LMFDB - Dirichlet character orbit 8464.br

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8464, base_ring=CyclotomicField(506)) M = H._module chi = DirichletCharacter(H, M([253,253,129])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(7,8464)) 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.bf	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	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8464}(7,\cdot)$	$1$	$1$	$e\left(\frac{20}{253}\right)$	$e\left(\frac{191}{253}\right)$	$e\left(\frac{98}{253}\right)$	$e\left(\frac{40}{253}\right)$	$e\left(\frac{237}{506}\right)$	$e\left(\frac{475}{506}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{199}{506}\right)$	$e\left(\frac{109}{506}\right)$	$e\left(\frac{118}{253}\right)$
$\chi_{8464}(103,\cdot)$	$1$	$1$	$e\left(\frac{94}{253}\right)$	$e\left(\frac{164}{253}\right)$	$e\left(\frac{157}{253}\right)$	$e\left(\frac{188}{253}\right)$	$e\left(\frac{279}{506}\right)$	$e\left(\frac{335}{506}\right)$	$e\left(\frac{5}{253}\right)$	$e\left(\frac{151}{506}\right)$	$e\left(\frac{487}{506}\right)$	$e\left(\frac{251}{253}\right)$
$\chi_{8464}(135,\cdot)$	$1$	$1$	$e\left(\frac{139}{253}\right)$	$e\left(\frac{151}{253}\right)$	$e\left(\frac{251}{253}\right)$	$e\left(\frac{25}{253}\right)$	$e\left(\frac{243}{506}\right)$	$e\left(\frac{455}{506}\right)$	$e\left(\frac{37}{253}\right)$	$e\left(\frac{409}{506}\right)$	$e\left(\frac{163}{506}\right)$	$e\left(\frac{137}{253}\right)$
$\chi_{8464}(199,\cdot)$	$1$	$1$	$e\left(\frac{15}{253}\right)$	$e\left(\frac{80}{253}\right)$	$e\left(\frac{200}{253}\right)$	$e\left(\frac{30}{253}\right)$	$e\left(\frac{241}{506}\right)$	$e\left(\frac{293}{506}\right)$	$e\left(\frac{95}{253}\right)$	$e\left(\frac{339}{506}\right)$	$e\left(\frac{145}{506}\right)$	$e\left(\frac{215}{253}\right)$
$\chi_{8464}(247,\cdot)$	$1$	$1$	$e\left(\frac{199}{253}\right)$	$e\left(\frac{218}{253}\right)$	$e\left(\frac{39}{253}\right)$	$e\left(\frac{145}{253}\right)$	$e\left(\frac{195}{506}\right)$	$e\left(\frac{109}{506}\right)$	$e\left(\frac{164}{253}\right)$	$e\left(\frac{247}{506}\right)$	$e\left(\frac{237}{506}\right)$	$e\left(\frac{238}{253}\right)$
$\chi_{8464}(295,\cdot)$	$1$	$1$	$e\left(\frac{87}{253}\right)$	$e\left(\frac{211}{253}\right)$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{174}{253}\right)$	$e\left(\frac{487}{506}\right)$	$e\left(\frac{485}{506}\right)$	$e\left(\frac{45}{253}\right)$	$e\left(\frac{347}{506}\right)$	$e\left(\frac{335}{506}\right)$	$e\left(\frac{235}{253}\right)$
$\chi_{8464}(327,\cdot)$	$1$	$1$	$e\left(\frac{195}{253}\right)$	$e\left(\frac{28}{253}\right)$	$e\left(\frac{70}{253}\right)$	$e\left(\frac{137}{253}\right)$	$e\left(\frac{97}{506}\right)$	$e\left(\frac{267}{506}\right)$	$e\left(\frac{223}{253}\right)$	$e\left(\frac{359}{506}\right)$	$e\left(\frac{367}{506}\right)$	$e\left(\frac{12}{253}\right)$
