LMFDB - Group of Dirichlet characters of modulus 5082

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(5082)

gp:g = idealstar(,5082,2)

magma:G = FullDirichletGroup(5082);

Character group

Order	=	1320	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{2}\times C_{330}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{5082}(3389,\cdot)$, $\chi_{5082}(4357,\cdot)$, $\chi_{5082}(2059,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 1320 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	$-1$	$1$	$5$	$13$	$17$	$19$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{5082}(1,\cdot)$	5082.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{5082}(5,\cdot)$	5082.cf	330	no	$1$	$1$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{26}{55}\right)$
$\chi_{5082}(13,\cdot)$	5082.ca	110	no	$1$	$1$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{34}{55}\right)$
$\chi_{5082}(17,\cdot)$	5082.ch	330	no	$-1$	$1$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{27}{110}\right)$
$\chi_{5082}(19,\cdot)$	5082.ck	330	no	$1$	$1$	$e\left(\frac{1}{330}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{47}{55}\right)$
$\chi_{5082}(23,\cdot)$	5082.bq	66	no	$-1$	$1$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{3}{22}\right)$
$\chi_{5082}(25,\cdot)$	5082.ce	165	no	$1$	$1$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{52}{55}\right)$
$\chi_{5082}(29,\cdot)$	5082.by	110	no	$1$	$1$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{67}{110}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{91}{110}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{3}{55}\right)$
$\chi_{5082}(31,\cdot)$	5082.cj	330	no	$-1$	$1$	$e\left(\frac{227}{330}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{157}{330}\right)$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{16}{55}\right)$	$e\left(\frac{133}{330}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{53}{110}\right)$
$\chi_{5082}(37,\cdot)$	5082.ce	165	no	$1$	$1$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{59}{165}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{5082}(41,\cdot)$	5082.cd	110	no	$-1$	$1$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{27}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{52}{55}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{89}{110}\right)$
$\chi_{5082}(43,\cdot)$	5082.bc	22	no	$-1$	$1$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{22}\right)$
$\chi_{5082}(47,\cdot)$	5082.cf	330	no	$1$	$1$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{53}{110}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{37}{330}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{27}{55}\right)$
$\chi_{5082}(53,\cdot)$	5082.cl	330	no	$-1$	$1$	$e\left(\frac{47}{330}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{127}{330}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{73}{110}\right)$
$\chi_{5082}(59,\cdot)$	5082.cf	330	no	$1$	$1$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{97}{110}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{323}{330}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{49}{110}\right)$	$e\left(\frac{61}{330}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{38}{55}\right)$
$\chi_{5082}(61,\cdot)$	5082.ck	330	no	$1$	$1$	$e\left(\frac{163}{330}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{17}{330}\right)$	$e\left(\frac{47}{165}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{5082}(65,\cdot)$	5082.bt	66	no	$1$	$1$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{15}{22}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{47}{66}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{1}{11}\right)$
$\chi_{5082}(67,\cdot)$	5082.bo	33	no	$1$	$1$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{26}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{7}{33}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{28}{33}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{10}{11}\right)$
$\chi_{5082}(71,\cdot)$	5082.bz	110	no	$-1$	$1$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{41}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{7}{22}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{3}{110}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{17}{110}\right)$
$\chi_{5082}(73,\cdot)$	5082.ck	330	no	$1$	$1$	$e\left(\frac{239}{330}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{31}{330}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{5082}(79,\cdot)$	5082.cg	330	no	$-1$	$1$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{197}{330}\right)$	$e\left(\frac{199}{330}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{63}{110}\right)$
$\chi_{5082}(83,\cdot)$	5082.cd	110	no	$-1$	$1$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{21}{22}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{19}{110}\right)$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{7}{110}\right)$
$\chi_{5082}(85,\cdot)$	5082.cb	110	no	$-1$	$1$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{103}{110}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{89}{110}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{1}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{53}{55}\right)$	$e\left(\frac{79}{110}\right)$
$\chi_{5082}(89,\cdot)$	5082.bw	66	no	$1$	$1$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{2}{33}\right)$	$e\left(\frac{17}{22}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{19}{33}\right)$	$e\left(\frac{6}{11}\right)$
$\chi_{5082}(95,\cdot)$	5082.ci	330	no	$1$	$1$	$e\left(\frac{149}{330}\right)$	$e\left(\frac{17}{110}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{263}{330}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{18}{55}\right)$
$\chi_{5082}(97,\cdot)$	5082.bx	110	no	$-1$	$1$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{61}{110}\right)$	$e\left(\frac{59}{110}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{3}{110}\right)$
$\chi_{5082}(101,\cdot)$	5082.ch	330	no	$-1$	$1$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{7}{330}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{193}{330}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{43}{110}\right)$
$\chi_{5082}(103,\cdot)$	5082.cj	330	no	$-1$	$1$	$e\left(\frac{79}{330}\right)$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{59}{330}\right)$	$e\left(\frac{73}{330}\right)$	$e\left(\frac{10}{33}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{71}{330}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{1}{110}\right)$
$\chi_{5082}(107,\cdot)$	5082.ci	330	no	$1$	$1$	$e\left(\frac{181}{330}\right)$	$e\left(\frac{93}{110}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{67}{330}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{37}{55}\right)$
$\chi_{5082}(109,\cdot)$	5082.bv	66	no	$-1$	$1$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{20}{33}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{33}\right)$	$e\left(\frac{23}{33}\right)$	$e\left(\frac{7}{22}\right)$
$\chi_{5082}(113,\cdot)$	5082.bz	110	no	$-1$	$1$	$e\left(\frac{57}{110}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{37}{110}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{51}{110}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{69}{110}\right)$
$\chi_{5082}(115,\cdot)$	5082.cj	330	no	$-1$	$1$	$e\left(\frac{233}{330}\right)$	$e\left(\frac{79}{110}\right)$	$e\left(\frac{103}{330}\right)$	$e\left(\frac{161}{330}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{247}{330}\right)$	$e\left(\frac{52}{165}\right)$	$e\left(\frac{67}{110}\right)$

