LMFDB - Group of Dirichlet characters of modulus 1049

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1049)

pari: g = idealstar(,1049,2)

Character group

sage: G.order() pari: g.no
Order	=	1048
sage: H.invariants() pari: g.cyc
Structure	=	$C_{1048}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1049}(3,\cdot)$

First 32 of 1048 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1049}(1,\cdot)$	1049.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1049}(2,\cdot)$	1049.f	262	yes	$1$	$1$	$e\left(\frac{124}{131}\right)$	$e\left(\frac{149}{262}\right)$	$e\left(\frac{117}{131}\right)$	$e\left(\frac{96}{131}\right)$	$e\left(\frac{135}{262}\right)$	$e\left(\frac{5}{262}\right)$	$e\left(\frac{110}{131}\right)$	$e\left(\frac{18}{131}\right)$	$e\left(\frac{89}{131}\right)$	$e\left(\frac{94}{131}\right)$
$\chi_{1049}(3,\cdot)$	1049.h	1048	yes	$-1$	$1$	$e\left(\frac{149}{262}\right)$	$e\left(\frac{1}{1048}\right)$	$e\left(\frac{18}{131}\right)$	$e\left(\frac{49}{524}\right)$	$e\left(\frac{597}{1048}\right)$	$e\left(\frac{255}{1048}\right)$	$e\left(\frac{185}{262}\right)$	$e\left(\frac{1}{524}\right)$	$e\left(\frac{347}{524}\right)$	$e\left(\frac{209}{524}\right)$
$\chi_{1049}(4,\cdot)$	1049.e	131	yes	$1$	$1$	$e\left(\frac{117}{131}\right)$	$e\left(\frac{18}{131}\right)$	$e\left(\frac{103}{131}\right)$	$e\left(\frac{61}{131}\right)$	$e\left(\frac{4}{131}\right)$	$e\left(\frac{5}{131}\right)$	$e\left(\frac{89}{131}\right)$	$e\left(\frac{36}{131}\right)$	$e\left(\frac{47}{131}\right)$	$e\left(\frac{57}{131}\right)$
$\chi_{1049}(5,\cdot)$	1049.g	524	yes	$1$	$1$	$e\left(\frac{96}{131}\right)$	$e\left(\frac{49}{524}\right)$	$e\left(\frac{61}{131}\right)$	$e\left(\frac{43}{262}\right)$	$e\left(\frac{433}{524}\right)$	$e\left(\frac{443}{524}\right)$	$e\left(\frac{26}{131}\right)$	$e\left(\frac{49}{262}\right)$	$e\left(\frac{235}{262}\right)$	$e\left(\frac{23}{262}\right)$
$\chi_{1049}(6,\cdot)$	1049.h	1048	yes	$-1$	$1$	$e\left(\frac{135}{262}\right)$	$e\left(\frac{597}{1048}\right)$	$e\left(\frac{4}{131}\right)$	$e\left(\frac{433}{524}\right)$	$e\left(\frac{89}{1048}\right)$	$e\left(\frac{275}{1048}\right)$	$e\left(\frac{143}{262}\right)$	$e\left(\frac{73}{524}\right)$	$e\left(\frac{179}{524}\right)$	$e\left(\frac{61}{524}\right)$
$\chi_{1049}(7,\cdot)$	1049.h	1048	yes	$-1$	$1$	$e\left(\frac{5}{262}\right)$	$e\left(\frac{255}{1048}\right)$	$e\left(\frac{5}{131}\right)$	$e\left(\frac{443}{524}\right)$	$e\left(\frac{275}{1048}\right)$	$e\left(\frac{49}{1048}\right)$	$e\left(\frac{15}{262}\right)$	$e\left(\frac{255}{524}\right)$	$e\left(\frac{453}{524}\right)$	$e\left(\frac{371}{524}\right)$
$\chi_{1049}(8,\cdot)$	1049.f	262	yes	$1$	$1$	$e\left(\frac{110}{131}\right)$	$e\left(\frac{185}{262}\right)$	$e\left(\frac{89}{131}\right)$	$e\left(\frac{26}{131}\right)$	$e\left(\frac{143}{262}\right)$	$e\left(\frac{15}{262}\right)$	$e\left(\frac{68}{131}\right)$	$e\left(\frac{54}{131}\right)$	$e\left(\frac{5}{131}\right)$	$e\left(\frac{20}{131}\right)$
