Properties

Label 24.h
Modulus 2424
Conductor 2424
Order 22
Real yes
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(24, base_ring=CyclotomicField(2)) M = H._module chi = DirichletCharacter(H, M([0,1,1])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(5,24)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Kronecker symbol representation

Copy content sage:kronecker_character(-24)
 
Copy content pari:znchartokronecker(g,chi)
 

(24)\displaystyle\left(\frac{-24}{\bullet}\right)

Basic properties

Modulus: 2424
Conductor: 2424
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: 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: Q\Q
Fixed field: Q(6)\Q(\sqrt{-6})

Characters in Galois orbit

Character 1-1 11 55 77 1111 1313 1717 1919
χ24(5,)\chi_{24}(5,\cdot) 1-1 11 11 11 11 1-1 1-1 1-1