LMFDB - Dirichlet character orbit 8464.bt

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8464, base_ring=CyclotomicField(1012)) M = H._module chi = DirichletCharacter(H, M([0,759,380])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,8464)) 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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8464}(13,\cdot)$	$1$	$1$	$e\left(\frac{261}{1012}\right)$	$e\left(\frac{127}{1012}\right)$	$e\left(\frac{475}{506}\right)$	$e\left(\frac{261}{506}\right)$	$e\left(\frac{351}{1012}\right)$	$e\left(\frac{601}{1012}\right)$	$e\left(\frac{97}{253}\right)$	$e\left(\frac{225}{253}\right)$	$e\left(\frac{629}{1012}\right)$	$e\left(\frac{199}{1012}\right)$
$\chi_{8464}(29,\cdot)$	$1$	$1$	$e\left(\frac{1005}{1012}\right)$	$e\left(\frac{47}{1012}\right)$	$e\left(\frac{375}{506}\right)$	$e\left(\frac{499}{506}\right)$	$e\left(\frac{863}{1012}\right)$	$e\left(\frac{581}{1012}\right)$	$e\left(\frac{10}{253}\right)$	$e\left(\frac{151}{253}\right)$	$e\left(\frac{177}{1012}\right)$	$e\left(\frac{743}{1012}\right)$
$\chi_{8464}(77,\cdot)$	$1$	$1$	$e\left(\frac{533}{1012}\right)$	$e\left(\frac{903}{1012}\right)$	$e\left(\frac{433}{506}\right)$	$e\left(\frac{27}{506}\right)$	$e\left(\frac{647}{1012}\right)$	$e\left(\frac{289}{1012}\right)$	$e\left(\frac{106}{253}\right)$	$e\left(\frac{32}{253}\right)$	$e\left(\frac{257}{1012}\right)$	$e\left(\frac{387}{1012}\right)$
$\chi_{8464}(85,\cdot)$	$1$	$1$	$e\left(\frac{707}{1012}\right)$	$e\left(\frac{313}{1012}\right)$	$e\left(\frac{75}{506}\right)$	$e\left(\frac{201}{506}\right)$	$e\left(\frac{881}{1012}\right)$	$e\left(\frac{15}{1012}\right)$	$e\left(\frac{2}{253}\right)$	$e\left(\frac{182}{253}\right)$	$e\left(\frac{339}{1012}\right)$	$e\left(\frac{857}{1012}\right)$
$\chi_{8464}(101,\cdot)$	$1$	$1$	$e\left(\frac{199}{1012}\right)$	$e\left(\frac{977}{1012}\right)$	$e\left(\frac{399}{506}\right)$	$e\left(\frac{199}{506}\right)$	$e\left(\frac{477}{1012}\right)$	$e\left(\frac{687}{1012}\right)$	$e\left(\frac{41}{253}\right)$	$e\left(\frac{189}{253}\right)$	$e\left(\frac{751}{1012}\right)$	$e\left(\frac{997}{1012}\right)$
$\chi_{8464}(117,\cdot)$	$1$	$1$	$e\left(\frac{779}{1012}\right)$	$e\left(\frac{697}{1012}\right)$	$e\left(\frac{49}{506}\right)$	$e\left(\frac{273}{506}\right)$	$e\left(\frac{245}{1012}\right)$	$e\left(\frac{111}{1012}\right)$	$e\left(\frac{116}{253}\right)$	$e\left(\frac{183}{253}\right)$	$e\left(\frac{687}{1012}\right)$	$e\left(\frac{877}{1012}\right)$
$\chi_{8464}(133,\cdot)$	$1$	$1$	$e\left(\frac{615}{1012}\right)$	$e\left(\frac{497}{1012}\right)$	$e\left(\frac{305}{506}\right)$	$e\left(\frac{109}{506}\right)$	$e\left(\frac{513}{1012}\right)$	$e\left(\frac{567}{1012}\right)$	$e\left(\frac{25}{253}\right)$	$e\left(\frac{251}{253}\right)$	$e\left(\frac{63}{1012}\right)$	$e\left(\frac{213}{1012}\right)$
