LMFDB - Group of Dirichlet characters of modulus 1021

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1021)

pari: g = idealstar(,1021,2)

Character group

sage: G.order() pari: g.no
Order	=	1020
sage: H.invariants() pari: g.cyc
Structure	=	$C_{1020}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{1021}(10,\cdot)$

First 32 of 1020 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	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{1021}(1,\cdot)$	1021.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{1021}(2,\cdot)$	1021.v	340	yes	$-1$	$1$	$e\left(\frac{243}{340}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{73}{170}\right)$	$e\left(\frac{52}{85}\right)$	$e\left(\frac{293}{340}\right)$	$e\left(\frac{113}{340}\right)$	$e\left(\frac{49}{340}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{111}{340}\right)$	$e\left(\frac{19}{85}\right)$
$\chi_{1021}(3,\cdot)$	1021.m	34	yes	$1$	$1$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{4}{17}\right)$
$\chi_{1021}(4,\cdot)$	1021.s	170	yes	$1$	$1$	$e\left(\frac{73}{170}\right)$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{73}{85}\right)$	$e\left(\frac{19}{85}\right)$	$e\left(\frac{123}{170}\right)$	$e\left(\frac{113}{170}\right)$	$e\left(\frac{49}{170}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{111}{170}\right)$	$e\left(\frac{38}{85}\right)$
$\chi_{1021}(5,\cdot)$	1021.u	255	yes	$1$	$1$	$e\left(\frac{52}{85}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{19}{85}\right)$	$e\left(\frac{16}{255}\right)$	$e\left(\frac{62}{85}\right)$	$e\left(\frac{77}{85}\right)$	$e\left(\frac{71}{85}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{172}{255}\right)$	$e\left(\frac{202}{255}\right)$
$\chi_{1021}(6,\cdot)$	1021.v	340	yes	$-1$	$1$	$e\left(\frac{293}{340}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{123}{170}\right)$	$e\left(\frac{62}{85}\right)$	$e\left(\frac{163}{340}\right)$	$e\left(\frac{223}{340}\right)$	$e\left(\frac{199}{340}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{201}{340}\right)$	$e\left(\frac{39}{85}\right)$
$\chi_{1021}(7,\cdot)$	1021.v	340	yes	$-1$	$1$	$e\left(\frac{113}{340}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{113}{170}\right)$	$e\left(\frac{77}{85}\right)$	$e\left(\frac{223}{340}\right)$	$e\left(\frac{303}{340}\right)$	$e\left(\frac{339}{340}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{81}{340}\right)$	$e\left(\frac{69}{85}\right)$
$\chi_{1021}(8,\cdot)$	1021.v	340	yes	$-1$	$1$	$e\left(\frac{49}{340}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{49}{170}\right)$	$e\left(\frac{71}{85}\right)$	$e\left(\frac{199}{340}\right)$	$e\left(\frac{339}{340}\right)$	$e\left(\frac{147}{340}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{333}{340}\right)$	$e\left(\frac{57}{85}\right)$
$\chi_{1021}(9,\cdot)$	1021.j	17	yes	$1$	$1$	$e\left(\frac{5}{17}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{8}{17}\right)$
$\chi_{1021}(10,\cdot)$	1021.x	1020	yes	$-1$	$1$	$e\left(\frac{111}{340}\right)$	$e\left(\frac{9}{34}\right)$	$e\left(\frac{111}{170}\right)$	$e\left(\frac{172}{255}\right)$	$e\left(\frac{201}{340}\right)$	$e\left(\frac{81}{340}\right)$	$e\left(\frac{333}{340}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{1}{1020}\right)$	$e\left(\frac{4}{255}\right)$
