LMFDB - Group of Dirichlet characters of modulus 4504

Show commands: PariGP / SageMath

sage: H = DirichletGroup(4504)

pari: g = idealstar(,4504,2)

Character group

sage: G.order() pari: g.no
Order	=	2248
sage: H.invariants() pari: g.cyc
Structure	=	$C_{2}\times C_{2}\times C_{562}$
sage: H.gens() pari: g.gen
Generators	=	$\chi_{4504}(1127,\cdot)$, $\chi_{4504}(2253,\cdot)$, $\chi_{4504}(2817,\cdot)$

First 32 of 2248 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{4504}(1,\cdot)$	4504.a	1	no	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
$\chi_{4504}(3,\cdot)$	4504.l	562	yes	$-1$	$1$	$e\left(\frac{231}{281}\right)$	$e\left(\frac{535}{562}\right)$	$e\left(\frac{55}{562}\right)$	$e\left(\frac{181}{281}\right)$	$e\left(\frac{128}{281}\right)$	$e\left(\frac{451}{562}\right)$	$e\left(\frac{435}{562}\right)$	$e\left(\frac{187}{281}\right)$	$e\left(\frac{107}{281}\right)$	$e\left(\frac{517}{562}\right)$
$\chi_{4504}(5,\cdot)$	4504.m	562	yes	$-1$	$1$	$e\left(\frac{535}{562}\right)$	$e\left(\frac{9}{281}\right)$	$e\left(\frac{169}{281}\right)$	$e\left(\frac{254}{281}\right)$	$e\left(\frac{485}{562}\right)$	$e\left(\frac{355}{562}\right)$	$e\left(\frac{553}{562}\right)$	$e\left(\frac{250}{281}\right)$	$e\left(\frac{513}{562}\right)$	$e\left(\frac{311}{562}\right)$
$\chi_{4504}(7,\cdot)$	4504.n	562	no	$-1$	$1$	$e\left(\frac{55}{562}\right)$	$e\left(\frac{169}{281}\right)$	$e\left(\frac{321}{562}\right)$	$e\left(\frac{55}{281}\right)$	$e\left(\frac{365}{562}\right)$	$e\left(\frac{164}{281}\right)$	$e\left(\frac{393}{562}\right)$	$e\left(\frac{136}{281}\right)$	$e\left(\frac{79}{562}\right)$	$e\left(\frac{188}{281}\right)$
$\chi_{4504}(9,\cdot)$	4504.i	281	no	$1$	$1$	$e\left(\frac{181}{281}\right)$	$e\left(\frac{254}{281}\right)$	$e\left(\frac{55}{281}\right)$	$e\left(\frac{81}{281}\right)$	$e\left(\frac{256}{281}\right)$	$e\left(\frac{170}{281}\right)$	$e\left(\frac{154}{281}\right)$	$e\left(\frac{93}{281}\right)$	$e\left(\frac{214}{281}\right)$	$e\left(\frac{236}{281}\right)$
$\chi_{4504}(11,\cdot)$	4504.l	562	yes	$-1$	$1$	$e\left(\frac{128}{281}\right)$	$e\left(\frac{485}{562}\right)$	$e\left(\frac{365}{562}\right)$	$e\left(\frac{256}{281}\right)$	$e\left(\frac{32}{281}\right)$	$e\left(\frac{183}{562}\right)$	$e\left(\frac{179}{562}\right)$	$e\left(\frac{117}{281}\right)$	$e\left(\frac{97}{281}\right)$	$e\left(\frac{59}{562}\right)$
$\chi_{4504}(13,\cdot)$	4504.o	562	yes	$1$	$1$	$e\left(\frac{451}{562}\right)$	$e\left(\frac{355}{562}\right)$	$e\left(\frac{164}{281}\right)$	$e\left(\frac{170}{281}\right)$	$e\left(\frac{183}{562}\right)$	$e\left(\frac{273}{562}\right)$	$e\left(\frac{122}{281}\right)$	$e\left(\frac{216}{281}\right)$	$e\left(\frac{423}{562}\right)$	$e\left(\frac{217}{562}\right)$
$\chi_{4504}(15,\cdot)$	4504.p	562	no	$1$	$1$	$e\left(\frac{435}{562}\right)$	$e\left(\frac{553}{562}\right)$	$e\left(\frac{393}{562}\right)$	$e\left(\frac{154}{281}\right)$	$e\left(\frac{179}{562}\right)$	$e\left(\frac{122}{281}\right)$	$e\left(\frac{213}{281}\right)$	$e\left(\frac{156}{281}\right)$	$e\left(\frac{165}{562}\right)$	$e\left(\frac{133}{281}\right)$