$\chi_{8464}(343,\cdot)$	$1$	$1$	$e\left(\frac{60}{253}\right)$	$e\left(\frac{67}{253}\right)$	$e\left(\frac{41}{253}\right)$	$e\left(\frac{120}{253}\right)$	$e\left(\frac{205}{506}\right)$	$e\left(\frac{413}{506}\right)$	$e\left(\frac{127}{253}\right)$	$e\left(\frac{91}{506}\right)$	$e\left(\frac{327}{506}\right)$	$e\left(\frac{101}{253}\right)$
$\chi_{8464}(375,\cdot)$	$1$	$1$	$e\left(\frac{152}{253}\right)$	$e\left(\frac{136}{253}\right)$	$e\left(\frac{87}{253}\right)$	$e\left(\frac{51}{253}\right)$	$e\left(\frac{435}{506}\right)$	$e\left(\frac{321}{506}\right)$	$e\left(\frac{35}{253}\right)$	$e\left(\frac{45}{506}\right)$	$e\left(\frac{373}{506}\right)$	$e\left(\frac{239}{253}\right)$
$\chi_{8464}(471,\cdot)$	$1$	$1$	$e\left(\frac{17}{253}\right)$	$e\left(\frac{175}{253}\right)$	$e\left(\frac{58}{253}\right)$	$e\left(\frac{34}{253}\right)$	$e\left(\frac{37}{506}\right)$	$e\left(\frac{467}{506}\right)$	$e\left(\frac{192}{253}\right)$	$e\left(\frac{283}{506}\right)$	$e\left(\frac{333}{506}\right)$	$e\left(\frac{75}{253}\right)$
$\chi_{8464}(503,\cdot)$	$1$	$1$	$e\left(\frac{84}{253}\right)$	$e\left(\frac{195}{253}\right)$	$e\left(\frac{108}{253}\right)$	$e\left(\frac{168}{253}\right)$	$e\left(\frac{287}{506}\right)$	$e\left(\frac{477}{506}\right)$	$e\left(\frac{26}{253}\right)$	$e\left(\frac{431}{506}\right)$	$e\left(\frac{53}{506}\right)$	$e\left(\frac{192}{253}\right)$
$\chi_{8464}(567,\cdot)$	$1$	$1$	$e\left(\frac{26}{253}\right)$	$e\left(\frac{223}{253}\right)$	$e\left(\frac{178}{253}\right)$	$e\left(\frac{52}{253}\right)$	$e\left(\frac{131}{506}\right)$	$e\left(\frac{491}{506}\right)$	$e\left(\frac{249}{253}\right)$	$e\left(\frac{31}{506}\right)$	$e\left(\frac{167}{506}\right)$	$e\left(\frac{204}{253}\right)$
$\chi_{8464}(615,\cdot)$	$1$	$1$	$e\left(\frac{45}{253}\right)$	$e\left(\frac{240}{253}\right)$	$e\left(\frac{94}{253}\right)$	$e\left(\frac{90}{253}\right)$	$e\left(\frac{217}{506}\right)$	$e\left(\frac{373}{506}\right)$	$e\left(\frac{32}{253}\right)$	$e\left(\frac{5}{506}\right)$	$e\left(\frac{435}{506}\right)$	$e\left(\frac{139}{253}\right)$
$\chi_{8464}(631,\cdot)$	$1$	$1$	$e\left(\frac{189}{253}\right)$	$e\left(\frac{249}{253}\right)$	$e\left(\frac{243}{253}\right)$	$e\left(\frac{125}{253}\right)$	$e\left(\frac{203}{506}\right)$	$e\left(\frac{251}{506}\right)$	$e\left(\frac{185}{253}\right)$	$e\left(\frac{21}{506}\right)$	$e\left(\frac{309}{506}\right)$	$e\left(\frac{179}{253}\right)$
$\chi_{8464}(663,\cdot)$	$1$	$1$	$e\left(\frac{109}{253}\right)$	$e\left(\frac{244}{253}\right)$	$e\left(\frac{104}{253}\right)$	$e\left(\frac{218}{253}\right)$	$e\left(\frac{267}{506}\right)$	$e\left(\frac{375}{506}\right)$	$e\left(\frac{100}{253}\right)$	$e\left(\frac{237}{506}\right)$	$e\left(\frac{379}{506}\right)$	$e\left(\frac{213}{253}\right)$
$\chi_{8464}(695,\cdot)$	$1$	$1$	$e\left(\frac{228}{253}\right)$	$e\left(\frac{204}{253}\right)$	$e\left(\frac{4}{253}\right)$	$e\left(\frac{203}{253}\right)$	$e\left(\frac{273}{506}\right)$	$e\left(\frac{355}{506}\right)$	$e\left(\frac{179}{253}\right)$	$e\left(\frac{447}{506}\right)$	$e\left(\frac{433}{506}\right)$	$e\left(\frac{232}{253}\right)$