$\chi_{1021}(11,\cdot)$	1021.u	255	yes	$1$	$1$	$e\left(\frac{19}{85}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{38}{85}\right)$	$e\left(\frac{202}{255}\right)$	$e\left(\frac{39}{85}\right)$	$e\left(\frac{69}{85}\right)$	$e\left(\frac{57}{85}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{4}{255}\right)$	$e\left(\frac{64}{255}\right)$
$\chi_{1021}(12,\cdot)$	1021.q	85	yes	$1$	$1$	$e\left(\frac{49}{85}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{13}{85}\right)$	$e\left(\frac{29}{85}\right)$	$e\left(\frac{29}{85}\right)$	$e\left(\frac{84}{85}\right)$	$e\left(\frac{62}{85}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{78}{85}\right)$	$e\left(\frac{58}{85}\right)$
$\chi_{1021}(13,\cdot)$	1021.p	68	yes	$-1$	$1$	$e\left(\frac{67}{68}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{57}{68}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{65}{68}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{3}{17}\right)$
$\chi_{1021}(14,\cdot)$	1021.q	85	yes	$1$	$1$	$e\left(\frac{4}{85}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{8}{85}\right)$	$e\left(\frac{44}{85}\right)$	$e\left(\frac{44}{85}\right)$	$e\left(\frac{19}{85}\right)$	$e\left(\frac{12}{85}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{48}{85}\right)$	$e\left(\frac{3}{85}\right)$
$\chi_{1021}(15,\cdot)$	1021.w	510	yes	$1$	$1$	$e\left(\frac{129}{170}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{44}{85}\right)$	$e\left(\frac{46}{255}\right)$	$e\left(\frac{59}{170}\right)$	$e\left(\frac{39}{170}\right)$	$e\left(\frac{47}{170}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{479}{510}\right)$	$e\left(\frac{7}{255}\right)$
$\chi_{1021}(16,\cdot)$	1021.q	85	yes	$1$	$1$	$e\left(\frac{73}{85}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{61}{85}\right)$	$e\left(\frac{38}{85}\right)$	$e\left(\frac{38}{85}\right)$	$e\left(\frac{28}{85}\right)$	$e\left(\frac{49}{85}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{26}{85}\right)$	$e\left(\frac{76}{85}\right)$
$\chi_{1021}(17,\cdot)$	1021.w	510	yes	$1$	$1$	$e\left(\frac{53}{170}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{53}{85}\right)$	$e\left(\frac{152}{255}\right)$	$e\left(\frac{73}{170}\right)$	$e\left(\frac{103}{170}\right)$	$e\left(\frac{159}{170}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{463}{510}\right)$	$e\left(\frac{134}{255}\right)$
$\chi_{1021}(18,\cdot)$	1021.v	340	yes	$-1$	$1$	$e\left(\frac{3}{340}\right)$	$e\left(\frac{3}{34}\right)$	$e\left(\frac{3}{170}\right)$	$e\left(\frac{72}{85}\right)$	$e\left(\frac{33}{340}\right)$	$e\left(\frac{333}{340}\right)$	$e\left(\frac{9}{340}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{291}{340}\right)$	$e\left(\frac{59}{85}\right)$
$\chi_{1021}(19,\cdot)$	1021.t	204	yes	$-1$	$1$	$e\left(\frac{31}{68}\right)$	$e\left(\frac{19}{34}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{5}{51}\right)$	$e\left(\frac{1}{68}\right)$	$e\left(\frac{41}{68}\right)$	$e\left(\frac{25}{68}\right)$	$e\left(\frac{2}{17}\right)$	$e\left(\frac{113}{204}\right)$	$e\left(\frac{44}{51}\right)$
