LMFDB - Dirichlet character orbit 8464.bq

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8464, base_ring=CyclotomicField(506)) M = H._module chi = DirichletCharacter(H, M([253,253,206])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(39, 8464)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8464.39"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$8464$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$4232$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$506$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 4232.be	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{253})$	comment:Field of values of chi sage:CyclotomicField(chi.multiplicative_order()) gp:nfinit(polcyclo(charorder(g,chi))) magma:CyclotomicField(Order(chi));
Fixed field:	Number field defined by a degree 506 polynomial (not computed)	comment:Fixed field sage:chi.fixed_field()

First 31 of 220 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8464}(39,\cdot)$	$-1$	$1$	$e\left(\frac{130}{253}\right)$	$e\left(\frac{459}{506}\right)$	$e\left(\frac{9}{506}\right)$	$e\left(\frac{7}{253}\right)$	$e\left(\frac{201}{253}\right)$	$e\left(\frac{431}{506}\right)$	$e\left(\frac{213}{506}\right)$	$e\left(\frac{204}{253}\right)$	$e\left(\frac{38}{253}\right)$	$e\left(\frac{269}{506}\right)$
$\chi_{8464}(55,\cdot)$	$-1$	$1$	$e\left(\frac{58}{253}\right)$	$e\left(\frac{197}{506}\right)$	$e\left(\frac{113}{506}\right)$	$e\left(\frac{116}{253}\right)$	$e\left(\frac{78}{253}\right)$	$e\left(\frac{239}{506}\right)$	$e\left(\frac{313}{506}\right)$	$e\left(\frac{200}{253}\right)$	$e\left(\frac{196}{253}\right)$	$e\left(\frac{229}{506}\right)$
$\chi_{8464}(71,\cdot)$	$-1$	$1$	$e\left(\frac{137}{253}\right)$	$e\left(\frac{365}{506}\right)$	$e\left(\frac{27}{506}\right)$	$e\left(\frac{21}{253}\right)$	$e\left(\frac{97}{253}\right)$	$e\left(\frac{281}{506}\right)$	$e\left(\frac{133}{506}\right)$	$e\left(\frac{106}{253}\right)$	$e\left(\frac{114}{253}\right)$	$e\left(\frac{301}{506}\right)$
$\chi_{8464}(87,\cdot)$	$-1$	$1$	$e\left(\frac{63}{253}\right)$	$e\left(\frac{419}{506}\right)$	$e\left(\frac{415}{506}\right)$	$e\left(\frac{126}{253}\right)$	$e\left(\frac{76}{253}\right)$	$e\left(\frac{421}{506}\right)$	$e\left(\frac{39}{506}\right)$	$e\left(\frac{130}{253}\right)$	$e\left(\frac{178}{253}\right)$	$e\left(\frac{35}{506}\right)$
$\chi_{8464}(119,\cdot)$	$-1$	$1$	$e\left(\frac{252}{253}\right)$	$e\left(\frac{411}{506}\right)$	$e\left(\frac{395}{506}\right)$	$e\left(\frac{251}{253}\right)$	$e\left(\frac{51}{253}\right)$	$e\left(\frac{419}{506}\right)$	$e\left(\frac{409}{506}\right)$	$e\left(\frac{14}{253}\right)$	$e\left(\frac{206}{253}\right)$	$e\left(\frac{393}{506}\right)$
$\chi_{8464}(151,\cdot)$	$-1$	$1$	$e\left(\frac{233}{253}\right)$	$e\left(\frac{377}{506}\right)$	$e\left(\frac{57}{506}\right)$	$e\left(\frac{213}{253}\right)$	$e\left(\frac{8}{253}\right)$	$e\left(\frac{31}{506}\right)$	$e\left(\frac{337}{506}\right)$	$e\left(\frac{27}{253}\right)$	$e\left(\frac{72}{253}\right)$	$e\left(\frac{17}{506}\right)$
