LMFDB - Dirichlet character orbit 8732.cp

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8732, base_ring=CyclotomicField(522)) M = H._module chi = DirichletCharacter(H, M([261,232,477])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(83,8732)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$8732$
Conductor:	$8732$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$522$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	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:	$\Q(\zeta_{261})$
Fixed field:	Number field defined by a degree 522 polynomial (not computed)

First 31 of 168 characters in Galois orbit

Character	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{8732}(83,\cdot)$	$1$	$1$	$e\left(\frac{389}{522}\right)$	$e\left(\frac{184}{261}\right)$	$e\left(\frac{89}{522}\right)$	$e\left(\frac{128}{261}\right)$	$e\left(\frac{59}{87}\right)$	$e\left(\frac{5}{522}\right)$	$e\left(\frac{235}{522}\right)$	$e\left(\frac{173}{261}\right)$	$e\left(\frac{407}{522}\right)$	$e\left(\frac{239}{261}\right)$
$\chi_{8732}(155,\cdot)$	$1$	$1$	$e\left(\frac{13}{522}\right)$	$e\left(\frac{35}{261}\right)$	$e\left(\frac{7}{522}\right)$	$e\left(\frac{13}{261}\right)$	$e\left(\frac{76}{87}\right)$	$e\left(\frac{235}{522}\right)$	$e\left(\frac{83}{522}\right)$	$e\left(\frac{40}{261}\right)$	$e\left(\frac{337}{522}\right)$	$e\left(\frac{10}{261}\right)$
$\chi_{8732}(219,\cdot)$	$1$	$1$	$e\left(\frac{397}{522}\right)$	$e\left(\frac{65}{261}\right)$	$e\left(\frac{13}{522}\right)$	$e\left(\frac{136}{261}\right)$	$e\left(\frac{79}{87}\right)$	$e\left(\frac{511}{522}\right)$	$e\left(\frac{5}{522}\right)$	$e\left(\frac{37}{261}\right)$	$e\left(\frac{253}{522}\right)$	$e\left(\frac{205}{261}\right)$
$\chi_{8732}(231,\cdot)$	$1$	$1$	$e\left(\frac{119}{522}\right)$	$e\left(\frac{220}{261}\right)$	$e\left(\frac{305}{522}\right)$	$e\left(\frac{119}{261}\right)$	$e\left(\frac{80}{87}\right)$	$e\left(\frac{23}{522}\right)$	$e\left(\frac{37}{522}\right)$	$e\left(\frac{65}{261}\right)$	$e\left(\frac{515}{522}\right)$	$e\left(\frac{212}{261}\right)$
$\chi_{8732}(275,\cdot)$	$1$	$1$	$e\left(\frac{149}{522}\right)$	$e\left(\frac{100}{261}\right)$	$e\left(\frac{281}{522}\right)$	$e\left(\frac{149}{261}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{485}{522}\right)$	$e\left(\frac{349}{522}\right)$	$e\left(\frac{77}{261}\right)$	$e\left(\frac{329}{522}\right)$	$e\left(\frac{215}{261}\right)$
$\chi_{8732}(303,\cdot)$	$1$	$1$	$e\left(\frac{103}{522}\right)$	$e\left(\frac{197}{261}\right)$	$e\left(\frac{457}{522}\right)$	$e\left(\frac{103}{261}\right)$	$e\left(\frac{40}{87}\right)$	$e\left(\frac{55}{522}\right)$	$e\left(\frac{497}{522}\right)$	$e\left(\frac{76}{261}\right)$	$e\left(\frac{301}{522}\right)$	$e\left(\frac{19}{261}\right)$
$\chi_{8732}(367,\cdot)$	$1$	$1$	$e\left(\frac{37}{522}\right)$	$e\left(\frac{200}{261}\right)$	$e\left(\frac{301}{522}\right)$	$e\left(\frac{37}{261}\right)$	$e\left(\frac{49}{87}\right)$	$e\left(\frac{187}{522}\right)$	$e\left(\frac{437}{522}\right)$	$e\left(\frac{154}{261}\right)$	$e\left(\frac{397}{522}\right)$	$e\left(\frac{169}{261}\right)$
