LMFDB - Dirichlet character orbit 8464.bs

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8464, base_ring=CyclotomicField(1012)) M = H._module chi = DirichletCharacter(H, M([506,253,898])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(11,8464)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8464$
Conductor:	$8464$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$1012$	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:	$\Q(\zeta_{1012})$
Fixed field:	Number field defined by a degree 1012 polynomial (not computed)

First 31 of 440 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8464}(11,\cdot)$	$1$	$1$	$e\left(\frac{453}{1012}\right)$	$e\left(\frac{139}{1012}\right)$	$e\left(\frac{237}{506}\right)$	$e\left(\frac{453}{506}\right)$	$e\left(\frac{173}{1012}\right)$	$e\left(\frac{351}{1012}\right)$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{371}{506}\right)$	$e\left(\frac{39}{1012}\right)$	$e\left(\frac{927}{1012}\right)$
$\chi_{8464}(19,\cdot)$	$1$	$1$	$e\left(\frac{535}{1012}\right)$	$e\left(\frac{745}{1012}\right)$	$e\left(\frac{109}{506}\right)$	$e\left(\frac{29}{506}\right)$	$e\left(\frac{39}{1012}\right)$	$e\left(\frac{629}{1012}\right)$	$e\left(\frac{67}{253}\right)$	$e\left(\frac{303}{506}\right)$	$e\left(\frac{857}{1012}\right)$	$e\left(\frac{753}{1012}\right)$
$\chi_{8464}(43,\cdot)$	$1$	$1$	$e\left(\frac{105}{1012}\right)$	$e\left(\frac{307}{1012}\right)$	$e\left(\frac{447}{506}\right)$	$e\left(\frac{105}{506}\right)$	$e\left(\frac{717}{1012}\right)$	$e\left(\frac{899}{1012}\right)$	$e\left(\frac{103}{253}\right)$	$e\left(\frac{277}{506}\right)$	$e\left(\frac{887}{1012}\right)$	$e\left(\frac{999}{1012}\right)$
$\chi_{8464}(51,\cdot)$	$1$	$1$	$e\left(\frac{175}{1012}\right)$	$e\left(\frac{849}{1012}\right)$	$e\left(\frac{239}{506}\right)$	$e\left(\frac{175}{506}\right)$	$e\left(\frac{183}{1012}\right)$	$e\left(\frac{149}{1012}\right)$	$e\left(\frac{3}{253}\right)$	$e\left(\frac{293}{506}\right)$	$e\left(\frac{129}{1012}\right)$	$e\left(\frac{653}{1012}\right)$
$\chi_{8464}(67,\cdot)$	$1$	$1$	$e\left(\frac{867}{1012}\right)$	$e\left(\frac{829}{1012}\right)$	$e\left(\frac{467}{506}\right)$	$e\left(\frac{361}{506}\right)$	$e\left(\frac{311}{1012}\right)$	$e\left(\frac{397}{1012}\right)$	$e\left(\frac{171}{253}\right)$	$e\left(\frac{3}{506}\right)$	$e\left(\frac{269}{1012}\right)$	$e\left(\frac{789}{1012}\right)$
$\chi_{8464}(83,\cdot)$	$1$	$1$	$e\left(\frac{331}{1012}\right)$	$e\left(\frac{669}{1012}\right)$	$e\left(\frac{267}{506}\right)$	$e\left(\frac{331}{506}\right)$	$e\left(\frac{323}{1012}\right)$	$e\left(\frac{357}{1012}\right)$	$e\left(\frac{250}{253}\right)$	$e\left(\frac{213}{506}\right)$	$e\left(\frac{377}{1012}\right)$	$e\left(\frac{865}{1012}\right)$
$\chi_{8464}(99,\cdot)$	$1$	$1$	$e\left(\frac{971}{1012}\right)$	$e\left(\frac{709}{1012}\right)$	$e\left(\frac{317}{506}\right)$	$e\left(\frac{465}{506}\right)$	$e\left(\frac{67}{1012}\right)$	$e\left(\frac{873}{1012}\right)$	$e\left(\frac{167}{253}\right)$	$e\left(\frac{287}{506}\right)$	$e\left(\frac{97}{1012}\right)$	$e\left(\frac{593}{1012}\right)$
