LMFDB - Group of Dirichlet characters of modulus 5054

Show commands: Pari/GP / SageMath

sage: H = DirichletGroup(5054)

pari: g = idealstar(,5054,2)

Character group

sage: G.order() pari: g.no
Order	=	2052
sage: H.invariants() pari: g.cyc
Structure	=	$C_{6}\times C_{342}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{5054}(1445,\cdot)$, $\chi_{5054}(1807,\cdot)$

First 32 of 2052 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$23$	$25$	$27$
$\chi_{5054}(1,\cdot)$	5054.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{5054}(3,\cdot)$	5054.ck	342	no	$1$	$1$	$e\left(\frac{113}{171}\right)$	$e\left(\frac{43}{342}\right)$	$e\left(\frac{55}{171}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{37}{171}\right)$	$e\left(\frac{269}{342}\right)$	$e\left(\frac{7}{342}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{43}{171}\right)$	$e\left(\frac{56}{57}\right)$
$\chi_{5054}(5,\cdot)$	5054.ce	342	no	$-1$	$1$	$e\left(\frac{43}{342}\right)$	$e\left(\frac{187}{342}\right)$	$e\left(\frac{43}{171}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{49}{342}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{16}{171}\right)$	$e\left(\frac{43}{114}\right)$
$\chi_{5054}(9,\cdot)$	5054.cb	171	no	$1$	$1$	$e\left(\frac{55}{171}\right)$	$e\left(\frac{43}{171}\right)$	$e\left(\frac{110}{171}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{7}{171}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{86}{171}\right)$	$e\left(\frac{55}{57}\right)$
$\chi_{5054}(11,\cdot)$	5054.bl	57	no	$1$	$1$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{10}{19}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{7}{19}\right)$
$\chi_{5054}(13,\cdot)$	5054.cl	342	no	$1$	$1$	$e\left(\frac{37}{171}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{74}{171}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{170}{171}\right)$	$e\left(\frac{307}{342}\right)$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{37}{57}\right)$
$\chi_{5054}(15,\cdot)$	5054.ch	342	no	$-1$	$1$	$e\left(\frac{269}{342}\right)$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{98}{171}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{307}{342}\right)$	$e\left(\frac{157}{342}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{41}{114}\right)$
$\chi_{5054}(17,\cdot)$	5054.cj	342	no	$-1$	$1$	$e\left(\frac{7}{342}\right)$	$e\left(\frac{49}{342}\right)$	$e\left(\frac{7}{171}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{28}{171}\right)$	$e\left(\frac{175}{342}\right)$	$e\left(\frac{139}{171}\right)$	$e\left(\frac{49}{171}\right)$	$e\left(\frac{7}{114}\right)$
$\chi_{5054}(23,\cdot)$	5054.cb	171	no	$1$	$1$	$e\left(\frac{115}{171}\right)$	$e\left(\frac{121}{171}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{65}{171}\right)$	$e\left(\frac{139}{171}\right)$	$e\left(\frac{170}{171}\right)$	$e\left(\frac{71}{171}\right)$	$e\left(\frac{1}{57}\right)$
$\chi_{5054}(25,\cdot)$	5054.ca	171	no	$1$	$1$	$e\left(\frac{43}{171}\right)$	$e\left(\frac{16}{171}\right)$	$e\left(\frac{86}{171}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{59}{171}\right)$	$e\left(\frac{49}{171}\right)$	$e\left(\frac{71}{171}\right)$	$e\left(\frac{32}{171}\right)$	$e\left(\frac{43}{57}\right)$
