LMFDB - Dirichlet character orbit 5243.z

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5243, base_ring=CyclotomicField(742)) M = H._module chi = DirichletCharacter(H, M([477,497])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(6,5243)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$5243$
Conductor:	$5243$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$742$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{371})$
Fixed field:	Number field defined by a degree 742 polynomial (not computed)

First 31 of 312 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{5243}(6,\cdot)$	$1$	$1$	$e\left(\frac{285}{742}\right)$	$e\left(\frac{393}{742}\right)$	$e\left(\frac{285}{371}\right)$	$e\left(\frac{46}{371}\right)$	$e\left(\frac{339}{371}\right)$	$e\left(\frac{113}{742}\right)$	$e\left(\frac{22}{371}\right)$	$e\left(\frac{377}{742}\right)$	$e\left(\frac{167}{371}\right)$	$e\left(\frac{221}{742}\right)$
$\chi_{5243}(20,\cdot)$	$1$	$1$	$e\left(\frac{449}{742}\right)$	$e\left(\frac{213}{742}\right)$	$e\left(\frac{78}{371}\right)$	$e\left(\frac{243}{371}\right)$	$e\left(\frac{331}{371}\right)$	$e\left(\frac{605}{742}\right)$	$e\left(\frac{213}{371}\right)$	$e\left(\frac{193}{742}\right)$	$e\left(\frac{116}{371}\right)$	$e\left(\frac{369}{742}\right)$
$\chi_{5243}(55,\cdot)$	$1$	$1$	$e\left(\frac{271}{742}\right)$	$e\left(\frac{155}{742}\right)$	$e\left(\frac{271}{371}\right)$	$e\left(\frac{88}{371}\right)$	$e\left(\frac{213}{371}\right)$	$e\left(\frac{71}{742}\right)$	$e\left(\frac{155}{371}\right)$	$e\left(\frac{447}{742}\right)$	$e\left(\frac{13}{371}\right)$	$e\left(\frac{697}{742}\right)$
$\chi_{5243}(104,\cdot)$	$1$	$1$	$e\left(\frac{649}{742}\right)$	$e\left(\frac{645}{742}\right)$	$e\left(\frac{278}{371}\right)$	$e\left(\frac{67}{371}\right)$	$e\left(\frac{276}{371}\right)$	$e\left(\frac{463}{742}\right)$	$e\left(\frac{274}{371}\right)$	$e\left(\frac{41}{742}\right)$	$e\left(\frac{90}{371}\right)$	$e\left(\frac{459}{742}\right)$
$\chi_{5243}(125,\cdot)$	$1$	$1$	$e\left(\frac{139}{742}\right)$	$e\left(\frac{137}{742}\right)$	$e\left(\frac{139}{371}\right)$	$e\left(\frac{219}{371}\right)$	$e\left(\frac{138}{371}\right)$	$e\left(\frac{417}{742}\right)$	$e\left(\frac{137}{371}\right)$	$e\left(\frac{577}{742}\right)$	$e\left(\frac{45}{371}\right)$	$e\left(\frac{415}{742}\right)$
$\chi_{5243}(139,\cdot)$	$1$	$1$	$e\left(\frac{247}{742}\right)$	$e\left(\frac{489}{742}\right)$	$e\left(\frac{247}{371}\right)$	$e\left(\frac{213}{371}\right)$	$e\left(\frac{368}{371}\right)$	$e\left(\frac{741}{742}\right)$	$e\left(\frac{118}{371}\right)$	$e\left(\frac{673}{742}\right)$	$e\left(\frac{120}{371}\right)$	$e\left(\frac{241}{742}\right)$
$\chi_{5243}(153,\cdot)$	$1$	$1$	$e\left(\frac{229}{742}\right)$	$e\left(\frac{183}{742}\right)$	$e\left(\frac{229}{371}\right)$	$e\left(\frac{214}{371}\right)$	$e\left(\frac{206}{371}\right)$	$e\left(\frac{687}{742}\right)$	$e\left(\frac{183}{371}\right)$	$e\left(\frac{657}{742}\right)$	$e\left(\frac{293}{371}\right)$	$e\left(\frac{641}{742}\right)$
