LMFDB - Dirichlet character orbit 243.j

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(243, base_ring=CyclotomicField(162)) M = H._module chi = DirichletCharacter(H, M([1])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(2,243)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$243$
Conductor:	$243$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$162$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{81})$
Fixed field:	Number field defined by a degree 162 polynomial (not computed)

First 31 of 54 characters in Galois orbit

Character	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{243}(2,\cdot)$	$-1$	$1$	$e\left(\frac{1}{162}\right)$	$e\left(\frac{1}{81}\right)$	$e\left(\frac{23}{162}\right)$	$e\left(\frac{35}{81}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{121}{162}\right)$	$e\left(\frac{4}{81}\right)$	$e\left(\frac{71}{162}\right)$	$e\left(\frac{2}{81}\right)$
$\chi_{243}(5,\cdot)$	$-1$	$1$	$e\left(\frac{23}{162}\right)$	$e\left(\frac{23}{81}\right)$	$e\left(\frac{43}{162}\right)$	$e\left(\frac{76}{81}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{29}{162}\right)$	$e\left(\frac{11}{81}\right)$	$e\left(\frac{13}{162}\right)$	$e\left(\frac{46}{81}\right)$
$\chi_{243}(11,\cdot)$	$-1$	$1$	$e\left(\frac{121}{162}\right)$	$e\left(\frac{40}{81}\right)$	$e\left(\frac{29}{162}\right)$	$e\left(\frac{23}{81}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{61}{162}\right)$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{5}{162}\right)$	$e\left(\frac{80}{81}\right)$
$\chi_{243}(14,\cdot)$	$-1$	$1$	$e\left(\frac{71}{162}\right)$	$e\left(\frac{71}{81}\right)$	$e\left(\frac{13}{162}\right)$	$e\left(\frac{55}{81}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{5}{162}\right)$	$e\left(\frac{41}{81}\right)$	$e\left(\frac{19}{162}\right)$	$e\left(\frac{61}{81}\right)$
$\chi_{243}(20,\cdot)$	$-1$	$1$	$e\left(\frac{25}{162}\right)$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{89}{162}\right)$	$e\left(\frac{65}{81}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{109}{162}\right)$	$e\left(\frac{19}{81}\right)$	$e\left(\frac{155}{162}\right)$	$e\left(\frac{50}{81}\right)$
$\chi_{243}(23,\cdot)$	$-1$	$1$	$e\left(\frac{65}{162}\right)$	$e\left(\frac{65}{81}\right)$	$e\left(\frac{37}{162}\right)$	$e\left(\frac{7}{81}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{89}{162}\right)$	$e\left(\frac{17}{81}\right)$	$e\left(\frac{79}{162}\right)$	$e\left(\frac{49}{81}\right)$
$\chi_{243}(29,\cdot)$	$-1$	$1$	$e\left(\frac{37}{162}\right)$	$e\left(\frac{37}{81}\right)$	$e\left(\frac{41}{162}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{103}{162}\right)$	$e\left(\frac{67}{81}\right)$	$e\left(\frac{35}{162}\right)$	$e\left(\frac{74}{81}\right)$
$\chi_{243}(32,\cdot)$	$-1$	$1$	$e\left(\frac{5}{162}\right)$	$e\left(\frac{5}{81}\right)$	$e\left(\frac{115}{162}\right)$	$e\left(\frac{13}{81}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{119}{162}\right)$	$e\left(\frac{20}{81}\right)$	$e\left(\frac{31}{162}\right)$	$e\left(\frac{10}{81}\right)$
$\chi_{243}(38,\cdot)$	$-1$	$1$	$e\left(\frac{157}{162}\right)$	$e\left(\frac{76}{81}\right)$	$e\left(\frac{47}{162}\right)$	$e\left(\frac{68}{81}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{43}{162}\right)$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{131}{162}\right)$	$e\left(\frac{71}{81}\right)$
$\chi_{243}(41,\cdot)$	$-1$	$1$	$e\left(\frac{53}{162}\right)$	$e\left(\frac{53}{81}\right)$	$e\left(\frac{85}{162}\right)$	$e\left(\frac{73}{81}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{95}{162}\right)$	$e\left(\frac{50}{81}\right)$	$e\left(\frac{37}{162}\right)$	$e\left(\frac{25}{81}\right)$