$\chi_{4504}(17,\cdot)$	4504.i	281	no	$1$	$1$	$e\left(\frac{187}{281}\right)$	$e\left(\frac{250}{281}\right)$	$e\left(\frac{136}{281}\right)$	$e\left(\frac{93}{281}\right)$	$e\left(\frac{117}{281}\right)$	$e\left(\frac{216}{281}\right)$	$e\left(\frac{156}{281}\right)$	$e\left(\frac{138}{281}\right)$	$e\left(\frac{100}{281}\right)$	$e\left(\frac{42}{281}\right)$
$\chi_{4504}(19,\cdot)$	4504.l	562	yes	$-1$	$1$	$e\left(\frac{107}{281}\right)$	$e\left(\frac{513}{562}\right)$	$e\left(\frac{79}{562}\right)$	$e\left(\frac{214}{281}\right)$	$e\left(\frac{97}{281}\right)$	$e\left(\frac{423}{562}\right)$	$e\left(\frac{165}{562}\right)$	$e\left(\frac{100}{281}\right)$	$e\left(\frac{215}{281}\right)$	$e\left(\frac{293}{562}\right)$
$\chi_{4504}(21,\cdot)$	4504.o	562	yes	$1$	$1$	$e\left(\frac{517}{562}\right)$	$e\left(\frac{311}{562}\right)$	$e\left(\frac{188}{281}\right)$	$e\left(\frac{236}{281}\right)$	$e\left(\frac{59}{562}\right)$	$e\left(\frac{217}{562}\right)$	$e\left(\frac{133}{281}\right)$	$e\left(\frac{42}{281}\right)$	$e\left(\frac{293}{562}\right)$	$e\left(\frac{331}{562}\right)$
$\chi_{4504}(23,\cdot)$	4504.n	562	no	$-1$	$1$	$e\left(\frac{171}{562}\right)$	$e\left(\frac{224}{281}\right)$	$e\left(\frac{201}{562}\right)$	$e\left(\frac{171}{281}\right)$	$e\left(\frac{113}{562}\right)$	$e\left(\frac{234}{281}\right)$	$e\left(\frac{57}{562}\right)$	$e\left(\frac{9}{281}\right)$	$e\left(\frac{123}{562}\right)$	$e\left(\frac{186}{281}\right)$
$\chi_{4504}(25,\cdot)$	4504.i	281	no	$1$	$1$	$e\left(\frac{254}{281}\right)$	$e\left(\frac{18}{281}\right)$	$e\left(\frac{57}{281}\right)$	$e\left(\frac{227}{281}\right)$	$e\left(\frac{204}{281}\right)$	$e\left(\frac{74}{281}\right)$	$e\left(\frac{272}{281}\right)$	$e\left(\frac{219}{281}\right)$	$e\left(\frac{232}{281}\right)$	$e\left(\frac{30}{281}\right)$
$\chi_{4504}(27,\cdot)$	4504.l	562	yes	$-1$	$1$	$e\left(\frac{131}{281}\right)$	$e\left(\frac{481}{562}\right)$	$e\left(\frac{165}{562}\right)$	$e\left(\frac{262}{281}\right)$	$e\left(\frac{103}{281}\right)$	$e\left(\frac{229}{562}\right)$	$e\left(\frac{181}{562}\right)$	$e\left(\frac{280}{281}\right)$	$e\left(\frac{40}{281}\right)$	$e\left(\frac{427}{562}\right)$
$\chi_{4504}(29,\cdot)$	4504.m	562	yes	$-1$	$1$	$e\left(\frac{465}{562}\right)$	$e\left(\frac{126}{281}\right)$	$e\left(\frac{118}{281}\right)$	$e\left(\frac{184}{281}\right)$	$e\left(\frac{327}{562}\right)$	$e\left(\frac{193}{562}\right)$	$e\left(\frac{155}{562}\right)$	$e\left(\frac{128}{281}\right)$	$e\left(\frac{157}{562}\right)$	$e\left(\frac{139}{562}\right)$
$\chi_{4504}(31,\cdot)$	4504.p	562	no	$1$	$1$	$e\left(\frac{205}{562}\right)$	$e\left(\frac{519}{562}\right)$	$e\left(\frac{379}{562}\right)$	$e\left(\frac{205}{281}\right)$	$e\left(\frac{543}{562}\right)$	$e\left(\frac{177}{281}\right)$	$e\left(\frac{81}{281}\right)$	$e\left(\frac{277}{281}\right)$	$e\left(\frac{39}{562}\right)$	$e\left(\frac{11}{281}\right)$
