}{161}\right)\)	\(e\left(\frac{5}{23}\right)\)
\(\chi_{20433}(5,\cdot)\)	20433.fz	966	yes	\(1\)	\(1\)	\(e\left(\frac{73}{966}\right)\)	\(e\left(\frac{73}{483}\right)\)	\(e\left(\frac{19}{161}\right)\)	\(e\left(\frac{73}{322}\right)\)	\(e\left(\frac{187}{966}\right)\)	\(e\left(\frac{155}{322}\right)\)	\(e\left(\frac{647}{966}\right)\)	\(e\left(\frac{146}{483}\right)\)	\(e\left(\frac{214}{483}\right)\)	\(e\left(\frac{25}{138}\right)\)
\(\chi_{20433}(8,\cdot)\)	20433.ev	322	yes	\(1\)	\(1\)	\(e\left(\frac{130}{161}\right)\)	\(e\left(\frac{99}{161}\right)\)	\(e\left(\frac{73}{322}\right)\)	\(e\left(\frac{68}{161}\right)\)	\(e\left(\frac{11}{322}\right)\)	\(e\left(\frac{141}{322}\right)\)	\(e\left(\frac{109}{161}\right)\)	\(e\left(\frac{37}{161}\right)\)	\(e\left(\frac{41}{161}\right)\)	\(e\left(\frac{15}{46}\right)\)
\(\chi_{20433}(10,\cdot)\)	20433.fv	966	no	\(1\)	\(1\)	\(e\left(\frac{655}{966}\right)\)	\(e\left(\frac{172}{483}\right)\)	\(e\left(\frac{187}{966}\right)\)	\(e\left(\frac{11}{322}\right)\)	\(e\left(\frac{421}{483}\right)\)	\(e\left(\frac{142}{483}\right)\)	\(e\left(\frac{181}{322}\right)\)	\(e\left(\frac{344}{483}\right)\)	\(e\left(\frac{94}{483}\right)\)	\(e\left(\frac{20}{69}\right)\)
\(\chi_{20433}(11,\cdot)\)	20433.fp	966	yes	\(-1\)	\(1\)	\(e\left(\frac{785}{966}\right)\)	\(e\left(\frac{302}{483}\right)\)	\(e\left(\frac{155}{322}\right)\)	\(e\left(\frac{141}{322}\right)\)	\(e\left(\frac{142}{483}\right)\)	\(e\left(\frac{145}{322}\right)\)	\(e\left(\frac{326}{483}\right)\)	\(e\left(\frac{121}{483}\right)\)	\(e\left(\frac{229}{966}\right)\)	\(e\left(\frac{64}{69}\right)\)
\(\chi_{20433}(13,\cdot)\)	20433.fk	966	no	\(-1\)	\(1\)	\(e\left(\frac{431}{483}\right)\)	\(e\left(\frac{379}{483}\right)\)	\(e\left(\frac{647}{966}\right)\)	\(e\left(\frac{109}{161}\right)\)	\(e\left(\frac{181}{322}\right)\)	\(e\left(\frac{326}{483}\right)\)	\(e\left(\frac{589}{966}\right)\)	\(e\left(\frac{275}{483}\right)\)	\(e\left(\frac{257}{966}\right)\)	\(e\left(\frac{109}{138}\right)\)
\(\chi_{20433}(16,\cdot)\)	20433.fb	483	no	\(1\)	\(1\)	\(e\left(\frac{66}{161}\right)\)	\(e\left(\frac{132}{161}\right)\)	\(e\left(\frac{146}{483}\right)\)	\(e\left(\frac{37}{161}\right)\)	\(e\left(\frac{344}{483}\right)\)	\(e\left(\frac{121}{483}\right)\)	\(e\left(\frac{275}{483}\right)\)	\(e\left(\frac{103}{161}\right)\)	\(e\left(\frac{1}{161}\right)\)	\(e\left(\frac{10}{23}\right)\)
\(\chi_{20433}(17,\cdot)\)	20433.gb	966	yes	\(-1\)	\(1\)	\(e\left(\frac{121}{161}\right)\)	\(e\left(\frac{81}{161}\right)\)	\(e\left(\frac{214}{483}\right)\)	\(e\left(\frac{41}{161}\right)\)	\(e\left(\frac{94}{483}\right)\)	\(e\left(\frac{229}{966}\right)\)	\(e\left(\frac{257}{966}\right)\)	\(e\left(\frac{1}{161}\right)\)	\(e\left(\frac{111}{322}\right)\)	\(e\left(\frac{3}{23}\right)\)
