LMFDB - Group of Dirichlet characters of modulus 8788

Show commands: PariGP / SageMath

sage: H = DirichletGroup(8788)

pari: g = idealstar(,8788,2)

Character group

sage: G.order() pari: g.no
Order	=	4056
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2028}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{8788}(4395,\cdot)$, $\chi_{8788}(6593,\cdot)$

First 32 of 4056 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{8788}(1,\cdot)$	8788.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{8788}(3,\cdot)$	8788.bf	1014	yes	$-1$	$1$	$e\left(\frac{5}{1014}\right)$	$e\left(\frac{93}{169}\right)$	$e\left(\frac{199}{1014}\right)$	$e\left(\frac{5}{507}\right)$	$e\left(\frac{965}{1014}\right)$	$e\left(\frac{563}{1014}\right)$	$e\left(\frac{158}{507}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{34}{169}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{8788}(5,\cdot)$	8788.be	676	no	$-1$	$1$	$e\left(\frac{93}{169}\right)$	$e\left(\frac{651}{676}\right)$	$e\left(\frac{373}{676}\right)$	$e\left(\frac{17}{169}\right)$	$e\left(\frac{309}{676}\right)$	$e\left(\frac{347}{676}\right)$	$e\left(\frac{297}{338}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{69}{676}\right)$	$e\left(\frac{25}{26}\right)$
$\chi_{8788}(7,\cdot)$	8788.bj	2028	yes	$1$	$1$	$e\left(\frac{199}{1014}\right)$	$e\left(\frac{373}{676}\right)$	$e\left(\frac{1543}{2028}\right)$	$e\left(\frac{199}{507}\right)$	$e\left(\frac{1271}{2028}\right)$	$e\left(\frac{1517}{2028}\right)$	$e\left(\frac{713}{1014}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{647}{676}\right)$	$e\left(\frac{32}{39}\right)$
$\chi_{8788}(9,\cdot)$	8788.bc	507	no	$1$	$1$	$e\left(\frac{5}{507}\right)$	$e\left(\frac{17}{169}\right)$	$e\left(\frac{199}{507}\right)$	$e\left(\frac{10}{507}\right)$	$e\left(\frac{458}{507}\right)$	$e\left(\frac{56}{507}\right)$	$e\left(\frac{316}{507}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{68}{169}\right)$	$e\left(\frac{2}{39}\right)$
$\chi_{8788}(11,\cdot)$	8788.bj	2028	yes	$1$	$1$	$e\left(\frac{965}{1014}\right)$	$e\left(\frac{309}{676}\right)$	$e\left(\frac{1271}{2028}\right)$	$e\left(\frac{458}{507}\right)$	$e\left(\frac{859}{2028}\right)$	$e\left(\frac{829}{2028}\right)$	$e\left(\frac{655}{1014}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{391}{676}\right)$	$e\left(\frac{37}{39}\right)$
$\chi_{8788}(15,\cdot)$	8788.bj	2028	yes	$1$	$1$	$e\left(\frac{563}{1014}\right)$	$e\left(\frac{347}{676}\right)$	$e\left(\frac{1517}{2028}\right)$	$e\left(\frac{56}{507}\right)$	$e\left(\frac{829}{2028}\right)$	$e\left(\frac{139}{2028}\right)$	$e\left(\frac{193}{1014}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{205}{676}\right)$	$e\left(\frac{19}{39}\right)$
$\chi_{8788}(17,\cdot)$	8788.bg	1014	no	$1$	$1$	$e\left(\frac{158}{507}\right)$	$e\left(\frac{297}{338}\right)$	$e\left(\frac{713}{1014}\right)$	$e\left(\frac{316}{507}\right)$	$e\left(\frac{655}{1014}\right)$	$e\left(\frac{193}{1014}\right)$	$e\left(\frac{454}{507}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{5}{338}\right)$	$e\left(\frac{32}{39}\right)$
