Properties

Label 6012.2671
Modulus $6012$
Conductor $6012$
Order $6$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(6012)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([3,4,3]))
 
pari: [g,chi] = znchar(Mod(2671,6012))
 

Basic properties

Modulus: \(6012\)
Conductor: \(6012\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(6\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6012.p

\(\chi_{6012}(2671,\cdot)\) \(\chi_{6012}(4675,\cdot)\)

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

Values on generators

\((3007,3341,4681)\) → \((-1,e\left(\frac{2}{3}\right),-1)\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{5}{6}\right)\)\(-1\)\(-1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{5}{6}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\sqrt{-3}) \)
Fixed field: 6.6.1955687343552.1