$\chi_{1049}(9,\cdot)$	1049.g	524	yes	$1$	$1$	$e\left(\frac{18}{131}\right)$	$e\left(\frac{1}{524}\right)$	$e\left(\frac{36}{131}\right)$	$e\left(\frac{49}{262}\right)$	$e\left(\frac{73}{524}\right)$	$e\left(\frac{255}{524}\right)$	$e\left(\frac{54}{131}\right)$	$e\left(\frac{1}{262}\right)$	$e\left(\frac{85}{262}\right)$	$e\left(\frac{209}{262}\right)$
$\chi_{1049}(10,\cdot)$	1049.g	524	yes	$1$	$1$	$e\left(\frac{89}{131}\right)$	$e\left(\frac{347}{524}\right)$	$e\left(\frac{47}{131}\right)$	$e\left(\frac{235}{262}\right)$	$e\left(\frac{179}{524}\right)$	$e\left(\frac{453}{524}\right)$	$e\left(\frac{5}{131}\right)$	$e\left(\frac{85}{262}\right)$	$e\left(\frac{151}{262}\right)$	$e\left(\frac{211}{262}\right)$
$\chi_{1049}(11,\cdot)$	1049.g	524	yes	$1$	$1$	$e\left(\frac{94}{131}\right)$	$e\left(\frac{209}{524}\right)$	$e\left(\frac{57}{131}\right)$	$e\left(\frac{23}{262}\right)$	$e\left(\frac{61}{524}\right)$	$e\left(\frac{371}{524}\right)$	$e\left(\frac{20}{131}\right)$	$e\left(\frac{209}{262}\right)$	$e\left(\frac{211}{262}\right)$	$e\left(\frac{189}{262}\right)$
$\chi_{1049}(12,\cdot)$	1049.h	1048	yes	$-1$	$1$	$e\left(\frac{121}{262}\right)$	$e\left(\frac{145}{1048}\right)$	$e\left(\frac{121}{131}\right)$	$e\left(\frac{293}{524}\right)$	$e\left(\frac{629}{1048}\right)$	$e\left(\frac{295}{1048}\right)$	$e\left(\frac{101}{262}\right)$	$e\left(\frac{145}{524}\right)$	$e\left(\frac{11}{524}\right)$	$e\left(\frac{437}{524}\right)$
$\chi_{1049}(13,\cdot)$	1049.f	262	yes	$1$	$1$	$e\left(\frac{81}{131}\right)$	$e\left(\frac{35}{262}\right)$	$e\left(\frac{31}{131}\right)$	$e\left(\frac{12}{131}\right)$	$e\left(\frac{197}{262}\right)$	$e\left(\frac{17}{262}\right)$	$e\left(\frac{112}{131}\right)$	$e\left(\frac{35}{131}\right)$	$e\left(\frac{93}{131}\right)$	$e\left(\frac{110}{131}\right)$
$\chi_{1049}(14,\cdot)$	1049.h	1048	yes	$-1$	$1$	$e\left(\frac{253}{262}\right)$	$e\left(\frac{851}{1048}\right)$	$e\left(\frac{122}{131}\right)$	$e\left(\frac{303}{524}\right)$	$e\left(\frac{815}{1048}\right)$	$e\left(\frac{69}{1048}\right)$	$e\left(\frac{235}{262}\right)$	$e\left(\frac{327}{524}\right)$	$e\left(\frac{285}{524}\right)$	$e\left(\frac{223}{524}\right)$
$\chi_{1049}(15,\cdot)$	1049.h	1048	yes	$-1$	$1$	$e\left(\frac{79}{262}\right)$	$e\left(\frac{99}{1048}\right)$	$e\left(\frac{79}{131}\right)$	$e\left(\frac{135}{524}\right)$	$e\left(\frac{415}{1048}\right)$	$e\left(\frac{93}{1048}\right)$	$e\left(\frac{237}{262}\right)$	$e\left(\frac{99}{524}\right)$	$e\left(\frac{293}{524}\right)$	$e\left(\frac{255}{524}\right)$
$\chi_{1049}(16,\cdot)$	1049.e	131	yes	$1$	$1$	$e\left(\frac{103}{131}\right)$	$e\left(\frac{36}{131}\right)$	$e\left(\frac{75}{131}\right)$	$e\left(\frac{122}{131}\right)$	$e\left(\frac{8}{131}\right)$	$e\left(\frac{10}{131}\right)$	$e\left(\frac{47}{131}\right)$	$e\left(\frac{72}{131}\right)$	$e\left(\frac{94}{131}\right)$	$e\left(\frac{114}{131}\right)$