$\chi_{8732}(419,\cdot)$	$1$	$1$	$e\left(\frac{359}{522}\right)$	$e\left(\frac{43}{261}\right)$	$e\left(\frac{113}{522}\right)$	$e\left(\frac{98}{261}\right)$	$e\left(\frac{71}{87}\right)$	$e\left(\frac{65}{522}\right)$	$e\left(\frac{445}{522}\right)$	$e\left(\frac{161}{261}\right)$	$e\left(\frac{71}{522}\right)$	$e\left(\frac{236}{261}\right)$
$\chi_{8732}(423,\cdot)$	$1$	$1$	$e\left(\frac{221}{522}\right)$	$e\left(\frac{73}{261}\right)$	$e\left(\frac{119}{522}\right)$	$e\left(\frac{221}{261}\right)$	$e\left(\frac{74}{87}\right)$	$e\left(\frac{341}{522}\right)$	$e\left(\frac{367}{522}\right)$	$e\left(\frac{158}{261}\right)$	$e\left(\frac{509}{522}\right)$	$e\left(\frac{170}{261}\right)$
$\chi_{8732}(451,\cdot)$	$1$	$1$	$e\left(\frac{121}{522}\right)$	$e\left(\frac{125}{261}\right)$	$e\left(\frac{25}{522}\right)$	$e\left(\frac{121}{261}\right)$	$e\left(\frac{85}{87}\right)$	$e\left(\frac{19}{522}\right)$	$e\left(\frac{371}{522}\right)$	$e\left(\frac{31}{261}\right)$	$e\left(\frac{85}{522}\right)$	$e\left(\frac{73}{261}\right)$
$\chi_{8732}(515,\cdot)$	$1$	$1$	$e\left(\frac{379}{522}\right)$	$e\left(\frac{137}{261}\right)$	$e\left(\frac{445}{522}\right)$	$e\left(\frac{118}{261}\right)$	$e\left(\frac{34}{87}\right)$	$e\left(\frac{25}{522}\right)$	$e\left(\frac{131}{522}\right)$	$e\left(\frac{82}{261}\right)$	$e\left(\frac{469}{522}\right)$	$e\left(\frac{151}{261}\right)$
$\chi_{8732}(527,\cdot)$	$1$	$1$	$e\left(\frac{407}{522}\right)$	$e\left(\frac{112}{261}\right)$	$e\left(\frac{179}{522}\right)$	$e\left(\frac{146}{261}\right)$	$e\left(\frac{17}{87}\right)$	$e\left(\frac{491}{522}\right)$	$e\left(\frac{109}{522}\right)$	$e\left(\frac{128}{261}\right)$	$e\left(\frac{191}{522}\right)$	$e\left(\frac{32}{261}\right)$
$\chi_{8732}(571,\cdot)$	$1$	$1$	$e\left(\frac{77}{522}\right)$	$e\left(\frac{127}{261}\right)$	$e\left(\frac{443}{522}\right)$	$e\left(\frac{77}{261}\right)$	$e\left(\frac{62}{87}\right)$	$e\left(\frac{107}{522}\right)$	$e\left(\frac{331}{522}\right)$	$e\left(\frac{257}{261}\right)$	$e\left(\frac{149}{522}\right)$	$e\left(\frac{260}{261}\right)$
$\chi_{8732}(663,\cdot)$	$1$	$1$	$e\left(\frac{343}{522}\right)$	$e\left(\frac{20}{261}\right)$	$e\left(\frac{265}{522}\right)$	$e\left(\frac{82}{261}\right)$	$e\left(\frac{31}{87}\right)$	$e\left(\frac{97}{522}\right)$	$e\left(\frac{383}{522}\right)$	$e\left(\frac{172}{261}\right)$	$e\left(\frac{379}{522}\right)$	$e\left(\frac{43}{261}\right)$
$\chi_{8732}(699,\cdot)$	$1$	$1$	$e\left(\frac{79}{522}\right)$	$e\left(\frac{32}{261}\right)$	$e\left(\frac{163}{522}\right)$	$e\left(\frac{79}{261}\right)$	$e\left(\frac{67}{87}\right)$	$e\left(\frac{103}{522}\right)$	$e\left(\frac{143}{522}\right)$	$e\left(\frac{223}{261}\right)$	$e\left(\frac{241}{522}\right)$	$e\left(\frac{121}{261}\right)$
