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Properties

Label 4998.f
Modulus $4998$
Conductor $21$
Order $2$
Real yes
Primitive no
Minimal yes
Parity even

Related objects

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4998, base_ring=CyclotomicField(2)) M = H._module chi = DirichletCharacter(H, M([1,1,0])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(4115,4998)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4998\)
Conductor: \(21\)
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: no, induced from 21.c
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q\)
Fixed field: \(\Q(\sqrt{21}) \)

Characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(11\) \(13\) \(19\) \(23\) \(25\) \(29\) \(31\) \(37\) \(41\)
\(\chi_{4998}(4115,\cdot)\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\) \(1\) \(1\)