$\chi_{8464}(711,\cdot)$	$1$	$1$	$e\left(\frac{104}{253}\right)$	$e\left(\frac{133}{253}\right)$	$e\left(\frac{206}{253}\right)$	$e\left(\frac{208}{253}\right)$	$e\left(\frac{271}{506}\right)$	$e\left(\frac{193}{506}\right)$	$e\left(\frac{237}{253}\right)$	$e\left(\frac{377}{506}\right)$	$e\left(\frac{415}{506}\right)$	$e\left(\frac{57}{253}\right)$
$\chi_{8464}(727,\cdot)$	$1$	$1$	$e\left(\frac{135}{253}\right)$	$e\left(\frac{214}{253}\right)$	$e\left(\frac{29}{253}\right)$	$e\left(\frac{17}{253}\right)$	$e\left(\frac{145}{506}\right)$	$e\left(\frac{107}{506}\right)$	$e\left(\frac{96}{253}\right)$	$e\left(\frac{15}{506}\right)$	$e\left(\frac{293}{506}\right)$	$e\left(\frac{164}{253}\right)$
$\chi_{8464}(743,\cdot)$	$1$	$1$	$e\left(\frac{31}{253}\right)$	$e\left(\frac{81}{253}\right)$	$e\left(\frac{76}{253}\right)$	$e\left(\frac{62}{253}\right)$	$e\left(\frac{127}{506}\right)$	$e\left(\frac{167}{506}\right)$	$e\left(\frac{112}{253}\right)$	$e\left(\frac{397}{506}\right)$	$e\left(\frac{131}{506}\right)$	$e\left(\frac{107}{253}\right)$
$\chi_{8464}(839,\cdot)$	$1$	$1$	$e\left(\frac{193}{253}\right)$	$e\left(\frac{186}{253}\right)$	$e\left(\frac{212}{253}\right)$	$e\left(\frac{133}{253}\right)$	$e\left(\frac{301}{506}\right)$	$e\left(\frac{93}{506}\right)$	$e\left(\frac{126}{253}\right)$	$e\left(\frac{415}{506}\right)$	$e\left(\frac{179}{506}\right)$	$e\left(\frac{152}{253}\right)$
$\chi_{8464}(871,\cdot)$	$1$	$1$	$e\left(\frac{29}{253}\right)$	$e\left(\frac{239}{253}\right)$	$e\left(\frac{218}{253}\right)$	$e\left(\frac{58}{253}\right)$	$e\left(\frac{331}{506}\right)$	$e\left(\frac{499}{506}\right)$	$e\left(\frac{15}{253}\right)$	$e\left(\frac{453}{506}\right)$	$e\left(\frac{449}{506}\right)$	$e\left(\frac{247}{253}\right)$
$\chi_{8464}(935,\cdot)$	$1$	$1$	$e\left(\frac{37}{253}\right)$	$e\left(\frac{113}{253}\right)$	$e\left(\frac{156}{253}\right)$	$e\left(\frac{74}{253}\right)$	$e\left(\frac{21}{506}\right)$	$e\left(\frac{183}{506}\right)$	$e\left(\frac{150}{253}\right)$	$e\left(\frac{229}{506}\right)$	$e\left(\frac{189}{506}\right)$	$e\left(\frac{193}{253}\right)$
$\chi_{8464}(983,\cdot)$	$1$	$1$	$e\left(\frac{144}{253}\right)$	$e\left(\frac{9}{253}\right)$	$e\left(\frac{149}{253}\right)$	$e\left(\frac{35}{253}\right)$	$e\left(\frac{239}{506}\right)$	$e\left(\frac{131}{506}\right)$	$e\left(\frac{153}{253}\right)$	$e\left(\frac{269}{506}\right)$	$e\left(\frac{127}{506}\right)$	$e\left(\frac{40}{253}\right)$
$\chi_{8464}(999,\cdot)$	$1$	$1$	$e\left(\frac{79}{253}\right)$	$e\left(\frac{84}{253}\right)$	$e\left(\frac{210}{253}\right)$	$e\left(\frac{158}{253}\right)$	$e\left(\frac{291}{506}\right)$	$e\left(\frac{295}{506}\right)$	$e\left(\frac{163}{253}\right)$	$e\left(\frac{65}{506}\right)$	$e\left(\frac{89}{506}\right)$	$e\left(\frac{36}{253}\right)$
