LMFDB - Dirichlet character orbit 9016.et

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9016, base_ring=CyclotomicField(462)) M = H._module chi = DirichletCharacter(H, M([231,0,374,168])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(39, 9016)) 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("9016.39"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$9016$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$4508$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$462$	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 4508.cj	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:	$\Q(\zeta_{231})$
Fixed field:	Number field defined by a degree 462 polynomial (not computed)

First 31 of 120 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$25$	$27$
$\chi_{9016}(39,\cdot)$	$-1$	$1$	$e\left(\frac{59}{462}\right)$	$e\left(\frac{194}{231}\right)$	$e\left(\frac{59}{231}\right)$	$e\left(\frac{71}{462}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{149}{154}\right)$	$e\left(\frac{181}{231}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{157}{231}\right)$	$e\left(\frac{59}{154}\right)$
$\chi_{9016}(95,\cdot)$	$-1$	$1$	$e\left(\frac{305}{462}\right)$	$e\left(\frac{212}{231}\right)$	$e\left(\frac{74}{231}\right)$	$e\left(\frac{461}{462}\right)$	$e\left(\frac{36}{77}\right)$	$e\left(\frac{89}{154}\right)$	$e\left(\frac{43}{231}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{193}{231}\right)$	$e\left(\frac{151}{154}\right)$
$\chi_{9016}(151,\cdot)$	$-1$	$1$	$e\left(\frac{425}{462}\right)$	$e\left(\frac{125}{231}\right)$	$e\left(\frac{194}{231}\right)$	$e\left(\frac{347}{462}\right)$	$e\left(\frac{59}{77}\right)$	$e\left(\frac{71}{154}\right)$	$e\left(\frac{94}{231}\right)$	$e\left(\frac{25}{66}\right)$	$e\left(\frac{19}{231}\right)$	$e\left(\frac{117}{154}\right)$
$\chi_{9016}(303,\cdot)$	$-1$	$1$	$e\left(\frac{211}{462}\right)$	$e\left(\frac{130}{231}\right)$	$e\left(\frac{211}{231}\right)$	$e\left(\frac{19}{462}\right)$	$e\left(\frac{9}{77}\right)$	$e\left(\frac{3}{154}\right)$	$e\left(\frac{107}{231}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{29}{231}\right)$	$e\left(\frac{57}{154}\right)$
$\chi_{9016}(487,\cdot)$	$-1$	$1$	$e\left(\frac{431}{462}\right)$	$e\left(\frac{86}{231}\right)$	$e\left(\frac{200}{231}\right)$	$e\left(\frac{41}{462}\right)$	$e\left(\frac{64}{77}\right)$	$e\left(\frac{47}{154}\right)$	$e\left(\frac{85}{231}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{172}{231}\right)$	$e\left(\frac{123}{154}\right)$
$\chi_{9016}(583,\cdot)$	$-1$	$1$	$e\left(\frac{25}{462}\right)$	$e\left(\frac{184}{231}\right)$	$e\left(\frac{25}{231}\right)$	$e\left(\frac{265}{462}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{131}{154}\right)$	$e\left(\frac{155}{231}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{137}{231}\right)$	$e\left(\frac{25}{154}\right)$
$\chi_{9016}(639,\cdot)$	$-1$	$1$	$e\left(\frac{391}{462}\right)$	$e\left(\frac{115}{231}\right)$	$e\left(\frac{160}{231}\right)$	$e\left(\frac{79}{462}\right)$	$e\left(\frac{5}{77}\right)$	$e\left(\frac{53}{154}\right)$	$e\left(\frac{68}{231}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{230}{231}\right)$	$e\left(\frac{83}{154}\right)$
$\chi_{9016}(767,\cdot)$	$-1$	$1$	$e\left(\frac{443}{462}\right)$	$e\left(\frac{8}{231}\right)$	$e\left(\frac{212}{231}\right)$	$e\left(\frac{353}{462}\right)$	$e\left(\frac{74}{77}\right)$	$e\left(\frac{153}{154}\right)$	$e\left(\frac{67}{231}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{16}{231}\right)$	$e\left(\frac{135}{154}\right)$