$\chi_{8464}(141,\cdot)$	$1$	$1$	$e\left(\frac{721}{1012}\right)$	$e\left(\frac{219}{1012}\right)$	$e\left(\frac{337}{506}\right)$	$e\left(\frac{215}{506}\right)$	$e\left(\frac{167}{1012}\right)$	$e\left(\frac{877}{1012}\right)$	$e\left(\frac{235}{253}\right)$	$e\left(\frac{133}{253}\right)$	$e\left(\frac{997}{1012}\right)$	$e\left(\frac{383}{1012}\right)$
$\chi_{8464}(165,\cdot)$	$1$	$1$	$e\left(\frac{491}{1012}\right)$	$e\left(\frac{173}{1012}\right)$	$e\left(\frac{153}{506}\right)$	$e\left(\frac{491}{506}\right)$	$e\left(\frac{765}{1012}\right)$	$e\left(\frac{739}{1012}\right)$	$e\left(\frac{166}{253}\right)$	$e\left(\frac{179}{253}\right)$	$e\left(\frac{307}{1012}\right)$	$e\left(\frac{797}{1012}\right)$
$\chi_{8464}(173,\cdot)$	$1$	$1$	$e\left(\frac{101}{1012}\right)$	$e\left(\frac{623}{1012}\right)$	$e\left(\frac{83}{506}\right)$	$e\left(\frac{101}{506}\right)$	$e\left(\frac{415}{1012}\right)$	$e\left(\frac{725}{1012}\right)$	$e\left(\frac{181}{253}\right)$	$e\left(\frac{26}{253}\right)$	$e\left(\frac{193}{1012}\right)$	$e\left(\frac{267}{1012}\right)$
$\chi_{8464}(197,\cdot)$	$1$	$1$	$e\left(\frac{987}{1012}\right)$	$e\left(\frac{457}{1012}\right)$	$e\left(\frac{255}{506}\right)$	$e\left(\frac{481}{506}\right)$	$e\left(\frac{769}{1012}\right)$	$e\left(\frac{51}{1012}\right)$	$e\left(\frac{108}{253}\right)$	$e\left(\frac{214}{253}\right)$	$e\left(\frac{343}{1012}\right)$	$e\left(\frac{485}{1012}\right)$
$\chi_{8464}(213,\cdot)$	$1$	$1$	$e\left(\frac{807}{1012}\right)$	$e\left(\frac{509}{1012}\right)$	$e\left(\frac{67}{506}\right)$	$e\left(\frac{301}{506}\right)$	$e\left(\frac{841}{1012}\right)$	$e\left(\frac{823}{1012}\right)$	$e\left(\frac{76}{253}\right)$	$e\left(\frac{85}{253}\right)$	$e\left(\frac{991}{1012}\right)$	$e\left(\frac{941}{1012}\right)$
$\chi_{8464}(261,\cdot)$	$1$	$1$	$e\left(\frac{511}{1012}\right)$	$e\left(\frac{617}{1012}\right)$	$e\left(\frac{455}{506}\right)$	$e\left(\frac{5}{506}\right)$	$e\left(\frac{757}{1012}\right)$	$e\left(\frac{91}{1012}\right)$	$e\left(\frac{29}{253}\right)$	$e\left(\frac{109}{253}\right)$	$e\left(\frac{235}{1012}\right)$	$e\left(\frac{409}{1012}\right)$
$\chi_{8464}(269,\cdot)$	$1$	$1$	$e\left(\frac{949}{1012}\right)$	$e\left(\frac{423}{1012}\right)$	$e\left(\frac{339}{506}\right)$	$e\left(\frac{443}{506}\right)$	$e\left(\frac{683}{1012}\right)$	$e\left(\frac{169}{1012}\right)$	$e\left(\frac{90}{253}\right)$	$e\left(\frac{94}{253}\right)$	$e\left(\frac{581}{1012}\right)$	$e\left(\frac{615}{1012}\right)$
$\chi_{8464}(285,\cdot)$	$1$	$1$	$e\left(\frac{573}{1012}\right)$	$e\left(\frac{779}{1012}\right)$	$e\left(\frac{25}{506}\right)$	$e\left(\frac{67}{506}\right)$	$e\left(\frac{631}{1012}\right)$	$e\left(\frac{5}{1012}\right)$	$e\left(\frac{85}{253}\right)$	$e\left(\frac{145}{253}\right)$	$e\left(\frac{113}{1012}\right)$	$e\left(\frac{623}{1012}\right)$
$\chi_{8464}(301,\cdot)$	$1$	$1$	$e\left(\frac{185}{1012}\right)$	$e\left(\frac{59}{1012}\right)$	$e\left(\frac{137}{506}\right)$	$e\left(\frac{185}{506}\right)$	$e\left(\frac{179}{1012}\right)$	$e\left(\frac{837}{1012}\right)$	$e\left(\frac{61}{253}\right)$	$e\left(\frac{238}{253}\right)$	$e\left(\frac{93}{1012}\right)$	$e\left(\frac{459}{1012}\right)$