$\chi_{8788}(19,\cdot)$	8788.w	156	no	$1$	$1$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{47}{52}\right)$	$e\left(\frac{73}{156}\right)$	$e\left(\frac{31}{39}\right)$	$e\left(\frac{149}{156}\right)$	$e\left(\frac{47}{156}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{2}{3}\right)$
$\chi_{8788}(21,\cdot)$	8788.be	676	no	$-1$	$1$	$e\left(\frac{34}{169}\right)$	$e\left(\frac{69}{676}\right)$	$e\left(\frac{647}{676}\right)$	$e\left(\frac{68}{169}\right)$	$e\left(\frac{391}{676}\right)$	$e\left(\frac{205}{676}\right)$	$e\left(\frac{5}{338}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{107}{676}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{8788}(23,\cdot)$	8788.u	78	no	$-1$	$1$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{39}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{19}{39}\right)$	$e\left(\frac{32}{39}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{9}{26}\right)$	$e\left(\frac{5}{6}\right)$
$\chi_{8788}(25,\cdot)$	8788.ba	338	no	$1$	$1$	$e\left(\frac{17}{169}\right)$	$e\left(\frac{313}{338}\right)$	$e\left(\frac{35}{338}\right)$	$e\left(\frac{34}{169}\right)$	$e\left(\frac{309}{338}\right)$	$e\left(\frac{9}{338}\right)$	$e\left(\frac{128}{169}\right)$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{69}{338}\right)$	$e\left(\frac{12}{13}\right)$
$\chi_{8788}(27,\cdot)$	8788.bb	338	yes	$-1$	$1$	$e\left(\frac{5}{338}\right)$	$e\left(\frac{110}{169}\right)$	$e\left(\frac{199}{338}\right)$	$e\left(\frac{5}{169}\right)$	$e\left(\frac{289}{338}\right)$	$e\left(\frac{225}{338}\right)$	$e\left(\frac{158}{169}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{102}{169}\right)$	$e\left(\frac{15}{26}\right)$
$\chi_{8788}(29,\cdot)$	8788.bc	507	no	$1$	$1$	$e\left(\frac{421}{507}\right)$	$e\left(\frac{147}{169}\right)$	$e\left(\frac{329}{507}\right)$	$e\left(\frac{335}{507}\right)$	$e\left(\frac{133}{507}\right)$	$e\left(\frac{355}{507}\right)$	$e\left(\frac{446}{507}\right)$	$e\left(\frac{5}{39}\right)$	$e\left(\frac{81}{169}\right)$	$e\left(\frac{28}{39}\right)$
$\chi_{8788}(31,\cdot)$	8788.bd	676	yes	$1$	$1$	$e\left(\frac{265}{338}\right)$	$e\left(\frac{167}{676}\right)$	$e\left(\frac{307}{676}\right)$	$e\left(\frac{96}{169}\right)$	$e\left(\frac{383}{676}\right)$	$e\left(\frac{21}{676}\right)$	$e\left(\frac{17}{338}\right)$	$e\left(\frac{49}{52}\right)$	$e\left(\frac{161}{676}\right)$	$e\left(\frac{1}{13}\right)$
$\chi_{8788}(33,\cdot)$	8788.bi	2028	no	$-1$	$1$	$e\left(\frac{485}{507}\right)$	$e\left(\frac{5}{676}\right)$	$e\left(\frac{1669}{2028}\right)$	$e\left(\frac{463}{507}\right)$	$e\left(\frac{761}{2028}\right)$	$e\left(\frac{1955}{2028}\right)$	$e\left(\frac{971}{1014}\right)$	$e\left(\frac{55}{156}\right)$	$e\left(\frac{527}{676}\right)$	$e\left(\frac{37}{78}\right)$
