LMFDB - Dirichlet character orbit 8464.bm

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8464, base_ring=CyclotomicField(506)) M = H._module chi = DirichletCharacter(H, M([253,0,17])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(15,8464)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8464$
Conductor:	$2116$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$506$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2116.n	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:	$\Q(\zeta_{253})$
Fixed field:	Number field defined by a degree 506 polynomial (not computed)

First 31 of 220 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8464}(15,\cdot)$	$1$	$1$	$e\left(\frac{19}{506}\right)$	$e\left(\frac{17}{506}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{19}{253}\right)$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{97}{253}\right)$	$e\left(\frac{18}{253}\right)$	$e\left(\frac{493}{506}\right)$	$e\left(\frac{67}{253}\right)$	$e\left(\frac{441}{506}\right)$
$\chi_{8464}(79,\cdot)$	$1$	$1$	$e\left(\frac{455}{506}\right)$	$e\left(\frac{487}{506}\right)$	$e\left(\frac{166}{253}\right)$	$e\left(\frac{202}{253}\right)$	$e\left(\frac{162}{253}\right)$	$e\left(\frac{219}{253}\right)$	$e\left(\frac{218}{253}\right)$	$e\left(\frac{461}{506}\right)$	$e\left(\frac{193}{253}\right)$	$e\left(\frac{281}{506}\right)$
$\chi_{8464}(111,\cdot)$	$1$	$1$	$e\left(\frac{405}{506}\right)$	$e\left(\frac{389}{506}\right)$	$e\left(\frac{170}{253}\right)$	$e\left(\frac{152}{253}\right)$	$e\left(\frac{172}{253}\right)$	$e\left(\frac{17}{253}\right)$	$e\left(\frac{144}{253}\right)$	$e\left(\frac{149}{506}\right)$	$e\left(\frac{30}{253}\right)$	$e\left(\frac{239}{506}\right)$
$\chi_{8464}(143,\cdot)$	$1$	$1$	$e\left(\frac{357}{506}\right)$	$e\left(\frac{133}{506}\right)$	$e\left(\frac{103}{253}\right)$	$e\left(\frac{104}{253}\right)$	$e\left(\frac{131}{253}\right)$	$e\left(\frac{238}{253}\right)$	$e\left(\frac{245}{253}\right)$	$e\left(\frac{315}{506}\right)$	$e\left(\frac{167}{253}\right)$	$e\left(\frac{57}{506}\right)$
$\chi_{8464}(159,\cdot)$	$1$	$1$	$e\left(\frac{329}{506}\right)$	$e\left(\frac{321}{506}\right)$	$e\left(\frac{85}{253}\right)$	$e\left(\frac{76}{253}\right)$	$e\left(\frac{86}{253}\right)$	$e\left(\frac{135}{253}\right)$	$e\left(\frac{72}{253}\right)$	$e\left(\frac{201}{506}\right)$	$e\left(\frac{15}{253}\right)$	$e\left(\frac{499}{506}\right)$
$\chi_{8464}(175,\cdot)$	$1$	$1$	$e\left(\frac{325}{506}\right)$	$e\left(\frac{131}{506}\right)$	$e\left(\frac{227}{253}\right)$	$e\left(\frac{72}{253}\right)$	$e\left(\frac{188}{253}\right)$	$e\left(\frac{48}{253}\right)$	$e\left(\frac{228}{253}\right)$	$e\left(\frac{257}{506}\right)$	$e\left(\frac{174}{253}\right)$	$e\left(\frac{273}{506}\right)$
$\chi_{8464}(191,\cdot)$	$1$	$1$	$e\left(\frac{425}{506}\right)$	$e\left(\frac{327}{506}\right)$	$e\left(\frac{219}{253}\right)$	$e\left(\frac{172}{253}\right)$	$e\left(\frac{168}{253}\right)$	$e\left(\frac{199}{253}\right)$	$e\left(\frac{123}{253}\right)$	$e\left(\frac{375}{506}\right)$	$e\left(\frac{247}{253}\right)$	$e\left(\frac{357}{506}\right)$
