LMFDB - Group of Dirichlet characters of modulus 1063

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(1063)

gp:g = idealstar(,1063,2)

magma:G = FullDirichletGroup(1063);

Character group

Order	=	1062	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{1062}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{1063}(3,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 1062 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1063}(1,\cdot)$	1063.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1063}(2,\cdot)$	1063.k	531	yes	$1$	$1$	$e\left(\frac{98}{531}\right)$	$e\left(\frac{524}{531}\right)$	$e\left(\frac{196}{531}\right)$	$e\left(\frac{110}{177}\right)$	$e\left(\frac{91}{531}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{98}{177}\right)$	$e\left(\frac{517}{531}\right)$	$e\left(\frac{428}{531}\right)$	$e\left(\frac{284}{531}\right)$
$\chi_{1063}(3,\cdot)$	1063.l	1062	yes	$-1$	$1$	$e\left(\frac{524}{531}\right)$	$e\left(\frac{1}{1062}\right)$	$e\left(\frac{517}{531}\right)$	$e\left(\frac{313}{354}\right)$	$e\left(\frac{1049}{1062}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{170}{177}\right)$	$e\left(\frac{1}{531}\right)$	$e\left(\frac{925}{1062}\right)$	$e\left(\frac{359}{531}\right)$
$\chi_{1063}(4,\cdot)$	1063.k	531	yes	$1$	$1$	$e\left(\frac{196}{531}\right)$	$e\left(\frac{517}{531}\right)$	$e\left(\frac{392}{531}\right)$	$e\left(\frac{43}{177}\right)$	$e\left(\frac{182}{531}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{177}\right)$	$e\left(\frac{503}{531}\right)$	$e\left(\frac{325}{531}\right)$	$e\left(\frac{37}{531}\right)$
$\chi_{1063}(5,\cdot)$	1063.j	354	yes	$-1$	$1$	$e\left(\frac{110}{177}\right)$	$e\left(\frac{313}{354}\right)$	$e\left(\frac{43}{177}\right)$	$e\left(\frac{29}{118}\right)$	$e\left(\frac{179}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{51}{59}\right)$	$e\left(\frac{136}{177}\right)$	$e\left(\frac{307}{354}\right)$	$e\left(\frac{149}{177}\right)$
$\chi_{1063}(6,\cdot)$	1063.l	1062	yes	$-1$	$1$	$e\left(\frac{91}{531}\right)$	$e\left(\frac{1049}{1062}\right)$	$e\left(\frac{182}{531}\right)$	$e\left(\frac{179}{354}\right)$	$e\left(\frac{169}{1062}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{91}{177}\right)$	$e\left(\frac{518}{531}\right)$	$e\left(\frac{719}{1062}\right)$	$e\left(\frac{112}{531}\right)$
$\chi_{1063}(7,\cdot)$	1063.e	9	yes	$1$	$1$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1063}(8,\cdot)$	1063.i	177	yes	$1$	$1$	$e\left(\frac{98}{177}\right)$	$e\left(\frac{170}{177}\right)$	$e\left(\frac{19}{177}\right)$	$e\left(\frac{51}{59}\right)$	$e\left(\frac{91}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{39}{59}\right)$	$e\left(\frac{163}{177}\right)$	$e\left(\frac{74}{177}\right)$	$e\left(\frac{107}{177}\right)$
