LMFDB - Group of Dirichlet characters of modulus 4729

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4729)

pari: g = idealstar(,4729,2)

Character group

sage: G.order() pari: g.no
Order	=	4728
sage: H.invariants() pari: g.cyc
Structure	=	$C_{4728}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4729}(17,\cdot)$

First 32 of 4728 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{4729}(1,\cdot)$	4729.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4729}(2,\cdot)$	4729.l	788	yes	$1$	$1$	$e\left(\frac{153}{394}\right)$	$e\left(\frac{171}{394}\right)$	$e\left(\frac{153}{197}\right)$	$e\left(\frac{87}{394}\right)$	$e\left(\frac{162}{197}\right)$	$e\left(\frac{13}{394}\right)$	$e\left(\frac{65}{394}\right)$	$e\left(\frac{171}{197}\right)$	$e\left(\frac{120}{197}\right)$	$e\left(\frac{143}{788}\right)$
$\chi_{4729}(3,\cdot)$	4729.l	788	yes	$1$	$1$	$e\left(\frac{171}{394}\right)$	$e\left(\frac{307}{394}\right)$	$e\left(\frac{171}{197}\right)$	$e\left(\frac{329}{394}\right)$	$e\left(\frac{42}{197}\right)$	$e\left(\frac{339}{394}\right)$	$e\left(\frac{119}{394}\right)$	$e\left(\frac{110}{197}\right)$	$e\left(\frac{53}{197}\right)$	$e\left(\frac{183}{788}\right)$
$\chi_{4729}(4,\cdot)$	4729.j	394	yes	$1$	$1$	$e\left(\frac{153}{197}\right)$	$e\left(\frac{171}{197}\right)$	$e\left(\frac{109}{197}\right)$	$e\left(\frac{87}{197}\right)$	$e\left(\frac{127}{197}\right)$	$e\left(\frac{13}{197}\right)$	$e\left(\frac{65}{197}\right)$	$e\left(\frac{145}{197}\right)$	$e\left(\frac{43}{197}\right)$	$e\left(\frac{143}{394}\right)$
$\chi_{4729}(5,\cdot)$	4729.o	2364	yes	$1$	$1$	$e\left(\frac{87}{394}\right)$	$e\left(\frac{329}{394}\right)$	$e\left(\frac{87}{197}\right)$	$e\left(\frac{751}{1182}\right)$	$e\left(\frac{11}{197}\right)$	$e\left(\frac{787}{1182}\right)$	$e\left(\frac{261}{394}\right)$	$e\left(\frac{132}{197}\right)$	$e\left(\frac{506}{591}\right)$	$e\left(\frac{259}{788}\right)$
$\chi_{4729}(6,\cdot)$	4729.j	394	yes	$1$	$1$	$e\left(\frac{162}{197}\right)$	$e\left(\frac{42}{197}\right)$	$e\left(\frac{127}{197}\right)$	$e\left(\frac{11}{197}\right)$	$e\left(\frac{7}{197}\right)$	$e\left(\frac{176}{197}\right)$	$e\left(\frac{92}{197}\right)$	$e\left(\frac{84}{197}\right)$	$e\left(\frac{173}{197}\right)$	$e\left(\frac{163}{394}\right)$
$\chi_{4729}(7,\cdot)$	4729.o	2364	yes	$1$	$1$	$e\left(\frac{13}{394}\right)$	$e\left(\frac{339}{394}\right)$	$e\left(\frac{13}{197}\right)$	$e\left(\frac{787}{1182}\right)$	$e\left(\frac{176}{197}\right)$	$e\left(\frac{181}{1182}\right)$	$e\left(\frac{39}{394}\right)$	$e\left(\frac{142}{197}\right)$	$e\left(\frac{413}{591}\right)$	$e\left(\frac{401}{788}\right)$
$\chi_{4729}(8,\cdot)$	4729.l	788	yes	$1$	$1$	$e\left(\frac{65}{394}\right)$	$e\left(\frac{119}{394}\right)$	$e\left(\frac{65}{197}\right)$	$e\left(\frac{261}{394}\right)$	$e\left(\frac{92}{197}\right)$	$e\left(\frac{39}{394}\right)$	$e\left(\frac{195}{394}\right)$	$e\left(\frac{119}{197}\right)$	$e\left(\frac{163}{197}\right)$	$e\left(\frac{429}{788}\right)$