$\chi_{8464}(1031,\cdot)$	$1$	$1$	$e\left(\frac{131}{253}\right)$	$e\left(\frac{24}{253}\right)$	$e\left(\frac{60}{253}\right)$	$e\left(\frac{9}{253}\right)$	$e\left(\frac{47}{506}\right)$	$e\left(\frac{265}{506}\right)$	$e\left(\frac{155}{253}\right)$	$e\left(\frac{127}{506}\right)$	$e\left(\frac{423}{506}\right)$	$e\left(\frac{191}{253}\right)$
$\chi_{8464}(1063,\cdot)$	$1$	$1$	$e\left(\frac{8}{253}\right)$	$e\left(\frac{127}{253}\right)$	$e\left(\frac{191}{253}\right)$	$e\left(\frac{16}{253}\right)$	$e\left(\frac{449}{506}\right)$	$e\left(\frac{443}{506}\right)$	$e\left(\frac{135}{253}\right)$	$e\left(\frac{29}{506}\right)$	$e\left(\frac{499}{506}\right)$	$e\left(\frac{199}{253}\right)$
$\chi_{8464}(1079,\cdot)$	$1$	$1$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{199}{253}\right)$	$e\left(\frac{118}{253}\right)$	$e\left(\frac{43}{253}\right)$	$e\left(\frac{337}{506}\right)$	$e\left(\frac{479}{506}\right)$	$e\left(\frac{94}{253}\right)$	$e\left(\frac{157}{506}\right)$	$e\left(\frac{503}{506}\right)$	$e\left(\frac{13}{253}\right)$
$\chi_{8464}(1095,\cdot)$	$1$	$1$	$e\left(\frac{201}{253}\right)$	$e\left(\frac{60}{253}\right)$	$e\left(\frac{150}{253}\right)$	$e\left(\frac{149}{253}\right)$	$e\left(\frac{497}{506}\right)$	$e\left(\frac{283}{506}\right)$	$e\left(\frac{8}{253}\right)$	$e\left(\frac{191}{506}\right)$	$e\left(\frac{425}{506}\right)$	$e\left(\frac{98}{253}\right)$
$\chi_{8464}(1111,\cdot)$	$1$	$1$	$e\left(\frac{163}{253}\right)$	$e\left(\frac{26}{253}\right)$	$e\left(\frac{65}{253}\right)$	$e\left(\frac{73}{253}\right)$	$e\left(\frac{325}{506}\right)$	$e\left(\frac{13}{506}\right)$	$e\left(\frac{189}{253}\right)$	$e\left(\frac{243}{506}\right)$	$e\left(\frac{395}{506}\right)$	$e\left(\frac{228}{253}\right)$
$\chi_{8464}(1207,\cdot)$	$1$	$1$	$e\left(\frac{116}{253}\right)$	$e\left(\frac{197}{253}\right)$	$e\left(\frac{113}{253}\right)$	$e\left(\frac{232}{253}\right)$	$e\left(\frac{59}{506}\right)$	$e\left(\frac{225}{506}\right)$	$e\left(\frac{60}{253}\right)$	$e\left(\frac{41}{506}\right)$	$e\left(\frac{25}{506}\right)$	$e\left(\frac{229}{253}\right)$
$\chi_{8464}(1239,\cdot)$	$1$	$1$	$e\left(\frac{227}{253}\right)$	$e\left(\frac{30}{253}\right)$	$e\left(\frac{75}{253}\right)$	$e\left(\frac{201}{253}\right)$	$e\left(\frac{375}{506}\right)$	$e\left(\frac{15}{506}\right)$	$e\left(\frac{4}{253}\right)$	$e\left(\frac{475}{506}\right)$	$e\left(\frac{339}{506}\right)$	$e\left(\frac{49}{253}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8464}(7,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{253}\right)\)	\(e\left(\frac{191}{253}\right)\)	\(e\left(\frac{98}{253}\right)\)	\(e\left(\frac{40}{253}\right)\)	\(e\left(\frac{237}{506}\right)\)	\(e\left(\frac{475}{506}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{199}{506}\right)\)	\(e\left(\frac{109}{506}\right)\)	\(e\left(\frac{118}{253}\right)\)