$\chi_{8732}(719,\cdot)$	$1$	$1$	$e\left(\frac{491}{522}\right)$	$e\left(\frac{37}{261}\right)$	$e\left(\frac{425}{522}\right)$	$e\left(\frac{230}{261}\right)$	$e\left(\frac{53}{87}\right)$	$e\left(\frac{323}{522}\right)$	$e\left(\frac{43}{522}\right)$	$e\left(\frac{5}{261}\right)$	$e\left(\frac{401}{522}\right)$	$e\left(\frac{197}{261}\right)$
$\chi_{8732}(747,\cdot)$	$1$	$1$	$e\left(\frac{265}{522}\right)$	$e\left(\frac{71}{261}\right)$	$e\left(\frac{223}{522}\right)$	$e\left(\frac{4}{261}\right)$	$e\left(\frac{10}{87}\right)$	$e\left(\frac{253}{522}\right)$	$e\left(\frac{407}{522}\right)$	$e\left(\frac{193}{261}\right)$	$e\left(\frac{445}{522}\right)$	$e\left(\frac{244}{261}\right)$
$\chi_{8732}(811,\cdot)$	$1$	$1$	$e\left(\frac{289}{522}\right)$	$e\left(\frac{236}{261}\right)$	$e\left(\frac{517}{522}\right)$	$e\left(\frac{28}{261}\right)$	$e\left(\frac{70}{87}\right)$	$e\left(\frac{205}{522}\right)$	$e\left(\frac{239}{522}\right)$	$e\left(\frac{46}{261}\right)$	$e\left(\frac{505}{522}\right)$	$e\left(\frac{142}{261}\right)$
$\chi_{8732}(823,\cdot)$	$1$	$1$	$e\left(\frac{83}{522}\right)$	$e\left(\frac{103}{261}\right)$	$e\left(\frac{125}{522}\right)$	$e\left(\frac{83}{261}\right)$	$e\left(\frac{77}{87}\right)$	$e\left(\frac{95}{522}\right)$	$e\left(\frac{289}{522}\right)$	$e\left(\frac{155}{261}\right)$	$e\left(\frac{425}{522}\right)$	$e\left(\frac{104}{261}\right)$
$\chi_{8732}(863,\cdot)$	$1$	$1$	$e\left(\frac{71}{522}\right)$	$e\left(\frac{151}{261}\right)$	$e\left(\frac{239}{522}\right)$	$e\left(\frac{71}{261}\right)$	$e\left(\frac{47}{87}\right)$	$e\left(\frac{119}{522}\right)$	$e\left(\frac{373}{522}\right)$	$e\left(\frac{98}{261}\right)$	$e\left(\frac{395}{522}\right)$	$e\left(\frac{155}{261}\right)$
$\chi_{8732}(895,\cdot)$	$1$	$1$	$e\left(\frac{337}{522}\right)$	$e\left(\frac{44}{261}\right)$	$e\left(\frac{61}{522}\right)$	$e\left(\frac{76}{261}\right)$	$e\left(\frac{16}{87}\right)$	$e\left(\frac{109}{522}\right)$	$e\left(\frac{425}{522}\right)$	$e\left(\frac{13}{261}\right)$	$e\left(\frac{103}{522}\right)$	$e\left(\frac{199}{261}\right)$
$\chi_{8732}(1011,\cdot)$	$1$	$1$	$e\left(\frac{161}{522}\right)$	$e\left(\frac{52}{261}\right)$	$e\left(\frac{167}{522}\right)$	$e\left(\frac{161}{261}\right)$	$e\left(\frac{11}{87}\right)$	$e\left(\frac{461}{522}\right)$	$e\left(\frac{265}{522}\right)$	$e\left(\frac{134}{261}\right)$	$e\left(\frac{359}{522}\right)$	$e\left(\frac{164}{261}\right)$
$\chi_{8732}(1043,\cdot)$	$1$	$1$	$e\left(\frac{193}{522}\right)$	$e\left(\frac{98}{261}\right)$	$e\left(\frac{385}{522}\right)$	$e\left(\frac{193}{261}\right)$	$e\left(\frac{4}{87}\right)$	$e\left(\frac{397}{522}\right)$	$e\left(\frac{389}{522}\right)$	$e\left(\frac{112}{261}\right)$	$e\left(\frac{265}{522}\right)$	$e\left(\frac{28}{261}\right)$
$\chi_{8732}(1159,\cdot)$	$1$	$1$	$e\left(\frac{179}{522}\right)$	$e\left(\frac{241}{261}\right)$	$e\left(\frac{257}{522}\right)$	$e\left(\frac{179}{261}\right)$	$e\left(\frac{56}{87}\right)$	$e\left(\frac{425}{522}\right)$	$e\left(\frac{139}{522}\right)$	$e\left(\frac{89}{261}\right)$	$e\left(\frac{143}{522}\right)$	$e\left(\frac{218}{261}\right)$