$\chi_{243}(47,\cdot)$	$-1$	$1$	$e\left(\frac{61}{162}\right)$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{107}{162}\right)$	$e\left(\frac{29}{81}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{91}{162}\right)$	$e\left(\frac{1}{81}\right)$	$e\left(\frac{119}{162}\right)$	$e\left(\frac{41}{81}\right)$
$\chi_{243}(50,\cdot)$	$-1$	$1$	$e\left(\frac{47}{162}\right)$	$e\left(\frac{47}{81}\right)$	$e\left(\frac{109}{162}\right)$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{17}{162}\right)$	$e\left(\frac{26}{81}\right)$	$e\left(\frac{97}{162}\right)$	$e\left(\frac{13}{81}\right)$
$\chi_{243}(56,\cdot)$	$-1$	$1$	$e\left(\frac{73}{162}\right)$	$e\left(\frac{73}{81}\right)$	$e\left(\frac{59}{162}\right)$	$e\left(\frac{44}{81}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{85}{162}\right)$	$e\left(\frac{49}{81}\right)$	$e\left(\frac{161}{162}\right)$	$e\left(\frac{65}{81}\right)$
$\chi_{243}(59,\cdot)$	$-1$	$1$	$e\left(\frac{149}{162}\right)$	$e\left(\frac{68}{81}\right)$	$e\left(\frac{25}{162}\right)$	$e\left(\frac{31}{81}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{47}{162}\right)$	$e\left(\frac{29}{81}\right)$	$e\left(\frac{49}{162}\right)$	$e\left(\frac{55}{81}\right)$
$\chi_{243}(65,\cdot)$	$-1$	$1$	$e\left(\frac{31}{162}\right)$	$e\left(\frac{31}{81}\right)$	$e\left(\frac{65}{162}\right)$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{25}{162}\right)$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{95}{162}\right)$	$e\left(\frac{62}{81}\right)$
$\chi_{243}(68,\cdot)$	$-1$	$1$	$e\left(\frac{35}{162}\right)$	$e\left(\frac{35}{81}\right)$	$e\left(\frac{157}{162}\right)$	$e\left(\frac{10}{81}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{23}{162}\right)$	$e\left(\frac{59}{81}\right)$	$e\left(\frac{55}{162}\right)$	$e\left(\frac{70}{81}\right)$
$\chi_{243}(74,\cdot)$	$-1$	$1$	$e\left(\frac{97}{162}\right)$	$e\left(\frac{16}{81}\right)$	$e\left(\frac{125}{162}\right)$	$e\left(\frac{74}{81}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{73}{162}\right)$	$e\left(\frac{64}{81}\right)$	$e\left(\frac{83}{162}\right)$	$e\left(\frac{32}{81}\right)$
$\chi_{243}(77,\cdot)$	$-1$	$1$	$e\left(\frac{29}{162}\right)$	$e\left(\frac{29}{81}\right)$	$e\left(\frac{19}{162}\right)$	$e\left(\frac{43}{81}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{107}{162}\right)$	$e\left(\frac{35}{81}\right)$	$e\left(\frac{115}{162}\right)$	$e\left(\frac{58}{81}\right)$
$\chi_{243}(83,\cdot)$	$-1$	$1$	$e\left(\frac{109}{162}\right)$	$e\left(\frac{28}{81}\right)$	$e\left(\frac{77}{162}\right)$	$e\left(\frac{8}{81}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{67}{162}\right)$	$e\left(\frac{31}{81}\right)$	$e\left(\frac{125}{162}\right)$	$e\left(\frac{56}{81}\right)$
$\chi_{243}(86,\cdot)$	$-1$	$1$	$e\left(\frac{131}{162}\right)$	$e\left(\frac{50}{81}\right)$	$e\left(\frac{97}{162}\right)$	$e\left(\frac{49}{81}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{137}{162}\right)$	$e\left(\frac{38}{81}\right)$	$e\left(\frac{67}{162}\right)$	$e\left(\frac{19}{81}\right)$
$\chi_{243}(92,\cdot)$	$-1$	$1$	$e\left(\frac{67}{162}\right)$	$e\left(\frac{67}{81}\right)$	$e\left(\frac{83}{162}\right)$	$e\left(\frac{77}{81}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{7}{162}\right)$	$e\left(\frac{25}{81}\right)$	$e\left(\frac{59}{162}\right)$	$e\left(\frac{53}{81}\right)$