$\chi_{1063}(9,\cdot)$	1063.k	531	yes	$1$	$1$	$e\left(\frac{517}{531}\right)$	$e\left(\frac{1}{531}\right)$	$e\left(\frac{503}{531}\right)$	$e\left(\frac{136}{177}\right)$	$e\left(\frac{518}{531}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{163}{177}\right)$	$e\left(\frac{2}{531}\right)$	$e\left(\frac{394}{531}\right)$	$e\left(\frac{187}{531}\right)$
$\chi_{1063}(10,\cdot)$	1063.l	1062	yes	$-1$	$1$	$e\left(\frac{428}{531}\right)$	$e\left(\frac{925}{1062}\right)$	$e\left(\frac{325}{531}\right)$	$e\left(\frac{307}{354}\right)$	$e\left(\frac{719}{1062}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{74}{177}\right)$	$e\left(\frac{394}{531}\right)$	$e\left(\frac{715}{1062}\right)$	$e\left(\frac{200}{531}\right)$
$\chi_{1063}(11,\cdot)$	1063.k	531	yes	$1$	$1$	$e\left(\frac{284}{531}\right)$	$e\left(\frac{359}{531}\right)$	$e\left(\frac{37}{531}\right)$	$e\left(\frac{149}{177}\right)$	$e\left(\frac{112}{531}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{107}{177}\right)$	$e\left(\frac{187}{531}\right)$	$e\left(\frac{200}{531}\right)$	$e\left(\frac{227}{531}\right)$
$\chi_{1063}(12,\cdot)$	1063.h	118	yes	$-1$	$1$	$e\left(\frac{21}{59}\right)$	$e\left(\frac{115}{118}\right)$	$e\left(\frac{42}{59}\right)$	$e\left(\frac{15}{118}\right)$	$e\left(\frac{39}{118}\right)$	$1$	$e\left(\frac{4}{59}\right)$	$e\left(\frac{56}{59}\right)$	$e\left(\frac{57}{118}\right)$	$e\left(\frac{44}{59}\right)$
$\chi_{1063}(13,\cdot)$	1063.i	177	yes	$1$	$1$	$e\left(\frac{152}{177}\right)$	$e\left(\frac{65}{177}\right)$	$e\left(\frac{127}{177}\right)$	$e\left(\frac{49}{59}\right)$	$e\left(\frac{40}{177}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{34}{59}\right)$	$e\left(\frac{130}{177}\right)$	$e\left(\frac{122}{177}\right)$	$e\left(\frac{119}{177}\right)$
$\chi_{1063}(14,\cdot)$	1063.k	531	yes	$1$	$1$	$e\left(\frac{334}{531}\right)$	$e\left(\frac{52}{531}\right)$	$e\left(\frac{137}{531}\right)$	$e\left(\frac{169}{177}\right)$	$e\left(\frac{386}{531}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{157}{177}\right)$	$e\left(\frac{104}{531}\right)$	$e\left(\frac{310}{531}\right)$	$e\left(\frac{166}{531}\right)$
$\chi_{1063}(15,\cdot)$	1063.k	531	yes	$1$	$1$	$e\left(\frac{323}{531}\right)$	$e\left(\frac{470}{531}\right)$	$e\left(\frac{115}{531}\right)$	$e\left(\frac{23}{177}\right)$	$e\left(\frac{262}{531}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{146}{177}\right)$	$e\left(\frac{409}{531}\right)$	$e\left(\frac{392}{531}\right)$	$e\left(\frac{275}{531}\right)$
$\chi_{1063}(16,\cdot)$	1063.k	531	yes	$1$	$1$	$e\left(\frac{392}{531}\right)$	$e\left(\frac{503}{531}\right)$	$e\left(\frac{253}{531}\right)$	$e\left(\frac{86}{177}\right)$	$e\left(\frac{364}{531}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{38}{177}\right)$	$e\left(\frac{475}{531}\right)$	$e\left(\frac{119}{531}\right)$	$e\left(\frac{74}{531}\right)$
$\chi_{1063}(17,\cdot)$	1063.g	59	yes	$1$	$1$	$e\left(\frac{8}{59}\right)$	$e\left(\frac{50}{59}\right)$	$e\left(\frac{16}{59}\right)$	$e\left(\frac{45}{59}\right)$	$e\left(\frac{58}{59}\right)$	$1$	$e\left(\frac{24}{59}\right)$	$e\left(\frac{41}{59}\right)$	$e\left(\frac{53}{59}\right)$	$e\left(\frac{28}{59}\right)$
