LMFDB - Dirichlet character orbit 8464.bk

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8464, base_ring=CyclotomicField(506)) M = H._module chi = DirichletCharacter(H, M([0,0,258])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(49,8464)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8464$
Conductor:	$529$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$253$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 529.g	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 253 polynomial (not computed)

First 31 of 220 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8464}(49,\cdot)$	$1$	$1$	$e\left(\frac{40}{253}\right)$	$e\left(\frac{129}{253}\right)$	$e\left(\frac{196}{253}\right)$	$e\left(\frac{80}{253}\right)$	$e\left(\frac{237}{253}\right)$	$e\left(\frac{222}{253}\right)$	$e\left(\frac{169}{253}\right)$	$e\left(\frac{199}{253}\right)$	$e\left(\frac{109}{253}\right)$	$e\left(\frac{236}{253}\right)$
$\chi_{8464}(81,\cdot)$	$1$	$1$	$e\left(\frac{6}{253}\right)$	$e\left(\frac{32}{253}\right)$	$e\left(\frac{80}{253}\right)$	$e\left(\frac{12}{253}\right)$	$e\left(\frac{200}{253}\right)$	$e\left(\frac{8}{253}\right)$	$e\left(\frac{38}{253}\right)$	$e\left(\frac{169}{253}\right)$	$e\left(\frac{29}{253}\right)$	$e\left(\frac{86}{253}\right)$
$\chi_{8464}(193,\cdot)$	$1$	$1$	$e\left(\frac{223}{253}\right)$	$e\left(\frac{93}{253}\right)$	$e\left(\frac{106}{253}\right)$	$e\left(\frac{193}{253}\right)$	$e\left(\frac{12}{253}\right)$	$e\left(\frac{213}{253}\right)$	$e\left(\frac{63}{253}\right)$	$e\left(\frac{167}{253}\right)$	$e\left(\frac{108}{253}\right)$	$e\left(\frac{76}{253}\right)$
$\chi_{8464}(209,\cdot)$	$1$	$1$	$e\left(\frac{247}{253}\right)$	$e\left(\frac{221}{253}\right)$	$e\left(\frac{173}{253}\right)$	$e\left(\frac{241}{253}\right)$	$e\left(\frac{53}{253}\right)$	$e\left(\frac{245}{253}\right)$	$e\left(\frac{215}{253}\right)$	$e\left(\frac{84}{253}\right)$	$e\left(\frac{224}{253}\right)$	$e\left(\frac{167}{253}\right)$
$\chi_{8464}(225,\cdot)$	$1$	$1$	$e\left(\frac{19}{253}\right)$	$e\left(\frac{17}{253}\right)$	$e\left(\frac{169}{253}\right)$	$e\left(\frac{38}{253}\right)$	$e\left(\frac{43}{253}\right)$	$e\left(\frac{194}{253}\right)$	$e\left(\frac{36}{253}\right)$	$e\left(\frac{240}{253}\right)$	$e\left(\frac{134}{253}\right)$	$e\left(\frac{188}{253}\right)$
$\chi_{8464}(257,\cdot)$	$1$	$1$	$e\left(\frac{54}{253}\right)$	$e\left(\frac{35}{253}\right)$	$e\left(\frac{214}{253}\right)$	$e\left(\frac{108}{253}\right)$	$e\left(\frac{29}{253}\right)$	$e\left(\frac{72}{253}\right)$	$e\left(\frac{89}{253}\right)$	$e\left(\frac{3}{253}\right)$	$e\left(\frac{8}{253}\right)$	$e\left(\frac{15}{253}\right)$
$\chi_{8464}(289,\cdot)$	$1$	$1$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{29}{253}\right)$	$e\left(\frac{199}{253}\right)$	$e\left(\frac{169}{253}\right)$	$e\left(\frac{118}{253}\right)$	$e\left(\frac{197}{253}\right)$	$e\left(\frac{240}{253}\right)$	$e\left(\frac{82}{253}\right)$	$e\left(\frac{50}{253}\right)$	$e\left(\frac{157}{253}\right)$