$\chi_{8464}(317,\cdot)$	$1$	$1$	$e\left(\frac{549}{1012}\right)$	$e\left(\frac{651}{1012}\right)$	$e\left(\frac{371}{506}\right)$	$e\left(\frac{43}{506}\right)$	$e\left(\frac{843}{1012}\right)$	$e\left(\frac{985}{1012}\right)$	$e\left(\frac{47}{253}\right)$	$e\left(\frac{229}{253}\right)$	$e\left(\frac{1009}{1012}\right)$	$e\left(\frac{279}{1012}\right)$
$\chi_{8464}(325,\cdot)$	$1$	$1$	$e\left(\frac{831}{1012}\right)$	$e\left(\frac{637}{1012}\right)$	$e\left(\frac{227}{506}\right)$	$e\left(\frac{325}{506}\right)$	$e\left(\frac{629}{1012}\right)$	$e\left(\frac{855}{1012}\right)$	$e\left(\frac{114}{253}\right)$	$e\left(\frac{1}{253}\right)$	$e\left(\frac{95}{1012}\right)$	$e\left(\frac{273}{1012}\right)$
$\chi_{8464}(349,\cdot)$	$1$	$1$	$e\left(\frac{953}{1012}\right)$	$e\left(\frac{107}{1012}\right)$	$e\left(\frac{197}{506}\right)$	$e\left(\frac{447}{506}\right)$	$e\left(\frac{479}{1012}\right)$	$e\left(\frac{849}{1012}\right)$	$e\left(\frac{12}{253}\right)$	$e\left(\frac{80}{253}\right)$	$e\left(\frac{769}{1012}\right)$	$e\left(\frac{335}{1012}\right)$
$\chi_{8464}(357,\cdot)$	$1$	$1$	$e\left(\frac{255}{1012}\right)$	$e\left(\frac{601}{1012}\right)$	$e\left(\frac{435}{506}\right)$	$e\left(\frac{255}{506}\right)$	$e\left(\frac{657}{1012}\right)$	$e\left(\frac{87}{1012}\right)$	$e\left(\frac{214}{253}\right)$	$e\left(\frac{246}{253}\right)$	$e\left(\frac{347}{1012}\right)$	$e\left(\frac{113}{1012}\right)$
$\chi_{8464}(381,\cdot)$	$1$	$1$	$e\left(\frac{701}{1012}\right)$	$e\left(\frac{787}{1012}\right)$	$e\left(\frac{35}{506}\right)$	$e\left(\frac{195}{506}\right)$	$e\left(\frac{175}{1012}\right)$	$e\left(\frac{513}{1012}\right)$	$e\left(\frac{119}{253}\right)$	$e\left(\frac{203}{253}\right)$	$e\left(\frac{57}{1012}\right)$	$e\left(\frac{771}{1012}\right)$
$\chi_{8464}(397,\cdot)$	$1$	$1$	$e\left(\frac{609}{1012}\right)$	$e\left(\frac{971}{1012}\right)$	$e\left(\frac{265}{506}\right)$	$e\left(\frac{103}{506}\right)$	$e\left(\frac{819}{1012}\right)$	$e\left(\frac{53}{1012}\right)$	$e\left(\frac{142}{253}\right)$	$e\left(\frac{19}{253}\right)$	$e\left(\frac{793}{1012}\right)$	$e\left(\frac{127}{1012}\right)$
$\chi_{8464}(445,\cdot)$	$1$	$1$	$e\left(\frac{489}{1012}\right)$	$e\left(\frac{331}{1012}\right)$	$e\left(\frac{477}{506}\right)$	$e\left(\frac{489}{506}\right)$	$e\left(\frac{867}{1012}\right)$	$e\left(\frac{905}{1012}\right)$	$e\left(\frac{205}{253}\right)$	$e\left(\frac{186}{253}\right)$	$e\left(\frac{213}{1012}\right)$	$e\left(\frac{431}{1012}\right)$
$\chi_{8464}(453,\cdot)$	$1$	$1$	$e\left(\frac{179}{1012}\right)$	$e\left(\frac{533}{1012}\right)$	$e\left(\frac{97}{506}\right)$	$e\left(\frac{179}{506}\right)$	$e\left(\frac{485}{1012}\right)$	$e\left(\frac{323}{1012}\right)$	$e\left(\frac{178}{253}\right)$	$e\left(\frac{6}{253}\right)$	$e\left(\frac{823}{1012}\right)$	$e\left(\frac{373}{1012}\right)$
