LMFDB - Dirichlet character orbit 5766.bc

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5766, base_ring=CyclotomicField(930)) M = H._module chi = DirichletCharacter(H, M([0,658])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(7,5766)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$5766$
Conductor:	$961$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$465$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 961.o	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{465})$
Fixed field:	Number field defined by a degree 465 polynomial (not computed)

First 31 of 240 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$35$
$\chi_{5766}(7,\cdot)$	$1$	$1$	$e\left(\frac{29}{93}\right)$	$e\left(\frac{257}{465}\right)$	$e\left(\frac{247}{465}\right)$	$e\left(\frac{334}{465}\right)$	$e\left(\frac{173}{465}\right)$	$e\left(\frac{191}{465}\right)$	$e\left(\frac{86}{155}\right)$	$e\left(\frac{58}{93}\right)$	$e\left(\frac{117}{155}\right)$	$e\left(\frac{134}{155}\right)$
$\chi_{5766}(19,\cdot)$	$1$	$1$	$e\left(\frac{23}{93}\right)$	$e\left(\frac{191}{465}\right)$	$e\left(\frac{151}{465}\right)$	$e\left(\frac{127}{465}\right)$	$e\left(\frac{134}{465}\right)$	$e\left(\frac{113}{465}\right)$	$e\left(\frac{3}{155}\right)$	$e\left(\frac{46}{93}\right)$	$e\left(\frac{96}{155}\right)$	$e\left(\frac{102}{155}\right)$
$\chi_{5766}(49,\cdot)$	$1$	$1$	$e\left(\frac{58}{93}\right)$	$e\left(\frac{49}{465}\right)$	$e\left(\frac{29}{465}\right)$	$e\left(\frac{203}{465}\right)$	$e\left(\frac{346}{465}\right)$	$e\left(\frac{382}{465}\right)$	$e\left(\frac{17}{155}\right)$	$e\left(\frac{23}{93}\right)$	$e\left(\frac{79}{155}\right)$	$e\left(\frac{113}{155}\right)$
$\chi_{5766}(103,\cdot)$	$1$	$1$	$e\left(\frac{22}{93}\right)$	$e\left(\frac{211}{465}\right)$	$e\left(\frac{11}{465}\right)$	$e\left(\frac{77}{465}\right)$	$e\left(\frac{19}{465}\right)$	$e\left(\frac{193}{465}\right)$	$e\left(\frac{108}{155}\right)$	$e\left(\frac{44}{93}\right)$	$e\left(\frac{46}{155}\right)$	$e\left(\frac{107}{155}\right)$
$\chi_{5766}(121,\cdot)$	$1$	$1$	$e\left(\frac{59}{93}\right)$	$e\left(\frac{29}{465}\right)$	$e\left(\frac{169}{465}\right)$	$e\left(\frac{253}{465}\right)$	$e\left(\frac{461}{465}\right)$	$e\left(\frac{302}{465}\right)$	$e\left(\frac{67}{155}\right)$	$e\left(\frac{25}{93}\right)$	$e\left(\frac{129}{155}\right)$	$e\left(\frac{108}{155}\right)$
$\chi_{5766}(133,\cdot)$	$1$	$1$	$e\left(\frac{52}{93}\right)$	$e\left(\frac{448}{465}\right)$	$e\left(\frac{398}{465}\right)$	$e\left(\frac{461}{465}\right)$	$e\left(\frac{307}{465}\right)$	$e\left(\frac{304}{465}\right)$	$e\left(\frac{89}{155}\right)$	$e\left(\frac{11}{93}\right)$	$e\left(\frac{58}{155}\right)$	$e\left(\frac{81}{155}\right)$
$\chi_{5766}(169,\cdot)$	$1$	$1$	$e\left(\frac{41}{93}\right)$	$e\left(\frac{203}{465}\right)$	$e\left(\frac{253}{465}\right)$	$e\left(\frac{376}{465}\right)$	$e\left(\frac{437}{465}\right)$	$e\left(\frac{254}{465}\right)$	$e\left(\frac{4}{155}\right)$	$e\left(\frac{82}{93}\right)$	$e\left(\frac{128}{155}\right)$	$e\left(\frac{136}{155}\right)$