Click here to search among the remaining 1288 characters.

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Modulus	$5082$
Structure	\(C_{2}\times C_{2}\times C_{330}\)
Order	$1320$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(5\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{5082}(1,\cdot)\)	5082.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{5082}(5,\cdot)\)	5082.cf	330	no	\(1\)	\(1\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{26}{55}\right)\)
\(\chi_{5082}(13,\cdot)\)	5082.ca	110	no	\(1\)	\(1\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)
\(\chi_{5082}(17,\cdot)\)	5082.ch	330	no	\(-1\)	\(1\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{27}{110}\right)\)
\(\chi_{5082}(19,\cdot)\)	5082.ck	330	no	\(1\)	\(1\)	\(e\left(\frac{1}{330}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{47}{55}\right)\)
\(\chi_{5082}(23,\cdot)\)	5082.bq	66	no	\(-1\)	\(1\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)
\(\chi_{5082}(25,\cdot)\)	5082.ce	165	no	\(1\)	\(1\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{52}{55}\right)\)
\(\chi_{5082}(29,\cdot)\)	5082.by	110	no	\(1\)	\(1\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{67}{110}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{91}{110}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)
\(\chi_{5082}(31,\cdot)\)	5082.cj	330	no	\(-1\)	\(1\)	\(e\left(\frac{227}{330}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{157}{330}\right)\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{16}{55}\right)\)	\(e\left(\frac{133}{330}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{53}{110}\right)\)
\(\chi_{5082}(37,\cdot)\)	5082.ce	165	no	\(1\)	\(1\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{59}{165}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{5082}(41,\cdot)\)	5082.cd	110	no	\(-1\)	\(1\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{34}{55}\right)\)	\(e\left(\frac{27}{110}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{52}{55}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{89}{110}\right)\)
\(\chi_{5082}(43,\cdot)\)	5082.bc	22	no	\(-1\)	\(1\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{19}{22}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{22}\right)\)
\(\chi_{5082}(47,\cdot)\)	5082.cf	330	no	\(1\)	\(1\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{53}{110}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{37}{330}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{27}{55}\right)\)
\(\chi_{5082}(53,\cdot)\)	5082.cl	330	no	\(-1\)	\(1\)	\(e\left(\frac{47}{330}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{127}{330}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{73}{110}\right)\)
\(\chi_{5082}(59,\cdot)\)	5082.cf	330	no	\(1\)	\(1\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{97}{110}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{323}{330}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{49}{110}\right)\)	\(e\left(\frac{61}{330}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{38}{55}\right)\)
\(\chi_{5082}(61,\cdot)\)	5082.ck	330	no	\(1\)	\(1\)	\(e\left(\frac{163}{330}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{17}{330}\right)\)	\(e\left(\frac{47}{165}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{5082}(65,\cdot)\)	5082.bt	66	no	\(1\)	\(1\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{15}{22}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{47}{66}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{16}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)
\(\chi_{5082}(67,\cdot)\)	5082.bo	33	no	\(1\)	\(1\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)
