LMFDB - Group of Dirichlet characters of modulus 443

Show commands: PariGP / SageMath

sage: H = DirichletGroup(443)

pari: g = idealstar(,443,2)

Character group

sage: G.order() pari: g.no
Order	=	442
sage: H.invariants() pari: g.cyc
Structure	=	$C_{442}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{443}(2,\cdot)$

First 32 of 442 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{443}(1,\cdot)$	443.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{443}(2,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{1}{442}\right)$	$e\left(\frac{159}{221}\right)$	$e\left(\frac{1}{221}\right)$	$e\left(\frac{241}{442}\right)$	$e\left(\frac{319}{442}\right)$	$e\left(\frac{235}{442}\right)$	$e\left(\frac{3}{442}\right)$	$e\left(\frac{97}{221}\right)$	$e\left(\frac{121}{221}\right)$	$e\left(\frac{295}{442}\right)$
$\chi_{443}(3,\cdot)$	443.g	221	yes	$1$	$1$	$e\left(\frac{159}{221}\right)$	$e\left(\frac{174}{221}\right)$	$e\left(\frac{97}{221}\right)$	$e\left(\frac{86}{221}\right)$	$e\left(\frac{112}{221}\right)$	$e\left(\frac{16}{221}\right)$	$e\left(\frac{35}{221}\right)$	$e\left(\frac{127}{221}\right)$	$e\left(\frac{24}{221}\right)$	$e\left(\frac{53}{221}\right)$
$\chi_{443}(4,\cdot)$	443.g	221	yes	$1$	$1$	$e\left(\frac{1}{221}\right)$	$e\left(\frac{97}{221}\right)$	$e\left(\frac{2}{221}\right)$	$e\left(\frac{20}{221}\right)$	$e\left(\frac{98}{221}\right)$	$e\left(\frac{14}{221}\right)$	$e\left(\frac{3}{221}\right)$	$e\left(\frac{194}{221}\right)$	$e\left(\frac{21}{221}\right)$	$e\left(\frac{74}{221}\right)$
$\chi_{443}(5,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{241}{442}\right)$	$e\left(\frac{86}{221}\right)$	$e\left(\frac{20}{221}\right)$	$e\left(\frac{179}{442}\right)$	$e\left(\frac{413}{442}\right)$	$e\left(\frac{59}{442}\right)$	$e\left(\frac{281}{442}\right)$	$e\left(\frac{172}{221}\right)$	$e\left(\frac{210}{221}\right)$	$e\left(\frac{375}{442}\right)$
$\chi_{443}(6,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{319}{442}\right)$	$e\left(\frac{112}{221}\right)$	$e\left(\frac{98}{221}\right)$	$e\left(\frac{413}{442}\right)$	$e\left(\frac{101}{442}\right)$	$e\left(\frac{267}{442}\right)$	$e\left(\frac{73}{442}\right)$	$e\left(\frac{3}{221}\right)$	$e\left(\frac{145}{221}\right)$	$e\left(\frac{401}{442}\right)$
$\chi_{443}(7,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{235}{442}\right)$	$e\left(\frac{16}{221}\right)$	$e\left(\frac{14}{221}\right)$	$e\left(\frac{59}{442}\right)$	$e\left(\frac{267}{442}\right)$	$e\left(\frac{417}{442}\right)$	$e\left(\frac{263}{442}\right)$	$e\left(\frac{32}{221}\right)$	$e\left(\frac{147}{221}\right)$	$e\left(\frac{373}{442}\right)$
$\chi_{443}(8,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{3}{442}\right)$	$e\left(\frac{35}{221}\right)$	$e\left(\frac{3}{221}\right)$	$e\left(\frac{281}{442}\right)$	$e\left(\frac{73}{442}\right)$	$e\left(\frac{263}{442}\right)$	$e\left(\frac{9}{442}\right)$	$e\left(\frac{70}{221}\right)$	$e\left(\frac{142}{221}\right)$	$e\left(\frac{1}{442}\right)$