\(\chi_{8464}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{253}\right)\)	\(e\left(\frac{164}{253}\right)\)	\(e\left(\frac{157}{253}\right)\)	\(e\left(\frac{188}{253}\right)\)	\(e\left(\frac{279}{506}\right)\)	\(e\left(\frac{335}{506}\right)\)	\(e\left(\frac{5}{253}\right)\)	\(e\left(\frac{151}{506}\right)\)	\(e\left(\frac{487}{506}\right)\)	\(e\left(\frac{251}{253}\right)\)
\(\chi_{8464}(135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{253}\right)\)	\(e\left(\frac{151}{253}\right)\)	\(e\left(\frac{251}{253}\right)\)	\(e\left(\frac{25}{253}\right)\)	\(e\left(\frac{243}{506}\right)\)	\(e\left(\frac{455}{506}\right)\)	\(e\left(\frac{37}{253}\right)\)	\(e\left(\frac{409}{506}\right)\)	\(e\left(\frac{163}{506}\right)\)	\(e\left(\frac{137}{253}\right)\)
\(\chi_{8464}(199,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{253}\right)\)	\(e\left(\frac{80}{253}\right)\)	\(e\left(\frac{200}{253}\right)\)	\(e\left(\frac{30}{253}\right)\)	\(e\left(\frac{241}{506}\right)\)	\(e\left(\frac{293}{506}\right)\)	\(e\left(\frac{95}{253}\right)\)	\(e\left(\frac{339}{506}\right)\)	\(e\left(\frac{145}{506}\right)\)	\(e\left(\frac{215}{253}\right)\)
\(\chi_{8464}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{199}{253}\right)\)	\(e\left(\frac{218}{253}\right)\)	\(e\left(\frac{39}{253}\right)\)	\(e\left(\frac{145}{253}\right)\)	\(e\left(\frac{195}{506}\right)\)	\(e\left(\frac{109}{506}\right)\)	\(e\left(\frac{164}{253}\right)\)	\(e\left(\frac{247}{506}\right)\)	\(e\left(\frac{237}{506}\right)\)	\(e\left(\frac{238}{253}\right)\)
\(\chi_{8464}(295,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{87}{253}\right)\)	\(e\left(\frac{211}{253}\right)\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{174}{253}\right)\)	\(e\left(\frac{487}{506}\right)\)	\(e\left(\frac{485}{506}\right)\)	\(e\left(\frac{45}{253}\right)\)	\(e\left(\frac{347}{506}\right)\)	\(e\left(\frac{335}{506}\right)\)	\(e\left(\frac{235}{253}\right)\)
\(\chi_{8464}(327,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{195}{253}\right)\)	\(e\left(\frac{28}{253}\right)\)	\(e\left(\frac{70}{253}\right)\)	\(e\left(\frac{137}{253}\right)\)	\(e\left(\frac{97}{506}\right)\)	\(e\left(\frac{267}{506}\right)\)	\(e\left(\frac{223}{253}\right)\)	\(e\left(\frac{359}{506}\right)\)	\(e\left(\frac{367}{506}\right)\)	\(e\left(\frac{12}{253}\right)\)
\(\chi_{8464}(343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{60}{253}\right)\)	\(e\left(\frac{67}{253}\right)\)	\(e\left(\frac{41}{253}\right)\)	\(e\left(\frac{120}{253}\right)\)	\(e\left(\frac{205}{506}\right)\)	\(e\left(\frac{413}{506}\right)\)	\(e\left(\frac{127}{253}\right)\)	\(e\left(\frac{91}{506}\right)\)	\(e\left(\frac{327}{506}\right)\)	\(e\left(\frac{101}{253}\right)\)
\(\chi_{8464}(375,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{152}{253}\right)\)	\(e\left(\frac{136}{253}\right)\)	\(e\left(\frac{87}{253}\right)\)	\(e\left(\frac{51}{253}\right)\)	\(e\left(\frac{435}{506}\right)\)	\(e\left(\frac{321}{506}\right)\)	\(e\left(\frac{35}{253}\right)\)	\(e\left(\frac{45}{506}\right)\)	\(e\left(\frac{373}{506}\right)\)	\(e\left(\frac{239}{253}\right)\)