$\chi_{8464}(287,\cdot)$	$1$	$1$	$e\left(\frac{111}{506}\right)$	$e\left(\frac{339}{506}\right)$	$e\left(\frac{234}{253}\right)$	$e\left(\frac{111}{253}\right)$	$e\left(\frac{79}{253}\right)$	$e\left(\frac{74}{253}\right)$	$e\left(\frac{225}{253}\right)$	$e\left(\frac{217}{506}\right)$	$e\left(\frac{205}{253}\right)$	$e\left(\frac{73}{506}\right)$
$\chi_{8464}(319,\cdot)$	$1$	$1$	$e\left(\frac{223}{506}\right)$	$e\left(\frac{93}{506}\right)$	$e\left(\frac{53}{253}\right)$	$e\left(\frac{223}{253}\right)$	$e\left(\frac{6}{253}\right)$	$e\left(\frac{233}{253}\right)$	$e\left(\frac{158}{253}\right)$	$e\left(\frac{167}{506}\right)$	$e\left(\frac{54}{253}\right)$	$e\left(\frac{329}{506}\right)$
$\chi_{8464}(383,\cdot)$	$1$	$1$	$e\left(\frac{41}{506}\right)$	$e\left(\frac{303}{506}\right)$	$e\left(\frac{189}{253}\right)$	$e\left(\frac{41}{253}\right)$	$e\left(\frac{93}{253}\right)$	$e\left(\frac{196}{253}\right)$	$e\left(\frac{172}{253}\right)$	$e\left(\frac{185}{506}\right)$	$e\left(\frac{78}{253}\right)$	$e\left(\frac{419}{506}\right)$
$\chi_{8464}(431,\cdot)$	$1$	$1$	$e\left(\frac{497}{506}\right)$	$e\left(\frac{205}{506}\right)$	$e\left(\frac{193}{253}\right)$	$e\left(\frac{244}{253}\right)$	$e\left(\frac{103}{253}\right)$	$e\left(\frac{247}{253}\right)$	$e\left(\frac{98}{253}\right)$	$e\left(\frac{379}{506}\right)$	$e\left(\frac{168}{253}\right)$	$e\left(\frac{377}{506}\right)$
$\chi_{8464}(447,\cdot)$	$1$	$1$	$e\left(\frac{235}{506}\right)$	$e\left(\frac{157}{506}\right)$	$e\left(\frac{133}{253}\right)$	$e\left(\frac{235}{253}\right)$	$e\left(\frac{206}{253}\right)$	$e\left(\frac{241}{253}\right)$	$e\left(\frac{196}{253}\right)$	$e\left(\frac{505}{506}\right)$	$e\left(\frac{83}{253}\right)$	$e\left(\frac{501}{506}\right)$
$\chi_{8464}(479,\cdot)$	$1$	$1$	$e\left(\frac{449}{506}\right)$	$e\left(\frac{455}{506}\right)$	$e\left(\frac{126}{253}\right)$	$e\left(\frac{196}{253}\right)$	$e\left(\frac{62}{253}\right)$	$e\left(\frac{215}{253}\right)$	$e\left(\frac{199}{253}\right)$	$e\left(\frac{39}{506}\right)$	$e\left(\frac{52}{253}\right)$	$e\left(\frac{195}{506}\right)$
$\chi_{8464}(511,\cdot)$	$1$	$1$	$e\left(\frac{423}{506}\right)$	$e\left(\frac{485}{506}\right)$	$e\left(\frac{37}{253}\right)$	$e\left(\frac{170}{253}\right)$	$e\left(\frac{219}{253}\right)$	$e\left(\frac{29}{253}\right)$	$e\left(\frac{201}{253}\right)$	$e\left(\frac{403}{506}\right)$	$e\left(\frac{200}{253}\right)$	$e\left(\frac{497}{506}\right)$
$\chi_{8464}(527,\cdot)$	$1$	$1$	$e\left(\frac{417}{506}\right)$	$e\left(\frac{453}{506}\right)$	$e\left(\frac{250}{253}\right)$	$e\left(\frac{164}{253}\right)$	$e\left(\frac{119}{253}\right)$	$e\left(\frac{25}{253}\right)$	$e\left(\frac{182}{253}\right)$	$e\left(\frac{487}{506}\right)$	$e\left(\frac{59}{253}\right)$	$e\left(\frac{411}{506}\right)$