\(\chi_{20433}(19,\cdot)\)	20433.en	138	no	\(1\)	\(1\)	\(e\left(\frac{5}{46}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{25}{138}\right)\)	\(e\left(\frac{15}{46}\right)\)	\(e\left(\frac{20}{69}\right)\)	\(e\left(\frac{64}{69}\right)\)	\(e\left(\frac{109}{138}\right)\)	\(e\left(\frac{10}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)	\(e\left(\frac{3}{23}\right)\)
\(\chi_{20433}(20,\cdot)\)	20433.fs	966	yes	\(1\)	\(1\)	\(e\left(\frac{271}{966}\right)\)	\(e\left(\frac{271}{483}\right)\)	\(e\left(\frac{130}{483}\right)\)	\(e\left(\frac{271}{322}\right)\)	\(e\left(\frac{177}{322}\right)\)	\(e\left(\frac{103}{966}\right)\)	\(e\left(\frac{439}{966}\right)\)	\(e\left(\frac{59}{483}\right)\)	\(e\left(\frac{457}{483}\right)\)	\(e\left(\frac{55}{138}\right)\)
\(\chi_{20433}(22,\cdot)\)	20433.fr	966	no	\(-1\)	\(1\)	\(e\left(\frac{401}{966}\right)\)	\(e\left(\frac{401}{483}\right)\)	\(e\left(\frac{269}{483}\right)\)	\(e\left(\frac{79}{322}\right)\)	\(e\left(\frac{313}{322}\right)\)	\(e\left(\frac{127}{483}\right)\)	\(e\left(\frac{274}{483}\right)\)	\(e\left(\frac{319}{483}\right)\)	\(e\left(\frac{955}{966}\right)\)	\(e\left(\frac{5}{138}\right)\)
\(\chi_{20433}(23,\cdot)\)	20433.fn	966	yes	\(1\)	\(1\)	\(e\left(\frac{106}{483}\right)\)	\(e\left(\frac{212}{483}\right)\)	\(e\left(\frac{545}{966}\right)\)	\(e\left(\frac{106}{161}\right)\)	\(e\left(\frac{757}{966}\right)\)	\(e\left(\frac{541}{966}\right)\)	\(e\left(\frac{61}{161}\right)\)	\(e\left(\frac{424}{483}\right)\)	\(e\left(\frac{26}{483}\right)\)	\(e\left(\frac{83}{138}\right)\)
\(\chi_{20433}(25,\cdot)\)	20433.fa	483	no	\(1\)	\(1\)	\(e\left(\frac{73}{483}\right)\)	\(e\left(\frac{146}{483}\right)\)	\(e\left(\frac{38}{161}\right)\)	\(e\left(\frac{73}{161}\right)\)	\(e\left(\frac{187}{483}\right)\)	\(e\left(\frac{155}{161}\right)\)	\(e\left(\frac{164}{483}\right)\)	\(e\left(\frac{292}{483}\right)\)	\(e\left(\frac{428}{483}\right)\)	\(e\left(\frac{25}{69}\right)\)
\(\chi_{20433}(26,\cdot)\)	20433.fo	966	yes	\(-1\)	\(1\)	\(e\left(\frac{239}{483}\right)\)	\(e\left(\frac{478}{483}\right)\)	\(e\left(\frac{120}{161}\right)\)	\(e\left(\frac{78}{161}\right)\)	\(e\left(\frac{116}{483}\right)\)	\(e\left(\frac{157}{322}\right)\)	\(e\left(\frac{485}{966}\right)\)	\(e\left(\frac{473}{483}\right)\)	\(e\left(\frac{17}{966}\right)\)	\(e\left(\frac{62}{69}\right)\)
\(\chi_{20433}(29,\cdot)\)	20433.fy	966	yes	\(-1\)	\(1\)	\(e\left(\frac{313}{966}\right)\)	\(e\left(\frac{313}{483}\right)\)	\(e\left(\frac{491}{966}\right)\)	\(e\left(\frac{313}{322}\right)\)	\(e\left(\frac{134}{161}\right)\)	\(e\left(\frac{397}{966}\right)\)	\(e\left(\frac{356}{483}\right)\)	\(e\left(\frac{143}{483}\right)\)	\(e\left(\frac{95}{966}\right)\)	\(e\left(\frac{38}{69}\right)\)
\(\chi_{20433}(31,\cdot)\)	20433.dp	138	no	\(-1\)	\(1\)	\(e\left(\frac{17}{23}\right)\)	\(e\left(\frac{11}{23}\right)\)	\(e\left(\frac{101}{138}\right)\)	\(e\left(\frac{5}{23}\right)\)	\(e\left(\frac{65}{138}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{65}{138}\right)\)	\(e\left(\frac{22}{23}\right)\)	\(e\left(\frac{27}{46}\right)\)	\(e\left(\frac{27}{46}\right)\)