$\chi_{9016}(807,\cdot)$	$-1$	$1$	$e\left(\frac{397}{462}\right)$	$e\left(\frac{76}{231}\right)$	$e\left(\frac{166}{231}\right)$	$e\left(\frac{235}{462}\right)$	$e\left(\frac{10}{77}\right)$	$e\left(\frac{29}{154}\right)$	$e\left(\frac{59}{231}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{152}{231}\right)$	$e\left(\frac{89}{154}\right)$
$\chi_{9016}(823,\cdot)$	$-1$	$1$	$e\left(\frac{17}{462}\right)$	$e\left(\frac{5}{231}\right)$	$e\left(\frac{17}{231}\right)$	$e\left(\frac{365}{462}\right)$	$e\left(\frac{27}{77}\right)$	$e\left(\frac{9}{154}\right)$	$e\left(\frac{13}{231}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{10}{231}\right)$	$e\left(\frac{17}{154}\right)$
$\chi_{9016}(975,\cdot)$	$-1$	$1$	$e\left(\frac{445}{462}\right)$	$e\left(\frac{226}{231}\right)$	$e\left(\frac{214}{231}\right)$	$e\left(\frac{97}{462}\right)$	$e\left(\frac{50}{77}\right)$	$e\left(\frac{145}{154}\right)$	$e\left(\frac{218}{231}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{221}{231}\right)$	$e\left(\frac{137}{154}\right)$
$\chi_{9016}(991,\cdot)$	$-1$	$1$	$e\left(\frac{419}{462}\right)$	$e\left(\frac{164}{231}\right)$	$e\left(\frac{188}{231}\right)$	$e\left(\frac{191}{462}\right)$	$e\left(\frac{54}{77}\right)$	$e\left(\frac{95}{154}\right)$	$e\left(\frac{103}{231}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{97}{231}\right)$	$e\left(\frac{111}{154}\right)$
$\chi_{9016}(1087,\cdot)$	$-1$	$1$	$e\left(\frac{295}{462}\right)$	$e\left(\frac{46}{231}\right)$	$e\left(\frac{64}{231}\right)$	$e\left(\frac{355}{462}\right)$	$e\left(\frac{2}{77}\right)$	$e\left(\frac{129}{154}\right)$	$e\left(\frac{212}{231}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{92}{231}\right)$	$e\left(\frac{141}{154}\right)$
$\chi_{9016}(1143,\cdot)$	$-1$	$1$	$e\left(\frac{367}{462}\right)$	$e\left(\frac{40}{231}\right)$	$e\left(\frac{136}{231}\right)$	$e\left(\frac{379}{462}\right)$	$e\left(\frac{62}{77}\right)$	$e\left(\frac{149}{154}\right)$	$e\left(\frac{104}{231}\right)$	$e\left(\frac{41}{66}\right)$	$e\left(\frac{80}{231}\right)$	$e\left(\frac{59}{154}\right)$
$\chi_{9016}(1159,\cdot)$	$-1$	$1$	$e\left(\frac{401}{462}\right)$	$e\left(\frac{50}{231}\right)$	$e\left(\frac{170}{231}\right)$	$e\left(\frac{185}{462}\right)$	$e\left(\frac{39}{77}\right)$	$e\left(\frac{13}{154}\right)$	$e\left(\frac{130}{231}\right)$	$e\left(\frac{43}{66}\right)$	$e\left(\frac{100}{231}\right)$	$e\left(\frac{93}{154}\right)$
$\chi_{9016}(1199,\cdot)$	$-1$	$1$	$e\left(\frac{19}{462}\right)$	$e\left(\frac{223}{231}\right)$	$e\left(\frac{19}{231}\right)$	$e\left(\frac{109}{462}\right)$	$e\left(\frac{3}{77}\right)$	$e\left(\frac{1}{154}\right)$	$e\left(\frac{164}{231}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{215}{231}\right)$	$e\left(\frac{19}{154}\right)$
$\chi_{9016}(1271,\cdot)$	$-1$	$1$	$e\left(\frac{53}{462}\right)$	$e\left(\frac{2}{231}\right)$	$e\left(\frac{53}{231}\right)$	$e\left(\frac{377}{462}\right)$	$e\left(\frac{57}{77}\right)$	$e\left(\frac{19}{154}\right)$	$e\left(\frac{190}{231}\right)$	$e\left(\frac{7}{66}\right)$	$e\left(\frac{4}{231}\right)$	$e\left(\frac{53}{154}\right)$
$\chi_{9016}(1327,\cdot)$	$-1$	$1$	$e\left(\frac{257}{462}\right)$	$e\left(\frac{62}{231}\right)$	$e\left(\frac{26}{231}\right)$	$e\left(\frac{137}{462}\right)$	$e\left(\frac{73}{77}\right)$	$e\left(\frac{127}{154}\right)$	$e\left(\frac{115}{231}\right)$	$e\left(\frac{19}{66}\right)$	$e\left(\frac{124}{231}\right)$	$e\left(\frac{103}{154}\right)$