$\chi_{8464}(305,\cdot)$	$1$	$1$	$e\left(\frac{177}{253}\right)$	$e\left(\frac{185}{253}\right)$	$e\left(\frac{83}{253}\right)$	$e\left(\frac{101}{253}\right)$	$e\left(\frac{81}{253}\right)$	$e\left(\frac{236}{253}\right)$	$e\left(\frac{109}{253}\right)$	$e\left(\frac{52}{253}\right)$	$e\left(\frac{223}{253}\right)$	$e\left(\frac{7}{253}\right)$
$\chi_{8464}(353,\cdot)$	$1$	$1$	$e\left(\frac{125}{253}\right)$	$e\left(\frac{245}{253}\right)$	$e\left(\frac{233}{253}\right)$	$e\left(\frac{250}{253}\right)$	$e\left(\frac{203}{253}\right)$	$e\left(\frac{251}{253}\right)$	$e\left(\frac{117}{253}\right)$	$e\left(\frac{21}{253}\right)$	$e\left(\frac{56}{253}\right)$	$e\left(\frac{105}{253}\right)$
$\chi_{8464}(417,\cdot)$	$1$	$1$	$e\left(\frac{95}{253}\right)$	$e\left(\frac{85}{253}\right)$	$e\left(\frac{86}{253}\right)$	$e\left(\frac{190}{253}\right)$	$e\left(\frac{215}{253}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{180}{253}\right)$	$e\left(\frac{188}{253}\right)$	$e\left(\frac{164}{253}\right)$	$e\left(\frac{181}{253}\right)$
$\chi_{8464}(449,\cdot)$	$1$	$1$	$e\left(\frac{83}{253}\right)$	$e\left(\frac{21}{253}\right)$	$e\left(\frac{179}{253}\right)$	$e\left(\frac{166}{253}\right)$	$e\left(\frac{68}{253}\right)$	$e\left(\frac{195}{253}\right)$	$e\left(\frac{104}{253}\right)$	$e\left(\frac{103}{253}\right)$	$e\left(\frac{106}{253}\right)$	$e\left(\frac{9}{253}\right)$
$\chi_{8464}(545,\cdot)$	$1$	$1$	$e\left(\frac{75}{253}\right)$	$e\left(\frac{147}{253}\right)$	$e\left(\frac{241}{253}\right)$	$e\left(\frac{150}{253}\right)$	$e\left(\frac{223}{253}\right)$	$e\left(\frac{100}{253}\right)$	$e\left(\frac{222}{253}\right)$	$e\left(\frac{215}{253}\right)$	$e\left(\frac{236}{253}\right)$	$e\left(\frac{63}{253}\right)$
$\chi_{8464}(561,\cdot)$	$1$	$1$	$e\left(\frac{157}{253}\right)$	$e\left(\frac{247}{253}\right)$	$e\left(\frac{238}{253}\right)$	$e\left(\frac{61}{253}\right)$	$e\left(\frac{89}{253}\right)$	$e\left(\frac{125}{253}\right)$	$e\left(\frac{151}{253}\right)$	$e\left(\frac{79}{253}\right)$	$e\left(\frac{42}{253}\right)$	$e\left(\frac{142}{253}\right)$
$\chi_{8464}(577,\cdot)$	$1$	$1$	$e\left(\frac{203}{253}\right)$	$e\left(\frac{155}{253}\right)$	$e\left(\frac{8}{253}\right)$	$e\left(\frac{153}{253}\right)$	$e\left(\frac{20}{253}\right)$	$e\left(\frac{102}{253}\right)$	$e\left(\frac{105}{253}\right)$	$e\left(\frac{194}{253}\right)$	$e\left(\frac{180}{253}\right)$	$e\left(\frac{211}{253}\right)$
$\chi_{8464}(593,\cdot)$	$1$	$1$	$e\left(\frac{239}{253}\right)$	$e\left(\frac{94}{253}\right)$	$e\left(\frac{235}{253}\right)$	$e\left(\frac{225}{253}\right)$	$e\left(\frac{208}{253}\right)$	$e\left(\frac{150}{253}\right)$	$e\left(\frac{80}{253}\right)$	$e\left(\frac{196}{253}\right)$	$e\left(\frac{101}{253}\right)$	$e\left(\frac{221}{253}\right)$
