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Properties

Label 3240.by
Modulus 32403240
Conductor 216216
Order 1818
Real no
Primitive no
Minimal no
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3240, base_ring=CyclotomicField(18))
 
M = H._module
 
chi = DirichletCharacter(H, M([9,9,8,0]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(91,3240))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 32403240
Conductor: 216216
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 1818
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 216.r
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ9)\Q(\zeta_{9})
Fixed field: 18.0.132173713091594538512566714368.2

Characters in Galois orbit

Character −1-1 11 77 1111 1313 1717 1919 2323 2929 3131 3737 4141
χ3240(91,⋅)\chi_{3240}(91,\cdot) −1-1 11 e(1118)e\left(\frac{11}{18}\right) e(79)e\left(\frac{7}{9}\right) e(118)e\left(\frac{1}{18}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) e(718)e\left(\frac{7}{18}\right) e(1718)e\left(\frac{17}{18}\right) e(718)e\left(\frac{7}{18}\right) e(16)e\left(\frac{1}{6}\right) e(59)e\left(\frac{5}{9}\right)
χ3240(451,⋅)\chi_{3240}(451,\cdot) −1-1 11 e(118)e\left(\frac{1}{18}\right) e(89)e\left(\frac{8}{9}\right) e(518)e\left(\frac{5}{18}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) e(1718)e\left(\frac{17}{18}\right) e(1318)e\left(\frac{13}{18}\right) e(1718)e\left(\frac{17}{18}\right) e(56)e\left(\frac{5}{6}\right) e(79)e\left(\frac{7}{9}\right)
χ3240(1171,⋅)\chi_{3240}(1171,\cdot) −1-1 11 e(1718)e\left(\frac{17}{18}\right) e(19)e\left(\frac{1}{9}\right) e(1318)e\left(\frac{13}{18}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) e(118)e\left(\frac{1}{18}\right) e(518)e\left(\frac{5}{18}\right) e(118)e\left(\frac{1}{18}\right) e(16)e\left(\frac{1}{6}\right) e(29)e\left(\frac{2}{9}\right)
χ3240(1531,⋅)\chi_{3240}(1531,\cdot) −1-1 11 e(718)e\left(\frac{7}{18}\right) e(29)e\left(\frac{2}{9}\right) e(1718)e\left(\frac{17}{18}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) e(1118)e\left(\frac{11}{18}\right) e(118)e\left(\frac{1}{18}\right) e(1118)e\left(\frac{11}{18}\right) e(56)e\left(\frac{5}{6}\right) e(49)e\left(\frac{4}{9}\right)
χ3240(2251,⋅)\chi_{3240}(2251,\cdot) −1-1 11 e(518)e\left(\frac{5}{18}\right) e(49)e\left(\frac{4}{9}\right) e(718)e\left(\frac{7}{18}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) e(1318)e\left(\frac{13}{18}\right) e(1118)e\left(\frac{11}{18}\right) e(1318)e\left(\frac{13}{18}\right) e(16)e\left(\frac{1}{6}\right) e(89)e\left(\frac{8}{9}\right)
χ3240(2611,⋅)\chi_{3240}(2611,\cdot) −1-1 11 e(1318)e\left(\frac{13}{18}\right) e(59)e\left(\frac{5}{9}\right) e(1118)e\left(\frac{11}{18}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) e(518)e\left(\frac{5}{18}\right) e(718)e\left(\frac{7}{18}\right) e(518)e\left(\frac{5}{18}\right) e(56)e\left(\frac{5}{6}\right) e(19)e\left(\frac{1}{9}\right)