$\chi_{9016}(1383,\cdot)$	$-1$	$1$	$e\left(\frac{41}{462}\right)$	$e\left(\frac{80}{231}\right)$	$e\left(\frac{41}{231}\right)$	$e\left(\frac{65}{462}\right)$	$e\left(\frac{47}{77}\right)$	$e\left(\frac{67}{154}\right)$	$e\left(\frac{208}{231}\right)$	$e\left(\frac{49}{66}\right)$	$e\left(\frac{160}{231}\right)$	$e\left(\frac{41}{154}\right)$
$\chi_{9016}(1591,\cdot)$	$-1$	$1$	$e\left(\frac{145}{462}\right)$	$e\left(\frac{97}{231}\right)$	$e\left(\frac{145}{231}\right)$	$e\left(\frac{151}{462}\right)$	$e\left(\frac{31}{77}\right)$	$e\left(\frac{113}{154}\right)$	$e\left(\frac{206}{231}\right)$	$e\left(\frac{59}{66}\right)$	$e\left(\frac{194}{231}\right)$	$e\left(\frac{145}{154}\right)$
$\chi_{9016}(1775,\cdot)$	$-1$	$1$	$e\left(\frac{167}{462}\right)$	$e\left(\frac{185}{231}\right)$	$e\left(\frac{167}{231}\right)$	$e\left(\frac{107}{462}\right)$	$e\left(\frac{75}{77}\right)$	$e\left(\frac{25}{154}\right)$	$e\left(\frac{19}{231}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{139}{231}\right)$	$e\left(\frac{13}{154}\right)$
$\chi_{9016}(1871,\cdot)$	$-1$	$1$	$e\left(\frac{421}{462}\right)$	$e\left(\frac{151}{231}\right)$	$e\left(\frac{190}{231}\right)$	$e\left(\frac{397}{462}\right)$	$e\left(\frac{30}{77}\right)$	$e\left(\frac{87}{154}\right)$	$e\left(\frac{23}{231}\right)$	$e\left(\frac{17}{66}\right)$	$e\left(\frac{71}{231}\right)$	$e\left(\frac{113}{154}\right)$
$\chi_{9016}(1927,\cdot)$	$-1$	$1$	$e\left(\frac{325}{462}\right)$	$e\left(\frac{82}{231}\right)$	$e\left(\frac{94}{231}\right)$	$e\left(\frac{211}{462}\right)$	$e\left(\frac{27}{77}\right)$	$e\left(\frac{9}{154}\right)$	$e\left(\frac{167}{231}\right)$	$e\left(\frac{23}{66}\right)$	$e\left(\frac{164}{231}\right)$	$e\left(\frac{17}{154}\right)$
$\chi_{9016}(2055,\cdot)$	$-1$	$1$	$e\left(\frac{179}{462}\right)$	$e\left(\frac{107}{231}\right)$	$e\left(\frac{179}{231}\right)$	$e\left(\frac{419}{462}\right)$	$e\left(\frac{8}{77}\right)$	$e\left(\frac{131}{154}\right)$	$e\left(\frac{1}{231}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{214}{231}\right)$	$e\left(\frac{25}{154}\right)$
$\chi_{9016}(2095,\cdot)$	$-1$	$1$	$e\left(\frac{331}{462}\right)$	$e\left(\frac{43}{231}\right)$	$e\left(\frac{100}{231}\right)$	$e\left(\frac{367}{462}\right)$	$e\left(\frac{32}{77}\right)$	$e\left(\frac{139}{154}\right)$	$e\left(\frac{158}{231}\right)$	$e\left(\frac{35}{66}\right)$	$e\left(\frac{86}{231}\right)$	$e\left(\frac{23}{154}\right)$
$\chi_{9016}(2111,\cdot)$	$-1$	$1$	$e\left(\frac{215}{462}\right)$	$e\left(\frac{104}{231}\right)$	$e\left(\frac{215}{231}\right)$	$e\left(\frac{431}{462}\right)$	$e\left(\frac{38}{77}\right)$	$e\left(\frac{141}{154}\right)$	$e\left(\frac{178}{231}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{208}{231}\right)$	$e\left(\frac{61}{154}\right)$
$\chi_{9016}(2151,\cdot)$	$-1$	$1$	$e\left(\frac{109}{462}\right)$	$e\left(\frac{100}{231}\right)$	$e\left(\frac{109}{231}\right)$	$e\left(\frac{139}{462}\right)$	$e\left(\frac{1}{77}\right)$	$e\left(\frac{103}{154}\right)$	$e\left(\frac{29}{231}\right)$	$e\left(\frac{53}{66}\right)$	$e\left(\frac{200}{231}\right)$	$e\left(\frac{109}{154}\right)$