$\chi_{8732}(1163,\cdot)$	$1$	$1$	$e\left(\frac{455}{522}\right)$	$e\left(\frac{181}{261}\right)$	$e\left(\frac{245}{522}\right)$	$e\left(\frac{194}{261}\right)$	$e\left(\frac{50}{87}\right)$	$e\left(\frac{395}{522}\right)$	$e\left(\frac{295}{522}\right)$	$e\left(\frac{95}{261}\right)$	$e\left(\frac{311}{522}\right)$	$e\left(\frac{89}{261}\right)$
$\chi_{8732}(1191,\cdot)$	$1$	$1$	$e\left(\frac{85}{522}\right)$	$e\left(\frac{8}{261}\right)$	$e\left(\frac{367}{522}\right)$	$e\left(\frac{85}{261}\right)$	$e\left(\frac{82}{87}\right)$	$e\left(\frac{91}{522}\right)$	$e\left(\frac{101}{522}\right)$	$e\left(\frac{121}{261}\right)$	$e\left(\frac{517}{522}\right)$	$e\left(\frac{226}{261}\right)$
$\chi_{8732}(1291,\cdot)$	$1$	$1$	$e\left(\frac{241}{522}\right)$	$e\left(\frac{167}{261}\right)$	$e\left(\frac{451}{522}\right)$	$e\left(\frac{241}{261}\right)$	$e\left(\frac{37}{87}\right)$	$e\left(\frac{301}{522}\right)$	$e\left(\frac{53}{522}\right)$	$e\left(\frac{79}{261}\right)$	$e\left(\frac{385}{522}\right)$	$e\left(\frac{85}{261}\right)$
$\chi_{8732}(1311,\cdot)$	$1$	$1$	$e\left(\frac{95}{522}\right)$	$e\left(\frac{55}{261}\right)$	$e\left(\frac{11}{522}\right)$	$e\left(\frac{95}{261}\right)$	$e\left(\frac{20}{87}\right)$	$e\left(\frac{71}{522}\right)$	$e\left(\frac{205}{522}\right)$	$e\left(\frac{212}{261}\right)$	$e\left(\frac{455}{522}\right)$	$e\left(\frac{53}{261}\right)$
$\chi_{8732}(1439,\cdot)$	$1$	$1$	$e\left(\frac{457}{522}\right)$	$e\left(\frac{86}{261}\right)$	$e\left(\frac{487}{522}\right)$	$e\left(\frac{196}{261}\right)$	$e\left(\frac{55}{87}\right)$	$e\left(\frac{391}{522}\right)$	$e\left(\frac{107}{522}\right)$	$e\left(\frac{61}{261}\right)$	$e\left(\frac{403}{522}\right)$	$e\left(\frac{211}{261}\right)$
$\chi_{8732}(1455,\cdot)$	$1$	$1$	$e\left(\frac{323}{522}\right)$	$e\left(\frac{187}{261}\right)$	$e\left(\frac{455}{522}\right)$	$e\left(\frac{62}{261}\right)$	$e\left(\frac{68}{87}\right)$	$e\left(\frac{137}{522}\right)$	$e\left(\frac{175}{522}\right)$	$e\left(\frac{251}{261}\right)$	$e\left(\frac{503}{522}\right)$	$e\left(\frac{128}{261}\right)$
$\chi_{8732}(1459,\cdot)$	$1$	$1$	$e\left(\frac{437}{522}\right)$	$e\left(\frac{253}{261}\right)$	$e\left(\frac{155}{522}\right)$	$e\left(\frac{176}{261}\right)$	$e\left(\frac{5}{87}\right)$	$e\left(\frac{431}{522}\right)$	$e\left(\frac{421}{522}\right)$	$e\left(\frac{140}{261}\right)$	$e\left(\frac{5}{522}\right)$	$e\left(\frac{35}{261}\right)$

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	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(13\)	\(15\)	\(17\)	\(19\)	\(21\)
\(\chi_{8732}(83,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{389}{522}\right)\)	\(e\left(\frac{184}{261}\right)\)	\(e\left(\frac{89}{522}\right)\)	\(e\left(\frac{128}{261}\right)\)	\(e\left(\frac{59}{87}\right)\)	\(e\left(\frac{5}{522}\right)\)	\(e\left(\frac{235}{522}\right)\)	\(e\left(\frac{173}{261}\right)\)	\(e\left(\frac{407}{522}\right)\)	\(e\left(\frac{239}{261}\right)\)