$\chi_{4504}(33,\cdot)$	4504.i	281	no	$1$	$1$	$e\left(\frac{78}{281}\right)$	$e\left(\frac{229}{281}\right)$	$e\left(\frac{210}{281}\right)$	$e\left(\frac{156}{281}\right)$	$e\left(\frac{160}{281}\right)$	$e\left(\frac{36}{281}\right)$	$e\left(\frac{26}{281}\right)$	$e\left(\frac{23}{281}\right)$	$e\left(\frac{204}{281}\right)$	$e\left(\frac{7}{281}\right)$
$\chi_{4504}(35,\cdot)$	4504.j	562	yes	$1$	$1$	$e\left(\frac{14}{281}\right)$	$e\left(\frac{178}{281}\right)$	$e\left(\frac{97}{562}\right)$	$e\left(\frac{28}{281}\right)$	$e\left(\frac{144}{281}\right)$	$e\left(\frac{121}{562}\right)$	$e\left(\frac{192}{281}\right)$	$e\left(\frac{105}{281}\right)$	$e\left(\frac{15}{281}\right)$	$e\left(\frac{125}{562}\right)$
$\chi_{4504}(37,\cdot)$	4504.m	562	yes	$-1$	$1$	$e\left(\frac{31}{562}\right)$	$e\left(\frac{177}{281}\right)$	$e\left(\frac{139}{281}\right)$	$e\left(\frac{31}{281}\right)$	$e\left(\frac{359}{562}\right)$	$e\left(\frac{425}{562}\right)$	$e\left(\frac{385}{562}\right)$	$e\left(\frac{46}{281}\right)$	$e\left(\frac{535}{562}\right)$	$e\left(\frac{309}{562}\right)$
$\chi_{4504}(39,\cdot)$	4504.n	562	no	$-1$	$1$	$e\left(\frac{351}{562}\right)$	$e\left(\frac{164}{281}\right)$	$e\left(\frac{383}{562}\right)$	$e\left(\frac{70}{281}\right)$	$e\left(\frac{439}{562}\right)$	$e\left(\frac{81}{281}\right)$	$e\left(\frac{117}{562}\right)$	$e\left(\frac{122}{281}\right)$	$e\left(\frac{75}{562}\right)$	$e\left(\frac{86}{281}\right)$
$\chi_{4504}(41,\cdot)$	4504.k	562	no	$-1$	$1$	$e\left(\frac{257}{281}\right)$	$e\left(\frac{313}{562}\right)$	$e\left(\frac{238}{281}\right)$	$e\left(\frac{233}{281}\right)$	$e\left(\frac{275}{281}\right)$	$e\left(\frac{97}{281}\right)$	$e\left(\frac{265}{562}\right)$	$e\left(\frac{101}{281}\right)$	$e\left(\frac{175}{281}\right)$	$e\left(\frac{214}{281}\right)$
$\chi_{4504}(43,\cdot)$	4504.j	562	yes	$1$	$1$	$e\left(\frac{164}{281}\right)$	$e\left(\frac{78}{281}\right)$	$e\left(\frac{213}{562}\right)$	$e\left(\frac{47}{281}\right)$	$e\left(\frac{41}{281}\right)$	$e\left(\frac{173}{562}\right)$	$e\left(\frac{242}{281}\right)$	$e\left(\frac{106}{281}\right)$	$e\left(\frac{256}{281}\right)$	$e\left(\frac{541}{562}\right)$
$\chi_{4504}(45,\cdot)$	4504.m	562	yes	$-1$	$1$	$e\left(\frac{335}{562}\right)$	$e\left(\frac{263}{281}\right)$	$e\left(\frac{224}{281}\right)$	$e\left(\frac{54}{281}\right)$	$e\left(\frac{435}{562}\right)$	$e\left(\frac{133}{562}\right)$	$e\left(\frac{299}{562}\right)$	$e\left(\frac{62}{281}\right)$	$e\left(\frac{379}{562}\right)$	$e\left(\frac{221}{562}\right)$
$\chi_{4504}(47,\cdot)$	4504.n	562	no	$-1$	$1$	$e\left(\frac{445}{562}\right)$	$e\left(\frac{39}{281}\right)$	$e\left(\frac{247}{562}\right)$	$e\left(\frac{164}{281}\right)$	$e\left(\frac{41}{562}\right)$	$e\left(\frac{254}{281}\right)$	$e\left(\frac{523}{562}\right)$	$e\left(\frac{53}{281}\right)$	$e\left(\frac{537}{562}\right)$	$e\left(\frac{65}{281}\right)$
$\chi_{4504}(49,\cdot)$	4504.i	281	no	$1$	$1$	$e\left(\frac{55}{281}\right)$	$e\left(\frac{57}{281}\right)$	$e\left(\frac{40}{281}\right)$	$e\left(\frac{110}{281}\right)$	$e\left(\frac{84}{281}\right)$	$e\left(\frac{47}{281}\right)$	$e\left(\frac{112}{281}\right)$	$e\left(\frac{272}{281}\right)$	$e\left(\frac{79}{281}\right)$	$e\left(\frac{95}{281}\right)$