$\chi_{5243}(167,\cdot)$	$1$	$1$	$e\left(\frac{197}{742}\right)$	$e\left(\frac{381}{742}\right)$	$e\left(\frac{197}{371}\right)$	$e\left(\frac{257}{371}\right)$	$e\left(\frac{289}{371}\right)$	$e\left(\frac{591}{742}\right)$	$e\left(\frac{10}{371}\right)$	$e\left(\frac{711}{742}\right)$	$e\left(\frac{312}{371}\right)$	$e\left(\frac{33}{742}\right)$
$\chi_{5243}(174,\cdot)$	$1$	$1$	$e\left(\frac{615}{742}\right)$	$e\left(\frac{67}{742}\right)$	$e\left(\frac{244}{371}\right)$	$e\left(\frac{275}{371}\right)$	$e\left(\frac{341}{371}\right)$	$e\left(\frac{361}{742}\right)$	$e\left(\frac{67}{371}\right)$	$e\left(\frac{423}{742}\right)$	$e\left(\frac{87}{371}\right)$	$e\left(\frac{555}{742}\right)$
$\chi_{5243}(181,\cdot)$	$1$	$1$	$e\left(\frac{697}{742}\right)$	$e\left(\frac{719}{742}\right)$	$e\left(\frac{326}{371}\right)$	$e\left(\frac{188}{371}\right)$	$e\left(\frac{337}{371}\right)$	$e\left(\frac{607}{742}\right)$	$e\left(\frac{348}{371}\right)$	$e\left(\frac{331}{742}\right)$	$e\left(\frac{247}{371}\right)$	$e\left(\frac{629}{742}\right)$
$\chi_{5243}(202,\cdot)$	$1$	$1$	$e\left(\frac{663}{742}\right)$	$e\left(\frac{141}{742}\right)$	$e\left(\frac{292}{371}\right)$	$e\left(\frac{25}{371}\right)$	$e\left(\frac{31}{371}\right)$	$e\left(\frac{505}{742}\right)$	$e\left(\frac{141}{371}\right)$	$e\left(\frac{713}{742}\right)$	$e\left(\frac{244}{371}\right)$	$e\left(\frac{725}{742}\right)$
$\chi_{5243}(216,\cdot)$	$1$	$1$	$e\left(\frac{113}{742}\right)$	$e\left(\frac{437}{742}\right)$	$e\left(\frac{113}{371}\right)$	$e\left(\frac{138}{371}\right)$	$e\left(\frac{275}{371}\right)$	$e\left(\frac{339}{742}\right)$	$e\left(\frac{66}{371}\right)$	$e\left(\frac{389}{742}\right)$	$e\left(\frac{130}{371}\right)$	$e\left(\frac{663}{742}\right)$
$\chi_{5243}(265,\cdot)$	$1$	$1$	$e\left(\frac{57}{742}\right)$	$e\left(\frac{227}{742}\right)$	$e\left(\frac{57}{371}\right)$	$e\left(\frac{306}{371}\right)$	$e\left(\frac{142}{371}\right)$	$e\left(\frac{171}{742}\right)$	$e\left(\frac{227}{371}\right)$	$e\left(\frac{669}{742}\right)$	$e\left(\frac{256}{371}\right)$	$e\left(\frac{341}{742}\right)$
$\chi_{5243}(272,\cdot)$	$1$	$1$	$e\left(\frac{125}{742}\right)$	$e\left(\frac{641}{742}\right)$	$e\left(\frac{125}{371}\right)$	$e\left(\frac{261}{371}\right)$	$e\left(\frac{12}{371}\right)$	$e\left(\frac{375}{742}\right)$	$e\left(\frac{270}{371}\right)$	$e\left(\frac{647}{742}\right)$	$e\left(\frac{262}{371}\right)$	$e\left(\frac{149}{742}\right)$
$\chi_{5243}(279,\cdot)$	$1$	$1$	$e\left(\frac{109}{742}\right)$	$e\left(\frac{369}{742}\right)$	$e\left(\frac{109}{371}\right)$	$e\left(\frac{97}{371}\right)$	$e\left(\frac{239}{371}\right)$	$e\left(\frac{327}{742}\right)$	$e\left(\frac{369}{371}\right)$	$e\left(\frac{303}{742}\right)$	$e\left(\frac{86}{371}\right)$	$e\left(\frac{587}{742}\right)$