$\chi_{243}(95,\cdot)$	$-1$	$1$	$e\left(\frac{17}{162}\right)$	$e\left(\frac{17}{81}\right)$	$e\left(\frac{67}{162}\right)$	$e\left(\frac{28}{81}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{113}{162}\right)$	$e\left(\frac{68}{81}\right)$	$e\left(\frac{73}{162}\right)$	$e\left(\frac{34}{81}\right)$
$\chi_{243}(101,\cdot)$	$-1$	$1$	$e\left(\frac{133}{162}\right)$	$e\left(\frac{52}{81}\right)$	$e\left(\frac{143}{162}\right)$	$e\left(\frac{38}{81}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{55}{162}\right)$	$e\left(\frac{46}{81}\right)$	$e\left(\frac{47}{162}\right)$	$e\left(\frac{23}{81}\right)$
$\chi_{243}(104,\cdot)$	$-1$	$1$	$e\left(\frac{11}{162}\right)$	$e\left(\frac{11}{81}\right)$	$e\left(\frac{91}{162}\right)$	$e\left(\frac{61}{81}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{35}{162}\right)$	$e\left(\frac{44}{81}\right)$	$e\left(\frac{133}{162}\right)$	$e\left(\frac{22}{81}\right)$
$\chi_{243}(110,\cdot)$	$-1$	$1$	$e\left(\frac{145}{162}\right)$	$e\left(\frac{64}{81}\right)$	$e\left(\frac{95}{162}\right)$	$e\left(\frac{53}{81}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{49}{162}\right)$	$e\left(\frac{13}{81}\right)$	$e\left(\frac{89}{162}\right)$	$e\left(\frac{47}{81}\right)$
$\chi_{243}(113,\cdot)$	$-1$	$1$	$e\left(\frac{113}{162}\right)$	$e\left(\frac{32}{81}\right)$	$e\left(\frac{7}{162}\right)$	$e\left(\frac{67}{81}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{65}{162}\right)$	$e\left(\frac{47}{81}\right)$	$e\left(\frac{85}{162}\right)$	$e\left(\frac{64}{81}\right)$
$\chi_{243}(119,\cdot)$	$-1$	$1$	$e\left(\frac{103}{162}\right)$	$e\left(\frac{22}{81}\right)$	$e\left(\frac{101}{162}\right)$	$e\left(\frac{41}{81}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{151}{162}\right)$	$e\left(\frac{7}{81}\right)$	$e\left(\frac{23}{162}\right)$	$e\left(\frac{44}{81}\right)$
$\chi_{243}(122,\cdot)$	$-1$	$1$	$e\left(\frac{161}{162}\right)$	$e\left(\frac{80}{81}\right)$	$e\left(\frac{139}{162}\right)$	$e\left(\frac{46}{81}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{41}{162}\right)$	$e\left(\frac{77}{81}\right)$	$e\left(\frac{91}{162}\right)$	$e\left(\frac{79}{81}\right)$
$\chi_{243}(128,\cdot)$	$-1$	$1$	$e\left(\frac{7}{162}\right)$	$e\left(\frac{7}{81}\right)$	$e\left(\frac{161}{162}\right)$	$e\left(\frac{2}{81}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{37}{162}\right)$	$e\left(\frac{28}{81}\right)$	$e\left(\frac{11}{162}\right)$	$e\left(\frac{14}{81}\right)$
$\chi_{243}(131,\cdot)$	$-1$	$1$	$e\left(\frac{155}{162}\right)$	$e\left(\frac{74}{81}\right)$	$e\left(\frac{1}{162}\right)$	$e\left(\frac{79}{81}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{125}{162}\right)$	$e\left(\frac{53}{81}\right)$	$e\left(\frac{151}{162}\right)$	$e\left(\frac{67}{81}\right)$
$\chi_{243}(137,\cdot)$	$-1$	$1$	$e\left(\frac{19}{162}\right)$	$e\left(\frac{19}{81}\right)$	$e\left(\frac{113}{162}\right)$	$e\left(\frac{17}{81}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{31}{162}\right)$	$e\left(\frac{76}{81}\right)$	$e\left(\frac{53}{162}\right)$	$e\left(\frac{38}{81}\right)$

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	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\(\chi_{243}(2,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{1}{162}\right)\)	\(e\left(\frac{1}{81}\right)\)	\(e\left(\frac{23}{162}\right)\)	\(e\left(\frac{35}{81}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{121}{162}\right)\)	\(e\left(\frac{4}{81}\right)\)	\(e\left(\frac{71}{162}\right)\)	\(e\left(\frac{2}{81}\right)\)
