LMFDB - Dirichlet character orbit 1089.bc

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1089, base_ring=CyclotomicField(330)) M = H._module chi = DirichletCharacter(H, M([110,6])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(4,1089)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1089$
Conductor:	$1089$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$165$	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:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 165 polynomial (not computed)

First 31 of 80 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{1089}(4,\cdot)$	$1$	$1$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{1089}(16,\cdot)$	$1$	$1$	$e\left(\frac{116}{165}\right)$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{43}{55}\right)$
$\chi_{1089}(25,\cdot)$	$1$	$1$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{2}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{51}{55}\right)$
$\chi_{1089}(31,\cdot)$	$1$	$1$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{1089}(49,\cdot)$	$1$	$1$	$e\left(\frac{76}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{1089}(58,\cdot)$	$1$	$1$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{128}{165}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{1}{55}\right)$
$\chi_{1089}(70,\cdot)$	$1$	$1$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{136}{165}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{29}{55}\right)$
$\chi_{1089}(97,\cdot)$	$1$	$1$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{158}{165}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{2}{55}\right)$
$\chi_{1089}(103,\cdot)$	$1$	$1$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{18}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{127}{165}\right)$	$e\left(\frac{19}{55}\right)$
$\chi_{1089}(115,\cdot)$	$1$	$1$	$e\left(\frac{161}{165}\right)$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{34}{165}\right)$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{91}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{8}{55}\right)$
$\chi_{1089}(157,\cdot)$	$1$	$1$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{17}{165}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{16}{55}\right)$
$\chi_{1089}(169,\cdot)$	$1$	$1$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{37}{165}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{54}{55}\right)$
$\chi_{1089}(196,\cdot)$	$1$	$1$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{24}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{7}{55}\right)$
$\chi_{1089}(214,\cdot)$	$1$	$1$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{64}{165}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{41}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{16}{165}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{28}{55}\right)$
$\chi_{1089}(223,\cdot)$	$1$	$1$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{26}{55}\right)$
$\chi_{1089}(229,\cdot)$	$1$	$1$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{43}{165}\right)$	$e\left(\frac{14}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{149}{165}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{27}{55}\right)$
$\chi_{1089}(247,\cdot)$	$1$	$1$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{1}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{101}{165}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{53}{55}\right)$
$\chi_{1089}(256,\cdot)$	$1$	$1$	$e\left(\frac{67}{165}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{139}{165}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{2}{165}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{31}{55}\right)$
$\chi_{1089}(268,\cdot)$	$1$	$1$	$e\left(\frac{98}{165}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{26}{165}\right)$	$e\left(\frac{43}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{24}{55}\right)$
$\chi_{1089}(295,\cdot)$	$1$	$1$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{43}{165}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{68}{165}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{12}{55}\right)$
$\chi_{1089}(301,\cdot)$	$1$	$1$	$e\left(\frac{103}{165}\right)$	$e\left(\frac{41}{165}\right)$	$e\left(\frac{32}{165}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{9}{11}\right)$	$e\left(\frac{8}{165}\right)$	$e\left(\frac{164}{165}\right)$	$e\left(\frac{82}{165}\right)$	$e\left(\frac{14}{55}\right)$
$\chi_{1089}(313,\cdot)$	$1$	$1$	$e\left(\frac{86}{165}\right)$	$e\left(\frac{7}{165}\right)$	$e\left(\frac{94}{165}\right)$	$e\left(\frac{107}{165}\right)$	$e\left(\frac{31}{55}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{14}{165}\right)$	$e\left(\frac{48}{55}\right)$
$\chi_{1089}(322,\cdot)$	$1$	$1$	$e\left(\frac{62}{165}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{133}{165}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{2}{11}\right)$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{83}{165}\right)$	$e\left(\frac{41}{55}\right)$
$\chi_{1089}(328,\cdot)$	$1$	$1$	$e\left(\frac{94}{165}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{26}{165}\right)$	$e\left(\frac{163}{165}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{89}{165}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{32}{55}\right)$
