LMFDB - Dirichlet character orbit 8611.es

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8611, base_ring=CyclotomicField(702)) M = H._module chi = DirichletCharacter(H, M([108,559])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(87, 8611)) 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("8611.87"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$8611$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$8611$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$702$	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:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);

Related number fields

Field of values:	$\Q(\zeta_{351})$
Fixed field:	Number field defined by a degree 702 polynomial (not computed)

First 31 of 216 characters in Galois orbit

Character	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{8611}(87,\cdot)$	$1$	$1$	$e\left(\frac{1}{234}\right)$	$e\left(\frac{197}{351}\right)$	$e\left(\frac{1}{117}\right)$	$e\left(\frac{20}{351}\right)$	$e\left(\frac{397}{702}\right)$	$e\left(\frac{2}{351}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{43}{351}\right)$	$e\left(\frac{43}{702}\right)$	$e\left(\frac{389}{702}\right)$
$\chi_{8611}(100,\cdot)$	$1$	$1$	$e\left(\frac{37}{234}\right)$	$e\left(\frac{269}{351}\right)$	$e\left(\frac{37}{117}\right)$	$e\left(\frac{38}{351}\right)$	$e\left(\frac{649}{702}\right)$	$e\left(\frac{74}{351}\right)$	$e\left(\frac{37}{78}\right)$	$e\left(\frac{187}{351}\right)$	$e\left(\frac{187}{702}\right)$	$e\left(\frac{353}{702}\right)$
$\chi_{8611}(196,\cdot)$	$1$	$1$	$e\left(\frac{55}{234}\right)$	$e\left(\frac{305}{351}\right)$	$e\left(\frac{55}{117}\right)$	$e\left(\frac{47}{351}\right)$	$e\left(\frac{73}{702}\right)$	$e\left(\frac{110}{351}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{259}{351}\right)$	$e\left(\frac{259}{702}\right)$	$e\left(\frac{335}{702}\right)$
$\chi_{8611}(247,\cdot)$	$1$	$1$	$e\left(\frac{77}{234}\right)$	$e\left(\frac{76}{351}\right)$	$e\left(\frac{77}{117}\right)$	$e\left(\frac{136}{351}\right)$	$e\left(\frac{383}{702}\right)$	$e\left(\frac{154}{351}\right)$	$e\left(\frac{77}{78}\right)$	$e\left(\frac{152}{351}\right)$	$e\left(\frac{503}{702}\right)$	$e\left(\frac{469}{702}\right)$
$\chi_{8611}(301,\cdot)$	$1$	$1$	$e\left(\frac{41}{234}\right)$	$e\left(\frac{4}{351}\right)$	$e\left(\frac{41}{117}\right)$	$e\left(\frac{118}{351}\right)$	$e\left(\frac{131}{702}\right)$	$e\left(\frac{82}{351}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{8}{351}\right)$	$e\left(\frac{359}{702}\right)$	$e\left(\frac{505}{702}\right)$
$\chi_{8611}(302,\cdot)$	$1$	$1$	$e\left(\frac{151}{234}\right)$	$e\left(\frac{146}{351}\right)$	$e\left(\frac{34}{117}\right)$	$e\left(\frac{95}{351}\right)$	$e\left(\frac{43}{702}\right)$	$e\left(\frac{185}{351}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{292}{351}\right)$	$e\left(\frac{643}{702}\right)$	$e\left(\frac{5}{702}\right)$