$\chi_{5766}(175,\cdot)$	$1$	$1$	$e\left(\frac{61}{93}\right)$	$e\left(\frac{82}{465}\right)$	$e\left(\frac{77}{465}\right)$	$e\left(\frac{74}{465}\right)$	$e\left(\frac{133}{465}\right)$	$e\left(\frac{421}{465}\right)$	$e\left(\frac{136}{155}\right)$	$e\left(\frac{29}{93}\right)$	$e\left(\frac{12}{155}\right)$	$e\left(\frac{129}{155}\right)$
$\chi_{5766}(193,\cdot)$	$1$	$1$	$e\left(\frac{26}{93}\right)$	$e\left(\frac{317}{465}\right)$	$e\left(\frac{292}{465}\right)$	$e\left(\frac{184}{465}\right)$	$e\left(\frac{293}{465}\right)$	$e\left(\frac{431}{465}\right)$	$e\left(\frac{91}{155}\right)$	$e\left(\frac{52}{93}\right)$	$e\left(\frac{122}{155}\right)$	$e\left(\frac{149}{155}\right)$
$\chi_{5766}(205,\cdot)$	$1$	$1$	$e\left(\frac{17}{93}\right)$	$e\left(\frac{311}{465}\right)$	$e\left(\frac{241}{465}\right)$	$e\left(\frac{292}{465}\right)$	$e\left(\frac{374}{465}\right)$	$e\left(\frac{128}{465}\right)$	$e\left(\frac{13}{155}\right)$	$e\left(\frac{34}{93}\right)$	$e\left(\frac{106}{155}\right)$	$e\left(\frac{132}{155}\right)$
$\chi_{5766}(289,\cdot)$	$1$	$1$	$e\left(\frac{85}{93}\right)$	$e\left(\frac{346}{465}\right)$	$e\left(\frac{461}{465}\right)$	$e\left(\frac{437}{465}\right)$	$e\left(\frac{289}{465}\right)$	$e\left(\frac{268}{465}\right)$	$e\left(\frac{3}{155}\right)$	$e\left(\frac{77}{93}\right)$	$e\left(\frac{96}{155}\right)$	$e\left(\frac{102}{155}\right)$
$\chi_{5766}(307,\cdot)$	$1$	$1$	$e\left(\frac{35}{93}\right)$	$e\left(\frac{44}{465}\right)$	$e\left(\frac{64}{465}\right)$	$e\left(\frac{448}{465}\right)$	$e\left(\frac{26}{465}\right)$	$e\left(\frac{362}{465}\right)$	$e\left(\frac{107}{155}\right)$	$e\left(\frac{70}{93}\right)$	$e\left(\frac{14}{155}\right)$	$e\left(\frac{73}{155}\right)$
$\chi_{5766}(319,\cdot)$	$1$	$1$	$e\left(\frac{91}{93}\right)$	$e\left(\frac{133}{465}\right)$	$e\left(\frac{278}{465}\right)$	$e\left(\frac{86}{465}\right)$	$e\left(\frac{142}{465}\right)$	$e\left(\frac{439}{465}\right)$	$e\left(\frac{24}{155}\right)$	$e\left(\frac{89}{93}\right)$	$e\left(\frac{148}{155}\right)$	$e\left(\frac{41}{155}\right)$
$\chi_{5766}(355,\cdot)$	$1$	$1$	$e\left(\frac{86}{93}\right)$	$e\left(\frac{233}{465}\right)$	$e\left(\frac{43}{465}\right)$	$e\left(\frac{301}{465}\right)$	$e\left(\frac{32}{465}\right)$	$e\left(\frac{374}{465}\right)$	$e\left(\frac{84}{155}\right)$	$e\left(\frac{79}{93}\right)$	$e\left(\frac{53}{155}\right)$	$e\left(\frac{66}{155}\right)$
$\chi_{5766}(361,\cdot)$	$1$	$1$	$e\left(\frac{46}{93}\right)$	$e\left(\frac{382}{465}\right)$	$e\left(\frac{302}{465}\right)$	$e\left(\frac{254}{465}\right)$	$e\left(\frac{268}{465}\right)$	$e\left(\frac{226}{465}\right)$	$e\left(\frac{6}{155}\right)$	$e\left(\frac{92}{93}\right)$	$e\left(\frac{37}{155}\right)$	$e\left(\frac{49}{155}\right)$