$\chi_{5243}(286,\cdot)$	$1$	$1$	$e\left(\frac{471}{742}\right)$	$e\left(\frac{587}{742}\right)$	$e\left(\frac{100}{371}\right)$	$e\left(\frac{283}{371}\right)$	$e\left(\frac{158}{371}\right)$	$e\left(\frac{671}{742}\right)$	$e\left(\frac{216}{371}\right)$	$e\left(\frac{295}{742}\right)$	$e\left(\frac{358}{371}\right)$	$e\left(\frac{45}{742}\right)$
$\chi_{5243}(307,\cdot)$	$1$	$1$	$e\left(\frac{255}{742}\right)$	$e\left(\frac{625}{742}\right)$	$e\left(\frac{255}{371}\right)$	$e\left(\frac{295}{371}\right)$	$e\left(\frac{69}{371}\right)$	$e\left(\frac{23}{742}\right)$	$e\left(\frac{254}{371}\right)$	$e\left(\frac{103}{742}\right)$	$e\left(\frac{208}{371}\right)$	$e\left(\frac{393}{742}\right)$
$\chi_{5243}(328,\cdot)$	$1$	$1$	$e\left(\frac{725}{742}\right)$	$e\left(\frac{453}{742}\right)$	$e\left(\frac{354}{371}\right)$	$e\left(\frac{104}{371}\right)$	$e\left(\frac{218}{371}\right)$	$e\left(\frac{691}{742}\right)$	$e\left(\frac{82}{371}\right)$	$e\left(\frac{191}{742}\right)$	$e\left(\frac{184}{371}\right)$	$e\left(\frac{419}{742}\right)$
$\chi_{5243}(349,\cdot)$	$1$	$1$	$e\left(\frac{103}{742}\right)$	$e\left(\frac{267}{742}\right)$	$e\left(\frac{103}{371}\right)$	$e\left(\frac{221}{371}\right)$	$e\left(\frac{185}{371}\right)$	$e\left(\frac{309}{742}\right)$	$e\left(\frac{267}{371}\right)$	$e\left(\frac{545}{742}\right)$	$e\left(\frac{20}{371}\right)$	$e\left(\frac{473}{742}\right)$
$\chi_{5243}(384,\cdot)$	$1$	$1$	$e\left(\frac{9}{742}\right)$	$e\left(\frac{153}{742}\right)$	$e\left(\frac{9}{371}\right)$	$e\left(\frac{185}{371}\right)$	$e\left(\frac{81}{371}\right)$	$e\left(\frac{27}{742}\right)$	$e\left(\frac{153}{371}\right)$	$e\left(\frac{379}{742}\right)$	$e\left(\frac{99}{371}\right)$	$e\left(\frac{171}{742}\right)$
$\chi_{5243}(398,\cdot)$	$1$	$1$	$e\left(\frac{243}{742}\right)$	$e\left(\frac{421}{742}\right)$	$e\left(\frac{243}{371}\right)$	$e\left(\frac{172}{371}\right)$	$e\left(\frac{332}{371}\right)$	$e\left(\frac{729}{742}\right)$	$e\left(\frac{50}{371}\right)$	$e\left(\frac{587}{742}\right)$	$e\left(\frac{76}{371}\right)$	$e\left(\frac{165}{742}\right)$
$\chi_{5243}(405,\cdot)$	$1$	$1$	$e\left(\frac{381}{742}\right)$	$e\left(\frac{541}{742}\right)$	$e\left(\frac{10}{371}\right)$	$e\left(\frac{288}{371}\right)$	$e\left(\frac{90}{371}\right)$	$e\left(\frac{401}{742}\right)$	$e\left(\frac{170}{371}\right)$	$e\left(\frac{215}{742}\right)$	$e\left(\frac{110}{371}\right)$	$e\left(\frac{561}{742}\right)$
$\chi_{5243}(412,\cdot)$	$1$	$1$	$e\left(\frac{505}{742}\right)$	$e\left(\frac{423}{742}\right)$	$e\left(\frac{134}{371}\right)$	$e\left(\frac{75}{371}\right)$	$e\left(\frac{93}{371}\right)$	$e\left(\frac{31}{742}\right)$	$e\left(\frac{52}{371}\right)$	$e\left(\frac{655}{742}\right)$	$e\left(\frac{361}{371}\right)$	$e\left(\frac{691}{742}\right)$
$\chi_{5243}(419,\cdot)$	$1$	$1$	$e\left(\frac{503}{742}\right)$	$e\left(\frac{389}{742}\right)$	$e\left(\frac{132}{371}\right)$	$e\left(\frac{240}{371}\right)$	$e\left(\frac{75}{371}\right)$	$e\left(\frac{25}{742}\right)$	$e\left(\frac{18}{371}\right)$	$e\left(\frac{241}{742}\right)$	$e\left(\frac{339}{371}\right)$	$e\left(\frac{653}{742}\right)$