$\chi_{8611}(324,\cdot)$	$1$	$1$	$e\left(\frac{131}{234}\right)$	$e\left(\frac{67}{351}\right)$	$e\left(\frac{14}{117}\right)$	$e\left(\frac{46}{351}\right)$	$e\left(\frac{527}{702}\right)$	$e\left(\frac{145}{351}\right)$	$e\left(\frac{53}{78}\right)$	$e\left(\frac{134}{351}\right)$	$e\left(\frac{485}{702}\right)$	$e\left(\frac{649}{702}\right)$
$\chi_{8611}(433,\cdot)$	$1$	$1$	$e\left(\frac{185}{234}\right)$	$e\left(\frac{175}{351}\right)$	$e\left(\frac{68}{117}\right)$	$e\left(\frac{73}{351}\right)$	$e\left(\frac{203}{702}\right)$	$e\left(\frac{253}{351}\right)$	$e\left(\frac{29}{78}\right)$	$e\left(\frac{350}{351}\right)$	$e\left(\frac{701}{702}\right)$	$e\left(\frac{595}{702}\right)$
$\chi_{8611}(496,\cdot)$	$1$	$1$	$e\left(\frac{97}{234}\right)$	$e\left(\frac{155}{351}\right)$	$e\left(\frac{97}{117}\right)$	$e\left(\frac{185}{351}\right)$	$e\left(\frac{601}{702}\right)$	$e\left(\frac{194}{351}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{310}{351}\right)$	$e\left(\frac{661}{702}\right)$	$e\left(\frac{527}{702}\right)$
$\chi_{8611}(520,\cdot)$	$1$	$1$	$e\left(\frac{61}{234}\right)$	$e\left(\frac{200}{351}\right)$	$e\left(\frac{61}{117}\right)$	$e\left(\frac{284}{351}\right)$	$e\left(\frac{583}{702}\right)$	$e\left(\frac{239}{351}\right)$	$e\left(\frac{61}{78}\right)$	$e\left(\frac{49}{351}\right)$	$e\left(\frac{49}{702}\right)$	$e\left(\frac{329}{702}\right)$
$\chi_{8611}(536,\cdot)$	$1$	$1$	$e\left(\frac{109}{234}\right)$	$e\left(\frac{296}{351}\right)$	$e\left(\frac{109}{117}\right)$	$e\left(\frac{308}{351}\right)$	$e\left(\frac{217}{702}\right)$	$e\left(\frac{101}{351}\right)$	$e\left(\frac{31}{78}\right)$	$e\left(\frac{241}{351}\right)$	$e\left(\frac{241}{702}\right)$	$e\left(\frac{515}{702}\right)$
$\chi_{8611}(538,\cdot)$	$1$	$1$	$e\left(\frac{197}{234}\right)$	$e\left(\frac{199}{351}\right)$	$e\left(\frac{80}{117}\right)$	$e\left(\frac{79}{351}\right)$	$e\left(\frac{287}{702}\right)$	$e\left(\frac{43}{351}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{47}{351}\right)$	$e\left(\frac{47}{702}\right)$	$e\left(\frac{115}{702}\right)$
$\chi_{8611}(574,\cdot)$	$1$	$1$	$e\left(\frac{167}{234}\right)$	$e\left(\frac{22}{351}\right)$	$e\left(\frac{50}{117}\right)$	$e\left(\frac{298}{351}\right)$	$e\left(\frac{545}{702}\right)$	$e\left(\frac{100}{351}\right)$	$e\left(\frac{11}{78}\right)$	$e\left(\frac{44}{351}\right)$	$e\left(\frac{395}{702}\right)$	$e\left(\frac{145}{702}\right)$
$\chi_{8611}(605,\cdot)$	$1$	$1$	$e\left(\frac{205}{234}\right)$	$e\left(\frac{20}{351}\right)$	$e\left(\frac{88}{117}\right)$	$e\left(\frac{239}{351}\right)$	$e\left(\frac{655}{702}\right)$	$e\left(\frac{59}{351}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{40}{351}\right)$	$e\left(\frac{391}{702}\right)$	$e\left(\frac{419}{702}\right)$
$\chi_{8611}(775,\cdot)$	$1$	$1$	$e\left(\frac{197}{234}\right)$	$e\left(\frac{82}{351}\right)$	$e\left(\frac{80}{117}\right)$	$e\left(\frac{313}{351}\right)$	$e\left(\frac{53}{702}\right)$	$e\left(\frac{277}{351}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{164}{351}\right)$	$e\left(\frac{515}{702}\right)$	$e\left(\frac{349}{702}\right)$