$\chi_{8464}(107,\cdot)$	$1$	$1$	$e\left(\frac{49}{1012}\right)$	$e\left(\frac{683}{1012}\right)$	$e\left(\frac{411}{506}\right)$	$e\left(\frac{49}{506}\right)$	$e\left(\frac{537}{1012}\right)$	$e\left(\frac{487}{1012}\right)$	$e\left(\frac{183}{253}\right)$	$e\left(\frac{163}{506}\right)$	$e\left(\frac{279}{1012}\right)$	$e\left(\frac{871}{1012}\right)$
$\chi_{8464}(155,\cdot)$	$1$	$1$	$e\left(\frac{697}{1012}\right)$	$e\left(\frac{91}{1012}\right)$	$e\left(\frac{177}{506}\right)$	$e\left(\frac{191}{506}\right)$	$e\left(\frac{885}{1012}\right)$	$e\left(\frac{339}{1012}\right)$	$e\left(\frac{197}{253}\right)$	$e\left(\frac{181}{506}\right)$	$e\left(\frac{375}{1012}\right)$	$e\left(\frac{39}{1012}\right)$
$\chi_{8464}(171,\cdot)$	$1$	$1$	$e\left(\frac{41}{1012}\right)$	$e\left(\frac{303}{1012}\right)$	$e\left(\frac{189}{506}\right)$	$e\left(\frac{41}{506}\right)$	$e\left(\frac{945}{1012}\right)$	$e\left(\frac{139}{1012}\right)$	$e\left(\frac{86}{253}\right)$	$e\left(\frac{219}{506}\right)$	$e\left(\frac{915}{1012}\right)$	$e\left(\frac{419}{1012}\right)$
$\chi_{8464}(203,\cdot)$	$1$	$1$	$e\left(\frac{73}{1012}\right)$	$e\left(\frac{811}{1012}\right)$	$e\left(\frac{65}{506}\right)$	$e\left(\frac{73}{506}\right)$	$e\left(\frac{325}{1012}\right)$	$e\left(\frac{519}{1012}\right)$	$e\left(\frac{221}{253}\right)$	$e\left(\frac{501}{506}\right)$	$e\left(\frac{395}{1012}\right)$	$e\left(\frac{203}{1012}\right)$
$\chi_{8464}(227,\cdot)$	$1$	$1$	$e\left(\frac{1007}{1012}\right)$	$e\left(\frac{901}{1012}\right)$	$e\left(\frac{51}{506}\right)$	$e\left(\frac{501}{506}\right)$	$e\left(\frac{255}{1012}\right)$	$e\left(\frac{921}{1012}\right)$	$e\left(\frac{224}{253}\right)$	$e\left(\frac{35}{506}\right)$	$e\left(\frac{777}{1012}\right)$	$e\left(\frac{97}{1012}\right)$
$\chi_{8464}(235,\cdot)$	$1$	$1$	$e\left(\frac{241}{1012}\right)$	$e\left(\frac{695}{1012}\right)$	$e\left(\frac{173}{506}\right)$	$e\left(\frac{241}{506}\right)$	$e\left(\frac{865}{1012}\right)$	$e\left(\frac{743}{1012}\right)$	$e\left(\frac{234}{253}\right)$	$e\left(\frac{337}{506}\right)$	$e\left(\frac{195}{1012}\right)$	$e\left(\frac{587}{1012}\right)$
$\chi_{8464}(251,\cdot)$	$1$	$1$	$e\left(\frac{449}{1012}\right)$	$e\left(\frac{455}{1012}\right)$	$e\left(\frac{379}{506}\right)$	$e\left(\frac{449}{506}\right)$	$e\left(\frac{377}{1012}\right)$	$e\left(\frac{683}{1012}\right)$	$e\left(\frac{226}{253}\right)$	$e\left(\frac{399}{506}\right)$	$e\left(\frac{863}{1012}\right)$	$e\left(\frac{195}{1012}\right)$
$\chi_{8464}(267,\cdot)$	$1$	$1$	$e\left(\frac{969}{1012}\right)$	$e\left(\frac{867}{1012}\right)$	$e\left(\frac{135}{506}\right)$	$e\left(\frac{463}{506}\right)$	$e\left(\frac{169}{1012}\right)$	$e\left(\frac{27}{1012}\right)$	$e\left(\frac{206}{253}\right)$	$e\left(\frac{301}{506}\right)$	$e\left(\frac{3}{1012}\right)$	$e\left(\frac{227}{1012}\right)$
