Properties

Modulus 6017
Conductor 6017
Order 42
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6017.bd

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(6017)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([21,41]))
 
pari: [g,chi] = znchar(Mod(3871,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 6017
Conductor = 6017
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 42
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 6017.bd
Orbit index = 30

Galois orbit

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{6017}(120,\cdot)\) \(\chi_{6017}(351,\cdot)\) \(\chi_{6017}(1627,\cdot)\) \(\chi_{6017}(2375,\cdot)\) \(\chi_{6017}(3156,\cdot)\) \(\chi_{6017}(3321,\cdot)\) \(\chi_{6017}(3651,\cdot)\) \(\chi_{6017}(3706,\cdot)\) \(\chi_{6017}(3816,\cdot)\) \(\chi_{6017}(3871,\cdot)\) \(\chi_{6017}(4806,\cdot)\) \(\chi_{6017}(5301,\cdot)\)

Values on generators

\((3830,2190)\) → \((-1,e\left(\frac{41}{42}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{10}{21}\right)\)\(e\left(\frac{11}{14}\right)\)\(e\left(\frac{20}{21}\right)\)\(e\left(\frac{31}{42}\right)\)\(e\left(\frac{11}{42}\right)\)\(e\left(\frac{1}{21}\right)\)\(e\left(\frac{3}{7}\right)\)\(e\left(\frac{4}{7}\right)\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{31}{42}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{21})\)