$\chi_{1049}(17,\cdot)$	1049.h	1048	yes	$-1$	$1$	$e\left(\frac{133}{262}\right)$	$e\left(\frac{757}{1048}\right)$	$e\left(\frac{2}{131}\right)$	$e\left(\frac{413}{524}\right)$	$e\left(\frac{241}{1048}\right)$	$e\left(\frac{203}{1048}\right)$	$e\left(\frac{137}{262}\right)$	$e\left(\frac{233}{524}\right)$	$e\left(\frac{155}{524}\right)$	$e\left(\frac{489}{524}\right)$
$\chi_{1049}(18,\cdot)$	1049.g	524	yes	$1$	$1$	$e\left(\frac{11}{131}\right)$	$e\left(\frac{299}{524}\right)$	$e\left(\frac{22}{131}\right)$	$e\left(\frac{241}{262}\right)$	$e\left(\frac{343}{524}\right)$	$e\left(\frac{265}{524}\right)$	$e\left(\frac{33}{131}\right)$	$e\left(\frac{37}{262}\right)$	$e\left(\frac{1}{262}\right)$	$e\left(\frac{135}{262}\right)$
$\chi_{1049}(19,\cdot)$	1049.e	131	yes	$1$	$1$	$e\left(\frac{58}{131}\right)$	$e\left(\frac{19}{131}\right)$	$e\left(\frac{116}{131}\right)$	$e\left(\frac{28}{131}\right)$	$e\left(\frac{77}{131}\right)$	$e\left(\frac{129}{131}\right)$	$e\left(\frac{43}{131}\right)$	$e\left(\frac{38}{131}\right)$	$e\left(\frac{86}{131}\right)$	$e\left(\frac{82}{131}\right)$
$\chi_{1049}(20,\cdot)$	1049.g	524	yes	$1$	$1$	$e\left(\frac{82}{131}\right)$	$e\left(\frac{121}{524}\right)$	$e\left(\frac{33}{131}\right)$	$e\left(\frac{165}{262}\right)$	$e\left(\frac{449}{524}\right)$	$e\left(\frac{463}{524}\right)$	$e\left(\frac{115}{131}\right)$	$e\left(\frac{121}{262}\right)$	$e\left(\frac{67}{262}\right)$	$e\left(\frac{137}{262}\right)$
$\chi_{1049}(21,\cdot)$	1049.e	131	yes	$1$	$1$	$e\left(\frac{77}{131}\right)$	$e\left(\frac{32}{131}\right)$	$e\left(\frac{23}{131}\right)$	$e\left(\frac{123}{131}\right)$	$e\left(\frac{109}{131}\right)$	$e\left(\frac{38}{131}\right)$	$e\left(\frac{100}{131}\right)$	$e\left(\frac{64}{131}\right)$	$e\left(\frac{69}{131}\right)$	$e\left(\frac{14}{131}\right)$
$\chi_{1049}(22,\cdot)$	1049.g	524	yes	$1$	$1$	$e\left(\frac{87}{131}\right)$	$e\left(\frac{507}{524}\right)$	$e\left(\frac{43}{131}\right)$	$e\left(\frac{215}{262}\right)$	$e\left(\frac{331}{524}\right)$	$e\left(\frac{381}{524}\right)$	$e\left(\frac{130}{131}\right)$	$e\left(\frac{245}{262}\right)$	$e\left(\frac{127}{262}\right)$	$e\left(\frac{115}{262}\right)$
$\chi_{1049}(23,\cdot)$	1049.h	1048	yes	$-1$	$1$	$e\left(\frac{25}{262}\right)$	$e\left(\frac{227}{1048}\right)$	$e\left(\frac{25}{131}\right)$	$e\left(\frac{119}{524}\right)$	$e\left(\frac{327}{1048}\right)$	$e\left(\frac{245}{1048}\right)$	$e\left(\frac{75}{262}\right)$	$e\left(\frac{227}{524}\right)$	$e\left(\frac{169}{524}\right)$	$e\left(\frac{283}{524}\right)$
$\chi_{1049}(24,\cdot)$	1049.h	1048	yes	$-1$	$1$	$e\left(\frac{107}{262}\right)$	$e\left(\frac{741}{1048}\right)$	$e\left(\frac{107}{131}\right)$	$e\left(\frac{153}{524}\right)$	$e\left(\frac{121}{1048}\right)$	$e\left(\frac{315}{1048}\right)$	$e\left(\frac{59}{262}\right)$	$e\left(\frac{217}{524}\right)$	$e\left(\frac{367}{524}\right)$	$e\left(\frac{289}{524}\right)$
$\chi_{1049}(25,\cdot)$	1049.f	262	yes	$1$	$1$	$e\left(\frac{61}{131}\right)$	$e\left(\frac{49}{262}\right)$	$e\left(\frac{122}{131}\right)$	$e\left(\frac{43}{131}\right)$	$e\left(\frac{171}{262}\right)$	$e\left(\frac{181}{262}\right)$	$e\left(\frac{52}{131}\right)$	$e\left(\frac{49}{131}\right)$	$e\left(\frac{104}{131}\right)$	$e\left(\frac{23}{131}\right)$