$\chi_{443}(9,\cdot)$	443.g	221	yes	$1$	$1$	$e\left(\frac{97}{221}\right)$	$e\left(\frac{127}{221}\right)$	$e\left(\frac{194}{221}\right)$	$e\left(\frac{172}{221}\right)$	$e\left(\frac{3}{221}\right)$	$e\left(\frac{32}{221}\right)$	$e\left(\frac{70}{221}\right)$	$e\left(\frac{33}{221}\right)$	$e\left(\frac{48}{221}\right)$	$e\left(\frac{106}{221}\right)$
$\chi_{443}(10,\cdot)$	443.g	221	yes	$1$	$1$	$e\left(\frac{121}{221}\right)$	$e\left(\frac{24}{221}\right)$	$e\left(\frac{21}{221}\right)$	$e\left(\frac{210}{221}\right)$	$e\left(\frac{145}{221}\right)$	$e\left(\frac{147}{221}\right)$	$e\left(\frac{142}{221}\right)$	$e\left(\frac{48}{221}\right)$	$e\left(\frac{110}{221}\right)$	$e\left(\frac{114}{221}\right)$
$\chi_{443}(11,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{295}{442}\right)$	$e\left(\frac{53}{221}\right)$	$e\left(\frac{74}{221}\right)$	$e\left(\frac{375}{442}\right)$	$e\left(\frac{401}{442}\right)$	$e\left(\frac{373}{442}\right)$	$e\left(\frac{1}{442}\right)$	$e\left(\frac{106}{221}\right)$	$e\left(\frac{114}{221}\right)$	$e\left(\frac{393}{442}\right)$
$\chi_{443}(12,\cdot)$	443.g	221	yes	$1$	$1$	$e\left(\frac{160}{221}\right)$	$e\left(\frac{50}{221}\right)$	$e\left(\frac{99}{221}\right)$	$e\left(\frac{106}{221}\right)$	$e\left(\frac{210}{221}\right)$	$e\left(\frac{30}{221}\right)$	$e\left(\frac{38}{221}\right)$	$e\left(\frac{100}{221}\right)$	$e\left(\frac{45}{221}\right)$	$e\left(\frac{127}{221}\right)$
$\chi_{443}(13,\cdot)$	443.d	17	yes	$1$	$1$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{15}{17}\right)$
$\chi_{443}(14,\cdot)$	443.g	221	yes	$1$	$1$	$e\left(\frac{118}{221}\right)$	$e\left(\frac{175}{221}\right)$	$e\left(\frac{15}{221}\right)$	$e\left(\frac{150}{221}\right)$	$e\left(\frac{72}{221}\right)$	$e\left(\frac{105}{221}\right)$	$e\left(\frac{133}{221}\right)$	$e\left(\frac{129}{221}\right)$	$e\left(\frac{47}{221}\right)$	$e\left(\frac{113}{221}\right)$
$\chi_{443}(15,\cdot)$	443.f	34	yes	$-1$	$1$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{7}{34}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{3}{34}\right)$
$\chi_{443}(16,\cdot)$	443.g	221	yes	$1$	$1$	$e\left(\frac{2}{221}\right)$	$e\left(\frac{194}{221}\right)$	$e\left(\frac{4}{221}\right)$	$e\left(\frac{40}{221}\right)$	$e\left(\frac{196}{221}\right)$	$e\left(\frac{28}{221}\right)$	$e\left(\frac{6}{221}\right)$	$e\left(\frac{167}{221}\right)$	$e\left(\frac{42}{221}\right)$	$e\left(\frac{148}{221}\right)$
$\chi_{443}(17,\cdot)$	443.g	221	yes	$1$	$1$	$e\left(\frac{188}{221}\right)$	$e\left(\frac{114}{221}\right)$	$e\left(\frac{155}{221}\right)$	$e\left(\frac{3}{221}\right)$	$e\left(\frac{81}{221}\right)$	$e\left(\frac{201}{221}\right)$	$e\left(\frac{122}{221}\right)$	$e\left(\frac{7}{221}\right)$	$e\left(\frac{191}{221}\right)$	$e\left(\frac{210}{221}\right)$