$\chi_{8788}(35,\cdot)$	8788.bf	1014	yes	$-1$	$1$	$e\left(\frac{757}{1014}\right)$	$e\left(\frac{87}{169}\right)$	$e\left(\frac{317}{1014}\right)$	$e\left(\frac{250}{507}\right)$	$e\left(\frac{85}{1014}\right)$	$e\left(\frac{265}{1014}\right)$	$e\left(\frac{295}{507}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{10}{169}\right)$	$e\left(\frac{61}{78}\right)$
$\chi_{8788}(37,\cdot)$	8788.bi	2028	no	$-1$	$1$	$e\left(\frac{1}{507}\right)$	$e\left(\frac{453}{676}\right)$	$e\left(\frac{869}{2028}\right)$	$e\left(\frac{2}{507}\right)$	$e\left(\frac{265}{2028}\right)$	$e\left(\frac{1363}{2028}\right)$	$e\left(\frac{25}{1014}\right)$	$e\left(\frac{95}{156}\right)$	$e\left(\frac{291}{676}\right)$	$e\left(\frac{71}{78}\right)$
$\chi_{8788}(41,\cdot)$	8788.bi	2028	no	$-1$	$1$	$e\left(\frac{412}{507}\right)$	$e\left(\frac{567}{676}\right)$	$e\left(\frac{1607}{2028}\right)$	$e\left(\frac{317}{507}\right)$	$e\left(\frac{175}{2028}\right)$	$e\left(\frac{1321}{2028}\right)$	$e\left(\frac{667}{1014}\right)$	$e\left(\frac{101}{156}\right)$	$e\left(\frac{409}{676}\right)$	$e\left(\frac{41}{78}\right)$
$\chi_{8788}(43,\cdot)$	8788.bh	1014	yes	$-1$	$1$	$e\left(\frac{661}{1014}\right)$	$e\left(\frac{287}{338}\right)$	$e\left(\frac{124}{507}\right)$	$e\left(\frac{154}{507}\right)$	$e\left(\frac{158}{507}\right)$	$e\left(\frac{254}{507}\right)$	$e\left(\frac{202}{507}\right)$	$e\left(\frac{25}{39}\right)$	$e\left(\frac{303}{338}\right)$	$e\left(\frac{7}{78}\right)$
$\chi_{8788}(45,\cdot)$	8788.bi	2028	no	$-1$	$1$	$e\left(\frac{284}{507}\right)$	$e\left(\frac{43}{676}\right)$	$e\left(\frac{1915}{2028}\right)$	$e\left(\frac{61}{507}\right)$	$e\left(\frac{731}{2028}\right)$	$e\left(\frac{1265}{2028}\right)$	$e\left(\frac{509}{1014}\right)$	$e\left(\frac{109}{156}\right)$	$e\left(\frac{341}{676}\right)$	$e\left(\frac{1}{78}\right)$
$\chi_{8788}(47,\cdot)$	8788.bd	676	yes	$1$	$1$	$e\left(\frac{249}{338}\right)$	$e\left(\frac{449}{676}\right)$	$e\left(\frac{453}{676}\right)$	$e\left(\frac{80}{169}\right)$	$e\left(\frac{629}{676}\right)$	$e\left(\frac{271}{676}\right)$	$e\left(\frac{155}{338}\right)$	$e\left(\frac{43}{52}\right)$	$e\left(\frac{275}{676}\right)$	$e\left(\frac{3}{13}\right)$
$\chi_{8788}(49,\cdot)$	8788.bg	1014	no	$1$	$1$	$e\left(\frac{199}{507}\right)$	$e\left(\frac{35}{338}\right)$	$e\left(\frac{529}{1014}\right)$	$e\left(\frac{398}{507}\right)$	$e\left(\frac{257}{1014}\right)$	$e\left(\frac{503}{1014}\right)$	$e\left(\frac{206}{507}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{309}{338}\right)$	$e\left(\frac{25}{39}\right)$
$\chi_{8788}(51,\cdot)$	8788.z	338	yes	$-1$	$1$	$e\left(\frac{107}{338}\right)$	$e\left(\frac{145}{338}\right)$	$e\left(\frac{152}{169}\right)$	$e\left(\frac{107}{169}\right)$	$e\left(\frac{101}{169}\right)$	$e\left(\frac{126}{169}\right)$	$e\left(\frac{35}{169}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{73}{338}\right)$	$e\left(\frac{9}{26}\right)$
$\chi_{8788}(53,\cdot)$	8788.y	169	no	$1$	$1$	$e\left(\frac{109}{169}\right)$	$e\left(\frac{64}{169}\right)$	$e\left(\frac{147}{169}\right)$	$e\left(\frac{49}{169}\right)$	$e\left(\frac{81}{169}\right)$	$e\left(\frac{4}{169}\right)$	$e\left(\frac{95}{169}\right)$	$e\left(\frac{5}{13}\right)$	$e\left(\frac{87}{169}\right)$	$e\left(\frac{2}{13}\right)$