$\chi_{4729}(9,\cdot)$	4729.j	394	yes	$1$	$1$	$e\left(\frac{171}{197}\right)$	$e\left(\frac{110}{197}\right)$	$e\left(\frac{145}{197}\right)$	$e\left(\frac{132}{197}\right)$	$e\left(\frac{84}{197}\right)$	$e\left(\frac{142}{197}\right)$	$e\left(\frac{119}{197}\right)$	$e\left(\frac{23}{197}\right)$	$e\left(\frac{106}{197}\right)$	$e\left(\frac{183}{394}\right)$
$\chi_{4729}(10,\cdot)$	4729.m	1182	yes	$1$	$1$	$e\left(\frac{120}{197}\right)$	$e\left(\frac{53}{197}\right)$	$e\left(\frac{43}{197}\right)$	$e\left(\frac{506}{591}\right)$	$e\left(\frac{173}{197}\right)$	$e\left(\frac{413}{591}\right)$	$e\left(\frac{163}{197}\right)$	$e\left(\frac{106}{197}\right)$	$e\left(\frac{275}{591}\right)$	$e\left(\frac{201}{394}\right)$
$\chi_{4729}(11,\cdot)$	4729.n	1576	yes	$-1$	$1$	$e\left(\frac{143}{788}\right)$	$e\left(\frac{183}{788}\right)$	$e\left(\frac{143}{394}\right)$	$e\left(\frac{259}{788}\right)$	$e\left(\frac{163}{394}\right)$	$e\left(\frac{401}{788}\right)$	$e\left(\frac{429}{788}\right)$	$e\left(\frac{183}{394}\right)$	$e\left(\frac{201}{394}\right)$	$e\left(\frac{1259}{1576}\right)$
$\chi_{4729}(12,\cdot)$	4729.l	788	yes	$1$	$1$	$e\left(\frac{83}{394}\right)$	$e\left(\frac{255}{394}\right)$	$e\left(\frac{83}{197}\right)$	$e\left(\frac{109}{394}\right)$	$e\left(\frac{169}{197}\right)$	$e\left(\frac{365}{394}\right)$	$e\left(\frac{249}{394}\right)$	$e\left(\frac{58}{197}\right)$	$e\left(\frac{96}{197}\right)$	$e\left(\frac{469}{788}\right)$
$\chi_{4729}(13,\cdot)$	4729.m	1182	yes	$1$	$1$	$e\left(\frac{160}{197}\right)$	$e\left(\frac{5}{197}\right)$	$e\left(\frac{123}{197}\right)$	$e\left(\frac{215}{591}\right)$	$e\left(\frac{165}{197}\right)$	$e\left(\frac{485}{591}\right)$	$e\left(\frac{86}{197}\right)$	$e\left(\frac{10}{197}\right)$	$e\left(\frac{104}{591}\right)$	$e\left(\frac{71}{394}\right)$
$\chi_{4729}(14,\cdot)$	4729.k	591	yes	$1$	$1$	$e\left(\frac{83}{197}\right)$	$e\left(\frac{58}{197}\right)$	$e\left(\frac{166}{197}\right)$	$e\left(\frac{524}{591}\right)$	$e\left(\frac{141}{197}\right)$	$e\left(\frac{110}{591}\right)$	$e\left(\frac{52}{197}\right)$	$e\left(\frac{116}{197}\right)$	$e\left(\frac{182}{591}\right)$	$e\left(\frac{136}{197}\right)$
$\chi_{4729}(15,\cdot)$	4729.m	1182	yes	$1$	$1$	$e\left(\frac{129}{197}\right)$	$e\left(\frac{121}{197}\right)$	$e\left(\frac{61}{197}\right)$	$e\left(\frac{278}{591}\right)$	$e\left(\frac{53}{197}\right)$	$e\left(\frac{311}{591}\right)$	$e\left(\frac{190}{197}\right)$	$e\left(\frac{45}{197}\right)$	$e\left(\frac{74}{591}\right)$	$e\left(\frac{221}{394}\right)$
$\chi_{4729}(16,\cdot)$	4729.i	197	yes	$1$	$1$	$e\left(\frac{109}{197}\right)$	$e\left(\frac{145}{197}\right)$	$e\left(\frac{21}{197}\right)$	$e\left(\frac{174}{197}\right)$	$e\left(\frac{57}{197}\right)$	$e\left(\frac{26}{197}\right)$	$e\left(\frac{130}{197}\right)$	$e\left(\frac{93}{197}\right)$	$e\left(\frac{86}{197}\right)$	$e\left(\frac{143}{197}\right)$