$\chi_{4504}(51,\cdot)$	4504.l	562	yes	$-1$	$1$	$e\left(\frac{137}{281}\right)$	$e\left(\frac{473}{562}\right)$	$e\left(\frac{327}{562}\right)$	$e\left(\frac{274}{281}\right)$	$e\left(\frac{245}{281}\right)$	$e\left(\frac{321}{562}\right)$	$e\left(\frac{185}{562}\right)$	$e\left(\frac{44}{281}\right)$	$e\left(\frac{207}{281}\right)$	$e\left(\frac{39}{562}\right)$
$\chi_{4504}(53,\cdot)$	4504.m	562	yes	$-1$	$1$	$e\left(\frac{215}{562}\right)$	$e\left(\frac{22}{281}\right)$	$e\left(\frac{257}{281}\right)$	$e\left(\frac{215}{281}\right)$	$e\left(\frac{405}{562}\right)$	$e\left(\frac{337}{562}\right)$	$e\left(\frac{259}{562}\right)$	$e\left(\frac{174}{281}\right)$	$e\left(\frac{411}{562}\right)$	$e\left(\frac{167}{562}\right)$
$\chi_{4504}(55,\cdot)$	4504.p	562	no	$1$	$1$	$e\left(\frac{229}{562}\right)$	$e\left(\frac{503}{562}\right)$	$e\left(\frac{141}{562}\right)$	$e\left(\frac{229}{281}\right)$	$e\left(\frac{549}{562}\right)$	$e\left(\frac{269}{281}\right)$	$e\left(\frac{85}{281}\right)$	$e\left(\frac{86}{281}\right)$	$e\left(\frac{145}{562}\right)$	$e\left(\frac{185}{281}\right)$
$\chi_{4504}(57,\cdot)$	4504.i	281	no	$1$	$1$	$e\left(\frac{57}{281}\right)$	$e\left(\frac{243}{281}\right)$	$e\left(\frac{67}{281}\right)$	$e\left(\frac{114}{281}\right)$	$e\left(\frac{225}{281}\right)$	$e\left(\frac{156}{281}\right)$	$e\left(\frac{19}{281}\right)$	$e\left(\frac{6}{281}\right)$	$e\left(\frac{41}{281}\right)$	$e\left(\frac{124}{281}\right)$
$\chi_{4504}(59,\cdot)$	4504.l	562	yes	$-1$	$1$	$e\left(\frac{20}{281}\right)$	$e\left(\frac{67}{562}\right)$	$e\left(\frac{259}{562}\right)$	$e\left(\frac{40}{281}\right)$	$e\left(\frac{5}{281}\right)$	$e\left(\frac{213}{562}\right)$	$e\left(\frac{107}{562}\right)$	$e\left(\frac{150}{281}\right)$	$e\left(\frac{182}{281}\right)$	$e\left(\frac{299}{562}\right)$
$\chi_{4504}(61,\cdot)$	4504.o	562	yes	$1$	$1$	$e\left(\frac{223}{562}\right)$	$e\left(\frac{507}{562}\right)$	$e\left(\frac{30}{281}\right)$	$e\left(\frac{223}{281}\right)$	$e\left(\frac{407}{562}\right)$	$e\left(\frac{211}{562}\right)$	$e\left(\frac{84}{281}\right)$	$e\left(\frac{204}{281}\right)$	$e\left(\frac{259}{562}\right)$	$e\left(\frac{283}{562}\right)$
$\chi_{4504}(63,\cdot)$	4504.n	562	no	$-1$	$1$	$e\left(\frac{417}{562}\right)$	$e\left(\frac{142}{281}\right)$	$e\left(\frac{431}{562}\right)$	$e\left(\frac{136}{281}\right)$	$e\left(\frac{315}{562}\right)$	$e\left(\frac{53}{281}\right)$	$e\left(\frac{139}{562}\right)$	$e\left(\frac{229}{281}\right)$	$e\left(\frac{507}{562}\right)$	$e\left(\frac{143}{281}\right)$

Click here to search among the remaining 2216 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	$4504$
Structure	\(C_{2}\times C_{2}\times C_{562}\)
Order	$2248$

Character	Orbit	Order	Primitive	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{4504}(1,\cdot)\)	4504.a	1	no	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)	\(1\)