$\chi_{9016}(2263,\cdot)$	$-1$	$1$	$e\left(\frac{379}{462}\right)$	$e\left(\frac{193}{231}\right)$	$e\left(\frac{148}{231}\right)$	$e\left(\frac{229}{462}\right)$	$e\left(\frac{72}{77}\right)$	$e\left(\frac{101}{154}\right)$	$e\left(\frac{86}{231}\right)$	$e\left(\frac{65}{66}\right)$	$e\left(\frac{155}{231}\right)$	$e\left(\frac{71}{154}\right)$
$\chi_{9016}(2279,\cdot)$	$-1$	$1$	$e\left(\frac{155}{462}\right)$	$e\left(\frac{32}{231}\right)$	$e\left(\frac{155}{231}\right)$	$e\left(\frac{257}{462}\right)$	$e\left(\frac{65}{77}\right)$	$e\left(\frac{73}{154}\right)$	$e\left(\frac{37}{231}\right)$	$e\left(\frac{13}{66}\right)$	$e\left(\frac{64}{231}\right)$	$e\left(\frac{1}{154}\right)$
$\chi_{9016}(2335,\cdot)$	$-1$	$1$	$e\left(\frac{65}{462}\right)$	$e\left(\frac{155}{231}\right)$	$e\left(\frac{65}{231}\right)$	$e\left(\frac{227}{462}\right)$	$e\left(\frac{67}{77}\right)$	$e\left(\frac{125}{154}\right)$	$e\left(\frac{172}{231}\right)$	$e\left(\frac{31}{66}\right)$	$e\left(\frac{79}{231}\right)$	$e\left(\frac{65}{154}\right)$
$\chi_{9016}(2375,\cdot)$	$-1$	$1$	$e\left(\frac{229}{462}\right)$	$e\left(\frac{13}{231}\right)$	$e\left(\frac{229}{231}\right)$	$e\left(\frac{25}{462}\right)$	$e\left(\frac{24}{77}\right)$	$e\left(\frac{85}{154}\right)$	$e\left(\frac{80}{231}\right)$	$e\left(\frac{29}{66}\right)$	$e\left(\frac{26}{231}\right)$	$e\left(\frac{75}{154}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(25\)	\(27\)
\(\chi_{9016}(39,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{59}{462}\right)\)	\(e\left(\frac{194}{231}\right)\)	\(e\left(\frac{59}{231}\right)\)	\(e\left(\frac{71}{462}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{149}{154}\right)\)	\(e\left(\frac{181}{231}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{157}{231}\right)\)	\(e\left(\frac{59}{154}\right)\)
\(\chi_{9016}(95,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{305}{462}\right)\)	\(e\left(\frac{212}{231}\right)\)	\(e\left(\frac{74}{231}\right)\)	\(e\left(\frac{461}{462}\right)\)	\(e\left(\frac{36}{77}\right)\)	\(e\left(\frac{89}{154}\right)\)	\(e\left(\frac{43}{231}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{193}{231}\right)\)	\(e\left(\frac{151}{154}\right)\)
\(\chi_{9016}(151,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{425}{462}\right)\)	\(e\left(\frac{125}{231}\right)\)	\(e\left(\frac{194}{231}\right)\)	\(e\left(\frac{347}{462}\right)\)	\(e\left(\frac{59}{77}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{94}{231}\right)\)	\(e\left(\frac{25}{66}\right)\)	\(e\left(\frac{19}{231}\right)\)	\(e\left(\frac{117}{154}\right)\)
\(\chi_{9016}(303,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{211}{462}\right)\)	\(e\left(\frac{130}{231}\right)\)	\(e\left(\frac{211}{231}\right)\)	\(e\left(\frac{19}{462}\right)\)	\(e\left(\frac{9}{77}\right)\)	\(e\left(\frac{3}{154}\right)\)	\(e\left(\frac{107}{231}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{29}{231}\right)\)	\(e\left(\frac{57}{154}\right)\)
\(\chi_{9016}(487,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{431}{462}\right)\)	\(e\left(\frac{86}{231}\right)\)	\(e\left(\frac{200}{231}\right)\)	\(e\left(\frac{41}{462}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{47}{154}\right)\)	\(e\left(\frac{85}{231}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{172}{231}\right)\)	\(e\left(\frac{123}{154}\right)\)
\(\chi_{9016}(583,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{462}\right)\)	\(e\left(\frac{184}{231}\right)\)	\(e\left(\frac{25}{231}\right)\)	\(e\left(\frac{265}{462}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{131}{154}\right)\)	\(e\left(\frac{155}{231}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{137}{231}\right)\)	\(e\left(\frac{25}{154}\right)\)