$\chi_{8788}(55,\cdot)$	8788.bf	1014	yes	$-1$	$1$	$e\left(\frac{509}{1014}\right)$	$e\left(\frac{71}{169}\right)$	$e\left(\frac{181}{1014}\right)$	$e\left(\frac{2}{507}\right)$	$e\left(\frac{893}{1014}\right)$	$e\left(\frac{935}{1014}\right)$	$e\left(\frac{266}{507}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{115}{169}\right)$	$e\left(\frac{71}{78}\right)$
$\chi_{8788}(57,\cdot)$	8788.be	676	no	$-1$	$1$	$e\left(\frac{68}{169}\right)$	$e\left(\frac{307}{676}\right)$	$e\left(\frac{449}{676}\right)$	$e\left(\frac{136}{169}\right)$	$e\left(\frac{613}{676}\right)$	$e\left(\frac{579}{676}\right)$	$e\left(\frac{179}{338}\right)$	$e\left(\frac{51}{52}\right)$	$e\left(\frac{45}{676}\right)$	$e\left(\frac{5}{26}\right)$
$\chi_{8788}(59,\cdot)$	8788.bj	2028	yes	$1$	$1$	$e\left(\frac{181}{1014}\right)$	$e\left(\frac{521}{676}\right)$	$e\left(\frac{1327}{2028}\right)$	$e\left(\frac{181}{507}\right)$	$e\left(\frac{407}{2028}\right)$	$e\left(\frac{1925}{2028}\right)$	$e\left(\frac{995}{1014}\right)$	$e\left(\frac{37}{156}\right)$	$e\left(\frac{563}{676}\right)$	$e\left(\frac{5}{39}\right)$
$\chi_{8788}(61,\cdot)$	8788.bc	507	no	$1$	$1$	$e\left(\frac{11}{507}\right)$	$e\left(\frac{105}{169}\right)$	$e\left(\frac{235}{507}\right)$	$e\left(\frac{22}{507}\right)$	$e\left(\frac{95}{507}\right)$	$e\left(\frac{326}{507}\right)$	$e\left(\frac{391}{507}\right)$	$e\left(\frac{37}{39}\right)$	$e\left(\frac{82}{169}\right)$	$e\left(\frac{20}{39}\right)$
$\chi_{8788}(63,\cdot)$	8788.bj	2028	yes	$1$	$1$	$e\left(\frac{209}{1014}\right)$	$e\left(\frac{441}{676}\right)$	$e\left(\frac{311}{2028}\right)$	$e\left(\frac{209}{507}\right)$	$e\left(\frac{1075}{2028}\right)$	$e\left(\frac{1741}{2028}\right)$	$e\left(\frac{331}{1014}\right)$	$e\left(\frac{41}{156}\right)$	$e\left(\frac{243}{676}\right)$	$e\left(\frac{34}{39}\right)$
$\chi_{8788}(67,\cdot)$	8788.bj	2028	yes	$1$	$1$	$e\left(\frac{227}{1014}\right)$	$e\left(\frac{631}{676}\right)$	$e\left(\frac{1541}{2028}\right)$	$e\left(\frac{227}{507}\right)$	$e\left(\frac{925}{2028}\right)$	$e\left(\frac{319}{2028}\right)$	$e\left(\frac{49}{1014}\right)$	$e\left(\frac{155}{156}\right)$	$e\left(\frac{665}{676}\right)$	$e\left(\frac{22}{39}\right)$
$\chi_{8788}(69,\cdot)$	8788.bg	1014	no	$1$	$1$	$e\left(\frac{269}{507}\right)$	$e\left(\frac{173}{338}\right)$	$e\left(\frac{17}{1014}\right)$	$e\left(\frac{31}{507}\right)$	$e\left(\frac{913}{1014}\right)$	$e\left(\frac{43}{1014}\right)$	$e\left(\frac{67}{507}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{185}{338}\right)$	$e\left(\frac{14}{39}\right)$

Click here to search among the remaining 4024 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	$8788$
Structure	\(C_{2}\times C_{2028}\)