$\chi_{8464}(283,\cdot)$	$1$	$1$	$e\left(\frac{729}{1012}\right)$	$e\left(\frac{599}{1012}\right)$	$e\left(\frac{53}{506}\right)$	$e\left(\frac{223}{506}\right)$	$e\left(\frac{265}{1012}\right)$	$e\left(\frac{719}{1012}\right)$	$e\left(\frac{79}{253}\right)$	$e\left(\frac{463}{506}\right)$	$e\left(\frac{867}{1012}\right)$	$e\left(\frac{835}{1012}\right)$
$\chi_{8464}(291,\cdot)$	$1$	$1$	$e\left(\frac{71}{1012}\right)$	$e\left(\frac{969}{1012}\right)$	$e\left(\frac{389}{506}\right)$	$e\left(\frac{71}{506}\right)$	$e\left(\frac{427}{1012}\right)$	$e\left(\frac{685}{1012}\right)$	$e\left(\frac{7}{253}\right)$	$e\left(\frac{9}{506}\right)$	$e\left(\frac{301}{1012}\right)$	$e\left(\frac{849}{1012}\right)$
$\chi_{8464}(339,\cdot)$	$1$	$1$	$e\left(\frac{895}{1012}\right)$	$e\left(\frac{641}{1012}\right)$	$e\left(\frac{485}{506}\right)$	$e\left(\frac{389}{506}\right)$	$e\left(\frac{907}{1012}\right)$	$e\left(\frac{97}{1012}\right)$	$e\left(\frac{131}{253}\right)$	$e\left(\frac{313}{506}\right)$	$e\left(\frac{573}{1012}\right)$	$e\left(\frac{853}{1012}\right)$
$\chi_{8464}(355,\cdot)$	$1$	$1$	$e\left(\frac{327}{1012}\right)$	$e\left(\frac{985}{1012}\right)$	$e\left(\frac{409}{506}\right)$	$e\left(\frac{327}{506}\right)$	$e\left(\frac{527}{1012}\right)$	$e\left(\frac{689}{1012}\right)$	$e\left(\frac{75}{253}\right)$	$e\left(\frac{241}{506}\right)$	$e\left(\frac{189}{1012}\right)$	$e\left(\frac{133}{1012}\right)$
$\chi_{8464}(379,\cdot)$	$1$	$1$	$e\left(\frac{145}{1012}\right)$	$e\left(\frac{183}{1012}\right)$	$e\left(\frac{39}{506}\right)$	$e\left(\frac{145}{506}\right)$	$e\left(\frac{701}{1012}\right)$	$e\left(\frac{615}{1012}\right)$	$e\left(\frac{82}{253}\right)$	$e\left(\frac{503}{506}\right)$	$e\left(\frac{743}{1012}\right)$	$e\left(\frac{223}{1012}\right)$
$\chi_{8464}(387,\cdot)$	$1$	$1$	$e\left(\frac{623}{1012}\right)$	$e\left(\frac{877}{1012}\right)$	$e\left(\frac{21}{506}\right)$	$e\left(\frac{117}{506}\right)$	$e\left(\frac{611}{1012}\right)$	$e\left(\frac{409}{1012}\right)$	$e\left(\frac{122}{253}\right)$	$e\left(\frac{193}{506}\right)$	$e\left(\frac{945}{1012}\right)$	$e\left(\frac{665}{1012}\right)$
$\chi_{8464}(419,\cdot)$	$1$	$1$	$e\left(\frac{307}{1012}\right)$	$e\left(\frac{541}{1012}\right)$	$e\left(\frac{107}{506}\right)$	$e\left(\frac{307}{506}\right)$	$e\left(\frac{535}{1012}\right)$	$e\left(\frac{325}{1012}\right)$	$e\left(\frac{212}{253}\right)$	$e\left(\frac{381}{506}\right)$	$e\left(\frac{261}{1012}\right)$	$e\left(\frac{521}{1012}\right)$
$\chi_{8464}(435,\cdot)$	$1$	$1$	$e\left(\frac{31}{1012}\right)$	$e\left(\frac{81}{1012}\right)$	$e\left(\frac{291}{506}\right)$	$e\left(\frac{31}{506}\right)$	$e\left(\frac{443}{1012}\right)$	$e\left(\frac{969}{1012}\right)$	$e\left(\frac{28}{253}\right)$	$e\left(\frac{289}{506}\right)$	$e\left(\frac{445}{1012}\right)$	$e\left(\frac{613}{1012}\right)$
$\chi_{8464}(451,\cdot)$	$1$	$1$	$e\left(\frac{595}{1012}\right)$	$e\left(\frac{53}{1012}\right)$	$e\left(\frac{3}{506}\right)$	$e\left(\frac{89}{506}\right)$	$e\left(\frac{15}{1012}\right)$	$e\left(\frac{709}{1012}\right)$	$e\left(\frac{162}{253}\right)$	$e\left(\frac{389}{506}\right)$	$e\left(\frac{641}{1012}\right)$	$e\left(\frac{601}{1012}\right)$