$\chi_{8464}(167,\cdot)$	$-1$	$1$	$e\left(\frac{56}{253}\right)$	$e\left(\frac{7}{506}\right)$	$e\left(\frac{397}{506}\right)$	$e\left(\frac{112}{253}\right)$	$e\left(\frac{180}{253}\right)$	$e\left(\frac{65}{506}\right)$	$e\left(\frac{119}{506}\right)$	$e\left(\frac{228}{253}\right)$	$e\left(\frac{102}{253}\right)$	$e\left(\frac{3}{506}\right)$
$\chi_{8464}(215,\cdot)$	$-1$	$1$	$e\left(\frac{224}{253}\right)$	$e\left(\frac{281}{506}\right)$	$e\left(\frac{323}{506}\right)$	$e\left(\frac{195}{253}\right)$	$e\left(\frac{214}{253}\right)$	$e\left(\frac{7}{506}\right)$	$e\left(\frac{223}{506}\right)$	$e\left(\frac{153}{253}\right)$	$e\left(\frac{155}{253}\right)$	$e\left(\frac{265}{506}\right)$
$\chi_{8464}(279,\cdot)$	$-1$	$1$	$e\left(\frac{106}{253}\right)$	$e\left(\frac{203}{506}\right)$	$e\left(\frac{381}{506}\right)$	$e\left(\frac{212}{253}\right)$	$e\left(\frac{160}{253}\right)$	$e\left(\frac{367}{506}\right)$	$e\left(\frac{415}{506}\right)$	$e\left(\frac{34}{253}\right)$	$e\left(\frac{175}{253}\right)$	$e\left(\frac{87}{506}\right)$
$\chi_{8464}(311,\cdot)$	$-1$	$1$	$e\left(\frac{149}{253}\right)$	$e\left(\frac{493}{506}\right)$	$e\left(\frac{347}{506}\right)$	$e\left(\frac{45}{253}\right)$	$e\left(\frac{244}{253}\right)$	$e\left(\frac{313}{506}\right)$	$e\left(\frac{285}{506}\right)$	$e\left(\frac{191}{253}\right)$	$e\left(\frac{172}{253}\right)$	$e\left(\frac{139}{506}\right)$
$\chi_{8464}(407,\cdot)$	$-1$	$1$	$e\left(\frac{251}{253}\right)$	$e\left(\frac{63}{506}\right)$	$e\left(\frac{31}{506}\right)$	$e\left(\frac{249}{253}\right)$	$e\left(\frac{102}{253}\right)$	$e\left(\frac{79}{506}\right)$	$e\left(\frac{59}{506}\right)$	$e\left(\frac{28}{253}\right)$	$e\left(\frac{159}{253}\right)$	$e\left(\frac{27}{506}\right)$
$\chi_{8464}(423,\cdot)$	$-1$	$1$	$e\left(\frac{245}{253}\right)$	$e\left(\frac{505}{506}\right)$	$e\left(\frac{377}{506}\right)$	$e\left(\frac{237}{253}\right)$	$e\left(\frac{155}{253}\right)$	$e\left(\frac{63}{506}\right)$	$e\left(\frac{489}{506}\right)$	$e\left(\frac{112}{253}\right)$	$e\left(\frac{130}{253}\right)$	$e\left(\frac{361}{506}\right)$
$\chi_{8464}(439,\cdot)$	$-1$	$1$	$e\left(\frac{93}{253}\right)$	$e\left(\frac{233}{506}\right)$	$e\left(\frac{203}{506}\right)$	$e\left(\frac{186}{253}\right)$	$e\left(\frac{64}{253}\right)$	$e\left(\frac{501}{506}\right)$	$e\left(\frac{419}{506}\right)$	$e\left(\frac{216}{253}\right)$	$e\left(\frac{70}{253}\right)$	$e\left(\frac{389}{506}\right)$
$\chi_{8464}(455,\cdot)$	$-1$	$1$	$e\left(\frac{30}{253}\right)$	$e\left(\frac{67}{506}\right)$	$e\left(\frac{41}{506}\right)$	$e\left(\frac{60}{253}\right)$	$e\left(\frac{241}{253}\right)$	$e\left(\frac{333}{506}\right)$	$e\left(\frac{127}{506}\right)$	$e\left(\frac{86}{253}\right)$	$e\left(\frac{145}{253}\right)$	$e\left(\frac{101}{506}\right)$
$\chi_{8464}(519,\cdot)$	$-1$	$1$	$e\left(\frac{90}{253}\right)$	$e\left(\frac{201}{506}\right)$	$e\left(\frac{123}{506}\right)$	$e\left(\frac{180}{253}\right)$	$e\left(\frac{217}{253}\right)$	$e\left(\frac{493}{506}\right)$	$e\left(\frac{381}{506}\right)$	$e\left(\frac{5}{253}\right)$	$e\left(\frac{182}{253}\right)$	$e\left(\frac{303}{506}\right)$
