LMFDB - Group of Dirichlet characters of modulus 58492

Show commands: Magma / Pari/GP / SageMath

comment:Define the Dirichlet group

sage:G = DirichletGroup(58492)

gp:g = idealstar(,58492,2)

magma:G = FullDirichletGroup(58492);

Character group

Order	=	25056	comment:Order sage:G.order() gp:g.no magma:Order(G);
Structure	=	$C_{2}\times C_{6}\times C_{2088}$	comment:Group structure sage:sorted(g.order() for g in G.gens()) gp:g.cyc magma:PrimaryInvariants(G);
Generators	=	$\chi_{58492}(29247,\cdot)$, $\chi_{58492}(50137,\cdot)$, $\chi_{58492}(54321,\cdot)$	comment:Generators sage:G.gens() gp:g.gen magma:Generators(G);

First 32 of 25056 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	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{58492}(1,\cdot)$	58492.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{58492}(3,\cdot)$	58492.jd	1044	yes	$1$	$1$	$e\left(\frac{67}{522}\right)$	$e\left(\frac{197}{261}\right)$	$e\left(\frac{67}{261}\right)$	$e\left(\frac{271}{1044}\right)$	$e\left(\frac{68}{261}\right)$	$e\left(\frac{461}{522}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{101}{116}\right)$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{133}{261}\right)$
$\chi_{58492}(5,\cdot)$	58492.jj	1044	no	$-1$	$1$	$e\left(\frac{197}{261}\right)$	$e\left(\frac{8}{261}\right)$	$e\left(\frac{133}{261}\right)$	$e\left(\frac{847}{1044}\right)$	$e\left(\frac{35}{261}\right)$	$e\left(\frac{205}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{263}{348}\right)$	$e\left(\frac{167}{348}\right)$	$e\left(\frac{16}{261}\right)$
$\chi_{58492}(9,\cdot)$	58492.ih	522	no	$1$	$1$	$e\left(\frac{67}{261}\right)$	$e\left(\frac{133}{261}\right)$	$e\left(\frac{134}{261}\right)$	$e\left(\frac{271}{522}\right)$	$e\left(\frac{136}{261}\right)$	$e\left(\frac{200}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{5}{261}\right)$
$\chi_{58492}(11,\cdot)$	58492.ju	2088	yes	$1$	$1$	$e\left(\frac{271}{1044}\right)$	$e\left(\frac{847}{1044}\right)$	$e\left(\frac{271}{522}\right)$	$e\left(\frac{517}{2088}\right)$	$e\left(\frac{541}{1044}\right)$	$e\left(\frac{37}{522}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{95}{696}\right)$	$e\left(\frac{581}{696}\right)$	$e\left(\frac{325}{522}\right)$
$\chi_{58492}(13,\cdot)$	58492.jh	1044	no	$-1$	$1$	$e\left(\frac{68}{261}\right)$	$e\left(\frac{35}{261}\right)$	$e\left(\frac{136}{261}\right)$	$e\left(\frac{541}{1044}\right)$	$e\left(\frac{164}{261}\right)$	$e\left(\frac{103}{261}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{277}{348}\right)$	$e\left(\frac{205}{348}\right)$	$e\left(\frac{70}{261}\right)$
$\chi_{58492}(15,\cdot)$	58492.hq	522	no	$-1$	$1$	$e\left(\frac{461}{522}\right)$	$e\left(\frac{205}{261}\right)$	$e\left(\frac{200}{261}\right)$	$e\left(\frac{37}{522}\right)$	$e\left(\frac{103}{261}\right)$	$e\left(\frac{349}{522}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{109}{174}\right)$	$e\left(\frac{97}{174}\right)$	$e\left(\frac{149}{261}\right)$
$\chi_{58492}(17,\cdot)$	58492.eb	36	no	$-1$	$1$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{58492}(19,\cdot)$	58492.iu	696	yes	$-1$	$1$	$e\left(\frac{101}{116}\right)$	$e\left(\frac{263}{348}\right)$	$e\left(\frac{43}{58}\right)$	$e\left(\frac{95}{696}\right)$	$e\left(\frac{277}{348}\right)$	$e\left(\frac{109}{174}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{443}{696}\right)$	$e\left(\frac{581}{696}\right)$	$e\left(\frac{89}{174}\right)$