$\chi_{1021}(20,\cdot)$	1021.w	510	yes	$1$	$1$	$e\left(\frac{7}{170}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{7}{85}\right)$	$e\left(\frac{73}{255}\right)$	$e\left(\frac{77}{170}\right)$	$e\left(\frac{97}{170}\right)$	$e\left(\frac{21}{170}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{167}{510}\right)$	$e\left(\frac{61}{255}\right)$
$\chi_{1021}(21,\cdot)$	1021.v	340	yes	$-1$	$1$	$e\left(\frac{163}{340}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{163}{170}\right)$	$e\left(\frac{2}{85}\right)$	$e\left(\frac{93}{340}\right)$	$e\left(\frac{73}{340}\right)$	$e\left(\frac{149}{340}\right)$	$e\left(\frac{10}{17}\right)$	$e\left(\frac{171}{340}\right)$	$e\left(\frac{4}{85}\right)$
$\chi_{1021}(22,\cdot)$	1021.x	1020	yes	$-1$	$1$	$e\left(\frac{319}{340}\right)$	$e\left(\frac{13}{34}\right)$	$e\left(\frac{149}{170}\right)$	$e\left(\frac{103}{255}\right)$	$e\left(\frac{109}{340}\right)$	$e\left(\frac{49}{340}\right)$	$e\left(\frac{277}{340}\right)$	$e\left(\frac{13}{17}\right)$	$e\left(\frac{349}{1020}\right)$	$e\left(\frac{121}{255}\right)$
$\chi_{1021}(23,\cdot)$	1021.u	255	yes	$1$	$1$	$e\left(\frac{12}{85}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{24}{85}\right)$	$e\left(\frac{56}{255}\right)$	$e\left(\frac{47}{85}\right)$	$e\left(\frac{57}{85}\right)$	$e\left(\frac{36}{85}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{92}{255}\right)$	$e\left(\frac{197}{255}\right)$
$\chi_{1021}(24,\cdot)$	1021.v	340	yes	$-1$	$1$	$e\left(\frac{99}{340}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{99}{170}\right)$	$e\left(\frac{81}{85}\right)$	$e\left(\frac{69}{340}\right)$	$e\left(\frac{109}{340}\right)$	$e\left(\frac{297}{340}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{83}{340}\right)$	$e\left(\frac{77}{85}\right)$
$\chi_{1021}(25,\cdot)$	1021.u	255	yes	$1$	$1$	$e\left(\frac{19}{85}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{38}{85}\right)$	$e\left(\frac{32}{255}\right)$	$e\left(\frac{39}{85}\right)$	$e\left(\frac{69}{85}\right)$	$e\left(\frac{57}{85}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{89}{255}\right)$	$e\left(\frac{149}{255}\right)$
$\chi_{1021}(26,\cdot)$	1021.g	10	yes	$1$	$1$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{10}\right)$	$1$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{2}{5}\right)$
$\chi_{1021}(27,\cdot)$	1021.m	34	yes	$1$	$1$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{29}{34}\right)$	$e\left(\frac{33}{34}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{27}{34}\right)$	$e\left(\frac{12}{17}\right)$
$\chi_{1021}(28,\cdot)$	1021.v	340	yes	$-1$	$1$	$e\left(\frac{259}{340}\right)$	$e\left(\frac{21}{34}\right)$	$e\left(\frac{89}{170}\right)$	$e\left(\frac{11}{85}\right)$	$e\left(\frac{129}{340}\right)$	$e\left(\frac{189}{340}\right)$	$e\left(\frac{97}{340}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{303}{340}\right)$	$e\left(\frac{22}{85}\right)$
$\chi_{1021}(29,\cdot)$	1021.w	510	yes	$1$	$1$	$e\left(\frac{71}{170}\right)$	$e\left(\frac{3}{17}\right)$	$e\left(\frac{71}{85}\right)$	$e\left(\frac{194}{255}\right)$	$e\left(\frac{101}{170}\right)$	$e\left(\frac{61}{170}\right)$	$e\left(\frac{43}{170}\right)$	$e\left(\frac{6}{17}\right)$	$e\left(\frac{91}{510}\right)$	$e\left(\frac{218}{255}\right)$