$\chi_{1089}(346,\cdot)$	$1$	$1$	$e\left(\frac{46}{165}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{104}{165}\right)$	$e\left(\frac{157}{165}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{26}{165}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{19}{165}\right)$	$e\left(\frac{18}{55}\right)$
$\chi_{1089}(355,\cdot)$	$1$	$1$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{4}{165}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{146}{165}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{46}{55}\right)$
$\chi_{1089}(367,\cdot)$	$1$	$1$	$e\left(\frac{113}{165}\right)$	$e\left(\frac{61}{165}\right)$	$e\left(\frac{112}{165}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{3}{55}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{28}{165}\right)$	$e\left(\frac{79}{165}\right)$	$e\left(\frac{122}{165}\right)$	$e\left(\frac{49}{55}\right)$
$\chi_{1089}(394,\cdot)$	$1$	$1$	$e\left(\frac{74}{165}\right)$	$e\left(\frac{148}{165}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{23}{165}\right)$	$e\left(\frac{19}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{49}{165}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{17}{55}\right)$
$\chi_{1089}(400,\cdot)$	$1$	$1$	$e\left(\frac{118}{165}\right)$	$e\left(\frac{71}{165}\right)$	$e\left(\frac{152}{165}\right)$	$e\left(\frac{1}{165}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{38}{165}\right)$	$e\left(\frac{119}{165}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{39}{55}\right)$
$\chi_{1089}(412,\cdot)$	$1$	$1$	$e\left(\frac{131}{165}\right)$	$e\left(\frac{97}{165}\right)$	$e\left(\frac{124}{165}\right)$	$e\left(\frac{92}{165}\right)$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{6}{11}\right)$	$e\left(\frac{31}{165}\right)$	$e\left(\frac{58}{165}\right)$	$e\left(\frac{29}{165}\right)$	$e\left(\frac{13}{55}\right)$
$\chi_{1089}(421,\cdot)$	$1$	$1$	$e\left(\frac{137}{165}\right)$	$e\left(\frac{109}{165}\right)$	$e\left(\frac{73}{165}\right)$	$e\left(\frac{134}{165}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{142}{165}\right)$	$e\left(\frac{106}{165}\right)$	$e\left(\frac{53}{165}\right)$	$e\left(\frac{1}{55}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(13\)	\(14\)	\(16\)	\(17\)
\(\chi_{1089}(4,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{1089}(16,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{116}{165}\right)\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{6}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{43}{55}\right)\)
\(\chi_{1089}(25,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{2}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{51}{55}\right)\)
\(\chi_{1089}(31,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{1089}(49,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{76}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{1089}(58,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{128}{165}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{1}{55}\right)\)
\(\chi_{1089}(70,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{136}{165}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{13}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{29}{55}\right)\)
\(\chi_{1089}(97,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{158}{165}\right)\)	\(e\left(\frac{54}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{2}{55}\right)\)
\(\chi_{1089}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{18}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{127}{165}\right)\)	\(e\left(\frac{19}{55}\right)\)
\(\chi_{1089}(115,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{165}\right)\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{34}{165}\right)\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{51}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{91}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{8}{55}\right)\)
\(\chi_{1089}(157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{47}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{17}{165}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{16}{55}\right)\)
\(\chi_{1089}(169,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{37}{165}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{28}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{54}{55}\right)\)
\(\chi_{1089}(196,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{24}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{7}{55}\right)\)
\(\chi_{1089}(214,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{64}{165}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{41}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{28}{55}\right)\)
\(\chi_{1089}(223,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{42}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{26}{55}\right)\)
\(\chi_{1089}(229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{43}{165}\right)\)	\(e\left(\frac{14}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{149}{165}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{27}{55}\right)\)
