LMFDB - Dirichlet character orbit 8464.bl

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8464, base_ring=CyclotomicField(506)) M = H._module chi = DirichletCharacter(H, M([0,253,32])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(9,8464)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8464$
Conductor:	$4232$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$506$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4232.z	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8464}(9,\cdot)$	$1$	$1$	$e\left(\frac{259}{506}\right)$	$e\left(\frac{285}{506}\right)$	$e\left(\frac{40}{253}\right)$	$e\left(\frac{6}{253}\right)$	$e\left(\frac{453}{506}\right)$	$e\left(\frac{261}{506}\right)$	$e\left(\frac{19}{253}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{29}{506}\right)$	$e\left(\frac{339}{506}\right)$
$\chi_{8464}(25,\cdot)$	$1$	$1$	$e\left(\frac{285}{506}\right)$	$e\left(\frac{255}{506}\right)$	$e\left(\frac{129}{253}\right)$	$e\left(\frac{32}{253}\right)$	$e\left(\frac{139}{506}\right)$	$e\left(\frac{127}{506}\right)$	$e\left(\frac{17}{253}\right)$	$e\left(\frac{29}{253}\right)$	$e\left(\frac{239}{506}\right)$	$e\left(\frac{37}{506}\right)$
$\chi_{8464}(41,\cdot)$	$1$	$1$	$e\left(\frac{71}{506}\right)$	$e\left(\frac{463}{506}\right)$	$e\left(\frac{136}{253}\right)$	$e\left(\frac{71}{253}\right)$	$e\left(\frac{427}{506}\right)$	$e\left(\frac{179}{506}\right)$	$e\left(\frac{14}{253}\right)$	$e\left(\frac{9}{253}\right)$	$e\left(\frac{301}{506}\right)$	$e\left(\frac{343}{506}\right)$
$\chi_{8464}(73,\cdot)$	$1$	$1$	$e\left(\frac{383}{506}\right)$	$e\left(\frac{103}{506}\right)$	$e\left(\frac{192}{253}\right)$	$e\left(\frac{130}{253}\right)$	$e\left(\frac{201}{506}\right)$	$e\left(\frac{89}{506}\right)$	$e\left(\frac{243}{253}\right)$	$e\left(\frac{102}{253}\right)$	$e\left(\frac{291}{506}\right)$	$e\left(\frac{261}{506}\right)$
$\chi_{8464}(105,\cdot)$	$1$	$1$	$e\left(\frac{59}{506}\right)$	$e\left(\frac{399}{506}\right)$	$e\left(\frac{56}{253}\right)$	$e\left(\frac{59}{253}\right)$	$e\left(\frac{27}{506}\right)$	$e\left(\frac{163}{506}\right)$	$e\left(\frac{229}{253}\right)$	$e\left(\frac{93}{253}\right)$	$e\left(\frac{243}{506}\right)$	$e\left(\frac{171}{506}\right)$
$\chi_{8464}(121,\cdot)$	$1$	$1$	$e\left(\frac{453}{506}\right)$	$e\left(\frac{139}{506}\right)$	$e\left(\frac{237}{253}\right)$	$e\left(\frac{200}{253}\right)$	$e\left(\frac{173}{506}\right)$	$e\left(\frac{351}{506}\right)$	$e\left(\frac{43}{253}\right)$	$e\left(\frac{118}{253}\right)$	$e\left(\frac{39}{506}\right)$	$e\left(\frac{421}{506}\right)$
$\chi_{8464}(169,\cdot)$	$1$	$1$	$e\left(\frac{261}{506}\right)$	$e\left(\frac{127}{506}\right)$	$e\left(\frac{222}{253}\right)$	$e\left(\frac{8}{253}\right)$	$e\left(\frac{351}{506}\right)$	$e\left(\frac{95}{506}\right)$	$e\left(\frac{194}{253}\right)$	$e\left(\frac{197}{253}\right)$	$e\left(\frac{123}{506}\right)$	$e\left(\frac{199}{506}\right)$