$\chi_{8464}(543,\cdot)$	$1$	$1$	$e\left(\frac{457}{506}\right)$	$e\left(\frac{329}{506}\right)$	$e\left(\frac{95}{253}\right)$	$e\left(\frac{204}{253}\right)$	$e\left(\frac{111}{253}\right)$	$e\left(\frac{136}{253}\right)$	$e\left(\frac{140}{253}\right)$	$e\left(\frac{433}{506}\right)$	$e\left(\frac{240}{253}\right)$	$e\left(\frac{141}{506}\right)$
$\chi_{8464}(559,\cdot)$	$1$	$1$	$e\left(\frac{183}{506}\right)$	$e\left(\frac{217}{506}\right)$	$e\left(\frac{208}{253}\right)$	$e\left(\frac{183}{253}\right)$	$e\left(\frac{14}{253}\right)$	$e\left(\frac{122}{253}\right)$	$e\left(\frac{200}{253}\right)$	$e\left(\frac{221}{506}\right)$	$e\left(\frac{126}{253}\right)$	$e\left(\frac{93}{506}\right)$
$\chi_{8464}(655,\cdot)$	$1$	$1$	$e\left(\frac{463}{506}\right)$	$e\left(\frac{361}{506}\right)$	$e\left(\frac{135}{253}\right)$	$e\left(\frac{210}{253}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{140}{253}\right)$	$e\left(\frac{159}{253}\right)$	$e\left(\frac{349}{506}\right)$	$e\left(\frac{128}{253}\right)$	$e\left(\frac{227}{506}\right)$
$\chi_{8464}(687,\cdot)$	$1$	$1$	$e\left(\frac{113}{506}\right)$	$e\left(\frac{181}{506}\right)$	$e\left(\frac{163}{253}\right)$	$e\left(\frac{113}{253}\right)$	$e\left(\frac{28}{253}\right)$	$e\left(\frac{244}{253}\right)$	$e\left(\frac{147}{253}\right)$	$e\left(\frac{189}{506}\right)$	$e\left(\frac{252}{253}\right)$	$e\left(\frac{439}{506}\right)$
$\chi_{8464}(751,\cdot)$	$1$	$1$	$e\left(\frac{63}{506}\right)$	$e\left(\frac{83}{506}\right)$	$e\left(\frac{167}{253}\right)$	$e\left(\frac{63}{253}\right)$	$e\left(\frac{38}{253}\right)$	$e\left(\frac{42}{253}\right)$	$e\left(\frac{73}{253}\right)$	$e\left(\frac{383}{506}\right)$	$e\left(\frac{89}{253}\right)$	$e\left(\frac{397}{506}\right)$
$\chi_{8464}(799,\cdot)$	$1$	$1$	$e\left(\frac{189}{506}\right)$	$e\left(\frac{249}{506}\right)$	$e\left(\frac{248}{253}\right)$	$e\left(\frac{189}{253}\right)$	$e\left(\frac{114}{253}\right)$	$e\left(\frac{126}{253}\right)$	$e\left(\frac{219}{253}\right)$	$e\left(\frac{137}{506}\right)$	$e\left(\frac{14}{253}\right)$	$e\left(\frac{179}{506}\right)$
$\chi_{8464}(815,\cdot)$	$1$	$1$	$e\left(\frac{15}{506}\right)$	$e\left(\frac{333}{506}\right)$	$e\left(\frac{100}{253}\right)$	$e\left(\frac{15}{253}\right)$	$e\left(\frac{250}{253}\right)$	$e\left(\frac{10}{253}\right)$	$e\left(\frac{174}{253}\right)$	$e\left(\frac{43}{506}\right)$	$e\left(\frac{226}{253}\right)$	$e\left(\frac{215}{506}\right)$
$\chi_{8464}(847,\cdot)$	$1$	$1$	$e\left(\frac{493}{506}\right)$	$e\left(\frac{15}{506}\right)$	$e\left(\frac{82}{253}\right)$	$e\left(\frac{240}{253}\right)$	$e\left(\frac{205}{253}\right)$	$e\left(\frac{160}{253}\right)$	$e\left(\frac{1}{253}\right)$	$e\left(\frac{435}{506}\right)$	$e\left(\frac{74}{253}\right)$	$e\left(\frac{151}{506}\right)$
$\chi_{8464}(879,\cdot)$	$1$	$1$	$e\left(\frac{489}{506}\right)$	$e\left(\frac{331}{506}\right)$	$e\left(\frac{224}{253}\right)$	$e\left(\frac{236}{253}\right)$	$e\left(\frac{54}{253}\right)$	$e\left(\frac{73}{253}\right)$	$e\left(\frac{157}{253}\right)$	$e\left(\frac{491}{506}\right)$	$e\left(\frac{233}{253}\right)$	$e\left(\frac{431}{506}\right)$