$\chi_{5243}(433,\cdot)$	$1$	$1$	$e\left(\frac{541}{742}\right)$	$e\left(\frac{293}{742}\right)$	$e\left(\frac{170}{371}\right)$	$e\left(\frac{73}{371}\right)$	$e\left(\frac{46}{371}\right)$	$e\left(\frac{139}{742}\right)$	$e\left(\frac{293}{371}\right)$	$e\left(\frac{687}{742}\right)$	$e\left(\frac{15}{371}\right)$	$e\left(\frac{633}{742}\right)$
$\chi_{5243}(454,\cdot)$	$1$	$1$	$e\left(\frac{423}{742}\right)$	$e\left(\frac{513}{742}\right)$	$e\left(\frac{52}{371}\right)$	$e\left(\frac{162}{371}\right)$	$e\left(\frac{97}{371}\right)$	$e\left(\frac{527}{742}\right)$	$e\left(\frac{142}{371}\right)$	$e\left(\frac{5}{742}\right)$	$e\left(\frac{201}{371}\right)$	$e\left(\frac{617}{742}\right)$
$\chi_{5243}(482,\cdot)$	$1$	$1$	$e\left(\frac{205}{742}\right)$	$e\left(\frac{517}{742}\right)$	$e\left(\frac{205}{371}\right)$	$e\left(\frac{339}{371}\right)$	$e\left(\frac{361}{371}\right)$	$e\left(\frac{615}{742}\right)$	$e\left(\frac{146}{371}\right)$	$e\left(\frac{141}{742}\right)$	$e\left(\frac{29}{371}\right)$	$e\left(\frac{185}{742}\right)$
$\chi_{5243}(496,\cdot)$	$1$	$1$	$e\left(\frac{5}{742}\right)$	$e\left(\frac{85}{742}\right)$	$e\left(\frac{5}{371}\right)$	$e\left(\frac{144}{371}\right)$	$e\left(\frac{45}{371}\right)$	$e\left(\frac{15}{742}\right)$	$e\left(\frac{85}{371}\right)$	$e\left(\frac{293}{742}\right)$	$e\left(\frac{55}{371}\right)$	$e\left(\frac{95}{742}\right)$
$\chi_{5243}(510,\cdot)$	$1$	$1$	$e\left(\frac{393}{742}\right)$	$e\left(\frac{3}{742}\right)$	$e\left(\frac{22}{371}\right)$	$e\left(\frac{40}{371}\right)$	$e\left(\frac{198}{371}\right)$	$e\left(\frac{437}{742}\right)$	$e\left(\frac{3}{371}\right)$	$e\left(\frac{473}{742}\right)$	$e\left(\frac{242}{371}\right)$	$e\left(\frac{47}{742}\right)$
$\chi_{5243}(524,\cdot)$	$1$	$1$	$e\left(\frac{207}{742}\right)$	$e\left(\frac{551}{742}\right)$	$e\left(\frac{207}{371}\right)$	$e\left(\frac{174}{371}\right)$	$e\left(\frac{8}{371}\right)$	$e\left(\frac{621}{742}\right)$	$e\left(\frac{180}{371}\right)$	$e\left(\frac{555}{742}\right)$	$e\left(\frac{51}{371}\right)$	$e\left(\frac{223}{742}\right)$
$\chi_{5243}(531,\cdot)$	$1$	$1$	$e\left(\frac{597}{742}\right)$	$e\left(\frac{503}{742}\right)$	$e\left(\frac{226}{371}\right)$	$e\left(\frac{276}{371}\right)$	$e\left(\frac{179}{371}\right)$	$e\left(\frac{307}{742}\right)$	$e\left(\frac{132}{371}\right)$	$e\left(\frac{407}{742}\right)$	$e\left(\frac{260}{371}\right)$	$e\left(\frac{213}{742}\right)$

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

Character	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(\chi_{5243}(6,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{285}{742}\right)\)	\(e\left(\frac{393}{742}\right)\)	\(e\left(\frac{285}{371}\right)\)	\(e\left(\frac{46}{371}\right)\)	\(e\left(\frac{339}{371}\right)\)	\(e\left(\frac{113}{742}\right)\)	\(e\left(\frac{22}{371}\right)\)	\(e\left(\frac{377}{742}\right)\)	\(e\left(\frac{167}{371}\right)\)	\(e\left(\frac{221}{742}\right)\)
