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Properties

Label 3744.dz
Modulus 37443744
Conductor 312312
Order 66
Real no
Primitive no
Minimal no
Parity even

Related objects

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3744, base_ring=CyclotomicField(6))
 
M = H._module
 
chi = DirichletCharacter(H, M([3,3,3,2]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(2447,3744))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 37443744
Conductor: 312312
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: 66
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 312.bn
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: Q(ζ3)\mathbb{Q}(\zeta_3)
Fixed field: 6.6.394827264.1

Characters in Galois orbit

Character −1-1 11 55 77 1111 1717 1919 2323 2525 2929 3131 3535
χ3744(2447,⋅)\chi_{3744}(2447,\cdot) 11 11 11 e(16)e\left(\frac{1}{6}\right) e(56)e\left(\frac{5}{6}\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) 11 e(13)e\left(\frac{1}{3}\right) −1-1 e(16)e\left(\frac{1}{6}\right)
χ3744(3311,⋅)\chi_{3744}(3311,\cdot) 11 11 11 e(56)e\left(\frac{5}{6}\right) e(16)e\left(\frac{1}{6}\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) 11 e(23)e\left(\frac{2}{3}\right) −1-1 e(56)e\left(\frac{5}{6}\right)