$\chi_{8464}(895,\cdot)$	$1$	$1$	$e\left(\frac{505}{506}\right)$	$e\left(\frac{79}{506}\right)$	$e\left(\frac{162}{253}\right)$	$e\left(\frac{252}{253}\right)$	$e\left(\frac{152}{253}\right)$	$e\left(\frac{168}{253}\right)$	$e\left(\frac{39}{253}\right)$	$e\left(\frac{267}{506}\right)$	$e\left(\frac{103}{253}\right)$	$e\left(\frac{323}{506}\right)$
$\chi_{8464}(911,\cdot)$	$1$	$1$	$e\left(\frac{83}{506}\right)$	$e\left(\frac{21}{506}\right)$	$e\left(\frac{216}{253}\right)$	$e\left(\frac{83}{253}\right)$	$e\left(\frac{34}{253}\right)$	$e\left(\frac{224}{253}\right)$	$e\left(\frac{52}{253}\right)$	$e\left(\frac{103}{506}\right)$	$e\left(\frac{53}{253}\right)$	$e\left(\frac{9}{506}\right)$
$\chi_{8464}(927,\cdot)$	$1$	$1$	$e\left(\frac{447}{506}\right)$	$e\left(\frac{107}{506}\right)$	$e\left(\frac{197}{253}\right)$	$e\left(\frac{194}{253}\right)$	$e\left(\frac{113}{253}\right)$	$e\left(\frac{45}{253}\right)$	$e\left(\frac{24}{253}\right)$	$e\left(\frac{67}{506}\right)$	$e\left(\frac{5}{253}\right)$	$e\left(\frac{335}{506}\right)$
$\chi_{8464}(1023,\cdot)$	$1$	$1$	$e\left(\frac{309}{506}\right)$	$e\left(\frac{383}{506}\right)$	$e\left(\frac{36}{253}\right)$	$e\left(\frac{56}{253}\right)$	$e\left(\frac{90}{253}\right)$	$e\left(\frac{206}{253}\right)$	$e\left(\frac{93}{253}\right)$	$e\left(\frac{481}{506}\right)$	$e\left(\frac{51}{253}\right)$	$e\left(\frac{381}{506}\right)$
$\chi_{8464}(1055,\cdot)$	$1$	$1$	$e\left(\frac{3}{506}\right)$	$e\left(\frac{269}{506}\right)$	$e\left(\frac{20}{253}\right)$	$e\left(\frac{3}{253}\right)$	$e\left(\frac{50}{253}\right)$	$e\left(\frac{2}{253}\right)$	$e\left(\frac{136}{253}\right)$	$e\left(\frac{211}{506}\right)$	$e\left(\frac{197}{253}\right)$	$e\left(\frac{43}{506}\right)$
$\chi_{8464}(1119,\cdot)$	$1$	$1$	$e\left(\frac{85}{506}\right)$	$e\left(\frac{369}{506}\right)$	$e\left(\frac{145}{253}\right)$	$e\left(\frac{85}{253}\right)$	$e\left(\frac{236}{253}\right)$	$e\left(\frac{141}{253}\right)$	$e\left(\frac{227}{253}\right)$	$e\left(\frac{75}{506}\right)$	$e\left(\frac{100}{253}\right)$	$e\left(\frac{375}{506}\right)$
$\chi_{8464}(1167,\cdot)$	$1$	$1$	$e\left(\frac{387}{506}\right)$	$e\left(\frac{293}{506}\right)$	$e\left(\frac{50}{253}\right)$	$e\left(\frac{134}{253}\right)$	$e\left(\frac{125}{253}\right)$	$e\left(\frac{5}{253}\right)$	$e\left(\frac{87}{253}\right)$	$e\left(\frac{401}{506}\right)$	$e\left(\frac{113}{253}\right)$	$e\left(\frac{487}{506}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8464}(15,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{506}\right)\)	\(e\left(\frac{17}{506}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{19}{253}\right)\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{97}{253}\right)\)	\(e\left(\frac{18}{253}\right)\)	\(e\left(\frac{493}{506}\right)\)	\(e\left(\frac{67}{253}\right)\)	\(e\left(\frac{441}{506}\right)\)