$\chi_{1063}(18,\cdot)$	1063.i	177	yes	$1$	$1$	$e\left(\frac{28}{177}\right)$	$e\left(\frac{175}{177}\right)$	$e\left(\frac{56}{177}\right)$	$e\left(\frac{23}{59}\right)$	$e\left(\frac{26}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{28}{59}\right)$	$e\left(\frac{173}{177}\right)$	$e\left(\frac{97}{177}\right)$	$e\left(\frac{157}{177}\right)$
$\chi_{1063}(19,\cdot)$	1063.k	531	yes	$1$	$1$	$e\left(\frac{1}{531}\right)$	$e\left(\frac{493}{531}\right)$	$e\left(\frac{2}{531}\right)$	$e\left(\frac{142}{177}\right)$	$e\left(\frac{494}{531}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{177}\right)$	$e\left(\frac{455}{531}\right)$	$e\left(\frac{427}{531}\right)$	$e\left(\frac{328}{531}\right)$
$\chi_{1063}(20,\cdot)$	1063.l	1062	yes	$-1$	$1$	$e\left(\frac{526}{531}\right)$	$e\left(\frac{911}{1062}\right)$	$e\left(\frac{521}{531}\right)$	$e\left(\frac{173}{354}\right)$	$e\left(\frac{901}{1062}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{172}{177}\right)$	$e\left(\frac{380}{531}\right)$	$e\left(\frac{509}{1062}\right)$	$e\left(\frac{484}{531}\right)$
$\chi_{1063}(21,\cdot)$	1063.l	1062	yes	$-1$	$1$	$e\left(\frac{229}{531}\right)$	$e\left(\frac{119}{1062}\right)$	$e\left(\frac{458}{531}\right)$	$e\left(\frac{77}{354}\right)$	$e\left(\frac{577}{1062}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{52}{177}\right)$	$e\left(\frac{119}{531}\right)$	$e\left(\frac{689}{1062}\right)$	$e\left(\frac{241}{531}\right)$
$\chi_{1063}(22,\cdot)$	1063.k	531	yes	$1$	$1$	$e\left(\frac{382}{531}\right)$	$e\left(\frac{352}{531}\right)$	$e\left(\frac{233}{531}\right)$	$e\left(\frac{82}{177}\right)$	$e\left(\frac{203}{531}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{28}{177}\right)$	$e\left(\frac{173}{531}\right)$	$e\left(\frac{97}{531}\right)$	$e\left(\frac{511}{531}\right)$
$\chi_{1063}(23,\cdot)$	1063.k	531	yes	$1$	$1$	$e\left(\frac{116}{531}\right)$	$e\left(\frac{371}{531}\right)$	$e\left(\frac{232}{531}\right)$	$e\left(\frac{11}{177}\right)$	$e\left(\frac{487}{531}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{116}{177}\right)$	$e\left(\frac{211}{531}\right)$	$e\left(\frac{149}{531}\right)$	$e\left(\frac{347}{531}\right)$
$\chi_{1063}(24,\cdot)$	1063.l	1062	yes	$-1$	$1$	$e\left(\frac{287}{531}\right)$	$e\left(\frac{1021}{1062}\right)$	$e\left(\frac{43}{531}\right)$	$e\left(\frac{265}{354}\right)$	$e\left(\frac{533}{1062}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{110}{177}\right)$	$e\left(\frac{490}{531}\right)$	$e\left(\frac{307}{1062}\right)$	$e\left(\frac{149}{531}\right)$
$\chi_{1063}(25,\cdot)$	1063.i	177	yes	$1$	$1$	$e\left(\frac{43}{177}\right)$	$e\left(\frac{136}{177}\right)$	$e\left(\frac{86}{177}\right)$	$e\left(\frac{29}{59}\right)$	$e\left(\frac{2}{177}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{43}{59}\right)$	$e\left(\frac{95}{177}\right)$	$e\left(\frac{130}{177}\right)$	$e\left(\frac{121}{177}\right)$