$\chi_{8464}(625,\cdot)$	$1$	$1$	$e\left(\frac{32}{253}\right)$	$e\left(\frac{2}{253}\right)$	$e\left(\frac{5}{253}\right)$	$e\left(\frac{64}{253}\right)$	$e\left(\frac{139}{253}\right)$	$e\left(\frac{127}{253}\right)$	$e\left(\frac{34}{253}\right)$	$e\left(\frac{58}{253}\right)$	$e\left(\frac{239}{253}\right)$	$e\left(\frac{37}{253}\right)$
$\chi_{8464}(657,\cdot)$	$1$	$1$	$e\left(\frac{68}{253}\right)$	$e\left(\frac{194}{253}\right)$	$e\left(\frac{232}{253}\right)$	$e\left(\frac{136}{253}\right)$	$e\left(\frac{74}{253}\right)$	$e\left(\frac{175}{253}\right)$	$e\left(\frac{9}{253}\right)$	$e\left(\frac{60}{253}\right)$	$e\left(\frac{160}{253}\right)$	$e\left(\frac{47}{253}\right)$
$\chi_{8464}(673,\cdot)$	$1$	$1$	$e\left(\frac{78}{253}\right)$	$e\left(\frac{163}{253}\right)$	$e\left(\frac{28}{253}\right)$	$e\left(\frac{156}{253}\right)$	$e\left(\frac{70}{253}\right)$	$e\left(\frac{104}{253}\right)$	$e\left(\frac{241}{253}\right)$	$e\left(\frac{173}{253}\right)$	$e\left(\frac{124}{253}\right)$	$e\left(\frac{106}{253}\right)$
$\chi_{8464}(721,\cdot)$	$1$	$1$	$e\left(\frac{114}{253}\right)$	$e\left(\frac{102}{253}\right)$	$e\left(\frac{2}{253}\right)$	$e\left(\frac{228}{253}\right)$	$e\left(\frac{5}{253}\right)$	$e\left(\frac{152}{253}\right)$	$e\left(\frac{216}{253}\right)$	$e\left(\frac{175}{253}\right)$	$e\left(\frac{45}{253}\right)$	$e\left(\frac{116}{253}\right)$
$\chi_{8464}(785,\cdot)$	$1$	$1$	$e\left(\frac{150}{253}\right)$	$e\left(\frac{41}{253}\right)$	$e\left(\frac{229}{253}\right)$	$e\left(\frac{47}{253}\right)$	$e\left(\frac{193}{253}\right)$	$e\left(\frac{200}{253}\right)$	$e\left(\frac{191}{253}\right)$	$e\left(\frac{177}{253}\right)$	$e\left(\frac{219}{253}\right)$	$e\left(\frac{126}{253}\right)$
$\chi_{8464}(817,\cdot)$	$1$	$1$	$e\left(\frac{160}{253}\right)$	$e\left(\frac{10}{253}\right)$	$e\left(\frac{25}{253}\right)$	$e\left(\frac{67}{253}\right)$	$e\left(\frac{189}{253}\right)$	$e\left(\frac{129}{253}\right)$	$e\left(\frac{170}{253}\right)$	$e\left(\frac{37}{253}\right)$	$e\left(\frac{183}{253}\right)$	$e\left(\frac{185}{253}\right)$
$\chi_{8464}(913,\cdot)$	$1$	$1$	$e\left(\frac{196}{253}\right)$	$e\left(\frac{202}{253}\right)$	$e\left(\frac{252}{253}\right)$	$e\left(\frac{139}{253}\right)$	$e\left(\frac{124}{253}\right)$	$e\left(\frac{177}{253}\right)$	$e\left(\frac{145}{253}\right)$	$e\left(\frac{39}{253}\right)$	$e\left(\frac{104}{253}\right)$	$e\left(\frac{195}{253}\right)$
$\chi_{8464}(929,\cdot)$	$1$	$1$	$e\left(\frac{91}{253}\right)$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{117}{253}\right)$	$e\left(\frac{182}{253}\right)$	$e\left(\frac{166}{253}\right)$	$e\left(\frac{37}{253}\right)$	$e\left(\frac{239}{253}\right)$	$e\left(\frac{244}{253}\right)$	$e\left(\frac{229}{253}\right)$	$e\left(\frac{208}{253}\right)$
$\chi_{8464}(945,\cdot)$	$1$	$1$	$e\left(\frac{159}{253}\right)$	$e\left(\frac{89}{253}\right)$	$e\left(\frac{96}{253}\right)$	$e\left(\frac{65}{253}\right)$	$e\left(\frac{240}{253}\right)$	$e\left(\frac{212}{253}\right)$	$e\left(\frac{248}{253}\right)$	$e\left(\frac{51}{253}\right)$	$e\left(\frac{136}{253}\right)$	$e\left(\frac{2}{253}\right)$