$\chi_{5054}(27,\cdot)$	5054.bv	114	no	$1$	$1$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{55}{57}\right)$	$e\left(\frac{7}{19}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{41}{114}\right)$	$e\left(\frac{7}{114}\right)$	$e\left(\frac{1}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{18}{19}\right)$
$\chi_{5054}(29,\cdot)$	5054.ch	342	no	$-1$	$1$	$e\left(\frac{311}{342}\right)$	$e\left(\frac{91}{171}\right)$	$e\left(\frac{140}{171}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{121}{342}\right)$	$e\left(\frac{151}{342}\right)$	$e\left(\frac{40}{171}\right)$	$e\left(\frac{44}{171}\right)$	$e\left(\frac{11}{171}\right)$	$e\left(\frac{83}{114}\right)$
$\chi_{5054}(31,\cdot)$	5054.bo	114	no	$1$	$1$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{43}{114}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{2}{57}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{79}{114}\right)$	$e\left(\frac{15}{38}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{18}{19}\right)$
$\chi_{5054}(33,\cdot)$	5054.cf	342	no	$1$	$1$	$e\left(\frac{134}{171}\right)$	$e\left(\frac{223}{342}\right)$	$e\left(\frac{97}{171}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{58}{171}\right)$	$e\left(\frac{149}{342}\right)$	$e\left(\frac{31}{342}\right)$	$e\left(\frac{94}{171}\right)$	$e\left(\frac{52}{171}\right)$	$e\left(\frac{20}{57}\right)$
$\chi_{5054}(37,\cdot)$	5054.bt	114	no	$-1$	$1$	$e\left(\frac{71}{114}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{11}{38}\right)$	$e\left(\frac{31}{38}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{22}{57}\right)$	$e\left(\frac{33}{38}\right)$
$\chi_{5054}(39,\cdot)$	5054.bn	57	no	$1$	$1$	$e\left(\frac{50}{57}\right)$	$e\left(\frac{46}{57}\right)$	$e\left(\frac{43}{57}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{4}{19}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{53}{57}\right)$	$e\left(\frac{7}{57}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{12}{19}\right)$
$\chi_{5054}(41,\cdot)$	5054.cl	342	no	$1$	$1$	$e\left(\frac{125}{171}\right)$	$e\left(\frac{325}{342}\right)$	$e\left(\frac{79}{171}\right)$	$e\left(\frac{56}{57}\right)$	$e\left(\frac{163}{171}\right)$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{265}{342}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{154}{171}\right)$	$e\left(\frac{11}{57}\right)$
$\chi_{5054}(43,\cdot)$	5054.cc	171	no	$1$	$1$	$e\left(\frac{23}{171}\right)$	$e\left(\frac{47}{171}\right)$	$e\left(\frac{46}{171}\right)$	$e\left(\frac{29}{57}\right)$	$e\left(\frac{4}{171}\right)$	$e\left(\frac{70}{171}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{34}{171}\right)$	$e\left(\frac{94}{171}\right)$	$e\left(\frac{23}{57}\right)$
$\chi_{5054}(45,\cdot)$	5054.by	114	no	$-1$	$1$	$e\left(\frac{17}{38}\right)$	$e\left(\frac{91}{114}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{13}{114}\right)$	$e\left(\frac{14}{57}\right)$	$e\left(\frac{7}{38}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{34}{57}\right)$	$e\left(\frac{13}{38}\right)$
