LMFDB - Dirichlet character orbit 8640.hk

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comment:Define the Dirichlet character orbit

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8640, base_ring=CyclotomicField(72)) M = H._module chi = DirichletCharacter(H, M([0,27,52,54])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(713, 8640)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8640.713"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };

Basic properties

Modulus:	$8640$	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	$4320$	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	$72$	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 4320.ge	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{8640}(713,\cdot)$	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{8640}(857,\cdot)$	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{8640}(1193,\cdot)$	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{8640}(1337,\cdot)$	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{8640}(2153,\cdot)$	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{8640}(2297,\cdot)$	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{8640}(2633,\cdot)$	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{8640}(2777,\cdot)$	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{8640}(3593,\cdot)$	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{8640}(3737,\cdot)$	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{8640}(4073,\cdot)$	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{8640}(4217,\cdot)$	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{8640}(5033,\cdot)$	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{8640}(5177,\cdot)$	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{8640}(5513,\cdot)$	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{8640}(5657,\cdot)$	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{8640}(6473,\cdot)$	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{8640}(6617,\cdot)$	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{8640}(6953,\cdot)$	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{8640}(7097,\cdot)$	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{8640}(7913,\cdot)$	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{8640}(8057,\cdot)$	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{8640}(8393,\cdot)$	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{8640}(8537,\cdot)$	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{36}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{8640}(713,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{8640}(857,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{8640}(1193,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{8640}(1337,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{8640}(2153,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{8640}(2297,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{8640}(2633,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{8640}(2777,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{8640}(3593,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{8640}(3737,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{8640}(4073,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{8640}(4217,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{8640}(5033,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{8640}(5177,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{8640}(5513,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{8640}(5657,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{8640}(6473,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{7}{9}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{8640}(6617,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{8640}(6953,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{8}{9}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{8640}(7097,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{8640}(7913,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{1}{9}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{8640}(8057,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{4}{9}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{8640}(8393,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{8640}(8537,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{5}{9}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{36}\right)\)

Introduction

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Varieties

Fields

Representations

Groups

Database

Properties

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Basic properties

Related number fields

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	8640.hk
Modulus	$8640$
Conductor	$4320$
Order	$72$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(8640\)	comment:Modulus sage:chi.modulus() gp:g[1][1] magma:Modulus(chi);
Conductor:	\(4320\)	comment:Conductor sage:chi.conductor() gp:znconreyconductor(g,chi) magma:Conductor(chi);
Order:	\(72\)	comment:Order sage:chi.multiplicative_order() gp:charorder(g,chi) magma:Order(chi);
Real:	no	comment:Whether the character is real sage:chi.multiplicative_order() <= 2 gp:charorder(g,chi) <= 2 magma:Order(chi) le 2;
Primitive:	no, induced from 4320.ge	comment:If the character is primitive sage:chi.is_primitive() gp:#znconreyconductor(g,chi)==1 magma:IsPrimitive(chi);
Minimal:	no
Parity:	even	comment:Parity sage:chi.is_odd() gp:zncharisodd(g,chi) magma:IsOdd(chi);