$\chi_{8464}(233,\cdot)$	$1$	$1$	$e\left(\frac{135}{506}\right)$	$e\left(\frac{467}{506}\right)$	$e\left(\frac{141}{253}\right)$	$e\left(\frac{135}{253}\right)$	$e\left(\frac{199}{506}\right)$	$e\left(\frac{433}{506}\right)$	$e\left(\frac{48}{253}\right)$	$e\left(\frac{67}{253}\right)$	$e\left(\frac{273}{506}\right)$	$e\left(\frac{417}{506}\right)$
$\chi_{8464}(265,\cdot)$	$1$	$1$	$e\left(\frac{89}{506}\right)$	$e\left(\frac{53}{506}\right)$	$e\left(\frac{3}{253}\right)$	$e\left(\frac{89}{253}\right)$	$e\left(\frac{15}{506}\right)$	$e\left(\frac{203}{506}\right)$	$e\left(\frac{71}{253}\right)$	$e\left(\frac{136}{253}\right)$	$e\left(\frac{135}{506}\right)$	$e\left(\frac{95}{506}\right)$
$\chi_{8464}(361,\cdot)$	$1$	$1$	$e\left(\frac{29}{506}\right)$	$e\left(\frac{239}{506}\right)$	$e\left(\frac{109}{253}\right)$	$e\left(\frac{29}{253}\right)$	$e\left(\frac{39}{506}\right)$	$e\left(\frac{123}{506}\right)$	$e\left(\frac{134}{253}\right)$	$e\left(\frac{50}{253}\right)$	$e\left(\frac{351}{506}\right)$	$e\left(\frac{247}{506}\right)$
$\chi_{8464}(377,\cdot)$	$1$	$1$	$e\left(\frac{127}{506}\right)$	$e\left(\frac{87}{506}\right)$	$e\left(\frac{172}{253}\right)$	$e\left(\frac{127}{253}\right)$	$e\left(\frac{101}{506}\right)$	$e\left(\frac{85}{506}\right)$	$e\left(\frac{107}{253}\right)$	$e\left(\frac{123}{253}\right)$	$e\left(\frac{403}{506}\right)$	$e\left(\frac{471}{506}\right)$
$\chi_{8464}(393,\cdot)$	$1$	$1$	$e\left(\frac{197}{506}\right)$	$e\left(\frac{123}{506}\right)$	$e\left(\frac{217}{253}\right)$	$e\left(\frac{197}{253}\right)$	$e\left(\frac{73}{506}\right)$	$e\left(\frac{347}{506}\right)$	$e\left(\frac{160}{253}\right)$	$e\left(\frac{139}{253}\right)$	$e\left(\frac{151}{506}\right)$	$e\left(\frac{125}{506}\right)$
$\chi_{8464}(409,\cdot)$	$1$	$1$	$e\left(\frac{5}{506}\right)$	$e\left(\frac{111}{506}\right)$	$e\left(\frac{202}{253}\right)$	$e\left(\frac{5}{253}\right)$	$e\left(\frac{251}{506}\right)$	$e\left(\frac{91}{506}\right)$	$e\left(\frac{58}{253}\right)$	$e\left(\frac{218}{253}\right)$	$e\left(\frac{235}{506}\right)$	$e\left(\frac{409}{506}\right)$
$\chi_{8464}(441,\cdot)$	$1$	$1$	$e\left(\frac{339}{506}\right)$	$e\left(\frac{37}{506}\right)$	$e\left(\frac{236}{253}\right)$	$e\left(\frac{86}{253}\right)$	$e\left(\frac{421}{506}\right)$	$e\left(\frac{199}{506}\right)$	$e\left(\frac{188}{253}\right)$	$e\left(\frac{157}{253}\right)$	$e\left(\frac{247}{506}\right)$	$e\left(\frac{305}{506}\right)$
$\chi_{8464}(473,\cdot)$	$1$	$1$	$e\left(\frac{279}{506}\right)$	$e\left(\frac{223}{506}\right)$	$e\left(\frac{89}{253}\right)$	$e\left(\frac{26}{253}\right)$	$e\left(\frac{445}{506}\right)$	$e\left(\frac{119}{506}\right)$	$e\left(\frac{251}{253}\right)$	$e\left(\frac{71}{253}\right)$	$e\left(\frac{463}{506}\right)$	$e\left(\frac{457}{506}\right)$
$\chi_{8464}(489,\cdot)$	$1$	$1$	$e\left(\frac{255}{506}\right)$	$e\left(\frac{95}{506}\right)$	$e\left(\frac{182}{253}\right)$	$e\left(\frac{2}{253}\right)$	$e\left(\frac{151}{506}\right)$	$e\left(\frac{87}{506}\right)$	$e\left(\frac{175}{253}\right)$	$e\left(\frac{239}{253}\right)$	$e\left(\frac{347}{506}\right)$	$e\left(\frac{113}{506}\right)$
