Properties

Label 9200.bj
Modulus 92009200
Conductor 18401840
Order 44
Real no
Primitive no
Minimal no
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9200, base_ring=CyclotomicField(4)) M = H._module chi = DirichletCharacter(H, M([2,1,2,2])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(2299,9200)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 92009200
Conductor: 18401840
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 44
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 1840.bj
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: Q(i)\mathbb{Q}(i)
Fixed field: 4.4.27084800.2

Characters in Galois orbit

Character 1-1 11 33 77 99 1111 1313 1717 1919 2121 2727 2929
χ9200(2299,)\chi_{9200}(2299,\cdot) 11 11 i-i 11 1-1 ii ii 11 i-i i-i ii i-i
χ9200(6899,)\chi_{9200}(6899,\cdot) 11 11 ii 11 1-1 i-i i-i 11 ii ii i-i ii