Order	$4056$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\(\chi_{8788}(1,\cdot)\)	8788.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{8788}(3,\cdot)\)	8788.bf	1014	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{1014}\right)\)	\(e\left(\frac{93}{169}\right)\)	\(e\left(\frac{199}{1014}\right)\)	\(e\left(\frac{5}{507}\right)\)	\(e\left(\frac{965}{1014}\right)\)	\(e\left(\frac{563}{1014}\right)\)	\(e\left(\frac{158}{507}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{34}{169}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{8788}(5,\cdot)\)	8788.be	676	no	\(-1\)	\(1\)	\(e\left(\frac{93}{169}\right)\)	\(e\left(\frac{651}{676}\right)\)	\(e\left(\frac{373}{676}\right)\)	\(e\left(\frac{17}{169}\right)\)	\(e\left(\frac{309}{676}\right)\)	\(e\left(\frac{347}{676}\right)\)	\(e\left(\frac{297}{338}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{69}{676}\right)\)	\(e\left(\frac{25}{26}\right)\)
\(\chi_{8788}(7,\cdot)\)	8788.bj	2028	yes	\(1\)	\(1\)	\(e\left(\frac{199}{1014}\right)\)	\(e\left(\frac{373}{676}\right)\)	\(e\left(\frac{1543}{2028}\right)\)	\(e\left(\frac{199}{507}\right)\)	\(e\left(\frac{1271}{2028}\right)\)	\(e\left(\frac{1517}{2028}\right)\)	\(e\left(\frac{713}{1014}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{647}{676}\right)\)	\(e\left(\frac{32}{39}\right)\)
\(\chi_{8788}(9,\cdot)\)	8788.bc	507	no	\(1\)	\(1\)	\(e\left(\frac{5}{507}\right)\)	\(e\left(\frac{17}{169}\right)\)	\(e\left(\frac{199}{507}\right)\)	\(e\left(\frac{10}{507}\right)\)	\(e\left(\frac{458}{507}\right)\)	\(e\left(\frac{56}{507}\right)\)	\(e\left(\frac{316}{507}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{68}{169}\right)\)	\(e\left(\frac{2}{39}\right)\)
\(\chi_{8788}(11,\cdot)\)	8788.bj	2028	yes	\(1\)	\(1\)	\(e\left(\frac{965}{1014}\right)\)	\(e\left(\frac{309}{676}\right)\)	\(e\left(\frac{1271}{2028}\right)\)	\(e\left(\frac{458}{507}\right)\)	\(e\left(\frac{859}{2028}\right)\)	\(e\left(\frac{829}{2028}\right)\)	\(e\left(\frac{655}{1014}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{391}{676}\right)\)	\(e\left(\frac{37}{39}\right)\)
\(\chi_{8788}(15,\cdot)\)	8788.bj	2028	yes	\(1\)	\(1\)	\(e\left(\frac{563}{1014}\right)\)	\(e\left(\frac{347}{676}\right)\)	\(e\left(\frac{1517}{2028}\right)\)	\(e\left(\frac{56}{507}\right)\)	\(e\left(\frac{829}{2028}\right)\)	\(e\left(\frac{139}{2028}\right)\)	\(e\left(\frac{193}{1014}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{205}{676}\right)\)	\(e\left(\frac{19}{39}\right)\)
\(\chi_{8788}(17,\cdot)\)	8788.bg	1014	no	\(1\)	\(1\)	\(e\left(\frac{158}{507}\right)\)	\(e\left(\frac{297}{338}\right)\)	\(e\left(\frac{713}{1014}\right)\)	\(e\left(\frac{316}{507}\right)\)	\(e\left(\frac{655}{1014}\right)\)	\(e\left(\frac{193}{1014}\right)\)	\(e\left(\frac{454}{507}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{5}{338}\right)\)	\(e\left(\frac{32}{39}\right)\)
\(\chi_{8788}(19,\cdot)\)	8788.w	156	no	\(1\)	\(1\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{47}{52}\right)\)	\(e\left(\frac{73}{156}\right)\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{47}{156}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{2}{3}\right)\)