$\chi_{8464}(537,\cdot)$	$1$	$1$	$e\left(\frac{239}{506}\right)$	$e\left(\frac{347}{506}\right)$	$e\left(\frac{244}{253}\right)$	$e\left(\frac{239}{253}\right)$	$e\left(\frac{461}{506}\right)$	$e\left(\frac{403}{506}\right)$	$e\left(\frac{40}{253}\right)$	$e\left(\frac{98}{253}\right)$	$e\left(\frac{101}{506}\right)$	$e\left(\frac{221}{506}\right)$
$\chi_{8464}(601,\cdot)$	$1$	$1$	$e\left(\frac{245}{506}\right)$	$e\left(\frac{379}{506}\right)$	$e\left(\frac{31}{253}\right)$	$e\left(\frac{245}{253}\right)$	$e\left(\frac{155}{506}\right)$	$e\left(\frac{411}{506}\right)$	$e\left(\frac{59}{253}\right)$	$e\left(\frac{56}{253}\right)$	$e\left(\frac{383}{506}\right)$	$e\left(\frac{307}{506}\right)$
$\chi_{8464}(633,\cdot)$	$1$	$1$	$e\left(\frac{243}{506}\right)$	$e\left(\frac{31}{506}\right)$	$e\left(\frac{102}{253}\right)$	$e\left(\frac{243}{253}\right)$	$e\left(\frac{257}{506}\right)$	$e\left(\frac{71}{506}\right)$	$e\left(\frac{137}{253}\right)$	$e\left(\frac{70}{253}\right)$	$e\left(\frac{289}{506}\right)$	$e\left(\frac{447}{506}\right)$
$\chi_{8464}(729,\cdot)$	$1$	$1$	$e\left(\frac{271}{506}\right)$	$e\left(\frac{349}{506}\right)$	$e\left(\frac{120}{253}\right)$	$e\left(\frac{18}{253}\right)$	$e\left(\frac{347}{506}\right)$	$e\left(\frac{277}{506}\right)$	$e\left(\frac{57}{253}\right)$	$e\left(\frac{127}{253}\right)$	$e\left(\frac{87}{506}\right)$	$e\left(\frac{5}{506}\right)$
$\chi_{8464}(745,\cdot)$	$1$	$1$	$e\left(\frac{501}{506}\right)$	$e\left(\frac{395}{506}\right)$	$e\left(\frac{51}{253}\right)$	$e\left(\frac{248}{253}\right)$	$e\left(\frac{255}{506}\right)$	$e\left(\frac{415}{506}\right)$	$e\left(\frac{195}{253}\right)$	$e\left(\frac{35}{253}\right)$	$e\left(\frac{271}{506}\right)$	$e\left(\frac{97}{506}\right)$
$\chi_{8464}(761,\cdot)$	$1$	$1$	$e\left(\frac{109}{506}\right)$	$e\left(\frac{497}{506}\right)$	$e\left(\frac{52}{253}\right)$	$e\left(\frac{109}{253}\right)$	$e\left(\frac{7}{506}\right)$	$e\left(\frac{61}{506}\right)$	$e\left(\frac{50}{253}\right)$	$e\left(\frac{249}{253}\right)$	$e\left(\frac{63}{506}\right)$	$e\left(\frac{213}{506}\right)$
$\chi_{8464}(777,\cdot)$	$1$	$1$	$e\left(\frac{445}{506}\right)$	$e\left(\frac{265}{506}\right)$	$e\left(\frac{15}{253}\right)$	$e\left(\frac{192}{253}\right)$	$e\left(\frac{75}{506}\right)$	$e\left(\frac{3}{506}\right)$	$e\left(\frac{102}{253}\right)$	$e\left(\frac{174}{253}\right)$	$e\left(\frac{169}{506}\right)$	$e\left(\frac{475}{506}\right)$
$\chi_{8464}(809,\cdot)$	$1$	$1$	$e\left(\frac{295}{506}\right)$	$e\left(\frac{477}{506}\right)$	$e\left(\frac{27}{253}\right)$	$e\left(\frac{42}{253}\right)$	$e\left(\frac{135}{506}\right)$	$e\left(\frac{309}{506}\right)$	$e\left(\frac{133}{253}\right)$	$e\left(\frac{212}{253}\right)$	$e\left(\frac{203}{506}\right)$	$e\left(\frac{349}{506}\right)$