$\chi_{1021}(30,\cdot)$	1021.x	1020	yes	$-1$	$1$	$e\left(\frac{161}{340}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{161}{170}\right)$	$e\left(\frac{202}{255}\right)$	$e\left(\frac{71}{340}\right)$	$e\left(\frac{191}{340}\right)$	$e\left(\frac{143}{340}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{271}{1020}\right)$	$e\left(\frac{64}{255}\right)$
$\chi_{1021}(31,\cdot)$	1021.x	1020	yes	$-1$	$1$	$e\left(\frac{117}{340}\right)$	$e\left(\frac{15}{34}\right)$	$e\left(\frac{117}{170}\right)$	$e\left(\frac{179}{255}\right)$	$e\left(\frac{267}{340}\right)$	$e\left(\frac{67}{340}\right)$	$e\left(\frac{11}{340}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{47}{1020}\right)$	$e\left(\frac{188}{255}\right)$
$\chi_{1021}(32,\cdot)$	1021.p	68	yes	$-1$	$1$	$e\left(\frac{39}{68}\right)$	$e\left(\frac{25}{34}\right)$	$e\left(\frac{5}{34}\right)$	$e\left(\frac{1}{17}\right)$	$e\left(\frac{21}{68}\right)$	$e\left(\frac{45}{68}\right)$	$e\left(\frac{49}{68}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{43}{68}\right)$	$e\left(\frac{2}{17}\right)$

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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	$1021$
Structure	\(C_{1020}\)
Order	$1020$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{1021}(1,\cdot)\)	1021.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{1021}(2,\cdot)\)	1021.v	340	yes	\(-1\)	\(1\)	\(e\left(\frac{243}{340}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{73}{170}\right)\)	\(e\left(\frac{52}{85}\right)\)	\(e\left(\frac{293}{340}\right)\)	\(e\left(\frac{113}{340}\right)\)	\(e\left(\frac{49}{340}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{111}{340}\right)\)	\(e\left(\frac{19}{85}\right)\)
\(\chi_{1021}(3,\cdot)\)	1021.m	34	yes	\(1\)	\(1\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{4}{17}\right)\)
\(\chi_{1021}(4,\cdot)\)	1021.s	170	yes	\(1\)	\(1\)	\(e\left(\frac{73}{170}\right)\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{73}{85}\right)\)	\(e\left(\frac{19}{85}\right)\)	\(e\left(\frac{123}{170}\right)\)	\(e\left(\frac{113}{170}\right)\)	\(e\left(\frac{49}{170}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{111}{170}\right)\)	\(e\left(\frac{38}{85}\right)\)
\(\chi_{1021}(5,\cdot)\)	1021.u	255	yes	\(1\)	\(1\)	\(e\left(\frac{52}{85}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{19}{85}\right)\)	\(e\left(\frac{16}{255}\right)\)	\(e\left(\frac{62}{85}\right)\)	\(e\left(\frac{77}{85}\right)\)	\(e\left(\frac{71}{85}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{172}{255}\right)\)	\(e\left(\frac{202}{255}\right)\)
\(\chi_{1021}(6,\cdot)\)	1021.v	340	yes	\(-1\)	\(1\)	\(e\left(\frac{293}{340}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{123}{170}\right)\)	\(e\left(\frac{62}{85}\right)\)	\(e\left(\frac{163}{340}\right)\)	\(e\left(\frac{223}{340}\right)\)	\(e\left(\frac{199}{340}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{201}{340}\right)\)	\(e\left(\frac{39}{85}\right)\)