$\chi_{1063}(26,\cdot)$	1063.k	531	yes	$1$	$1$	$e\left(\frac{23}{531}\right)$	$e\left(\frac{188}{531}\right)$	$e\left(\frac{46}{531}\right)$	$e\left(\frac{80}{177}\right)$	$e\left(\frac{211}{531}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{23}{177}\right)$	$e\left(\frac{376}{531}\right)$	$e\left(\frac{263}{531}\right)$	$e\left(\frac{110}{531}\right)$
$\chi_{1063}(27,\cdot)$	1063.j	354	yes	$-1$	$1$	$e\left(\frac{170}{177}\right)$	$e\left(\frac{1}{354}\right)$	$e\left(\frac{163}{177}\right)$	$e\left(\frac{77}{118}\right)$	$e\left(\frac{341}{354}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{52}{59}\right)$	$e\left(\frac{1}{177}\right)$	$e\left(\frac{217}{354}\right)$	$e\left(\frac{5}{177}\right)$
$\chi_{1063}(28,\cdot)$	1063.g	59	yes	$1$	$1$	$e\left(\frac{48}{59}\right)$	$e\left(\frac{5}{59}\right)$	$e\left(\frac{37}{59}\right)$	$e\left(\frac{34}{59}\right)$	$e\left(\frac{53}{59}\right)$	$1$	$e\left(\frac{26}{59}\right)$	$e\left(\frac{10}{59}\right)$	$e\left(\frac{23}{59}\right)$	$e\left(\frac{50}{59}\right)$
$\chi_{1063}(29,\cdot)$	1063.l	1062	yes	$-1$	$1$	$e\left(\frac{350}{531}\right)$	$e\left(\frac{481}{1062}\right)$	$e\left(\frac{169}{531}\right)$	$e\left(\frac{103}{354}\right)$	$e\left(\frac{119}{1062}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{173}{177}\right)$	$e\left(\frac{481}{531}\right)$	$e\left(\frac{1009}{1062}\right)$	$e\left(\frac{104}{531}\right)$
$\chi_{1063}(30,\cdot)$	1063.k	531	yes	$1$	$1$	$e\left(\frac{421}{531}\right)$	$e\left(\frac{463}{531}\right)$	$e\left(\frac{311}{531}\right)$	$e\left(\frac{133}{177}\right)$	$e\left(\frac{353}{531}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{67}{177}\right)$	$e\left(\frac{395}{531}\right)$	$e\left(\frac{289}{531}\right)$	$e\left(\frac{28}{531}\right)$
$\chi_{1063}(31,\cdot)$	1063.l	1062	yes	$-1$	$1$	$e\left(\frac{347}{531}\right)$	$e\left(\frac{709}{1062}\right)$	$e\left(\frac{163}{531}\right)$	$e\left(\frac{313}{354}\right)$	$e\left(\frac{341}{1062}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{170}{177}\right)$	$e\left(\frac{178}{531}\right)$	$e\left(\frac{571}{1062}\right)$	$e\left(\frac{182}{531}\right)$
$\chi_{1063}(32,\cdot)$	1063.k	531	yes	$1$	$1$	$e\left(\frac{490}{531}\right)$	$e\left(\frac{496}{531}\right)$	$e\left(\frac{449}{531}\right)$	$e\left(\frac{19}{177}\right)$	$e\left(\frac{455}{531}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{136}{177}\right)$	$e\left(\frac{461}{531}\right)$	$e\left(\frac{16}{531}\right)$	$e\left(\frac{358}{531}\right)$

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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	$1063$
Structure	\(C_{1062}\)