$\chi_{5054}(47,\cdot)$	5054.cj	342	no	$-1$	$1$	$e\left(\frac{137}{342}\right)$	$e\left(\frac{275}{342}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{175}{342}\right)$	$e\left(\frac{35}{171}\right)$	$e\left(\frac{5}{342}\right)$	$e\left(\frac{131}{171}\right)$	$e\left(\frac{104}{171}\right)$	$e\left(\frac{23}{114}\right)$
$\chi_{5054}(51,\cdot)$	5054.ci	342	no	$-1$	$1$	$e\left(\frac{233}{342}\right)$	$e\left(\frac{46}{171}\right)$	$e\left(\frac{62}{171}\right)$	$e\left(\frac{11}{57}\right)$	$e\left(\frac{43}{342}\right)$	$e\left(\frac{325}{342}\right)$	$e\left(\frac{91}{171}\right)$	$e\left(\frac{83}{171}\right)$	$e\left(\frac{92}{171}\right)$	$e\left(\frac{5}{114}\right)$
$\chi_{5054}(53,\cdot)$	5054.cd	342	no	$-1$	$1$	$e\left(\frac{137}{342}\right)$	$e\left(\frac{109}{171}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{8}{19}\right)$	$e\left(\frac{289}{342}\right)$	$e\left(\frac{13}{342}\right)$	$e\left(\frac{88}{171}\right)$	$e\left(\frac{131}{171}\right)$	$e\left(\frac{47}{171}\right)$	$e\left(\frac{23}{114}\right)$
$\chi_{5054}(55,\cdot)$	5054.cg	342	no	$-1$	$1$	$e\left(\frac{85}{342}\right)$	$e\left(\frac{25}{342}\right)$	$e\left(\frac{85}{171}\right)$	$e\left(\frac{35}{57}\right)$	$e\left(\frac{275}{342}\right)$	$e\left(\frac{55}{171}\right)$	$e\left(\frac{73}{342}\right)$	$e\left(\frac{100}{171}\right)$	$e\left(\frac{25}{171}\right)$	$e\left(\frac{85}{114}\right)$
$\chi_{5054}(59,\cdot)$	5054.ck	342	no	$1$	$1$	$e\left(\frac{125}{171}\right)$	$e\left(\frac{211}{342}\right)$	$e\left(\frac{79}{171}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{119}{342}\right)$	$e\left(\frac{265}{342}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{40}{171}\right)$	$e\left(\frac{11}{57}\right)$
$\chi_{5054}(61,\cdot)$	5054.cj	342	no	$-1$	$1$	$e\left(\frac{77}{342}\right)$	$e\left(\frac{197}{342}\right)$	$e\left(\frac{77}{171}\right)$	$e\left(\frac{44}{57}\right)$	$e\left(\frac{1}{342}\right)$	$e\left(\frac{137}{171}\right)$	$e\left(\frac{215}{342}\right)$	$e\left(\frac{161}{171}\right)$	$e\left(\frac{26}{171}\right)$	$e\left(\frac{77}{114}\right)$
$\chi_{5054}(65,\cdot)$	5054.bz	114	no	$-1$	$1$	$e\left(\frac{13}{38}\right)$	$e\left(\frac{13}{57}\right)$	$e\left(\frac{13}{19}\right)$	$e\left(\frac{37}{57}\right)$	$e\left(\frac{77}{114}\right)$	$e\left(\frac{65}{114}\right)$	$e\left(\frac{1}{19}\right)$	$e\left(\frac{3}{19}\right)$	$e\left(\frac{26}{57}\right)$	$e\left(\frac{1}{38}\right)$
$\chi_{5054}(67,\cdot)$	5054.cd	342	no	$-1$	$1$	$e\left(\frac{341}{342}\right)$	$e\left(\frac{139}{171}\right)$	$e\left(\frac{170}{171}\right)$	$e\left(\frac{17}{19}\right)$	$e\left(\frac{265}{342}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{73}{171}\right)$	$e\left(\frac{29}{171}\right)$	$e\left(\frac{107}{171}\right)$	$e\left(\frac{113}{114}\right)$
$\chi_{5054}(69,\cdot)$	5054.m	6	no	$1$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$