\(\chi_{8732}(155,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{522}\right)\)	\(e\left(\frac{35}{261}\right)\)	\(e\left(\frac{7}{522}\right)\)	\(e\left(\frac{13}{261}\right)\)	\(e\left(\frac{76}{87}\right)\)	\(e\left(\frac{235}{522}\right)\)	\(e\left(\frac{83}{522}\right)\)	\(e\left(\frac{40}{261}\right)\)	\(e\left(\frac{337}{522}\right)\)	\(e\left(\frac{10}{261}\right)\)
\(\chi_{8732}(219,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{397}{522}\right)\)	\(e\left(\frac{65}{261}\right)\)	\(e\left(\frac{13}{522}\right)\)	\(e\left(\frac{136}{261}\right)\)	\(e\left(\frac{79}{87}\right)\)	\(e\left(\frac{511}{522}\right)\)	\(e\left(\frac{5}{522}\right)\)	\(e\left(\frac{37}{261}\right)\)	\(e\left(\frac{253}{522}\right)\)	\(e\left(\frac{205}{261}\right)\)
\(\chi_{8732}(231,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{522}\right)\)	\(e\left(\frac{220}{261}\right)\)	\(e\left(\frac{305}{522}\right)\)	\(e\left(\frac{119}{261}\right)\)	\(e\left(\frac{80}{87}\right)\)	\(e\left(\frac{23}{522}\right)\)	\(e\left(\frac{37}{522}\right)\)	\(e\left(\frac{65}{261}\right)\)	\(e\left(\frac{515}{522}\right)\)	\(e\left(\frac{212}{261}\right)\)
\(\chi_{8732}(275,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{522}\right)\)	\(e\left(\frac{100}{261}\right)\)	\(e\left(\frac{281}{522}\right)\)	\(e\left(\frac{149}{261}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{485}{522}\right)\)	\(e\left(\frac{349}{522}\right)\)	\(e\left(\frac{77}{261}\right)\)	\(e\left(\frac{329}{522}\right)\)	\(e\left(\frac{215}{261}\right)\)
\(\chi_{8732}(303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{522}\right)\)	\(e\left(\frac{197}{261}\right)\)	\(e\left(\frac{457}{522}\right)\)	\(e\left(\frac{103}{261}\right)\)	\(e\left(\frac{40}{87}\right)\)	\(e\left(\frac{55}{522}\right)\)	\(e\left(\frac{497}{522}\right)\)	\(e\left(\frac{76}{261}\right)\)	\(e\left(\frac{301}{522}\right)\)	\(e\left(\frac{19}{261}\right)\)
\(\chi_{8732}(367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{522}\right)\)	\(e\left(\frac{200}{261}\right)\)	\(e\left(\frac{301}{522}\right)\)	\(e\left(\frac{37}{261}\right)\)	\(e\left(\frac{49}{87}\right)\)	\(e\left(\frac{187}{522}\right)\)	\(e\left(\frac{437}{522}\right)\)	\(e\left(\frac{154}{261}\right)\)	\(e\left(\frac{397}{522}\right)\)	\(e\left(\frac{169}{261}\right)\)
\(\chi_{8732}(419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{359}{522}\right)\)	\(e\left(\frac{43}{261}\right)\)	\(e\left(\frac{113}{522}\right)\)	\(e\left(\frac{98}{261}\right)\)	\(e\left(\frac{71}{87}\right)\)	\(e\left(\frac{65}{522}\right)\)	\(e\left(\frac{445}{522}\right)\)	\(e\left(\frac{161}{261}\right)\)	\(e\left(\frac{71}{522}\right)\)	\(e\left(\frac{236}{261}\right)\)
\(\chi_{8732}(423,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{221}{522}\right)\)	\(e\left(\frac{73}{261}\right)\)	\(e\left(\frac{119}{522}\right)\)	\(e\left(\frac{221}{261}\right)\)	\(e\left(\frac{74}{87}\right)\)	\(e\left(\frac{341}{522}\right)\)	\(e\left(\frac{367}{522}\right)\)	\(e\left(\frac{158}{261}\right)\)	\(e\left(\frac{509}{522}\right)\)	\(e\left(\frac{170}{261}\right)\)