Order	$1062$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1063}(1,\cdot)\)	1063.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1063}(2,\cdot)\)	1063.k	531	yes	\(1\)	\(1\)	\(e\left(\frac{98}{531}\right)\)	\(e\left(\frac{524}{531}\right)\)	\(e\left(\frac{196}{531}\right)\)	\(e\left(\frac{110}{177}\right)\)	\(e\left(\frac{91}{531}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{98}{177}\right)\)	\(e\left(\frac{517}{531}\right)\)	\(e\left(\frac{428}{531}\right)\)	\(e\left(\frac{284}{531}\right)\)
\(\chi_{1063}(3,\cdot)\)	1063.l	1062	yes	\(-1\)	\(1\)	\(e\left(\frac{524}{531}\right)\)	\(e\left(\frac{1}{1062}\right)\)	\(e\left(\frac{517}{531}\right)\)	\(e\left(\frac{313}{354}\right)\)	\(e\left(\frac{1049}{1062}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{170}{177}\right)\)	\(e\left(\frac{1}{531}\right)\)	\(e\left(\frac{925}{1062}\right)\)	\(e\left(\frac{359}{531}\right)\)
\(\chi_{1063}(4,\cdot)\)	1063.k	531	yes	\(1\)	\(1\)	\(e\left(\frac{196}{531}\right)\)	\(e\left(\frac{517}{531}\right)\)	\(e\left(\frac{392}{531}\right)\)	\(e\left(\frac{43}{177}\right)\)	\(e\left(\frac{182}{531}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{177}\right)\)	\(e\left(\frac{503}{531}\right)\)	\(e\left(\frac{325}{531}\right)\)	\(e\left(\frac{37}{531}\right)\)
\(\chi_{1063}(5,\cdot)\)	1063.j	354	yes	\(-1\)	\(1\)	\(e\left(\frac{110}{177}\right)\)	\(e\left(\frac{313}{354}\right)\)	\(e\left(\frac{43}{177}\right)\)	\(e\left(\frac{29}{118}\right)\)	\(e\left(\frac{179}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{51}{59}\right)\)	\(e\left(\frac{136}{177}\right)\)	\(e\left(\frac{307}{354}\right)\)	\(e\left(\frac{149}{177}\right)\)
\(\chi_{1063}(6,\cdot)\)	1063.l	1062	yes	\(-1\)	\(1\)	\(e\left(\frac{91}{531}\right)\)	\(e\left(\frac{1049}{1062}\right)\)	\(e\left(\frac{182}{531}\right)\)	\(e\left(\frac{179}{354}\right)\)	\(e\left(\frac{169}{1062}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{91}{177}\right)\)	\(e\left(\frac{518}{531}\right)\)	\(e\left(\frac{719}{1062}\right)\)	\(e\left(\frac{112}{531}\right)\)
\(\chi_{1063}(7,\cdot)\)	1063.e	9	yes	\(1\)	\(1\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1063}(8,\cdot)\)	1063.i	177	yes	\(1\)	\(1\)	\(e\left(\frac{98}{177}\right)\)	\(e\left(\frac{170}{177}\right)\)	\(e\left(\frac{19}{177}\right)\)	\(e\left(\frac{51}{59}\right)\)	\(e\left(\frac{91}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{39}{59}\right)\)	\(e\left(\frac{163}{177}\right)\)	\(e\left(\frac{74}{177}\right)\)	\(e\left(\frac{107}{177}\right)\)
\(\chi_{1063}(9,\cdot)\)	1063.k	531	yes	\(1\)	\(1\)	\(e\left(\frac{517}{531}\right)\)	\(e\left(\frac{1}{531}\right)\)	\(e\left(\frac{503}{531}\right)\)	\(e\left(\frac{136}{177}\right)\)	\(e\left(\frac{518}{531}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{163}{177}\right)\)	\(e\left(\frac{2}{531}\right)\)	\(e\left(\frac{394}{531}\right)\)	\(e\left(\frac{187}{531}\right)\)