$\chi_{8464}(467,\cdot)$	$1$	$1$	$e\left(\frac{487}{1012}\right)$	$e\left(\frac{489}{1012}\right)$	$e\left(\frac{295}{506}\right)$	$e\left(\frac{487}{506}\right)$	$e\left(\frac{463}{1012}\right)$	$e\left(\frac{565}{1012}\right)$	$e\left(\frac{244}{253}\right)$	$e\left(\frac{133}{506}\right)$	$e\left(\frac{625}{1012}\right)$	$e\left(\frac{65}{1012}\right)$
$\chi_{8464}(475,\cdot)$	$1$	$1$	$e\left(\frac{93}{1012}\right)$	$e\left(\frac{243}{1012}\right)$	$e\left(\frac{367}{506}\right)$	$e\left(\frac{93}{506}\right)$	$e\left(\frac{317}{1012}\right)$	$e\left(\frac{883}{1012}\right)$	$e\left(\frac{84}{253}\right)$	$e\left(\frac{361}{506}\right)$	$e\left(\frac{323}{1012}\right)$	$e\left(\frac{827}{1012}\right)$
$\chi_{8464}(523,\cdot)$	$1$	$1$	$e\left(\frac{81}{1012}\right)$	$e\left(\frac{179}{1012}\right)$	$e\left(\frac{287}{506}\right)$	$e\left(\frac{81}{506}\right)$	$e\left(\frac{929}{1012}\right)$	$e\left(\frac{867}{1012}\right)$	$e\left(\frac{65}{253}\right)$	$e\left(\frac{445}{506}\right)$	$e\left(\frac{771}{1012}\right)$	$e\left(\frac{655}{1012}\right)$
$\chi_{8464}(539,\cdot)$	$1$	$1$	$e\left(\frac{613}{1012}\right)$	$e\left(\frac{655}{1012}\right)$	$e\left(\frac{123}{506}\right)$	$e\left(\frac{107}{506}\right)$	$e\left(\frac{109}{1012}\right)$	$e\left(\frac{227}{1012}\right)$	$e\left(\frac{64}{253}\right)$	$e\left(\frac{263}{506}\right)$	$e\left(\frac{475}{1012}\right)$	$e\left(\frac{859}{1012}\right)$
$\chi_{8464}(563,\cdot)$	$1$	$1$	$e\left(\frac{1003}{1012}\right)$	$e\left(\frac{205}{1012}\right)$	$e\left(\frac{193}{506}\right)$	$e\left(\frac{497}{506}\right)$	$e\left(\frac{459}{1012}\right)$	$e\left(\frac{241}{1012}\right)$	$e\left(\frac{49}{253}\right)$	$e\left(\frac{63}{506}\right)$	$e\left(\frac{589}{1012}\right)$	$e\left(\frac{377}{1012}\right)$
$\chi_{8464}(595,\cdot)$	$1$	$1$	$e\left(\frac{787}{1012}\right)$	$e\left(\frac{65}{1012}\right)$	$e\left(\frac{271}{506}\right)$	$e\left(\frac{281}{506}\right)$	$e\left(\frac{343}{1012}\right)$	$e\left(\frac{965}{1012}\right)$	$e\left(\frac{213}{253}\right)$	$e\left(\frac{57}{506}\right)$	$e\left(\frac{557}{1012}\right)$	$e\left(\frac{317}{1012}\right)$
$\chi_{8464}(603,\cdot)$	$1$	$1$	$e\left(\frac{373}{1012}\right)$	$e\left(\frac{387}{1012}\right)$	$e\left(\frac{41}{506}\right)$	$e\left(\frac{373}{506}\right)$	$e\left(\frac{205}{1012}\right)$	$e\left(\frac{919}{1012}\right)$	$e\left(\frac{190}{253}\right)$	$e\left(\frac{425}{506}\right)$	$e\left(\frac{327}{1012}\right)$	$e\left(\frac{455}{1012}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8464}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{453}{1012}\right)\)	\(e\left(\frac{139}{1012}\right)\)	\(e\left(\frac{237}{506}\right)\)	\(e\left(\frac{453}{506}\right)\)	\(e\left(\frac{173}{1012}\right)\)	\(e\left(\frac{351}{1012}\right)\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{371}{506}\right)\)	\(e\left(\frac{39}{1012}\right)\)	\(e\left(\frac{927}{1012}\right)\)