\(\chi_{9016}(639,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{391}{462}\right)\)	\(e\left(\frac{115}{231}\right)\)	\(e\left(\frac{160}{231}\right)\)	\(e\left(\frac{79}{462}\right)\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{53}{154}\right)\)	\(e\left(\frac{68}{231}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{230}{231}\right)\)	\(e\left(\frac{83}{154}\right)\)
\(\chi_{9016}(767,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{443}{462}\right)\)	\(e\left(\frac{8}{231}\right)\)	\(e\left(\frac{212}{231}\right)\)	\(e\left(\frac{353}{462}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{153}{154}\right)\)	\(e\left(\frac{67}{231}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{16}{231}\right)\)	\(e\left(\frac{135}{154}\right)\)
\(\chi_{9016}(807,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{397}{462}\right)\)	\(e\left(\frac{76}{231}\right)\)	\(e\left(\frac{166}{231}\right)\)	\(e\left(\frac{235}{462}\right)\)	\(e\left(\frac{10}{77}\right)\)	\(e\left(\frac{29}{154}\right)\)	\(e\left(\frac{59}{231}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{152}{231}\right)\)	\(e\left(\frac{89}{154}\right)\)
\(\chi_{9016}(823,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{462}\right)\)	\(e\left(\frac{5}{231}\right)\)	\(e\left(\frac{17}{231}\right)\)	\(e\left(\frac{365}{462}\right)\)	\(e\left(\frac{27}{77}\right)\)	\(e\left(\frac{9}{154}\right)\)	\(e\left(\frac{13}{231}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{10}{231}\right)\)	\(e\left(\frac{17}{154}\right)\)
\(\chi_{9016}(975,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{445}{462}\right)\)	\(e\left(\frac{226}{231}\right)\)	\(e\left(\frac{214}{231}\right)\)	\(e\left(\frac{97}{462}\right)\)	\(e\left(\frac{50}{77}\right)\)	\(e\left(\frac{145}{154}\right)\)	\(e\left(\frac{218}{231}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{221}{231}\right)\)	\(e\left(\frac{137}{154}\right)\)
\(\chi_{9016}(991,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{419}{462}\right)\)	\(e\left(\frac{164}{231}\right)\)	\(e\left(\frac{188}{231}\right)\)	\(e\left(\frac{191}{462}\right)\)	\(e\left(\frac{54}{77}\right)\)	\(e\left(\frac{95}{154}\right)\)	\(e\left(\frac{103}{231}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{97}{231}\right)\)	\(e\left(\frac{111}{154}\right)\)
\(\chi_{9016}(1087,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{295}{462}\right)\)	\(e\left(\frac{46}{231}\right)\)	\(e\left(\frac{64}{231}\right)\)	\(e\left(\frac{355}{462}\right)\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{129}{154}\right)\)	\(e\left(\frac{212}{231}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{92}{231}\right)\)	\(e\left(\frac{141}{154}\right)\)
\(\chi_{9016}(1143,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{367}{462}\right)\)	\(e\left(\frac{40}{231}\right)\)	\(e\left(\frac{136}{231}\right)\)	\(e\left(\frac{379}{462}\right)\)	\(e\left(\frac{62}{77}\right)\)	\(e\left(\frac{149}{154}\right)\)	\(e\left(\frac{104}{231}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{80}{231}\right)\)	\(e\left(\frac{59}{154}\right)\)