$\chi_{5054}(71,\cdot)$	5054.ch	342	no	$-1$	$1$	$e\left(\frac{37}{342}\right)$	$e\left(\frac{101}{171}\right)$	$e\left(\frac{37}{171}\right)$	$e\left(\frac{32}{57}\right)$	$e\left(\frac{341}{342}\right)$	$e\left(\frac{239}{342}\right)$	$e\left(\frac{35}{171}\right)$	$e\left(\frac{124}{171}\right)$	$e\left(\frac{31}{171}\right)$	$e\left(\frac{37}{114}\right)$
$\chi_{5054}(73,\cdot)$	5054.cj	342	no	$-1$	$1$	$e\left(\frac{235}{342}\right)$	$e\left(\frac{277}{342}\right)$	$e\left(\frac{64}{171}\right)$	$e\left(\frac{4}{57}\right)$	$e\left(\frac{83}{342}\right)$	$e\left(\frac{85}{171}\right)$	$e\left(\frac{61}{342}\right)$	$e\left(\frac{25}{171}\right)$	$e\left(\frac{106}{171}\right)$	$e\left(\frac{7}{114}\right)$
$\chi_{5054}(75,\cdot)$	5054.bw	114	no	$1$	$1$	$e\left(\frac{52}{57}\right)$	$e\left(\frac{25}{114}\right)$	$e\left(\frac{47}{57}\right)$	$e\left(\frac{10}{57}\right)$	$e\left(\frac{11}{19}\right)$	$e\left(\frac{5}{38}\right)$	$e\left(\frac{35}{114}\right)$	$e\left(\frac{5}{57}\right)$	$e\left(\frac{25}{57}\right)$	$e\left(\frac{14}{19}\right)$
$\chi_{5054}(79,\cdot)$	5054.cd	342	no	$-1$	$1$	$e\left(\frac{103}{342}\right)$	$e\left(\frac{47}{171}\right)$	$e\left(\frac{103}{171}\right)$	$e\left(\frac{16}{19}\right)$	$e\left(\frac{65}{342}\right)$	$e\left(\frac{197}{342}\right)$	$e\left(\frac{5}{171}\right)$	$e\left(\frac{91}{171}\right)$	$e\left(\frac{94}{171}\right)$	$e\left(\frac{103}{114}\right)$

Click here to search among the remaining 2020 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 $\F_{q}$

Modulus	$5054$
Structure	\(C_{6}\times C_{342}\)
Order	$2052$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(23\)	\(25\)	\(27\)
\(\chi_{5054}(1,\cdot)\)	5054.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{5054}(3,\cdot)\)	5054.ck	342	no	\(1\)	\(1\)	\(e\left(\frac{113}{171}\right)\)	\(e\left(\frac{43}{342}\right)\)	\(e\left(\frac{55}{171}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{37}{171}\right)\)	\(e\left(\frac{269}{342}\right)\)	\(e\left(\frac{7}{342}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{43}{171}\right)\)	\(e\left(\frac{56}{57}\right)\)
\(\chi_{5054}(5,\cdot)\)	5054.ce	342	no	\(-1\)	\(1\)	\(e\left(\frac{43}{342}\right)\)	\(e\left(\frac{187}{342}\right)\)	\(e\left(\frac{43}{171}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{49}{342}\right)\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{16}{171}\right)\)	\(e\left(\frac{43}{114}\right)\)
\(\chi_{5054}(9,\cdot)\)	5054.cb	171	no	\(1\)	\(1\)	\(e\left(\frac{55}{171}\right)\)	\(e\left(\frac{43}{171}\right)\)	\(e\left(\frac{110}{171}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{74}{171}\right)\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{7}{171}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{86}{171}\right)\)	\(e\left(\frac{55}{57}\right)\)
\(\chi_{5054}(11,\cdot)\)	5054.bl	57	no	\(1\)	\(1\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{10}{19}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{7}{19}\right)\)