$\chi_{8464}(841,\cdot)$	$1$	$1$	$e\left(\frac{499}{506}\right)$	$e\left(\frac{47}{506}\right)$	$e\left(\frac{122}{253}\right)$	$e\left(\frac{246}{253}\right)$	$e\left(\frac{357}{506}\right)$	$e\left(\frac{75}{506}\right)$	$e\left(\frac{20}{253}\right)$	$e\left(\frac{49}{253}\right)$	$e\left(\frac{177}{506}\right)$	$e\left(\frac{237}{506}\right)$
$\chi_{8464}(857,\cdot)$	$1$	$1$	$e\left(\frac{57}{506}\right)$	$e\left(\frac{51}{506}\right)$	$e\left(\frac{127}{253}\right)$	$e\left(\frac{57}{253}\right)$	$e\left(\frac{129}{506}\right)$	$e\left(\frac{329}{506}\right)$	$e\left(\frac{54}{253}\right)$	$e\left(\frac{107}{253}\right)$	$e\left(\frac{149}{506}\right)$	$e\left(\frac{311}{506}\right)$
$\chi_{8464}(905,\cdot)$	$1$	$1$	$e\left(\frac{217}{506}\right)$	$e\left(\frac{61}{506}\right)$	$e\left(\frac{13}{253}\right)$	$e\left(\frac{217}{253}\right)$	$e\left(\frac{65}{506}\right)$	$e\left(\frac{205}{506}\right)$	$e\left(\frac{139}{253}\right)$	$e\left(\frac{252}{253}\right)$	$e\left(\frac{79}{506}\right)$	$e\left(\frac{243}{506}\right)$
$\chi_{8464}(969,\cdot)$	$1$	$1$	$e\left(\frac{355}{506}\right)$	$e\left(\frac{291}{506}\right)$	$e\left(\frac{174}{253}\right)$	$e\left(\frac{102}{253}\right)$	$e\left(\frac{111}{506}\right)$	$e\left(\frac{389}{506}\right)$	$e\left(\frac{70}{253}\right)$	$e\left(\frac{45}{253}\right)$	$e\left(\frac{493}{506}\right)$	$e\left(\frac{197}{506}\right)$
$\chi_{8464}(1001,\cdot)$	$1$	$1$	$e\left(\frac{397}{506}\right)$	$e\left(\frac{9}{506}\right)$	$e\left(\frac{201}{253}\right)$	$e\left(\frac{144}{253}\right)$	$e\left(\frac{499}{506}\right)$	$e\left(\frac{445}{506}\right)$	$e\left(\frac{203}{253}\right)$	$e\left(\frac{4}{253}\right)$	$e\left(\frac{443}{506}\right)$	$e\left(\frac{293}{506}\right)$
$\chi_{8464}(1097,\cdot)$	$1$	$1$	$e\left(\frac{7}{506}\right)$	$e\left(\frac{459}{506}\right)$	$e\left(\frac{131}{253}\right)$	$e\left(\frac{7}{253}\right)$	$e\left(\frac{149}{506}\right)$	$e\left(\frac{431}{506}\right)$	$e\left(\frac{233}{253}\right)$	$e\left(\frac{204}{253}\right)$	$e\left(\frac{329}{506}\right)$	$e\left(\frac{269}{506}\right)$
$\chi_{8464}(1113,\cdot)$	$1$	$1$	$e\left(\frac{369}{506}\right)$	$e\left(\frac{197}{506}\right)$	$e\left(\frac{183}{253}\right)$	$e\left(\frac{116}{253}\right)$	$e\left(\frac{409}{506}\right)$	$e\left(\frac{239}{506}\right)$	$e\left(\frac{30}{253}\right)$	$e\left(\frac{200}{253}\right)$	$e\left(\frac{139}{506}\right)$	$e\left(\frac{229}{506}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8464}(9,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{259}{506}\right)\)	\(e\left(\frac{285}{506}\right)\)	\(e\left(\frac{40}{253}\right)\)	\(e\left(\frac{6}{253}\right)\)	\(e\left(\frac{453}{506}\right)\)	\(e\left(\frac{261}{506}\right)\)	\(e\left(\frac{19}{253}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{29}{506}\right)\)	\(e\left(\frac{339}{506}\right)\)
\(\chi_{8464}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{285}{506}\right)\)	\(e\left(\frac{255}{506}\right)\)	\(e\left(\frac{129}{253}\right)\)	\(e\left(\frac{32}{253}\right)\)	\(e\left(\frac{139}{506}\right)\)	\(e\left(\frac{127}{506}\right)\)	\(e\left(\frac{17}{253}\right)\)	\(e\left(\frac{29}{253}\right)\)	\(e\left(\frac{239}{506}\right)\)	\(e\left(\frac{37}{506}\right)\)