\(\chi_{5243}(20,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{449}{742}\right)\)	\(e\left(\frac{213}{742}\right)\)	\(e\left(\frac{78}{371}\right)\)	\(e\left(\frac{243}{371}\right)\)	\(e\left(\frac{331}{371}\right)\)	\(e\left(\frac{605}{742}\right)\)	\(e\left(\frac{213}{371}\right)\)	\(e\left(\frac{193}{742}\right)\)	\(e\left(\frac{116}{371}\right)\)	\(e\left(\frac{369}{742}\right)\)
\(\chi_{5243}(55,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{271}{742}\right)\)	\(e\left(\frac{155}{742}\right)\)	\(e\left(\frac{271}{371}\right)\)	\(e\left(\frac{88}{371}\right)\)	\(e\left(\frac{213}{371}\right)\)	\(e\left(\frac{71}{742}\right)\)	\(e\left(\frac{155}{371}\right)\)	\(e\left(\frac{447}{742}\right)\)	\(e\left(\frac{13}{371}\right)\)	\(e\left(\frac{697}{742}\right)\)
\(\chi_{5243}(104,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{649}{742}\right)\)	\(e\left(\frac{645}{742}\right)\)	\(e\left(\frac{278}{371}\right)\)	\(e\left(\frac{67}{371}\right)\)	\(e\left(\frac{276}{371}\right)\)	\(e\left(\frac{463}{742}\right)\)	\(e\left(\frac{274}{371}\right)\)	\(e\left(\frac{41}{742}\right)\)	\(e\left(\frac{90}{371}\right)\)	\(e\left(\frac{459}{742}\right)\)
\(\chi_{5243}(125,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{742}\right)\)	\(e\left(\frac{137}{742}\right)\)	\(e\left(\frac{139}{371}\right)\)	\(e\left(\frac{219}{371}\right)\)	\(e\left(\frac{138}{371}\right)\)	\(e\left(\frac{417}{742}\right)\)	\(e\left(\frac{137}{371}\right)\)	\(e\left(\frac{577}{742}\right)\)	\(e\left(\frac{45}{371}\right)\)	\(e\left(\frac{415}{742}\right)\)
\(\chi_{5243}(139,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{247}{742}\right)\)	\(e\left(\frac{489}{742}\right)\)	\(e\left(\frac{247}{371}\right)\)	\(e\left(\frac{213}{371}\right)\)	\(e\left(\frac{368}{371}\right)\)	\(e\left(\frac{741}{742}\right)\)	\(e\left(\frac{118}{371}\right)\)	\(e\left(\frac{673}{742}\right)\)	\(e\left(\frac{120}{371}\right)\)	\(e\left(\frac{241}{742}\right)\)
\(\chi_{5243}(153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{229}{742}\right)\)	\(e\left(\frac{183}{742}\right)\)	\(e\left(\frac{229}{371}\right)\)	\(e\left(\frac{214}{371}\right)\)	\(e\left(\frac{206}{371}\right)\)	\(e\left(\frac{687}{742}\right)\)	\(e\left(\frac{183}{371}\right)\)	\(e\left(\frac{657}{742}\right)\)	\(e\left(\frac{293}{371}\right)\)	\(e\left(\frac{641}{742}\right)\)
\(\chi_{5243}(167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{742}\right)\)	\(e\left(\frac{381}{742}\right)\)	\(e\left(\frac{197}{371}\right)\)	\(e\left(\frac{257}{371}\right)\)	\(e\left(\frac{289}{371}\right)\)	\(e\left(\frac{591}{742}\right)\)	\(e\left(\frac{10}{371}\right)\)	\(e\left(\frac{711}{742}\right)\)	\(e\left(\frac{312}{371}\right)\)	\(e\left(\frac{33}{742}\right)\)
\(\chi_{5243}(174,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{615}{742}\right)\)	\(e\left(\frac{67}{742}\right)\)	\(e\left(\frac{244}{371}\right)\)	\(e\left(\frac{275}{371}\right)\)	\(e\left(\frac{341}{371}\right)\)	\(e\left(\frac{361}{742}\right)\)	\(e\left(\frac{67}{371}\right)\)	\(e\left(\frac{423}{742}\right)\)	\(e\left(\frac{87}{371}\right)\)	\(e\left(\frac{555}{742}\right)\)