\(\chi_{8464}(79,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{455}{506}\right)\)	\(e\left(\frac{487}{506}\right)\)	\(e\left(\frac{166}{253}\right)\)	\(e\left(\frac{202}{253}\right)\)	\(e\left(\frac{162}{253}\right)\)	\(e\left(\frac{219}{253}\right)\)	\(e\left(\frac{218}{253}\right)\)	\(e\left(\frac{461}{506}\right)\)	\(e\left(\frac{193}{253}\right)\)	\(e\left(\frac{281}{506}\right)\)
\(\chi_{8464}(111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{405}{506}\right)\)	\(e\left(\frac{389}{506}\right)\)	\(e\left(\frac{170}{253}\right)\)	\(e\left(\frac{152}{253}\right)\)	\(e\left(\frac{172}{253}\right)\)	\(e\left(\frac{17}{253}\right)\)	\(e\left(\frac{144}{253}\right)\)	\(e\left(\frac{149}{506}\right)\)	\(e\left(\frac{30}{253}\right)\)	\(e\left(\frac{239}{506}\right)\)
\(\chi_{8464}(143,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{357}{506}\right)\)	\(e\left(\frac{133}{506}\right)\)	\(e\left(\frac{103}{253}\right)\)	\(e\left(\frac{104}{253}\right)\)	\(e\left(\frac{131}{253}\right)\)	\(e\left(\frac{238}{253}\right)\)	\(e\left(\frac{245}{253}\right)\)	\(e\left(\frac{315}{506}\right)\)	\(e\left(\frac{167}{253}\right)\)	\(e\left(\frac{57}{506}\right)\)
\(\chi_{8464}(159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{329}{506}\right)\)	\(e\left(\frac{321}{506}\right)\)	\(e\left(\frac{85}{253}\right)\)	\(e\left(\frac{76}{253}\right)\)	\(e\left(\frac{86}{253}\right)\)	\(e\left(\frac{135}{253}\right)\)	\(e\left(\frac{72}{253}\right)\)	\(e\left(\frac{201}{506}\right)\)	\(e\left(\frac{15}{253}\right)\)	\(e\left(\frac{499}{506}\right)\)
\(\chi_{8464}(175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{325}{506}\right)\)	\(e\left(\frac{131}{506}\right)\)	\(e\left(\frac{227}{253}\right)\)	\(e\left(\frac{72}{253}\right)\)	\(e\left(\frac{188}{253}\right)\)	\(e\left(\frac{48}{253}\right)\)	\(e\left(\frac{228}{253}\right)\)	\(e\left(\frac{257}{506}\right)\)	\(e\left(\frac{174}{253}\right)\)	\(e\left(\frac{273}{506}\right)\)
\(\chi_{8464}(191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{425}{506}\right)\)	\(e\left(\frac{327}{506}\right)\)	\(e\left(\frac{219}{253}\right)\)	\(e\left(\frac{172}{253}\right)\)	\(e\left(\frac{168}{253}\right)\)	\(e\left(\frac{199}{253}\right)\)	\(e\left(\frac{123}{253}\right)\)	\(e\left(\frac{375}{506}\right)\)	\(e\left(\frac{247}{253}\right)\)	\(e\left(\frac{357}{506}\right)\)
\(\chi_{8464}(287,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{111}{506}\right)\)	\(e\left(\frac{339}{506}\right)\)	\(e\left(\frac{234}{253}\right)\)	\(e\left(\frac{111}{253}\right)\)	\(e\left(\frac{79}{253}\right)\)	\(e\left(\frac{74}{253}\right)\)	\(e\left(\frac{225}{253}\right)\)	\(e\left(\frac{217}{506}\right)\)	\(e\left(\frac{205}{253}\right)\)	\(e\left(\frac{73}{506}\right)\)
\(\chi_{8464}(319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{223}{506}\right)\)	\(e\left(\frac{93}{506}\right)\)	\(e\left(\frac{53}{253}\right)\)	\(e\left(\frac{223}{253}\right)\)	\(e\left(\frac{6}{253}\right)\)	\(e\left(\frac{233}{253}\right)\)	\(e\left(\frac{158}{253}\right)\)	\(e\left(\frac{167}{506}\right)\)	\(e\left(\frac{54}{253}\right)\)	\(e\left(\frac{329}{506}\right)\)