$\chi_{58492}(23,\cdot)$	58492.iv	696	yes	$1$	$1$	$e\left(\frac{9}{116}\right)$	$e\left(\frac{167}{348}\right)$	$e\left(\frac{9}{58}\right)$	$e\left(\frac{581}{696}\right)$	$e\left(\frac{205}{348}\right)$	$e\left(\frac{97}{174}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{581}{696}\right)$	$e\left(\frac{359}{696}\right)$	$e\left(\frac{167}{174}\right)$
$\chi_{58492}(25,\cdot)$	58492.hs	522	no	$1$	$1$	$e\left(\frac{133}{261}\right)$	$e\left(\frac{16}{261}\right)$	$e\left(\frac{5}{261}\right)$	$e\left(\frac{325}{522}\right)$	$e\left(\frac{70}{261}\right)$	$e\left(\frac{149}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{89}{174}\right)$	$e\left(\frac{167}{174}\right)$	$e\left(\frac{32}{261}\right)$
$\chi_{58492}(27,\cdot)$	58492.hd	348	yes	$1$	$1$	$e\left(\frac{67}{174}\right)$	$e\left(\frac{23}{87}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{271}{348}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{113}{174}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{71}{116}\right)$	$e\left(\frac{27}{116}\right)$	$e\left(\frac{46}{87}\right)$
$\chi_{58492}(29,\cdot)$	58492.gv	261	no	$1$	$1$	$e\left(\frac{191}{261}\right)$	$e\left(\frac{248}{261}\right)$	$e\left(\frac{121}{261}\right)$	$e\left(\frac{235}{261}\right)$	$e\left(\frac{215}{261}\right)$	$e\left(\frac{178}{261}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{235}{261}\right)$
$\chi_{58492}(31,\cdot)$	58492.jo	2088	yes	$-1$	$1$	$e\left(\frac{263}{1044}\right)$	$e\left(\frac{935}{1044}\right)$	$e\left(\frac{263}{522}\right)$	$e\left(\frac{347}{2088}\right)$	$e\left(\frac{1013}{1044}\right)$	$e\left(\frac{77}{522}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{103}{232}\right)$	$e\left(\frac{89}{232}\right)$	$e\left(\frac{413}{522}\right)$
$\chi_{58492}(33,\cdot)$	58492.iw	696	no	$1$	$1$	$e\left(\frac{45}{116}\right)$	$e\left(\frac{197}{348}\right)$	$e\left(\frac{45}{58}\right)$	$e\left(\frac{353}{696}\right)$	$e\left(\frac{271}{348}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{696}\right)$	$e\left(\frac{635}{696}\right)$	$e\left(\frac{23}{174}\right)$
$\chi_{58492}(37,\cdot)$	58492.ij	696	no	$-1$	$1$	$e\left(\frac{53}{348}\right)$	$e\left(\frac{55}{348}\right)$	$e\left(\frac{53}{174}\right)$	$e\left(\frac{481}{696}\right)$	$e\left(\frac{79}{116}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{696}\right)$	$e\left(\frac{419}{696}\right)$	$e\left(\frac{55}{174}\right)$
$\chi_{58492}(39,\cdot)$	58492.cu	18	yes	$-1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{58492}(41,\cdot)$	58492.et	58	no	$-1$	$1$	$e\left(\frac{25}{58}\right)$	$e\left(\frac{15}{58}\right)$	$e\left(\frac{25}{29}\right)$	$e\left(\frac{1}{58}\right)$	$e\left(\frac{33}{58}\right)$	$e\left(\frac{20}{29}\right)$	$-1$	$e\left(\frac{15}{29}\right)$	$e\left(\frac{11}{58}\right)$	$e\left(\frac{15}{29}\right)$
$\chi_{58492}(43,\cdot)$	58492.jg	1044	no	$-1$	$1$	$e\left(\frac{23}{261}\right)$	$e\left(\frac{277}{522}\right)$	$e\left(\frac{46}{261}\right)$	$e\left(\frac{325}{1044}\right)$	$e\left(\frac{157}{522}\right)$	$e\left(\frac{323}{522}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{31}{348}\right)$	$e\left(\frac{109}{348}\right)$	$e\left(\frac{16}{261}\right)$