\(\chi_{243}(5,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{23}{162}\right)\)	\(e\left(\frac{23}{81}\right)\)	\(e\left(\frac{43}{162}\right)\)	\(e\left(\frac{76}{81}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{29}{162}\right)\)	\(e\left(\frac{11}{81}\right)\)	\(e\left(\frac{13}{162}\right)\)	\(e\left(\frac{46}{81}\right)\)
\(\chi_{243}(11,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{162}\right)\)	\(e\left(\frac{40}{81}\right)\)	\(e\left(\frac{29}{162}\right)\)	\(e\left(\frac{23}{81}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{61}{162}\right)\)	\(e\left(\frac{79}{81}\right)\)	\(e\left(\frac{5}{162}\right)\)	\(e\left(\frac{80}{81}\right)\)
\(\chi_{243}(14,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{162}\right)\)	\(e\left(\frac{71}{81}\right)\)	\(e\left(\frac{13}{162}\right)\)	\(e\left(\frac{55}{81}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{5}{162}\right)\)	\(e\left(\frac{41}{81}\right)\)	\(e\left(\frac{19}{162}\right)\)	\(e\left(\frac{61}{81}\right)\)
\(\chi_{243}(20,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{25}{162}\right)\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{89}{162}\right)\)	\(e\left(\frac{65}{81}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{109}{162}\right)\)	\(e\left(\frac{19}{81}\right)\)	\(e\left(\frac{155}{162}\right)\)	\(e\left(\frac{50}{81}\right)\)
\(\chi_{243}(23,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{162}\right)\)	\(e\left(\frac{65}{81}\right)\)	\(e\left(\frac{37}{162}\right)\)	\(e\left(\frac{7}{81}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{89}{162}\right)\)	\(e\left(\frac{17}{81}\right)\)	\(e\left(\frac{79}{162}\right)\)	\(e\left(\frac{49}{81}\right)\)
\(\chi_{243}(29,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{162}\right)\)	\(e\left(\frac{37}{81}\right)\)	\(e\left(\frac{41}{162}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{103}{162}\right)\)	\(e\left(\frac{67}{81}\right)\)	\(e\left(\frac{35}{162}\right)\)	\(e\left(\frac{74}{81}\right)\)
\(\chi_{243}(32,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{162}\right)\)	\(e\left(\frac{5}{81}\right)\)	\(e\left(\frac{115}{162}\right)\)	\(e\left(\frac{13}{81}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{119}{162}\right)\)	\(e\left(\frac{20}{81}\right)\)	\(e\left(\frac{31}{162}\right)\)	\(e\left(\frac{10}{81}\right)\)
\(\chi_{243}(38,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{157}{162}\right)\)	\(e\left(\frac{76}{81}\right)\)	\(e\left(\frac{47}{162}\right)\)	\(e\left(\frac{68}{81}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{43}{162}\right)\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{131}{162}\right)\)	\(e\left(\frac{71}{81}\right)\)
\(\chi_{243}(41,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{162}\right)\)	\(e\left(\frac{53}{81}\right)\)	\(e\left(\frac{85}{162}\right)\)	\(e\left(\frac{73}{81}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{95}{162}\right)\)	\(e\left(\frac{50}{81}\right)\)	\(e\left(\frac{37}{162}\right)\)	\(e\left(\frac{25}{81}\right)\)
\(\chi_{243}(47,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{162}\right)\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{107}{162}\right)\)	\(e\left(\frac{29}{81}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{91}{162}\right)\)	\(e\left(\frac{1}{81}\right)\)	\(e\left(\frac{119}{162}\right)\)	\(e\left(\frac{41}{81}\right)\)