$\chi_{1049}(26,\cdot)$	1049.e	131	yes	$1$	$1$	$e\left(\frac{74}{131}\right)$	$e\left(\frac{92}{131}\right)$	$e\left(\frac{17}{131}\right)$	$e\left(\frac{108}{131}\right)$	$e\left(\frac{35}{131}\right)$	$e\left(\frac{11}{131}\right)$	$e\left(\frac{91}{131}\right)$	$e\left(\frac{53}{131}\right)$	$e\left(\frac{51}{131}\right)$	$e\left(\frac{73}{131}\right)$
$\chi_{1049}(27,\cdot)$	1049.h	1048	yes	$-1$	$1$	$e\left(\frac{185}{262}\right)$	$e\left(\frac{3}{1048}\right)$	$e\left(\frac{54}{131}\right)$	$e\left(\frac{147}{524}\right)$	$e\left(\frac{743}{1048}\right)$	$e\left(\frac{765}{1048}\right)$	$e\left(\frac{31}{262}\right)$	$e\left(\frac{3}{524}\right)$	$e\left(\frac{517}{524}\right)$	$e\left(\frac{103}{524}\right)$
$\chi_{1049}(28,\cdot)$	1049.h	1048	yes	$-1$	$1$	$e\left(\frac{239}{262}\right)$	$e\left(\frac{399}{1048}\right)$	$e\left(\frac{108}{131}\right)$	$e\left(\frac{163}{524}\right)$	$e\left(\frac{307}{1048}\right)$	$e\left(\frac{89}{1048}\right)$	$e\left(\frac{193}{262}\right)$	$e\left(\frac{399}{524}\right)$	$e\left(\frac{117}{524}\right)$	$e\left(\frac{75}{524}\right)$
$\chi_{1049}(29,\cdot)$	1049.f	262	yes	$1$	$1$	$e\left(\frac{92}{131}\right)$	$e\left(\frac{119}{262}\right)$	$e\left(\frac{53}{131}\right)$	$e\left(\frac{67}{131}\right)$	$e\left(\frac{41}{262}\right)$	$e\left(\frac{215}{262}\right)$	$e\left(\frac{14}{131}\right)$	$e\left(\frac{119}{131}\right)$	$e\left(\frac{28}{131}\right)$	$e\left(\frac{112}{131}\right)$
$\chi_{1049}(30,\cdot)$	1049.h	1048	yes	$-1$	$1$	$e\left(\frac{65}{262}\right)$	$e\left(\frac{695}{1048}\right)$	$e\left(\frac{65}{131}\right)$	$e\left(\frac{519}{524}\right)$	$e\left(\frac{955}{1048}\right)$	$e\left(\frac{113}{1048}\right)$	$e\left(\frac{195}{262}\right)$	$e\left(\frac{171}{524}\right)$	$e\left(\frac{125}{524}\right)$	$e\left(\frac{107}{524}\right)$
$\chi_{1049}(31,\cdot)$	1049.h	1048	yes	$-1$	$1$	$e\left(\frac{73}{262}\right)$	$e\left(\frac{841}{1048}\right)$	$e\left(\frac{73}{131}\right)$	$e\left(\frac{337}{524}\right)$	$e\left(\frac{85}{1048}\right)$	$e\left(\frac{663}{1048}\right)$	$e\left(\frac{219}{262}\right)$	$e\left(\frac{317}{524}\right)$	$e\left(\frac{483}{524}\right)$	$e\left(\frac{229}{524}\right)$
$\chi_{1049}(32,\cdot)$	1049.f	262	yes	$1$	$1$	$e\left(\frac{96}{131}\right)$	$e\left(\frac{221}{262}\right)$	$e\left(\frac{61}{131}\right)$	$e\left(\frac{87}{131}\right)$	$e\left(\frac{151}{262}\right)$	$e\left(\frac{25}{262}\right)$	$e\left(\frac{26}{131}\right)$	$e\left(\frac{90}{131}\right)$	$e\left(\frac{52}{131}\right)$	$e\left(\frac{77}{131}\right)$

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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	$1049$
Structure	\(C_{1048}\)