$\chi_{8464}(961,\cdot)$	$1$	$1$	$e\left(\frac{206}{253}\right)$	$e\left(\frac{171}{253}\right)$	$e\left(\frac{48}{253}\right)$	$e\left(\frac{159}{253}\right)$	$e\left(\frac{120}{253}\right)$	$e\left(\frac{106}{253}\right)$	$e\left(\frac{124}{253}\right)$	$e\left(\frac{152}{253}\right)$	$e\left(\frac{68}{253}\right)$	$e\left(\frac{1}{253}\right)$
$\chi_{8464}(993,\cdot)$	$1$	$1$	$e\left(\frac{10}{253}\right)$	$e\left(\frac{222}{253}\right)$	$e\left(\frac{49}{253}\right)$	$e\left(\frac{20}{253}\right)$	$e\left(\frac{249}{253}\right)$	$e\left(\frac{182}{253}\right)$	$e\left(\frac{232}{253}\right)$	$e\left(\frac{113}{253}\right)$	$e\left(\frac{217}{253}\right)$	$e\left(\frac{59}{253}\right)$
$\chi_{8464}(1025,\cdot)$	$1$	$1$	$e\left(\frac{178}{253}\right)$	$e\left(\frac{106}{253}\right)$	$e\left(\frac{12}{253}\right)$	$e\left(\frac{103}{253}\right)$	$e\left(\frac{30}{253}\right)$	$e\left(\frac{153}{253}\right)$	$e\left(\frac{31}{253}\right)$	$e\left(\frac{38}{253}\right)$	$e\left(\frac{17}{253}\right)$	$e\left(\frac{190}{253}\right)$
$\chi_{8464}(1041,\cdot)$	$1$	$1$	$e\left(\frac{232}{253}\right)$	$e\left(\frac{141}{253}\right)$	$e\left(\frac{226}{253}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{59}{253}\right)$	$e\left(\frac{225}{253}\right)$	$e\left(\frac{120}{253}\right)$	$e\left(\frac{41}{253}\right)$	$e\left(\frac{25}{253}\right)$	$e\left(\frac{205}{253}\right)$
$\chi_{8464}(1089,\cdot)$	$1$	$1$	$e\left(\frac{103}{253}\right)$	$e\left(\frac{212}{253}\right)$	$e\left(\frac{24}{253}\right)$	$e\left(\frac{206}{253}\right)$	$e\left(\frac{60}{253}\right)$	$e\left(\frac{53}{253}\right)$	$e\left(\frac{62}{253}\right)$	$e\left(\frac{76}{253}\right)$	$e\left(\frac{34}{253}\right)$	$e\left(\frac{127}{253}\right)$
$\chi_{8464}(1153,\cdot)$	$1$	$1$	$e\left(\frac{205}{253}\right)$	$e\left(\frac{250}{253}\right)$	$e\left(\frac{119}{253}\right)$	$e\left(\frac{157}{253}\right)$	$e\left(\frac{171}{253}\right)$	$e\left(\frac{189}{253}\right)$	$e\left(\frac{202}{253}\right)$	$e\left(\frac{166}{253}\right)$	$e\left(\frac{21}{253}\right)$	$e\left(\frac{71}{253}\right)$
$\chi_{8464}(1185,\cdot)$	$1$	$1$	$e\left(\frac{237}{253}\right)$	$e\left(\frac{252}{253}\right)$	$e\left(\frac{124}{253}\right)$	$e\left(\frac{221}{253}\right)$	$e\left(\frac{57}{253}\right)$	$e\left(\frac{63}{253}\right)$	$e\left(\frac{236}{253}\right)$	$e\left(\frac{224}{253}\right)$	$e\left(\frac{7}{253}\right)$	$e\left(\frac{108}{253}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8464}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{40}{253}\right)\)	\(e\left(\frac{129}{253}\right)\)	\(e\left(\frac{196}{253}\right)\)	\(e\left(\frac{80}{253}\right)\)	\(e\left(\frac{237}{253}\right)\)	\(e\left(\frac{222}{253}\right)\)	\(e\left(\frac{169}{253}\right)\)	\(e\left(\frac{199}{253}\right)\)	\(e\left(\frac{109}{253}\right)\)	\(e\left(\frac{236}{253}\right)\)