\(\chi_{20433}(32,\cdot)\)	20433.gd	966	yes	\(1\)	\(1\)	\(e\left(\frac{2}{161}\right)\)	\(e\left(\frac{4}{161}\right)\)	\(e\left(\frac{365}{966}\right)\)	\(e\left(\frac{6}{161}\right)\)	\(e\left(\frac{377}{966}\right)\)	\(e\left(\frac{61}{966}\right)\)	\(e\left(\frac{223}{483}\right)\)	\(e\left(\frac{8}{161}\right)\)	\(e\left(\frac{122}{161}\right)\)	\(e\left(\frac{25}{46}\right)\)
\(\chi_{20433}(34,\cdot)\)	20433.ew	322	no	\(-1\)	\(1\)	\(e\left(\frac{57}{161}\right)\)	\(e\left(\frac{114}{161}\right)\)	\(e\left(\frac{167}{322}\right)\)	\(e\left(\frac{10}{161}\right)\)	\(e\left(\frac{281}{322}\right)\)	\(e\left(\frac{8}{161}\right)\)	\(e\left(\frac{51}{322}\right)\)	\(e\left(\frac{67}{161}\right)\)	\(e\left(\frac{31}{322}\right)\)	\(e\left(\frac{11}{46}\right)\)
\(\chi_{20433}(37,\cdot)\)	20433.fa	483	no	\(1\)	\(1\)	\(e\left(\frac{188}{483}\right)\)	\(e\left(\frac{376}{483}\right)\)	\(e\left(\frac{153}{161}\right)\)	\(e\left(\frac{27}{161}\right)\)	\(e\left(\frac{164}{483}\right)\)	\(e\left(\frac{86}{161}\right)\)	\(e\left(\frac{118}{483}\right)\)	\(e\left(\frac{269}{483}\right)\)	\(e\left(\frac{37}{483}\right)\)	\(e\left(\frac{2}{69}\right)\)
\(\chi_{20433}(38,\cdot)\)	20433.fd	966	yes	\(1\)	\(1\)	\(e\left(\frac{229}{322}\right)\)	\(e\left(\frac{68}{161}\right)\)	\(e\left(\frac{124}{483}\right)\)	\(e\left(\frac{43}{322}\right)\)	\(e\left(\frac{935}{966}\right)\)	\(e\left(\frac{715}{966}\right)\)	\(e\left(\frac{659}{966}\right)\)	\(e\left(\frac{136}{161}\right)\)	\(e\left(\frac{142}{161}\right)\)	\(e\left(\frac{11}{46}\right)\)
\(\chi_{20433}(40,\cdot)\)	20433.fq	966	no	\(1\)	\(1\)	\(e\left(\frac{853}{966}\right)\)	\(e\left(\frac{370}{483}\right)\)	\(e\left(\frac{111}{322}\right)\)	\(e\left(\frac{209}{322}\right)\)	\(e\left(\frac{110}{483}\right)\)	\(e\left(\frac{148}{161}\right)\)	\(e\left(\frac{335}{966}\right)\)	\(e\left(\frac{257}{483}\right)\)	\(e\left(\frac{337}{483}\right)\)	\(e\left(\frac{35}{69}\right)\)
\(\chi_{20433}(41,\cdot)\)	20433.fs	966	yes	\(1\)	\(1\)	\(e\left(\frac{17}{966}\right)\)	\(e\left(\frac{17}{483}\right)\)	\(e\left(\frac{386}{483}\right)\)	\(e\left(\frac{17}{322}\right)\)	\(e\left(\frac{263}{322}\right)\)	\(e\left(\frac{395}{966}\right)\)	\(e\left(\frac{605}{966}\right)\)	\(e\left(\frac{34}{483}\right)\)	\(e\left(\frac{116}{483}\right)\)	\(e\left(\frac{89}{138}\right)\)