$\chi_{58492}(45,\cdot)$	58492.hi	348	no	$-1$	$1$	$e\left(\frac{1}{87}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{2}{87}\right)$	$e\left(\frac{115}{348}\right)$	$e\left(\frac{19}{29}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{173}{348}\right)$	$e\left(\frac{221}{348}\right)$	$e\left(\frac{7}{87}\right)$
$\chi_{58492}(47,\cdot)$	58492.ib	522	yes	$1$	$1$	$e\left(\frac{182}{261}\right)$	$e\left(\frac{85}{522}\right)$	$e\left(\frac{103}{261}\right)$	$e\left(\frac{431}{522}\right)$	$e\left(\frac{13}{522}\right)$	$e\left(\frac{449}{522}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{38}{87}\right)$	$e\left(\frac{169}{174}\right)$	$e\left(\frac{85}{261}\right)$
$\chi_{58492}(51,\cdot)$	58492.fz	174	yes	$-1$	$1$	$e\left(\frac{61}{174}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{61}{87}\right)$	$e\left(\frac{83}{87}\right)$	$e\left(\frac{14}{29}\right)$	$e\left(\frac{19}{58}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{87}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{83}{87}\right)$
$\chi_{58492}(53,\cdot)$	58492.ij	696	no	$-1$	$1$	$e\left(\frac{343}{348}\right)$	$e\left(\frac{113}{348}\right)$	$e\left(\frac{169}{174}\right)$	$e\left(\frac{539}{696}\right)$	$e\left(\frac{21}{116}\right)$	$e\left(\frac{9}{29}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{307}{696}\right)$	$e\left(\frac{361}{696}\right)$	$e\left(\frac{113}{174}\right)$
$\chi_{58492}(55,\cdot)$	58492.ik	696	yes	$-1$	$1$	$e\left(\frac{5}{348}\right)$	$e\left(\frac{293}{348}\right)$	$e\left(\frac{5}{174}\right)$	$e\left(\frac{41}{696}\right)$	$e\left(\frac{227}{348}\right)$	$e\left(\frac{149}{174}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{207}{232}\right)$	$e\left(\frac{73}{232}\right)$	$e\left(\frac{119}{174}\right)$
$\chi_{58492}(57,\cdot)$	58492.jv	2088	no	$-1$	$1$	$e\left(\frac{1043}{1044}\right)$	$e\left(\frac{533}{1044}\right)$	$e\left(\frac{521}{522}\right)$	$e\left(\frac{827}{2088}\right)$	$e\left(\frac{59}{1044}\right)$	$e\left(\frac{133}{261}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{353}{696}\right)$	$e\left(\frac{635}{696}\right)$	$e\left(\frac{11}{522}\right)$
$\chi_{58492}(59,\cdot)$	58492.jo	2088	yes	$-1$	$1$	$e\left(\frac{689}{1044}\right)$	$e\left(\frac{425}{1044}\right)$	$e\left(\frac{167}{522}\right)$	$e\left(\frac{1961}{2088}\right)$	$e\left(\frac{935}{1044}\right)$	$e\left(\frac{35}{522}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{205}{232}\right)$	$e\left(\frac{51}{232}\right)$	$e\left(\frac{425}{522}\right)$
$\chi_{58492}(61,\cdot)$	58492.hi	348	no	$-1$	$1$	$e\left(\frac{62}{87}\right)$	$e\left(\frac{43}{87}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{83}{348}\right)$	$e\left(\frac{18}{29}\right)$	$e\left(\frac{6}{29}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{348}\right)$	$e\left(\frac{217}{348}\right)$	$e\left(\frac{86}{87}\right)$
$\chi_{58492}(65,\cdot)$	58492.gu	261	no	$1$	$1$	$e\left(\frac{4}{261}\right)$	$e\left(\frac{43}{261}\right)$	$e\left(\frac{8}{261}\right)$	$e\left(\frac{86}{261}\right)$	$e\left(\frac{199}{261}\right)$	$e\left(\frac{47}{261}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{16}{29}\right)$	$e\left(\frac{2}{29}\right)$	$e\left(\frac{86}{261}\right)$