$\chi_{4729}(17,\cdot)$	4729.p	4728	yes	$-1$	$1$	$e\left(\frac{53}{788}\right)$	$e\left(\frac{685}{788}\right)$	$e\left(\frac{53}{394}\right)$	$e\left(\frac{299}{2364}\right)$	$e\left(\frac{369}{394}\right)$	$e\left(\frac{1829}{2364}\right)$	$e\left(\frac{159}{788}\right)$	$e\left(\frac{291}{394}\right)$	$e\left(\frac{229}{1182}\right)$	$e\left(\frac{1453}{1576}\right)$
$\chi_{4729}(18,\cdot)$	4729.l	788	yes	$1$	$1$	$e\left(\frac{101}{394}\right)$	$e\left(\frac{391}{394}\right)$	$e\left(\frac{101}{197}\right)$	$e\left(\frac{351}{394}\right)$	$e\left(\frac{49}{197}\right)$	$e\left(\frac{297}{394}\right)$	$e\left(\frac{303}{394}\right)$	$e\left(\frac{194}{197}\right)$	$e\left(\frac{29}{197}\right)$	$e\left(\frac{509}{788}\right)$
$\chi_{4729}(19,\cdot)$	4729.k	591	yes	$1$	$1$	$e\left(\frac{82}{197}\right)$	$e\left(\frac{138}{197}\right)$	$e\left(\frac{164}{197}\right)$	$e\left(\frac{221}{591}\right)$	$e\left(\frac{23}{197}\right)$	$e\left(\frac{581}{591}\right)$	$e\left(\frac{49}{197}\right)$	$e\left(\frac{79}{197}\right)$	$e\left(\frac{467}{591}\right)$	$e\left(\frac{113}{197}\right)$
$\chi_{4729}(20,\cdot)$	4729.o	2364	yes	$1$	$1$	$e\left(\frac{393}{394}\right)$	$e\left(\frac{277}{394}\right)$	$e\left(\frac{196}{197}\right)$	$e\left(\frac{91}{1182}\right)$	$e\left(\frac{138}{197}\right)$	$e\left(\frac{865}{1182}\right)$	$e\left(\frac{391}{394}\right)$	$e\left(\frac{80}{197}\right)$	$e\left(\frac{44}{591}\right)$	$e\left(\frac{545}{788}\right)$
$\chi_{4729}(21,\cdot)$	4729.k	591	yes	$1$	$1$	$e\left(\frac{92}{197}\right)$	$e\left(\frac{126}{197}\right)$	$e\left(\frac{184}{197}\right)$	$e\left(\frac{296}{591}\right)$	$e\left(\frac{21}{197}\right)$	$e\left(\frac{8}{591}\right)$	$e\left(\frac{79}{197}\right)$	$e\left(\frac{55}{197}\right)$	$e\left(\frac{572}{591}\right)$	$e\left(\frac{146}{197}\right)$
$\chi_{4729}(22,\cdot)$	4729.n	1576	yes	$-1$	$1$	$e\left(\frac{449}{788}\right)$	$e\left(\frac{525}{788}\right)$	$e\left(\frac{55}{394}\right)$	$e\left(\frac{433}{788}\right)$	$e\left(\frac{93}{394}\right)$	$e\left(\frac{427}{788}\right)$	$e\left(\frac{559}{788}\right)$	$e\left(\frac{131}{394}\right)$	$e\left(\frac{47}{394}\right)$	$e\left(\frac{1545}{1576}\right)$
$\chi_{4729}(23,\cdot)$	4729.n	1576	yes	$-1$	$1$	$e\left(\frac{29}{788}\right)$	$e\left(\frac{241}{788}\right)$	$e\left(\frac{29}{394}\right)$	$e\left(\frac{565}{788}\right)$	$e\left(\frac{135}{394}\right)$	$e\left(\frac{175}{788}\right)$	$e\left(\frac{87}{788}\right)$	$e\left(\frac{241}{394}\right)$	$e\left(\frac{297}{394}\right)$	$e\left(\frac{349}{1576}\right)$
$\chi_{4729}(24,\cdot)$	4729.i	197	yes	$1$	$1$	$e\left(\frac{118}{197}\right)$	$e\left(\frac{16}{197}\right)$	$e\left(\frac{39}{197}\right)$	$e\left(\frac{98}{197}\right)$	$e\left(\frac{134}{197}\right)$	$e\left(\frac{189}{197}\right)$	$e\left(\frac{157}{197}\right)$	$e\left(\frac{32}{197}\right)$	$e\left(\frac{19}{197}\right)$	$e\left(\frac{153}{197}\right)$
$\chi_{4729}(25,\cdot)$	4729.m	1182	yes	$1$	$1$	$e\left(\frac{87}{197}\right)$	$e\left(\frac{132}{197}\right)$	$e\left(\frac{174}{197}\right)$	$e\left(\frac{160}{591}\right)$	$e\left(\frac{22}{197}\right)$	$e\left(\frac{196}{591}\right)$	$e\left(\frac{64}{197}\right)$	$e\left(\frac{67}{197}\right)$	$e\left(\frac{421}{591}\right)$	$e\left(\frac{259}{394}\right)$
