Properties

Label 1344.17
Modulus $1344$
Conductor $336$
Order $12$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1344)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,9,6,2]))
 
pari: [g,chi] = znchar(Mod(17,1344))
 

Basic properties

Modulus: \(1344\)
Conductor: \(336\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(12\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{336}(269,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1344.bw

\(\chi_{1344}(17,\cdot)\) \(\chi_{1344}(593,\cdot)\) \(\chi_{1344}(689,\cdot)\) \(\chi_{1344}(1265,\cdot)\)

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

\((127,1093,449,577)\) → \((1,-i,-1,e\left(\frac{1}{6}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\(1\)\(1\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{11}{12}\right)\)\(-i\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{1}{6}\right)\)\(-i\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{12}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{12})\)
Fixed field: 12.12.1768877612408537874432.1