$\chi_{8464}(469,\cdot)$	$1$	$1$	$e\left(\frac{947}{1012}\right)$	$e\left(\frac{581}{1012}\right)$	$e\left(\frac{157}{506}\right)$	$e\left(\frac{441}{506}\right)$	$e\left(\frac{785}{1012}\right)$	$e\left(\frac{335}{1012}\right)$	$e\left(\frac{129}{253}\right)$	$e\left(\frac{101}{253}\right)$	$e\left(\frac{487}{1012}\right)$	$e\left(\frac{249}{1012}\right)$
$\chi_{8464}(485,\cdot)$	$1$	$1$	$e\left(\frac{603}{1012}\right)$	$e\left(\frac{433}{1012}\right)$	$e\left(\frac{225}{506}\right)$	$e\left(\frac{97}{506}\right)$	$e\left(\frac{113}{1012}\right)$	$e\left(\frac{551}{1012}\right)$	$e\left(\frac{6}{253}\right)$	$e\left(\frac{40}{253}\right)$	$e\left(\frac{511}{1012}\right)$	$e\left(\frac{41}{1012}\right)$
$\chi_{8464}(509,\cdot)$	$1$	$1$	$e\left(\frac{941}{1012}\right)$	$e\left(\frac{43}{1012}\right)$	$e\left(\frac{117}{506}\right)$	$e\left(\frac{435}{506}\right)$	$e\left(\frac{79}{1012}\right)$	$e\left(\frac{833}{1012}\right)$	$e\left(\frac{246}{253}\right)$	$e\left(\frac{122}{253}\right)$	$e\left(\frac{205}{1012}\right)$	$e\left(\frac{163}{1012}\right)$
$\chi_{8464}(533,\cdot)$	$1$	$1$	$e\left(\frac{403}{1012}\right)$	$e\left(\frac{41}{1012}\right)$	$e\left(\frac{241}{506}\right)$	$e\left(\frac{403}{506}\right)$	$e\left(\frac{193}{1012}\right)$	$e\left(\frac{959}{1012}\right)$	$e\left(\frac{111}{253}\right)$	$e\left(\frac{234}{253}\right)$	$e\left(\frac{219}{1012}\right)$	$e\left(\frac{885}{1012}\right)$
$\chi_{8464}(541,\cdot)$	$1$	$1$	$e\left(\frac{409}{1012}\right)$	$e\left(\frac{579}{1012}\right)$	$e\left(\frac{281}{506}\right)$	$e\left(\frac{409}{506}\right)$	$e\left(\frac{899}{1012}\right)$	$e\left(\frac{461}{1012}\right)$	$e\left(\frac{247}{253}\right)$	$e\left(\frac{213}{253}\right)$	$e\left(\frac{501}{1012}\right)$	$e\left(\frac{971}{1012}\right)$
$\chi_{8464}(565,\cdot)$	$1$	$1$	$e\left(\frac{415}{1012}\right)$	$e\left(\frac{105}{1012}\right)$	$e\left(\frac{321}{506}\right)$	$e\left(\frac{415}{506}\right)$	$e\left(\frac{593}{1012}\right)$	$e\left(\frac{975}{1012}\right)$	$e\left(\frac{130}{253}\right)$	$e\left(\frac{192}{253}\right)$	$e\left(\frac{783}{1012}\right)$	$e\left(\frac{45}{1012}\right)$
$\chi_{8464}(581,\cdot)$	$1$	$1$	$e\left(\frac{411}{1012}\right)$	$e\left(\frac{421}{1012}\right)$	$e\left(\frac{463}{506}\right)$	$e\left(\frac{411}{506}\right)$	$e\left(\frac{797}{1012}\right)$	$e\left(\frac{295}{1012}\right)$	$e\left(\frac{208}{253}\right)$	$e\left(\frac{206}{253}\right)$	$e\left(\frac{595}{1012}\right)$	$e\left(\frac{325}{1012}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8464}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{261}{1012}\right)\)	\(e\left(\frac{127}{1012}\right)\)	\(e\left(\frac{475}{506}\right)\)	\(e\left(\frac{261}{506}\right)\)	\(e\left(\frac{351}{1012}\right)\)	\(e\left(\frac{601}{1012}\right)\)	\(e\left(\frac{97}{253}\right)\)	\(e\left(\frac{225}{253}\right)\)	\(e\left(\frac{629}{1012}\right)\)	\(e\left(\frac{199}{1012}\right)\)