$\chi_{8464}(535,\cdot)$	$-1$	$1$	$e\left(\frac{210}{253}\right)$	$e\left(\frac{469}{506}\right)$	$e\left(\frac{287}{506}\right)$	$e\left(\frac{167}{253}\right)$	$e\left(\frac{169}{253}\right)$	$e\left(\frac{307}{506}\right)$	$e\left(\frac{383}{506}\right)$	$e\left(\frac{96}{253}\right)$	$e\left(\frac{3}{253}\right)$	$e\left(\frac{201}{506}\right)$
$\chi_{8464}(583,\cdot)$	$-1$	$1$	$e\left(\frac{213}{253}\right)$	$e\left(\frac{501}{506}\right)$	$e\left(\frac{367}{506}\right)$	$e\left(\frac{173}{253}\right)$	$e\left(\frac{16}{253}\right)$	$e\left(\frac{315}{506}\right)$	$e\left(\frac{421}{506}\right)$	$e\left(\frac{54}{253}\right)$	$e\left(\frac{144}{253}\right)$	$e\left(\frac{287}{506}\right)$
$\chi_{8464}(679,\cdot)$	$-1$	$1$	$e\left(\frac{226}{253}\right)$	$e\left(\frac{471}{506}\right)$	$e\left(\frac{39}{506}\right)$	$e\left(\frac{199}{253}\right)$	$e\left(\frac{112}{253}\right)$	$e\left(\frac{181}{506}\right)$	$e\left(\frac{417}{506}\right)$	$e\left(\frac{125}{253}\right)$	$e\left(\frac{249}{253}\right)$	$e\left(\frac{491}{506}\right)$
$\chi_{8464}(775,\cdot)$	$-1$	$1$	$e\left(\frac{119}{253}\right)$	$e\left(\frac{173}{506}\right)$	$e\left(\frac{53}{506}\right)$	$e\left(\frac{238}{253}\right)$	$e\left(\frac{3}{253}\right)$	$e\left(\frac{233}{506}\right)$	$e\left(\frac{411}{506}\right)$	$e\left(\frac{105}{253}\right)$	$e\left(\frac{27}{253}\right)$	$e\left(\frac{291}{506}\right)$
$\chi_{8464}(791,\cdot)$	$-1$	$1$	$e\left(\frac{179}{253}\right)$	$e\left(\frac{307}{506}\right)$	$e\left(\frac{135}{506}\right)$	$e\left(\frac{105}{253}\right)$	$e\left(\frac{232}{253}\right)$	$e\left(\frac{393}{506}\right)$	$e\left(\frac{159}{506}\right)$	$e\left(\frac{24}{253}\right)$	$e\left(\frac{64}{253}\right)$	$e\left(\frac{493}{506}\right)$
$\chi_{8464}(807,\cdot)$	$-1$	$1$	$e\left(\frac{49}{253}\right)$	$e\left(\frac{101}{506}\right)$	$e\left(\frac{379}{506}\right)$	$e\left(\frac{98}{253}\right)$	$e\left(\frac{31}{253}\right)$	$e\left(\frac{215}{506}\right)$	$e\left(\frac{199}{506}\right)$	$e\left(\frac{73}{253}\right)$	$e\left(\frac{26}{253}\right)$	$e\left(\frac{477}{506}\right)$
$\chi_{8464}(823,\cdot)$	$-1$	$1$	$e\left(\frac{250}{253}\right)$	$e\left(\frac{221}{506}\right)$	$e\left(\frac{173}{506}\right)$	$e\left(\frac{247}{253}\right)$	$e\left(\frac{153}{253}\right)$	$e\left(\frac{245}{506}\right)$	$e\left(\frac{215}{506}\right)$	$e\left(\frac{42}{253}\right)$	$e\left(\frac{112}{253}\right)$	$e\left(\frac{167}{506}\right)$
$\chi_{8464}(855,\cdot)$	$-1$	$1$	$e\left(\frac{208}{253}\right)$	$e\left(\frac{279}{506}\right)$	$e\left(\frac{65}{506}\right)$	$e\left(\frac{163}{253}\right)$	$e\left(\frac{18}{253}\right)$	$e\left(\frac{133}{506}\right)$	$e\left(\frac{189}{506}\right)$	$e\left(\frac{124}{253}\right)$	$e\left(\frac{162}{253}\right)$	$e\left(\frac{481}{506}\right)$
$\chi_{8464}(887,\cdot)$	$-1$	$1$	$e\left(\frac{200}{253}\right)$	$e\left(\frac{25}{506}\right)$	$e\left(\frac{189}{506}\right)$	$e\left(\frac{147}{253}\right)$	$e\left(\frac{173}{253}\right)$	$e\left(\frac{449}{506}\right)$	$e\left(\frac{425}{506}\right)$	$e\left(\frac{236}{253}\right)$	$e\left(\frac{39}{253}\right)$	$e\left(\frac{83}{506}\right)$