\(\chi_{8464}(471,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{253}\right)\)	\(e\left(\frac{175}{253}\right)\)	\(e\left(\frac{58}{253}\right)\)	\(e\left(\frac{34}{253}\right)\)	\(e\left(\frac{37}{506}\right)\)	\(e\left(\frac{467}{506}\right)\)	\(e\left(\frac{192}{253}\right)\)	\(e\left(\frac{283}{506}\right)\)	\(e\left(\frac{333}{506}\right)\)	\(e\left(\frac{75}{253}\right)\)
\(\chi_{8464}(503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{84}{253}\right)\)	\(e\left(\frac{195}{253}\right)\)	\(e\left(\frac{108}{253}\right)\)	\(e\left(\frac{168}{253}\right)\)	\(e\left(\frac{287}{506}\right)\)	\(e\left(\frac{477}{506}\right)\)	\(e\left(\frac{26}{253}\right)\)	\(e\left(\frac{431}{506}\right)\)	\(e\left(\frac{53}{506}\right)\)	\(e\left(\frac{192}{253}\right)\)
\(\chi_{8464}(567,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{253}\right)\)	\(e\left(\frac{223}{253}\right)\)	\(e\left(\frac{178}{253}\right)\)	\(e\left(\frac{52}{253}\right)\)	\(e\left(\frac{131}{506}\right)\)	\(e\left(\frac{491}{506}\right)\)	\(e\left(\frac{249}{253}\right)\)	\(e\left(\frac{31}{506}\right)\)	\(e\left(\frac{167}{506}\right)\)	\(e\left(\frac{204}{253}\right)\)
\(\chi_{8464}(615,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{253}\right)\)	\(e\left(\frac{240}{253}\right)\)	\(e\left(\frac{94}{253}\right)\)	\(e\left(\frac{90}{253}\right)\)	\(e\left(\frac{217}{506}\right)\)	\(e\left(\frac{373}{506}\right)\)	\(e\left(\frac{32}{253}\right)\)	\(e\left(\frac{5}{506}\right)\)	\(e\left(\frac{435}{506}\right)\)	\(e\left(\frac{139}{253}\right)\)
\(\chi_{8464}(631,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{189}{253}\right)\)	\(e\left(\frac{249}{253}\right)\)	\(e\left(\frac{243}{253}\right)\)	\(e\left(\frac{125}{253}\right)\)	\(e\left(\frac{203}{506}\right)\)	\(e\left(\frac{251}{506}\right)\)	\(e\left(\frac{185}{253}\right)\)	\(e\left(\frac{21}{506}\right)\)	\(e\left(\frac{309}{506}\right)\)	\(e\left(\frac{179}{253}\right)\)
\(\chi_{8464}(663,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{253}\right)\)	\(e\left(\frac{244}{253}\right)\)	\(e\left(\frac{104}{253}\right)\)	\(e\left(\frac{218}{253}\right)\)	\(e\left(\frac{267}{506}\right)\)	\(e\left(\frac{375}{506}\right)\)	\(e\left(\frac{100}{253}\right)\)	\(e\left(\frac{237}{506}\right)\)	\(e\left(\frac{379}{506}\right)\)	\(e\left(\frac{213}{253}\right)\)
\(\chi_{8464}(695,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{228}{253}\right)\)	\(e\left(\frac{204}{253}\right)\)	\(e\left(\frac{4}{253}\right)\)	\(e\left(\frac{203}{253}\right)\)	\(e\left(\frac{273}{506}\right)\)	\(e\left(\frac{355}{506}\right)\)	\(e\left(\frac{179}{253}\right)\)	\(e\left(\frac{447}{506}\right)\)	\(e\left(\frac{433}{506}\right)\)	\(e\left(\frac{232}{253}\right)\)
