# SageMath code for working with Dirichlet character 6076.eq.4315


# Define the Dirichlet character: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6076, base_ring=CyclotomicField(42))
M = H._module
chi = DirichletCharacter(H, M([21,1,35]))

# 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()

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

# Fixed field: 
chi.fixed_field()