$\chi_{443}(18,\cdot)$	443.f	34	yes	$-1$	$1$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{23}{34}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{5}{34}\right)$
$\chi_{443}(19,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{407}{442}\right)$	$e\left(\frac{181}{221}\right)$	$e\left(\frac{186}{221}\right)$	$e\left(\frac{405}{442}\right)$	$e\left(\frac{327}{442}\right)$	$e\left(\frac{173}{442}\right)$	$e\left(\frac{337}{442}\right)$	$e\left(\frac{141}{221}\right)$	$e\left(\frac{185}{221}\right)$	$e\left(\frac{283}{442}\right)$
$\chi_{443}(20,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{243}{442}\right)$	$e\left(\frac{183}{221}\right)$	$e\left(\frac{22}{221}\right)$	$e\left(\frac{219}{442}\right)$	$e\left(\frac{167}{442}\right)$	$e\left(\frac{87}{442}\right)$	$e\left(\frac{287}{442}\right)$	$e\left(\frac{145}{221}\right)$	$e\left(\frac{10}{221}\right)$	$e\left(\frac{81}{442}\right)$
$\chi_{443}(21,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{111}{442}\right)$	$e\left(\frac{190}{221}\right)$	$e\left(\frac{111}{221}\right)$	$e\left(\frac{231}{442}\right)$	$e\left(\frac{49}{442}\right)$	$e\left(\frac{7}{442}\right)$	$e\left(\frac{333}{442}\right)$	$e\left(\frac{159}{221}\right)$	$e\left(\frac{171}{221}\right)$	$e\left(\frac{37}{442}\right)$
$\chi_{443}(22,\cdot)$	443.g	221	yes	$1$	$1$	$e\left(\frac{148}{221}\right)$	$e\left(\frac{212}{221}\right)$	$e\left(\frac{75}{221}\right)$	$e\left(\frac{87}{221}\right)$	$e\left(\frac{139}{221}\right)$	$e\left(\frac{83}{221}\right)$	$e\left(\frac{2}{221}\right)$	$e\left(\frac{203}{221}\right)$	$e\left(\frac{14}{221}\right)$	$e\left(\frac{123}{221}\right)$
$\chi_{443}(23,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{133}{442}\right)$	$e\left(\frac{152}{221}\right)$	$e\left(\frac{133}{221}\right)$	$e\left(\frac{229}{442}\right)$	$e\left(\frac{437}{442}\right)$	$e\left(\frac{315}{442}\right)$	$e\left(\frac{399}{442}\right)$	$e\left(\frac{83}{221}\right)$	$e\left(\frac{181}{221}\right)$	$e\left(\frac{339}{442}\right)$
$\chi_{443}(24,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{321}{442}\right)$	$e\left(\frac{209}{221}\right)$	$e\left(\frac{100}{221}\right)$	$e\left(\frac{11}{442}\right)$	$e\left(\frac{297}{442}\right)$	$e\left(\frac{295}{442}\right)$	$e\left(\frac{79}{442}\right)$	$e\left(\frac{197}{221}\right)$	$e\left(\frac{166}{221}\right)$	$e\left(\frac{107}{442}\right)$
$\chi_{443}(25,\cdot)$	443.g	221	yes	$1$	$1$	$e\left(\frac{20}{221}\right)$	$e\left(\frac{172}{221}\right)$	$e\left(\frac{40}{221}\right)$	$e\left(\frac{179}{221}\right)$	$e\left(\frac{192}{221}\right)$	$e\left(\frac{59}{221}\right)$	$e\left(\frac{60}{221}\right)$	$e\left(\frac{123}{221}\right)$	$e\left(\frac{199}{221}\right)$	$e\left(\frac{154}{221}\right)$
