LMFDB - Dirichlet character orbit 3240.dn

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3240, base_ring=CyclotomicField(108)) M = H._module chi = DirichletCharacter(H, M([54,54,44,81])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(43,3240)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3240$
Conductor:	$3240$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$108$	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:	$\Q(\zeta_{108})$
Fixed field:	Number field defined by a degree 108 polynomial (not computed)

First 31 of 36 characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{3240}(43,\cdot)$	$1$	$1$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{16}{27}\right)$
$\chi_{3240}(67,\cdot)$	$1$	$1$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{27}\right)$
$\chi_{3240}(187,\cdot)$	$1$	$1$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{4}{27}\right)$
$\chi_{3240}(283,\cdot)$	$1$	$1$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{14}{27}\right)$
$\chi_{3240}(403,\cdot)$	$1$	$1$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{13}{27}\right)$
$\chi_{3240}(427,\cdot)$	$1$	$1$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{20}{27}\right)$
$\chi_{3240}(547,\cdot)$	$1$	$1$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{27}\right)$
$\chi_{3240}(643,\cdot)$	$1$	$1$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{17}{108}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{2}{27}\right)$
$\chi_{3240}(763,\cdot)$	$1$	$1$	$e\left(\frac{35}{108}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{10}{27}\right)$
$\chi_{3240}(787,\cdot)$	$1$	$1$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{8}{27}\right)$
$\chi_{3240}(907,\cdot)$	$1$	$1$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{91}{108}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{108}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{25}{27}\right)$
$\chi_{3240}(1003,\cdot)$	$1$	$1$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{27}\right)$
$\chi_{3240}(1123,\cdot)$	$1$	$1$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{73}{108}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{97}{108}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{17}{54}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{27}\right)$
$\chi_{3240}(1147,\cdot)$	$1$	$1$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{23}{27}\right)$
$\chi_{3240}(1267,\cdot)$	$1$	$1$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{22}{27}\right)$
$\chi_{3240}(1363,\cdot)$	$1$	$1$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{77}{108}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{27}\right)$
$\chi_{3240}(1483,\cdot)$	$1$	$1$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{29}{54}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{4}{27}\right)$
$\chi_{3240}(1507,\cdot)$	$1$	$1$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{107}{108}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{83}{108}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{19}{54}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{27}\right)$
$\chi_{3240}(1627,\cdot)$	$1$	$1$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{19}{27}\right)$
$\chi_{3240}(1723,\cdot)$	$1$	$1$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{65}{108}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{20}{27}\right)$
$\chi_{3240}(1843,\cdot)$	$1$	$1$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{17}{27}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{27}\right)$
$\chi_{3240}(1867,\cdot)$	$1$	$1$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{13}{54}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{26}{27}\right)$
$\chi_{3240}(1987,\cdot)$	$1$	$1$	$e\left(\frac{29}{108}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{79}{108}\right)$	$e\left(\frac{2}{27}\right)$	$e\left(\frac{35}{54}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{16}{27}\right)$
$\chi_{3240}(2083,\cdot)$	$1$	$1$	$e\left(\frac{55}{108}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{53}{108}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{31}{54}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{8}{27}\right)$
$\chi_{3240}(2203,\cdot)$	$1$	$1$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{37}{108}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{25}{27}\right)$
$\chi_{3240}(2227,\cdot)$	$1$	$1$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{11}{108}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{59}{108}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{7}{54}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{14}{27}\right)$
$\chi_{3240}(2347,\cdot)$	$1$	$1$	$e\left(\frac{5}{108}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{103}{108}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{47}{54}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{27}\right)$
$\chi_{3240}(2443,\cdot)$	$1$	$1$	$e\left(\frac{67}{108}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{101}{108}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{41}{108}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{23}{27}\right)$
$\chi_{3240}(2563,\cdot)$	$1$	$1$	$e\left(\frac{23}{108}\right)$	$e\left(\frac{11}{27}\right)$	$e\left(\frac{25}{108}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{85}{108}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{11}{54}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{22}{27}\right)$
$\chi_{3240}(2587,\cdot)$	$1$	$1$	$e\left(\frac{61}{108}\right)$	$e\left(\frac{1}{27}\right)$	$e\left(\frac{71}{108}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{7}{27}\right)$	$e\left(\frac{1}{54}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{2}{27}\right)$
$\chi_{3240}(2707,\cdot)$	$1$	$1$	$e\left(\frac{89}{108}\right)$	$e\left(\frac{5}{27}\right)$	$e\left(\frac{31}{108}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{19}{108}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{5}{54}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{10}{27}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{3240}(43,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{16}{27}\right)\)
\(\chi_{3240}(67,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{27}\right)\)
\(\chi_{3240}(187,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{4}{27}\right)\)