\(\chi_{5243}(181,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{697}{742}\right)\)	\(e\left(\frac{719}{742}\right)\)	\(e\left(\frac{326}{371}\right)\)	\(e\left(\frac{188}{371}\right)\)	\(e\left(\frac{337}{371}\right)\)	\(e\left(\frac{607}{742}\right)\)	\(e\left(\frac{348}{371}\right)\)	\(e\left(\frac{331}{742}\right)\)	\(e\left(\frac{247}{371}\right)\)	\(e\left(\frac{629}{742}\right)\)
\(\chi_{5243}(202,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{663}{742}\right)\)	\(e\left(\frac{141}{742}\right)\)	\(e\left(\frac{292}{371}\right)\)	\(e\left(\frac{25}{371}\right)\)	\(e\left(\frac{31}{371}\right)\)	\(e\left(\frac{505}{742}\right)\)	\(e\left(\frac{141}{371}\right)\)	\(e\left(\frac{713}{742}\right)\)	\(e\left(\frac{244}{371}\right)\)	\(e\left(\frac{725}{742}\right)\)
\(\chi_{5243}(216,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{742}\right)\)	\(e\left(\frac{437}{742}\right)\)	\(e\left(\frac{113}{371}\right)\)	\(e\left(\frac{138}{371}\right)\)	\(e\left(\frac{275}{371}\right)\)	\(e\left(\frac{339}{742}\right)\)	\(e\left(\frac{66}{371}\right)\)	\(e\left(\frac{389}{742}\right)\)	\(e\left(\frac{130}{371}\right)\)	\(e\left(\frac{663}{742}\right)\)
\(\chi_{5243}(265,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{742}\right)\)	\(e\left(\frac{227}{742}\right)\)	\(e\left(\frac{57}{371}\right)\)	\(e\left(\frac{306}{371}\right)\)	\(e\left(\frac{142}{371}\right)\)	\(e\left(\frac{171}{742}\right)\)	\(e\left(\frac{227}{371}\right)\)	\(e\left(\frac{669}{742}\right)\)	\(e\left(\frac{256}{371}\right)\)	\(e\left(\frac{341}{742}\right)\)
\(\chi_{5243}(272,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{742}\right)\)	\(e\left(\frac{641}{742}\right)\)	\(e\left(\frac{125}{371}\right)\)	\(e\left(\frac{261}{371}\right)\)	\(e\left(\frac{12}{371}\right)\)	\(e\left(\frac{375}{742}\right)\)	\(e\left(\frac{270}{371}\right)\)	\(e\left(\frac{647}{742}\right)\)	\(e\left(\frac{262}{371}\right)\)	\(e\left(\frac{149}{742}\right)\)
\(\chi_{5243}(279,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{742}\right)\)	\(e\left(\frac{369}{742}\right)\)	\(e\left(\frac{109}{371}\right)\)	\(e\left(\frac{97}{371}\right)\)	\(e\left(\frac{239}{371}\right)\)	\(e\left(\frac{327}{742}\right)\)	\(e\left(\frac{369}{371}\right)\)	\(e\left(\frac{303}{742}\right)\)	\(e\left(\frac{86}{371}\right)\)	\(e\left(\frac{587}{742}\right)\)
\(\chi_{5243}(286,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{471}{742}\right)\)	\(e\left(\frac{587}{742}\right)\)	\(e\left(\frac{100}{371}\right)\)	\(e\left(\frac{283}{371}\right)\)	\(e\left(\frac{158}{371}\right)\)	\(e\left(\frac{671}{742}\right)\)	\(e\left(\frac{216}{371}\right)\)	\(e\left(\frac{295}{742}\right)\)	\(e\left(\frac{358}{371}\right)\)	\(e\left(\frac{45}{742}\right)\)
\(\chi_{5243}(307,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{255}{742}\right)\)	\(e\left(\frac{625}{742}\right)\)	\(e\left(\frac{255}{371}\right)\)	\(e\left(\frac{295}{371}\right)\)	\(e\left(\frac{69}{371}\right)\)	\(e\left(\frac{23}{742}\right)\)	\(e\left(\frac{254}{371}\right)\)	\(e\left(\frac{103}{742}\right)\)	\(e\left(\frac{208}{371}\right)\)	\(e\left(\frac{393}{742}\right)\)