\(\chi_{5054}(13,\cdot)\)	5054.cl	342	no	\(1\)	\(1\)	\(e\left(\frac{37}{171}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{74}{171}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{170}{171}\right)\)	\(e\left(\frac{307}{342}\right)\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{37}{57}\right)\)
\(\chi_{5054}(15,\cdot)\)	5054.ch	342	no	\(-1\)	\(1\)	\(e\left(\frac{269}{342}\right)\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{98}{171}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{307}{342}\right)\)	\(e\left(\frac{157}{342}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{41}{114}\right)\)
\(\chi_{5054}(17,\cdot)\)	5054.cj	342	no	\(-1\)	\(1\)	\(e\left(\frac{7}{342}\right)\)	\(e\left(\frac{49}{342}\right)\)	\(e\left(\frac{7}{171}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{28}{171}\right)\)	\(e\left(\frac{175}{342}\right)\)	\(e\left(\frac{139}{171}\right)\)	\(e\left(\frac{49}{171}\right)\)	\(e\left(\frac{7}{114}\right)\)
\(\chi_{5054}(23,\cdot)\)	5054.cb	171	no	\(1\)	\(1\)	\(e\left(\frac{115}{171}\right)\)	\(e\left(\frac{121}{171}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{65}{171}\right)\)	\(e\left(\frac{139}{171}\right)\)	\(e\left(\frac{170}{171}\right)\)	\(e\left(\frac{71}{171}\right)\)	\(e\left(\frac{1}{57}\right)\)
\(\chi_{5054}(25,\cdot)\)	5054.ca	171	no	\(1\)	\(1\)	\(e\left(\frac{43}{171}\right)\)	\(e\left(\frac{16}{171}\right)\)	\(e\left(\frac{86}{171}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{59}{171}\right)\)	\(e\left(\frac{49}{171}\right)\)	\(e\left(\frac{71}{171}\right)\)	\(e\left(\frac{32}{171}\right)\)	\(e\left(\frac{43}{57}\right)\)
\(\chi_{5054}(27,\cdot)\)	5054.bv	114	no	\(1\)	\(1\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{7}{19}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{41}{114}\right)\)	\(e\left(\frac{7}{114}\right)\)	\(e\left(\frac{1}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)
\(\chi_{5054}(29,\cdot)\)	5054.ch	342	no	\(-1\)	\(1\)	\(e\left(\frac{311}{342}\right)\)	\(e\left(\frac{91}{171}\right)\)	\(e\left(\frac{140}{171}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{121}{342}\right)\)	\(e\left(\frac{151}{342}\right)\)	\(e\left(\frac{40}{171}\right)\)	\(e\left(\frac{44}{171}\right)\)	\(e\left(\frac{11}{171}\right)\)	\(e\left(\frac{83}{114}\right)\)
\(\chi_{5054}(31,\cdot)\)	5054.bo	114	no	\(1\)	\(1\)	\(e\left(\frac{6}{19}\right)\)	\(e\left(\frac{43}{114}\right)\)	\(e\left(\frac{12}{19}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{79}{114}\right)\)	\(e\left(\frac{15}{38}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{18}{19}\right)\)
\(\chi_{5054}(33,\cdot)\)	5054.cf	342	no	\(1\)	\(1\)	\(e\left(\frac{134}{171}\right)\)	\(e\left(\frac{223}{342}\right)\)	\(e\left(\frac{97}{171}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{58}{171}\right)\)	\(e\left(\frac{149}{342}\right)\)	\(e\left(\frac{31}{342}\right)\)	\(e\left(\frac{94}{171}\right)\)	\(e\left(\frac{52}{171}\right)\)	\(e\left(\frac{20}{57}\right)\)
\(\chi_{5054}(37,\cdot)\)	5054.bt	114	no	\(-1\)	\(1\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{31}{38}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{22}{57}\right)\)	\(e\left(\frac{33}{38}\right)\)