\(\chi_{8464}(19,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{535}{1012}\right)\)	\(e\left(\frac{745}{1012}\right)\)	\(e\left(\frac{109}{506}\right)\)	\(e\left(\frac{29}{506}\right)\)	\(e\left(\frac{39}{1012}\right)\)	\(e\left(\frac{629}{1012}\right)\)	\(e\left(\frac{67}{253}\right)\)	\(e\left(\frac{303}{506}\right)\)	\(e\left(\frac{857}{1012}\right)\)	\(e\left(\frac{753}{1012}\right)\)
\(\chi_{8464}(43,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{105}{1012}\right)\)	\(e\left(\frac{307}{1012}\right)\)	\(e\left(\frac{447}{506}\right)\)	\(e\left(\frac{105}{506}\right)\)	\(e\left(\frac{717}{1012}\right)\)	\(e\left(\frac{899}{1012}\right)\)	\(e\left(\frac{103}{253}\right)\)	\(e\left(\frac{277}{506}\right)\)	\(e\left(\frac{887}{1012}\right)\)	\(e\left(\frac{999}{1012}\right)\)
\(\chi_{8464}(51,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{175}{1012}\right)\)	\(e\left(\frac{849}{1012}\right)\)	\(e\left(\frac{239}{506}\right)\)	\(e\left(\frac{175}{506}\right)\)	\(e\left(\frac{183}{1012}\right)\)	\(e\left(\frac{149}{1012}\right)\)	\(e\left(\frac{3}{253}\right)\)	\(e\left(\frac{293}{506}\right)\)	\(e\left(\frac{129}{1012}\right)\)	\(e\left(\frac{653}{1012}\right)\)
\(\chi_{8464}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{867}{1012}\right)\)	\(e\left(\frac{829}{1012}\right)\)	\(e\left(\frac{467}{506}\right)\)	\(e\left(\frac{361}{506}\right)\)	\(e\left(\frac{311}{1012}\right)\)	\(e\left(\frac{397}{1012}\right)\)	\(e\left(\frac{171}{253}\right)\)	\(e\left(\frac{3}{506}\right)\)	\(e\left(\frac{269}{1012}\right)\)	\(e\left(\frac{789}{1012}\right)\)
\(\chi_{8464}(83,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{331}{1012}\right)\)	\(e\left(\frac{669}{1012}\right)\)	\(e\left(\frac{267}{506}\right)\)	\(e\left(\frac{331}{506}\right)\)	\(e\left(\frac{323}{1012}\right)\)	\(e\left(\frac{357}{1012}\right)\)	\(e\left(\frac{250}{253}\right)\)	\(e\left(\frac{213}{506}\right)\)	\(e\left(\frac{377}{1012}\right)\)	\(e\left(\frac{865}{1012}\right)\)
\(\chi_{8464}(99,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{971}{1012}\right)\)	\(e\left(\frac{709}{1012}\right)\)	\(e\left(\frac{317}{506}\right)\)	\(e\left(\frac{465}{506}\right)\)	\(e\left(\frac{67}{1012}\right)\)	\(e\left(\frac{873}{1012}\right)\)	\(e\left(\frac{167}{253}\right)\)	\(e\left(\frac{287}{506}\right)\)	\(e\left(\frac{97}{1012}\right)\)	\(e\left(\frac{593}{1012}\right)\)
\(\chi_{8464}(107,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{1012}\right)\)	\(e\left(\frac{683}{1012}\right)\)	\(e\left(\frac{411}{506}\right)\)	\(e\left(\frac{49}{506}\right)\)	\(e\left(\frac{537}{1012}\right)\)	\(e\left(\frac{487}{1012}\right)\)	\(e\left(\frac{183}{253}\right)\)	\(e\left(\frac{163}{506}\right)\)	\(e\left(\frac{279}{1012}\right)\)	\(e\left(\frac{871}{1012}\right)\)
\(\chi_{8464}(155,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{697}{1012}\right)\)	\(e\left(\frac{91}{1012}\right)\)	\(e\left(\frac{177}{506}\right)\)	\(e\left(\frac{191}{506}\right)\)	\(e\left(\frac{885}{1012}\right)\)	\(e\left(\frac{339}{1012}\right)\)	\(e\left(\frac{197}{253}\right)\)	\(e\left(\frac{181}{506}\right)\)	\(e\left(\frac{375}{1012}\right)\)	\(e\left(\frac{39}{1012}\right)\)