\(\chi_{8732}(451,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{522}\right)\)	\(e\left(\frac{125}{261}\right)\)	\(e\left(\frac{25}{522}\right)\)	\(e\left(\frac{121}{261}\right)\)	\(e\left(\frac{85}{87}\right)\)	\(e\left(\frac{19}{522}\right)\)	\(e\left(\frac{371}{522}\right)\)	\(e\left(\frac{31}{261}\right)\)	\(e\left(\frac{85}{522}\right)\)	\(e\left(\frac{73}{261}\right)\)
\(\chi_{8732}(515,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{379}{522}\right)\)	\(e\left(\frac{137}{261}\right)\)	\(e\left(\frac{445}{522}\right)\)	\(e\left(\frac{118}{261}\right)\)	\(e\left(\frac{34}{87}\right)\)	\(e\left(\frac{25}{522}\right)\)	\(e\left(\frac{131}{522}\right)\)	\(e\left(\frac{82}{261}\right)\)	\(e\left(\frac{469}{522}\right)\)	\(e\left(\frac{151}{261}\right)\)
\(\chi_{8732}(527,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{407}{522}\right)\)	\(e\left(\frac{112}{261}\right)\)	\(e\left(\frac{179}{522}\right)\)	\(e\left(\frac{146}{261}\right)\)	\(e\left(\frac{17}{87}\right)\)	\(e\left(\frac{491}{522}\right)\)	\(e\left(\frac{109}{522}\right)\)	\(e\left(\frac{128}{261}\right)\)	\(e\left(\frac{191}{522}\right)\)	\(e\left(\frac{32}{261}\right)\)
\(\chi_{8732}(571,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{522}\right)\)	\(e\left(\frac{127}{261}\right)\)	\(e\left(\frac{443}{522}\right)\)	\(e\left(\frac{77}{261}\right)\)	\(e\left(\frac{62}{87}\right)\)	\(e\left(\frac{107}{522}\right)\)	\(e\left(\frac{331}{522}\right)\)	\(e\left(\frac{257}{261}\right)\)	\(e\left(\frac{149}{522}\right)\)	\(e\left(\frac{260}{261}\right)\)
\(\chi_{8732}(663,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{343}{522}\right)\)	\(e\left(\frac{20}{261}\right)\)	\(e\left(\frac{265}{522}\right)\)	\(e\left(\frac{82}{261}\right)\)	\(e\left(\frac{31}{87}\right)\)	\(e\left(\frac{97}{522}\right)\)	\(e\left(\frac{383}{522}\right)\)	\(e\left(\frac{172}{261}\right)\)	\(e\left(\frac{379}{522}\right)\)	\(e\left(\frac{43}{261}\right)\)
\(\chi_{8732}(699,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{522}\right)\)	\(e\left(\frac{32}{261}\right)\)	\(e\left(\frac{163}{522}\right)\)	\(e\left(\frac{79}{261}\right)\)	\(e\left(\frac{67}{87}\right)\)	\(e\left(\frac{103}{522}\right)\)	\(e\left(\frac{143}{522}\right)\)	\(e\left(\frac{223}{261}\right)\)	\(e\left(\frac{241}{522}\right)\)	\(e\left(\frac{121}{261}\right)\)
\(\chi_{8732}(719,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{491}{522}\right)\)	\(e\left(\frac{37}{261}\right)\)	\(e\left(\frac{425}{522}\right)\)	\(e\left(\frac{230}{261}\right)\)	\(e\left(\frac{53}{87}\right)\)	\(e\left(\frac{323}{522}\right)\)	\(e\left(\frac{43}{522}\right)\)	\(e\left(\frac{5}{261}\right)\)	\(e\left(\frac{401}{522}\right)\)	\(e\left(\frac{197}{261}\right)\)
\(\chi_{8732}(747,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{265}{522}\right)\)	\(e\left(\frac{71}{261}\right)\)	\(e\left(\frac{223}{522}\right)\)	\(e\left(\frac{4}{261}\right)\)	\(e\left(\frac{10}{87}\right)\)	\(e\left(\frac{253}{522}\right)\)	\(e\left(\frac{407}{522}\right)\)	\(e\left(\frac{193}{261}\right)\)	\(e\left(\frac{445}{522}\right)\)	\(e\left(\frac{244}{261}\right)\)
