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Properties

Label 176.l
Modulus $176$
Conductor $176$
Order $4$
Real no
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(176, base_ring=CyclotomicField(4)) M = H._module chi = DirichletCharacter(H, M([0,1,2])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(21,176)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(176\)
Conductor: \(176\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(4\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
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: \(\mathbb{Q}(i)\)
Fixed field: 4.0.247808.2

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(13\) \(15\) \(17\) \(19\) \(21\) \(23\)
\(\chi_{176}(21,\cdot)\) \(-1\) \(1\) \(-i\) \(i\) \(1\) \(-1\) \(i\) \(1\) \(-1\) \(i\) \(-i\) \(-1\)
\(\chi_{176}(109,\cdot)\) \(-1\) \(1\) \(i\) \(-i\) \(1\) \(-1\) \(-i\) \(1\) \(-1\) \(-i\) \(i\) \(-1\)