LMFDB - Dirichlet character orbit 8640.hj

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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([36,9,56,54])) chi.galois_orbit()

gp:[g,chi] = znchar(Mod(103, 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("8640.103"); 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.gd	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	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{8640}(103,\cdot)$	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{8640}(247,\cdot)$	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{8640}(583,\cdot)$	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{8640}(727,\cdot)$	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{8640}(1543,\cdot)$	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{8640}(1687,\cdot)$	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{8640}(2023,\cdot)$	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{8640}(2167,\cdot)$	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{8640}(2983,\cdot)$	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{8640}(3127,\cdot)$	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{8640}(3463,\cdot)$	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{8640}(3607,\cdot)$	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{36}\right)$
$\chi_{8640}(4423,\cdot)$	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{8640}(4567,\cdot)$	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{8640}(4903,\cdot)$	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{8640}(5047,\cdot)$	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{8640}(5863,\cdot)$	$1$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{8640}(6007,\cdot)$	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{8640}(6343,\cdot)$	$1$	$1$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{8640}(6487,\cdot)$	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{8640}(7303,\cdot)$	$1$	$1$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{8640}(7447,\cdot)$	$1$	$1$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{8640}(7783,\cdot)$	$1$	$1$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{8640}(7927,\cdot)$	$1$	$1$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{1}{36}\right)$

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	\(-1\)	\(1\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(29\)	\(31\)	\(37\)	\(41\)
\(\chi_{8640}(103,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{8640}(247,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{8640}(583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{8640}(727,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{8640}(1543,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{8640}(1687,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{8640}(2023,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{8640}(2167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{8640}(2983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{8640}(3127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{8640}(3463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{8640}(3607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{36}\right)\)
\(\chi_{8640}(4423,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{35}{36}\right)\)
\(\chi_{8640}(4567,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{36}\right)\)
\(\chi_{8640}(4903,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{19}{36}\right)\)
\(\chi_{8640}(5047,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{25}{36}\right)\)
\(\chi_{8640}(5863,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{23}{36}\right)\)
\(\chi_{8640}(6007,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{29}{36}\right)\)
\(\chi_{8640}(6343,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{36}\right)\)
\(\chi_{8640}(6487,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{13}{36}\right)\)
\(\chi_{8640}(7303,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{11}{36}\right)\)
\(\chi_{8640}(7447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{36}\right)\)
\(\chi_{8640}(7783,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{31}{36}\right)\)
\(\chi_{8640}(7927,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{1}{36}\right)\)

Introduction

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Varieties

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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.hj
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.gd	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);