$\chi_{58492}(67,\cdot)$	58492.iv	696	yes	$1$	$1$	$e\left(\frac{109}{116}\right)$	$e\left(\frac{115}{348}\right)$	$e\left(\frac{51}{58}\right)$	$e\left(\frac{25}{696}\right)$	$e\left(\frac{137}{348}\right)$	$e\left(\frac{47}{174}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{25}{696}\right)$	$e\left(\frac{43}{696}\right)$	$e\left(\frac{115}{174}\right)$
$\chi_{58492}(69,\cdot)$	58492.jp	2088	no	$1$	$1$	$e\left(\frac{215}{1044}\right)$	$e\left(\frac{245}{1044}\right)$	$e\left(\frac{215}{522}\right)$	$e\left(\frac{197}{2088}\right)$	$e\left(\frac{887}{1044}\right)$	$e\left(\frac{115}{261}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{491}{696}\right)$	$e\left(\frac{413}{696}\right)$	$e\left(\frac{245}{522}\right)$
$\chi_{58492}(71,\cdot)$	58492.id	522	no	$-1$	$1$	$e\left(\frac{313}{522}\right)$	$e\left(\frac{236}{261}\right)$	$e\left(\frac{52}{261}\right)$	$e\left(\frac{211}{261}\right)$	$e\left(\frac{32}{261}\right)$	$e\left(\frac{263}{522}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{22}{87}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{211}{261}\right)$
$\chi_{58492}(73,\cdot)$	58492.jm	2088	no	$1$	$1$	$e\left(\frac{233}{1044}\right)$	$e\left(\frac{743}{1044}\right)$	$e\left(\frac{233}{522}\right)$	$e\left(\frac{1667}{2088}\right)$	$e\left(\frac{173}{1044}\right)$	$e\left(\frac{244}{261}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{95}{232}\right)$	$e\left(\frac{1}{232}\right)$	$e\left(\frac{221}{522}\right)$

Click here to search among the remaining 25024 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	$58492$
Structure	\(C_{2}\times C_{6}\times C_{2088}\)
Order	$25056$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(23\)	\(25\)
\(\chi_{58492}(1,\cdot)\)	58492.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{58492}(3,\cdot)\)	58492.jd	1044	yes	\(1\)	\(1\)	\(e\left(\frac{67}{522}\right)\)	\(e\left(\frac{197}{261}\right)\)	\(e\left(\frac{67}{261}\right)\)	\(e\left(\frac{271}{1044}\right)\)	\(e\left(\frac{68}{261}\right)\)	\(e\left(\frac{461}{522}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{101}{116}\right)\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{133}{261}\right)\)
\(\chi_{58492}(5,\cdot)\)	58492.jj	1044	no	\(-1\)	\(1\)	\(e\left(\frac{197}{261}\right)\)	\(e\left(\frac{8}{261}\right)\)	\(e\left(\frac{133}{261}\right)\)	\(e\left(\frac{847}{1044}\right)\)	\(e\left(\frac{35}{261}\right)\)	\(e\left(\frac{205}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{263}{348}\right)\)	\(e\left(\frac{167}{348}\right)\)	\(e\left(\frac{16}{261}\right)\)
\(\chi_{58492}(9,\cdot)\)	58492.ih	522	no	\(1\)	\(1\)	\(e\left(\frac{67}{261}\right)\)	\(e\left(\frac{133}{261}\right)\)	\(e\left(\frac{134}{261}\right)\)	\(e\left(\frac{271}{522}\right)\)	\(e\left(\frac{136}{261}\right)\)	\(e\left(\frac{200}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{5}{261}\right)\)
\(\chi_{58492}(11,\cdot)\)	58492.ju	2088	yes	\(1\)	\(1\)	\(e\left(\frac{271}{1044}\right)\)	\(e\left(\frac{847}{1044}\right)\)	\(e\left(\frac{271}{522}\right)\)	\(e\left(\frac{517}{2088}\right)\)	\(e\left(\frac{541}{1044}\right)\)	\(e\left(\frac{37}{522}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{95}{696}\right)\)	\(e\left(\frac{581}{696}\right)\)	\(e\left(\frac{325}{522}\right)\)
