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Properties

Label 585.bl
Modulus 585585
Conductor 585585
Order 66
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(585, base_ring=CyclotomicField(6))
 
M = H._module
 
chi = DirichletCharacter(H, M([2,3,2]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(94,585))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 585585
Conductor: 585585
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 66
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(ζ3)\mathbb{Q}(\zeta_3)
Fixed field: 6.6.23423590125.2

Characters in Galois orbit

Character −1-1 11 22 44 77 88 1111 1414 1616 1717 1919 2222
χ585(94,⋅)\chi_{585}(94,\cdot) 11 11 e(16)e\left(\frac{1}{6}\right) e(13)e\left(\frac{1}{3}\right) −1-1 −1-1 e(23)e\left(\frac{2}{3}\right) e(23)e\left(\frac{2}{3}\right) e(23)e\left(\frac{2}{3}\right) e(16)e\left(\frac{1}{6}\right) e(23)e\left(\frac{2}{3}\right) e(56)e\left(\frac{5}{6}\right)
χ585(529,⋅)\chi_{585}(529,\cdot) 11 11 e(56)e\left(\frac{5}{6}\right) e(23)e\left(\frac{2}{3}\right) −1-1 −1-1 e(13)e\left(\frac{1}{3}\right) e(13)e\left(\frac{1}{3}\right) e(13)e\left(\frac{1}{3}\right) e(56)e\left(\frac{5}{6}\right) e(13)e\left(\frac{1}{3}\right) e(16)e\left(\frac{1}{6}\right)