\(\chi_{5243}(328,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{725}{742}\right)\)	\(e\left(\frac{453}{742}\right)\)	\(e\left(\frac{354}{371}\right)\)	\(e\left(\frac{104}{371}\right)\)	\(e\left(\frac{218}{371}\right)\)	\(e\left(\frac{691}{742}\right)\)	\(e\left(\frac{82}{371}\right)\)	\(e\left(\frac{191}{742}\right)\)	\(e\left(\frac{184}{371}\right)\)	\(e\left(\frac{419}{742}\right)\)
\(\chi_{5243}(349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{742}\right)\)	\(e\left(\frac{267}{742}\right)\)	\(e\left(\frac{103}{371}\right)\)	\(e\left(\frac{221}{371}\right)\)	\(e\left(\frac{185}{371}\right)\)	\(e\left(\frac{309}{742}\right)\)	\(e\left(\frac{267}{371}\right)\)	\(e\left(\frac{545}{742}\right)\)	\(e\left(\frac{20}{371}\right)\)	\(e\left(\frac{473}{742}\right)\)
\(\chi_{5243}(384,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{742}\right)\)	\(e\left(\frac{153}{742}\right)\)	\(e\left(\frac{9}{371}\right)\)	\(e\left(\frac{185}{371}\right)\)	\(e\left(\frac{81}{371}\right)\)	\(e\left(\frac{27}{742}\right)\)	\(e\left(\frac{153}{371}\right)\)	\(e\left(\frac{379}{742}\right)\)	\(e\left(\frac{99}{371}\right)\)	\(e\left(\frac{171}{742}\right)\)
\(\chi_{5243}(398,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{243}{742}\right)\)	\(e\left(\frac{421}{742}\right)\)	\(e\left(\frac{243}{371}\right)\)	\(e\left(\frac{172}{371}\right)\)	\(e\left(\frac{332}{371}\right)\)	\(e\left(\frac{729}{742}\right)\)	\(e\left(\frac{50}{371}\right)\)	\(e\left(\frac{587}{742}\right)\)	\(e\left(\frac{76}{371}\right)\)	\(e\left(\frac{165}{742}\right)\)
\(\chi_{5243}(405,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{381}{742}\right)\)	\(e\left(\frac{541}{742}\right)\)	\(e\left(\frac{10}{371}\right)\)	\(e\left(\frac{288}{371}\right)\)	\(e\left(\frac{90}{371}\right)\)	\(e\left(\frac{401}{742}\right)\)	\(e\left(\frac{170}{371}\right)\)	\(e\left(\frac{215}{742}\right)\)	\(e\left(\frac{110}{371}\right)\)	\(e\left(\frac{561}{742}\right)\)
\(\chi_{5243}(412,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{505}{742}\right)\)	\(e\left(\frac{423}{742}\right)\)	\(e\left(\frac{134}{371}\right)\)	\(e\left(\frac{75}{371}\right)\)	\(e\left(\frac{93}{371}\right)\)	\(e\left(\frac{31}{742}\right)\)	\(e\left(\frac{52}{371}\right)\)	\(e\left(\frac{655}{742}\right)\)	\(e\left(\frac{361}{371}\right)\)	\(e\left(\frac{691}{742}\right)\)
\(\chi_{5243}(419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{503}{742}\right)\)	\(e\left(\frac{389}{742}\right)\)	\(e\left(\frac{132}{371}\right)\)	\(e\left(\frac{240}{371}\right)\)	\(e\left(\frac{75}{371}\right)\)	\(e\left(\frac{25}{742}\right)\)	\(e\left(\frac{18}{371}\right)\)	\(e\left(\frac{241}{742}\right)\)	\(e\left(\frac{339}{371}\right)\)	\(e\left(\frac{653}{742}\right)\)