\(\chi_{8464}(383,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{506}\right)\)	\(e\left(\frac{303}{506}\right)\)	\(e\left(\frac{189}{253}\right)\)	\(e\left(\frac{41}{253}\right)\)	\(e\left(\frac{93}{253}\right)\)	\(e\left(\frac{196}{253}\right)\)	\(e\left(\frac{172}{253}\right)\)	\(e\left(\frac{185}{506}\right)\)	\(e\left(\frac{78}{253}\right)\)	\(e\left(\frac{419}{506}\right)\)
\(\chi_{8464}(431,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{497}{506}\right)\)	\(e\left(\frac{205}{506}\right)\)	\(e\left(\frac{193}{253}\right)\)	\(e\left(\frac{244}{253}\right)\)	\(e\left(\frac{103}{253}\right)\)	\(e\left(\frac{247}{253}\right)\)	\(e\left(\frac{98}{253}\right)\)	\(e\left(\frac{379}{506}\right)\)	\(e\left(\frac{168}{253}\right)\)	\(e\left(\frac{377}{506}\right)\)
\(\chi_{8464}(447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{235}{506}\right)\)	\(e\left(\frac{157}{506}\right)\)	\(e\left(\frac{133}{253}\right)\)	\(e\left(\frac{235}{253}\right)\)	\(e\left(\frac{206}{253}\right)\)	\(e\left(\frac{241}{253}\right)\)	\(e\left(\frac{196}{253}\right)\)	\(e\left(\frac{505}{506}\right)\)	\(e\left(\frac{83}{253}\right)\)	\(e\left(\frac{501}{506}\right)\)
\(\chi_{8464}(479,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{449}{506}\right)\)	\(e\left(\frac{455}{506}\right)\)	\(e\left(\frac{126}{253}\right)\)	\(e\left(\frac{196}{253}\right)\)	\(e\left(\frac{62}{253}\right)\)	\(e\left(\frac{215}{253}\right)\)	\(e\left(\frac{199}{253}\right)\)	\(e\left(\frac{39}{506}\right)\)	\(e\left(\frac{52}{253}\right)\)	\(e\left(\frac{195}{506}\right)\)
\(\chi_{8464}(511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{423}{506}\right)\)	\(e\left(\frac{485}{506}\right)\)	\(e\left(\frac{37}{253}\right)\)	\(e\left(\frac{170}{253}\right)\)	\(e\left(\frac{219}{253}\right)\)	\(e\left(\frac{29}{253}\right)\)	\(e\left(\frac{201}{253}\right)\)	\(e\left(\frac{403}{506}\right)\)	\(e\left(\frac{200}{253}\right)\)	\(e\left(\frac{497}{506}\right)\)
\(\chi_{8464}(527,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{417}{506}\right)\)	\(e\left(\frac{453}{506}\right)\)	\(e\left(\frac{250}{253}\right)\)	\(e\left(\frac{164}{253}\right)\)	\(e\left(\frac{119}{253}\right)\)	\(e\left(\frac{25}{253}\right)\)	\(e\left(\frac{182}{253}\right)\)	\(e\left(\frac{487}{506}\right)\)	\(e\left(\frac{59}{253}\right)\)	\(e\left(\frac{411}{506}\right)\)
\(\chi_{8464}(543,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{457}{506}\right)\)	\(e\left(\frac{329}{506}\right)\)	\(e\left(\frac{95}{253}\right)\)	\(e\left(\frac{204}{253}\right)\)	\(e\left(\frac{111}{253}\right)\)	\(e\left(\frac{136}{253}\right)\)	\(e\left(\frac{140}{253}\right)\)	\(e\left(\frac{433}{506}\right)\)	\(e\left(\frac{240}{253}\right)\)	\(e\left(\frac{141}{506}\right)\)
\(\chi_{8464}(559,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{183}{506}\right)\)	\(e\left(\frac{217}{506}\right)\)	\(e\left(\frac{208}{253}\right)\)	\(e\left(\frac{183}{253}\right)\)	\(e\left(\frac{14}{253}\right)\)	\(e\left(\frac{122}{253}\right)\)	\(e\left(\frac{200}{253}\right)\)	\(e\left(\frac{221}{506}\right)\)	\(e\left(\frac{126}{253}\right)\)	\(e\left(\frac{93}{506}\right)\)