\(\chi_{1021}(7,\cdot)\)	1021.v	340	yes	\(-1\)	\(1\)	\(e\left(\frac{113}{340}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{113}{170}\right)\)	\(e\left(\frac{77}{85}\right)\)	\(e\left(\frac{223}{340}\right)\)	\(e\left(\frac{303}{340}\right)\)	\(e\left(\frac{339}{340}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{81}{340}\right)\)	\(e\left(\frac{69}{85}\right)\)
\(\chi_{1021}(8,\cdot)\)	1021.v	340	yes	\(-1\)	\(1\)	\(e\left(\frac{49}{340}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{49}{170}\right)\)	\(e\left(\frac{71}{85}\right)\)	\(e\left(\frac{199}{340}\right)\)	\(e\left(\frac{339}{340}\right)\)	\(e\left(\frac{147}{340}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{333}{340}\right)\)	\(e\left(\frac{57}{85}\right)\)
\(\chi_{1021}(9,\cdot)\)	1021.j	17	yes	\(1\)	\(1\)	\(e\left(\frac{5}{17}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{11}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{8}{17}\right)\)
\(\chi_{1021}(10,\cdot)\)	1021.x	1020	yes	\(-1\)	\(1\)	\(e\left(\frac{111}{340}\right)\)	\(e\left(\frac{9}{34}\right)\)	\(e\left(\frac{111}{170}\right)\)	\(e\left(\frac{172}{255}\right)\)	\(e\left(\frac{201}{340}\right)\)	\(e\left(\frac{81}{340}\right)\)	\(e\left(\frac{333}{340}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{1}{1020}\right)\)	\(e\left(\frac{4}{255}\right)\)
\(\chi_{1021}(11,\cdot)\)	1021.u	255	yes	\(1\)	\(1\)	\(e\left(\frac{19}{85}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{38}{85}\right)\)	\(e\left(\frac{202}{255}\right)\)	\(e\left(\frac{39}{85}\right)\)	\(e\left(\frac{69}{85}\right)\)	\(e\left(\frac{57}{85}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{4}{255}\right)\)	\(e\left(\frac{64}{255}\right)\)
\(\chi_{1021}(12,\cdot)\)	1021.q	85	yes	\(1\)	\(1\)	\(e\left(\frac{49}{85}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{13}{85}\right)\)	\(e\left(\frac{29}{85}\right)\)	\(e\left(\frac{29}{85}\right)\)	\(e\left(\frac{84}{85}\right)\)	\(e\left(\frac{62}{85}\right)\)	\(e\left(\frac{9}{17}\right)\)	\(e\left(\frac{78}{85}\right)\)	\(e\left(\frac{58}{85}\right)\)
\(\chi_{1021}(13,\cdot)\)	1021.p	68	yes	\(-1\)	\(1\)	\(e\left(\frac{67}{68}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{57}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{65}{68}\right)\)	\(e\left(\frac{12}{17}\right)\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{3}{17}\right)\)
\(\chi_{1021}(14,\cdot)\)	1021.q	85	yes	\(1\)	\(1\)	\(e\left(\frac{4}{85}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{8}{85}\right)\)	\(e\left(\frac{44}{85}\right)\)	\(e\left(\frac{44}{85}\right)\)	\(e\left(\frac{19}{85}\right)\)	\(e\left(\frac{12}{85}\right)\)	\(e\left(\frac{16}{17}\right)\)	\(e\left(\frac{48}{85}\right)\)	\(e\left(\frac{3}{85}\right)\)
\(\chi_{1021}(15,\cdot)\)	1021.w	510	yes	\(1\)	\(1\)	\(e\left(\frac{129}{170}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{44}{85}\right)\)	\(e\left(\frac{46}{255}\right)\)	\(e\left(\frac{59}{170}\right)\)	\(e\left(\frac{39}{170}\right)\)	\(e\left(\frac{47}{170}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{479}{510}\right)\)	\(e\left(\frac{7}{255}\right)\)
\(\chi_{1021}(16,\cdot)\)	1021.q	85	yes	\(1\)	\(1\)	\(e\left(\frac{73}{85}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{61}{85}\right)\)	\(e\left(\frac{38}{85}\right)\)	\(e\left(\frac{38}{85}\right)\)	\(e\left(\frac{28}{85}\right)\)	\(e\left(\frac{49}{85}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{26}{85}\right)\)	\(e\left(\frac{76}{85}\right)\)