\(\chi_{5243}(433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{541}{742}\right)\)	\(e\left(\frac{293}{742}\right)\)	\(e\left(\frac{170}{371}\right)\)	\(e\left(\frac{73}{371}\right)\)	\(e\left(\frac{46}{371}\right)\)	\(e\left(\frac{139}{742}\right)\)	\(e\left(\frac{293}{371}\right)\)	\(e\left(\frac{687}{742}\right)\)	\(e\left(\frac{15}{371}\right)\)	\(e\left(\frac{633}{742}\right)\)
\(\chi_{5243}(454,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{423}{742}\right)\)	\(e\left(\frac{513}{742}\right)\)	\(e\left(\frac{52}{371}\right)\)	\(e\left(\frac{162}{371}\right)\)	\(e\left(\frac{97}{371}\right)\)	\(e\left(\frac{527}{742}\right)\)	\(e\left(\frac{142}{371}\right)\)	\(e\left(\frac{5}{742}\right)\)	\(e\left(\frac{201}{371}\right)\)	\(e\left(\frac{617}{742}\right)\)
\(\chi_{5243}(482,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{742}\right)\)	\(e\left(\frac{517}{742}\right)\)	\(e\left(\frac{205}{371}\right)\)	\(e\left(\frac{339}{371}\right)\)	\(e\left(\frac{361}{371}\right)\)	\(e\left(\frac{615}{742}\right)\)	\(e\left(\frac{146}{371}\right)\)	\(e\left(\frac{141}{742}\right)\)	\(e\left(\frac{29}{371}\right)\)	\(e\left(\frac{185}{742}\right)\)
\(\chi_{5243}(496,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{742}\right)\)	\(e\left(\frac{85}{742}\right)\)	\(e\left(\frac{5}{371}\right)\)	\(e\left(\frac{144}{371}\right)\)	\(e\left(\frac{45}{371}\right)\)	\(e\left(\frac{15}{742}\right)\)	\(e\left(\frac{85}{371}\right)\)	\(e\left(\frac{293}{742}\right)\)	\(e\left(\frac{55}{371}\right)\)	\(e\left(\frac{95}{742}\right)\)
\(\chi_{5243}(510,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{393}{742}\right)\)	\(e\left(\frac{3}{742}\right)\)	\(e\left(\frac{22}{371}\right)\)	\(e\left(\frac{40}{371}\right)\)	\(e\left(\frac{198}{371}\right)\)	\(e\left(\frac{437}{742}\right)\)	\(e\left(\frac{3}{371}\right)\)	\(e\left(\frac{473}{742}\right)\)	\(e\left(\frac{242}{371}\right)\)	\(e\left(\frac{47}{742}\right)\)
\(\chi_{5243}(524,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{207}{742}\right)\)	\(e\left(\frac{551}{742}\right)\)	\(e\left(\frac{207}{371}\right)\)	\(e\left(\frac{174}{371}\right)\)	\(e\left(\frac{8}{371}\right)\)	\(e\left(\frac{621}{742}\right)\)	\(e\left(\frac{180}{371}\right)\)	\(e\left(\frac{555}{742}\right)\)	\(e\left(\frac{51}{371}\right)\)	\(e\left(\frac{223}{742}\right)\)
\(\chi_{5243}(531,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{597}{742}\right)\)	\(e\left(\frac{503}{742}\right)\)	\(e\left(\frac{226}{371}\right)\)	\(e\left(\frac{276}{371}\right)\)	\(e\left(\frac{179}{371}\right)\)	\(e\left(\frac{307}{742}\right)\)	\(e\left(\frac{132}{371}\right)\)	\(e\left(\frac{407}{742}\right)\)	\(e\left(\frac{260}{371}\right)\)	\(e\left(\frac{213}{742}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 312 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	5243.z
Modulus	$5243$
Conductor	$5243$
Order	$742$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(5243\)
Conductor:	\(5243\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(742\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)