\(\chi_{8464}(81,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{6}{253}\right)\)	\(e\left(\frac{32}{253}\right)\)	\(e\left(\frac{80}{253}\right)\)	\(e\left(\frac{12}{253}\right)\)	\(e\left(\frac{200}{253}\right)\)	\(e\left(\frac{8}{253}\right)\)	\(e\left(\frac{38}{253}\right)\)	\(e\left(\frac{169}{253}\right)\)	\(e\left(\frac{29}{253}\right)\)	\(e\left(\frac{86}{253}\right)\)
\(\chi_{8464}(193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{223}{253}\right)\)	\(e\left(\frac{93}{253}\right)\)	\(e\left(\frac{106}{253}\right)\)	\(e\left(\frac{193}{253}\right)\)	\(e\left(\frac{12}{253}\right)\)	\(e\left(\frac{213}{253}\right)\)	\(e\left(\frac{63}{253}\right)\)	\(e\left(\frac{167}{253}\right)\)	\(e\left(\frac{108}{253}\right)\)	\(e\left(\frac{76}{253}\right)\)
\(\chi_{8464}(209,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{247}{253}\right)\)	\(e\left(\frac{221}{253}\right)\)	\(e\left(\frac{173}{253}\right)\)	\(e\left(\frac{241}{253}\right)\)	\(e\left(\frac{53}{253}\right)\)	\(e\left(\frac{245}{253}\right)\)	\(e\left(\frac{215}{253}\right)\)	\(e\left(\frac{84}{253}\right)\)	\(e\left(\frac{224}{253}\right)\)	\(e\left(\frac{167}{253}\right)\)
\(\chi_{8464}(225,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{253}\right)\)	\(e\left(\frac{17}{253}\right)\)	\(e\left(\frac{169}{253}\right)\)	\(e\left(\frac{38}{253}\right)\)	\(e\left(\frac{43}{253}\right)\)	\(e\left(\frac{194}{253}\right)\)	\(e\left(\frac{36}{253}\right)\)	\(e\left(\frac{240}{253}\right)\)	\(e\left(\frac{134}{253}\right)\)	\(e\left(\frac{188}{253}\right)\)
\(\chi_{8464}(257,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{54}{253}\right)\)	\(e\left(\frac{35}{253}\right)\)	\(e\left(\frac{214}{253}\right)\)	\(e\left(\frac{108}{253}\right)\)	\(e\left(\frac{29}{253}\right)\)	\(e\left(\frac{72}{253}\right)\)	\(e\left(\frac{89}{253}\right)\)	\(e\left(\frac{3}{253}\right)\)	\(e\left(\frac{8}{253}\right)\)	\(e\left(\frac{15}{253}\right)\)
\(\chi_{8464}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{29}{253}\right)\)	\(e\left(\frac{199}{253}\right)\)	\(e\left(\frac{169}{253}\right)\)	\(e\left(\frac{118}{253}\right)\)	\(e\left(\frac{197}{253}\right)\)	\(e\left(\frac{240}{253}\right)\)	\(e\left(\frac{82}{253}\right)\)	\(e\left(\frac{50}{253}\right)\)	\(e\left(\frac{157}{253}\right)\)
\(\chi_{8464}(305,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{177}{253}\right)\)	\(e\left(\frac{185}{253}\right)\)	\(e\left(\frac{83}{253}\right)\)	\(e\left(\frac{101}{253}\right)\)	\(e\left(\frac{81}{253}\right)\)	\(e\left(\frac{236}{253}\right)\)	\(e\left(\frac{109}{253}\right)\)	\(e\left(\frac{52}{253}\right)\)	\(e\left(\frac{223}{253}\right)\)	\(e\left(\frac{7}{253}\right)\)
\(\chi_{8464}(353,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{125}{253}\right)\)	\(e\left(\frac{245}{253}\right)\)	\(e\left(\frac{233}{253}\right)\)	\(e\left(\frac{250}{253}\right)\)	\(e\left(\frac{203}{253}\right)\)	\(e\left(\frac{251}{253}\right)\)	\(e\left(\frac{117}{253}\right)\)	\(e\left(\frac{21}{253}\right)\)	\(e\left(\frac{56}{253}\right)\)	\(e\left(\frac{105}{253}\right)\)