\(\chi_{1063}(10,\cdot)\)	1063.l	1062	yes	\(-1\)	\(1\)	\(e\left(\frac{428}{531}\right)\)	\(e\left(\frac{925}{1062}\right)\)	\(e\left(\frac{325}{531}\right)\)	\(e\left(\frac{307}{354}\right)\)	\(e\left(\frac{719}{1062}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{74}{177}\right)\)	\(e\left(\frac{394}{531}\right)\)	\(e\left(\frac{715}{1062}\right)\)	\(e\left(\frac{200}{531}\right)\)
\(\chi_{1063}(11,\cdot)\)	1063.k	531	yes	\(1\)	\(1\)	\(e\left(\frac{284}{531}\right)\)	\(e\left(\frac{359}{531}\right)\)	\(e\left(\frac{37}{531}\right)\)	\(e\left(\frac{149}{177}\right)\)	\(e\left(\frac{112}{531}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{107}{177}\right)\)	\(e\left(\frac{187}{531}\right)\)	\(e\left(\frac{200}{531}\right)\)	\(e\left(\frac{227}{531}\right)\)
\(\chi_{1063}(12,\cdot)\)	1063.h	118	yes	\(-1\)	\(1\)	\(e\left(\frac{21}{59}\right)\)	\(e\left(\frac{115}{118}\right)\)	\(e\left(\frac{42}{59}\right)\)	\(e\left(\frac{15}{118}\right)\)	\(e\left(\frac{39}{118}\right)\)	\(1\)	\(e\left(\frac{4}{59}\right)\)	\(e\left(\frac{56}{59}\right)\)	\(e\left(\frac{57}{118}\right)\)	\(e\left(\frac{44}{59}\right)\)
\(\chi_{1063}(13,\cdot)\)	1063.i	177	yes	\(1\)	\(1\)	\(e\left(\frac{152}{177}\right)\)	\(e\left(\frac{65}{177}\right)\)	\(e\left(\frac{127}{177}\right)\)	\(e\left(\frac{49}{59}\right)\)	\(e\left(\frac{40}{177}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{34}{59}\right)\)	\(e\left(\frac{130}{177}\right)\)	\(e\left(\frac{122}{177}\right)\)	\(e\left(\frac{119}{177}\right)\)
\(\chi_{1063}(14,\cdot)\)	1063.k	531	yes	\(1\)	\(1\)	\(e\left(\frac{334}{531}\right)\)	\(e\left(\frac{52}{531}\right)\)	\(e\left(\frac{137}{531}\right)\)	\(e\left(\frac{169}{177}\right)\)	\(e\left(\frac{386}{531}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{157}{177}\right)\)	\(e\left(\frac{104}{531}\right)\)	\(e\left(\frac{310}{531}\right)\)	\(e\left(\frac{166}{531}\right)\)
\(\chi_{1063}(15,\cdot)\)	1063.k	531	yes	\(1\)	\(1\)	\(e\left(\frac{323}{531}\right)\)	\(e\left(\frac{470}{531}\right)\)	\(e\left(\frac{115}{531}\right)\)	\(e\left(\frac{23}{177}\right)\)	\(e\left(\frac{262}{531}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{146}{177}\right)\)	\(e\left(\frac{409}{531}\right)\)	\(e\left(\frac{392}{531}\right)\)	\(e\left(\frac{275}{531}\right)\)
\(\chi_{1063}(16,\cdot)\)	1063.k	531	yes	\(1\)	\(1\)	\(e\left(\frac{392}{531}\right)\)	\(e\left(\frac{503}{531}\right)\)	\(e\left(\frac{253}{531}\right)\)	\(e\left(\frac{86}{177}\right)\)	\(e\left(\frac{364}{531}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{38}{177}\right)\)	\(e\left(\frac{475}{531}\right)\)	\(e\left(\frac{119}{531}\right)\)	\(e\left(\frac{74}{531}\right)\)
\(\chi_{1063}(17,\cdot)\)	1063.g	59	yes	\(1\)	\(1\)	\(e\left(\frac{8}{59}\right)\)	\(e\left(\frac{50}{59}\right)\)	\(e\left(\frac{16}{59}\right)\)	\(e\left(\frac{45}{59}\right)\)	\(e\left(\frac{58}{59}\right)\)	\(1\)	\(e\left(\frac{24}{59}\right)\)	\(e\left(\frac{41}{59}\right)\)	\(e\left(\frac{53}{59}\right)\)	\(e\left(\frac{28}{59}\right)\)