$\chi_{4729}(26,\cdot)$	4729.o	2364	yes	$1$	$1$	$e\left(\frac{79}{394}\right)$	$e\left(\frac{181}{394}\right)$	$e\left(\frac{79}{197}\right)$	$e\left(\frac{691}{1182}\right)$	$e\left(\frac{130}{197}\right)$	$e\left(\frac{1009}{1182}\right)$	$e\left(\frac{237}{394}\right)$	$e\left(\frac{181}{197}\right)$	$e\left(\frac{464}{591}\right)$	$e\left(\frac{285}{788}\right)$
$\chi_{4729}(27,\cdot)$	4729.l	788	yes	$1$	$1$	$e\left(\frac{119}{394}\right)$	$e\left(\frac{133}{394}\right)$	$e\left(\frac{119}{197}\right)$	$e\left(\frac{199}{394}\right)$	$e\left(\frac{126}{197}\right)$	$e\left(\frac{229}{394}\right)$	$e\left(\frac{357}{394}\right)$	$e\left(\frac{133}{197}\right)$	$e\left(\frac{159}{197}\right)$	$e\left(\frac{549}{788}\right)$
$\chi_{4729}(28,\cdot)$	4729.o	2364	yes	$1$	$1$	$e\left(\frac{319}{394}\right)$	$e\left(\frac{287}{394}\right)$	$e\left(\frac{122}{197}\right)$	$e\left(\frac{127}{1182}\right)$	$e\left(\frac{106}{197}\right)$	$e\left(\frac{259}{1182}\right)$	$e\left(\frac{169}{394}\right)$	$e\left(\frac{90}{197}\right)$	$e\left(\frac{542}{591}\right)$	$e\left(\frac{687}{788}\right)$
$\chi_{4729}(29,\cdot)$	4729.n	1576	yes	$-1$	$1$	$e\left(\frac{285}{788}\right)$	$e\left(\frac{249}{788}\right)$	$e\left(\frac{285}{394}\right)$	$e\left(\frac{417}{788}\right)$	$e\left(\frac{267}{394}\right)$	$e\left(\frac{171}{788}\right)$	$e\left(\frac{67}{788}\right)$	$e\left(\frac{249}{394}\right)$	$e\left(\frac{351}{394}\right)$	$e\left(\frac{1093}{1576}\right)$
$\chi_{4729}(30,\cdot)$	4729.o	2364	yes	$1$	$1$	$e\left(\frac{17}{394}\right)$	$e\left(\frac{19}{394}\right)$	$e\left(\frac{17}{197}\right)$	$e\left(\frac{817}{1182}\right)$	$e\left(\frac{18}{197}\right)$	$e\left(\frac{661}{1182}\right)$	$e\left(\frac{51}{394}\right)$	$e\left(\frac{19}{197}\right)$	$e\left(\frac{434}{591}\right)$	$e\left(\frac{585}{788}\right)$
$\chi_{4729}(31,\cdot)$	4729.n	1576	yes	$-1$	$1$	$e\left(\frac{383}{788}\right)$	$e\left(\frac{683}{788}\right)$	$e\left(\frac{383}{394}\right)$	$e\left(\frac{71}{788}\right)$	$e\left(\frac{139}{394}\right)$	$e\left(\frac{545}{788}\right)$	$e\left(\frac{361}{788}\right)$	$e\left(\frac{289}{394}\right)$	$e\left(\frac{227}{394}\right)$	$e\left(\frac{479}{1576}\right)$
$\chi_{4729}(32,\cdot)$	4729.l	788	yes	$1$	$1$	$e\left(\frac{371}{394}\right)$	$e\left(\frac{67}{394}\right)$	$e\left(\frac{174}{197}\right)$	$e\left(\frac{41}{394}\right)$	$e\left(\frac{22}{197}\right)$	$e\left(\frac{65}{394}\right)$	$e\left(\frac{325}{394}\right)$	$e\left(\frac{67}{197}\right)$	$e\left(\frac{9}{197}\right)$	$e\left(\frac{715}{788}\right)$

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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	$4729$
Structure	\(C_{4728}\)