\(\chi_{8464}(29,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1005}{1012}\right)\)	\(e\left(\frac{47}{1012}\right)\)	\(e\left(\frac{375}{506}\right)\)	\(e\left(\frac{499}{506}\right)\)	\(e\left(\frac{863}{1012}\right)\)	\(e\left(\frac{581}{1012}\right)\)	\(e\left(\frac{10}{253}\right)\)	\(e\left(\frac{151}{253}\right)\)	\(e\left(\frac{177}{1012}\right)\)	\(e\left(\frac{743}{1012}\right)\)
\(\chi_{8464}(77,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{533}{1012}\right)\)	\(e\left(\frac{903}{1012}\right)\)	\(e\left(\frac{433}{506}\right)\)	\(e\left(\frac{27}{506}\right)\)	\(e\left(\frac{647}{1012}\right)\)	\(e\left(\frac{289}{1012}\right)\)	\(e\left(\frac{106}{253}\right)\)	\(e\left(\frac{32}{253}\right)\)	\(e\left(\frac{257}{1012}\right)\)	\(e\left(\frac{387}{1012}\right)\)
\(\chi_{8464}(85,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{707}{1012}\right)\)	\(e\left(\frac{313}{1012}\right)\)	\(e\left(\frac{75}{506}\right)\)	\(e\left(\frac{201}{506}\right)\)	\(e\left(\frac{881}{1012}\right)\)	\(e\left(\frac{15}{1012}\right)\)	\(e\left(\frac{2}{253}\right)\)	\(e\left(\frac{182}{253}\right)\)	\(e\left(\frac{339}{1012}\right)\)	\(e\left(\frac{857}{1012}\right)\)
\(\chi_{8464}(101,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{1012}\right)\)	\(e\left(\frac{977}{1012}\right)\)	\(e\left(\frac{399}{506}\right)\)	\(e\left(\frac{199}{506}\right)\)	\(e\left(\frac{477}{1012}\right)\)	\(e\left(\frac{687}{1012}\right)\)	\(e\left(\frac{41}{253}\right)\)	\(e\left(\frac{189}{253}\right)\)	\(e\left(\frac{751}{1012}\right)\)	\(e\left(\frac{997}{1012}\right)\)
\(\chi_{8464}(117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{779}{1012}\right)\)	\(e\left(\frac{697}{1012}\right)\)	\(e\left(\frac{49}{506}\right)\)	\(e\left(\frac{273}{506}\right)\)	\(e\left(\frac{245}{1012}\right)\)	\(e\left(\frac{111}{1012}\right)\)	\(e\left(\frac{116}{253}\right)\)	\(e\left(\frac{183}{253}\right)\)	\(e\left(\frac{687}{1012}\right)\)	\(e\left(\frac{877}{1012}\right)\)
\(\chi_{8464}(133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{615}{1012}\right)\)	\(e\left(\frac{497}{1012}\right)\)	\(e\left(\frac{305}{506}\right)\)	\(e\left(\frac{109}{506}\right)\)	\(e\left(\frac{513}{1012}\right)\)	\(e\left(\frac{567}{1012}\right)\)	\(e\left(\frac{25}{253}\right)\)	\(e\left(\frac{251}{253}\right)\)	\(e\left(\frac{63}{1012}\right)\)	\(e\left(\frac{213}{1012}\right)\)
\(\chi_{8464}(141,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{721}{1012}\right)\)	\(e\left(\frac{219}{1012}\right)\)	\(e\left(\frac{337}{506}\right)\)	\(e\left(\frac{215}{506}\right)\)	\(e\left(\frac{167}{1012}\right)\)	\(e\left(\frac{877}{1012}\right)\)	\(e\left(\frac{235}{253}\right)\)	\(e\left(\frac{133}{253}\right)\)	\(e\left(\frac{997}{1012}\right)\)	\(e\left(\frac{383}{1012}\right)\)
\(\chi_{8464}(165,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{491}{1012}\right)\)	\(e\left(\frac{173}{1012}\right)\)	\(e\left(\frac{153}{506}\right)\)	\(e\left(\frac{491}{506}\right)\)	\(e\left(\frac{765}{1012}\right)\)	\(e\left(\frac{739}{1012}\right)\)	\(e\left(\frac{166}{253}\right)\)	\(e\left(\frac{179}{253}\right)\)	\(e\left(\frac{307}{1012}\right)\)	\(e\left(\frac{797}{1012}\right)\)