Order	$1048$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1049}(1,\cdot)\)	1049.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1049}(2,\cdot)\)	1049.f	262	yes	\(1\)	\(1\)	\(e\left(\frac{124}{131}\right)\)	\(e\left(\frac{149}{262}\right)\)	\(e\left(\frac{117}{131}\right)\)	\(e\left(\frac{96}{131}\right)\)	\(e\left(\frac{135}{262}\right)\)	\(e\left(\frac{5}{262}\right)\)	\(e\left(\frac{110}{131}\right)\)	\(e\left(\frac{18}{131}\right)\)	\(e\left(\frac{89}{131}\right)\)	\(e\left(\frac{94}{131}\right)\)
\(\chi_{1049}(3,\cdot)\)	1049.h	1048	yes	\(-1\)	\(1\)	\(e\left(\frac{149}{262}\right)\)	\(e\left(\frac{1}{1048}\right)\)	\(e\left(\frac{18}{131}\right)\)	\(e\left(\frac{49}{524}\right)\)	\(e\left(\frac{597}{1048}\right)\)	\(e\left(\frac{255}{1048}\right)\)	\(e\left(\frac{185}{262}\right)\)	\(e\left(\frac{1}{524}\right)\)	\(e\left(\frac{347}{524}\right)\)	\(e\left(\frac{209}{524}\right)\)
\(\chi_{1049}(4,\cdot)\)	1049.e	131	yes	\(1\)	\(1\)	\(e\left(\frac{117}{131}\right)\)	\(e\left(\frac{18}{131}\right)\)	\(e\left(\frac{103}{131}\right)\)	\(e\left(\frac{61}{131}\right)\)	\(e\left(\frac{4}{131}\right)\)	\(e\left(\frac{5}{131}\right)\)	\(e\left(\frac{89}{131}\right)\)	\(e\left(\frac{36}{131}\right)\)	\(e\left(\frac{47}{131}\right)\)	\(e\left(\frac{57}{131}\right)\)
\(\chi_{1049}(5,\cdot)\)	1049.g	524	yes	\(1\)	\(1\)	\(e\left(\frac{96}{131}\right)\)	\(e\left(\frac{49}{524}\right)\)	\(e\left(\frac{61}{131}\right)\)	\(e\left(\frac{43}{262}\right)\)	\(e\left(\frac{433}{524}\right)\)	\(e\left(\frac{443}{524}\right)\)	\(e\left(\frac{26}{131}\right)\)	\(e\left(\frac{49}{262}\right)\)	\(e\left(\frac{235}{262}\right)\)	\(e\left(\frac{23}{262}\right)\)
\(\chi_{1049}(6,\cdot)\)	1049.h	1048	yes	\(-1\)	\(1\)	\(e\left(\frac{135}{262}\right)\)	\(e\left(\frac{597}{1048}\right)\)	\(e\left(\frac{4}{131}\right)\)	\(e\left(\frac{433}{524}\right)\)	\(e\left(\frac{89}{1048}\right)\)	\(e\left(\frac{275}{1048}\right)\)	\(e\left(\frac{143}{262}\right)\)	\(e\left(\frac{73}{524}\right)\)	\(e\left(\frac{179}{524}\right)\)	\(e\left(\frac{61}{524}\right)\)
\(\chi_{1049}(7,\cdot)\)	1049.h	1048	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{262}\right)\)	\(e\left(\frac{255}{1048}\right)\)	\(e\left(\frac{5}{131}\right)\)	\(e\left(\frac{443}{524}\right)\)	\(e\left(\frac{275}{1048}\right)\)	\(e\left(\frac{49}{1048}\right)\)	\(e\left(\frac{15}{262}\right)\)	\(e\left(\frac{255}{524}\right)\)	\(e\left(\frac{453}{524}\right)\)	\(e\left(\frac{371}{524}\right)\)
\(\chi_{1049}(8,\cdot)\)	1049.f	262	yes	\(1\)	\(1\)	\(e\left(\frac{110}{131}\right)\)	\(e\left(\frac{185}{262}\right)\)	\(e\left(\frac{89}{131}\right)\)	\(e\left(\frac{26}{131}\right)\)	\(e\left(\frac{143}{262}\right)\)	\(e\left(\frac{15}{262}\right)\)	\(e\left(\frac{68}{131}\right)\)	\(e\left(\frac{54}{131}\right)\)	\(e\left(\frac{5}{131}\right)\)	\(e\left(\frac{20}{131}\right)\)
\(\chi_{1049}(9,\cdot)\)	1049.g	524	yes	\(1\)	\(1\)	\(e\left(\frac{18}{131}\right)\)	\(e\left(\frac{1}{524}\right)\)	\(e\left(\frac{36}{131}\right)\)	\(e\left(\frac{49}{262}\right)\)	\(e\left(\frac{73}{524}\right)\)	\(e\left(\frac{255}{524}\right)\)	\(e\left(\frac{54}{131}\right)\)	\(e\left(\frac{1}{262}\right)\)	\(e\left(\frac{85}{262}\right)\)	\(e\left(\frac{209}{262}\right)\)