$\chi_{5766}(379,\cdot)$	$1$	$1$	$e\left(\frac{23}{93}\right)$	$e\left(\frac{377}{465}\right)$	$e\left(\frac{337}{465}\right)$	$e\left(\frac{34}{465}\right)$	$e\left(\frac{413}{465}\right)$	$e\left(\frac{206}{465}\right)$	$e\left(\frac{96}{155}\right)$	$e\left(\frac{46}{93}\right)$	$e\left(\frac{127}{155}\right)$	$e\left(\frac{9}{155}\right)$
$\chi_{5766}(391,\cdot)$	$1$	$1$	$e\left(\frac{11}{93}\right)$	$e\left(\frac{431}{465}\right)$	$e\left(\frac{331}{465}\right)$	$e\left(\frac{457}{465}\right)$	$e\left(\frac{149}{465}\right)$	$e\left(\frac{143}{465}\right)$	$e\left(\frac{23}{155}\right)$	$e\left(\frac{22}{93}\right)$	$e\left(\frac{116}{155}\right)$	$e\left(\frac{7}{155}\right)$
$\chi_{5766}(421,\cdot)$	$1$	$1$	$e\left(\frac{4}{93}\right)$	$e\left(\frac{199}{465}\right)$	$e\left(\frac{374}{465}\right)$	$e\left(\frac{293}{465}\right)$	$e\left(\frac{181}{465}\right)$	$e\left(\frac{52}{465}\right)$	$e\left(\frac{107}{155}\right)$	$e\left(\frac{8}{93}\right)$	$e\left(\frac{14}{155}\right)$	$e\left(\frac{73}{155}\right)$
$\chi_{5766}(475,\cdot)$	$1$	$1$	$e\left(\frac{55}{93}\right)$	$e\left(\frac{16}{465}\right)$	$e\left(\frac{446}{465}\right)$	$e\left(\frac{332}{465}\right)$	$e\left(\frac{94}{465}\right)$	$e\left(\frac{343}{465}\right)$	$e\left(\frac{53}{155}\right)$	$e\left(\frac{17}{93}\right)$	$e\left(\frac{146}{155}\right)$	$e\left(\frac{97}{155}\right)$
$\chi_{5766}(493,\cdot)$	$1$	$1$	$e\left(\frac{11}{93}\right)$	$e\left(\frac{59}{465}\right)$	$e\left(\frac{424}{465}\right)$	$e\left(\frac{178}{465}\right)$	$e\left(\frac{56}{465}\right)$	$e\left(\frac{422}{465}\right)$	$e\left(\frac{147}{155}\right)$	$e\left(\frac{22}{93}\right)$	$e\left(\frac{54}{155}\right)$	$e\left(\frac{38}{155}\right)$
$\chi_{5766}(505,\cdot)$	$1$	$1$	$e\left(\frac{37}{93}\right)$	$e\left(\frac{283}{465}\right)$	$e\left(\frac{158}{465}\right)$	$e\left(\frac{176}{465}\right)$	$e\left(\frac{442}{465}\right)$	$e\left(\frac{109}{465}\right)$	$e\left(\frac{114}{155}\right)$	$e\left(\frac{74}{93}\right)$	$e\left(\frac{83}{155}\right)$	$e\left(\frac{1}{155}\right)$
$\chi_{5766}(541,\cdot)$	$1$	$1$	$e\left(\frac{38}{93}\right)$	$e\left(\frac{263}{465}\right)$	$e\left(\frac{298}{465}\right)$	$e\left(\frac{226}{465}\right)$	$e\left(\frac{92}{465}\right)$	$e\left(\frac{29}{465}\right)$	$e\left(\frac{9}{155}\right)$	$e\left(\frac{76}{93}\right)$	$e\left(\frac{133}{155}\right)$	$e\left(\frac{151}{155}\right)$
$\chi_{5766}(565,\cdot)$	$1$	$1$	$e\left(\frac{20}{93}\right)$	$e\left(\frac{437}{465}\right)$	$e\left(\frac{382}{465}\right)$	$e\left(\frac{349}{465}\right)$	$e\left(\frac{68}{465}\right)$	$e\left(\frac{446}{465}\right)$	$e\left(\frac{101}{155}\right)$	$e\left(\frac{40}{93}\right)$	$e\left(\frac{132}{155}\right)$	$e\left(\frac{24}{155}\right)$
$\chi_{5766}(577,\cdot)$	$1$	$1$	$e\left(\frac{5}{93}\right)$	$e\left(\frac{86}{465}\right)$	$e\left(\frac{421}{465}\right)$	$e\left(\frac{157}{465}\right)$	$e\left(\frac{389}{465}\right)$	$e\left(\frac{158}{465}\right)$	$e\left(\frac{33}{155}\right)$	$e\left(\frac{10}{93}\right)$	$e\left(\frac{126}{155}\right)$	$e\left(\frac{37}{155}\right)$
