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Properties

Label 228.b
Modulus $228$
Conductor $228$
Order $2$
Real yes
Primitive yes
Minimal yes
Parity odd

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(228, base_ring=CyclotomicField(2)) M = H._module chi = DirichletCharacter(H, M([1,1,1])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(227,228)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Kronecker symbol representation

Copy content sage:kronecker_character(-228)
 
Copy content pari:znchartokronecker(g,chi)
 

\(\displaystyle\left(\frac{-228}{\bullet}\right)\)

Basic properties

Modulus: \(228\)
Conductor: \(228\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(2\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: yes
Primitive: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q\)
Fixed field: \(\Q(\sqrt{-57}) \)

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(23\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{228}(227,\cdot)\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(1\) \(1\) \(1\) \(1\)