$\chi_{443}(26,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{287}{442}\right)$	$e\left(\frac{107}{221}\right)$	$e\left(\frac{66}{221}\right)$	$e\left(\frac{215}{442}\right)$	$e\left(\frac{59}{442}\right)$	$e\left(\frac{261}{442}\right)$	$e\left(\frac{419}{442}\right)$	$e\left(\frac{214}{221}\right)$	$e\left(\frac{30}{221}\right)$	$e\left(\frac{243}{442}\right)$
$\chi_{443}(27,\cdot)$	443.g	221	yes	$1$	$1$	$e\left(\frac{35}{221}\right)$	$e\left(\frac{80}{221}\right)$	$e\left(\frac{70}{221}\right)$	$e\left(\frac{37}{221}\right)$	$e\left(\frac{115}{221}\right)$	$e\left(\frac{48}{221}\right)$	$e\left(\frac{105}{221}\right)$	$e\left(\frac{160}{221}\right)$	$e\left(\frac{72}{221}\right)$	$e\left(\frac{159}{221}\right)$
$\chi_{443}(28,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{237}{442}\right)$	$e\left(\frac{113}{221}\right)$	$e\left(\frac{16}{221}\right)$	$e\left(\frac{99}{442}\right)$	$e\left(\frac{21}{442}\right)$	$e\left(\frac{3}{442}\right)$	$e\left(\frac{269}{442}\right)$	$e\left(\frac{5}{221}\right)$	$e\left(\frac{168}{221}\right)$	$e\left(\frac{79}{442}\right)$
$\chi_{443}(29,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{107}{442}\right)$	$e\left(\frac{217}{221}\right)$	$e\left(\frac{107}{221}\right)$	$e\left(\frac{151}{442}\right)$	$e\left(\frac{99}{442}\right)$	$e\left(\frac{393}{442}\right)$	$e\left(\frac{321}{442}\right)$	$e\left(\frac{213}{221}\right)$	$e\left(\frac{129}{221}\right)$	$e\left(\frac{183}{442}\right)$
$\chi_{443}(30,\cdot)$	443.g	221	yes	$1$	$1$	$e\left(\frac{59}{221}\right)$	$e\left(\frac{198}{221}\right)$	$e\left(\frac{118}{221}\right)$	$e\left(\frac{75}{221}\right)$	$e\left(\frac{36}{221}\right)$	$e\left(\frac{163}{221}\right)$	$e\left(\frac{177}{221}\right)$	$e\left(\frac{175}{221}\right)$	$e\left(\frac{134}{221}\right)$	$e\left(\frac{167}{221}\right)$
$\chi_{443}(31,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{179}{442}\right)$	$e\left(\frac{173}{221}\right)$	$e\left(\frac{179}{221}\right)$	$e\left(\frac{265}{442}\right)$	$e\left(\frac{83}{442}\right)$	$e\left(\frac{75}{442}\right)$	$e\left(\frac{95}{442}\right)$	$e\left(\frac{125}{221}\right)$	$e\left(\frac{1}{221}\right)$	$e\left(\frac{207}{442}\right)$
$\chi_{443}(32,\cdot)$	443.h	442	yes	$-1$	$1$	$e\left(\frac{5}{442}\right)$	$e\left(\frac{132}{221}\right)$	$e\left(\frac{5}{221}\right)$	$e\left(\frac{321}{442}\right)$	$e\left(\frac{269}{442}\right)$	$e\left(\frac{291}{442}\right)$	$e\left(\frac{15}{442}\right)$	$e\left(\frac{43}{221}\right)$	$e\left(\frac{163}{221}\right)$	$e\left(\frac{149}{442}\right)$

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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	$443$
Structure	\(C_{442}\)