$\chi_{5766}(607,\cdot)$	$1$	$1$	$e\left(\frac{70}{93}\right)$	$e\left(\frac{274}{465}\right)$	$e\left(\frac{314}{465}\right)$	$e\left(\frac{338}{465}\right)$	$e\left(\frac{331}{465}\right)$	$e\left(\frac{352}{465}\right)$	$e\left(\frac{152}{155}\right)$	$e\left(\frac{47}{93}\right)$	$e\left(\frac{59}{155}\right)$	$e\left(\frac{53}{155}\right)$
$\chi_{5766}(661,\cdot)$	$1$	$1$	$e\left(\frac{25}{93}\right)$	$e\left(\frac{151}{465}\right)$	$e\left(\frac{431}{465}\right)$	$e\left(\frac{227}{465}\right)$	$e\left(\frac{364}{465}\right)$	$e\left(\frac{418}{465}\right)$	$e\left(\frac{103}{155}\right)$	$e\left(\frac{50}{93}\right)$	$e\left(\frac{41}{155}\right)$	$e\left(\frac{92}{155}\right)$
$\chi_{5766}(679,\cdot)$	$1$	$1$	$e\left(\frac{80}{93}\right)$	$e\left(\frac{74}{465}\right)$	$e\left(\frac{319}{465}\right)$	$e\left(\frac{373}{465}\right)$	$e\left(\frac{86}{465}\right)$	$e\left(\frac{17}{465}\right)$	$e\left(\frac{32}{155}\right)$	$e\left(\frac{67}{93}\right)$	$e\left(\frac{94}{155}\right)$	$e\left(\frac{3}{155}\right)$
$\chi_{5766}(691,\cdot)$	$1$	$1$	$e\left(\frac{76}{93}\right)$	$e\left(\frac{433}{465}\right)$	$e\left(\frac{38}{465}\right)$	$e\left(\frac{266}{465}\right)$	$e\left(\frac{277}{465}\right)$	$e\left(\frac{244}{465}\right)$	$e\left(\frac{49}{155}\right)$	$e\left(\frac{59}{93}\right)$	$e\left(\frac{18}{155}\right)$	$e\left(\frac{116}{155}\right)$
$\chi_{5766}(727,\cdot)$	$1$	$1$	$e\left(\frac{83}{93}\right)$	$e\left(\frac{293}{465}\right)$	$e\left(\frac{88}{465}\right)$	$e\left(\frac{151}{465}\right)$	$e\left(\frac{152}{465}\right)$	$e\left(\frac{149}{465}\right)$	$e\left(\frac{89}{155}\right)$	$e\left(\frac{73}{93}\right)$	$e\left(\frac{58}{155}\right)$	$e\left(\frac{81}{155}\right)$
$\chi_{5766}(733,\cdot)$	$1$	$1$	$e\left(\frac{16}{93}\right)$	$e\left(\frac{52}{465}\right)$	$e\left(\frac{287}{465}\right)$	$e\left(\frac{149}{465}\right)$	$e\left(\frac{73}{465}\right)$	$e\left(\frac{301}{465}\right)$	$e\left(\frac{56}{155}\right)$	$e\left(\frac{32}{93}\right)$	$e\left(\frac{87}{155}\right)$	$e\left(\frac{44}{155}\right)$
$\chi_{5766}(751,\cdot)$	$1$	$1$	$e\left(\frac{17}{93}\right)$	$e\left(\frac{32}{465}\right)$	$e\left(\frac{427}{465}\right)$	$e\left(\frac{199}{465}\right)$	$e\left(\frac{188}{465}\right)$	$e\left(\frac{221}{465}\right)$	$e\left(\frac{106}{155}\right)$	$e\left(\frac{34}{93}\right)$	$e\left(\frac{137}{155}\right)$	$e\left(\frac{39}{155}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(35\)
\(\chi_{5766}(7,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{93}\right)\)	\(e\left(\frac{257}{465}\right)\)	\(e\left(\frac{247}{465}\right)\)	\(e\left(\frac{334}{465}\right)\)	\(e\left(\frac{173}{465}\right)\)	\(e\left(\frac{191}{465}\right)\)	\(e\left(\frac{86}{155}\right)\)	\(e\left(\frac{58}{93}\right)\)	\(e\left(\frac{117}{155}\right)\)	\(e\left(\frac{134}{155}\right)\)