\(\chi_{8464}(41,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{506}\right)\)	\(e\left(\frac{463}{506}\right)\)	\(e\left(\frac{136}{253}\right)\)	\(e\left(\frac{71}{253}\right)\)	\(e\left(\frac{427}{506}\right)\)	\(e\left(\frac{179}{506}\right)\)	\(e\left(\frac{14}{253}\right)\)	\(e\left(\frac{9}{253}\right)\)	\(e\left(\frac{301}{506}\right)\)	\(e\left(\frac{343}{506}\right)\)
\(\chi_{8464}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{383}{506}\right)\)	\(e\left(\frac{103}{506}\right)\)	\(e\left(\frac{192}{253}\right)\)	\(e\left(\frac{130}{253}\right)\)	\(e\left(\frac{201}{506}\right)\)	\(e\left(\frac{89}{506}\right)\)	\(e\left(\frac{243}{253}\right)\)	\(e\left(\frac{102}{253}\right)\)	\(e\left(\frac{291}{506}\right)\)	\(e\left(\frac{261}{506}\right)\)
\(\chi_{8464}(105,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{506}\right)\)	\(e\left(\frac{399}{506}\right)\)	\(e\left(\frac{56}{253}\right)\)	\(e\left(\frac{59}{253}\right)\)	\(e\left(\frac{27}{506}\right)\)	\(e\left(\frac{163}{506}\right)\)	\(e\left(\frac{229}{253}\right)\)	\(e\left(\frac{93}{253}\right)\)	\(e\left(\frac{243}{506}\right)\)	\(e\left(\frac{171}{506}\right)\)
\(\chi_{8464}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{453}{506}\right)\)	\(e\left(\frac{139}{506}\right)\)	\(e\left(\frac{237}{253}\right)\)	\(e\left(\frac{200}{253}\right)\)	\(e\left(\frac{173}{506}\right)\)	\(e\left(\frac{351}{506}\right)\)	\(e\left(\frac{43}{253}\right)\)	\(e\left(\frac{118}{253}\right)\)	\(e\left(\frac{39}{506}\right)\)	\(e\left(\frac{421}{506}\right)\)
\(\chi_{8464}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{261}{506}\right)\)	\(e\left(\frac{127}{506}\right)\)	\(e\left(\frac{222}{253}\right)\)	\(e\left(\frac{8}{253}\right)\)	\(e\left(\frac{351}{506}\right)\)	\(e\left(\frac{95}{506}\right)\)	\(e\left(\frac{194}{253}\right)\)	\(e\left(\frac{197}{253}\right)\)	\(e\left(\frac{123}{506}\right)\)	\(e\left(\frac{199}{506}\right)\)
\(\chi_{8464}(233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{135}{506}\right)\)	\(e\left(\frac{467}{506}\right)\)	\(e\left(\frac{141}{253}\right)\)	\(e\left(\frac{135}{253}\right)\)	\(e\left(\frac{199}{506}\right)\)	\(e\left(\frac{433}{506}\right)\)	\(e\left(\frac{48}{253}\right)\)	\(e\left(\frac{67}{253}\right)\)	\(e\left(\frac{273}{506}\right)\)	\(e\left(\frac{417}{506}\right)\)
\(\chi_{8464}(265,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{506}\right)\)	\(e\left(\frac{53}{506}\right)\)	\(e\left(\frac{3}{253}\right)\)	\(e\left(\frac{89}{253}\right)\)	\(e\left(\frac{15}{506}\right)\)	\(e\left(\frac{203}{506}\right)\)	\(e\left(\frac{71}{253}\right)\)	\(e\left(\frac{136}{253}\right)\)	\(e\left(\frac{135}{506}\right)\)	\(e\left(\frac{95}{506}\right)\)