\(\chi_{9016}(1159,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{401}{462}\right)\)	\(e\left(\frac{50}{231}\right)\)	\(e\left(\frac{170}{231}\right)\)	\(e\left(\frac{185}{462}\right)\)	\(e\left(\frac{39}{77}\right)\)	\(e\left(\frac{13}{154}\right)\)	\(e\left(\frac{130}{231}\right)\)	\(e\left(\frac{43}{66}\right)\)	\(e\left(\frac{100}{231}\right)\)	\(e\left(\frac{93}{154}\right)\)
\(\chi_{9016}(1199,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{462}\right)\)	\(e\left(\frac{223}{231}\right)\)	\(e\left(\frac{19}{231}\right)\)	\(e\left(\frac{109}{462}\right)\)	\(e\left(\frac{3}{77}\right)\)	\(e\left(\frac{1}{154}\right)\)	\(e\left(\frac{164}{231}\right)\)	\(e\left(\frac{5}{66}\right)\)	\(e\left(\frac{215}{231}\right)\)	\(e\left(\frac{19}{154}\right)\)
\(\chi_{9016}(1271,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{462}\right)\)	\(e\left(\frac{2}{231}\right)\)	\(e\left(\frac{53}{231}\right)\)	\(e\left(\frac{377}{462}\right)\)	\(e\left(\frac{57}{77}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{190}{231}\right)\)	\(e\left(\frac{7}{66}\right)\)	\(e\left(\frac{4}{231}\right)\)	\(e\left(\frac{53}{154}\right)\)
\(\chi_{9016}(1327,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{257}{462}\right)\)	\(e\left(\frac{62}{231}\right)\)	\(e\left(\frac{26}{231}\right)\)	\(e\left(\frac{137}{462}\right)\)	\(e\left(\frac{73}{77}\right)\)	\(e\left(\frac{127}{154}\right)\)	\(e\left(\frac{115}{231}\right)\)	\(e\left(\frac{19}{66}\right)\)	\(e\left(\frac{124}{231}\right)\)	\(e\left(\frac{103}{154}\right)\)
\(\chi_{9016}(1383,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{41}{462}\right)\)	\(e\left(\frac{80}{231}\right)\)	\(e\left(\frac{41}{231}\right)\)	\(e\left(\frac{65}{462}\right)\)	\(e\left(\frac{47}{77}\right)\)	\(e\left(\frac{67}{154}\right)\)	\(e\left(\frac{208}{231}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{160}{231}\right)\)	\(e\left(\frac{41}{154}\right)\)
\(\chi_{9016}(1591,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{145}{462}\right)\)	\(e\left(\frac{97}{231}\right)\)	\(e\left(\frac{145}{231}\right)\)	\(e\left(\frac{151}{462}\right)\)	\(e\left(\frac{31}{77}\right)\)	\(e\left(\frac{113}{154}\right)\)	\(e\left(\frac{206}{231}\right)\)	\(e\left(\frac{59}{66}\right)\)	\(e\left(\frac{194}{231}\right)\)	\(e\left(\frac{145}{154}\right)\)
\(\chi_{9016}(1775,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{462}\right)\)	\(e\left(\frac{185}{231}\right)\)	\(e\left(\frac{167}{231}\right)\)	\(e\left(\frac{107}{462}\right)\)	\(e\left(\frac{75}{77}\right)\)	\(e\left(\frac{25}{154}\right)\)	\(e\left(\frac{19}{231}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{139}{231}\right)\)	\(e\left(\frac{13}{154}\right)\)
\(\chi_{9016}(1871,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{421}{462}\right)\)	\(e\left(\frac{151}{231}\right)\)	\(e\left(\frac{190}{231}\right)\)	\(e\left(\frac{397}{462}\right)\)	\(e\left(\frac{30}{77}\right)\)	\(e\left(\frac{87}{154}\right)\)	\(e\left(\frac{23}{231}\right)\)	\(e\left(\frac{17}{66}\right)\)	\(e\left(\frac{71}{231}\right)\)	\(e\left(\frac{113}{154}\right)\)
\(\chi_{9016}(1927,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{325}{462}\right)\)	\(e\left(\frac{82}{231}\right)\)	\(e\left(\frac{94}{231}\right)\)	\(e\left(\frac{211}{462}\right)\)	\(e\left(\frac{27}{77}\right)\)	\(e\left(\frac{9}{154}\right)\)	\(e\left(\frac{167}{231}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{164}{231}\right)\)	\(e\left(\frac{17}{154}\right)\)