\(\chi_{8464}(711,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{104}{253}\right)\)	\(e\left(\frac{133}{253}\right)\)	\(e\left(\frac{206}{253}\right)\)	\(e\left(\frac{208}{253}\right)\)	\(e\left(\frac{271}{506}\right)\)	\(e\left(\frac{193}{506}\right)\)	\(e\left(\frac{237}{253}\right)\)	\(e\left(\frac{377}{506}\right)\)	\(e\left(\frac{415}{506}\right)\)	\(e\left(\frac{57}{253}\right)\)
\(\chi_{8464}(727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{135}{253}\right)\)	\(e\left(\frac{214}{253}\right)\)	\(e\left(\frac{29}{253}\right)\)	\(e\left(\frac{17}{253}\right)\)	\(e\left(\frac{145}{506}\right)\)	\(e\left(\frac{107}{506}\right)\)	\(e\left(\frac{96}{253}\right)\)	\(e\left(\frac{15}{506}\right)\)	\(e\left(\frac{293}{506}\right)\)	\(e\left(\frac{164}{253}\right)\)
\(\chi_{8464}(743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{253}\right)\)	\(e\left(\frac{81}{253}\right)\)	\(e\left(\frac{76}{253}\right)\)	\(e\left(\frac{62}{253}\right)\)	\(e\left(\frac{127}{506}\right)\)	\(e\left(\frac{167}{506}\right)\)	\(e\left(\frac{112}{253}\right)\)	\(e\left(\frac{397}{506}\right)\)	\(e\left(\frac{131}{506}\right)\)	\(e\left(\frac{107}{253}\right)\)
\(\chi_{8464}(839,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{253}\right)\)	\(e\left(\frac{186}{253}\right)\)	\(e\left(\frac{212}{253}\right)\)	\(e\left(\frac{133}{253}\right)\)	\(e\left(\frac{301}{506}\right)\)	\(e\left(\frac{93}{506}\right)\)	\(e\left(\frac{126}{253}\right)\)	\(e\left(\frac{415}{506}\right)\)	\(e\left(\frac{179}{506}\right)\)	\(e\left(\frac{152}{253}\right)\)
\(\chi_{8464}(871,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{253}\right)\)	\(e\left(\frac{239}{253}\right)\)	\(e\left(\frac{218}{253}\right)\)	\(e\left(\frac{58}{253}\right)\)	\(e\left(\frac{331}{506}\right)\)	\(e\left(\frac{499}{506}\right)\)	\(e\left(\frac{15}{253}\right)\)	\(e\left(\frac{453}{506}\right)\)	\(e\left(\frac{449}{506}\right)\)	\(e\left(\frac{247}{253}\right)\)
\(\chi_{8464}(935,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{253}\right)\)	\(e\left(\frac{113}{253}\right)\)	\(e\left(\frac{156}{253}\right)\)	\(e\left(\frac{74}{253}\right)\)	\(e\left(\frac{21}{506}\right)\)	\(e\left(\frac{183}{506}\right)\)	\(e\left(\frac{150}{253}\right)\)	\(e\left(\frac{229}{506}\right)\)	\(e\left(\frac{189}{506}\right)\)	\(e\left(\frac{193}{253}\right)\)
\(\chi_{8464}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{144}{253}\right)\)	\(e\left(\frac{9}{253}\right)\)	\(e\left(\frac{149}{253}\right)\)	\(e\left(\frac{35}{253}\right)\)	\(e\left(\frac{239}{506}\right)\)	\(e\left(\frac{131}{506}\right)\)	\(e\left(\frac{153}{253}\right)\)	\(e\left(\frac{269}{506}\right)\)	\(e\left(\frac{127}{506}\right)\)	\(e\left(\frac{40}{253}\right)\)
\(\chi_{8464}(999,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{253}\right)\)	\(e\left(\frac{84}{253}\right)\)	\(e\left(\frac{210}{253}\right)\)	\(e\left(\frac{158}{253}\right)\)	\(e\left(\frac{291}{506}\right)\)	\(e\left(\frac{295}{506}\right)\)	\(e\left(\frac{163}{253}\right)\)	\(e\left(\frac{65}{506}\right)\)	\(e\left(\frac{89}{506}\right)\)	\(e\left(\frac{36}{253}\right)\)