\(\chi_{8464}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{506}\right)\)	\(e\left(\frac{239}{506}\right)\)	\(e\left(\frac{109}{253}\right)\)	\(e\left(\frac{29}{253}\right)\)	\(e\left(\frac{39}{506}\right)\)	\(e\left(\frac{123}{506}\right)\)	\(e\left(\frac{134}{253}\right)\)	\(e\left(\frac{50}{253}\right)\)	\(e\left(\frac{351}{506}\right)\)	\(e\left(\frac{247}{506}\right)\)
\(\chi_{8464}(377,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{506}\right)\)	\(e\left(\frac{87}{506}\right)\)	\(e\left(\frac{172}{253}\right)\)	\(e\left(\frac{127}{253}\right)\)	\(e\left(\frac{101}{506}\right)\)	\(e\left(\frac{85}{506}\right)\)	\(e\left(\frac{107}{253}\right)\)	\(e\left(\frac{123}{253}\right)\)	\(e\left(\frac{403}{506}\right)\)	\(e\left(\frac{471}{506}\right)\)
\(\chi_{8464}(393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{506}\right)\)	\(e\left(\frac{123}{506}\right)\)	\(e\left(\frac{217}{253}\right)\)	\(e\left(\frac{197}{253}\right)\)	\(e\left(\frac{73}{506}\right)\)	\(e\left(\frac{347}{506}\right)\)	\(e\left(\frac{160}{253}\right)\)	\(e\left(\frac{139}{253}\right)\)	\(e\left(\frac{151}{506}\right)\)	\(e\left(\frac{125}{506}\right)\)
\(\chi_{8464}(409,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{506}\right)\)	\(e\left(\frac{111}{506}\right)\)	\(e\left(\frac{202}{253}\right)\)	\(e\left(\frac{5}{253}\right)\)	\(e\left(\frac{251}{506}\right)\)	\(e\left(\frac{91}{506}\right)\)	\(e\left(\frac{58}{253}\right)\)	\(e\left(\frac{218}{253}\right)\)	\(e\left(\frac{235}{506}\right)\)	\(e\left(\frac{409}{506}\right)\)
\(\chi_{8464}(441,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{339}{506}\right)\)	\(e\left(\frac{37}{506}\right)\)	\(e\left(\frac{236}{253}\right)\)	\(e\left(\frac{86}{253}\right)\)	\(e\left(\frac{421}{506}\right)\)	\(e\left(\frac{199}{506}\right)\)	\(e\left(\frac{188}{253}\right)\)	\(e\left(\frac{157}{253}\right)\)	\(e\left(\frac{247}{506}\right)\)	\(e\left(\frac{305}{506}\right)\)
\(\chi_{8464}(473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{279}{506}\right)\)	\(e\left(\frac{223}{506}\right)\)	\(e\left(\frac{89}{253}\right)\)	\(e\left(\frac{26}{253}\right)\)	\(e\left(\frac{445}{506}\right)\)	\(e\left(\frac{119}{506}\right)\)	\(e\left(\frac{251}{253}\right)\)	\(e\left(\frac{71}{253}\right)\)	\(e\left(\frac{463}{506}\right)\)	\(e\left(\frac{457}{506}\right)\)
\(\chi_{8464}(489,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{255}{506}\right)\)	\(e\left(\frac{95}{506}\right)\)	\(e\left(\frac{182}{253}\right)\)	\(e\left(\frac{2}{253}\right)\)	\(e\left(\frac{151}{506}\right)\)	\(e\left(\frac{87}{506}\right)\)	\(e\left(\frac{175}{253}\right)\)	\(e\left(\frac{239}{253}\right)\)	\(e\left(\frac{347}{506}\right)\)	\(e\left(\frac{113}{506}\right)\)
\(\chi_{8464}(537,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{506}\right)\)	\(e\left(\frac{347}{506}\right)\)	\(e\left(\frac{244}{253}\right)\)	\(e\left(\frac{239}{253}\right)\)	\(e\left(\frac{461}{506}\right)\)	\(e\left(\frac{403}{506}\right)\)	\(e\left(\frac{40}{253}\right)\)	\(e\left(\frac{98}{253}\right)\)	\(e\left(\frac{101}{506}\right)\)	\(e\left(\frac{221}{506}\right)\)