\(\chi_{58492}(13,\cdot)\)	58492.jh	1044	no	\(-1\)	\(1\)	\(e\left(\frac{68}{261}\right)\)	\(e\left(\frac{35}{261}\right)\)	\(e\left(\frac{136}{261}\right)\)	\(e\left(\frac{541}{1044}\right)\)	\(e\left(\frac{164}{261}\right)\)	\(e\left(\frac{103}{261}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{277}{348}\right)\)	\(e\left(\frac{205}{348}\right)\)	\(e\left(\frac{70}{261}\right)\)
\(\chi_{58492}(15,\cdot)\)	58492.hq	522	no	\(-1\)	\(1\)	\(e\left(\frac{461}{522}\right)\)	\(e\left(\frac{205}{261}\right)\)	\(e\left(\frac{200}{261}\right)\)	\(e\left(\frac{37}{522}\right)\)	\(e\left(\frac{103}{261}\right)\)	\(e\left(\frac{349}{522}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{109}{174}\right)\)	\(e\left(\frac{97}{174}\right)\)	\(e\left(\frac{149}{261}\right)\)
\(\chi_{58492}(17,\cdot)\)	58492.eb	36	no	\(-1\)	\(1\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{58492}(19,\cdot)\)	58492.iu	696	yes	\(-1\)	\(1\)	\(e\left(\frac{101}{116}\right)\)	\(e\left(\frac{263}{348}\right)\)	\(e\left(\frac{43}{58}\right)\)	\(e\left(\frac{95}{696}\right)\)	\(e\left(\frac{277}{348}\right)\)	\(e\left(\frac{109}{174}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{443}{696}\right)\)	\(e\left(\frac{581}{696}\right)\)	\(e\left(\frac{89}{174}\right)\)
\(\chi_{58492}(23,\cdot)\)	58492.iv	696	yes	\(1\)	\(1\)	\(e\left(\frac{9}{116}\right)\)	\(e\left(\frac{167}{348}\right)\)	\(e\left(\frac{9}{58}\right)\)	\(e\left(\frac{581}{696}\right)\)	\(e\left(\frac{205}{348}\right)\)	\(e\left(\frac{97}{174}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{581}{696}\right)\)	\(e\left(\frac{359}{696}\right)\)	\(e\left(\frac{167}{174}\right)\)
\(\chi_{58492}(25,\cdot)\)	58492.hs	522	no	\(1\)	\(1\)	\(e\left(\frac{133}{261}\right)\)	\(e\left(\frac{16}{261}\right)\)	\(e\left(\frac{5}{261}\right)\)	\(e\left(\frac{325}{522}\right)\)	\(e\left(\frac{70}{261}\right)\)	\(e\left(\frac{149}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{89}{174}\right)\)	\(e\left(\frac{167}{174}\right)\)	\(e\left(\frac{32}{261}\right)\)
\(\chi_{58492}(27,\cdot)\)	58492.hd	348	yes	\(1\)	\(1\)	\(e\left(\frac{67}{174}\right)\)	\(e\left(\frac{23}{87}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{271}{348}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{113}{174}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{71}{116}\right)\)	\(e\left(\frac{27}{116}\right)\)	\(e\left(\frac{46}{87}\right)\)
\(\chi_{58492}(29,\cdot)\)	58492.gv	261	no	\(1\)	\(1\)	\(e\left(\frac{191}{261}\right)\)	\(e\left(\frac{248}{261}\right)\)	\(e\left(\frac{121}{261}\right)\)	\(e\left(\frac{235}{261}\right)\)	\(e\left(\frac{215}{261}\right)\)	\(e\left(\frac{178}{261}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{235}{261}\right)\)
\(\chi_{58492}(31,\cdot)\)	58492.jo	2088	yes	\(-1\)	\(1\)	\(e\left(\frac{263}{1044}\right)\)	\(e\left(\frac{935}{1044}\right)\)	\(e\left(\frac{263}{522}\right)\)	\(e\left(\frac{347}{2088}\right)\)	\(e\left(\frac{1013}{1044}\right)\)	\(e\left(\frac{77}{522}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{103}{232}\right)\)	\(e\left(\frac{89}{232}\right)\)	\(e\left(\frac{413}{522}\right)\)