\(\chi_{8464}(417,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{253}\right)\)	\(e\left(\frac{85}{253}\right)\)	\(e\left(\frac{86}{253}\right)\)	\(e\left(\frac{190}{253}\right)\)	\(e\left(\frac{215}{253}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{180}{253}\right)\)	\(e\left(\frac{188}{253}\right)\)	\(e\left(\frac{164}{253}\right)\)	\(e\left(\frac{181}{253}\right)\)
\(\chi_{8464}(449,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{253}\right)\)	\(e\left(\frac{21}{253}\right)\)	\(e\left(\frac{179}{253}\right)\)	\(e\left(\frac{166}{253}\right)\)	\(e\left(\frac{68}{253}\right)\)	\(e\left(\frac{195}{253}\right)\)	\(e\left(\frac{104}{253}\right)\)	\(e\left(\frac{103}{253}\right)\)	\(e\left(\frac{106}{253}\right)\)	\(e\left(\frac{9}{253}\right)\)
\(\chi_{8464}(545,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{75}{253}\right)\)	\(e\left(\frac{147}{253}\right)\)	\(e\left(\frac{241}{253}\right)\)	\(e\left(\frac{150}{253}\right)\)	\(e\left(\frac{223}{253}\right)\)	\(e\left(\frac{100}{253}\right)\)	\(e\left(\frac{222}{253}\right)\)	\(e\left(\frac{215}{253}\right)\)	\(e\left(\frac{236}{253}\right)\)	\(e\left(\frac{63}{253}\right)\)
\(\chi_{8464}(561,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{253}\right)\)	\(e\left(\frac{247}{253}\right)\)	\(e\left(\frac{238}{253}\right)\)	\(e\left(\frac{61}{253}\right)\)	\(e\left(\frac{89}{253}\right)\)	\(e\left(\frac{125}{253}\right)\)	\(e\left(\frac{151}{253}\right)\)	\(e\left(\frac{79}{253}\right)\)	\(e\left(\frac{42}{253}\right)\)	\(e\left(\frac{142}{253}\right)\)
\(\chi_{8464}(577,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{203}{253}\right)\)	\(e\left(\frac{155}{253}\right)\)	\(e\left(\frac{8}{253}\right)\)	\(e\left(\frac{153}{253}\right)\)	\(e\left(\frac{20}{253}\right)\)	\(e\left(\frac{102}{253}\right)\)	\(e\left(\frac{105}{253}\right)\)	\(e\left(\frac{194}{253}\right)\)	\(e\left(\frac{180}{253}\right)\)	\(e\left(\frac{211}{253}\right)\)
\(\chi_{8464}(593,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{239}{253}\right)\)	\(e\left(\frac{94}{253}\right)\)	\(e\left(\frac{235}{253}\right)\)	\(e\left(\frac{225}{253}\right)\)	\(e\left(\frac{208}{253}\right)\)	\(e\left(\frac{150}{253}\right)\)	\(e\left(\frac{80}{253}\right)\)	\(e\left(\frac{196}{253}\right)\)	\(e\left(\frac{101}{253}\right)\)	\(e\left(\frac{221}{253}\right)\)
\(\chi_{8464}(625,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{32}{253}\right)\)	\(e\left(\frac{2}{253}\right)\)	\(e\left(\frac{5}{253}\right)\)	\(e\left(\frac{64}{253}\right)\)	\(e\left(\frac{139}{253}\right)\)	\(e\left(\frac{127}{253}\right)\)	\(e\left(\frac{34}{253}\right)\)	\(e\left(\frac{58}{253}\right)\)	\(e\left(\frac{239}{253}\right)\)	\(e\left(\frac{37}{253}\right)\)
\(\chi_{8464}(657,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{253}\right)\)	\(e\left(\frac{194}{253}\right)\)	\(e\left(\frac{232}{253}\right)\)	\(e\left(\frac{136}{253}\right)\)	\(e\left(\frac{74}{253}\right)\)	\(e\left(\frac{175}{253}\right)\)	\(e\left(\frac{9}{253}\right)\)	\(e\left(\frac{60}{253}\right)\)	\(e\left(\frac{160}{253}\right)\)	\(e\left(\frac{47}{253}\right)\)