$\chi_{8611}(857,\cdot)$	$1$	$1$	$e\left(\frac{121}{234}\right)$	$e\left(\frac{86}{351}\right)$	$e\left(\frac{4}{117}\right)$	$e\left(\frac{80}{351}\right)$	$e\left(\frac{535}{702}\right)$	$e\left(\frac{8}{351}\right)$	$e\left(\frac{43}{78}\right)$	$e\left(\frac{172}{351}\right)$	$e\left(\frac{523}{702}\right)$	$e\left(\frac{503}{702}\right)$
$\chi_{8611}(933,\cdot)$	$1$	$1$	$e\left(\frac{119}{234}\right)$	$e\left(\frac{43}{351}\right)$	$e\left(\frac{2}{117}\right)$	$e\left(\frac{40}{351}\right)$	$e\left(\frac{443}{702}\right)$	$e\left(\frac{4}{351}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{86}{351}\right)$	$e\left(\frac{437}{702}\right)$	$e\left(\frac{427}{702}\right)$
$\chi_{8611}(956,\cdot)$	$1$	$1$	$e\left(\frac{79}{234}\right)$	$e\left(\frac{119}{351}\right)$	$e\left(\frac{79}{117}\right)$	$e\left(\frac{176}{351}\right)$	$e\left(\frac{475}{702}\right)$	$e\left(\frac{158}{351}\right)$	$e\left(\frac{1}{78}\right)$	$e\left(\frac{238}{351}\right)$	$e\left(\frac{589}{702}\right)$	$e\left(\frac{545}{702}\right)$
$\chi_{8611}(966,\cdot)$	$1$	$1$	$e\left(\frac{85}{234}\right)$	$e\left(\frac{248}{351}\right)$	$e\left(\frac{85}{117}\right)$	$e\left(\frac{296}{351}\right)$	$e\left(\frac{49}{702}\right)$	$e\left(\frac{170}{351}\right)$	$e\left(\frac{7}{78}\right)$	$e\left(\frac{145}{351}\right)$	$e\left(\frac{145}{702}\right)$	$e\left(\frac{71}{702}\right)$
$\chi_{8611}(1010,\cdot)$	$1$	$1$	$e\left(\frac{5}{234}\right)$	$e\left(\frac{49}{351}\right)$	$e\left(\frac{5}{117}\right)$	$e\left(\frac{217}{351}\right)$	$e\left(\frac{113}{702}\right)$	$e\left(\frac{127}{351}\right)$	$e\left(\frac{5}{78}\right)$	$e\left(\frac{98}{351}\right)$	$e\left(\frac{449}{702}\right)$	$e\left(\frac{307}{702}\right)$
$\chi_{8611}(1012,\cdot)$	$1$	$1$	$e\left(\frac{145}{234}\right)$	$e\left(\frac{17}{351}\right)$	$e\left(\frac{28}{117}\right)$	$e\left(\frac{326}{351}\right)$	$e\left(\frac{469}{702}\right)$	$e\left(\frac{173}{351}\right)$	$e\left(\frac{67}{78}\right)$	$e\left(\frac{34}{351}\right)$	$e\left(\frac{385}{702}\right)$	$e\left(\frac{479}{702}\right)$
$\chi_{8611}(1065,\cdot)$	$1$	$1$	$e\left(\frac{133}{234}\right)$	$e\left(\frac{227}{351}\right)$	$e\left(\frac{16}{117}\right)$	$e\left(\frac{203}{351}\right)$	$e\left(\frac{151}{702}\right)$	$e\left(\frac{266}{351}\right)$	$e\left(\frac{55}{78}\right)$	$e\left(\frac{103}{351}\right)$	$e\left(\frac{103}{702}\right)$	$e\left(\frac{491}{702}\right)$
$\chi_{8611}(1173,\cdot)$	$1$	$1$	$e\left(\frac{95}{234}\right)$	$e\left(\frac{112}{351}\right)$	$e\left(\frac{95}{117}\right)$	$e\left(\frac{145}{351}\right)$	$e\left(\frac{509}{702}\right)$	$e\left(\frac{190}{351}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{224}{351}\right)$	$e\left(\frac{575}{702}\right)$	$e\left(\frac{451}{702}\right)$
$\chi_{8611}(1282,\cdot)$	$1$	$1$	$e\left(\frac{59}{234}\right)$	$e\left(\frac{274}{351}\right)$	$e\left(\frac{59}{117}\right)$	$e\left(\frac{10}{351}\right)$	$e\left(\frac{23}{702}\right)$	$e\left(\frac{1}{351}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{197}{351}\right)$	$e\left(\frac{197}{702}\right)$	$e\left(\frac{19}{702}\right)$