Order	$4728$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{4729}(1,\cdot)\)	4729.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4729}(2,\cdot)\)	4729.l	788	yes	\(1\)	\(1\)	\(e\left(\frac{153}{394}\right)\)	\(e\left(\frac{171}{394}\right)\)	\(e\left(\frac{153}{197}\right)\)	\(e\left(\frac{87}{394}\right)\)	\(e\left(\frac{162}{197}\right)\)	\(e\left(\frac{13}{394}\right)\)	\(e\left(\frac{65}{394}\right)\)	\(e\left(\frac{171}{197}\right)\)	\(e\left(\frac{120}{197}\right)\)	\(e\left(\frac{143}{788}\right)\)
\(\chi_{4729}(3,\cdot)\)	4729.l	788	yes	\(1\)	\(1\)	\(e\left(\frac{171}{394}\right)\)	\(e\left(\frac{307}{394}\right)\)	\(e\left(\frac{171}{197}\right)\)	\(e\left(\frac{329}{394}\right)\)	\(e\left(\frac{42}{197}\right)\)	\(e\left(\frac{339}{394}\right)\)	\(e\left(\frac{119}{394}\right)\)	\(e\left(\frac{110}{197}\right)\)	\(e\left(\frac{53}{197}\right)\)	\(e\left(\frac{183}{788}\right)\)
\(\chi_{4729}(4,\cdot)\)	4729.j	394	yes	\(1\)	\(1\)	\(e\left(\frac{153}{197}\right)\)	\(e\left(\frac{171}{197}\right)\)	\(e\left(\frac{109}{197}\right)\)	\(e\left(\frac{87}{197}\right)\)	\(e\left(\frac{127}{197}\right)\)	\(e\left(\frac{13}{197}\right)\)	\(e\left(\frac{65}{197}\right)\)	\(e\left(\frac{145}{197}\right)\)	\(e\left(\frac{43}{197}\right)\)	\(e\left(\frac{143}{394}\right)\)
\(\chi_{4729}(5,\cdot)\)	4729.o	2364	yes	\(1\)	\(1\)	\(e\left(\frac{87}{394}\right)\)	\(e\left(\frac{329}{394}\right)\)	\(e\left(\frac{87}{197}\right)\)	\(e\left(\frac{751}{1182}\right)\)	\(e\left(\frac{11}{197}\right)\)	\(e\left(\frac{787}{1182}\right)\)	\(e\left(\frac{261}{394}\right)\)	\(e\left(\frac{132}{197}\right)\)	\(e\left(\frac{506}{591}\right)\)	\(e\left(\frac{259}{788}\right)\)
\(\chi_{4729}(6,\cdot)\)	4729.j	394	yes	\(1\)	\(1\)	\(e\left(\frac{162}{197}\right)\)	\(e\left(\frac{42}{197}\right)\)	\(e\left(\frac{127}{197}\right)\)	\(e\left(\frac{11}{197}\right)\)	\(e\left(\frac{7}{197}\right)\)	\(e\left(\frac{176}{197}\right)\)	\(e\left(\frac{92}{197}\right)\)	\(e\left(\frac{84}{197}\right)\)	\(e\left(\frac{173}{197}\right)\)	\(e\left(\frac{163}{394}\right)\)
\(\chi_{4729}(7,\cdot)\)	4729.o	2364	yes	\(1\)	\(1\)	\(e\left(\frac{13}{394}\right)\)	\(e\left(\frac{339}{394}\right)\)	\(e\left(\frac{13}{197}\right)\)	\(e\left(\frac{787}{1182}\right)\)	\(e\left(\frac{176}{197}\right)\)	\(e\left(\frac{181}{1182}\right)\)	\(e\left(\frac{39}{394}\right)\)	\(e\left(\frac{142}{197}\right)\)	\(e\left(\frac{413}{591}\right)\)	\(e\left(\frac{401}{788}\right)\)
\(\chi_{4729}(8,\cdot)\)	4729.l	788	yes	\(1\)	\(1\)	\(e\left(\frac{65}{394}\right)\)	\(e\left(\frac{119}{394}\right)\)	\(e\left(\frac{65}{197}\right)\)	\(e\left(\frac{261}{394}\right)\)	\(e\left(\frac{92}{197}\right)\)	\(e\left(\frac{39}{394}\right)\)	\(e\left(\frac{195}{394}\right)\)	\(e\left(\frac{119}{197}\right)\)	\(e\left(\frac{163}{197}\right)\)	\(e\left(\frac{429}{788}\right)\)
\(\chi_{4729}(9,\cdot)\)	4729.j	394	yes	\(1\)	\(1\)	\(e\left(\frac{171}{197}\right)\)	\(e\left(\frac{110}{197}\right)\)	\(e\left(\frac{145}{197}\right)\)	\(e\left(\frac{132}{197}\right)\)	\(e\left(\frac{84}{197}\right)\)	\(e\left(\frac{142}{197}\right)\)	\(e\left(\frac{119}{197}\right)\)	\(e\left(\frac{23}{197}\right)\)	\(e\left(\frac{106}{197}\right)\)	\(e\left(\frac{183}{394}\right)\)
