# SageMath code for working with Dirichlet character orbit 2600.fn


# Define the Dirichlet character orbit: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2600, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([30,30,39,5]))
chi.galois_orbit()

# 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()

# Field of values of chi: 
CyclotomicField(chi.multiplicative_order())

# Fixed field: 
chi.fixed_field()