Order	$442$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{443}(1,\cdot)\)	443.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{443}(2,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{1}{442}\right)\)	\(e\left(\frac{159}{221}\right)\)	\(e\left(\frac{1}{221}\right)\)	\(e\left(\frac{241}{442}\right)\)	\(e\left(\frac{319}{442}\right)\)	\(e\left(\frac{235}{442}\right)\)	\(e\left(\frac{3}{442}\right)\)	\(e\left(\frac{97}{221}\right)\)	\(e\left(\frac{121}{221}\right)\)	\(e\left(\frac{295}{442}\right)\)
\(\chi_{443}(3,\cdot)\)	443.g	221	yes	\(1\)	\(1\)	\(e\left(\frac{159}{221}\right)\)	\(e\left(\frac{174}{221}\right)\)	\(e\left(\frac{97}{221}\right)\)	\(e\left(\frac{86}{221}\right)\)	\(e\left(\frac{112}{221}\right)\)	\(e\left(\frac{16}{221}\right)\)	\(e\left(\frac{35}{221}\right)\)	\(e\left(\frac{127}{221}\right)\)	\(e\left(\frac{24}{221}\right)\)	\(e\left(\frac{53}{221}\right)\)
\(\chi_{443}(4,\cdot)\)	443.g	221	yes	\(1\)	\(1\)	\(e\left(\frac{1}{221}\right)\)	\(e\left(\frac{97}{221}\right)\)	\(e\left(\frac{2}{221}\right)\)	\(e\left(\frac{20}{221}\right)\)	\(e\left(\frac{98}{221}\right)\)	\(e\left(\frac{14}{221}\right)\)	\(e\left(\frac{3}{221}\right)\)	\(e\left(\frac{194}{221}\right)\)	\(e\left(\frac{21}{221}\right)\)	\(e\left(\frac{74}{221}\right)\)
\(\chi_{443}(5,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{241}{442}\right)\)	\(e\left(\frac{86}{221}\right)\)	\(e\left(\frac{20}{221}\right)\)	\(e\left(\frac{179}{442}\right)\)	\(e\left(\frac{413}{442}\right)\)	\(e\left(\frac{59}{442}\right)\)	\(e\left(\frac{281}{442}\right)\)	\(e\left(\frac{172}{221}\right)\)	\(e\left(\frac{210}{221}\right)\)	\(e\left(\frac{375}{442}\right)\)
\(\chi_{443}(6,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{319}{442}\right)\)	\(e\left(\frac{112}{221}\right)\)	\(e\left(\frac{98}{221}\right)\)	\(e\left(\frac{413}{442}\right)\)	\(e\left(\frac{101}{442}\right)\)	\(e\left(\frac{267}{442}\right)\)	\(e\left(\frac{73}{442}\right)\)	\(e\left(\frac{3}{221}\right)\)	\(e\left(\frac{145}{221}\right)\)	\(e\left(\frac{401}{442}\right)\)
\(\chi_{443}(7,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{235}{442}\right)\)	\(e\left(\frac{16}{221}\right)\)	\(e\left(\frac{14}{221}\right)\)	\(e\left(\frac{59}{442}\right)\)	\(e\left(\frac{267}{442}\right)\)	\(e\left(\frac{417}{442}\right)\)	\(e\left(\frac{263}{442}\right)\)	\(e\left(\frac{32}{221}\right)\)	\(e\left(\frac{147}{221}\right)\)	\(e\left(\frac{373}{442}\right)\)
\(\chi_{443}(8,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{442}\right)\)	\(e\left(\frac{35}{221}\right)\)	\(e\left(\frac{3}{221}\right)\)	\(e\left(\frac{281}{442}\right)\)	\(e\left(\frac{73}{442}\right)\)	\(e\left(\frac{263}{442}\right)\)	\(e\left(\frac{9}{442}\right)\)	\(e\left(\frac{70}{221}\right)\)	\(e\left(\frac{142}{221}\right)\)	\(e\left(\frac{1}{442}\right)\)
\(\chi_{443}(9,\cdot)\)	443.g	221	yes	\(1\)	\(1\)	\(e\left(\frac{97}{221}\right)\)	\(e\left(\frac{127}{221}\right)\)	\(e\left(\frac{194}{221}\right)\)	\(e\left(\frac{172}{221}\right)\)	\(e\left(\frac{3}{221}\right)\)	\(e\left(\frac{32}{221}\right)\)	\(e\left(\frac{70}{221}\right)\)	\(e\left(\frac{33}{221}\right)\)	\(e\left(\frac{48}{221}\right)\)	\(e\left(\frac{106}{221}\right)\)