\(\chi_{4729}(10,\cdot)\)	4729.m	1182	yes	\(1\)	\(1\)	\(e\left(\frac{120}{197}\right)\)	\(e\left(\frac{53}{197}\right)\)	\(e\left(\frac{43}{197}\right)\)	\(e\left(\frac{506}{591}\right)\)	\(e\left(\frac{173}{197}\right)\)	\(e\left(\frac{413}{591}\right)\)	\(e\left(\frac{163}{197}\right)\)	\(e\left(\frac{106}{197}\right)\)	\(e\left(\frac{275}{591}\right)\)	\(e\left(\frac{201}{394}\right)\)
\(\chi_{4729}(11,\cdot)\)	4729.n	1576	yes	\(-1\)	\(1\)	\(e\left(\frac{143}{788}\right)\)	\(e\left(\frac{183}{788}\right)\)	\(e\left(\frac{143}{394}\right)\)	\(e\left(\frac{259}{788}\right)\)	\(e\left(\frac{163}{394}\right)\)	\(e\left(\frac{401}{788}\right)\)	\(e\left(\frac{429}{788}\right)\)	\(e\left(\frac{183}{394}\right)\)	\(e\left(\frac{201}{394}\right)\)	\(e\left(\frac{1259}{1576}\right)\)
\(\chi_{4729}(12,\cdot)\)	4729.l	788	yes	\(1\)	\(1\)	\(e\left(\frac{83}{394}\right)\)	\(e\left(\frac{255}{394}\right)\)	\(e\left(\frac{83}{197}\right)\)	\(e\left(\frac{109}{394}\right)\)	\(e\left(\frac{169}{197}\right)\)	\(e\left(\frac{365}{394}\right)\)	\(e\left(\frac{249}{394}\right)\)	\(e\left(\frac{58}{197}\right)\)	\(e\left(\frac{96}{197}\right)\)	\(e\left(\frac{469}{788}\right)\)
\(\chi_{4729}(13,\cdot)\)	4729.m	1182	yes	\(1\)	\(1\)	\(e\left(\frac{160}{197}\right)\)	\(e\left(\frac{5}{197}\right)\)	\(e\left(\frac{123}{197}\right)\)	\(e\left(\frac{215}{591}\right)\)	\(e\left(\frac{165}{197}\right)\)	\(e\left(\frac{485}{591}\right)\)	\(e\left(\frac{86}{197}\right)\)	\(e\left(\frac{10}{197}\right)\)	\(e\left(\frac{104}{591}\right)\)	\(e\left(\frac{71}{394}\right)\)
\(\chi_{4729}(14,\cdot)\)	4729.k	591	yes	\(1\)	\(1\)	\(e\left(\frac{83}{197}\right)\)	\(e\left(\frac{58}{197}\right)\)	\(e\left(\frac{166}{197}\right)\)	\(e\left(\frac{524}{591}\right)\)	\(e\left(\frac{141}{197}\right)\)	\(e\left(\frac{110}{591}\right)\)	\(e\left(\frac{52}{197}\right)\)	\(e\left(\frac{116}{197}\right)\)	\(e\left(\frac{182}{591}\right)\)	\(e\left(\frac{136}{197}\right)\)
\(\chi_{4729}(15,\cdot)\)	4729.m	1182	yes	\(1\)	\(1\)	\(e\left(\frac{129}{197}\right)\)	\(e\left(\frac{121}{197}\right)\)	\(e\left(\frac{61}{197}\right)\)	\(e\left(\frac{278}{591}\right)\)	\(e\left(\frac{53}{197}\right)\)	\(e\left(\frac{311}{591}\right)\)	\(e\left(\frac{190}{197}\right)\)	\(e\left(\frac{45}{197}\right)\)	\(e\left(\frac{74}{591}\right)\)	\(e\left(\frac{221}{394}\right)\)
\(\chi_{4729}(16,\cdot)\)	4729.i	197	yes	\(1\)	\(1\)	\(e\left(\frac{109}{197}\right)\)	\(e\left(\frac{145}{197}\right)\)	\(e\left(\frac{21}{197}\right)\)	\(e\left(\frac{174}{197}\right)\)	\(e\left(\frac{57}{197}\right)\)	\(e\left(\frac{26}{197}\right)\)	\(e\left(\frac{130}{197}\right)\)	\(e\left(\frac{93}{197}\right)\)	\(e\left(\frac{86}{197}\right)\)	\(e\left(\frac{143}{197}\right)\)
\(\chi_{4729}(17,\cdot)\)	4729.p	4728	yes	\(-1\)	\(1\)	\(e\left(\frac{53}{788}\right)\)	\(e\left(\frac{685}{788}\right)\)	\(e\left(\frac{53}{394}\right)\)	\(e\left(\frac{299}{2364}\right)\)	\(e\left(\frac{369}{394}\right)\)	\(e\left(\frac{1829}{2364}\right)\)	\(e\left(\frac{159}{788}\right)\)	\(e\left(\frac{291}{394}\right)\)	\(e\left(\frac{229}{1182}\right)\)	\(e\left(\frac{1453}{1576}\right)\)