$\chi_{8464}(903,\cdot)$	$-1$	$1$	$e\left(\frac{111}{253}\right)$	$e\left(\frac{425}{506}\right)$	$e\left(\frac{177}{506}\right)$	$e\left(\frac{222}{253}\right)$	$e\left(\frac{158}{253}\right)$	$e\left(\frac{43}{506}\right)$	$e\left(\frac{141}{506}\right)$	$e\left(\frac{217}{253}\right)$	$e\left(\frac{157}{253}\right)$	$e\left(\frac{399}{506}\right)$
$\chi_{8464}(951,\cdot)$	$-1$	$1$	$e\left(\frac{202}{253}\right)$	$e\left(\frac{215}{506}\right)$	$e\left(\frac{411}{506}\right)$	$e\left(\frac{151}{253}\right)$	$e\left(\frac{71}{253}\right)$	$e\left(\frac{117}{506}\right)$	$e\left(\frac{113}{506}\right)$	$e\left(\frac{208}{253}\right)$	$e\left(\frac{133}{253}\right)$	$e\left(\frac{309}{506}\right)$
$\chi_{8464}(1015,\cdot)$	$-1$	$1$	$e\left(\frac{216}{253}\right)$	$e\left(\frac{27}{506}\right)$	$e\left(\frac{447}{506}\right)$	$e\left(\frac{179}{253}\right)$	$e\left(\frac{116}{253}\right)$	$e\left(\frac{323}{506}\right)$	$e\left(\frac{459}{506}\right)$	$e\left(\frac{12}{253}\right)$	$e\left(\frac{32}{253}\right)$	$e\left(\frac{373}{506}\right)$
$\chi_{8464}(1047,\cdot)$	$-1$	$1$	$e\left(\frac{50}{253}\right)$	$e\left(\frac{449}{506}\right)$	$e\left(\frac{237}{506}\right)$	$e\left(\frac{100}{253}\right)$	$e\left(\frac{233}{253}\right)$	$e\left(\frac{49}{506}\right)$	$e\left(\frac{43}{506}\right)$	$e\left(\frac{59}{253}\right)$	$e\left(\frac{73}{253}\right)$	$e\left(\frac{337}{506}\right)$
$\chi_{8464}(1143,\cdot)$	$-1$	$1$	$e\left(\frac{240}{253}\right)$	$e\left(\frac{283}{506}\right)$	$e\left(\frac{75}{506}\right)$	$e\left(\frac{227}{253}\right)$	$e\left(\frac{157}{253}\right)$	$e\left(\frac{387}{506}\right)$	$e\left(\frac{257}{506}\right)$	$e\left(\frac{182}{253}\right)$	$e\left(\frac{148}{253}\right)$	$e\left(\frac{49}{506}\right)$
$\chi_{8464}(1159,\cdot)$	$-1$	$1$	$e\left(\frac{113}{253}\right)$	$e\left(\frac{109}{506}\right)$	$e\left(\frac{399}{506}\right)$	$e\left(\frac{226}{253}\right)$	$e\left(\frac{56}{253}\right)$	$e\left(\frac{217}{506}\right)$	$e\left(\frac{335}{506}\right)$	$e\left(\frac{189}{253}\right)$	$e\left(\frac{251}{253}\right)$	$e\left(\frac{119}{506}\right)$
$\chi_{8464}(1175,\cdot)$	$-1$	$1$	$e\left(\frac{5}{253}\right)$	$e\left(\frac{475}{506}\right)$	$e\left(\frac{49}{506}\right)$	$e\left(\frac{10}{253}\right)$	$e\left(\frac{251}{253}\right)$	$e\left(\frac{435}{506}\right)$	$e\left(\frac{485}{506}\right)$	$e\left(\frac{183}{253}\right)$	$e\left(\frac{235}{253}\right)$	$e\left(\frac{59}{506}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8464}(39,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{130}{253}\right)\)	\(e\left(\frac{459}{506}\right)\)	\(e\left(\frac{9}{506}\right)\)	\(e\left(\frac{7}{253}\right)\)	\(e\left(\frac{201}{253}\right)\)	\(e\left(\frac{431}{506}\right)\)	\(e\left(\frac{213}{506}\right)\)	\(e\left(\frac{204}{253}\right)\)	\(e\left(\frac{38}{253}\right)\)	\(e\left(\frac{269}{506}\right)\)