$\chi_{8611}(1286,\cdot)$	$1$	$1$	$e\left(\frac{19}{234}\right)$	$e\left(\frac{116}{351}\right)$	$e\left(\frac{19}{117}\right)$	$e\left(\frac{263}{351}\right)$	$e\left(\frac{289}{702}\right)$	$e\left(\frac{272}{351}\right)$	$e\left(\frac{19}{78}\right)$	$e\left(\frac{232}{351}\right)$	$e\left(\frac{583}{702}\right)$	$e\left(\frac{605}{702}\right)$
$\chi_{8611}(1328,\cdot)$	$1$	$1$	$e\left(\frac{119}{234}\right)$	$e\left(\frac{277}{351}\right)$	$e\left(\frac{2}{117}\right)$	$e\left(\frac{274}{351}\right)$	$e\left(\frac{209}{702}\right)$	$e\left(\frac{238}{351}\right)$	$e\left(\frac{41}{78}\right)$	$e\left(\frac{203}{351}\right)$	$e\left(\frac{203}{702}\right)$	$e\left(\frac{661}{702}\right)$
$\chi_{8611}(1395,\cdot)$	$1$	$1$	$e\left(\frac{127}{234}\right)$	$e\left(\frac{332}{351}\right)$	$e\left(\frac{10}{117}\right)$	$e\left(\frac{317}{351}\right)$	$e\left(\frac{343}{702}\right)$	$e\left(\frac{137}{351}\right)$	$e\left(\frac{49}{78}\right)$	$e\left(\frac{313}{351}\right)$	$e\left(\frac{313}{702}\right)$	$e\left(\frac{497}{702}\right)$
$\chi_{8611}(1408,\cdot)$	$1$	$1$	$e\left(\frac{73}{234}\right)$	$e\left(\frac{107}{351}\right)$	$e\left(\frac{73}{117}\right)$	$e\left(\frac{173}{351}\right)$	$e\left(\frac{433}{702}\right)$	$e\left(\frac{263}{351}\right)$	$e\left(\frac{73}{78}\right)$	$e\left(\frac{214}{351}\right)$	$e\left(\frac{565}{702}\right)$	$e\left(\frac{83}{702}\right)$
$\chi_{8611}(1410,\cdot)$	$1$	$1$	$e\left(\frac{17}{234}\right)$	$e\left(\frac{307}{351}\right)$	$e\left(\frac{17}{117}\right)$	$e\left(\frac{106}{351}\right)$	$e\left(\frac{665}{702}\right)$	$e\left(\frac{151}{351}\right)$	$e\left(\frac{17}{78}\right)$	$e\left(\frac{263}{351}\right)$	$e\left(\frac{263}{702}\right)$	$e\left(\frac{61}{702}\right)$
$\chi_{8611}(1511,\cdot)$	$1$	$1$	$e\left(\frac{103}{234}\right)$	$e\left(\frac{167}{351}\right)$	$e\left(\frac{103}{117}\right)$	$e\left(\frac{188}{351}\right)$	$e\left(\frac{643}{702}\right)$	$e\left(\frac{89}{351}\right)$	$e\left(\frac{25}{78}\right)$	$e\left(\frac{334}{351}\right)$	$e\left(\frac{685}{702}\right)$	$e\left(\frac{287}{702}\right)$
$\chi_{8611}(1519,\cdot)$	$1$	$1$	$e\left(\frac{215}{234}\right)$	$e\left(\frac{118}{351}\right)$	$e\left(\frac{98}{117}\right)$	$e\left(\frac{322}{351}\right)$	$e\left(\frac{179}{702}\right)$	$e\left(\frac{313}{351}\right)$	$e\left(\frac{59}{78}\right)$	$e\left(\frac{236}{351}\right)$	$e\left(\frac{587}{702}\right)$	$e\left(\frac{331}{702}\right)$

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	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(\chi_{8611}(87,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{234}\right)\)	\(e\left(\frac{197}{351}\right)\)	\(e\left(\frac{1}{117}\right)\)	\(e\left(\frac{20}{351}\right)\)	\(e\left(\frac{397}{702}\right)\)	\(e\left(\frac{2}{351}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{43}{351}\right)\)	\(e\left(\frac{43}{702}\right)\)	\(e\left(\frac{389}{702}\right)\)