\(\chi_{58492}(33,\cdot)\)	58492.iw	696	no	\(1\)	\(1\)	\(e\left(\frac{45}{116}\right)\)	\(e\left(\frac{197}{348}\right)\)	\(e\left(\frac{45}{58}\right)\)	\(e\left(\frac{353}{696}\right)\)	\(e\left(\frac{271}{348}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{696}\right)\)	\(e\left(\frac{635}{696}\right)\)	\(e\left(\frac{23}{174}\right)\)
\(\chi_{58492}(37,\cdot)\)	58492.ij	696	no	\(-1\)	\(1\)	\(e\left(\frac{53}{348}\right)\)	\(e\left(\frac{55}{348}\right)\)	\(e\left(\frac{53}{174}\right)\)	\(e\left(\frac{481}{696}\right)\)	\(e\left(\frac{79}{116}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{17}{696}\right)\)	\(e\left(\frac{419}{696}\right)\)	\(e\left(\frac{55}{174}\right)\)
\(\chi_{58492}(39,\cdot)\)	58492.cu	18	yes	\(-1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{58492}(41,\cdot)\)	58492.et	58	no	\(-1\)	\(1\)	\(e\left(\frac{25}{58}\right)\)	\(e\left(\frac{15}{58}\right)\)	\(e\left(\frac{25}{29}\right)\)	\(e\left(\frac{1}{58}\right)\)	\(e\left(\frac{33}{58}\right)\)	\(e\left(\frac{20}{29}\right)\)	\(-1\)	\(e\left(\frac{15}{29}\right)\)	\(e\left(\frac{11}{58}\right)\)	\(e\left(\frac{15}{29}\right)\)
\(\chi_{58492}(43,\cdot)\)	58492.jg	1044	no	\(-1\)	\(1\)	\(e\left(\frac{23}{261}\right)\)	\(e\left(\frac{277}{522}\right)\)	\(e\left(\frac{46}{261}\right)\)	\(e\left(\frac{325}{1044}\right)\)	\(e\left(\frac{157}{522}\right)\)	\(e\left(\frac{323}{522}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{31}{348}\right)\)	\(e\left(\frac{109}{348}\right)\)	\(e\left(\frac{16}{261}\right)\)
\(\chi_{58492}(45,\cdot)\)	58492.hi	348	no	\(-1\)	\(1\)	\(e\left(\frac{1}{87}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{2}{87}\right)\)	\(e\left(\frac{115}{348}\right)\)	\(e\left(\frac{19}{29}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{173}{348}\right)\)	\(e\left(\frac{221}{348}\right)\)	\(e\left(\frac{7}{87}\right)\)
\(\chi_{58492}(47,\cdot)\)	58492.ib	522	yes	\(1\)	\(1\)	\(e\left(\frac{182}{261}\right)\)	\(e\left(\frac{85}{522}\right)\)	\(e\left(\frac{103}{261}\right)\)	\(e\left(\frac{431}{522}\right)\)	\(e\left(\frac{13}{522}\right)\)	\(e\left(\frac{449}{522}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{38}{87}\right)\)	\(e\left(\frac{169}{174}\right)\)	\(e\left(\frac{85}{261}\right)\)
\(\chi_{58492}(51,\cdot)\)	58492.fz	174	yes	\(-1\)	\(1\)	\(e\left(\frac{61}{174}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{61}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)	\(e\left(\frac{14}{29}\right)\)	\(e\left(\frac{19}{58}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{87}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{83}{87}\right)\)
\(\chi_{58492}(53,\cdot)\)	58492.ij	696	no	\(-1\)	\(1\)	\(e\left(\frac{343}{348}\right)\)	\(e\left(\frac{113}{348}\right)\)	\(e\left(\frac{169}{174}\right)\)	\(e\left(\frac{539}{696}\right)\)	\(e\left(\frac{21}{116}\right)\)	\(e\left(\frac{9}{29}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{307}{696}\right)\)	\(e\left(\frac{361}{696}\right)\)	\(e\left(\frac{113}{174}\right)\)
\(\chi_{58492}(55,\cdot)\)	58492.ik	696	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{348}\right)\)	\(e\left(\frac{293}{348}\right)\)	\(e\left(\frac{5}{174}\right)\)	\(e\left(\frac{41}{696}\right)\)	\(e\left(\frac{227}{348}\right)\)	\(e\left(\frac{149}{174}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{207}{232}\right)\)	\(e\left(\frac{73}{232}\right)\)	\(e\left(\frac{119}{174}\right)\)