\(\chi_{5054}(39,\cdot)\)	5054.bn	57	no	\(1\)	\(1\)	\(e\left(\frac{50}{57}\right)\)	\(e\left(\frac{46}{57}\right)\)	\(e\left(\frac{43}{57}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{4}{19}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{7}{57}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{12}{19}\right)\)
\(\chi_{5054}(41,\cdot)\)	5054.cl	342	no	\(1\)	\(1\)	\(e\left(\frac{125}{171}\right)\)	\(e\left(\frac{325}{342}\right)\)	\(e\left(\frac{79}{171}\right)\)	\(e\left(\frac{56}{57}\right)\)	\(e\left(\frac{163}{171}\right)\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{265}{342}\right)\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{154}{171}\right)\)	\(e\left(\frac{11}{57}\right)\)
\(\chi_{5054}(43,\cdot)\)	5054.cc	171	no	\(1\)	\(1\)	\(e\left(\frac{23}{171}\right)\)	\(e\left(\frac{47}{171}\right)\)	\(e\left(\frac{46}{171}\right)\)	\(e\left(\frac{29}{57}\right)\)	\(e\left(\frac{4}{171}\right)\)	\(e\left(\frac{70}{171}\right)\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{34}{171}\right)\)	\(e\left(\frac{94}{171}\right)\)	\(e\left(\frac{23}{57}\right)\)
\(\chi_{5054}(45,\cdot)\)	5054.by	114	no	\(-1\)	\(1\)	\(e\left(\frac{17}{38}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{13}{114}\right)\)	\(e\left(\frac{14}{57}\right)\)	\(e\left(\frac{7}{38}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{34}{57}\right)\)	\(e\left(\frac{13}{38}\right)\)
\(\chi_{5054}(47,\cdot)\)	5054.cj	342	no	\(-1\)	\(1\)	\(e\left(\frac{137}{342}\right)\)	\(e\left(\frac{275}{342}\right)\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{175}{342}\right)\)	\(e\left(\frac{35}{171}\right)\)	\(e\left(\frac{5}{342}\right)\)	\(e\left(\frac{131}{171}\right)\)	\(e\left(\frac{104}{171}\right)\)	\(e\left(\frac{23}{114}\right)\)
\(\chi_{5054}(51,\cdot)\)	5054.ci	342	no	\(-1\)	\(1\)	\(e\left(\frac{233}{342}\right)\)	\(e\left(\frac{46}{171}\right)\)	\(e\left(\frac{62}{171}\right)\)	\(e\left(\frac{11}{57}\right)\)	\(e\left(\frac{43}{342}\right)\)	\(e\left(\frac{325}{342}\right)\)	\(e\left(\frac{91}{171}\right)\)	\(e\left(\frac{83}{171}\right)\)	\(e\left(\frac{92}{171}\right)\)	\(e\left(\frac{5}{114}\right)\)
\(\chi_{5054}(53,\cdot)\)	5054.cd	342	no	\(-1\)	\(1\)	\(e\left(\frac{137}{342}\right)\)	\(e\left(\frac{109}{171}\right)\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{8}{19}\right)\)	\(e\left(\frac{289}{342}\right)\)	\(e\left(\frac{13}{342}\right)\)	\(e\left(\frac{88}{171}\right)\)	\(e\left(\frac{131}{171}\right)\)	\(e\left(\frac{47}{171}\right)\)	\(e\left(\frac{23}{114}\right)\)
\(\chi_{5054}(55,\cdot)\)	5054.cg	342	no	\(-1\)	\(1\)	\(e\left(\frac{85}{342}\right)\)	\(e\left(\frac{25}{342}\right)\)	\(e\left(\frac{85}{171}\right)\)	\(e\left(\frac{35}{57}\right)\)	\(e\left(\frac{275}{342}\right)\)	\(e\left(\frac{55}{171}\right)\)	\(e\left(\frac{73}{342}\right)\)	\(e\left(\frac{100}{171}\right)\)	\(e\left(\frac{25}{171}\right)\)	\(e\left(\frac{85}{114}\right)\)