\(\chi_{8464}(601,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{245}{506}\right)\)	\(e\left(\frac{379}{506}\right)\)	\(e\left(\frac{31}{253}\right)\)	\(e\left(\frac{245}{253}\right)\)	\(e\left(\frac{155}{506}\right)\)	\(e\left(\frac{411}{506}\right)\)	\(e\left(\frac{59}{253}\right)\)	\(e\left(\frac{56}{253}\right)\)	\(e\left(\frac{383}{506}\right)\)	\(e\left(\frac{307}{506}\right)\)
\(\chi_{8464}(633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{243}{506}\right)\)	\(e\left(\frac{31}{506}\right)\)	\(e\left(\frac{102}{253}\right)\)	\(e\left(\frac{243}{253}\right)\)	\(e\left(\frac{257}{506}\right)\)	\(e\left(\frac{71}{506}\right)\)	\(e\left(\frac{137}{253}\right)\)	\(e\left(\frac{70}{253}\right)\)	\(e\left(\frac{289}{506}\right)\)	\(e\left(\frac{447}{506}\right)\)
\(\chi_{8464}(729,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{271}{506}\right)\)	\(e\left(\frac{349}{506}\right)\)	\(e\left(\frac{120}{253}\right)\)	\(e\left(\frac{18}{253}\right)\)	\(e\left(\frac{347}{506}\right)\)	\(e\left(\frac{277}{506}\right)\)	\(e\left(\frac{57}{253}\right)\)	\(e\left(\frac{127}{253}\right)\)	\(e\left(\frac{87}{506}\right)\)	\(e\left(\frac{5}{506}\right)\)
\(\chi_{8464}(745,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{501}{506}\right)\)	\(e\left(\frac{395}{506}\right)\)	\(e\left(\frac{51}{253}\right)\)	\(e\left(\frac{248}{253}\right)\)	\(e\left(\frac{255}{506}\right)\)	\(e\left(\frac{415}{506}\right)\)	\(e\left(\frac{195}{253}\right)\)	\(e\left(\frac{35}{253}\right)\)	\(e\left(\frac{271}{506}\right)\)	\(e\left(\frac{97}{506}\right)\)
\(\chi_{8464}(761,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{506}\right)\)	\(e\left(\frac{497}{506}\right)\)	\(e\left(\frac{52}{253}\right)\)	\(e\left(\frac{109}{253}\right)\)	\(e\left(\frac{7}{506}\right)\)	\(e\left(\frac{61}{506}\right)\)	\(e\left(\frac{50}{253}\right)\)	\(e\left(\frac{249}{253}\right)\)	\(e\left(\frac{63}{506}\right)\)	\(e\left(\frac{213}{506}\right)\)
\(\chi_{8464}(777,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{445}{506}\right)\)	\(e\left(\frac{265}{506}\right)\)	\(e\left(\frac{15}{253}\right)\)	\(e\left(\frac{192}{253}\right)\)	\(e\left(\frac{75}{506}\right)\)	\(e\left(\frac{3}{506}\right)\)	\(e\left(\frac{102}{253}\right)\)	\(e\left(\frac{174}{253}\right)\)	\(e\left(\frac{169}{506}\right)\)	\(e\left(\frac{475}{506}\right)\)
\(\chi_{8464}(809,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{295}{506}\right)\)	\(e\left(\frac{477}{506}\right)\)	\(e\left(\frac{27}{253}\right)\)	\(e\left(\frac{42}{253}\right)\)	\(e\left(\frac{135}{506}\right)\)	\(e\left(\frac{309}{506}\right)\)	\(e\left(\frac{133}{253}\right)\)	\(e\left(\frac{212}{253}\right)\)	\(e\left(\frac{203}{506}\right)\)	\(e\left(\frac{349}{506}\right)\)