\(\chi_{443}(10,\cdot)\)	443.g	221	yes	\(1\)	\(1\)	\(e\left(\frac{121}{221}\right)\)	\(e\left(\frac{24}{221}\right)\)	\(e\left(\frac{21}{221}\right)\)	\(e\left(\frac{210}{221}\right)\)	\(e\left(\frac{145}{221}\right)\)	\(e\left(\frac{147}{221}\right)\)	\(e\left(\frac{142}{221}\right)\)	\(e\left(\frac{48}{221}\right)\)	\(e\left(\frac{110}{221}\right)\)	\(e\left(\frac{114}{221}\right)\)
\(\chi_{443}(11,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{295}{442}\right)\)	\(e\left(\frac{53}{221}\right)\)	\(e\left(\frac{74}{221}\right)\)	\(e\left(\frac{375}{442}\right)\)	\(e\left(\frac{401}{442}\right)\)	\(e\left(\frac{373}{442}\right)\)	\(e\left(\frac{1}{442}\right)\)	\(e\left(\frac{106}{221}\right)\)	\(e\left(\frac{114}{221}\right)\)	\(e\left(\frac{393}{442}\right)\)
\(\chi_{443}(12,\cdot)\)	443.g	221	yes	\(1\)	\(1\)	\(e\left(\frac{160}{221}\right)\)	\(e\left(\frac{50}{221}\right)\)	\(e\left(\frac{99}{221}\right)\)	\(e\left(\frac{106}{221}\right)\)	\(e\left(\frac{210}{221}\right)\)	\(e\left(\frac{30}{221}\right)\)	\(e\left(\frac{38}{221}\right)\)	\(e\left(\frac{100}{221}\right)\)	\(e\left(\frac{45}{221}\right)\)	\(e\left(\frac{127}{221}\right)\)
\(\chi_{443}(13,\cdot)\)	443.d	17	yes	\(1\)	\(1\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)
\(\chi_{443}(14,\cdot)\)	443.g	221	yes	\(1\)	\(1\)	\(e\left(\frac{118}{221}\right)\)	\(e\left(\frac{175}{221}\right)\)	\(e\left(\frac{15}{221}\right)\)	\(e\left(\frac{150}{221}\right)\)	\(e\left(\frac{72}{221}\right)\)	\(e\left(\frac{105}{221}\right)\)	\(e\left(\frac{133}{221}\right)\)	\(e\left(\frac{129}{221}\right)\)	\(e\left(\frac{47}{221}\right)\)	\(e\left(\frac{113}{221}\right)\)
\(\chi_{443}(15,\cdot)\)	443.f	34	yes	\(-1\)	\(1\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{7}{34}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{3}{34}\right)\)
\(\chi_{443}(16,\cdot)\)	443.g	221	yes	\(1\)	\(1\)	\(e\left(\frac{2}{221}\right)\)	\(e\left(\frac{194}{221}\right)\)	\(e\left(\frac{4}{221}\right)\)	\(e\left(\frac{40}{221}\right)\)	\(e\left(\frac{196}{221}\right)\)	\(e\left(\frac{28}{221}\right)\)	\(e\left(\frac{6}{221}\right)\)	\(e\left(\frac{167}{221}\right)\)	\(e\left(\frac{42}{221}\right)\)	\(e\left(\frac{148}{221}\right)\)
\(\chi_{443}(17,\cdot)\)	443.g	221	yes	\(1\)	\(1\)	\(e\left(\frac{188}{221}\right)\)	\(e\left(\frac{114}{221}\right)\)	\(e\left(\frac{155}{221}\right)\)	\(e\left(\frac{3}{221}\right)\)	\(e\left(\frac{81}{221}\right)\)	\(e\left(\frac{201}{221}\right)\)	\(e\left(\frac{122}{221}\right)\)	\(e\left(\frac{7}{221}\right)\)	\(e\left(\frac{191}{221}\right)\)	\(e\left(\frac{210}{221}\right)\)