\(\chi_{1021}(17,\cdot)\)	1021.w	510	yes	\(1\)	\(1\)	\(e\left(\frac{53}{170}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{53}{85}\right)\)	\(e\left(\frac{152}{255}\right)\)	\(e\left(\frac{73}{170}\right)\)	\(e\left(\frac{103}{170}\right)\)	\(e\left(\frac{159}{170}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{463}{510}\right)\)	\(e\left(\frac{134}{255}\right)\)
\(\chi_{1021}(18,\cdot)\)	1021.v	340	yes	\(-1\)	\(1\)	\(e\left(\frac{3}{340}\right)\)	\(e\left(\frac{3}{34}\right)\)	\(e\left(\frac{3}{170}\right)\)	\(e\left(\frac{72}{85}\right)\)	\(e\left(\frac{33}{340}\right)\)	\(e\left(\frac{333}{340}\right)\)	\(e\left(\frac{9}{340}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{291}{340}\right)\)	\(e\left(\frac{59}{85}\right)\)
\(\chi_{1021}(19,\cdot)\)	1021.t	204	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{68}\right)\)	\(e\left(\frac{19}{34}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{5}{51}\right)\)	\(e\left(\frac{1}{68}\right)\)	\(e\left(\frac{41}{68}\right)\)	\(e\left(\frac{25}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)	\(e\left(\frac{113}{204}\right)\)	\(e\left(\frac{44}{51}\right)\)
\(\chi_{1021}(20,\cdot)\)	1021.w	510	yes	\(1\)	\(1\)	\(e\left(\frac{7}{170}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{7}{85}\right)\)	\(e\left(\frac{73}{255}\right)\)	\(e\left(\frac{77}{170}\right)\)	\(e\left(\frac{97}{170}\right)\)	\(e\left(\frac{21}{170}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{167}{510}\right)\)	\(e\left(\frac{61}{255}\right)\)
\(\chi_{1021}(21,\cdot)\)	1021.v	340	yes	\(-1\)	\(1\)	\(e\left(\frac{163}{340}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{163}{170}\right)\)	\(e\left(\frac{2}{85}\right)\)	\(e\left(\frac{93}{340}\right)\)	\(e\left(\frac{73}{340}\right)\)	\(e\left(\frac{149}{340}\right)\)	\(e\left(\frac{10}{17}\right)\)	\(e\left(\frac{171}{340}\right)\)	\(e\left(\frac{4}{85}\right)\)
\(\chi_{1021}(22,\cdot)\)	1021.x	1020	yes	\(-1\)	\(1\)	\(e\left(\frac{319}{340}\right)\)	\(e\left(\frac{13}{34}\right)\)	\(e\left(\frac{149}{170}\right)\)	\(e\left(\frac{103}{255}\right)\)	\(e\left(\frac{109}{340}\right)\)	\(e\left(\frac{49}{340}\right)\)	\(e\left(\frac{277}{340}\right)\)	\(e\left(\frac{13}{17}\right)\)	\(e\left(\frac{349}{1020}\right)\)	\(e\left(\frac{121}{255}\right)\)
\(\chi_{1021}(23,\cdot)\)	1021.u	255	yes	\(1\)	\(1\)	\(e\left(\frac{12}{85}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{24}{85}\right)\)	\(e\left(\frac{56}{255}\right)\)	\(e\left(\frac{47}{85}\right)\)	\(e\left(\frac{57}{85}\right)\)	\(e\left(\frac{36}{85}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{92}{255}\right)\)	\(e\left(\frac{197}{255}\right)\)
\(\chi_{1021}(24,\cdot)\)	1021.v	340	yes	\(-1\)	\(1\)	\(e\left(\frac{99}{340}\right)\)	\(e\left(\frac{31}{34}\right)\)	\(e\left(\frac{99}{170}\right)\)	\(e\left(\frac{81}{85}\right)\)	\(e\left(\frac{69}{340}\right)\)	\(e\left(\frac{109}{340}\right)\)	\(e\left(\frac{297}{340}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{83}{340}\right)\)	\(e\left(\frac{77}{85}\right)\)