\(\chi_{5054}(59,\cdot)\)	5054.ck	342	no	\(1\)	\(1\)	\(e\left(\frac{125}{171}\right)\)	\(e\left(\frac{211}{342}\right)\)	\(e\left(\frac{79}{171}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{119}{342}\right)\)	\(e\left(\frac{265}{342}\right)\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{40}{171}\right)\)	\(e\left(\frac{11}{57}\right)\)
\(\chi_{5054}(61,\cdot)\)	5054.cj	342	no	\(-1\)	\(1\)	\(e\left(\frac{77}{342}\right)\)	\(e\left(\frac{197}{342}\right)\)	\(e\left(\frac{77}{171}\right)\)	\(e\left(\frac{44}{57}\right)\)	\(e\left(\frac{1}{342}\right)\)	\(e\left(\frac{137}{171}\right)\)	\(e\left(\frac{215}{342}\right)\)	\(e\left(\frac{161}{171}\right)\)	\(e\left(\frac{26}{171}\right)\)	\(e\left(\frac{77}{114}\right)\)
\(\chi_{5054}(65,\cdot)\)	5054.bz	114	no	\(-1\)	\(1\)	\(e\left(\frac{13}{38}\right)\)	\(e\left(\frac{13}{57}\right)\)	\(e\left(\frac{13}{19}\right)\)	\(e\left(\frac{37}{57}\right)\)	\(e\left(\frac{77}{114}\right)\)	\(e\left(\frac{65}{114}\right)\)	\(e\left(\frac{1}{19}\right)\)	\(e\left(\frac{3}{19}\right)\)	\(e\left(\frac{26}{57}\right)\)	\(e\left(\frac{1}{38}\right)\)
\(\chi_{5054}(67,\cdot)\)	5054.cd	342	no	\(-1\)	\(1\)	\(e\left(\frac{341}{342}\right)\)	\(e\left(\frac{139}{171}\right)\)	\(e\left(\frac{170}{171}\right)\)	\(e\left(\frac{17}{19}\right)\)	\(e\left(\frac{265}{342}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{73}{171}\right)\)	\(e\left(\frac{29}{171}\right)\)	\(e\left(\frac{107}{171}\right)\)	\(e\left(\frac{113}{114}\right)\)
\(\chi_{5054}(69,\cdot)\)	5054.m	6	no	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(1\)
\(\chi_{5054}(71,\cdot)\)	5054.ch	342	no	\(-1\)	\(1\)	\(e\left(\frac{37}{342}\right)\)	\(e\left(\frac{101}{171}\right)\)	\(e\left(\frac{37}{171}\right)\)	\(e\left(\frac{32}{57}\right)\)	\(e\left(\frac{341}{342}\right)\)	\(e\left(\frac{239}{342}\right)\)	\(e\left(\frac{35}{171}\right)\)	\(e\left(\frac{124}{171}\right)\)	\(e\left(\frac{31}{171}\right)\)	\(e\left(\frac{37}{114}\right)\)
\(\chi_{5054}(73,\cdot)\)	5054.cj	342	no	\(-1\)	\(1\)	\(e\left(\frac{235}{342}\right)\)	\(e\left(\frac{277}{342}\right)\)	\(e\left(\frac{64}{171}\right)\)	\(e\left(\frac{4}{57}\right)\)	\(e\left(\frac{83}{342}\right)\)	\(e\left(\frac{85}{171}\right)\)	\(e\left(\frac{61}{342}\right)\)	\(e\left(\frac{25}{171}\right)\)	\(e\left(\frac{106}{171}\right)\)	\(e\left(\frac{7}{114}\right)\)
\(\chi_{5054}(75,\cdot)\)	5054.bw	114	no	\(1\)	\(1\)	\(e\left(\frac{52}{57}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{47}{57}\right)\)	\(e\left(\frac{10}{57}\right)\)	\(e\left(\frac{11}{19}\right)\)	\(e\left(\frac{5}{38}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{5}{57}\right)\)	\(e\left(\frac{25}{57}\right)\)	\(e\left(\frac{14}{19}\right)\)
\(\chi_{5054}(79,\cdot)\)	5054.cd	342	no	\(-1\)	\(1\)	\(e\left(\frac{103}{342}\right)\)	\(e\left(\frac{47}{171}\right)\)	\(e\left(\frac{103}{171}\right)\)	\(e\left(\frac{16}{19}\right)\)	\(e\left(\frac{65}{342}\right)\)	\(e\left(\frac{197}{342}\right)\)	\(e\left(\frac{5}{171}\right)\)	\(e\left(\frac{91}{171}\right)\)	\(e\left(\frac{94}{171}\right)\)	\(e\left(\frac{103}{114}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 2052 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.