LMFDB - Dirichlet character orbit 2592.cj

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2592, base_ring=CyclotomicField(216)) M = H._module chi = DirichletCharacter(H, M([0,27,92])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(5,2592)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$2592$
Conductor:	$2592$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$216$	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:	$\Q(\zeta_{216})$
Fixed field:	Number field defined by a degree 216 polynomial (not computed)

First 31 of 72 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{2592}(5,\cdot)$	$-1$	$1$	$e\left(\frac{199}{216}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{35}{216}\right)$	$e\left(\frac{61}{216}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{29}{216}\right)$	$e\left(\frac{14}{27}\right)$
$\chi_{2592}(29,\cdot)$	$-1$	$1$	$e\left(\frac{29}{216}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{169}{216}\right)$	$e\left(\frac{23}{216}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{103}{216}\right)$	$e\left(\frac{19}{27}\right)$
$\chi_{2592}(77,\cdot)$	$-1$	$1$	$e\left(\frac{49}{216}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{77}{216}\right)$	$e\left(\frac{91}{216}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{107}{216}\right)$	$e\left(\frac{20}{27}\right)$
$\chi_{2592}(101,\cdot)$	$-1$	$1$	$e\left(\frac{167}{216}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{139}{216}\right)$	$e\left(\frac{125}{216}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{109}{216}\right)$	$e\left(\frac{7}{27}\right)$
$\chi_{2592}(149,\cdot)$	$-1$	$1$	$e\left(\frac{115}{216}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{119}{216}\right)$	$e\left(\frac{121}{216}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{185}{216}\right)$	$e\left(\frac{26}{27}\right)$
$\chi_{2592}(173,\cdot)$	$-1$	$1$	$e\left(\frac{89}{216}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{109}{216}\right)$	$e\left(\frac{11}{216}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{115}{216}\right)$	$e\left(\frac{22}{27}\right)$
$\chi_{2592}(221,\cdot)$	$-1$	$1$	$e\left(\frac{181}{216}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{161}{216}\right)$	$e\left(\frac{151}{216}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{47}{216}\right)$	$e\left(\frac{5}{27}\right)$
$\chi_{2592}(245,\cdot)$	$-1$	$1$	$e\left(\frac{11}{216}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{79}{216}\right)$	$e\left(\frac{113}{216}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{121}{216}\right)$	$e\left(\frac{10}{27}\right)$
$\chi_{2592}(293,\cdot)$	$-1$	$1$	$e\left(\frac{31}{216}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{203}{216}\right)$	$e\left(\frac{181}{216}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{125}{216}\right)$	$e\left(\frac{11}{27}\right)$
$\chi_{2592}(317,\cdot)$	$-1$	$1$	$e\left(\frac{149}{216}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{49}{216}\right)$	$e\left(\frac{215}{216}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{127}{216}\right)$	$e\left(\frac{25}{27}\right)$
$\chi_{2592}(365,\cdot)$	$-1$	$1$	$e\left(\frac{97}{216}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{29}{216}\right)$	$e\left(\frac{211}{216}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{203}{216}\right)$	$e\left(\frac{17}{27}\right)$
$\chi_{2592}(389,\cdot)$	$-1$	$1$	$e\left(\frac{71}{216}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{19}{216}\right)$	$e\left(\frac{101}{216}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{133}{216}\right)$	$e\left(\frac{13}{27}\right)$
$\chi_{2592}(437,\cdot)$	$-1$	$1$	$e\left(\frac{163}{216}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{71}{216}\right)$	$e\left(\frac{25}{216}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{65}{216}\right)$	$e\left(\frac{23}{27}\right)$
$\chi_{2592}(461,\cdot)$	$-1$	$1$	$e\left(\frac{209}{216}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{205}{216}\right)$	$e\left(\frac{203}{216}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{139}{216}\right)$	$e\left(\frac{1}{27}\right)$
$\chi_{2592}(509,\cdot)$	$-1$	$1$	$e\left(\frac{13}{216}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{113}{216}\right)$	$e\left(\frac{55}{216}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{143}{216}\right)$	$e\left(\frac{2}{27}\right)$
$\chi_{2592}(533,\cdot)$	$-1$	$1$	$e\left(\frac{131}{216}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{175}{216}\right)$	$e\left(\frac{89}{216}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{145}{216}\right)$	$e\left(\frac{16}{27}\right)$
$\chi_{2592}(581,\cdot)$	$-1$	$1$	$e\left(\frac{79}{216}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{155}{216}\right)$	$e\left(\frac{85}{216}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{5}{216}\right)$	$e\left(\frac{8}{27}\right)$
$\chi_{2592}(605,\cdot)$	$-1$	$1$	$e\left(\frac{53}{216}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{145}{216}\right)$	$e\left(\frac{191}{216}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{151}{216}\right)$	$e\left(\frac{4}{27}\right)$
$\chi_{2592}(653,\cdot)$	$-1$	$1$	$e\left(\frac{145}{216}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{197}{216}\right)$	$e\left(\frac{115}{216}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{83}{216}\right)$	$e\left(\frac{14}{27}\right)$
$\chi_{2592}(677,\cdot)$	$-1$	$1$	$e\left(\frac{191}{216}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{115}{216}\right)$	$e\left(\frac{77}{216}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{157}{216}\right)$	$e\left(\frac{19}{27}\right)$
$\chi_{2592}(725,\cdot)$	$-1$	$1$	$e\left(\frac{211}{216}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{23}{216}\right)$	$e\left(\frac{145}{216}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{161}{216}\right)$	$e\left(\frac{20}{27}\right)$