\(\chi_{8611}(100,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{234}\right)\)	\(e\left(\frac{269}{351}\right)\)	\(e\left(\frac{37}{117}\right)\)	\(e\left(\frac{38}{351}\right)\)	\(e\left(\frac{649}{702}\right)\)	\(e\left(\frac{74}{351}\right)\)	\(e\left(\frac{37}{78}\right)\)	\(e\left(\frac{187}{351}\right)\)	\(e\left(\frac{187}{702}\right)\)	\(e\left(\frac{353}{702}\right)\)
\(\chi_{8611}(196,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{234}\right)\)	\(e\left(\frac{305}{351}\right)\)	\(e\left(\frac{55}{117}\right)\)	\(e\left(\frac{47}{351}\right)\)	\(e\left(\frac{73}{702}\right)\)	\(e\left(\frac{110}{351}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{259}{351}\right)\)	\(e\left(\frac{259}{702}\right)\)	\(e\left(\frac{335}{702}\right)\)
\(\chi_{8611}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{234}\right)\)	\(e\left(\frac{76}{351}\right)\)	\(e\left(\frac{77}{117}\right)\)	\(e\left(\frac{136}{351}\right)\)	\(e\left(\frac{383}{702}\right)\)	\(e\left(\frac{154}{351}\right)\)	\(e\left(\frac{77}{78}\right)\)	\(e\left(\frac{152}{351}\right)\)	\(e\left(\frac{503}{702}\right)\)	\(e\left(\frac{469}{702}\right)\)
\(\chi_{8611}(301,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{234}\right)\)	\(e\left(\frac{4}{351}\right)\)	\(e\left(\frac{41}{117}\right)\)	\(e\left(\frac{118}{351}\right)\)	\(e\left(\frac{131}{702}\right)\)	\(e\left(\frac{82}{351}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{8}{351}\right)\)	\(e\left(\frac{359}{702}\right)\)	\(e\left(\frac{505}{702}\right)\)
\(\chi_{8611}(302,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{151}{234}\right)\)	\(e\left(\frac{146}{351}\right)\)	\(e\left(\frac{34}{117}\right)\)	\(e\left(\frac{95}{351}\right)\)	\(e\left(\frac{43}{702}\right)\)	\(e\left(\frac{185}{351}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{292}{351}\right)\)	\(e\left(\frac{643}{702}\right)\)	\(e\left(\frac{5}{702}\right)\)
\(\chi_{8611}(324,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{234}\right)\)	\(e\left(\frac{67}{351}\right)\)	\(e\left(\frac{14}{117}\right)\)	\(e\left(\frac{46}{351}\right)\)	\(e\left(\frac{527}{702}\right)\)	\(e\left(\frac{145}{351}\right)\)	\(e\left(\frac{53}{78}\right)\)	\(e\left(\frac{134}{351}\right)\)	\(e\left(\frac{485}{702}\right)\)	\(e\left(\frac{649}{702}\right)\)
\(\chi_{8611}(433,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{185}{234}\right)\)	\(e\left(\frac{175}{351}\right)\)	\(e\left(\frac{68}{117}\right)\)	\(e\left(\frac{73}{351}\right)\)	\(e\left(\frac{203}{702}\right)\)	\(e\left(\frac{253}{351}\right)\)	\(e\left(\frac{29}{78}\right)\)	\(e\left(\frac{350}{351}\right)\)	\(e\left(\frac{701}{702}\right)\)	\(e\left(\frac{595}{702}\right)\)
\(\chi_{8611}(496,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{234}\right)\)	\(e\left(\frac{155}{351}\right)\)	\(e\left(\frac{97}{117}\right)\)	\(e\left(\frac{185}{351}\right)\)	\(e\left(\frac{601}{702}\right)\)	\(e\left(\frac{194}{351}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{310}{351}\right)\)	\(e\left(\frac{661}{702}\right)\)	\(e\left(\frac{527}{702}\right)\)