\(\chi_{1049}(10,\cdot)\)	1049.g	524	yes	\(1\)	\(1\)	\(e\left(\frac{89}{131}\right)\)	\(e\left(\frac{347}{524}\right)\)	\(e\left(\frac{47}{131}\right)\)	\(e\left(\frac{235}{262}\right)\)	\(e\left(\frac{179}{524}\right)\)	\(e\left(\frac{453}{524}\right)\)	\(e\left(\frac{5}{131}\right)\)	\(e\left(\frac{85}{262}\right)\)	\(e\left(\frac{151}{262}\right)\)	\(e\left(\frac{211}{262}\right)\)
\(\chi_{1049}(11,\cdot)\)	1049.g	524	yes	\(1\)	\(1\)	\(e\left(\frac{94}{131}\right)\)	\(e\left(\frac{209}{524}\right)\)	\(e\left(\frac{57}{131}\right)\)	\(e\left(\frac{23}{262}\right)\)	\(e\left(\frac{61}{524}\right)\)	\(e\left(\frac{371}{524}\right)\)	\(e\left(\frac{20}{131}\right)\)	\(e\left(\frac{209}{262}\right)\)	\(e\left(\frac{211}{262}\right)\)	\(e\left(\frac{189}{262}\right)\)
\(\chi_{1049}(12,\cdot)\)	1049.h	1048	yes	\(-1\)	\(1\)	\(e\left(\frac{121}{262}\right)\)	\(e\left(\frac{145}{1048}\right)\)	\(e\left(\frac{121}{131}\right)\)	\(e\left(\frac{293}{524}\right)\)	\(e\left(\frac{629}{1048}\right)\)	\(e\left(\frac{295}{1048}\right)\)	\(e\left(\frac{101}{262}\right)\)	\(e\left(\frac{145}{524}\right)\)	\(e\left(\frac{11}{524}\right)\)	\(e\left(\frac{437}{524}\right)\)
\(\chi_{1049}(13,\cdot)\)	1049.f	262	yes	\(1\)	\(1\)	\(e\left(\frac{81}{131}\right)\)	\(e\left(\frac{35}{262}\right)\)	\(e\left(\frac{31}{131}\right)\)	\(e\left(\frac{12}{131}\right)\)	\(e\left(\frac{197}{262}\right)\)	\(e\left(\frac{17}{262}\right)\)	\(e\left(\frac{112}{131}\right)\)	\(e\left(\frac{35}{131}\right)\)	\(e\left(\frac{93}{131}\right)\)	\(e\left(\frac{110}{131}\right)\)
\(\chi_{1049}(14,\cdot)\)	1049.h	1048	yes	\(-1\)	\(1\)	\(e\left(\frac{253}{262}\right)\)	\(e\left(\frac{851}{1048}\right)\)	\(e\left(\frac{122}{131}\right)\)	\(e\left(\frac{303}{524}\right)\)	\(e\left(\frac{815}{1048}\right)\)	\(e\left(\frac{69}{1048}\right)\)	\(e\left(\frac{235}{262}\right)\)	\(e\left(\frac{327}{524}\right)\)	\(e\left(\frac{285}{524}\right)\)	\(e\left(\frac{223}{524}\right)\)
\(\chi_{1049}(15,\cdot)\)	1049.h	1048	yes	\(-1\)	\(1\)	\(e\left(\frac{79}{262}\right)\)	\(e\left(\frac{99}{1048}\right)\)	\(e\left(\frac{79}{131}\right)\)	\(e\left(\frac{135}{524}\right)\)	\(e\left(\frac{415}{1048}\right)\)	\(e\left(\frac{93}{1048}\right)\)	\(e\left(\frac{237}{262}\right)\)	\(e\left(\frac{99}{524}\right)\)	\(e\left(\frac{293}{524}\right)\)	\(e\left(\frac{255}{524}\right)\)
\(\chi_{1049}(16,\cdot)\)	1049.e	131	yes	\(1\)	\(1\)	\(e\left(\frac{103}{131}\right)\)	\(e\left(\frac{36}{131}\right)\)	\(e\left(\frac{75}{131}\right)\)	\(e\left(\frac{122}{131}\right)\)	\(e\left(\frac{8}{131}\right)\)	\(e\left(\frac{10}{131}\right)\)	\(e\left(\frac{47}{131}\right)\)	\(e\left(\frac{72}{131}\right)\)	\(e\left(\frac{94}{131}\right)\)	\(e\left(\frac{114}{131}\right)\)
\(\chi_{1049}(17,\cdot)\)	1049.h	1048	yes	\(-1\)	\(1\)	\(e\left(\frac{133}{262}\right)\)	\(e\left(\frac{757}{1048}\right)\)	\(e\left(\frac{2}{131}\right)\)	\(e\left(\frac{413}{524}\right)\)	\(e\left(\frac{241}{1048}\right)\)	\(e\left(\frac{203}{1048}\right)\)	\(e\left(\frac{137}{262}\right)\)	\(e\left(\frac{233}{524}\right)\)	\(e\left(\frac{155}{524}\right)\)	\(e\left(\frac{489}{524}\right)\)