$\chi_{2592}(749,\cdot)$	$-1$	$1$	$e\left(\frac{113}{216}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{85}{216}\right)$	$e\left(\frac{179}{216}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{163}{216}\right)$	$e\left(\frac{7}{27}\right)$
$\chi_{2592}(797,\cdot)$	$-1$	$1$	$e\left(\frac{61}{216}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{65}{216}\right)$	$e\left(\frac{175}{216}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{23}{216}\right)$	$e\left(\frac{26}{27}\right)$
$\chi_{2592}(821,\cdot)$	$-1$	$1$	$e\left(\frac{35}{216}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{55}{216}\right)$	$e\left(\frac{65}{216}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{169}{216}\right)$	$e\left(\frac{22}{27}\right)$
$\chi_{2592}(869,\cdot)$	$-1$	$1$	$e\left(\frac{127}{216}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{107}{216}\right)$	$e\left(\frac{205}{216}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{101}{216}\right)$	$e\left(\frac{5}{27}\right)$
$\chi_{2592}(893,\cdot)$	$-1$	$1$	$e\left(\frac{173}{216}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{25}{216}\right)$	$e\left(\frac{167}{216}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{175}{216}\right)$	$e\left(\frac{10}{27}\right)$
$\chi_{2592}(941,\cdot)$	$-1$	$1$	$e\left(\frac{193}{216}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{149}{216}\right)$	$e\left(\frac{19}{216}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{179}{216}\right)$	$e\left(\frac{11}{27}\right)$
$\chi_{2592}(965,\cdot)$	$-1$	$1$	$e\left(\frac{95}{216}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{211}{216}\right)$	$e\left(\frac{53}{216}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{181}{216}\right)$	$e\left(\frac{25}{27}\right)$
$\chi_{2592}(1013,\cdot)$	$-1$	$1$	$e\left(\frac{43}{216}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{191}{216}\right)$	$e\left(\frac{49}{216}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{41}{216}\right)$	$e\left(\frac{17}{27}\right)$
$\chi_{2592}(1037,\cdot)$	$-1$	$1$	$e\left(\frac{17}{216}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{181}{216}\right)$	$e\left(\frac{155}{216}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{187}{216}\right)$	$e\left(\frac{13}{27}\right)$
$\chi_{2592}(1085,\cdot)$	$-1$	$1$	$e\left(\frac{109}{216}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{17}{216}\right)$	$e\left(\frac{79}{216}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{119}{216}\right)$	$e\left(\frac{23}{27}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{2592}(5,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{199}{216}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{35}{216}\right)\)	\(e\left(\frac{61}{216}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{29}{216}\right)\)	\(e\left(\frac{14}{27}\right)\)
\(\chi_{2592}(29,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{29}{216}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{169}{216}\right)\)	\(e\left(\frac{23}{216}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{103}{216}\right)\)	\(e\left(\frac{19}{27}\right)\)
\(\chi_{2592}(77,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{49}{216}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{77}{216}\right)\)	\(e\left(\frac{91}{216}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{107}{216}\right)\)	\(e\left(\frac{20}{27}\right)\)
\(\chi_{2592}(101,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{167}{216}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{139}{216}\right)\)	\(e\left(\frac{125}{216}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{109}{216}\right)\)	\(e\left(\frac{7}{27}\right)\)
\(\chi_{2592}(149,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{115}{216}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{119}{216}\right)\)	\(e\left(\frac{121}{216}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{185}{216}\right)\)	\(e\left(\frac{26}{27}\right)\)
\(\chi_{2592}(173,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{216}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{109}{216}\right)\)	\(e\left(\frac{11}{216}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{115}{216}\right)\)	\(e\left(\frac{22}{27}\right)\)
\(\chi_{2592}(221,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{181}{216}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{161}{216}\right)\)	\(e\left(\frac{151}{216}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{47}{216}\right)\)	\(e\left(\frac{5}{27}\right)\)
\(\chi_{2592}(245,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{216}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{79}{216}\right)\)	\(e\left(\frac{113}{216}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{121}{216}\right)\)	\(e\left(\frac{10}{27}\right)\)
\(\chi_{2592}(293,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{31}{216}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{203}{216}\right)\)	\(e\left(\frac{181}{216}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{125}{216}\right)\)	\(e\left(\frac{11}{27}\right)\)
\(\chi_{2592}(317,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{149}{216}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{49}{216}\right)\)	\(e\left(\frac{215}{216}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{127}{216}\right)\)	\(e\left(\frac{25}{27}\right)\)
\(\chi_{2592}(365,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{216}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{29}{216}\right)\)	\(e\left(\frac{211}{216}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{203}{216}\right)\)	\(e\left(\frac{17}{27}\right)\)
