Properties

Label 1344.89
Modulus $1344$
Conductor $672$
Order $24$
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([0,3,12,20]))
 
pari: [g,chi] = znchar(Mod(89,1344))
 

Basic properties

Modulus: \(1344\)
Conductor: \(672\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(24\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{672}(5,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1344.ct

\(\chi_{1344}(89,\cdot)\) \(\chi_{1344}(185,\cdot)\) \(\chi_{1344}(425,\cdot)\) \(\chi_{1344}(521,\cdot)\) \(\chi_{1344}(761,\cdot)\) \(\chi_{1344}(857,\cdot)\) \(\chi_{1344}(1097,\cdot)\) \(\chi_{1344}(1193,\cdot)\)

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

\((127,1093,449,577)\) → \((1,e\left(\frac{1}{8}\right),-1,e\left(\frac{5}{6}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\(1\)\(1\)\(e\left(\frac{19}{24}\right)\)\(e\left(\frac{11}{24}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{19}{24}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{24})\)
Fixed field: 24.24.419957608266393538093113781921531638278568932278272.1