Properties

Label 8470.m
Modulus $8470$
Conductor $55$
Order $4$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(8470, base_ring=CyclotomicField(4))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([1,0,2]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(967,8470))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(8470\)
Conductor: \(55\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 55.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: \(\Q(\sqrt{-1}) \)
Fixed field: 4.4.15125.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(9\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\) \(37\)
\(\chi_{8470}(967,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(i\) \(-i\) \(1\) \(-i\) \(i\) \(1\) \(1\) \(i\)
\(\chi_{8470}(7743,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(-i\) \(i\) \(1\) \(i\) \(-i\) \(1\) \(1\) \(-i\)