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Properties

Label 740.v
Modulus 740740
Conductor 740740
Order 66
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(740, base_ring=CyclotomicField(6))
 
M = H._module
 
chi = DirichletCharacter(H, M([3,3,5]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(159,740))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 740740
Conductor: 740740
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: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ3)\mathbb{Q}(\zeta_3)
Fixed field: 6.0.554751656000.1

Characters in Galois orbit

Character −1-1 11 33 77 99 1111 1313 1717 1919 2121 2323 2727
χ740(159,⋅)\chi_{740}(159,\cdot) −1-1 11 e(23)e\left(\frac{2}{3}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) −1-1 e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) −1-1 11
χ740(619,⋅)\chi_{740}(619,\cdot) −1-1 11 e(13)e\left(\frac{1}{3}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) −1-1 e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) −1-1 11