\(\chi_{9016}(2055,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{179}{462}\right)\)	\(e\left(\frac{107}{231}\right)\)	\(e\left(\frac{179}{231}\right)\)	\(e\left(\frac{419}{462}\right)\)	\(e\left(\frac{8}{77}\right)\)	\(e\left(\frac{131}{154}\right)\)	\(e\left(\frac{1}{231}\right)\)	\(e\left(\frac{61}{66}\right)\)	\(e\left(\frac{214}{231}\right)\)	\(e\left(\frac{25}{154}\right)\)
\(\chi_{9016}(2095,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{331}{462}\right)\)	\(e\left(\frac{43}{231}\right)\)	\(e\left(\frac{100}{231}\right)\)	\(e\left(\frac{367}{462}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{139}{154}\right)\)	\(e\left(\frac{158}{231}\right)\)	\(e\left(\frac{35}{66}\right)\)	\(e\left(\frac{86}{231}\right)\)	\(e\left(\frac{23}{154}\right)\)
\(\chi_{9016}(2111,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{215}{462}\right)\)	\(e\left(\frac{104}{231}\right)\)	\(e\left(\frac{215}{231}\right)\)	\(e\left(\frac{431}{462}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{141}{154}\right)\)	\(e\left(\frac{178}{231}\right)\)	\(e\left(\frac{1}{66}\right)\)	\(e\left(\frac{208}{231}\right)\)	\(e\left(\frac{61}{154}\right)\)
\(\chi_{9016}(2151,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{462}\right)\)	\(e\left(\frac{100}{231}\right)\)	\(e\left(\frac{109}{231}\right)\)	\(e\left(\frac{139}{462}\right)\)	\(e\left(\frac{1}{77}\right)\)	\(e\left(\frac{103}{154}\right)\)	\(e\left(\frac{29}{231}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{200}{231}\right)\)	\(e\left(\frac{109}{154}\right)\)
\(\chi_{9016}(2263,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{379}{462}\right)\)	\(e\left(\frac{193}{231}\right)\)	\(e\left(\frac{148}{231}\right)\)	\(e\left(\frac{229}{462}\right)\)	\(e\left(\frac{72}{77}\right)\)	\(e\left(\frac{101}{154}\right)\)	\(e\left(\frac{86}{231}\right)\)	\(e\left(\frac{65}{66}\right)\)	\(e\left(\frac{155}{231}\right)\)	\(e\left(\frac{71}{154}\right)\)
\(\chi_{9016}(2279,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{155}{462}\right)\)	\(e\left(\frac{32}{231}\right)\)	\(e\left(\frac{155}{231}\right)\)	\(e\left(\frac{257}{462}\right)\)	\(e\left(\frac{65}{77}\right)\)	\(e\left(\frac{73}{154}\right)\)	\(e\left(\frac{37}{231}\right)\)	\(e\left(\frac{13}{66}\right)\)	\(e\left(\frac{64}{231}\right)\)	\(e\left(\frac{1}{154}\right)\)
\(\chi_{9016}(2335,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{462}\right)\)	\(e\left(\frac{155}{231}\right)\)	\(e\left(\frac{65}{231}\right)\)	\(e\left(\frac{227}{462}\right)\)	\(e\left(\frac{67}{77}\right)\)	\(e\left(\frac{125}{154}\right)\)	\(e\left(\frac{172}{231}\right)\)	\(e\left(\frac{31}{66}\right)\)	\(e\left(\frac{79}{231}\right)\)	\(e\left(\frac{65}{154}\right)\)
\(\chi_{9016}(2375,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{229}{462}\right)\)	\(e\left(\frac{13}{231}\right)\)	\(e\left(\frac{229}{231}\right)\)	\(e\left(\frac{25}{462}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{85}{154}\right)\)	\(e\left(\frac{80}{231}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{26}{231}\right)\)	\(e\left(\frac{75}{154}\right)\)

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First 31 of 120 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	9016.et
Modulus	$9016$
Conductor	$4508$
Order	$462$
Real	no
Primitive	no
Minimal	no
Parity	odd

Modulus:	\(9016\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(4508\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(462\)	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 4508.cj	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);