\(\chi_{8464}(673,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{78}{253}\right)\)	\(e\left(\frac{163}{253}\right)\)	\(e\left(\frac{28}{253}\right)\)	\(e\left(\frac{156}{253}\right)\)	\(e\left(\frac{70}{253}\right)\)	\(e\left(\frac{104}{253}\right)\)	\(e\left(\frac{241}{253}\right)\)	\(e\left(\frac{173}{253}\right)\)	\(e\left(\frac{124}{253}\right)\)	\(e\left(\frac{106}{253}\right)\)
\(\chi_{8464}(721,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{114}{253}\right)\)	\(e\left(\frac{102}{253}\right)\)	\(e\left(\frac{2}{253}\right)\)	\(e\left(\frac{228}{253}\right)\)	\(e\left(\frac{5}{253}\right)\)	\(e\left(\frac{152}{253}\right)\)	\(e\left(\frac{216}{253}\right)\)	\(e\left(\frac{175}{253}\right)\)	\(e\left(\frac{45}{253}\right)\)	\(e\left(\frac{116}{253}\right)\)
\(\chi_{8464}(785,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{150}{253}\right)\)	\(e\left(\frac{41}{253}\right)\)	\(e\left(\frac{229}{253}\right)\)	\(e\left(\frac{47}{253}\right)\)	\(e\left(\frac{193}{253}\right)\)	\(e\left(\frac{200}{253}\right)\)	\(e\left(\frac{191}{253}\right)\)	\(e\left(\frac{177}{253}\right)\)	\(e\left(\frac{219}{253}\right)\)	\(e\left(\frac{126}{253}\right)\)
\(\chi_{8464}(817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{160}{253}\right)\)	\(e\left(\frac{10}{253}\right)\)	\(e\left(\frac{25}{253}\right)\)	\(e\left(\frac{67}{253}\right)\)	\(e\left(\frac{189}{253}\right)\)	\(e\left(\frac{129}{253}\right)\)	\(e\left(\frac{170}{253}\right)\)	\(e\left(\frac{37}{253}\right)\)	\(e\left(\frac{183}{253}\right)\)	\(e\left(\frac{185}{253}\right)\)
\(\chi_{8464}(913,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{196}{253}\right)\)	\(e\left(\frac{202}{253}\right)\)	\(e\left(\frac{252}{253}\right)\)	\(e\left(\frac{139}{253}\right)\)	\(e\left(\frac{124}{253}\right)\)	\(e\left(\frac{177}{253}\right)\)	\(e\left(\frac{145}{253}\right)\)	\(e\left(\frac{39}{253}\right)\)	\(e\left(\frac{104}{253}\right)\)	\(e\left(\frac{195}{253}\right)\)
\(\chi_{8464}(929,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{253}\right)\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{117}{253}\right)\)	\(e\left(\frac{182}{253}\right)\)	\(e\left(\frac{166}{253}\right)\)	\(e\left(\frac{37}{253}\right)\)	\(e\left(\frac{239}{253}\right)\)	\(e\left(\frac{244}{253}\right)\)	\(e\left(\frac{229}{253}\right)\)	\(e\left(\frac{208}{253}\right)\)
\(\chi_{8464}(945,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{159}{253}\right)\)	\(e\left(\frac{89}{253}\right)\)	\(e\left(\frac{96}{253}\right)\)	\(e\left(\frac{65}{253}\right)\)	\(e\left(\frac{240}{253}\right)\)	\(e\left(\frac{212}{253}\right)\)	\(e\left(\frac{248}{253}\right)\)	\(e\left(\frac{51}{253}\right)\)	\(e\left(\frac{136}{253}\right)\)	\(e\left(\frac{2}{253}\right)\)