\(\chi_{8464}(655,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{463}{506}\right)\)	\(e\left(\frac{361}{506}\right)\)	\(e\left(\frac{135}{253}\right)\)	\(e\left(\frac{210}{253}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{140}{253}\right)\)	\(e\left(\frac{159}{253}\right)\)	\(e\left(\frac{349}{506}\right)\)	\(e\left(\frac{128}{253}\right)\)	\(e\left(\frac{227}{506}\right)\)
\(\chi_{8464}(687,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{506}\right)\)	\(e\left(\frac{181}{506}\right)\)	\(e\left(\frac{163}{253}\right)\)	\(e\left(\frac{113}{253}\right)\)	\(e\left(\frac{28}{253}\right)\)	\(e\left(\frac{244}{253}\right)\)	\(e\left(\frac{147}{253}\right)\)	\(e\left(\frac{189}{506}\right)\)	\(e\left(\frac{252}{253}\right)\)	\(e\left(\frac{439}{506}\right)\)
\(\chi_{8464}(751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{63}{506}\right)\)	\(e\left(\frac{83}{506}\right)\)	\(e\left(\frac{167}{253}\right)\)	\(e\left(\frac{63}{253}\right)\)	\(e\left(\frac{38}{253}\right)\)	\(e\left(\frac{42}{253}\right)\)	\(e\left(\frac{73}{253}\right)\)	\(e\left(\frac{383}{506}\right)\)	\(e\left(\frac{89}{253}\right)\)	\(e\left(\frac{397}{506}\right)\)
\(\chi_{8464}(799,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{189}{506}\right)\)	\(e\left(\frac{249}{506}\right)\)	\(e\left(\frac{248}{253}\right)\)	\(e\left(\frac{189}{253}\right)\)	\(e\left(\frac{114}{253}\right)\)	\(e\left(\frac{126}{253}\right)\)	\(e\left(\frac{219}{253}\right)\)	\(e\left(\frac{137}{506}\right)\)	\(e\left(\frac{14}{253}\right)\)	\(e\left(\frac{179}{506}\right)\)
\(\chi_{8464}(815,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{506}\right)\)	\(e\left(\frac{333}{506}\right)\)	\(e\left(\frac{100}{253}\right)\)	\(e\left(\frac{15}{253}\right)\)	\(e\left(\frac{250}{253}\right)\)	\(e\left(\frac{10}{253}\right)\)	\(e\left(\frac{174}{253}\right)\)	\(e\left(\frac{43}{506}\right)\)	\(e\left(\frac{226}{253}\right)\)	\(e\left(\frac{215}{506}\right)\)
\(\chi_{8464}(847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{493}{506}\right)\)	\(e\left(\frac{15}{506}\right)\)	\(e\left(\frac{82}{253}\right)\)	\(e\left(\frac{240}{253}\right)\)	\(e\left(\frac{205}{253}\right)\)	\(e\left(\frac{160}{253}\right)\)	\(e\left(\frac{1}{253}\right)\)	\(e\left(\frac{435}{506}\right)\)	\(e\left(\frac{74}{253}\right)\)	\(e\left(\frac{151}{506}\right)\)
\(\chi_{8464}(879,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{489}{506}\right)\)	\(e\left(\frac{331}{506}\right)\)	\(e\left(\frac{224}{253}\right)\)	\(e\left(\frac{236}{253}\right)\)	\(e\left(\frac{54}{253}\right)\)	\(e\left(\frac{73}{253}\right)\)	\(e\left(\frac{157}{253}\right)\)	\(e\left(\frac{491}{506}\right)\)	\(e\left(\frac{233}{253}\right)\)	\(e\left(\frac{431}{506}\right)\)