\(\chi_{4729}(18,\cdot)\)	4729.l	788	yes	\(1\)	\(1\)	\(e\left(\frac{101}{394}\right)\)	\(e\left(\frac{391}{394}\right)\)	\(e\left(\frac{101}{197}\right)\)	\(e\left(\frac{351}{394}\right)\)	\(e\left(\frac{49}{197}\right)\)	\(e\left(\frac{297}{394}\right)\)	\(e\left(\frac{303}{394}\right)\)	\(e\left(\frac{194}{197}\right)\)	\(e\left(\frac{29}{197}\right)\)	\(e\left(\frac{509}{788}\right)\)
\(\chi_{4729}(19,\cdot)\)	4729.k	591	yes	\(1\)	\(1\)	\(e\left(\frac{82}{197}\right)\)	\(e\left(\frac{138}{197}\right)\)	\(e\left(\frac{164}{197}\right)\)	\(e\left(\frac{221}{591}\right)\)	\(e\left(\frac{23}{197}\right)\)	\(e\left(\frac{581}{591}\right)\)	\(e\left(\frac{49}{197}\right)\)	\(e\left(\frac{79}{197}\right)\)	\(e\left(\frac{467}{591}\right)\)	\(e\left(\frac{113}{197}\right)\)
\(\chi_{4729}(20,\cdot)\)	4729.o	2364	yes	\(1\)	\(1\)	\(e\left(\frac{393}{394}\right)\)	\(e\left(\frac{277}{394}\right)\)	\(e\left(\frac{196}{197}\right)\)	\(e\left(\frac{91}{1182}\right)\)	\(e\left(\frac{138}{197}\right)\)	\(e\left(\frac{865}{1182}\right)\)	\(e\left(\frac{391}{394}\right)\)	\(e\left(\frac{80}{197}\right)\)	\(e\left(\frac{44}{591}\right)\)	\(e\left(\frac{545}{788}\right)\)
\(\chi_{4729}(21,\cdot)\)	4729.k	591	yes	\(1\)	\(1\)	\(e\left(\frac{92}{197}\right)\)	\(e\left(\frac{126}{197}\right)\)	\(e\left(\frac{184}{197}\right)\)	\(e\left(\frac{296}{591}\right)\)	\(e\left(\frac{21}{197}\right)\)	\(e\left(\frac{8}{591}\right)\)	\(e\left(\frac{79}{197}\right)\)	\(e\left(\frac{55}{197}\right)\)	\(e\left(\frac{572}{591}\right)\)	\(e\left(\frac{146}{197}\right)\)
\(\chi_{4729}(22,\cdot)\)	4729.n	1576	yes	\(-1\)	\(1\)	\(e\left(\frac{449}{788}\right)\)	\(e\left(\frac{525}{788}\right)\)	\(e\left(\frac{55}{394}\right)\)	\(e\left(\frac{433}{788}\right)\)	\(e\left(\frac{93}{394}\right)\)	\(e\left(\frac{427}{788}\right)\)	\(e\left(\frac{559}{788}\right)\)	\(e\left(\frac{131}{394}\right)\)	\(e\left(\frac{47}{394}\right)\)	\(e\left(\frac{1545}{1576}\right)\)
\(\chi_{4729}(23,\cdot)\)	4729.n	1576	yes	\(-1\)	\(1\)	\(e\left(\frac{29}{788}\right)\)	\(e\left(\frac{241}{788}\right)\)	\(e\left(\frac{29}{394}\right)\)	\(e\left(\frac{565}{788}\right)\)	\(e\left(\frac{135}{394}\right)\)	\(e\left(\frac{175}{788}\right)\)	\(e\left(\frac{87}{788}\right)\)	\(e\left(\frac{241}{394}\right)\)	\(e\left(\frac{297}{394}\right)\)	\(e\left(\frac{349}{1576}\right)\)
\(\chi_{4729}(24,\cdot)\)	4729.i	197	yes	\(1\)	\(1\)	\(e\left(\frac{118}{197}\right)\)	\(e\left(\frac{16}{197}\right)\)	\(e\left(\frac{39}{197}\right)\)	\(e\left(\frac{98}{197}\right)\)	\(e\left(\frac{134}{197}\right)\)	\(e\left(\frac{189}{197}\right)\)	\(e\left(\frac{157}{197}\right)\)	\(e\left(\frac{32}{197}\right)\)	\(e\left(\frac{19}{197}\right)\)	\(e\left(\frac{153}{197}\right)\)
\(\chi_{4729}(25,\cdot)\)	4729.m	1182	yes	\(1\)	\(1\)	\(e\left(\frac{87}{197}\right)\)	\(e\left(\frac{132}{197}\right)\)	\(e\left(\frac{174}{197}\right)\)	\(e\left(\frac{160}{591}\right)\)	\(e\left(\frac{22}{197}\right)\)	\(e\left(\frac{196}{591}\right)\)	\(e\left(\frac{64}{197}\right)\)	\(e\left(\frac{67}{197}\right)\)	\(e\left(\frac{421}{591}\right)\)	\(e\left(\frac{259}{394}\right)\)
