Properties

Label 273.o
Modulus $273$
Conductor $273$
Order $4$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(273, base_ring=CyclotomicField(4))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([2,2,3]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(83,273))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(273\)
Conductor: \(273\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
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: \(\Q(\sqrt{-1}) \)
Fixed field: 4.0.968877.2

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(11\) \(16\) \(17\) \(19\) \(20\)
\(\chi_{273}(83,\cdot)\) \(-1\) \(1\) \(i\) \(-1\) \(-i\) \(-i\) \(1\) \(-i\) \(1\) \(-1\) \(i\) \(i\)
\(\chi_{273}(125,\cdot)\) \(-1\) \(1\) \(-i\) \(-1\) \(i\) \(i\) \(1\) \(i\) \(1\) \(-1\) \(-i\) \(-i\)