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Properties

Label 5733.ct
Modulus 57335733
Conductor 1313
Order 66
Real no
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5733, base_ring=CyclotomicField(6))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,5]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(1765,5733))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 57335733
Conductor: 1313
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 66
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 13.e
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: Q(ζ13)+\Q(\zeta_{13})^+

Characters in Galois orbit

Character −1-1 11 22 44 55 88 1010 1111 1616 1717 1919 2020
χ5733(1765,⋅)\chi_{5733}(1765,\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(56)e\left(\frac{5}{6}\right) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\right) e(16)e\left(\frac{1}{6}\right) e(16)e\left(\frac{1}{6}\right)
χ5733(4411,⋅)\chi_{5733}(4411,\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(16)e\left(\frac{1}{6}\right) e(23)e\left(\frac{2}{3}\right) e(13)e\left(\frac{1}{3}\right) e(56)e\left(\frac{5}{6}\right) e(56)e\left(\frac{5}{6}\right)