\(\chi_{1063}(18,\cdot)\)	1063.i	177	yes	\(1\)	\(1\)	\(e\left(\frac{28}{177}\right)\)	\(e\left(\frac{175}{177}\right)\)	\(e\left(\frac{56}{177}\right)\)	\(e\left(\frac{23}{59}\right)\)	\(e\left(\frac{26}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{28}{59}\right)\)	\(e\left(\frac{173}{177}\right)\)	\(e\left(\frac{97}{177}\right)\)	\(e\left(\frac{157}{177}\right)\)
\(\chi_{1063}(19,\cdot)\)	1063.k	531	yes	\(1\)	\(1\)	\(e\left(\frac{1}{531}\right)\)	\(e\left(\frac{493}{531}\right)\)	\(e\left(\frac{2}{531}\right)\)	\(e\left(\frac{142}{177}\right)\)	\(e\left(\frac{494}{531}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{177}\right)\)	\(e\left(\frac{455}{531}\right)\)	\(e\left(\frac{427}{531}\right)\)	\(e\left(\frac{328}{531}\right)\)
\(\chi_{1063}(20,\cdot)\)	1063.l	1062	yes	\(-1\)	\(1\)	\(e\left(\frac{526}{531}\right)\)	\(e\left(\frac{911}{1062}\right)\)	\(e\left(\frac{521}{531}\right)\)	\(e\left(\frac{173}{354}\right)\)	\(e\left(\frac{901}{1062}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{172}{177}\right)\)	\(e\left(\frac{380}{531}\right)\)	\(e\left(\frac{509}{1062}\right)\)	\(e\left(\frac{484}{531}\right)\)
\(\chi_{1063}(21,\cdot)\)	1063.l	1062	yes	\(-1\)	\(1\)	\(e\left(\frac{229}{531}\right)\)	\(e\left(\frac{119}{1062}\right)\)	\(e\left(\frac{458}{531}\right)\)	\(e\left(\frac{77}{354}\right)\)	\(e\left(\frac{577}{1062}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{52}{177}\right)\)	\(e\left(\frac{119}{531}\right)\)	\(e\left(\frac{689}{1062}\right)\)	\(e\left(\frac{241}{531}\right)\)
\(\chi_{1063}(22,\cdot)\)	1063.k	531	yes	\(1\)	\(1\)	\(e\left(\frac{382}{531}\right)\)	\(e\left(\frac{352}{531}\right)\)	\(e\left(\frac{233}{531}\right)\)	\(e\left(\frac{82}{177}\right)\)	\(e\left(\frac{203}{531}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{28}{177}\right)\)	\(e\left(\frac{173}{531}\right)\)	\(e\left(\frac{97}{531}\right)\)	\(e\left(\frac{511}{531}\right)\)
\(\chi_{1063}(23,\cdot)\)	1063.k	531	yes	\(1\)	\(1\)	\(e\left(\frac{116}{531}\right)\)	\(e\left(\frac{371}{531}\right)\)	\(e\left(\frac{232}{531}\right)\)	\(e\left(\frac{11}{177}\right)\)	\(e\left(\frac{487}{531}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{116}{177}\right)\)	\(e\left(\frac{211}{531}\right)\)	\(e\left(\frac{149}{531}\right)\)	\(e\left(\frac{347}{531}\right)\)
\(\chi_{1063}(24,\cdot)\)	1063.l	1062	yes	\(-1\)	\(1\)	\(e\left(\frac{287}{531}\right)\)	\(e\left(\frac{1021}{1062}\right)\)	\(e\left(\frac{43}{531}\right)\)	\(e\left(\frac{265}{354}\right)\)	\(e\left(\frac{533}{1062}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{110}{177}\right)\)	\(e\left(\frac{490}{531}\right)\)	\(e\left(\frac{307}{1062}\right)\)	\(e\left(\frac{149}{531}\right)\)
\(\chi_{1063}(25,\cdot)\)	1063.i	177	yes	\(1\)	\(1\)	\(e\left(\frac{43}{177}\right)\)	\(e\left(\frac{136}{177}\right)\)	\(e\left(\frac{86}{177}\right)\)	\(e\left(\frac{29}{59}\right)\)	\(e\left(\frac{2}{177}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{43}{59}\right)\)	\(e\left(\frac{95}{177}\right)\)	\(e\left(\frac{130}{177}\right)\)	\(e\left(\frac{121}{177}\right)\)