\(\chi_{243}(50,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{47}{162}\right)\)	\(e\left(\frac{47}{81}\right)\)	\(e\left(\frac{109}{162}\right)\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{17}{162}\right)\)	\(e\left(\frac{26}{81}\right)\)	\(e\left(\frac{97}{162}\right)\)	\(e\left(\frac{13}{81}\right)\)
\(\chi_{243}(56,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{162}\right)\)	\(e\left(\frac{73}{81}\right)\)	\(e\left(\frac{59}{162}\right)\)	\(e\left(\frac{44}{81}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{85}{162}\right)\)	\(e\left(\frac{49}{81}\right)\)	\(e\left(\frac{161}{162}\right)\)	\(e\left(\frac{65}{81}\right)\)
\(\chi_{243}(59,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{162}\right)\)	\(e\left(\frac{68}{81}\right)\)	\(e\left(\frac{25}{162}\right)\)	\(e\left(\frac{31}{81}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{47}{162}\right)\)	\(e\left(\frac{29}{81}\right)\)	\(e\left(\frac{49}{162}\right)\)	\(e\left(\frac{55}{81}\right)\)
\(\chi_{243}(65,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{162}\right)\)	\(e\left(\frac{31}{81}\right)\)	\(e\left(\frac{65}{162}\right)\)	\(e\left(\frac{32}{81}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{25}{162}\right)\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{95}{162}\right)\)	\(e\left(\frac{62}{81}\right)\)
\(\chi_{243}(68,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{162}\right)\)	\(e\left(\frac{35}{81}\right)\)	\(e\left(\frac{157}{162}\right)\)	\(e\left(\frac{10}{81}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{23}{162}\right)\)	\(e\left(\frac{59}{81}\right)\)	\(e\left(\frac{55}{162}\right)\)	\(e\left(\frac{70}{81}\right)\)
\(\chi_{243}(74,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{162}\right)\)	\(e\left(\frac{16}{81}\right)\)	\(e\left(\frac{125}{162}\right)\)	\(e\left(\frac{74}{81}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{73}{162}\right)\)	\(e\left(\frac{64}{81}\right)\)	\(e\left(\frac{83}{162}\right)\)	\(e\left(\frac{32}{81}\right)\)
\(\chi_{243}(77,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{162}\right)\)	\(e\left(\frac{29}{81}\right)\)	\(e\left(\frac{19}{162}\right)\)	\(e\left(\frac{43}{81}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{107}{162}\right)\)	\(e\left(\frac{35}{81}\right)\)	\(e\left(\frac{115}{162}\right)\)	\(e\left(\frac{58}{81}\right)\)
\(\chi_{243}(83,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{162}\right)\)	\(e\left(\frac{28}{81}\right)\)	\(e\left(\frac{77}{162}\right)\)	\(e\left(\frac{8}{81}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{67}{162}\right)\)	\(e\left(\frac{31}{81}\right)\)	\(e\left(\frac{125}{162}\right)\)	\(e\left(\frac{56}{81}\right)\)
\(\chi_{243}(86,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{162}\right)\)	\(e\left(\frac{50}{81}\right)\)	\(e\left(\frac{97}{162}\right)\)	\(e\left(\frac{49}{81}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{137}{162}\right)\)	\(e\left(\frac{38}{81}\right)\)	\(e\left(\frac{67}{162}\right)\)	\(e\left(\frac{19}{81}\right)\)
\(\chi_{243}(92,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{67}{162}\right)\)	\(e\left(\frac{67}{81}\right)\)	\(e\left(\frac{83}{162}\right)\)	\(e\left(\frac{77}{81}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{7}{162}\right)\)	\(e\left(\frac{25}{81}\right)\)	\(e\left(\frac{59}{162}\right)\)	\(e\left(\frac{53}{81}\right)\)
\(\chi_{243}(95,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{162}\right)\)	\(e\left(\frac{17}{81}\right)\)	\(e\left(\frac{67}{162}\right)\)	\(e\left(\frac{28}{81}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{113}{162}\right)\)	\(e\left(\frac{68}{81}\right)\)	\(e\left(\frac{73}{162}\right)\)	\(e\left(\frac{34}{81}\right)\)