\(\chi_{4504}(3,\cdot)\)	4504.l	562	yes	\(-1\)	\(1\)	\(e\left(\frac{231}{281}\right)\)	\(e\left(\frac{535}{562}\right)\)	\(e\left(\frac{55}{562}\right)\)	\(e\left(\frac{181}{281}\right)\)	\(e\left(\frac{128}{281}\right)\)	\(e\left(\frac{451}{562}\right)\)	\(e\left(\frac{435}{562}\right)\)	\(e\left(\frac{187}{281}\right)\)	\(e\left(\frac{107}{281}\right)\)	\(e\left(\frac{517}{562}\right)\)
\(\chi_{4504}(5,\cdot)\)	4504.m	562	yes	\(-1\)	\(1\)	\(e\left(\frac{535}{562}\right)\)	\(e\left(\frac{9}{281}\right)\)	\(e\left(\frac{169}{281}\right)\)	\(e\left(\frac{254}{281}\right)\)	\(e\left(\frac{485}{562}\right)\)	\(e\left(\frac{355}{562}\right)\)	\(e\left(\frac{553}{562}\right)\)	\(e\left(\frac{250}{281}\right)\)	\(e\left(\frac{513}{562}\right)\)	\(e\left(\frac{311}{562}\right)\)
\(\chi_{4504}(7,\cdot)\)	4504.n	562	no	\(-1\)	\(1\)	\(e\left(\frac{55}{562}\right)\)	\(e\left(\frac{169}{281}\right)\)	\(e\left(\frac{321}{562}\right)\)	\(e\left(\frac{55}{281}\right)\)	\(e\left(\frac{365}{562}\right)\)	\(e\left(\frac{164}{281}\right)\)	\(e\left(\frac{393}{562}\right)\)	\(e\left(\frac{136}{281}\right)\)	\(e\left(\frac{79}{562}\right)\)	\(e\left(\frac{188}{281}\right)\)
\(\chi_{4504}(9,\cdot)\)	4504.i	281	no	\(1\)	\(1\)	\(e\left(\frac{181}{281}\right)\)	\(e\left(\frac{254}{281}\right)\)	\(e\left(\frac{55}{281}\right)\)	\(e\left(\frac{81}{281}\right)\)	\(e\left(\frac{256}{281}\right)\)	\(e\left(\frac{170}{281}\right)\)	\(e\left(\frac{154}{281}\right)\)	\(e\left(\frac{93}{281}\right)\)	\(e\left(\frac{214}{281}\right)\)	\(e\left(\frac{236}{281}\right)\)
\(\chi_{4504}(11,\cdot)\)	4504.l	562	yes	\(-1\)	\(1\)	\(e\left(\frac{128}{281}\right)\)	\(e\left(\frac{485}{562}\right)\)	\(e\left(\frac{365}{562}\right)\)	\(e\left(\frac{256}{281}\right)\)	\(e\left(\frac{32}{281}\right)\)	\(e\left(\frac{183}{562}\right)\)	\(e\left(\frac{179}{562}\right)\)	\(e\left(\frac{117}{281}\right)\)	\(e\left(\frac{97}{281}\right)\)	\(e\left(\frac{59}{562}\right)\)
\(\chi_{4504}(13,\cdot)\)	4504.o	562	yes	\(1\)	\(1\)	\(e\left(\frac{451}{562}\right)\)	\(e\left(\frac{355}{562}\right)\)	\(e\left(\frac{164}{281}\right)\)	\(e\left(\frac{170}{281}\right)\)	\(e\left(\frac{183}{562}\right)\)	\(e\left(\frac{273}{562}\right)\)	\(e\left(\frac{122}{281}\right)\)	\(e\left(\frac{216}{281}\right)\)	\(e\left(\frac{423}{562}\right)\)	\(e\left(\frac{217}{562}\right)\)
\(\chi_{4504}(15,\cdot)\)	4504.p	562	no	\(1\)	\(1\)	\(e\left(\frac{435}{562}\right)\)	\(e\left(\frac{553}{562}\right)\)	\(e\left(\frac{393}{562}\right)\)	\(e\left(\frac{154}{281}\right)\)	\(e\left(\frac{179}{562}\right)\)	\(e\left(\frac{122}{281}\right)\)	\(e\left(\frac{213}{281}\right)\)	\(e\left(\frac{156}{281}\right)\)	\(e\left(\frac{165}{562}\right)\)	\(e\left(\frac{133}{281}\right)\)
\(\chi_{4504}(17,\cdot)\)	4504.i	281	no	\(1\)	\(1\)	\(e\left(\frac{187}{281}\right)\)	\(e\left(\frac{250}{281}\right)\)	\(e\left(\frac{136}{281}\right)\)	\(e\left(\frac{93}{281}\right)\)	\(e\left(\frac{117}{281}\right)\)	\(e\left(\frac{216}{281}\right)\)	\(e\left(\frac{156}{281}\right)\)	\(e\left(\frac{138}{281}\right)\)	\(e\left(\frac{100}{281}\right)\)	\(e\left(\frac{42}{281}\right)\)