\(\chi_{4729}(26,\cdot)\)	4729.o	2364	yes	\(1\)	\(1\)	\(e\left(\frac{79}{394}\right)\)	\(e\left(\frac{181}{394}\right)\)	\(e\left(\frac{79}{197}\right)\)	\(e\left(\frac{691}{1182}\right)\)	\(e\left(\frac{130}{197}\right)\)	\(e\left(\frac{1009}{1182}\right)\)	\(e\left(\frac{237}{394}\right)\)	\(e\left(\frac{181}{197}\right)\)	\(e\left(\frac{464}{591}\right)\)	\(e\left(\frac{285}{788}\right)\)
\(\chi_{4729}(27,\cdot)\)	4729.l	788	yes	\(1\)	\(1\)	\(e\left(\frac{119}{394}\right)\)	\(e\left(\frac{133}{394}\right)\)	\(e\left(\frac{119}{197}\right)\)	\(e\left(\frac{199}{394}\right)\)	\(e\left(\frac{126}{197}\right)\)	\(e\left(\frac{229}{394}\right)\)	\(e\left(\frac{357}{394}\right)\)	\(e\left(\frac{133}{197}\right)\)	\(e\left(\frac{159}{197}\right)\)	\(e\left(\frac{549}{788}\right)\)
\(\chi_{4729}(28,\cdot)\)	4729.o	2364	yes	\(1\)	\(1\)	\(e\left(\frac{319}{394}\right)\)	\(e\left(\frac{287}{394}\right)\)	\(e\left(\frac{122}{197}\right)\)	\(e\left(\frac{127}{1182}\right)\)	\(e\left(\frac{106}{197}\right)\)	\(e\left(\frac{259}{1182}\right)\)	\(e\left(\frac{169}{394}\right)\)	\(e\left(\frac{90}{197}\right)\)	\(e\left(\frac{542}{591}\right)\)	\(e\left(\frac{687}{788}\right)\)
\(\chi_{4729}(29,\cdot)\)	4729.n	1576	yes	\(-1\)	\(1\)	\(e\left(\frac{285}{788}\right)\)	\(e\left(\frac{249}{788}\right)\)	\(e\left(\frac{285}{394}\right)\)	\(e\left(\frac{417}{788}\right)\)	\(e\left(\frac{267}{394}\right)\)	\(e\left(\frac{171}{788}\right)\)	\(e\left(\frac{67}{788}\right)\)	\(e\left(\frac{249}{394}\right)\)	\(e\left(\frac{351}{394}\right)\)	\(e\left(\frac{1093}{1576}\right)\)
\(\chi_{4729}(30,\cdot)\)	4729.o	2364	yes	\(1\)	\(1\)	\(e\left(\frac{17}{394}\right)\)	\(e\left(\frac{19}{394}\right)\)	\(e\left(\frac{17}{197}\right)\)	\(e\left(\frac{817}{1182}\right)\)	\(e\left(\frac{18}{197}\right)\)	\(e\left(\frac{661}{1182}\right)\)	\(e\left(\frac{51}{394}\right)\)	\(e\left(\frac{19}{197}\right)\)	\(e\left(\frac{434}{591}\right)\)	\(e\left(\frac{585}{788}\right)\)
\(\chi_{4729}(31,\cdot)\)	4729.n	1576	yes	\(-1\)	\(1\)	\(e\left(\frac{383}{788}\right)\)	\(e\left(\frac{683}{788}\right)\)	\(e\left(\frac{383}{394}\right)\)	\(e\left(\frac{71}{788}\right)\)	\(e\left(\frac{139}{394}\right)\)	\(e\left(\frac{545}{788}\right)\)	\(e\left(\frac{361}{788}\right)\)	\(e\left(\frac{289}{394}\right)\)	\(e\left(\frac{227}{394}\right)\)	\(e\left(\frac{479}{1576}\right)\)
\(\chi_{4729}(32,\cdot)\)	4729.l	788	yes	\(1\)	\(1\)	\(e\left(\frac{371}{394}\right)\)	\(e\left(\frac{67}{394}\right)\)	\(e\left(\frac{174}{197}\right)\)	\(e\left(\frac{41}{394}\right)\)	\(e\left(\frac{22}{197}\right)\)	\(e\left(\frac{65}{394}\right)\)	\(e\left(\frac{325}{394}\right)\)	\(e\left(\frac{67}{197}\right)\)	\(e\left(\frac{9}{197}\right)\)	\(e\left(\frac{715}{788}\right)\)

Introduction

L-functions

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Character group

First 32 of 4728 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.