\(\chi_{1063}(26,\cdot)\)	1063.k	531	yes	\(1\)	\(1\)	\(e\left(\frac{23}{531}\right)\)	\(e\left(\frac{188}{531}\right)\)	\(e\left(\frac{46}{531}\right)\)	\(e\left(\frac{80}{177}\right)\)	\(e\left(\frac{211}{531}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{23}{177}\right)\)	\(e\left(\frac{376}{531}\right)\)	\(e\left(\frac{263}{531}\right)\)	\(e\left(\frac{110}{531}\right)\)
\(\chi_{1063}(27,\cdot)\)	1063.j	354	yes	\(-1\)	\(1\)	\(e\left(\frac{170}{177}\right)\)	\(e\left(\frac{1}{354}\right)\)	\(e\left(\frac{163}{177}\right)\)	\(e\left(\frac{77}{118}\right)\)	\(e\left(\frac{341}{354}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{52}{59}\right)\)	\(e\left(\frac{1}{177}\right)\)	\(e\left(\frac{217}{354}\right)\)	\(e\left(\frac{5}{177}\right)\)
\(\chi_{1063}(28,\cdot)\)	1063.g	59	yes	\(1\)	\(1\)	\(e\left(\frac{48}{59}\right)\)	\(e\left(\frac{5}{59}\right)\)	\(e\left(\frac{37}{59}\right)\)	\(e\left(\frac{34}{59}\right)\)	\(e\left(\frac{53}{59}\right)\)	\(1\)	\(e\left(\frac{26}{59}\right)\)	\(e\left(\frac{10}{59}\right)\)	\(e\left(\frac{23}{59}\right)\)	\(e\left(\frac{50}{59}\right)\)
\(\chi_{1063}(29,\cdot)\)	1063.l	1062	yes	\(-1\)	\(1\)	\(e\left(\frac{350}{531}\right)\)	\(e\left(\frac{481}{1062}\right)\)	\(e\left(\frac{169}{531}\right)\)	\(e\left(\frac{103}{354}\right)\)	\(e\left(\frac{119}{1062}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{173}{177}\right)\)	\(e\left(\frac{481}{531}\right)\)	\(e\left(\frac{1009}{1062}\right)\)	\(e\left(\frac{104}{531}\right)\)
\(\chi_{1063}(30,\cdot)\)	1063.k	531	yes	\(1\)	\(1\)	\(e\left(\frac{421}{531}\right)\)	\(e\left(\frac{463}{531}\right)\)	\(e\left(\frac{311}{531}\right)\)	\(e\left(\frac{133}{177}\right)\)	\(e\left(\frac{353}{531}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{67}{177}\right)\)	\(e\left(\frac{395}{531}\right)\)	\(e\left(\frac{289}{531}\right)\)	\(e\left(\frac{28}{531}\right)\)
\(\chi_{1063}(31,\cdot)\)	1063.l	1062	yes	\(-1\)	\(1\)	\(e\left(\frac{347}{531}\right)\)	\(e\left(\frac{709}{1062}\right)\)	\(e\left(\frac{163}{531}\right)\)	\(e\left(\frac{313}{354}\right)\)	\(e\left(\frac{341}{1062}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{170}{177}\right)\)	\(e\left(\frac{178}{531}\right)\)	\(e\left(\frac{571}{1062}\right)\)	\(e\left(\frac{182}{531}\right)\)
\(\chi_{1063}(32,\cdot)\)	1063.k	531	yes	\(1\)	\(1\)	\(e\left(\frac{490}{531}\right)\)	\(e\left(\frac{496}{531}\right)\)	\(e\left(\frac{449}{531}\right)\)	\(e\left(\frac{19}{177}\right)\)	\(e\left(\frac{455}{531}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{136}{177}\right)\)	\(e\left(\frac{461}{531}\right)\)	\(e\left(\frac{16}{531}\right)\)	\(e\left(\frac{358}{531}\right)\)

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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.