\(\chi_{3240}(283,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{14}{27}\right)\)
\(\chi_{3240}(403,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{13}{27}\right)\)
\(\chi_{3240}(427,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{20}{27}\right)\)
\(\chi_{3240}(547,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{27}\right)\)
\(\chi_{3240}(643,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{17}{108}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{2}{27}\right)\)
\(\chi_{3240}(763,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{108}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{10}{27}\right)\)
\(\chi_{3240}(787,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{108}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{8}{27}\right)\)
\(\chi_{3240}(907,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{91}{108}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{108}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{25}{27}\right)\)
\(\chi_{3240}(1003,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{49}{54}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{27}\right)\)
\(\chi_{3240}(1123,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{73}{108}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{97}{108}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{17}{54}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{27}\right)\)
\(\chi_{3240}(1147,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{23}{27}\right)\)
\(\chi_{3240}(1267,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{22}{27}\right)\)
\(\chi_{3240}(1363,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{77}{108}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{43}{54}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{27}\right)\)
\(\chi_{3240}(1483,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{108}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{13}{108}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{29}{54}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{4}{27}\right)\)
\(\chi_{3240}(1507,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{19}{27}\right)\)	\(e\left(\frac{107}{108}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{83}{108}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{19}{54}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{27}\right)\)
\(\chi_{3240}(1627,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{23}{54}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{19}{27}\right)\)
\(\chi_{3240}(1723,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{65}{108}\right)\)	\(e\left(\frac{16}{27}\right)\)	\(e\left(\frac{37}{54}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{20}{27}\right)\)
\(\chi_{3240}(1843,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{14}{27}\right)\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{17}{27}\right)\)	\(e\left(\frac{41}{54}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{27}\right)\)
\(\chi_{3240}(1867,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{10}{27}\right)\)	\(e\left(\frac{13}{54}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{26}{27}\right)\)
\(\chi_{3240}(1987,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{108}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{79}{108}\right)\)	\(e\left(\frac{2}{27}\right)\)	\(e\left(\frac{35}{54}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{16}{27}\right)\)
\(\chi_{3240}(2083,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{108}\right)\)	\(e\left(\frac{4}{27}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{53}{108}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{31}{54}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{8}{27}\right)\)
\(\chi_{3240}(2203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{26}{27}\right)\)	\(e\left(\frac{37}{108}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{53}{54}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{25}{27}\right)\)
\(\chi_{3240}(2227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{108}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{11}{108}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{59}{108}\right)\)	\(e\left(\frac{22}{27}\right)\)	\(e\left(\frac{7}{54}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{14}{27}\right)\)
\(\chi_{3240}(2347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{108}\right)\)	\(e\left(\frac{20}{27}\right)\)	\(e\left(\frac{43}{108}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{103}{108}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{47}{54}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{13}{27}\right)\)
\(\chi_{3240}(2443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{108}\right)\)	\(e\left(\frac{25}{27}\right)\)	\(e\left(\frac{101}{108}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{41}{108}\right)\)	\(e\left(\frac{13}{27}\right)\)	\(e\left(\frac{25}{54}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{23}{27}\right)\)
\(\chi_{3240}(2563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{108}\right)\)	\(e\left(\frac{11}{27}\right)\)	\(e\left(\frac{25}{108}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{85}{108}\right)\)	\(e\left(\frac{23}{27}\right)\)	\(e\left(\frac{11}{54}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{22}{27}\right)\)
\(\chi_{3240}(2587,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{108}\right)\)	\(e\left(\frac{1}{27}\right)\)	\(e\left(\frac{71}{108}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{47}{108}\right)\)	\(e\left(\frac{7}{27}\right)\)	\(e\left(\frac{1}{54}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{2}{27}\right)\)
\(\chi_{3240}(2707,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{108}\right)\)	\(e\left(\frac{5}{27}\right)\)	\(e\left(\frac{31}{108}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{19}{108}\right)\)	\(e\left(\frac{8}{27}\right)\)	\(e\left(\frac{5}{54}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{10}{27}\right)\)

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First 31 of 36 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	3240.dn
Modulus	$3240$
Conductor	$3240$
Order	$108$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(3240\)
Conductor:	\(3240\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(108\)	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)