\(\chi_{443}(18,\cdot)\)	443.f	34	yes	\(-1\)	\(1\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{23}{34}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{5}{34}\right)\)
\(\chi_{443}(19,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{407}{442}\right)\)	\(e\left(\frac{181}{221}\right)\)	\(e\left(\frac{186}{221}\right)\)	\(e\left(\frac{405}{442}\right)\)	\(e\left(\frac{327}{442}\right)\)	\(e\left(\frac{173}{442}\right)\)	\(e\left(\frac{337}{442}\right)\)	\(e\left(\frac{141}{221}\right)\)	\(e\left(\frac{185}{221}\right)\)	\(e\left(\frac{283}{442}\right)\)
\(\chi_{443}(20,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{243}{442}\right)\)	\(e\left(\frac{183}{221}\right)\)	\(e\left(\frac{22}{221}\right)\)	\(e\left(\frac{219}{442}\right)\)	\(e\left(\frac{167}{442}\right)\)	\(e\left(\frac{87}{442}\right)\)	\(e\left(\frac{287}{442}\right)\)	\(e\left(\frac{145}{221}\right)\)	\(e\left(\frac{10}{221}\right)\)	\(e\left(\frac{81}{442}\right)\)
\(\chi_{443}(21,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{111}{442}\right)\)	\(e\left(\frac{190}{221}\right)\)	\(e\left(\frac{111}{221}\right)\)	\(e\left(\frac{231}{442}\right)\)	\(e\left(\frac{49}{442}\right)\)	\(e\left(\frac{7}{442}\right)\)	\(e\left(\frac{333}{442}\right)\)	\(e\left(\frac{159}{221}\right)\)	\(e\left(\frac{171}{221}\right)\)	\(e\left(\frac{37}{442}\right)\)
\(\chi_{443}(22,\cdot)\)	443.g	221	yes	\(1\)	\(1\)	\(e\left(\frac{148}{221}\right)\)	\(e\left(\frac{212}{221}\right)\)	\(e\left(\frac{75}{221}\right)\)	\(e\left(\frac{87}{221}\right)\)	\(e\left(\frac{139}{221}\right)\)	\(e\left(\frac{83}{221}\right)\)	\(e\left(\frac{2}{221}\right)\)	\(e\left(\frac{203}{221}\right)\)	\(e\left(\frac{14}{221}\right)\)	\(e\left(\frac{123}{221}\right)\)
\(\chi_{443}(23,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{133}{442}\right)\)	\(e\left(\frac{152}{221}\right)\)	\(e\left(\frac{133}{221}\right)\)	\(e\left(\frac{229}{442}\right)\)	\(e\left(\frac{437}{442}\right)\)	\(e\left(\frac{315}{442}\right)\)	\(e\left(\frac{399}{442}\right)\)	\(e\left(\frac{83}{221}\right)\)	\(e\left(\frac{181}{221}\right)\)	\(e\left(\frac{339}{442}\right)\)
\(\chi_{443}(24,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{321}{442}\right)\)	\(e\left(\frac{209}{221}\right)\)	\(e\left(\frac{100}{221}\right)\)	\(e\left(\frac{11}{442}\right)\)	\(e\left(\frac{297}{442}\right)\)	\(e\left(\frac{295}{442}\right)\)	\(e\left(\frac{79}{442}\right)\)	\(e\left(\frac{197}{221}\right)\)	\(e\left(\frac{166}{221}\right)\)	\(e\left(\frac{107}{442}\right)\)
\(\chi_{443}(25,\cdot)\)	443.g	221	yes	\(1\)	\(1\)	\(e\left(\frac{20}{221}\right)\)	\(e\left(\frac{172}{221}\right)\)	\(e\left(\frac{40}{221}\right)\)	\(e\left(\frac{179}{221}\right)\)	\(e\left(\frac{192}{221}\right)\)	\(e\left(\frac{59}{221}\right)\)	\(e\left(\frac{60}{221}\right)\)	\(e\left(\frac{123}{221}\right)\)	\(e\left(\frac{199}{221}\right)\)	\(e\left(\frac{154}{221}\right)\)