\(\chi_{8464}(55,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{58}{253}\right)\)	\(e\left(\frac{197}{506}\right)\)	\(e\left(\frac{113}{506}\right)\)	\(e\left(\frac{116}{253}\right)\)	\(e\left(\frac{78}{253}\right)\)	\(e\left(\frac{239}{506}\right)\)	\(e\left(\frac{313}{506}\right)\)	\(e\left(\frac{200}{253}\right)\)	\(e\left(\frac{196}{253}\right)\)	\(e\left(\frac{229}{506}\right)\)
\(\chi_{8464}(71,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{253}\right)\)	\(e\left(\frac{365}{506}\right)\)	\(e\left(\frac{27}{506}\right)\)	\(e\left(\frac{21}{253}\right)\)	\(e\left(\frac{97}{253}\right)\)	\(e\left(\frac{281}{506}\right)\)	\(e\left(\frac{133}{506}\right)\)	\(e\left(\frac{106}{253}\right)\)	\(e\left(\frac{114}{253}\right)\)	\(e\left(\frac{301}{506}\right)\)
\(\chi_{8464}(87,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{63}{253}\right)\)	\(e\left(\frac{419}{506}\right)\)	\(e\left(\frac{415}{506}\right)\)	\(e\left(\frac{126}{253}\right)\)	\(e\left(\frac{76}{253}\right)\)	\(e\left(\frac{421}{506}\right)\)	\(e\left(\frac{39}{506}\right)\)	\(e\left(\frac{130}{253}\right)\)	\(e\left(\frac{178}{253}\right)\)	\(e\left(\frac{35}{506}\right)\)
\(\chi_{8464}(119,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{252}{253}\right)\)	\(e\left(\frac{411}{506}\right)\)	\(e\left(\frac{395}{506}\right)\)	\(e\left(\frac{251}{253}\right)\)	\(e\left(\frac{51}{253}\right)\)	\(e\left(\frac{419}{506}\right)\)	\(e\left(\frac{409}{506}\right)\)	\(e\left(\frac{14}{253}\right)\)	\(e\left(\frac{206}{253}\right)\)	\(e\left(\frac{393}{506}\right)\)
\(\chi_{8464}(151,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{233}{253}\right)\)	\(e\left(\frac{377}{506}\right)\)	\(e\left(\frac{57}{506}\right)\)	\(e\left(\frac{213}{253}\right)\)	\(e\left(\frac{8}{253}\right)\)	\(e\left(\frac{31}{506}\right)\)	\(e\left(\frac{337}{506}\right)\)	\(e\left(\frac{27}{253}\right)\)	\(e\left(\frac{72}{253}\right)\)	\(e\left(\frac{17}{506}\right)\)
\(\chi_{8464}(167,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{56}{253}\right)\)	\(e\left(\frac{7}{506}\right)\)	\(e\left(\frac{397}{506}\right)\)	\(e\left(\frac{112}{253}\right)\)	\(e\left(\frac{180}{253}\right)\)	\(e\left(\frac{65}{506}\right)\)	\(e\left(\frac{119}{506}\right)\)	\(e\left(\frac{228}{253}\right)\)	\(e\left(\frac{102}{253}\right)\)	\(e\left(\frac{3}{506}\right)\)
\(\chi_{8464}(215,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{224}{253}\right)\)	\(e\left(\frac{281}{506}\right)\)	\(e\left(\frac{323}{506}\right)\)	\(e\left(\frac{195}{253}\right)\)	\(e\left(\frac{214}{253}\right)\)	\(e\left(\frac{7}{506}\right)\)	\(e\left(\frac{223}{506}\right)\)	\(e\left(\frac{153}{253}\right)\)	\(e\left(\frac{155}{253}\right)\)	\(e\left(\frac{265}{506}\right)\)
\(\chi_{8464}(279,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{106}{253}\right)\)	\(e\left(\frac{203}{506}\right)\)	\(e\left(\frac{381}{506}\right)\)	\(e\left(\frac{212}{253}\right)\)	\(e\left(\frac{160}{253}\right)\)	\(e\left(\frac{367}{506}\right)\)	\(e\left(\frac{415}{506}\right)\)	\(e\left(\frac{34}{253}\right)\)	\(e\left(\frac{175}{253}\right)\)	\(e\left(\frac{87}{506}\right)\)