\(\chi_{4504}(19,\cdot)\)	4504.l	562	yes	\(-1\)	\(1\)	\(e\left(\frac{107}{281}\right)\)	\(e\left(\frac{513}{562}\right)\)	\(e\left(\frac{79}{562}\right)\)	\(e\left(\frac{214}{281}\right)\)	\(e\left(\frac{97}{281}\right)\)	\(e\left(\frac{423}{562}\right)\)	\(e\left(\frac{165}{562}\right)\)	\(e\left(\frac{100}{281}\right)\)	\(e\left(\frac{215}{281}\right)\)	\(e\left(\frac{293}{562}\right)\)
\(\chi_{4504}(21,\cdot)\)	4504.o	562	yes	\(1\)	\(1\)	\(e\left(\frac{517}{562}\right)\)	\(e\left(\frac{311}{562}\right)\)	\(e\left(\frac{188}{281}\right)\)	\(e\left(\frac{236}{281}\right)\)	\(e\left(\frac{59}{562}\right)\)	\(e\left(\frac{217}{562}\right)\)	\(e\left(\frac{133}{281}\right)\)	\(e\left(\frac{42}{281}\right)\)	\(e\left(\frac{293}{562}\right)\)	\(e\left(\frac{331}{562}\right)\)
\(\chi_{4504}(23,\cdot)\)	4504.n	562	no	\(-1\)	\(1\)	\(e\left(\frac{171}{562}\right)\)	\(e\left(\frac{224}{281}\right)\)	\(e\left(\frac{201}{562}\right)\)	\(e\left(\frac{171}{281}\right)\)	\(e\left(\frac{113}{562}\right)\)	\(e\left(\frac{234}{281}\right)\)	\(e\left(\frac{57}{562}\right)\)	\(e\left(\frac{9}{281}\right)\)	\(e\left(\frac{123}{562}\right)\)	\(e\left(\frac{186}{281}\right)\)
\(\chi_{4504}(25,\cdot)\)	4504.i	281	no	\(1\)	\(1\)	\(e\left(\frac{254}{281}\right)\)	\(e\left(\frac{18}{281}\right)\)	\(e\left(\frac{57}{281}\right)\)	\(e\left(\frac{227}{281}\right)\)	\(e\left(\frac{204}{281}\right)\)	\(e\left(\frac{74}{281}\right)\)	\(e\left(\frac{272}{281}\right)\)	\(e\left(\frac{219}{281}\right)\)	\(e\left(\frac{232}{281}\right)\)	\(e\left(\frac{30}{281}\right)\)
\(\chi_{4504}(27,\cdot)\)	4504.l	562	yes	\(-1\)	\(1\)	\(e\left(\frac{131}{281}\right)\)	\(e\left(\frac{481}{562}\right)\)	\(e\left(\frac{165}{562}\right)\)	\(e\left(\frac{262}{281}\right)\)	\(e\left(\frac{103}{281}\right)\)	\(e\left(\frac{229}{562}\right)\)	\(e\left(\frac{181}{562}\right)\)	\(e\left(\frac{280}{281}\right)\)	\(e\left(\frac{40}{281}\right)\)	\(e\left(\frac{427}{562}\right)\)
\(\chi_{4504}(29,\cdot)\)	4504.m	562	yes	\(-1\)	\(1\)	\(e\left(\frac{465}{562}\right)\)	\(e\left(\frac{126}{281}\right)\)	\(e\left(\frac{118}{281}\right)\)	\(e\left(\frac{184}{281}\right)\)	\(e\left(\frac{327}{562}\right)\)	\(e\left(\frac{193}{562}\right)\)	\(e\left(\frac{155}{562}\right)\)	\(e\left(\frac{128}{281}\right)\)	\(e\left(\frac{157}{562}\right)\)	\(e\left(\frac{139}{562}\right)\)
\(\chi_{4504}(31,\cdot)\)	4504.p	562	no	\(1\)	\(1\)	\(e\left(\frac{205}{562}\right)\)	\(e\left(\frac{519}{562}\right)\)	\(e\left(\frac{379}{562}\right)\)	\(e\left(\frac{205}{281}\right)\)	\(e\left(\frac{543}{562}\right)\)	\(e\left(\frac{177}{281}\right)\)	\(e\left(\frac{81}{281}\right)\)	\(e\left(\frac{277}{281}\right)\)	\(e\left(\frac{39}{562}\right)\)	\(e\left(\frac{11}{281}\right)\)
\(\chi_{4504}(33,\cdot)\)	4504.i	281	no	\(1\)	\(1\)	\(e\left(\frac{78}{281}\right)\)	\(e\left(\frac{229}{281}\right)\)	\(e\left(\frac{210}{281}\right)\)	\(e\left(\frac{156}{281}\right)\)	\(e\left(\frac{160}{281}\right)\)	\(e\left(\frac{36}{281}\right)\)	\(e\left(\frac{26}{281}\right)\)	\(e\left(\frac{23}{281}\right)\)	\(e\left(\frac{204}{281}\right)\)	\(e\left(\frac{7}{281}\right)\)