\(\chi_{1049}(18,\cdot)\)	1049.g	524	yes	\(1\)	\(1\)	\(e\left(\frac{11}{131}\right)\)	\(e\left(\frac{299}{524}\right)\)	\(e\left(\frac{22}{131}\right)\)	\(e\left(\frac{241}{262}\right)\)	\(e\left(\frac{343}{524}\right)\)	\(e\left(\frac{265}{524}\right)\)	\(e\left(\frac{33}{131}\right)\)	\(e\left(\frac{37}{262}\right)\)	\(e\left(\frac{1}{262}\right)\)	\(e\left(\frac{135}{262}\right)\)
\(\chi_{1049}(19,\cdot)\)	1049.e	131	yes	\(1\)	\(1\)	\(e\left(\frac{58}{131}\right)\)	\(e\left(\frac{19}{131}\right)\)	\(e\left(\frac{116}{131}\right)\)	\(e\left(\frac{28}{131}\right)\)	\(e\left(\frac{77}{131}\right)\)	\(e\left(\frac{129}{131}\right)\)	\(e\left(\frac{43}{131}\right)\)	\(e\left(\frac{38}{131}\right)\)	\(e\left(\frac{86}{131}\right)\)	\(e\left(\frac{82}{131}\right)\)
\(\chi_{1049}(20,\cdot)\)	1049.g	524	yes	\(1\)	\(1\)	\(e\left(\frac{82}{131}\right)\)	\(e\left(\frac{121}{524}\right)\)	\(e\left(\frac{33}{131}\right)\)	\(e\left(\frac{165}{262}\right)\)	\(e\left(\frac{449}{524}\right)\)	\(e\left(\frac{463}{524}\right)\)	\(e\left(\frac{115}{131}\right)\)	\(e\left(\frac{121}{262}\right)\)	\(e\left(\frac{67}{262}\right)\)	\(e\left(\frac{137}{262}\right)\)
\(\chi_{1049}(21,\cdot)\)	1049.e	131	yes	\(1\)	\(1\)	\(e\left(\frac{77}{131}\right)\)	\(e\left(\frac{32}{131}\right)\)	\(e\left(\frac{23}{131}\right)\)	\(e\left(\frac{123}{131}\right)\)	\(e\left(\frac{109}{131}\right)\)	\(e\left(\frac{38}{131}\right)\)	\(e\left(\frac{100}{131}\right)\)	\(e\left(\frac{64}{131}\right)\)	\(e\left(\frac{69}{131}\right)\)	\(e\left(\frac{14}{131}\right)\)
\(\chi_{1049}(22,\cdot)\)	1049.g	524	yes	\(1\)	\(1\)	\(e\left(\frac{87}{131}\right)\)	\(e\left(\frac{507}{524}\right)\)	\(e\left(\frac{43}{131}\right)\)	\(e\left(\frac{215}{262}\right)\)	\(e\left(\frac{331}{524}\right)\)	\(e\left(\frac{381}{524}\right)\)	\(e\left(\frac{130}{131}\right)\)	\(e\left(\frac{245}{262}\right)\)	\(e\left(\frac{127}{262}\right)\)	\(e\left(\frac{115}{262}\right)\)
\(\chi_{1049}(23,\cdot)\)	1049.h	1048	yes	\(-1\)	\(1\)	\(e\left(\frac{25}{262}\right)\)	\(e\left(\frac{227}{1048}\right)\)	\(e\left(\frac{25}{131}\right)\)	\(e\left(\frac{119}{524}\right)\)	\(e\left(\frac{327}{1048}\right)\)	\(e\left(\frac{245}{1048}\right)\)	\(e\left(\frac{75}{262}\right)\)	\(e\left(\frac{227}{524}\right)\)	\(e\left(\frac{169}{524}\right)\)	\(e\left(\frac{283}{524}\right)\)
\(\chi_{1049}(24,\cdot)\)	1049.h	1048	yes	\(-1\)	\(1\)	\(e\left(\frac{107}{262}\right)\)	\(e\left(\frac{741}{1048}\right)\)	\(e\left(\frac{107}{131}\right)\)	\(e\left(\frac{153}{524}\right)\)	\(e\left(\frac{121}{1048}\right)\)	\(e\left(\frac{315}{1048}\right)\)	\(e\left(\frac{59}{262}\right)\)	\(e\left(\frac{217}{524}\right)\)	\(e\left(\frac{367}{524}\right)\)	\(e\left(\frac{289}{524}\right)\)
\(\chi_{1049}(25,\cdot)\)	1049.f	262	yes	\(1\)	\(1\)	\(e\left(\frac{61}{131}\right)\)	\(e\left(\frac{49}{262}\right)\)	\(e\left(\frac{122}{131}\right)\)	\(e\left(\frac{43}{131}\right)\)	\(e\left(\frac{171}{262}\right)\)	\(e\left(\frac{181}{262}\right)\)	\(e\left(\frac{52}{131}\right)\)	\(e\left(\frac{49}{131}\right)\)	\(e\left(\frac{104}{131}\right)\)	\(e\left(\frac{23}{131}\right)\)