\(\chi_{8464}(173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{1012}\right)\)	\(e\left(\frac{623}{1012}\right)\)	\(e\left(\frac{83}{506}\right)\)	\(e\left(\frac{101}{506}\right)\)	\(e\left(\frac{415}{1012}\right)\)	\(e\left(\frac{725}{1012}\right)\)	\(e\left(\frac{181}{253}\right)\)	\(e\left(\frac{26}{253}\right)\)	\(e\left(\frac{193}{1012}\right)\)	\(e\left(\frac{267}{1012}\right)\)
\(\chi_{8464}(197,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{987}{1012}\right)\)	\(e\left(\frac{457}{1012}\right)\)	\(e\left(\frac{255}{506}\right)\)	\(e\left(\frac{481}{506}\right)\)	\(e\left(\frac{769}{1012}\right)\)	\(e\left(\frac{51}{1012}\right)\)	\(e\left(\frac{108}{253}\right)\)	\(e\left(\frac{214}{253}\right)\)	\(e\left(\frac{343}{1012}\right)\)	\(e\left(\frac{485}{1012}\right)\)
\(\chi_{8464}(213,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{807}{1012}\right)\)	\(e\left(\frac{509}{1012}\right)\)	\(e\left(\frac{67}{506}\right)\)	\(e\left(\frac{301}{506}\right)\)	\(e\left(\frac{841}{1012}\right)\)	\(e\left(\frac{823}{1012}\right)\)	\(e\left(\frac{76}{253}\right)\)	\(e\left(\frac{85}{253}\right)\)	\(e\left(\frac{991}{1012}\right)\)	\(e\left(\frac{941}{1012}\right)\)
\(\chi_{8464}(261,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{511}{1012}\right)\)	\(e\left(\frac{617}{1012}\right)\)	\(e\left(\frac{455}{506}\right)\)	\(e\left(\frac{5}{506}\right)\)	\(e\left(\frac{757}{1012}\right)\)	\(e\left(\frac{91}{1012}\right)\)	\(e\left(\frac{29}{253}\right)\)	\(e\left(\frac{109}{253}\right)\)	\(e\left(\frac{235}{1012}\right)\)	\(e\left(\frac{409}{1012}\right)\)
\(\chi_{8464}(269,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{949}{1012}\right)\)	\(e\left(\frac{423}{1012}\right)\)	\(e\left(\frac{339}{506}\right)\)	\(e\left(\frac{443}{506}\right)\)	\(e\left(\frac{683}{1012}\right)\)	\(e\left(\frac{169}{1012}\right)\)	\(e\left(\frac{90}{253}\right)\)	\(e\left(\frac{94}{253}\right)\)	\(e\left(\frac{581}{1012}\right)\)	\(e\left(\frac{615}{1012}\right)\)
\(\chi_{8464}(285,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{573}{1012}\right)\)	\(e\left(\frac{779}{1012}\right)\)	\(e\left(\frac{25}{506}\right)\)	\(e\left(\frac{67}{506}\right)\)	\(e\left(\frac{631}{1012}\right)\)	\(e\left(\frac{5}{1012}\right)\)	\(e\left(\frac{85}{253}\right)\)	\(e\left(\frac{145}{253}\right)\)	\(e\left(\frac{113}{1012}\right)\)	\(e\left(\frac{623}{1012}\right)\)
\(\chi_{8464}(301,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{1012}\right)\)	\(e\left(\frac{59}{1012}\right)\)	\(e\left(\frac{137}{506}\right)\)	\(e\left(\frac{185}{506}\right)\)	\(e\left(\frac{179}{1012}\right)\)	\(e\left(\frac{837}{1012}\right)\)	\(e\left(\frac{61}{253}\right)\)	\(e\left(\frac{238}{253}\right)\)	\(e\left(\frac{93}{1012}\right)\)	\(e\left(\frac{459}{1012}\right)\)