\(\chi_{5082}(71,\cdot)\)	5082.bz	110	no	\(-1\)	\(1\)	\(e\left(\frac{81}{110}\right)\)	\(e\left(\frac{17}{55}\right)\)	\(e\left(\frac{41}{110}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{7}{22}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{3}{110}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{17}{110}\right)\)
\(\chi_{5082}(73,\cdot)\)	5082.ck	330	no	\(1\)	\(1\)	\(e\left(\frac{239}{330}\right)\)	\(e\left(\frac{26}{55}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{31}{330}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{5082}(79,\cdot)\)	5082.cg	330	no	\(-1\)	\(1\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{197}{330}\right)\)	\(e\left(\frac{199}{330}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{63}{110}\right)\)
\(\chi_{5082}(83,\cdot)\)	5082.cd	110	no	\(-1\)	\(1\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{101}{110}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{21}{22}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{19}{110}\right)\)	\(e\left(\frac{4}{55}\right)\)	\(e\left(\frac{7}{110}\right)\)
\(\chi_{5082}(85,\cdot)\)	5082.cb	110	no	\(-1\)	\(1\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{103}{110}\right)\)	\(e\left(\frac{87}{110}\right)\)	\(e\left(\frac{89}{110}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{1}{110}\right)\)	\(e\left(\frac{9}{55}\right)\)	\(e\left(\frac{53}{55}\right)\)	\(e\left(\frac{79}{110}\right)\)
\(\chi_{5082}(89,\cdot)\)	5082.bw	66	no	\(1\)	\(1\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)
\(\chi_{5082}(95,\cdot)\)	5082.ci	330	no	\(1\)	\(1\)	\(e\left(\frac{149}{330}\right)\)	\(e\left(\frac{17}{110}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{263}{330}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{18}{55}\right)\)
\(\chi_{5082}(97,\cdot)\)	5082.bx	110	no	\(-1\)	\(1\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{59}{110}\right)\)	\(e\left(\frac{73}{110}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{71}{110}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{3}{110}\right)\)
\(\chi_{5082}(101,\cdot)\)	5082.ch	330	no	\(-1\)	\(1\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{7}{330}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{193}{330}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{43}{110}\right)\)
\(\chi_{5082}(103,\cdot)\)	5082.cj	330	no	\(-1\)	\(1\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{59}{330}\right)\)	\(e\left(\frac{73}{330}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{71}{330}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{1}{110}\right)\)
\(\chi_{5082}(107,\cdot)\)	5082.ci	330	no	\(1\)	\(1\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{67}{330}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{37}{55}\right)\)
\(\chi_{5082}(109,\cdot)\)	5082.bv	66	no	\(-1\)	\(1\)	\(e\left(\frac{29}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{20}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{7}{22}\right)\)
\(\chi_{5082}(113,\cdot)\)	5082.bz	110	no	\(-1\)	\(1\)	\(e\left(\frac{57}{110}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{37}{110}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{9}{22}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{51}{110}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{69}{110}\right)\)
\(\chi_{5082}(115,\cdot)\)	5082.cj	330	no	\(-1\)	\(1\)	\(e\left(\frac{233}{330}\right)\)	\(e\left(\frac{79}{110}\right)\)	\(e\left(\frac{103}{330}\right)\)	\(e\left(\frac{161}{330}\right)\)	\(e\left(\frac{32}{33}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{247}{330}\right)\)	\(e\left(\frac{52}{165}\right)\)	\(e\left(\frac{67}{110}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Downloads

Learn more

Character group

First 32 of 1320 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.