\(\chi_{8611}(520,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{234}\right)\)	\(e\left(\frac{200}{351}\right)\)	\(e\left(\frac{61}{117}\right)\)	\(e\left(\frac{284}{351}\right)\)	\(e\left(\frac{583}{702}\right)\)	\(e\left(\frac{239}{351}\right)\)	\(e\left(\frac{61}{78}\right)\)	\(e\left(\frac{49}{351}\right)\)	\(e\left(\frac{49}{702}\right)\)	\(e\left(\frac{329}{702}\right)\)
\(\chi_{8611}(536,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{234}\right)\)	\(e\left(\frac{296}{351}\right)\)	\(e\left(\frac{109}{117}\right)\)	\(e\left(\frac{308}{351}\right)\)	\(e\left(\frac{217}{702}\right)\)	\(e\left(\frac{101}{351}\right)\)	\(e\left(\frac{31}{78}\right)\)	\(e\left(\frac{241}{351}\right)\)	\(e\left(\frac{241}{702}\right)\)	\(e\left(\frac{515}{702}\right)\)
\(\chi_{8611}(538,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{234}\right)\)	\(e\left(\frac{199}{351}\right)\)	\(e\left(\frac{80}{117}\right)\)	\(e\left(\frac{79}{351}\right)\)	\(e\left(\frac{287}{702}\right)\)	\(e\left(\frac{43}{351}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{47}{351}\right)\)	\(e\left(\frac{47}{702}\right)\)	\(e\left(\frac{115}{702}\right)\)
\(\chi_{8611}(574,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{167}{234}\right)\)	\(e\left(\frac{22}{351}\right)\)	\(e\left(\frac{50}{117}\right)\)	\(e\left(\frac{298}{351}\right)\)	\(e\left(\frac{545}{702}\right)\)	\(e\left(\frac{100}{351}\right)\)	\(e\left(\frac{11}{78}\right)\)	\(e\left(\frac{44}{351}\right)\)	\(e\left(\frac{395}{702}\right)\)	\(e\left(\frac{145}{702}\right)\)
\(\chi_{8611}(605,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{205}{234}\right)\)	\(e\left(\frac{20}{351}\right)\)	\(e\left(\frac{88}{117}\right)\)	\(e\left(\frac{239}{351}\right)\)	\(e\left(\frac{655}{702}\right)\)	\(e\left(\frac{59}{351}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{40}{351}\right)\)	\(e\left(\frac{391}{702}\right)\)	\(e\left(\frac{419}{702}\right)\)
\(\chi_{8611}(775,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{197}{234}\right)\)	\(e\left(\frac{82}{351}\right)\)	\(e\left(\frac{80}{117}\right)\)	\(e\left(\frac{313}{351}\right)\)	\(e\left(\frac{53}{702}\right)\)	\(e\left(\frac{277}{351}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{164}{351}\right)\)	\(e\left(\frac{515}{702}\right)\)	\(e\left(\frac{349}{702}\right)\)
\(\chi_{8611}(857,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{234}\right)\)	\(e\left(\frac{86}{351}\right)\)	\(e\left(\frac{4}{117}\right)\)	\(e\left(\frac{80}{351}\right)\)	\(e\left(\frac{535}{702}\right)\)	\(e\left(\frac{8}{351}\right)\)	\(e\left(\frac{43}{78}\right)\)	\(e\left(\frac{172}{351}\right)\)	\(e\left(\frac{523}{702}\right)\)	\(e\left(\frac{503}{702}\right)\)
\(\chi_{8611}(933,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{234}\right)\)	\(e\left(\frac{43}{351}\right)\)	\(e\left(\frac{2}{117}\right)\)	\(e\left(\frac{40}{351}\right)\)	\(e\left(\frac{443}{702}\right)\)	\(e\left(\frac{4}{351}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{86}{351}\right)\)	\(e\left(\frac{437}{702}\right)\)	\(e\left(\frac{427}{702}\right)\)