\(\chi_{8464}(895,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{505}{506}\right)\)	\(e\left(\frac{79}{506}\right)\)	\(e\left(\frac{162}{253}\right)\)	\(e\left(\frac{252}{253}\right)\)	\(e\left(\frac{152}{253}\right)\)	\(e\left(\frac{168}{253}\right)\)	\(e\left(\frac{39}{253}\right)\)	\(e\left(\frac{267}{506}\right)\)	\(e\left(\frac{103}{253}\right)\)	\(e\left(\frac{323}{506}\right)\)
\(\chi_{8464}(911,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{506}\right)\)	\(e\left(\frac{21}{506}\right)\)	\(e\left(\frac{216}{253}\right)\)	\(e\left(\frac{83}{253}\right)\)	\(e\left(\frac{34}{253}\right)\)	\(e\left(\frac{224}{253}\right)\)	\(e\left(\frac{52}{253}\right)\)	\(e\left(\frac{103}{506}\right)\)	\(e\left(\frac{53}{253}\right)\)	\(e\left(\frac{9}{506}\right)\)
\(\chi_{8464}(927,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{447}{506}\right)\)	\(e\left(\frac{107}{506}\right)\)	\(e\left(\frac{197}{253}\right)\)	\(e\left(\frac{194}{253}\right)\)	\(e\left(\frac{113}{253}\right)\)	\(e\left(\frac{45}{253}\right)\)	\(e\left(\frac{24}{253}\right)\)	\(e\left(\frac{67}{506}\right)\)	\(e\left(\frac{5}{253}\right)\)	\(e\left(\frac{335}{506}\right)\)
\(\chi_{8464}(1023,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{309}{506}\right)\)	\(e\left(\frac{383}{506}\right)\)	\(e\left(\frac{36}{253}\right)\)	\(e\left(\frac{56}{253}\right)\)	\(e\left(\frac{90}{253}\right)\)	\(e\left(\frac{206}{253}\right)\)	\(e\left(\frac{93}{253}\right)\)	\(e\left(\frac{481}{506}\right)\)	\(e\left(\frac{51}{253}\right)\)	\(e\left(\frac{381}{506}\right)\)
\(\chi_{8464}(1055,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{506}\right)\)	\(e\left(\frac{269}{506}\right)\)	\(e\left(\frac{20}{253}\right)\)	\(e\left(\frac{3}{253}\right)\)	\(e\left(\frac{50}{253}\right)\)	\(e\left(\frac{2}{253}\right)\)	\(e\left(\frac{136}{253}\right)\)	\(e\left(\frac{211}{506}\right)\)	\(e\left(\frac{197}{253}\right)\)	\(e\left(\frac{43}{506}\right)\)
\(\chi_{8464}(1119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{506}\right)\)	\(e\left(\frac{369}{506}\right)\)	\(e\left(\frac{145}{253}\right)\)	\(e\left(\frac{85}{253}\right)\)	\(e\left(\frac{236}{253}\right)\)	\(e\left(\frac{141}{253}\right)\)	\(e\left(\frac{227}{253}\right)\)	\(e\left(\frac{75}{506}\right)\)	\(e\left(\frac{100}{253}\right)\)	\(e\left(\frac{375}{506}\right)\)
\(\chi_{8464}(1167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{387}{506}\right)\)	\(e\left(\frac{293}{506}\right)\)	\(e\left(\frac{50}{253}\right)\)	\(e\left(\frac{134}{253}\right)\)	\(e\left(\frac{125}{253}\right)\)	\(e\left(\frac{5}{253}\right)\)	\(e\left(\frac{87}{253}\right)\)	\(e\left(\frac{401}{506}\right)\)	\(e\left(\frac{113}{253}\right)\)	\(e\left(\frac{487}{506}\right)\)

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First 31 of 220 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.bm
Modulus	$8464$
Conductor	$2116$
Order	$506$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(8464\)
Conductor:	\(2116\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(506\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 2116.n	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)