\(\chi_{8464}(317,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{549}{1012}\right)\)	\(e\left(\frac{651}{1012}\right)\)	\(e\left(\frac{371}{506}\right)\)	\(e\left(\frac{43}{506}\right)\)	\(e\left(\frac{843}{1012}\right)\)	\(e\left(\frac{985}{1012}\right)\)	\(e\left(\frac{47}{253}\right)\)	\(e\left(\frac{229}{253}\right)\)	\(e\left(\frac{1009}{1012}\right)\)	\(e\left(\frac{279}{1012}\right)\)
\(\chi_{8464}(325,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{831}{1012}\right)\)	\(e\left(\frac{637}{1012}\right)\)	\(e\left(\frac{227}{506}\right)\)	\(e\left(\frac{325}{506}\right)\)	\(e\left(\frac{629}{1012}\right)\)	\(e\left(\frac{855}{1012}\right)\)	\(e\left(\frac{114}{253}\right)\)	\(e\left(\frac{1}{253}\right)\)	\(e\left(\frac{95}{1012}\right)\)	\(e\left(\frac{273}{1012}\right)\)
\(\chi_{8464}(349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{953}{1012}\right)\)	\(e\left(\frac{107}{1012}\right)\)	\(e\left(\frac{197}{506}\right)\)	\(e\left(\frac{447}{506}\right)\)	\(e\left(\frac{479}{1012}\right)\)	\(e\left(\frac{849}{1012}\right)\)	\(e\left(\frac{12}{253}\right)\)	\(e\left(\frac{80}{253}\right)\)	\(e\left(\frac{769}{1012}\right)\)	\(e\left(\frac{335}{1012}\right)\)
\(\chi_{8464}(357,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{255}{1012}\right)\)	\(e\left(\frac{601}{1012}\right)\)	\(e\left(\frac{435}{506}\right)\)	\(e\left(\frac{255}{506}\right)\)	\(e\left(\frac{657}{1012}\right)\)	\(e\left(\frac{87}{1012}\right)\)	\(e\left(\frac{214}{253}\right)\)	\(e\left(\frac{246}{253}\right)\)	\(e\left(\frac{347}{1012}\right)\)	\(e\left(\frac{113}{1012}\right)\)
\(\chi_{8464}(381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{701}{1012}\right)\)	\(e\left(\frac{787}{1012}\right)\)	\(e\left(\frac{35}{506}\right)\)	\(e\left(\frac{195}{506}\right)\)	\(e\left(\frac{175}{1012}\right)\)	\(e\left(\frac{513}{1012}\right)\)	\(e\left(\frac{119}{253}\right)\)	\(e\left(\frac{203}{253}\right)\)	\(e\left(\frac{57}{1012}\right)\)	\(e\left(\frac{771}{1012}\right)\)
\(\chi_{8464}(397,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{609}{1012}\right)\)	\(e\left(\frac{971}{1012}\right)\)	\(e\left(\frac{265}{506}\right)\)	\(e\left(\frac{103}{506}\right)\)	\(e\left(\frac{819}{1012}\right)\)	\(e\left(\frac{53}{1012}\right)\)	\(e\left(\frac{142}{253}\right)\)	\(e\left(\frac{19}{253}\right)\)	\(e\left(\frac{793}{1012}\right)\)	\(e\left(\frac{127}{1012}\right)\)
\(\chi_{8464}(445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{489}{1012}\right)\)	\(e\left(\frac{331}{1012}\right)\)	\(e\left(\frac{477}{506}\right)\)	\(e\left(\frac{489}{506}\right)\)	\(e\left(\frac{867}{1012}\right)\)	\(e\left(\frac{905}{1012}\right)\)	\(e\left(\frac{205}{253}\right)\)	\(e\left(\frac{186}{253}\right)\)	\(e\left(\frac{213}{1012}\right)\)	\(e\left(\frac{431}{1012}\right)\)
\(\chi_{8464}(453,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{1012}\right)\)	\(e\left(\frac{533}{1012}\right)\)	\(e\left(\frac{97}{506}\right)\)	\(e\left(\frac{179}{506}\right)\)	\(e\left(\frac{485}{1012}\right)\)	\(e\left(\frac{323}{1012}\right)\)	\(e\left(\frac{178}{253}\right)\)	\(e\left(\frac{6}{253}\right)\)	\(e\left(\frac{823}{1012}\right)\)	\(e\left(\frac{373}{1012}\right)\)