\(\chi_{8611}(956,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{234}\right)\)	\(e\left(\frac{119}{351}\right)\)	\(e\left(\frac{79}{117}\right)\)	\(e\left(\frac{176}{351}\right)\)	\(e\left(\frac{475}{702}\right)\)	\(e\left(\frac{158}{351}\right)\)	\(e\left(\frac{1}{78}\right)\)	\(e\left(\frac{238}{351}\right)\)	\(e\left(\frac{589}{702}\right)\)	\(e\left(\frac{545}{702}\right)\)
\(\chi_{8611}(966,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{234}\right)\)	\(e\left(\frac{248}{351}\right)\)	\(e\left(\frac{85}{117}\right)\)	\(e\left(\frac{296}{351}\right)\)	\(e\left(\frac{49}{702}\right)\)	\(e\left(\frac{170}{351}\right)\)	\(e\left(\frac{7}{78}\right)\)	\(e\left(\frac{145}{351}\right)\)	\(e\left(\frac{145}{702}\right)\)	\(e\left(\frac{71}{702}\right)\)
\(\chi_{8611}(1010,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{234}\right)\)	\(e\left(\frac{49}{351}\right)\)	\(e\left(\frac{5}{117}\right)\)	\(e\left(\frac{217}{351}\right)\)	\(e\left(\frac{113}{702}\right)\)	\(e\left(\frac{127}{351}\right)\)	\(e\left(\frac{5}{78}\right)\)	\(e\left(\frac{98}{351}\right)\)	\(e\left(\frac{449}{702}\right)\)	\(e\left(\frac{307}{702}\right)\)
\(\chi_{8611}(1012,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{234}\right)\)	\(e\left(\frac{17}{351}\right)\)	\(e\left(\frac{28}{117}\right)\)	\(e\left(\frac{326}{351}\right)\)	\(e\left(\frac{469}{702}\right)\)	\(e\left(\frac{173}{351}\right)\)	\(e\left(\frac{67}{78}\right)\)	\(e\left(\frac{34}{351}\right)\)	\(e\left(\frac{385}{702}\right)\)	\(e\left(\frac{479}{702}\right)\)
\(\chi_{8611}(1065,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{234}\right)\)	\(e\left(\frac{227}{351}\right)\)	\(e\left(\frac{16}{117}\right)\)	\(e\left(\frac{203}{351}\right)\)	\(e\left(\frac{151}{702}\right)\)	\(e\left(\frac{266}{351}\right)\)	\(e\left(\frac{55}{78}\right)\)	\(e\left(\frac{103}{351}\right)\)	\(e\left(\frac{103}{702}\right)\)	\(e\left(\frac{491}{702}\right)\)
\(\chi_{8611}(1173,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{234}\right)\)	\(e\left(\frac{112}{351}\right)\)	\(e\left(\frac{95}{117}\right)\)	\(e\left(\frac{145}{351}\right)\)	\(e\left(\frac{509}{702}\right)\)	\(e\left(\frac{190}{351}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{224}{351}\right)\)	\(e\left(\frac{575}{702}\right)\)	\(e\left(\frac{451}{702}\right)\)
\(\chi_{8611}(1282,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{234}\right)\)	\(e\left(\frac{274}{351}\right)\)	\(e\left(\frac{59}{117}\right)\)	\(e\left(\frac{10}{351}\right)\)	\(e\left(\frac{23}{702}\right)\)	\(e\left(\frac{1}{351}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{197}{351}\right)\)	\(e\left(\frac{197}{702}\right)\)	\(e\left(\frac{19}{702}\right)\)
\(\chi_{8611}(1286,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{234}\right)\)	\(e\left(\frac{116}{351}\right)\)	\(e\left(\frac{19}{117}\right)\)	\(e\left(\frac{263}{351}\right)\)	\(e\left(\frac{289}{702}\right)\)	\(e\left(\frac{272}{351}\right)\)	\(e\left(\frac{19}{78}\right)\)	\(e\left(\frac{232}{351}\right)\)	\(e\left(\frac{583}{702}\right)\)	\(e\left(\frac{605}{702}\right)\)