\(\chi_{5766}(19,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{93}\right)\)	\(e\left(\frac{191}{465}\right)\)	\(e\left(\frac{151}{465}\right)\)	\(e\left(\frac{127}{465}\right)\)	\(e\left(\frac{134}{465}\right)\)	\(e\left(\frac{113}{465}\right)\)	\(e\left(\frac{3}{155}\right)\)	\(e\left(\frac{46}{93}\right)\)	\(e\left(\frac{96}{155}\right)\)	\(e\left(\frac{102}{155}\right)\)
\(\chi_{5766}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{93}\right)\)	\(e\left(\frac{49}{465}\right)\)	\(e\left(\frac{29}{465}\right)\)	\(e\left(\frac{203}{465}\right)\)	\(e\left(\frac{346}{465}\right)\)	\(e\left(\frac{382}{465}\right)\)	\(e\left(\frac{17}{155}\right)\)	\(e\left(\frac{23}{93}\right)\)	\(e\left(\frac{79}{155}\right)\)	\(e\left(\frac{113}{155}\right)\)
\(\chi_{5766}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{22}{93}\right)\)	\(e\left(\frac{211}{465}\right)\)	\(e\left(\frac{11}{465}\right)\)	\(e\left(\frac{77}{465}\right)\)	\(e\left(\frac{19}{465}\right)\)	\(e\left(\frac{193}{465}\right)\)	\(e\left(\frac{108}{155}\right)\)	\(e\left(\frac{44}{93}\right)\)	\(e\left(\frac{46}{155}\right)\)	\(e\left(\frac{107}{155}\right)\)
\(\chi_{5766}(121,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{93}\right)\)	\(e\left(\frac{29}{465}\right)\)	\(e\left(\frac{169}{465}\right)\)	\(e\left(\frac{253}{465}\right)\)	\(e\left(\frac{461}{465}\right)\)	\(e\left(\frac{302}{465}\right)\)	\(e\left(\frac{67}{155}\right)\)	\(e\left(\frac{25}{93}\right)\)	\(e\left(\frac{129}{155}\right)\)	\(e\left(\frac{108}{155}\right)\)
\(\chi_{5766}(133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{52}{93}\right)\)	\(e\left(\frac{448}{465}\right)\)	\(e\left(\frac{398}{465}\right)\)	\(e\left(\frac{461}{465}\right)\)	\(e\left(\frac{307}{465}\right)\)	\(e\left(\frac{304}{465}\right)\)	\(e\left(\frac{89}{155}\right)\)	\(e\left(\frac{11}{93}\right)\)	\(e\left(\frac{58}{155}\right)\)	\(e\left(\frac{81}{155}\right)\)
\(\chi_{5766}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{93}\right)\)	\(e\left(\frac{203}{465}\right)\)	\(e\left(\frac{253}{465}\right)\)	\(e\left(\frac{376}{465}\right)\)	\(e\left(\frac{437}{465}\right)\)	\(e\left(\frac{254}{465}\right)\)	\(e\left(\frac{4}{155}\right)\)	\(e\left(\frac{82}{93}\right)\)	\(e\left(\frac{128}{155}\right)\)	\(e\left(\frac{136}{155}\right)\)
\(\chi_{5766}(175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{93}\right)\)	\(e\left(\frac{82}{465}\right)\)	\(e\left(\frac{77}{465}\right)\)	\(e\left(\frac{74}{465}\right)\)	\(e\left(\frac{133}{465}\right)\)	\(e\left(\frac{421}{465}\right)\)	\(e\left(\frac{136}{155}\right)\)	\(e\left(\frac{29}{93}\right)\)	\(e\left(\frac{12}{155}\right)\)	\(e\left(\frac{129}{155}\right)\)
\(\chi_{5766}(193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{26}{93}\right)\)	\(e\left(\frac{317}{465}\right)\)	\(e\left(\frac{292}{465}\right)\)	\(e\left(\frac{184}{465}\right)\)	\(e\left(\frac{293}{465}\right)\)	\(e\left(\frac{431}{465}\right)\)	\(e\left(\frac{91}{155}\right)\)	\(e\left(\frac{52}{93}\right)\)	\(e\left(\frac{122}{155}\right)\)	\(e\left(\frac{149}{155}\right)\)