\(\chi_{243}(101,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{162}\right)\)	\(e\left(\frac{52}{81}\right)\)	\(e\left(\frac{143}{162}\right)\)	\(e\left(\frac{38}{81}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{55}{162}\right)\)	\(e\left(\frac{46}{81}\right)\)	\(e\left(\frac{47}{162}\right)\)	\(e\left(\frac{23}{81}\right)\)
\(\chi_{243}(104,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{162}\right)\)	\(e\left(\frac{11}{81}\right)\)	\(e\left(\frac{91}{162}\right)\)	\(e\left(\frac{61}{81}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{35}{162}\right)\)	\(e\left(\frac{44}{81}\right)\)	\(e\left(\frac{133}{162}\right)\)	\(e\left(\frac{22}{81}\right)\)
\(\chi_{243}(110,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{145}{162}\right)\)	\(e\left(\frac{64}{81}\right)\)	\(e\left(\frac{95}{162}\right)\)	\(e\left(\frac{53}{81}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{49}{162}\right)\)	\(e\left(\frac{13}{81}\right)\)	\(e\left(\frac{89}{162}\right)\)	\(e\left(\frac{47}{81}\right)\)
\(\chi_{243}(113,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{162}\right)\)	\(e\left(\frac{32}{81}\right)\)	\(e\left(\frac{7}{162}\right)\)	\(e\left(\frac{67}{81}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{65}{162}\right)\)	\(e\left(\frac{47}{81}\right)\)	\(e\left(\frac{85}{162}\right)\)	\(e\left(\frac{64}{81}\right)\)
\(\chi_{243}(119,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{162}\right)\)	\(e\left(\frac{22}{81}\right)\)	\(e\left(\frac{101}{162}\right)\)	\(e\left(\frac{41}{81}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{151}{162}\right)\)	\(e\left(\frac{7}{81}\right)\)	\(e\left(\frac{23}{162}\right)\)	\(e\left(\frac{44}{81}\right)\)
\(\chi_{243}(122,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{161}{162}\right)\)	\(e\left(\frac{80}{81}\right)\)	\(e\left(\frac{139}{162}\right)\)	\(e\left(\frac{46}{81}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{41}{162}\right)\)	\(e\left(\frac{77}{81}\right)\)	\(e\left(\frac{91}{162}\right)\)	\(e\left(\frac{79}{81}\right)\)
\(\chi_{243}(128,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{162}\right)\)	\(e\left(\frac{7}{81}\right)\)	\(e\left(\frac{161}{162}\right)\)	\(e\left(\frac{2}{81}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{37}{162}\right)\)	\(e\left(\frac{28}{81}\right)\)	\(e\left(\frac{11}{162}\right)\)	\(e\left(\frac{14}{81}\right)\)
\(\chi_{243}(131,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{155}{162}\right)\)	\(e\left(\frac{74}{81}\right)\)	\(e\left(\frac{1}{162}\right)\)	\(e\left(\frac{79}{81}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{125}{162}\right)\)	\(e\left(\frac{53}{81}\right)\)	\(e\left(\frac{151}{162}\right)\)	\(e\left(\frac{67}{81}\right)\)
\(\chi_{243}(137,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{19}{162}\right)\)	\(e\left(\frac{19}{81}\right)\)	\(e\left(\frac{113}{162}\right)\)	\(e\left(\frac{17}{81}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{31}{162}\right)\)	\(e\left(\frac{76}{81}\right)\)	\(e\left(\frac{53}{162}\right)\)	\(e\left(\frac{38}{81}\right)\)

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First 31 of 54 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	243.j
Modulus	$243$
Conductor	$243$
Order	$162$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(243\)
Conductor:	\(243\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(162\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)