\(\chi_{8464}(469,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{947}{1012}\right)\)	\(e\left(\frac{581}{1012}\right)\)	\(e\left(\frac{157}{506}\right)\)	\(e\left(\frac{441}{506}\right)\)	\(e\left(\frac{785}{1012}\right)\)	\(e\left(\frac{335}{1012}\right)\)	\(e\left(\frac{129}{253}\right)\)	\(e\left(\frac{101}{253}\right)\)	\(e\left(\frac{487}{1012}\right)\)	\(e\left(\frac{249}{1012}\right)\)
\(\chi_{8464}(485,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{603}{1012}\right)\)	\(e\left(\frac{433}{1012}\right)\)	\(e\left(\frac{225}{506}\right)\)	\(e\left(\frac{97}{506}\right)\)	\(e\left(\frac{113}{1012}\right)\)	\(e\left(\frac{551}{1012}\right)\)	\(e\left(\frac{6}{253}\right)\)	\(e\left(\frac{40}{253}\right)\)	\(e\left(\frac{511}{1012}\right)\)	\(e\left(\frac{41}{1012}\right)\)
\(\chi_{8464}(509,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{941}{1012}\right)\)	\(e\left(\frac{43}{1012}\right)\)	\(e\left(\frac{117}{506}\right)\)	\(e\left(\frac{435}{506}\right)\)	\(e\left(\frac{79}{1012}\right)\)	\(e\left(\frac{833}{1012}\right)\)	\(e\left(\frac{246}{253}\right)\)	\(e\left(\frac{122}{253}\right)\)	\(e\left(\frac{205}{1012}\right)\)	\(e\left(\frac{163}{1012}\right)\)
\(\chi_{8464}(533,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{403}{1012}\right)\)	\(e\left(\frac{41}{1012}\right)\)	\(e\left(\frac{241}{506}\right)\)	\(e\left(\frac{403}{506}\right)\)	\(e\left(\frac{193}{1012}\right)\)	\(e\left(\frac{959}{1012}\right)\)	\(e\left(\frac{111}{253}\right)\)	\(e\left(\frac{234}{253}\right)\)	\(e\left(\frac{219}{1012}\right)\)	\(e\left(\frac{885}{1012}\right)\)
\(\chi_{8464}(541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{409}{1012}\right)\)	\(e\left(\frac{579}{1012}\right)\)	\(e\left(\frac{281}{506}\right)\)	\(e\left(\frac{409}{506}\right)\)	\(e\left(\frac{899}{1012}\right)\)	\(e\left(\frac{461}{1012}\right)\)	\(e\left(\frac{247}{253}\right)\)	\(e\left(\frac{213}{253}\right)\)	\(e\left(\frac{501}{1012}\right)\)	\(e\left(\frac{971}{1012}\right)\)
\(\chi_{8464}(565,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{415}{1012}\right)\)	\(e\left(\frac{105}{1012}\right)\)	\(e\left(\frac{321}{506}\right)\)	\(e\left(\frac{415}{506}\right)\)	\(e\left(\frac{593}{1012}\right)\)	\(e\left(\frac{975}{1012}\right)\)	\(e\left(\frac{130}{253}\right)\)	\(e\left(\frac{192}{253}\right)\)	\(e\left(\frac{783}{1012}\right)\)	\(e\left(\frac{45}{1012}\right)\)
\(\chi_{8464}(581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{411}{1012}\right)\)	\(e\left(\frac{421}{1012}\right)\)	\(e\left(\frac{463}{506}\right)\)	\(e\left(\frac{411}{506}\right)\)	\(e\left(\frac{797}{1012}\right)\)	\(e\left(\frac{295}{1012}\right)\)	\(e\left(\frac{208}{253}\right)\)	\(e\left(\frac{206}{253}\right)\)	\(e\left(\frac{595}{1012}\right)\)	\(e\left(\frac{325}{1012}\right)\)

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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.bt
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)