\(\chi_{8611}(1328,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{234}\right)\)	\(e\left(\frac{277}{351}\right)\)	\(e\left(\frac{2}{117}\right)\)	\(e\left(\frac{274}{351}\right)\)	\(e\left(\frac{209}{702}\right)\)	\(e\left(\frac{238}{351}\right)\)	\(e\left(\frac{41}{78}\right)\)	\(e\left(\frac{203}{351}\right)\)	\(e\left(\frac{203}{702}\right)\)	\(e\left(\frac{661}{702}\right)\)
\(\chi_{8611}(1395,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{234}\right)\)	\(e\left(\frac{332}{351}\right)\)	\(e\left(\frac{10}{117}\right)\)	\(e\left(\frac{317}{351}\right)\)	\(e\left(\frac{343}{702}\right)\)	\(e\left(\frac{137}{351}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{313}{351}\right)\)	\(e\left(\frac{313}{702}\right)\)	\(e\left(\frac{497}{702}\right)\)
\(\chi_{8611}(1408,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{234}\right)\)	\(e\left(\frac{107}{351}\right)\)	\(e\left(\frac{73}{117}\right)\)	\(e\left(\frac{173}{351}\right)\)	\(e\left(\frac{433}{702}\right)\)	\(e\left(\frac{263}{351}\right)\)	\(e\left(\frac{73}{78}\right)\)	\(e\left(\frac{214}{351}\right)\)	\(e\left(\frac{565}{702}\right)\)	\(e\left(\frac{83}{702}\right)\)
\(\chi_{8611}(1410,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{234}\right)\)	\(e\left(\frac{307}{351}\right)\)	\(e\left(\frac{17}{117}\right)\)	\(e\left(\frac{106}{351}\right)\)	\(e\left(\frac{665}{702}\right)\)	\(e\left(\frac{151}{351}\right)\)	\(e\left(\frac{17}{78}\right)\)	\(e\left(\frac{263}{351}\right)\)	\(e\left(\frac{263}{702}\right)\)	\(e\left(\frac{61}{702}\right)\)
\(\chi_{8611}(1511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{234}\right)\)	\(e\left(\frac{167}{351}\right)\)	\(e\left(\frac{103}{117}\right)\)	\(e\left(\frac{188}{351}\right)\)	\(e\left(\frac{643}{702}\right)\)	\(e\left(\frac{89}{351}\right)\)	\(e\left(\frac{25}{78}\right)\)	\(e\left(\frac{334}{351}\right)\)	\(e\left(\frac{685}{702}\right)\)	\(e\left(\frac{287}{702}\right)\)
\(\chi_{8611}(1519,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{215}{234}\right)\)	\(e\left(\frac{118}{351}\right)\)	\(e\left(\frac{98}{117}\right)\)	\(e\left(\frac{322}{351}\right)\)	\(e\left(\frac{179}{702}\right)\)	\(e\left(\frac{313}{351}\right)\)	\(e\left(\frac{59}{78}\right)\)	\(e\left(\frac{236}{351}\right)\)	\(e\left(\frac{587}{702}\right)\)	\(e\left(\frac{331}{702}\right)\)

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First 31 of 216 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	8611.es
Modulus	$8611$
Conductor	$8611$
Order	$702$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8611\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(8611\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(702\)	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:	yes	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	yes
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);