\(\chi_{20433}(43,\cdot)\)	20433.cn	42	no	\(-1\)	\(1\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{2}{21}\right)\)	\(e\left(\frac{17}{21}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{5}{14}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{1}{21}\right)\)	\(e\left(\frac{4}{21}\right)\)	\(e\left(\frac{31}{42}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{20433}(44,\cdot)\)	20433.fw	966	yes	\(-1\)	\(1\)	\(e\left(\frac{17}{966}\right)\)	\(e\left(\frac{17}{483}\right)\)	\(e\left(\frac{611}{966}\right)\)	\(e\left(\frac{17}{322}\right)\)	\(e\left(\frac{314}{483}\right)\)	\(e\left(\frac{73}{966}\right)\)	\(e\left(\frac{74}{161}\right)\)	\(e\left(\frac{34}{483}\right)\)	\(e\left(\frac{715}{966}\right)\)	\(e\left(\frac{10}{69}\right)\)
\(\chi_{20433}(46,\cdot)\)	20433.fa	483	no	\(1\)	\(1\)	\(e\left(\frac{397}{483}\right)\)	\(e\left(\frac{311}{483}\right)\)	\(e\left(\frac{103}{161}\right)\)	\(e\left(\frac{75}{161}\right)\)	\(e\left(\frac{223}{483}\right)\)	\(e\left(\frac{60}{161}\right)\)	\(e\left(\frac{131}{483}\right)\)	\(e\left(\frac{139}{483}\right)\)	\(e\left(\frac{389}{483}\right)\)	\(e\left(\frac{49}{69}\right)\)
\(\chi_{20433}(47,\cdot)\)	20433.fz	966	yes	\(1\)	\(1\)	\(e\left(\frac{295}{966}\right)\)	\(e\left(\frac{295}{483}\right)\)	\(e\left(\frac{4}{161}\right)\)	\(e\left(\frac{295}{322}\right)\)	\(e\left(\frac{319}{966}\right)\)	\(e\left(\frac{75}{322}\right)\)	\(e\left(\frac{365}{966}\right)\)	\(e\left(\frac{107}{483}\right)\)	\(e\left(\frac{223}{483}\right)\)	\(e\left(\frac{67}{138}\right)\)
\(\chi_{20433}(50,\cdot)\)	20433.eg	138	no	\(1\)	\(1\)	\(e\left(\frac{52}{69}\right)\)	\(e\left(\frac{35}{69}\right)\)	\(e\left(\frac{43}{138}\right)\)	\(e\left(\frac{6}{23}\right)\)	\(e\left(\frac{3}{46}\right)\)	\(e\left(\frac{107}{138}\right)\)	\(e\left(\frac{16}{69}\right)\)	\(e\left(\frac{1}{69}\right)\)	\(e\left(\frac{44}{69}\right)\)	\(e\left(\frac{65}{138}\right)\)
\(\chi_{20433}(52,\cdot)\)	20433.fm	966	no	\(-1\)	\(1\)	\(e\left(\frac{47}{483}\right)\)	\(e\left(\frac{94}{483}\right)\)	\(e\left(\frac{793}{966}\right)\)	\(e\left(\frac{47}{161}\right)\)	\(e\left(\frac{887}{966}\right)\)	\(e\left(\frac{145}{483}\right)\)	\(e\left(\frac{127}{322}\right)\)	\(e\left(\frac{188}{483}\right)\)	\(e\left(\frac{743}{966}\right)\)	\(e\left(\frac{1}{138}\right)\)
\(\chi_{20433}(53,\cdot)\)	20433.gd	966	yes	\(1\)	\(1\)	\(e\left(\frac{5}{161}\right)\)	\(e\left(\frac{10}{161}\right)\)	\(e\left(\frac{671}{966}\right)\)	\(e\left(\frac{15}{161}\right)\)	\(e\left(\frac{701}{966}\right)\)	\(e\left(\frac{877}{966}\right)\)	\(e\left(\frac{316}{483}\right)\)	\(e\left(\frac{20}{161}\right)\)	\(e\left(\frac{144}{161}\right)\)	\(e\left(\frac{5}{46}\right)\)
\(\chi_{20433}(55,\cdot)\)	20433.ew	322	no	\(-1\)	\(1\)	\(e\left(\frac{143}{161}\right)\)	\(e\left(\frac{125}{161}\right)\)	\(e\left(\frac{193}{322}\right)\)	\(e\left(\frac{107}{161}\right)\)	\(e\left(\frac{157}{322}\right)\)	\(e\left(\frac{150}{161}\right)\)	\(e\left(\frac{111}{322}\right)\)	\(e\left(\frac{89}{161}\right)\)	\(e\left(\frac{219}{322}\right)\)	\(e\left(\frac{5}{46}\right)\)

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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.