\(\chi_{1049}(26,\cdot)\)	1049.e	131	yes	\(1\)	\(1\)	\(e\left(\frac{74}{131}\right)\)	\(e\left(\frac{92}{131}\right)\)	\(e\left(\frac{17}{131}\right)\)	\(e\left(\frac{108}{131}\right)\)	\(e\left(\frac{35}{131}\right)\)	\(e\left(\frac{11}{131}\right)\)	\(e\left(\frac{91}{131}\right)\)	\(e\left(\frac{53}{131}\right)\)	\(e\left(\frac{51}{131}\right)\)	\(e\left(\frac{73}{131}\right)\)
\(\chi_{1049}(27,\cdot)\)	1049.h	1048	yes	\(-1\)	\(1\)	\(e\left(\frac{185}{262}\right)\)	\(e\left(\frac{3}{1048}\right)\)	\(e\left(\frac{54}{131}\right)\)	\(e\left(\frac{147}{524}\right)\)	\(e\left(\frac{743}{1048}\right)\)	\(e\left(\frac{765}{1048}\right)\)	\(e\left(\frac{31}{262}\right)\)	\(e\left(\frac{3}{524}\right)\)	\(e\left(\frac{517}{524}\right)\)	\(e\left(\frac{103}{524}\right)\)
\(\chi_{1049}(28,\cdot)\)	1049.h	1048	yes	\(-1\)	\(1\)	\(e\left(\frac{239}{262}\right)\)	\(e\left(\frac{399}{1048}\right)\)	\(e\left(\frac{108}{131}\right)\)	\(e\left(\frac{163}{524}\right)\)	\(e\left(\frac{307}{1048}\right)\)	\(e\left(\frac{89}{1048}\right)\)	\(e\left(\frac{193}{262}\right)\)	\(e\left(\frac{399}{524}\right)\)	\(e\left(\frac{117}{524}\right)\)	\(e\left(\frac{75}{524}\right)\)
\(\chi_{1049}(29,\cdot)\)	1049.f	262	yes	\(1\)	\(1\)	\(e\left(\frac{92}{131}\right)\)	\(e\left(\frac{119}{262}\right)\)	\(e\left(\frac{53}{131}\right)\)	\(e\left(\frac{67}{131}\right)\)	\(e\left(\frac{41}{262}\right)\)	\(e\left(\frac{215}{262}\right)\)	\(e\left(\frac{14}{131}\right)\)	\(e\left(\frac{119}{131}\right)\)	\(e\left(\frac{28}{131}\right)\)	\(e\left(\frac{112}{131}\right)\)
\(\chi_{1049}(30,\cdot)\)	1049.h	1048	yes	\(-1\)	\(1\)	\(e\left(\frac{65}{262}\right)\)	\(e\left(\frac{695}{1048}\right)\)	\(e\left(\frac{65}{131}\right)\)	\(e\left(\frac{519}{524}\right)\)	\(e\left(\frac{955}{1048}\right)\)	\(e\left(\frac{113}{1048}\right)\)	\(e\left(\frac{195}{262}\right)\)	\(e\left(\frac{171}{524}\right)\)	\(e\left(\frac{125}{524}\right)\)	\(e\left(\frac{107}{524}\right)\)
\(\chi_{1049}(31,\cdot)\)	1049.h	1048	yes	\(-1\)	\(1\)	\(e\left(\frac{73}{262}\right)\)	\(e\left(\frac{841}{1048}\right)\)	\(e\left(\frac{73}{131}\right)\)	\(e\left(\frac{337}{524}\right)\)	\(e\left(\frac{85}{1048}\right)\)	\(e\left(\frac{663}{1048}\right)\)	\(e\left(\frac{219}{262}\right)\)	\(e\left(\frac{317}{524}\right)\)	\(e\left(\frac{483}{524}\right)\)	\(e\left(\frac{229}{524}\right)\)
\(\chi_{1049}(32,\cdot)\)	1049.f	262	yes	\(1\)	\(1\)	\(e\left(\frac{96}{131}\right)\)	\(e\left(\frac{221}{262}\right)\)	\(e\left(\frac{61}{131}\right)\)	\(e\left(\frac{87}{131}\right)\)	\(e\left(\frac{151}{262}\right)\)	\(e\left(\frac{25}{262}\right)\)	\(e\left(\frac{26}{131}\right)\)	\(e\left(\frac{90}{131}\right)\)	\(e\left(\frac{52}{131}\right)\)	\(e\left(\frac{77}{131}\right)\)

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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.