LMFDB - Dirichlet character orbit 5184.ck

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5184, base_ring=CyclotomicField(72)) M = H._module chi = DirichletCharacter(H, M([0,27,40])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(73,5184)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$5184$
Conductor:	$864$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$72$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 864.bu	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{72})$
Fixed field:	Number field defined by a degree 72 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{5184}(73,\cdot)$	$1$	$1$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{5184}(361,\cdot)$	$1$	$1$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{5184}(505,\cdot)$	$1$	$1$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{5184}(793,\cdot)$	$1$	$1$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{5184}(937,\cdot)$	$1$	$1$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{5184}(1225,\cdot)$	$1$	$1$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{5184}(1369,\cdot)$	$1$	$1$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{5184}(1657,\cdot)$	$1$	$1$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{5184}(1801,\cdot)$	$1$	$1$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{5184}(2089,\cdot)$	$1$	$1$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{5184}(2233,\cdot)$	$1$	$1$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{5184}(2521,\cdot)$	$1$	$1$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{5184}(2665,\cdot)$	$1$	$1$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{5184}(2953,\cdot)$	$1$	$1$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{5184}(3097,\cdot)$	$1$	$1$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{5184}(3385,\cdot)$	$1$	$1$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{5184}(3529,\cdot)$	$1$	$1$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{5184}(3817,\cdot)$	$1$	$1$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{5184}(3961,\cdot)$	$1$	$1$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{5184}(4249,\cdot)$	$1$	$1$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{5184}(4393,\cdot)$	$1$	$1$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{5184}(4681,\cdot)$	$1$	$1$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{5184}(4825,\cdot)$	$1$	$1$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{5184}(5113,\cdot)$	$1$	$1$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{8}{9}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{5184}(73,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{5184}(361,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{5184}(505,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{5184}(793,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{5184}(937,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{5184}(1225,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{5184}(1369,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{5184}(1657,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{5184}(1801,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{5184}(2089,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{5184}(2233,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{5184}(2521,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{5184}(2665,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{5184}(2953,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{5184}(3097,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{5184}(3385,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{5184}(3529,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{5184}(3817,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{5184}(3961,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{5184}(4249,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{5184}(4393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{5184}(4681,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{5184}(4825,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{5184}(5113,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{8}{9}\right)\)

Introduction

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Groups

Database

Properties

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Basic properties

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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	5184.ck
Modulus	$5184$
Conductor	$864$
Order	$72$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(5184\)
Conductor:	\(864\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(72\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 864.bu	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)