# SageMath code for working with Dirichlet character 1309.w.1233


# Define the Dirichlet character: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1309, base_ring=CyclotomicField(8))
M = H._module
chi = DirichletCharacter(H, M([0,0,1]))

# Modulus: 
chi.modulus()

# Conductor: 
chi.conductor()

# Order: 
chi.multiplicative_order()

# Whether the character is real: 
chi.multiplicative_order() <= 2

# If the character is primitive: 
chi.is_primitive()

# Parity: 
chi.is_odd()

# Galois orbit: 
chi.galois_orbit()