\(\chi_{8464}(311,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{253}\right)\)	\(e\left(\frac{493}{506}\right)\)	\(e\left(\frac{347}{506}\right)\)	\(e\left(\frac{45}{253}\right)\)	\(e\left(\frac{244}{253}\right)\)	\(e\left(\frac{313}{506}\right)\)	\(e\left(\frac{285}{506}\right)\)	\(e\left(\frac{191}{253}\right)\)	\(e\left(\frac{172}{253}\right)\)	\(e\left(\frac{139}{506}\right)\)
\(\chi_{8464}(407,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{251}{253}\right)\)	\(e\left(\frac{63}{506}\right)\)	\(e\left(\frac{31}{506}\right)\)	\(e\left(\frac{249}{253}\right)\)	\(e\left(\frac{102}{253}\right)\)	\(e\left(\frac{79}{506}\right)\)	\(e\left(\frac{59}{506}\right)\)	\(e\left(\frac{28}{253}\right)\)	\(e\left(\frac{159}{253}\right)\)	\(e\left(\frac{27}{506}\right)\)
\(\chi_{8464}(423,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{245}{253}\right)\)	\(e\left(\frac{505}{506}\right)\)	\(e\left(\frac{377}{506}\right)\)	\(e\left(\frac{237}{253}\right)\)	\(e\left(\frac{155}{253}\right)\)	\(e\left(\frac{63}{506}\right)\)	\(e\left(\frac{489}{506}\right)\)	\(e\left(\frac{112}{253}\right)\)	\(e\left(\frac{130}{253}\right)\)	\(e\left(\frac{361}{506}\right)\)
\(\chi_{8464}(439,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{93}{253}\right)\)	\(e\left(\frac{233}{506}\right)\)	\(e\left(\frac{203}{506}\right)\)	\(e\left(\frac{186}{253}\right)\)	\(e\left(\frac{64}{253}\right)\)	\(e\left(\frac{501}{506}\right)\)	\(e\left(\frac{419}{506}\right)\)	\(e\left(\frac{216}{253}\right)\)	\(e\left(\frac{70}{253}\right)\)	\(e\left(\frac{389}{506}\right)\)
\(\chi_{8464}(455,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{30}{253}\right)\)	\(e\left(\frac{67}{506}\right)\)	\(e\left(\frac{41}{506}\right)\)	\(e\left(\frac{60}{253}\right)\)	\(e\left(\frac{241}{253}\right)\)	\(e\left(\frac{333}{506}\right)\)	\(e\left(\frac{127}{506}\right)\)	\(e\left(\frac{86}{253}\right)\)	\(e\left(\frac{145}{253}\right)\)	\(e\left(\frac{101}{506}\right)\)
\(\chi_{8464}(519,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{90}{253}\right)\)	\(e\left(\frac{201}{506}\right)\)	\(e\left(\frac{123}{506}\right)\)	\(e\left(\frac{180}{253}\right)\)	\(e\left(\frac{217}{253}\right)\)	\(e\left(\frac{493}{506}\right)\)	\(e\left(\frac{381}{506}\right)\)	\(e\left(\frac{5}{253}\right)\)	\(e\left(\frac{182}{253}\right)\)	\(e\left(\frac{303}{506}\right)\)
\(\chi_{8464}(535,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{210}{253}\right)\)	\(e\left(\frac{469}{506}\right)\)	\(e\left(\frac{287}{506}\right)\)	\(e\left(\frac{167}{253}\right)\)	\(e\left(\frac{169}{253}\right)\)	\(e\left(\frac{307}{506}\right)\)	\(e\left(\frac{383}{506}\right)\)	\(e\left(\frac{96}{253}\right)\)	\(e\left(\frac{3}{253}\right)\)	\(e\left(\frac{201}{506}\right)\)
\(\chi_{8464}(583,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{213}{253}\right)\)	\(e\left(\frac{501}{506}\right)\)	\(e\left(\frac{367}{506}\right)\)	\(e\left(\frac{173}{253}\right)\)	\(e\left(\frac{16}{253}\right)\)	\(e\left(\frac{315}{506}\right)\)	\(e\left(\frac{421}{506}\right)\)	\(e\left(\frac{54}{253}\right)\)	\(e\left(\frac{144}{253}\right)\)	\(e\left(\frac{287}{506}\right)\)
