Properties

Label 99.d
Modulus $99$
Conductor $33$
Order $2$
Real yes
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(2))
 
M = H._module
 
chi = DirichletCharacter(H, M([1,1]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(98,99))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(99\)
Conductor: \(33\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(2\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: no, induced from 33.d
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q\)
Fixed field: \(\Q(\sqrt{33}) \)

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(13\) \(14\) \(16\) \(17\)
\(\chi_{99}(98,\cdot)\) \(1\) \(1\) \(1\) \(1\) \(-1\) \(-1\) \(1\) \(-1\) \(-1\) \(-1\) \(1\) \(1\)