\(\chi_{8464}(841,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{499}{506}\right)\)	\(e\left(\frac{47}{506}\right)\)	\(e\left(\frac{122}{253}\right)\)	\(e\left(\frac{246}{253}\right)\)	\(e\left(\frac{357}{506}\right)\)	\(e\left(\frac{75}{506}\right)\)	\(e\left(\frac{20}{253}\right)\)	\(e\left(\frac{49}{253}\right)\)	\(e\left(\frac{177}{506}\right)\)	\(e\left(\frac{237}{506}\right)\)
\(\chi_{8464}(857,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{506}\right)\)	\(e\left(\frac{51}{506}\right)\)	\(e\left(\frac{127}{253}\right)\)	\(e\left(\frac{57}{253}\right)\)	\(e\left(\frac{129}{506}\right)\)	\(e\left(\frac{329}{506}\right)\)	\(e\left(\frac{54}{253}\right)\)	\(e\left(\frac{107}{253}\right)\)	\(e\left(\frac{149}{506}\right)\)	\(e\left(\frac{311}{506}\right)\)
\(\chi_{8464}(905,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{217}{506}\right)\)	\(e\left(\frac{61}{506}\right)\)	\(e\left(\frac{13}{253}\right)\)	\(e\left(\frac{217}{253}\right)\)	\(e\left(\frac{65}{506}\right)\)	\(e\left(\frac{205}{506}\right)\)	\(e\left(\frac{139}{253}\right)\)	\(e\left(\frac{252}{253}\right)\)	\(e\left(\frac{79}{506}\right)\)	\(e\left(\frac{243}{506}\right)\)
\(\chi_{8464}(969,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{355}{506}\right)\)	\(e\left(\frac{291}{506}\right)\)	\(e\left(\frac{174}{253}\right)\)	\(e\left(\frac{102}{253}\right)\)	\(e\left(\frac{111}{506}\right)\)	\(e\left(\frac{389}{506}\right)\)	\(e\left(\frac{70}{253}\right)\)	\(e\left(\frac{45}{253}\right)\)	\(e\left(\frac{493}{506}\right)\)	\(e\left(\frac{197}{506}\right)\)
\(\chi_{8464}(1001,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{397}{506}\right)\)	\(e\left(\frac{9}{506}\right)\)	\(e\left(\frac{201}{253}\right)\)	\(e\left(\frac{144}{253}\right)\)	\(e\left(\frac{499}{506}\right)\)	\(e\left(\frac{445}{506}\right)\)	\(e\left(\frac{203}{253}\right)\)	\(e\left(\frac{4}{253}\right)\)	\(e\left(\frac{443}{506}\right)\)	\(e\left(\frac{293}{506}\right)\)
\(\chi_{8464}(1097,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{506}\right)\)	\(e\left(\frac{459}{506}\right)\)	\(e\left(\frac{131}{253}\right)\)	\(e\left(\frac{7}{253}\right)\)	\(e\left(\frac{149}{506}\right)\)	\(e\left(\frac{431}{506}\right)\)	\(e\left(\frac{233}{253}\right)\)	\(e\left(\frac{204}{253}\right)\)	\(e\left(\frac{329}{506}\right)\)	\(e\left(\frac{269}{506}\right)\)
\(\chi_{8464}(1113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{369}{506}\right)\)	\(e\left(\frac{197}{506}\right)\)	\(e\left(\frac{183}{253}\right)\)	\(e\left(\frac{116}{253}\right)\)	\(e\left(\frac{409}{506}\right)\)	\(e\left(\frac{239}{506}\right)\)	\(e\left(\frac{30}{253}\right)\)	\(e\left(\frac{200}{253}\right)\)	\(e\left(\frac{139}{506}\right)\)	\(e\left(\frac{229}{506}\right)\)

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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.bl
Modulus	$8464$
Conductor	$4232$
Order	$506$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(8464\)
Conductor:	\(4232\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(506\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4232.z	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)