\(\chi_{8464}(171,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{1012}\right)\)	\(e\left(\frac{303}{1012}\right)\)	\(e\left(\frac{189}{506}\right)\)	\(e\left(\frac{41}{506}\right)\)	\(e\left(\frac{945}{1012}\right)\)	\(e\left(\frac{139}{1012}\right)\)	\(e\left(\frac{86}{253}\right)\)	\(e\left(\frac{219}{506}\right)\)	\(e\left(\frac{915}{1012}\right)\)	\(e\left(\frac{419}{1012}\right)\)
\(\chi_{8464}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{1012}\right)\)	\(e\left(\frac{811}{1012}\right)\)	\(e\left(\frac{65}{506}\right)\)	\(e\left(\frac{73}{506}\right)\)	\(e\left(\frac{325}{1012}\right)\)	\(e\left(\frac{519}{1012}\right)\)	\(e\left(\frac{221}{253}\right)\)	\(e\left(\frac{501}{506}\right)\)	\(e\left(\frac{395}{1012}\right)\)	\(e\left(\frac{203}{1012}\right)\)
\(\chi_{8464}(227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1007}{1012}\right)\)	\(e\left(\frac{901}{1012}\right)\)	\(e\left(\frac{51}{506}\right)\)	\(e\left(\frac{501}{506}\right)\)	\(e\left(\frac{255}{1012}\right)\)	\(e\left(\frac{921}{1012}\right)\)	\(e\left(\frac{224}{253}\right)\)	\(e\left(\frac{35}{506}\right)\)	\(e\left(\frac{777}{1012}\right)\)	\(e\left(\frac{97}{1012}\right)\)
\(\chi_{8464}(235,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{241}{1012}\right)\)	\(e\left(\frac{695}{1012}\right)\)	\(e\left(\frac{173}{506}\right)\)	\(e\left(\frac{241}{506}\right)\)	\(e\left(\frac{865}{1012}\right)\)	\(e\left(\frac{743}{1012}\right)\)	\(e\left(\frac{234}{253}\right)\)	\(e\left(\frac{337}{506}\right)\)	\(e\left(\frac{195}{1012}\right)\)	\(e\left(\frac{587}{1012}\right)\)
\(\chi_{8464}(251,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{449}{1012}\right)\)	\(e\left(\frac{455}{1012}\right)\)	\(e\left(\frac{379}{506}\right)\)	\(e\left(\frac{449}{506}\right)\)	\(e\left(\frac{377}{1012}\right)\)	\(e\left(\frac{683}{1012}\right)\)	\(e\left(\frac{226}{253}\right)\)	\(e\left(\frac{399}{506}\right)\)	\(e\left(\frac{863}{1012}\right)\)	\(e\left(\frac{195}{1012}\right)\)
\(\chi_{8464}(267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{969}{1012}\right)\)	\(e\left(\frac{867}{1012}\right)\)	\(e\left(\frac{135}{506}\right)\)	\(e\left(\frac{463}{506}\right)\)	\(e\left(\frac{169}{1012}\right)\)	\(e\left(\frac{27}{1012}\right)\)	\(e\left(\frac{206}{253}\right)\)	\(e\left(\frac{301}{506}\right)\)	\(e\left(\frac{3}{1012}\right)\)	\(e\left(\frac{227}{1012}\right)\)
\(\chi_{8464}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{729}{1012}\right)\)	\(e\left(\frac{599}{1012}\right)\)	\(e\left(\frac{53}{506}\right)\)	\(e\left(\frac{223}{506}\right)\)	\(e\left(\frac{265}{1012}\right)\)	\(e\left(\frac{719}{1012}\right)\)	\(e\left(\frac{79}{253}\right)\)	\(e\left(\frac{463}{506}\right)\)	\(e\left(\frac{867}{1012}\right)\)	\(e\left(\frac{835}{1012}\right)\)
\(\chi_{8464}(291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{1012}\right)\)	\(e\left(\frac{969}{1012}\right)\)	\(e\left(\frac{389}{506}\right)\)	\(e\left(\frac{71}{506}\right)\)	\(e\left(\frac{427}{1012}\right)\)	\(e\left(\frac{685}{1012}\right)\)	\(e\left(\frac{7}{253}\right)\)	\(e\left(\frac{9}{506}\right)\)	\(e\left(\frac{301}{1012}\right)\)	\(e\left(\frac{849}{1012}\right)\)