\(\chi_{5766}(205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{93}\right)\)	\(e\left(\frac{311}{465}\right)\)	\(e\left(\frac{241}{465}\right)\)	\(e\left(\frac{292}{465}\right)\)	\(e\left(\frac{374}{465}\right)\)	\(e\left(\frac{128}{465}\right)\)	\(e\left(\frac{13}{155}\right)\)	\(e\left(\frac{34}{93}\right)\)	\(e\left(\frac{106}{155}\right)\)	\(e\left(\frac{132}{155}\right)\)
\(\chi_{5766}(289,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{93}\right)\)	\(e\left(\frac{346}{465}\right)\)	\(e\left(\frac{461}{465}\right)\)	\(e\left(\frac{437}{465}\right)\)	\(e\left(\frac{289}{465}\right)\)	\(e\left(\frac{268}{465}\right)\)	\(e\left(\frac{3}{155}\right)\)	\(e\left(\frac{77}{93}\right)\)	\(e\left(\frac{96}{155}\right)\)	\(e\left(\frac{102}{155}\right)\)
\(\chi_{5766}(307,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{93}\right)\)	\(e\left(\frac{44}{465}\right)\)	\(e\left(\frac{64}{465}\right)\)	\(e\left(\frac{448}{465}\right)\)	\(e\left(\frac{26}{465}\right)\)	\(e\left(\frac{362}{465}\right)\)	\(e\left(\frac{107}{155}\right)\)	\(e\left(\frac{70}{93}\right)\)	\(e\left(\frac{14}{155}\right)\)	\(e\left(\frac{73}{155}\right)\)
\(\chi_{5766}(319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{93}\right)\)	\(e\left(\frac{133}{465}\right)\)	\(e\left(\frac{278}{465}\right)\)	\(e\left(\frac{86}{465}\right)\)	\(e\left(\frac{142}{465}\right)\)	\(e\left(\frac{439}{465}\right)\)	\(e\left(\frac{24}{155}\right)\)	\(e\left(\frac{89}{93}\right)\)	\(e\left(\frac{148}{155}\right)\)	\(e\left(\frac{41}{155}\right)\)
\(\chi_{5766}(355,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{86}{93}\right)\)	\(e\left(\frac{233}{465}\right)\)	\(e\left(\frac{43}{465}\right)\)	\(e\left(\frac{301}{465}\right)\)	\(e\left(\frac{32}{465}\right)\)	\(e\left(\frac{374}{465}\right)\)	\(e\left(\frac{84}{155}\right)\)	\(e\left(\frac{79}{93}\right)\)	\(e\left(\frac{53}{155}\right)\)	\(e\left(\frac{66}{155}\right)\)
\(\chi_{5766}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{93}\right)\)	\(e\left(\frac{382}{465}\right)\)	\(e\left(\frac{302}{465}\right)\)	\(e\left(\frac{254}{465}\right)\)	\(e\left(\frac{268}{465}\right)\)	\(e\left(\frac{226}{465}\right)\)	\(e\left(\frac{6}{155}\right)\)	\(e\left(\frac{92}{93}\right)\)	\(e\left(\frac{37}{155}\right)\)	\(e\left(\frac{49}{155}\right)\)
\(\chi_{5766}(379,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{93}\right)\)	\(e\left(\frac{377}{465}\right)\)	\(e\left(\frac{337}{465}\right)\)	\(e\left(\frac{34}{465}\right)\)	\(e\left(\frac{413}{465}\right)\)	\(e\left(\frac{206}{465}\right)\)	\(e\left(\frac{96}{155}\right)\)	\(e\left(\frac{46}{93}\right)\)	\(e\left(\frac{127}{155}\right)\)	\(e\left(\frac{9}{155}\right)\)
\(\chi_{5766}(391,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{93}\right)\)	\(e\left(\frac{431}{465}\right)\)	\(e\left(\frac{331}{465}\right)\)	\(e\left(\frac{457}{465}\right)\)	\(e\left(\frac{149}{465}\right)\)	\(e\left(\frac{143}{465}\right)\)	\(e\left(\frac{23}{155}\right)\)	\(e\left(\frac{22}{93}\right)\)	\(e\left(\frac{116}{155}\right)\)	\(e\left(\frac{7}{155}\right)\)