\(\chi_{2592}(389,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{71}{216}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{19}{216}\right)\)	\(e\left(\frac{101}{216}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{133}{216}\right)\)	\(e\left(\frac{13}{27}\right)\)
\(\chi_{2592}(437,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{163}{216}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{71}{216}\right)\)	\(e\left(\frac{25}{216}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{65}{216}\right)\)	\(e\left(\frac{23}{27}\right)\)
\(\chi_{2592}(461,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{209}{216}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{205}{216}\right)\)	\(e\left(\frac{203}{216}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{139}{216}\right)\)	\(e\left(\frac{1}{27}\right)\)
\(\chi_{2592}(509,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{216}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{113}{216}\right)\)	\(e\left(\frac{55}{216}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{143}{216}\right)\)	\(e\left(\frac{2}{27}\right)\)
\(\chi_{2592}(533,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{216}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{175}{216}\right)\)	\(e\left(\frac{89}{216}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{145}{216}\right)\)	\(e\left(\frac{16}{27}\right)\)
\(\chi_{2592}(581,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{216}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{155}{216}\right)\)	\(e\left(\frac{85}{216}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{5}{216}\right)\)	\(e\left(\frac{8}{27}\right)\)
\(\chi_{2592}(605,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{53}{216}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{145}{216}\right)\)	\(e\left(\frac{191}{216}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{151}{216}\right)\)	\(e\left(\frac{4}{27}\right)\)
\(\chi_{2592}(653,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{145}{216}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{197}{216}\right)\)	\(e\left(\frac{115}{216}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{83}{216}\right)\)	\(e\left(\frac{14}{27}\right)\)
\(\chi_{2592}(677,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{191}{216}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{115}{216}\right)\)	\(e\left(\frac{77}{216}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{157}{216}\right)\)	\(e\left(\frac{19}{27}\right)\)
\(\chi_{2592}(725,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{211}{216}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{23}{216}\right)\)	\(e\left(\frac{145}{216}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{161}{216}\right)\)	\(e\left(\frac{20}{27}\right)\)
\(\chi_{2592}(749,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{216}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{85}{216}\right)\)	\(e\left(\frac{179}{216}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{163}{216}\right)\)	\(e\left(\frac{7}{27}\right)\)
\(\chi_{2592}(797,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{61}{216}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{65}{216}\right)\)	\(e\left(\frac{175}{216}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{23}{216}\right)\)	\(e\left(\frac{26}{27}\right)\)
\(\chi_{2592}(821,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{35}{216}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{55}{216}\right)\)	\(e\left(\frac{65}{216}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{169}{216}\right)\)	\(e\left(\frac{22}{27}\right)\)
\(\chi_{2592}(869,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{127}{216}\right)\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{107}{216}\right)\)	\(e\left(\frac{205}{216}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{101}{216}\right)\)	\(e\left(\frac{5}{27}\right)\)
\(\chi_{2592}(893,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{173}{216}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{25}{216}\right)\)	\(e\left(\frac{167}{216}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{175}{216}\right)\)	\(e\left(\frac{10}{27}\right)\)
\(\chi_{2592}(941,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{193}{216}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{149}{216}\right)\)	\(e\left(\frac{19}{216}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{179}{216}\right)\)	\(e\left(\frac{11}{27}\right)\)
\(\chi_{2592}(965,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{216}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{211}{216}\right)\)	\(e\left(\frac{53}{216}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{181}{216}\right)\)	\(e\left(\frac{25}{27}\right)\)
\(\chi_{2592}(1013,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{43}{216}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{191}{216}\right)\)	\(e\left(\frac{49}{216}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{41}{216}\right)\)	\(e\left(\frac{17}{27}\right)\)
\(\chi_{2592}(1037,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{216}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{181}{216}\right)\)	\(e\left(\frac{155}{216}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{187}{216}\right)\)	\(e\left(\frac{13}{27}\right)\)
\(\chi_{2592}(1085,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{216}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{17}{216}\right)\)	\(e\left(\frac{79}{216}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{119}{216}\right)\)	\(e\left(\frac{23}{27}\right)\)

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First 31 of 72 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	2592.cj
Modulus	$2592$
Conductor	$2592$
Order	$216$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(2592\)
Conductor:	\(2592\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(216\)	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)