\(\chi_{8788}(21,\cdot)\)	8788.be	676	no	\(-1\)	\(1\)	\(e\left(\frac{34}{169}\right)\)	\(e\left(\frac{69}{676}\right)\)	\(e\left(\frac{647}{676}\right)\)	\(e\left(\frac{68}{169}\right)\)	\(e\left(\frac{391}{676}\right)\)	\(e\left(\frac{205}{676}\right)\)	\(e\left(\frac{5}{338}\right)\)	\(e\left(\frac{45}{52}\right)\)	\(e\left(\frac{107}{676}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{8788}(23,\cdot)\)	8788.u	78	no	\(-1\)	\(1\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{25}{26}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{39}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{19}{39}\right)\)	\(e\left(\frac{32}{39}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{9}{26}\right)\)	\(e\left(\frac{5}{6}\right)\)
\(\chi_{8788}(25,\cdot)\)	8788.ba	338	no	\(1\)	\(1\)	\(e\left(\frac{17}{169}\right)\)	\(e\left(\frac{313}{338}\right)\)	\(e\left(\frac{35}{338}\right)\)	\(e\left(\frac{34}{169}\right)\)	\(e\left(\frac{309}{338}\right)\)	\(e\left(\frac{9}{338}\right)\)	\(e\left(\frac{128}{169}\right)\)	\(e\left(\frac{21}{26}\right)\)	\(e\left(\frac{69}{338}\right)\)	\(e\left(\frac{12}{13}\right)\)
\(\chi_{8788}(27,\cdot)\)	8788.bb	338	yes	\(-1\)	\(1\)	\(e\left(\frac{5}{338}\right)\)	\(e\left(\frac{110}{169}\right)\)	\(e\left(\frac{199}{338}\right)\)	\(e\left(\frac{5}{169}\right)\)	\(e\left(\frac{289}{338}\right)\)	\(e\left(\frac{225}{338}\right)\)	\(e\left(\frac{158}{169}\right)\)	\(e\left(\frac{5}{26}\right)\)	\(e\left(\frac{102}{169}\right)\)	\(e\left(\frac{15}{26}\right)\)
\(\chi_{8788}(29,\cdot)\)	8788.bc	507	no	\(1\)	\(1\)	\(e\left(\frac{421}{507}\right)\)	\(e\left(\frac{147}{169}\right)\)	\(e\left(\frac{329}{507}\right)\)	\(e\left(\frac{335}{507}\right)\)	\(e\left(\frac{133}{507}\right)\)	\(e\left(\frac{355}{507}\right)\)	\(e\left(\frac{446}{507}\right)\)	\(e\left(\frac{5}{39}\right)\)	\(e\left(\frac{81}{169}\right)\)	\(e\left(\frac{28}{39}\right)\)
\(\chi_{8788}(31,\cdot)\)	8788.bd	676	yes	\(1\)	\(1\)	\(e\left(\frac{265}{338}\right)\)	\(e\left(\frac{167}{676}\right)\)	\(e\left(\frac{307}{676}\right)\)	\(e\left(\frac{96}{169}\right)\)	\(e\left(\frac{383}{676}\right)\)	\(e\left(\frac{21}{676}\right)\)	\(e\left(\frac{17}{338}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{161}{676}\right)\)	\(e\left(\frac{1}{13}\right)\)
\(\chi_{8788}(33,\cdot)\)	8788.bi	2028	no	\(-1\)	\(1\)	\(e\left(\frac{485}{507}\right)\)	\(e\left(\frac{5}{676}\right)\)	\(e\left(\frac{1669}{2028}\right)\)	\(e\left(\frac{463}{507}\right)\)	\(e\left(\frac{761}{2028}\right)\)	\(e\left(\frac{1955}{2028}\right)\)	\(e\left(\frac{971}{1014}\right)\)	\(e\left(\frac{55}{156}\right)\)	\(e\left(\frac{527}{676}\right)\)	\(e\left(\frac{37}{78}\right)\)
\(\chi_{8788}(35,\cdot)\)	8788.bf	1014	yes	\(-1\)	\(1\)	\(e\left(\frac{757}{1014}\right)\)	\(e\left(\frac{87}{169}\right)\)	\(e\left(\frac{317}{1014}\right)\)	\(e\left(\frac{250}{507}\right)\)	\(e\left(\frac{85}{1014}\right)\)	\(e\left(\frac{265}{1014}\right)\)	\(e\left(\frac{295}{507}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{10}{169}\right)\)	\(e\left(\frac{61}{78}\right)\)