\(\chi_{8464}(961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{206}{253}\right)\)	\(e\left(\frac{171}{253}\right)\)	\(e\left(\frac{48}{253}\right)\)	\(e\left(\frac{159}{253}\right)\)	\(e\left(\frac{120}{253}\right)\)	\(e\left(\frac{106}{253}\right)\)	\(e\left(\frac{124}{253}\right)\)	\(e\left(\frac{152}{253}\right)\)	\(e\left(\frac{68}{253}\right)\)	\(e\left(\frac{1}{253}\right)\)
\(\chi_{8464}(993,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{10}{253}\right)\)	\(e\left(\frac{222}{253}\right)\)	\(e\left(\frac{49}{253}\right)\)	\(e\left(\frac{20}{253}\right)\)	\(e\left(\frac{249}{253}\right)\)	\(e\left(\frac{182}{253}\right)\)	\(e\left(\frac{232}{253}\right)\)	\(e\left(\frac{113}{253}\right)\)	\(e\left(\frac{217}{253}\right)\)	\(e\left(\frac{59}{253}\right)\)
\(\chi_{8464}(1025,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{178}{253}\right)\)	\(e\left(\frac{106}{253}\right)\)	\(e\left(\frac{12}{253}\right)\)	\(e\left(\frac{103}{253}\right)\)	\(e\left(\frac{30}{253}\right)\)	\(e\left(\frac{153}{253}\right)\)	\(e\left(\frac{31}{253}\right)\)	\(e\left(\frac{38}{253}\right)\)	\(e\left(\frac{17}{253}\right)\)	\(e\left(\frac{190}{253}\right)\)
\(\chi_{8464}(1041,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{232}{253}\right)\)	\(e\left(\frac{141}{253}\right)\)	\(e\left(\frac{226}{253}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{59}{253}\right)\)	\(e\left(\frac{225}{253}\right)\)	\(e\left(\frac{120}{253}\right)\)	\(e\left(\frac{41}{253}\right)\)	\(e\left(\frac{25}{253}\right)\)	\(e\left(\frac{205}{253}\right)\)
\(\chi_{8464}(1089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{253}\right)\)	\(e\left(\frac{212}{253}\right)\)	\(e\left(\frac{24}{253}\right)\)	\(e\left(\frac{206}{253}\right)\)	\(e\left(\frac{60}{253}\right)\)	\(e\left(\frac{53}{253}\right)\)	\(e\left(\frac{62}{253}\right)\)	\(e\left(\frac{76}{253}\right)\)	\(e\left(\frac{34}{253}\right)\)	\(e\left(\frac{127}{253}\right)\)
\(\chi_{8464}(1153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{253}\right)\)	\(e\left(\frac{250}{253}\right)\)	\(e\left(\frac{119}{253}\right)\)	\(e\left(\frac{157}{253}\right)\)	\(e\left(\frac{171}{253}\right)\)	\(e\left(\frac{189}{253}\right)\)	\(e\left(\frac{202}{253}\right)\)	\(e\left(\frac{166}{253}\right)\)	\(e\left(\frac{21}{253}\right)\)	\(e\left(\frac{71}{253}\right)\)
\(\chi_{8464}(1185,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{237}{253}\right)\)	\(e\left(\frac{252}{253}\right)\)	\(e\left(\frac{124}{253}\right)\)	\(e\left(\frac{221}{253}\right)\)	\(e\left(\frac{57}{253}\right)\)	\(e\left(\frac{63}{253}\right)\)	\(e\left(\frac{236}{253}\right)\)	\(e\left(\frac{224}{253}\right)\)	\(e\left(\frac{7}{253}\right)\)	\(e\left(\frac{108}{253}\right)\)

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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.bk
Modulus	$8464$
Conductor	$529$
Order	$253$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(8464\)
Conductor:	\(529\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(253\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 529.g	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)