\(\chi_{8464}(679,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{226}{253}\right)\)	\(e\left(\frac{471}{506}\right)\)	\(e\left(\frac{39}{506}\right)\)	\(e\left(\frac{199}{253}\right)\)	\(e\left(\frac{112}{253}\right)\)	\(e\left(\frac{181}{506}\right)\)	\(e\left(\frac{417}{506}\right)\)	\(e\left(\frac{125}{253}\right)\)	\(e\left(\frac{249}{253}\right)\)	\(e\left(\frac{491}{506}\right)\)
\(\chi_{8464}(775,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{253}\right)\)	\(e\left(\frac{173}{506}\right)\)	\(e\left(\frac{53}{506}\right)\)	\(e\left(\frac{238}{253}\right)\)	\(e\left(\frac{3}{253}\right)\)	\(e\left(\frac{233}{506}\right)\)	\(e\left(\frac{411}{506}\right)\)	\(e\left(\frac{105}{253}\right)\)	\(e\left(\frac{27}{253}\right)\)	\(e\left(\frac{291}{506}\right)\)
\(\chi_{8464}(791,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{253}\right)\)	\(e\left(\frac{307}{506}\right)\)	\(e\left(\frac{135}{506}\right)\)	\(e\left(\frac{105}{253}\right)\)	\(e\left(\frac{232}{253}\right)\)	\(e\left(\frac{393}{506}\right)\)	\(e\left(\frac{159}{506}\right)\)	\(e\left(\frac{24}{253}\right)\)	\(e\left(\frac{64}{253}\right)\)	\(e\left(\frac{493}{506}\right)\)
\(\chi_{8464}(807,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{253}\right)\)	\(e\left(\frac{101}{506}\right)\)	\(e\left(\frac{379}{506}\right)\)	\(e\left(\frac{98}{253}\right)\)	\(e\left(\frac{31}{253}\right)\)	\(e\left(\frac{215}{506}\right)\)	\(e\left(\frac{199}{506}\right)\)	\(e\left(\frac{73}{253}\right)\)	\(e\left(\frac{26}{253}\right)\)	\(e\left(\frac{477}{506}\right)\)
\(\chi_{8464}(823,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{250}{253}\right)\)	\(e\left(\frac{221}{506}\right)\)	\(e\left(\frac{173}{506}\right)\)	\(e\left(\frac{247}{253}\right)\)	\(e\left(\frac{153}{253}\right)\)	\(e\left(\frac{245}{506}\right)\)	\(e\left(\frac{215}{506}\right)\)	\(e\left(\frac{42}{253}\right)\)	\(e\left(\frac{112}{253}\right)\)	\(e\left(\frac{167}{506}\right)\)
\(\chi_{8464}(855,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{208}{253}\right)\)	\(e\left(\frac{279}{506}\right)\)	\(e\left(\frac{65}{506}\right)\)	\(e\left(\frac{163}{253}\right)\)	\(e\left(\frac{18}{253}\right)\)	\(e\left(\frac{133}{506}\right)\)	\(e\left(\frac{189}{506}\right)\)	\(e\left(\frac{124}{253}\right)\)	\(e\left(\frac{162}{253}\right)\)	\(e\left(\frac{481}{506}\right)\)
\(\chi_{8464}(887,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{200}{253}\right)\)	\(e\left(\frac{25}{506}\right)\)	\(e\left(\frac{189}{506}\right)\)	\(e\left(\frac{147}{253}\right)\)	\(e\left(\frac{173}{253}\right)\)	\(e\left(\frac{449}{506}\right)\)	\(e\left(\frac{425}{506}\right)\)	\(e\left(\frac{236}{253}\right)\)	\(e\left(\frac{39}{253}\right)\)	\(e\left(\frac{83}{506}\right)\)