\(\chi_{1089}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{1}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{101}{165}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{53}{55}\right)\)
\(\chi_{1089}(256,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{165}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{139}{165}\right)\)	\(e\left(\frac{12}{55}\right)\)	\(e\left(\frac{5}{11}\right)\)	\(e\left(\frac{2}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{31}{55}\right)\)
\(\chi_{1089}(268,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{98}{165}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{26}{165}\right)\)	\(e\left(\frac{43}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{24}{55}\right)\)
\(\chi_{1089}(295,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{43}{165}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{68}{165}\right)\)	\(e\left(\frac{49}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{12}{55}\right)\)
\(\chi_{1089}(301,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{165}\right)\)	\(e\left(\frac{41}{165}\right)\)	\(e\left(\frac{32}{165}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{48}{55}\right)\)	\(e\left(\frac{9}{11}\right)\)	\(e\left(\frac{8}{165}\right)\)	\(e\left(\frac{164}{165}\right)\)	\(e\left(\frac{82}{165}\right)\)	\(e\left(\frac{14}{55}\right)\)
\(\chi_{1089}(313,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{86}{165}\right)\)	\(e\left(\frac{7}{165}\right)\)	\(e\left(\frac{94}{165}\right)\)	\(e\left(\frac{107}{165}\right)\)	\(e\left(\frac{31}{55}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{14}{165}\right)\)	\(e\left(\frac{48}{55}\right)\)
\(\chi_{1089}(322,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{62}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{133}{165}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{7}{55}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{83}{165}\right)\)	\(e\left(\frac{41}{55}\right)\)
\(\chi_{1089}(328,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{94}{165}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{26}{165}\right)\)	\(e\left(\frac{163}{165}\right)\)	\(e\left(\frac{39}{55}\right)\)	\(e\left(\frac{8}{11}\right)\)	\(e\left(\frac{89}{165}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{32}{55}\right)\)
\(\chi_{1089}(346,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{46}{165}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{104}{165}\right)\)	\(e\left(\frac{157}{165}\right)\)	\(e\left(\frac{46}{55}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{26}{165}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{19}{165}\right)\)	\(e\left(\frac{18}{55}\right)\)
\(\chi_{1089}(355,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{4}{165}\right)\)	\(e\left(\frac{32}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{146}{165}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{46}{55}\right)\)
\(\chi_{1089}(367,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{61}{165}\right)\)	\(e\left(\frac{112}{165}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{3}{55}\right)\)	\(e\left(\frac{4}{11}\right)\)	\(e\left(\frac{28}{165}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{122}{165}\right)\)	\(e\left(\frac{49}{55}\right)\)
\(\chi_{1089}(394,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{74}{165}\right)\)	\(e\left(\frac{148}{165}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{23}{165}\right)\)	\(e\left(\frac{19}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{49}{165}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{17}{55}\right)\)
\(\chi_{1089}(400,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{118}{165}\right)\)	\(e\left(\frac{71}{165}\right)\)	\(e\left(\frac{152}{165}\right)\)	\(e\left(\frac{1}{165}\right)\)	\(e\left(\frac{8}{55}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{38}{165}\right)\)	\(e\left(\frac{119}{165}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{39}{55}\right)\)
\(\chi_{1089}(412,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{165}\right)\)	\(e\left(\frac{97}{165}\right)\)	\(e\left(\frac{124}{165}\right)\)	\(e\left(\frac{92}{165}\right)\)	\(e\left(\frac{21}{55}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{58}{165}\right)\)	\(e\left(\frac{29}{165}\right)\)	\(e\left(\frac{13}{55}\right)\)
\(\chi_{1089}(421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{165}\right)\)	\(e\left(\frac{109}{165}\right)\)	\(e\left(\frac{73}{165}\right)\)	\(e\left(\frac{134}{165}\right)\)	\(e\left(\frac{27}{55}\right)\)	\(e\left(\frac{3}{11}\right)\)	\(e\left(\frac{142}{165}\right)\)	\(e\left(\frac{106}{165}\right)\)	\(e\left(\frac{53}{165}\right)\)	\(e\left(\frac{1}{55}\right)\)

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First 31 of 80 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	1089.bc
Modulus	$1089$
Conductor	$1089$
Order	$165$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(1089\)
Conductor:	\(1089\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(165\)	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)