\(\chi_{443}(26,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{287}{442}\right)\)	\(e\left(\frac{107}{221}\right)\)	\(e\left(\frac{66}{221}\right)\)	\(e\left(\frac{215}{442}\right)\)	\(e\left(\frac{59}{442}\right)\)	\(e\left(\frac{261}{442}\right)\)	\(e\left(\frac{419}{442}\right)\)	\(e\left(\frac{214}{221}\right)\)	\(e\left(\frac{30}{221}\right)\)	\(e\left(\frac{243}{442}\right)\)
\(\chi_{443}(27,\cdot)\)	443.g	221	yes	\(1\)	\(1\)	\(e\left(\frac{35}{221}\right)\)	\(e\left(\frac{80}{221}\right)\)	\(e\left(\frac{70}{221}\right)\)	\(e\left(\frac{37}{221}\right)\)	\(e\left(\frac{115}{221}\right)\)	\(e\left(\frac{48}{221}\right)\)	\(e\left(\frac{105}{221}\right)\)	\(e\left(\frac{160}{221}\right)\)	\(e\left(\frac{72}{221}\right)\)	\(e\left(\frac{159}{221}\right)\)
\(\chi_{443}(28,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{237}{442}\right)\)	\(e\left(\frac{113}{221}\right)\)	\(e\left(\frac{16}{221}\right)\)	\(e\left(\frac{99}{442}\right)\)	\(e\left(\frac{21}{442}\right)\)	\(e\left(\frac{3}{442}\right)\)	\(e\left(\frac{269}{442}\right)\)	\(e\left(\frac{5}{221}\right)\)	\(e\left(\frac{168}{221}\right)\)	\(e\left(\frac{79}{442}\right)\)
\(\chi_{443}(29,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{107}{442}\right)\)	\(e\left(\frac{217}{221}\right)\)	\(e\left(\frac{107}{221}\right)\)	\(e\left(\frac{151}{442}\right)\)	\(e\left(\frac{99}{442}\right)\)	\(e\left(\frac{393}{442}\right)\)	\(e\left(\frac{321}{442}\right)\)	\(e\left(\frac{213}{221}\right)\)	\(e\left(\frac{129}{221}\right)\)	\(e\left(\frac{183}{442}\right)\)
\(\chi_{443}(30,\cdot)\)	443.g	221	yes	\(1\)	\(1\)	\(e\left(\frac{59}{221}\right)\)	\(e\left(\frac{198}{221}\right)\)	\(e\left(\frac{118}{221}\right)\)	\(e\left(\frac{75}{221}\right)\)	\(e\left(\frac{36}{221}\right)\)	\(e\left(\frac{163}{221}\right)\)	\(e\left(\frac{177}{221}\right)\)	\(e\left(\frac{175}{221}\right)\)	\(e\left(\frac{134}{221}\right)\)	\(e\left(\frac{167}{221}\right)\)
\(\chi_{443}(31,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{179}{442}\right)\)	\(e\left(\frac{173}{221}\right)\)	\(e\left(\frac{179}{221}\right)\)	\(e\left(\frac{265}{442}\right)\)	\(e\left(\frac{83}{442}\right)\)	\(e\left(\frac{75}{442}\right)\)	\(e\left(\frac{95}{442}\right)\)	\(e\left(\frac{125}{221}\right)\)	\(e\left(\frac{1}{221}\right)\)	\(e\left(\frac{207}{442}\right)\)
\(\chi_{443}(32,\cdot)\)	443.h	442	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{442}\right)\)	\(e\left(\frac{132}{221}\right)\)	\(e\left(\frac{5}{221}\right)\)	\(e\left(\frac{321}{442}\right)\)	\(e\left(\frac{269}{442}\right)\)	\(e\left(\frac{291}{442}\right)\)	\(e\left(\frac{15}{442}\right)\)	\(e\left(\frac{43}{221}\right)\)	\(e\left(\frac{163}{221}\right)\)	\(e\left(\frac{149}{442}\right)\)

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Character group

First 32 of 442 characters

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.