\(\chi_{8464}(903,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{111}{253}\right)\)	\(e\left(\frac{425}{506}\right)\)	\(e\left(\frac{177}{506}\right)\)	\(e\left(\frac{222}{253}\right)\)	\(e\left(\frac{158}{253}\right)\)	\(e\left(\frac{43}{506}\right)\)	\(e\left(\frac{141}{506}\right)\)	\(e\left(\frac{217}{253}\right)\)	\(e\left(\frac{157}{253}\right)\)	\(e\left(\frac{399}{506}\right)\)
\(\chi_{8464}(951,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{202}{253}\right)\)	\(e\left(\frac{215}{506}\right)\)	\(e\left(\frac{411}{506}\right)\)	\(e\left(\frac{151}{253}\right)\)	\(e\left(\frac{71}{253}\right)\)	\(e\left(\frac{117}{506}\right)\)	\(e\left(\frac{113}{506}\right)\)	\(e\left(\frac{208}{253}\right)\)	\(e\left(\frac{133}{253}\right)\)	\(e\left(\frac{309}{506}\right)\)
\(\chi_{8464}(1015,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{216}{253}\right)\)	\(e\left(\frac{27}{506}\right)\)	\(e\left(\frac{447}{506}\right)\)	\(e\left(\frac{179}{253}\right)\)	\(e\left(\frac{116}{253}\right)\)	\(e\left(\frac{323}{506}\right)\)	\(e\left(\frac{459}{506}\right)\)	\(e\left(\frac{12}{253}\right)\)	\(e\left(\frac{32}{253}\right)\)	\(e\left(\frac{373}{506}\right)\)
\(\chi_{8464}(1047,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{50}{253}\right)\)	\(e\left(\frac{449}{506}\right)\)	\(e\left(\frac{237}{506}\right)\)	\(e\left(\frac{100}{253}\right)\)	\(e\left(\frac{233}{253}\right)\)	\(e\left(\frac{49}{506}\right)\)	\(e\left(\frac{43}{506}\right)\)	\(e\left(\frac{59}{253}\right)\)	\(e\left(\frac{73}{253}\right)\)	\(e\left(\frac{337}{506}\right)\)
\(\chi_{8464}(1143,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{240}{253}\right)\)	\(e\left(\frac{283}{506}\right)\)	\(e\left(\frac{75}{506}\right)\)	\(e\left(\frac{227}{253}\right)\)	\(e\left(\frac{157}{253}\right)\)	\(e\left(\frac{387}{506}\right)\)	\(e\left(\frac{257}{506}\right)\)	\(e\left(\frac{182}{253}\right)\)	\(e\left(\frac{148}{253}\right)\)	\(e\left(\frac{49}{506}\right)\)
\(\chi_{8464}(1159,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{253}\right)\)	\(e\left(\frac{109}{506}\right)\)	\(e\left(\frac{399}{506}\right)\)	\(e\left(\frac{226}{253}\right)\)	\(e\left(\frac{56}{253}\right)\)	\(e\left(\frac{217}{506}\right)\)	\(e\left(\frac{335}{506}\right)\)	\(e\left(\frac{189}{253}\right)\)	\(e\left(\frac{251}{253}\right)\)	\(e\left(\frac{119}{506}\right)\)
\(\chi_{8464}(1175,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{253}\right)\)	\(e\left(\frac{475}{506}\right)\)	\(e\left(\frac{49}{506}\right)\)	\(e\left(\frac{10}{253}\right)\)	\(e\left(\frac{251}{253}\right)\)	\(e\left(\frac{435}{506}\right)\)	\(e\left(\frac{485}{506}\right)\)	\(e\left(\frac{183}{253}\right)\)	\(e\left(\frac{235}{253}\right)\)	\(e\left(\frac{59}{506}\right)\)

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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.bq
Modulus	$8464$
Conductor	$4232$
Order	$506$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(8464\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(4232\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(506\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 4232.be	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	odd	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);