\(\chi_{4504}(35,\cdot)\)	4504.j	562	yes	\(1\)	\(1\)	\(e\left(\frac{14}{281}\right)\)	\(e\left(\frac{178}{281}\right)\)	\(e\left(\frac{97}{562}\right)\)	\(e\left(\frac{28}{281}\right)\)	\(e\left(\frac{144}{281}\right)\)	\(e\left(\frac{121}{562}\right)\)	\(e\left(\frac{192}{281}\right)\)	\(e\left(\frac{105}{281}\right)\)	\(e\left(\frac{15}{281}\right)\)	\(e\left(\frac{125}{562}\right)\)
\(\chi_{4504}(37,\cdot)\)	4504.m	562	yes	\(-1\)	\(1\)	\(e\left(\frac{31}{562}\right)\)	\(e\left(\frac{177}{281}\right)\)	\(e\left(\frac{139}{281}\right)\)	\(e\left(\frac{31}{281}\right)\)	\(e\left(\frac{359}{562}\right)\)	\(e\left(\frac{425}{562}\right)\)	\(e\left(\frac{385}{562}\right)\)	\(e\left(\frac{46}{281}\right)\)	\(e\left(\frac{535}{562}\right)\)	\(e\left(\frac{309}{562}\right)\)
\(\chi_{4504}(39,\cdot)\)	4504.n	562	no	\(-1\)	\(1\)	\(e\left(\frac{351}{562}\right)\)	\(e\left(\frac{164}{281}\right)\)	\(e\left(\frac{383}{562}\right)\)	\(e\left(\frac{70}{281}\right)\)	\(e\left(\frac{439}{562}\right)\)	\(e\left(\frac{81}{281}\right)\)	\(e\left(\frac{117}{562}\right)\)	\(e\left(\frac{122}{281}\right)\)	\(e\left(\frac{75}{562}\right)\)	\(e\left(\frac{86}{281}\right)\)
\(\chi_{4504}(41,\cdot)\)	4504.k	562	no	\(-1\)	\(1\)	\(e\left(\frac{257}{281}\right)\)	\(e\left(\frac{313}{562}\right)\)	\(e\left(\frac{238}{281}\right)\)	\(e\left(\frac{233}{281}\right)\)	\(e\left(\frac{275}{281}\right)\)	\(e\left(\frac{97}{281}\right)\)	\(e\left(\frac{265}{562}\right)\)	\(e\left(\frac{101}{281}\right)\)	\(e\left(\frac{175}{281}\right)\)	\(e\left(\frac{214}{281}\right)\)
\(\chi_{4504}(43,\cdot)\)	4504.j	562	yes	\(1\)	\(1\)	\(e\left(\frac{164}{281}\right)\)	\(e\left(\frac{78}{281}\right)\)	\(e\left(\frac{213}{562}\right)\)	\(e\left(\frac{47}{281}\right)\)	\(e\left(\frac{41}{281}\right)\)	\(e\left(\frac{173}{562}\right)\)	\(e\left(\frac{242}{281}\right)\)	\(e\left(\frac{106}{281}\right)\)	\(e\left(\frac{256}{281}\right)\)	\(e\left(\frac{541}{562}\right)\)
\(\chi_{4504}(45,\cdot)\)	4504.m	562	yes	\(-1\)	\(1\)	\(e\left(\frac{335}{562}\right)\)	\(e\left(\frac{263}{281}\right)\)	\(e\left(\frac{224}{281}\right)\)	\(e\left(\frac{54}{281}\right)\)	\(e\left(\frac{435}{562}\right)\)	\(e\left(\frac{133}{562}\right)\)	\(e\left(\frac{299}{562}\right)\)	\(e\left(\frac{62}{281}\right)\)	\(e\left(\frac{379}{562}\right)\)	\(e\left(\frac{221}{562}\right)\)
\(\chi_{4504}(47,\cdot)\)	4504.n	562	no	\(-1\)	\(1\)	\(e\left(\frac{445}{562}\right)\)	\(e\left(\frac{39}{281}\right)\)	\(e\left(\frac{247}{562}\right)\)	\(e\left(\frac{164}{281}\right)\)	\(e\left(\frac{41}{562}\right)\)	\(e\left(\frac{254}{281}\right)\)	\(e\left(\frac{523}{562}\right)\)	\(e\left(\frac{53}{281}\right)\)	\(e\left(\frac{537}{562}\right)\)	\(e\left(\frac{65}{281}\right)\)
\(\chi_{4504}(49,\cdot)\)	4504.i	281	no	\(1\)	\(1\)	\(e\left(\frac{55}{281}\right)\)	\(e\left(\frac{57}{281}\right)\)	\(e\left(\frac{40}{281}\right)\)	\(e\left(\frac{110}{281}\right)\)	\(e\left(\frac{84}{281}\right)\)	\(e\left(\frac{47}{281}\right)\)	\(e\left(\frac{112}{281}\right)\)	\(e\left(\frac{272}{281}\right)\)	\(e\left(\frac{79}{281}\right)\)	\(e\left(\frac{95}{281}\right)\)