\(\chi_{5766}(421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{4}{93}\right)\)	\(e\left(\frac{199}{465}\right)\)	\(e\left(\frac{374}{465}\right)\)	\(e\left(\frac{293}{465}\right)\)	\(e\left(\frac{181}{465}\right)\)	\(e\left(\frac{52}{465}\right)\)	\(e\left(\frac{107}{155}\right)\)	\(e\left(\frac{8}{93}\right)\)	\(e\left(\frac{14}{155}\right)\)	\(e\left(\frac{73}{155}\right)\)
\(\chi_{5766}(475,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{93}\right)\)	\(e\left(\frac{16}{465}\right)\)	\(e\left(\frac{446}{465}\right)\)	\(e\left(\frac{332}{465}\right)\)	\(e\left(\frac{94}{465}\right)\)	\(e\left(\frac{343}{465}\right)\)	\(e\left(\frac{53}{155}\right)\)	\(e\left(\frac{17}{93}\right)\)	\(e\left(\frac{146}{155}\right)\)	\(e\left(\frac{97}{155}\right)\)
\(\chi_{5766}(493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{93}\right)\)	\(e\left(\frac{59}{465}\right)\)	\(e\left(\frac{424}{465}\right)\)	\(e\left(\frac{178}{465}\right)\)	\(e\left(\frac{56}{465}\right)\)	\(e\left(\frac{422}{465}\right)\)	\(e\left(\frac{147}{155}\right)\)	\(e\left(\frac{22}{93}\right)\)	\(e\left(\frac{54}{155}\right)\)	\(e\left(\frac{38}{155}\right)\)
\(\chi_{5766}(505,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{93}\right)\)	\(e\left(\frac{283}{465}\right)\)	\(e\left(\frac{158}{465}\right)\)	\(e\left(\frac{176}{465}\right)\)	\(e\left(\frac{442}{465}\right)\)	\(e\left(\frac{109}{465}\right)\)	\(e\left(\frac{114}{155}\right)\)	\(e\left(\frac{74}{93}\right)\)	\(e\left(\frac{83}{155}\right)\)	\(e\left(\frac{1}{155}\right)\)
\(\chi_{5766}(541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{38}{93}\right)\)	\(e\left(\frac{263}{465}\right)\)	\(e\left(\frac{298}{465}\right)\)	\(e\left(\frac{226}{465}\right)\)	\(e\left(\frac{92}{465}\right)\)	\(e\left(\frac{29}{465}\right)\)	\(e\left(\frac{9}{155}\right)\)	\(e\left(\frac{76}{93}\right)\)	\(e\left(\frac{133}{155}\right)\)	\(e\left(\frac{151}{155}\right)\)
\(\chi_{5766}(565,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{20}{93}\right)\)	\(e\left(\frac{437}{465}\right)\)	\(e\left(\frac{382}{465}\right)\)	\(e\left(\frac{349}{465}\right)\)	\(e\left(\frac{68}{465}\right)\)	\(e\left(\frac{446}{465}\right)\)	\(e\left(\frac{101}{155}\right)\)	\(e\left(\frac{40}{93}\right)\)	\(e\left(\frac{132}{155}\right)\)	\(e\left(\frac{24}{155}\right)\)
\(\chi_{5766}(577,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{93}\right)\)	\(e\left(\frac{86}{465}\right)\)	\(e\left(\frac{421}{465}\right)\)	\(e\left(\frac{157}{465}\right)\)	\(e\left(\frac{389}{465}\right)\)	\(e\left(\frac{158}{465}\right)\)	\(e\left(\frac{33}{155}\right)\)	\(e\left(\frac{10}{93}\right)\)	\(e\left(\frac{126}{155}\right)\)	\(e\left(\frac{37}{155}\right)\)