\(\chi_{8788}(37,\cdot)\)	8788.bi	2028	no	\(-1\)	\(1\)	\(e\left(\frac{1}{507}\right)\)	\(e\left(\frac{453}{676}\right)\)	\(e\left(\frac{869}{2028}\right)\)	\(e\left(\frac{2}{507}\right)\)	\(e\left(\frac{265}{2028}\right)\)	\(e\left(\frac{1363}{2028}\right)\)	\(e\left(\frac{25}{1014}\right)\)	\(e\left(\frac{95}{156}\right)\)	\(e\left(\frac{291}{676}\right)\)	\(e\left(\frac{71}{78}\right)\)
\(\chi_{8788}(41,\cdot)\)	8788.bi	2028	no	\(-1\)	\(1\)	\(e\left(\frac{412}{507}\right)\)	\(e\left(\frac{567}{676}\right)\)	\(e\left(\frac{1607}{2028}\right)\)	\(e\left(\frac{317}{507}\right)\)	\(e\left(\frac{175}{2028}\right)\)	\(e\left(\frac{1321}{2028}\right)\)	\(e\left(\frac{667}{1014}\right)\)	\(e\left(\frac{101}{156}\right)\)	\(e\left(\frac{409}{676}\right)\)	\(e\left(\frac{41}{78}\right)\)
\(\chi_{8788}(43,\cdot)\)	8788.bh	1014	yes	\(-1\)	\(1\)	\(e\left(\frac{661}{1014}\right)\)	\(e\left(\frac{287}{338}\right)\)	\(e\left(\frac{124}{507}\right)\)	\(e\left(\frac{154}{507}\right)\)	\(e\left(\frac{158}{507}\right)\)	\(e\left(\frac{254}{507}\right)\)	\(e\left(\frac{202}{507}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{303}{338}\right)\)	\(e\left(\frac{7}{78}\right)\)
\(\chi_{8788}(45,\cdot)\)	8788.bi	2028	no	\(-1\)	\(1\)	\(e\left(\frac{284}{507}\right)\)	\(e\left(\frac{43}{676}\right)\)	\(e\left(\frac{1915}{2028}\right)\)	\(e\left(\frac{61}{507}\right)\)	\(e\left(\frac{731}{2028}\right)\)	\(e\left(\frac{1265}{2028}\right)\)	\(e\left(\frac{509}{1014}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{341}{676}\right)\)	\(e\left(\frac{1}{78}\right)\)
\(\chi_{8788}(47,\cdot)\)	8788.bd	676	yes	\(1\)	\(1\)	\(e\left(\frac{249}{338}\right)\)	\(e\left(\frac{449}{676}\right)\)	\(e\left(\frac{453}{676}\right)\)	\(e\left(\frac{80}{169}\right)\)	\(e\left(\frac{629}{676}\right)\)	\(e\left(\frac{271}{676}\right)\)	\(e\left(\frac{155}{338}\right)\)	\(e\left(\frac{43}{52}\right)\)	\(e\left(\frac{275}{676}\right)\)	\(e\left(\frac{3}{13}\right)\)
\(\chi_{8788}(49,\cdot)\)	8788.bg	1014	no	\(1\)	\(1\)	\(e\left(\frac{199}{507}\right)\)	\(e\left(\frac{35}{338}\right)\)	\(e\left(\frac{529}{1014}\right)\)	\(e\left(\frac{398}{507}\right)\)	\(e\left(\frac{257}{1014}\right)\)	\(e\left(\frac{503}{1014}\right)\)	\(e\left(\frac{206}{507}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{309}{338}\right)\)	\(e\left(\frac{25}{39}\right)\)
\(\chi_{8788}(51,\cdot)\)	8788.z	338	yes	\(-1\)	\(1\)	\(e\left(\frac{107}{338}\right)\)	\(e\left(\frac{145}{338}\right)\)	\(e\left(\frac{152}{169}\right)\)	\(e\left(\frac{107}{169}\right)\)	\(e\left(\frac{101}{169}\right)\)	\(e\left(\frac{126}{169}\right)\)	\(e\left(\frac{35}{169}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{73}{338}\right)\)	\(e\left(\frac{9}{26}\right)\)
\(\chi_{8788}(53,\cdot)\)	8788.y	169	no	\(1\)	\(1\)	\(e\left(\frac{109}{169}\right)\)	\(e\left(\frac{64}{169}\right)\)	\(e\left(\frac{147}{169}\right)\)	\(e\left(\frac{49}{169}\right)\)	\(e\left(\frac{81}{169}\right)\)	\(e\left(\frac{4}{169}\right)\)	\(e\left(\frac{95}{169}\right)\)	\(e\left(\frac{5}{13}\right)\)	\(e\left(\frac{87}{169}\right)\)	\(e\left(\frac{2}{13}\right)\)