\(\chi_{8464}(339,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{895}{1012}\right)\)	\(e\left(\frac{641}{1012}\right)\)	\(e\left(\frac{485}{506}\right)\)	\(e\left(\frac{389}{506}\right)\)	\(e\left(\frac{907}{1012}\right)\)	\(e\left(\frac{97}{1012}\right)\)	\(e\left(\frac{131}{253}\right)\)	\(e\left(\frac{313}{506}\right)\)	\(e\left(\frac{573}{1012}\right)\)	\(e\left(\frac{853}{1012}\right)\)
\(\chi_{8464}(355,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{327}{1012}\right)\)	\(e\left(\frac{985}{1012}\right)\)	\(e\left(\frac{409}{506}\right)\)	\(e\left(\frac{327}{506}\right)\)	\(e\left(\frac{527}{1012}\right)\)	\(e\left(\frac{689}{1012}\right)\)	\(e\left(\frac{75}{253}\right)\)	\(e\left(\frac{241}{506}\right)\)	\(e\left(\frac{189}{1012}\right)\)	\(e\left(\frac{133}{1012}\right)\)
\(\chi_{8464}(379,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{1012}\right)\)	\(e\left(\frac{183}{1012}\right)\)	\(e\left(\frac{39}{506}\right)\)	\(e\left(\frac{145}{506}\right)\)	\(e\left(\frac{701}{1012}\right)\)	\(e\left(\frac{615}{1012}\right)\)	\(e\left(\frac{82}{253}\right)\)	\(e\left(\frac{503}{506}\right)\)	\(e\left(\frac{743}{1012}\right)\)	\(e\left(\frac{223}{1012}\right)\)
\(\chi_{8464}(387,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{623}{1012}\right)\)	\(e\left(\frac{877}{1012}\right)\)	\(e\left(\frac{21}{506}\right)\)	\(e\left(\frac{117}{506}\right)\)	\(e\left(\frac{611}{1012}\right)\)	\(e\left(\frac{409}{1012}\right)\)	\(e\left(\frac{122}{253}\right)\)	\(e\left(\frac{193}{506}\right)\)	\(e\left(\frac{945}{1012}\right)\)	\(e\left(\frac{665}{1012}\right)\)
\(\chi_{8464}(419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{307}{1012}\right)\)	\(e\left(\frac{541}{1012}\right)\)	\(e\left(\frac{107}{506}\right)\)	\(e\left(\frac{307}{506}\right)\)	\(e\left(\frac{535}{1012}\right)\)	\(e\left(\frac{325}{1012}\right)\)	\(e\left(\frac{212}{253}\right)\)	\(e\left(\frac{381}{506}\right)\)	\(e\left(\frac{261}{1012}\right)\)	\(e\left(\frac{521}{1012}\right)\)
\(\chi_{8464}(435,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{1012}\right)\)	\(e\left(\frac{81}{1012}\right)\)	\(e\left(\frac{291}{506}\right)\)	\(e\left(\frac{31}{506}\right)\)	\(e\left(\frac{443}{1012}\right)\)	\(e\left(\frac{969}{1012}\right)\)	\(e\left(\frac{28}{253}\right)\)	\(e\left(\frac{289}{506}\right)\)	\(e\left(\frac{445}{1012}\right)\)	\(e\left(\frac{613}{1012}\right)\)
\(\chi_{8464}(451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{595}{1012}\right)\)	\(e\left(\frac{53}{1012}\right)\)	\(e\left(\frac{3}{506}\right)\)	\(e\left(\frac{89}{506}\right)\)	\(e\left(\frac{15}{1012}\right)\)	\(e\left(\frac{709}{1012}\right)\)	\(e\left(\frac{162}{253}\right)\)	\(e\left(\frac{389}{506}\right)\)	\(e\left(\frac{641}{1012}\right)\)	\(e\left(\frac{601}{1012}\right)\)