\(\chi_{8732}(811,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{289}{522}\right)\)	\(e\left(\frac{236}{261}\right)\)	\(e\left(\frac{517}{522}\right)\)	\(e\left(\frac{28}{261}\right)\)	\(e\left(\frac{70}{87}\right)\)	\(e\left(\frac{205}{522}\right)\)	\(e\left(\frac{239}{522}\right)\)	\(e\left(\frac{46}{261}\right)\)	\(e\left(\frac{505}{522}\right)\)	\(e\left(\frac{142}{261}\right)\)
\(\chi_{8732}(823,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{522}\right)\)	\(e\left(\frac{103}{261}\right)\)	\(e\left(\frac{125}{522}\right)\)	\(e\left(\frac{83}{261}\right)\)	\(e\left(\frac{77}{87}\right)\)	\(e\left(\frac{95}{522}\right)\)	\(e\left(\frac{289}{522}\right)\)	\(e\left(\frac{155}{261}\right)\)	\(e\left(\frac{425}{522}\right)\)	\(e\left(\frac{104}{261}\right)\)
\(\chi_{8732}(863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{522}\right)\)	\(e\left(\frac{151}{261}\right)\)	\(e\left(\frac{239}{522}\right)\)	\(e\left(\frac{71}{261}\right)\)	\(e\left(\frac{47}{87}\right)\)	\(e\left(\frac{119}{522}\right)\)	\(e\left(\frac{373}{522}\right)\)	\(e\left(\frac{98}{261}\right)\)	\(e\left(\frac{395}{522}\right)\)	\(e\left(\frac{155}{261}\right)\)
\(\chi_{8732}(895,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{337}{522}\right)\)	\(e\left(\frac{44}{261}\right)\)	\(e\left(\frac{61}{522}\right)\)	\(e\left(\frac{76}{261}\right)\)	\(e\left(\frac{16}{87}\right)\)	\(e\left(\frac{109}{522}\right)\)	\(e\left(\frac{425}{522}\right)\)	\(e\left(\frac{13}{261}\right)\)	\(e\left(\frac{103}{522}\right)\)	\(e\left(\frac{199}{261}\right)\)
\(\chi_{8732}(1011,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{522}\right)\)	\(e\left(\frac{52}{261}\right)\)	\(e\left(\frac{167}{522}\right)\)	\(e\left(\frac{161}{261}\right)\)	\(e\left(\frac{11}{87}\right)\)	\(e\left(\frac{461}{522}\right)\)	\(e\left(\frac{265}{522}\right)\)	\(e\left(\frac{134}{261}\right)\)	\(e\left(\frac{359}{522}\right)\)	\(e\left(\frac{164}{261}\right)\)
\(\chi_{8732}(1043,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{193}{522}\right)\)	\(e\left(\frac{98}{261}\right)\)	\(e\left(\frac{385}{522}\right)\)	\(e\left(\frac{193}{261}\right)\)	\(e\left(\frac{4}{87}\right)\)	\(e\left(\frac{397}{522}\right)\)	\(e\left(\frac{389}{522}\right)\)	\(e\left(\frac{112}{261}\right)\)	\(e\left(\frac{265}{522}\right)\)	\(e\left(\frac{28}{261}\right)\)
\(\chi_{8732}(1159,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{179}{522}\right)\)	\(e\left(\frac{241}{261}\right)\)	\(e\left(\frac{257}{522}\right)\)	\(e\left(\frac{179}{261}\right)\)	\(e\left(\frac{56}{87}\right)\)	\(e\left(\frac{425}{522}\right)\)	\(e\left(\frac{139}{522}\right)\)	\(e\left(\frac{89}{261}\right)\)	\(e\left(\frac{143}{522}\right)\)	\(e\left(\frac{218}{261}\right)\)