\(\chi_{5766}(607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{70}{93}\right)\)	\(e\left(\frac{274}{465}\right)\)	\(e\left(\frac{314}{465}\right)\)	\(e\left(\frac{338}{465}\right)\)	\(e\left(\frac{331}{465}\right)\)	\(e\left(\frac{352}{465}\right)\)	\(e\left(\frac{152}{155}\right)\)	\(e\left(\frac{47}{93}\right)\)	\(e\left(\frac{59}{155}\right)\)	\(e\left(\frac{53}{155}\right)\)
\(\chi_{5766}(661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{93}\right)\)	\(e\left(\frac{151}{465}\right)\)	\(e\left(\frac{431}{465}\right)\)	\(e\left(\frac{227}{465}\right)\)	\(e\left(\frac{364}{465}\right)\)	\(e\left(\frac{418}{465}\right)\)	\(e\left(\frac{103}{155}\right)\)	\(e\left(\frac{50}{93}\right)\)	\(e\left(\frac{41}{155}\right)\)	\(e\left(\frac{92}{155}\right)\)
\(\chi_{5766}(679,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{80}{93}\right)\)	\(e\left(\frac{74}{465}\right)\)	\(e\left(\frac{319}{465}\right)\)	\(e\left(\frac{373}{465}\right)\)	\(e\left(\frac{86}{465}\right)\)	\(e\left(\frac{17}{465}\right)\)	\(e\left(\frac{32}{155}\right)\)	\(e\left(\frac{67}{93}\right)\)	\(e\left(\frac{94}{155}\right)\)	\(e\left(\frac{3}{155}\right)\)
\(\chi_{5766}(691,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{93}\right)\)	\(e\left(\frac{433}{465}\right)\)	\(e\left(\frac{38}{465}\right)\)	\(e\left(\frac{266}{465}\right)\)	\(e\left(\frac{277}{465}\right)\)	\(e\left(\frac{244}{465}\right)\)	\(e\left(\frac{49}{155}\right)\)	\(e\left(\frac{59}{93}\right)\)	\(e\left(\frac{18}{155}\right)\)	\(e\left(\frac{116}{155}\right)\)
\(\chi_{5766}(727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{93}\right)\)	\(e\left(\frac{293}{465}\right)\)	\(e\left(\frac{88}{465}\right)\)	\(e\left(\frac{151}{465}\right)\)	\(e\left(\frac{152}{465}\right)\)	\(e\left(\frac{149}{465}\right)\)	\(e\left(\frac{89}{155}\right)\)	\(e\left(\frac{73}{93}\right)\)	\(e\left(\frac{58}{155}\right)\)	\(e\left(\frac{81}{155}\right)\)
\(\chi_{5766}(733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{16}{93}\right)\)	\(e\left(\frac{52}{465}\right)\)	\(e\left(\frac{287}{465}\right)\)	\(e\left(\frac{149}{465}\right)\)	\(e\left(\frac{73}{465}\right)\)	\(e\left(\frac{301}{465}\right)\)	\(e\left(\frac{56}{155}\right)\)	\(e\left(\frac{32}{93}\right)\)	\(e\left(\frac{87}{155}\right)\)	\(e\left(\frac{44}{155}\right)\)
\(\chi_{5766}(751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{93}\right)\)	\(e\left(\frac{32}{465}\right)\)	\(e\left(\frac{427}{465}\right)\)	\(e\left(\frac{199}{465}\right)\)	\(e\left(\frac{188}{465}\right)\)	\(e\left(\frac{221}{465}\right)\)	\(e\left(\frac{106}{155}\right)\)	\(e\left(\frac{34}{93}\right)\)	\(e\left(\frac{137}{155}\right)\)	\(e\left(\frac{39}{155}\right)\)

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First 31 of 240 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	5766.bc
Modulus	$5766$
Conductor	$961$
Order	$465$
Real	no
Primitive	no
Minimal	yes
Parity	even

Modulus:	\(5766\)
Conductor:	\(961\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(465\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 961.o	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)