Properties

Label 1344.11
Modulus $1344$
Conductor $1344$
Order $48$
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(1344)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([24,15,24,32]))
 
pari: [g,chi] = znchar(Mod(11,1344))
 

Basic properties

Modulus: \(1344\)
Conductor: \(1344\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(48\)
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 1344.cx

\(\chi_{1344}(11,\cdot)\) \(\chi_{1344}(107,\cdot)\) \(\chi_{1344}(179,\cdot)\) \(\chi_{1344}(275,\cdot)\) \(\chi_{1344}(347,\cdot)\) \(\chi_{1344}(443,\cdot)\) \(\chi_{1344}(515,\cdot)\) \(\chi_{1344}(611,\cdot)\) \(\chi_{1344}(683,\cdot)\) \(\chi_{1344}(779,\cdot)\) \(\chi_{1344}(851,\cdot)\) \(\chi_{1344}(947,\cdot)\) \(\chi_{1344}(1019,\cdot)\) \(\chi_{1344}(1115,\cdot)\) \(\chi_{1344}(1187,\cdot)\) \(\chi_{1344}(1283,\cdot)\)

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

\((127,1093,449,577)\) → \((-1,e\left(\frac{5}{16}\right),-1,e\left(\frac{2}{3}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\(1\)\(1\)\(e\left(\frac{7}{48}\right)\)\(e\left(\frac{11}{48}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{1}{48}\right)\)\(e\left(\frac{17}{24}\right)\)\(e\left(\frac{7}{24}\right)\)\(e\left(\frac{15}{16}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{7}{48}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{48})\)
Fixed field: Number field defined by a degree 48 polynomial