\(\chi_{58492}(57,\cdot)\)	58492.jv	2088	no	\(-1\)	\(1\)	\(e\left(\frac{1043}{1044}\right)\)	\(e\left(\frac{533}{1044}\right)\)	\(e\left(\frac{521}{522}\right)\)	\(e\left(\frac{827}{2088}\right)\)	\(e\left(\frac{59}{1044}\right)\)	\(e\left(\frac{133}{261}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{353}{696}\right)\)	\(e\left(\frac{635}{696}\right)\)	\(e\left(\frac{11}{522}\right)\)
\(\chi_{58492}(59,\cdot)\)	58492.jo	2088	yes	\(-1\)	\(1\)	\(e\left(\frac{689}{1044}\right)\)	\(e\left(\frac{425}{1044}\right)\)	\(e\left(\frac{167}{522}\right)\)	\(e\left(\frac{1961}{2088}\right)\)	\(e\left(\frac{935}{1044}\right)\)	\(e\left(\frac{35}{522}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{205}{232}\right)\)	\(e\left(\frac{51}{232}\right)\)	\(e\left(\frac{425}{522}\right)\)
\(\chi_{58492}(61,\cdot)\)	58492.hi	348	no	\(-1\)	\(1\)	\(e\left(\frac{62}{87}\right)\)	\(e\left(\frac{43}{87}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{83}{348}\right)\)	\(e\left(\frac{18}{29}\right)\)	\(e\left(\frac{6}{29}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{348}\right)\)	\(e\left(\frac{217}{348}\right)\)	\(e\left(\frac{86}{87}\right)\)
\(\chi_{58492}(65,\cdot)\)	58492.gu	261	no	\(1\)	\(1\)	\(e\left(\frac{4}{261}\right)\)	\(e\left(\frac{43}{261}\right)\)	\(e\left(\frac{8}{261}\right)\)	\(e\left(\frac{86}{261}\right)\)	\(e\left(\frac{199}{261}\right)\)	\(e\left(\frac{47}{261}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{16}{29}\right)\)	\(e\left(\frac{2}{29}\right)\)	\(e\left(\frac{86}{261}\right)\)
\(\chi_{58492}(67,\cdot)\)	58492.iv	696	yes	\(1\)	\(1\)	\(e\left(\frac{109}{116}\right)\)	\(e\left(\frac{115}{348}\right)\)	\(e\left(\frac{51}{58}\right)\)	\(e\left(\frac{25}{696}\right)\)	\(e\left(\frac{137}{348}\right)\)	\(e\left(\frac{47}{174}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{25}{696}\right)\)	\(e\left(\frac{43}{696}\right)\)	\(e\left(\frac{115}{174}\right)\)
\(\chi_{58492}(69,\cdot)\)	58492.jp	2088	no	\(1\)	\(1\)	\(e\left(\frac{215}{1044}\right)\)	\(e\left(\frac{245}{1044}\right)\)	\(e\left(\frac{215}{522}\right)\)	\(e\left(\frac{197}{2088}\right)\)	\(e\left(\frac{887}{1044}\right)\)	\(e\left(\frac{115}{261}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{491}{696}\right)\)	\(e\left(\frac{413}{696}\right)\)	\(e\left(\frac{245}{522}\right)\)
\(\chi_{58492}(71,\cdot)\)	58492.id	522	no	\(-1\)	\(1\)	\(e\left(\frac{313}{522}\right)\)	\(e\left(\frac{236}{261}\right)\)	\(e\left(\frac{52}{261}\right)\)	\(e\left(\frac{211}{261}\right)\)	\(e\left(\frac{32}{261}\right)\)	\(e\left(\frac{263}{522}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{22}{87}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{211}{261}\right)\)
\(\chi_{58492}(73,\cdot)\)	58492.jm	2088	no	\(1\)	\(1\)	\(e\left(\frac{233}{1044}\right)\)	\(e\left(\frac{743}{1044}\right)\)	\(e\left(\frac{233}{522}\right)\)	\(e\left(\frac{1667}{2088}\right)\)	\(e\left(\frac{173}{1044}\right)\)	\(e\left(\frac{244}{261}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{95}{232}\right)\)	\(e\left(\frac{1}{232}\right)\)	\(e\left(\frac{221}{522}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Downloads

Learn more

Character group

First 32 of 25056 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.