Properties

Label 3800.h
Modulus 38003800
Conductor 1919
Order 22
Real yes
Primitive no
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3800, base_ring=CyclotomicField(2)) M = H._module chi = DirichletCharacter(H, M([0,0,0,1])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(3001,3800)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: 38003800
Conductor: 1919
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: 22
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: yes
Primitive: no, induced from 19.b
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\Q
Fixed field: Q(19)\Q(\sqrt{-19})

Characters in Galois orbit

Character 1-1 11 33 77 99 1111 1313 1717 2121 2323 2727 2929
χ3800(3001,)\chi_{3800}(3001,\cdot) 1-1 11 1-1 11 11 11 1-1 11 1-1 11 1-1 1-1