\(\chi_{1021}(25,\cdot)\)	1021.u	255	yes	\(1\)	\(1\)	\(e\left(\frac{19}{85}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{38}{85}\right)\)	\(e\left(\frac{32}{255}\right)\)	\(e\left(\frac{39}{85}\right)\)	\(e\left(\frac{69}{85}\right)\)	\(e\left(\frac{57}{85}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{89}{255}\right)\)	\(e\left(\frac{149}{255}\right)\)
\(\chi_{1021}(26,\cdot)\)	1021.g	10	yes	\(1\)	\(1\)	\(e\left(\frac{7}{10}\right)\)	\(1\)	\(e\left(\frac{2}{5}\right)\)	\(e\left(\frac{1}{5}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{7}{10}\right)\)	\(e\left(\frac{1}{10}\right)\)	\(1\)	\(e\left(\frac{9}{10}\right)\)	\(e\left(\frac{2}{5}\right)\)
\(\chi_{1021}(27,\cdot)\)	1021.m	34	yes	\(1\)	\(1\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{7}{17}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{29}{34}\right)\)	\(e\left(\frac{33}{34}\right)\)	\(e\left(\frac{11}{34}\right)\)	\(e\left(\frac{14}{17}\right)\)	\(e\left(\frac{27}{34}\right)\)	\(e\left(\frac{12}{17}\right)\)
\(\chi_{1021}(28,\cdot)\)	1021.v	340	yes	\(-1\)	\(1\)	\(e\left(\frac{259}{340}\right)\)	\(e\left(\frac{21}{34}\right)\)	\(e\left(\frac{89}{170}\right)\)	\(e\left(\frac{11}{85}\right)\)	\(e\left(\frac{129}{340}\right)\)	\(e\left(\frac{189}{340}\right)\)	\(e\left(\frac{97}{340}\right)\)	\(e\left(\frac{4}{17}\right)\)	\(e\left(\frac{303}{340}\right)\)	\(e\left(\frac{22}{85}\right)\)
\(\chi_{1021}(29,\cdot)\)	1021.w	510	yes	\(1\)	\(1\)	\(e\left(\frac{71}{170}\right)\)	\(e\left(\frac{3}{17}\right)\)	\(e\left(\frac{71}{85}\right)\)	\(e\left(\frac{194}{255}\right)\)	\(e\left(\frac{101}{170}\right)\)	\(e\left(\frac{61}{170}\right)\)	\(e\left(\frac{43}{170}\right)\)	\(e\left(\frac{6}{17}\right)\)	\(e\left(\frac{91}{510}\right)\)	\(e\left(\frac{218}{255}\right)\)
\(\chi_{1021}(30,\cdot)\)	1021.x	1020	yes	\(-1\)	\(1\)	\(e\left(\frac{161}{340}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{161}{170}\right)\)	\(e\left(\frac{202}{255}\right)\)	\(e\left(\frac{71}{340}\right)\)	\(e\left(\frac{191}{340}\right)\)	\(e\left(\frac{143}{340}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{271}{1020}\right)\)	\(e\left(\frac{64}{255}\right)\)
\(\chi_{1021}(31,\cdot)\)	1021.x	1020	yes	\(-1\)	\(1\)	\(e\left(\frac{117}{340}\right)\)	\(e\left(\frac{15}{34}\right)\)	\(e\left(\frac{117}{170}\right)\)	\(e\left(\frac{179}{255}\right)\)	\(e\left(\frac{267}{340}\right)\)	\(e\left(\frac{67}{340}\right)\)	\(e\left(\frac{11}{340}\right)\)	\(e\left(\frac{15}{17}\right)\)	\(e\left(\frac{47}{1020}\right)\)	\(e\left(\frac{188}{255}\right)\)
\(\chi_{1021}(32,\cdot)\)	1021.p	68	yes	\(-1\)	\(1\)	\(e\left(\frac{39}{68}\right)\)	\(e\left(\frac{25}{34}\right)\)	\(e\left(\frac{5}{34}\right)\)	\(e\left(\frac{1}{17}\right)\)	\(e\left(\frac{21}{68}\right)\)	\(e\left(\frac{45}{68}\right)\)	\(e\left(\frac{49}{68}\right)\)	\(e\left(\frac{8}{17}\right)\)	\(e\left(\frac{43}{68}\right)\)	\(e\left(\frac{2}{17}\right)\)

Introduction

L-functions

Modular forms

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Properties

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Character group

First 32 of 1020 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.