\(\chi_{8788}(55,\cdot)\)	8788.bf	1014	yes	\(-1\)	\(1\)	\(e\left(\frac{509}{1014}\right)\)	\(e\left(\frac{71}{169}\right)\)	\(e\left(\frac{181}{1014}\right)\)	\(e\left(\frac{2}{507}\right)\)	\(e\left(\frac{893}{1014}\right)\)	\(e\left(\frac{935}{1014}\right)\)	\(e\left(\frac{266}{507}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{115}{169}\right)\)	\(e\left(\frac{71}{78}\right)\)
\(\chi_{8788}(57,\cdot)\)	8788.be	676	no	\(-1\)	\(1\)	\(e\left(\frac{68}{169}\right)\)	\(e\left(\frac{307}{676}\right)\)	\(e\left(\frac{449}{676}\right)\)	\(e\left(\frac{136}{169}\right)\)	\(e\left(\frac{613}{676}\right)\)	\(e\left(\frac{579}{676}\right)\)	\(e\left(\frac{179}{338}\right)\)	\(e\left(\frac{51}{52}\right)\)	\(e\left(\frac{45}{676}\right)\)	\(e\left(\frac{5}{26}\right)\)
\(\chi_{8788}(59,\cdot)\)	8788.bj	2028	yes	\(1\)	\(1\)	\(e\left(\frac{181}{1014}\right)\)	\(e\left(\frac{521}{676}\right)\)	\(e\left(\frac{1327}{2028}\right)\)	\(e\left(\frac{181}{507}\right)\)	\(e\left(\frac{407}{2028}\right)\)	\(e\left(\frac{1925}{2028}\right)\)	\(e\left(\frac{995}{1014}\right)\)	\(e\left(\frac{37}{156}\right)\)	\(e\left(\frac{563}{676}\right)\)	\(e\left(\frac{5}{39}\right)\)
\(\chi_{8788}(61,\cdot)\)	8788.bc	507	no	\(1\)	\(1\)	\(e\left(\frac{11}{507}\right)\)	\(e\left(\frac{105}{169}\right)\)	\(e\left(\frac{235}{507}\right)\)	\(e\left(\frac{22}{507}\right)\)	\(e\left(\frac{95}{507}\right)\)	\(e\left(\frac{326}{507}\right)\)	\(e\left(\frac{391}{507}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{82}{169}\right)\)	\(e\left(\frac{20}{39}\right)\)
\(\chi_{8788}(63,\cdot)\)	8788.bj	2028	yes	\(1\)	\(1\)	\(e\left(\frac{209}{1014}\right)\)	\(e\left(\frac{441}{676}\right)\)	\(e\left(\frac{311}{2028}\right)\)	\(e\left(\frac{209}{507}\right)\)	\(e\left(\frac{1075}{2028}\right)\)	\(e\left(\frac{1741}{2028}\right)\)	\(e\left(\frac{331}{1014}\right)\)	\(e\left(\frac{41}{156}\right)\)	\(e\left(\frac{243}{676}\right)\)	\(e\left(\frac{34}{39}\right)\)
\(\chi_{8788}(67,\cdot)\)	8788.bj	2028	yes	\(1\)	\(1\)	\(e\left(\frac{227}{1014}\right)\)	\(e\left(\frac{631}{676}\right)\)	\(e\left(\frac{1541}{2028}\right)\)	\(e\left(\frac{227}{507}\right)\)	\(e\left(\frac{925}{2028}\right)\)	\(e\left(\frac{319}{2028}\right)\)	\(e\left(\frac{49}{1014}\right)\)	\(e\left(\frac{155}{156}\right)\)	\(e\left(\frac{665}{676}\right)\)	\(e\left(\frac{22}{39}\right)\)
\(\chi_{8788}(69,\cdot)\)	8788.bg	1014	no	\(1\)	\(1\)	\(e\left(\frac{269}{507}\right)\)	\(e\left(\frac{173}{338}\right)\)	\(e\left(\frac{17}{1014}\right)\)	\(e\left(\frac{31}{507}\right)\)	\(e\left(\frac{913}{1014}\right)\)	\(e\left(\frac{43}{1014}\right)\)	\(e\left(\frac{67}{507}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{185}{338}\right)\)	\(e\left(\frac{14}{39}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 4056 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.