\(\chi_{8464}(467,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{487}{1012}\right)\)	\(e\left(\frac{489}{1012}\right)\)	\(e\left(\frac{295}{506}\right)\)	\(e\left(\frac{487}{506}\right)\)	\(e\left(\frac{463}{1012}\right)\)	\(e\left(\frac{565}{1012}\right)\)	\(e\left(\frac{244}{253}\right)\)	\(e\left(\frac{133}{506}\right)\)	\(e\left(\frac{625}{1012}\right)\)	\(e\left(\frac{65}{1012}\right)\)
\(\chi_{8464}(475,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{93}{1012}\right)\)	\(e\left(\frac{243}{1012}\right)\)	\(e\left(\frac{367}{506}\right)\)	\(e\left(\frac{93}{506}\right)\)	\(e\left(\frac{317}{1012}\right)\)	\(e\left(\frac{883}{1012}\right)\)	\(e\left(\frac{84}{253}\right)\)	\(e\left(\frac{361}{506}\right)\)	\(e\left(\frac{323}{1012}\right)\)	\(e\left(\frac{827}{1012}\right)\)
\(\chi_{8464}(523,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{81}{1012}\right)\)	\(e\left(\frac{179}{1012}\right)\)	\(e\left(\frac{287}{506}\right)\)	\(e\left(\frac{81}{506}\right)\)	\(e\left(\frac{929}{1012}\right)\)	\(e\left(\frac{867}{1012}\right)\)	\(e\left(\frac{65}{253}\right)\)	\(e\left(\frac{445}{506}\right)\)	\(e\left(\frac{771}{1012}\right)\)	\(e\left(\frac{655}{1012}\right)\)
\(\chi_{8464}(539,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{613}{1012}\right)\)	\(e\left(\frac{655}{1012}\right)\)	\(e\left(\frac{123}{506}\right)\)	\(e\left(\frac{107}{506}\right)\)	\(e\left(\frac{109}{1012}\right)\)	\(e\left(\frac{227}{1012}\right)\)	\(e\left(\frac{64}{253}\right)\)	\(e\left(\frac{263}{506}\right)\)	\(e\left(\frac{475}{1012}\right)\)	\(e\left(\frac{859}{1012}\right)\)
\(\chi_{8464}(563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1003}{1012}\right)\)	\(e\left(\frac{205}{1012}\right)\)	\(e\left(\frac{193}{506}\right)\)	\(e\left(\frac{497}{506}\right)\)	\(e\left(\frac{459}{1012}\right)\)	\(e\left(\frac{241}{1012}\right)\)	\(e\left(\frac{49}{253}\right)\)	\(e\left(\frac{63}{506}\right)\)	\(e\left(\frac{589}{1012}\right)\)	\(e\left(\frac{377}{1012}\right)\)
\(\chi_{8464}(595,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{787}{1012}\right)\)	\(e\left(\frac{65}{1012}\right)\)	\(e\left(\frac{271}{506}\right)\)	\(e\left(\frac{281}{506}\right)\)	\(e\left(\frac{343}{1012}\right)\)	\(e\left(\frac{965}{1012}\right)\)	\(e\left(\frac{213}{253}\right)\)	\(e\left(\frac{57}{506}\right)\)	\(e\left(\frac{557}{1012}\right)\)	\(e\left(\frac{317}{1012}\right)\)
\(\chi_{8464}(603,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{373}{1012}\right)\)	\(e\left(\frac{387}{1012}\right)\)	\(e\left(\frac{41}{506}\right)\)	\(e\left(\frac{373}{506}\right)\)	\(e\left(\frac{205}{1012}\right)\)	\(e\left(\frac{919}{1012}\right)\)	\(e\left(\frac{190}{253}\right)\)	\(e\left(\frac{425}{506}\right)\)	\(e\left(\frac{327}{1012}\right)\)	\(e\left(\frac{455}{1012}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

First 31 of 440 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	8464.bs
Modulus	$8464$
Conductor	$8464$
Order	$1012$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8464\)
Conductor:	\(8464\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(1012\)	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)