\(\chi_{8464}(1031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{253}\right)\)	\(e\left(\frac{24}{253}\right)\)	\(e\left(\frac{60}{253}\right)\)	\(e\left(\frac{9}{253}\right)\)	\(e\left(\frac{47}{506}\right)\)	\(e\left(\frac{265}{506}\right)\)	\(e\left(\frac{155}{253}\right)\)	\(e\left(\frac{127}{506}\right)\)	\(e\left(\frac{423}{506}\right)\)	\(e\left(\frac{191}{253}\right)\)
\(\chi_{8464}(1063,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{8}{253}\right)\)	\(e\left(\frac{127}{253}\right)\)	\(e\left(\frac{191}{253}\right)\)	\(e\left(\frac{16}{253}\right)\)	\(e\left(\frac{449}{506}\right)\)	\(e\left(\frac{443}{506}\right)\)	\(e\left(\frac{135}{253}\right)\)	\(e\left(\frac{29}{506}\right)\)	\(e\left(\frac{499}{506}\right)\)	\(e\left(\frac{199}{253}\right)\)
\(\chi_{8464}(1079,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{199}{253}\right)\)	\(e\left(\frac{118}{253}\right)\)	\(e\left(\frac{43}{253}\right)\)	\(e\left(\frac{337}{506}\right)\)	\(e\left(\frac{479}{506}\right)\)	\(e\left(\frac{94}{253}\right)\)	\(e\left(\frac{157}{506}\right)\)	\(e\left(\frac{503}{506}\right)\)	\(e\left(\frac{13}{253}\right)\)
\(\chi_{8464}(1095,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{201}{253}\right)\)	\(e\left(\frac{60}{253}\right)\)	\(e\left(\frac{150}{253}\right)\)	\(e\left(\frac{149}{253}\right)\)	\(e\left(\frac{497}{506}\right)\)	\(e\left(\frac{283}{506}\right)\)	\(e\left(\frac{8}{253}\right)\)	\(e\left(\frac{191}{506}\right)\)	\(e\left(\frac{425}{506}\right)\)	\(e\left(\frac{98}{253}\right)\)
\(\chi_{8464}(1111,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{163}{253}\right)\)	\(e\left(\frac{26}{253}\right)\)	\(e\left(\frac{65}{253}\right)\)	\(e\left(\frac{73}{253}\right)\)	\(e\left(\frac{325}{506}\right)\)	\(e\left(\frac{13}{506}\right)\)	\(e\left(\frac{189}{253}\right)\)	\(e\left(\frac{243}{506}\right)\)	\(e\left(\frac{395}{506}\right)\)	\(e\left(\frac{228}{253}\right)\)
\(\chi_{8464}(1207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{116}{253}\right)\)	\(e\left(\frac{197}{253}\right)\)	\(e\left(\frac{113}{253}\right)\)	\(e\left(\frac{232}{253}\right)\)	\(e\left(\frac{59}{506}\right)\)	\(e\left(\frac{225}{506}\right)\)	\(e\left(\frac{60}{253}\right)\)	\(e\left(\frac{41}{506}\right)\)	\(e\left(\frac{25}{506}\right)\)	\(e\left(\frac{229}{253}\right)\)
\(\chi_{8464}(1239,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{227}{253}\right)\)	\(e\left(\frac{30}{253}\right)\)	\(e\left(\frac{75}{253}\right)\)	\(e\left(\frac{201}{253}\right)\)	\(e\left(\frac{375}{506}\right)\)	\(e\left(\frac{15}{506}\right)\)	\(e\left(\frac{4}{253}\right)\)	\(e\left(\frac{475}{506}\right)\)	\(e\left(\frac{339}{506}\right)\)	\(e\left(\frac{49}{253}\right)\)

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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.br
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.bf	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)