Properties

Modulus 6017
Conductor 547
Order 13
Real no
Primitive no
Minimal yes
Parity even
Orbit label 6017.n

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([0,11]))
 
pari: [g,chi] = znchar(Mod(5820,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 6017
Conductor = 547
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 13
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 6017.n
Orbit index = 14

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 ]
 

\(\chi_{6017}(353,\cdot)\) \(\chi_{6017}(375,\cdot)\) \(\chi_{6017}(1387,\cdot)\) \(\chi_{6017}(2234,\cdot)\) \(\chi_{6017}(2663,\cdot)\) \(\chi_{6017}(2707,\cdot)\) \(\chi_{6017}(3543,\cdot)\) \(\chi_{6017}(4269,\cdot)\) \(\chi_{6017}(4346,\cdot)\) \(\chi_{6017}(4885,\cdot)\) \(\chi_{6017}(5160,\cdot)\) \(\chi_{6017}(5820,\cdot)\)

Values on generators

\((3830,2190)\) → \((1,e\left(\frac{11}{13}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{11}{13}\right)\)\(1\)\(e\left(\frac{9}{13}\right)\)\(e\left(\frac{6}{13}\right)\)\(e\left(\frac{11}{13}\right)\)\(e\left(\frac{2}{13}\right)\)\(e\left(\frac{7}{13}\right)\)\(1\)\(e\left(\frac{4}{13}\right)\)\(e\left(\frac{9}{13}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{13})\)