\(\chi_{4504}(51,\cdot)\)	4504.l	562	yes	\(-1\)	\(1\)	\(e\left(\frac{137}{281}\right)\)	\(e\left(\frac{473}{562}\right)\)	\(e\left(\frac{327}{562}\right)\)	\(e\left(\frac{274}{281}\right)\)	\(e\left(\frac{245}{281}\right)\)	\(e\left(\frac{321}{562}\right)\)	\(e\left(\frac{185}{562}\right)\)	\(e\left(\frac{44}{281}\right)\)	\(e\left(\frac{207}{281}\right)\)	\(e\left(\frac{39}{562}\right)\)
\(\chi_{4504}(53,\cdot)\)	4504.m	562	yes	\(-1\)	\(1\)	\(e\left(\frac{215}{562}\right)\)	\(e\left(\frac{22}{281}\right)\)	\(e\left(\frac{257}{281}\right)\)	\(e\left(\frac{215}{281}\right)\)	\(e\left(\frac{405}{562}\right)\)	\(e\left(\frac{337}{562}\right)\)	\(e\left(\frac{259}{562}\right)\)	\(e\left(\frac{174}{281}\right)\)	\(e\left(\frac{411}{562}\right)\)	\(e\left(\frac{167}{562}\right)\)
\(\chi_{4504}(55,\cdot)\)	4504.p	562	no	\(1\)	\(1\)	\(e\left(\frac{229}{562}\right)\)	\(e\left(\frac{503}{562}\right)\)	\(e\left(\frac{141}{562}\right)\)	\(e\left(\frac{229}{281}\right)\)	\(e\left(\frac{549}{562}\right)\)	\(e\left(\frac{269}{281}\right)\)	\(e\left(\frac{85}{281}\right)\)	\(e\left(\frac{86}{281}\right)\)	\(e\left(\frac{145}{562}\right)\)	\(e\left(\frac{185}{281}\right)\)
\(\chi_{4504}(57,\cdot)\)	4504.i	281	no	\(1\)	\(1\)	\(e\left(\frac{57}{281}\right)\)	\(e\left(\frac{243}{281}\right)\)	\(e\left(\frac{67}{281}\right)\)	\(e\left(\frac{114}{281}\right)\)	\(e\left(\frac{225}{281}\right)\)	\(e\left(\frac{156}{281}\right)\)	\(e\left(\frac{19}{281}\right)\)	\(e\left(\frac{6}{281}\right)\)	\(e\left(\frac{41}{281}\right)\)	\(e\left(\frac{124}{281}\right)\)
\(\chi_{4504}(59,\cdot)\)	4504.l	562	yes	\(-1\)	\(1\)	\(e\left(\frac{20}{281}\right)\)	\(e\left(\frac{67}{562}\right)\)	\(e\left(\frac{259}{562}\right)\)	\(e\left(\frac{40}{281}\right)\)	\(e\left(\frac{5}{281}\right)\)	\(e\left(\frac{213}{562}\right)\)	\(e\left(\frac{107}{562}\right)\)	\(e\left(\frac{150}{281}\right)\)	\(e\left(\frac{182}{281}\right)\)	\(e\left(\frac{299}{562}\right)\)
\(\chi_{4504}(61,\cdot)\)	4504.o	562	yes	\(1\)	\(1\)	\(e\left(\frac{223}{562}\right)\)	\(e\left(\frac{507}{562}\right)\)	\(e\left(\frac{30}{281}\right)\)	\(e\left(\frac{223}{281}\right)\)	\(e\left(\frac{407}{562}\right)\)	\(e\left(\frac{211}{562}\right)\)	\(e\left(\frac{84}{281}\right)\)	\(e\left(\frac{204}{281}\right)\)	\(e\left(\frac{259}{562}\right)\)	\(e\left(\frac{283}{562}\right)\)
\(\chi_{4504}(63,\cdot)\)	4504.n	562	no	\(-1\)	\(1\)	\(e\left(\frac{417}{562}\right)\)	\(e\left(\frac{142}{281}\right)\)	\(e\left(\frac{431}{562}\right)\)	\(e\left(\frac{136}{281}\right)\)	\(e\left(\frac{315}{562}\right)\)	\(e\left(\frac{53}{281}\right)\)	\(e\left(\frac{139}{562}\right)\)	\(e\left(\frac{229}{281}\right)\)	\(e\left(\frac{507}{562}\right)\)	\(e\left(\frac{143}{281}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Learn more

Character group

First 32 of 2248 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.