\(\chi_{8732}(1163,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{455}{522}\right)\)	\(e\left(\frac{181}{261}\right)\)	\(e\left(\frac{245}{522}\right)\)	\(e\left(\frac{194}{261}\right)\)	\(e\left(\frac{50}{87}\right)\)	\(e\left(\frac{395}{522}\right)\)	\(e\left(\frac{295}{522}\right)\)	\(e\left(\frac{95}{261}\right)\)	\(e\left(\frac{311}{522}\right)\)	\(e\left(\frac{89}{261}\right)\)
\(\chi_{8732}(1191,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{522}\right)\)	\(e\left(\frac{8}{261}\right)\)	\(e\left(\frac{367}{522}\right)\)	\(e\left(\frac{85}{261}\right)\)	\(e\left(\frac{82}{87}\right)\)	\(e\left(\frac{91}{522}\right)\)	\(e\left(\frac{101}{522}\right)\)	\(e\left(\frac{121}{261}\right)\)	\(e\left(\frac{517}{522}\right)\)	\(e\left(\frac{226}{261}\right)\)
\(\chi_{8732}(1291,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{241}{522}\right)\)	\(e\left(\frac{167}{261}\right)\)	\(e\left(\frac{451}{522}\right)\)	\(e\left(\frac{241}{261}\right)\)	\(e\left(\frac{37}{87}\right)\)	\(e\left(\frac{301}{522}\right)\)	\(e\left(\frac{53}{522}\right)\)	\(e\left(\frac{79}{261}\right)\)	\(e\left(\frac{385}{522}\right)\)	\(e\left(\frac{85}{261}\right)\)
\(\chi_{8732}(1311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{522}\right)\)	\(e\left(\frac{55}{261}\right)\)	\(e\left(\frac{11}{522}\right)\)	\(e\left(\frac{95}{261}\right)\)	\(e\left(\frac{20}{87}\right)\)	\(e\left(\frac{71}{522}\right)\)	\(e\left(\frac{205}{522}\right)\)	\(e\left(\frac{212}{261}\right)\)	\(e\left(\frac{455}{522}\right)\)	\(e\left(\frac{53}{261}\right)\)
\(\chi_{8732}(1439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{457}{522}\right)\)	\(e\left(\frac{86}{261}\right)\)	\(e\left(\frac{487}{522}\right)\)	\(e\left(\frac{196}{261}\right)\)	\(e\left(\frac{55}{87}\right)\)	\(e\left(\frac{391}{522}\right)\)	\(e\left(\frac{107}{522}\right)\)	\(e\left(\frac{61}{261}\right)\)	\(e\left(\frac{403}{522}\right)\)	\(e\left(\frac{211}{261}\right)\)
\(\chi_{8732}(1455,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{323}{522}\right)\)	\(e\left(\frac{187}{261}\right)\)	\(e\left(\frac{455}{522}\right)\)	\(e\left(\frac{62}{261}\right)\)	\(e\left(\frac{68}{87}\right)\)	\(e\left(\frac{137}{522}\right)\)	\(e\left(\frac{175}{522}\right)\)	\(e\left(\frac{251}{261}\right)\)	\(e\left(\frac{503}{522}\right)\)	\(e\left(\frac{128}{261}\right)\)
\(\chi_{8732}(1459,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{437}{522}\right)\)	\(e\left(\frac{253}{261}\right)\)	\(e\left(\frac{155}{522}\right)\)	\(e\left(\frac{176}{261}\right)\)	\(e\left(\frac{5}{87}\right)\)	\(e\left(\frac{431}{522}\right)\)	\(e\left(\frac{421}{522}\right)\)	\(e\left(\frac{140}{261}\right)\)	\(e\left(\frac{5}{522}\right)\)	\(e\left(\frac{35}{261}\right)\)

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First 31 of 168 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	8732.cp
Modulus	$8732$
Conductor	$8732$
Order	$522$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(8732\)
Conductor:	\(8732\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(522\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)