Properties

Label 1344.5
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([0,3,24,40]))
 
pari: [g,chi] = znchar(Mod(5,1344))
 

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.cw

\(\chi_{1344}(5,\cdot)\) \(\chi_{1344}(101,\cdot)\) \(\chi_{1344}(173,\cdot)\) \(\chi_{1344}(269,\cdot)\) \(\chi_{1344}(341,\cdot)\) \(\chi_{1344}(437,\cdot)\) \(\chi_{1344}(509,\cdot)\) \(\chi_{1344}(605,\cdot)\) \(\chi_{1344}(677,\cdot)\) \(\chi_{1344}(773,\cdot)\) \(\chi_{1344}(845,\cdot)\) \(\chi_{1344}(941,\cdot)\) \(\chi_{1344}(1013,\cdot)\) \(\chi_{1344}(1109,\cdot)\) \(\chi_{1344}(1181,\cdot)\) \(\chi_{1344}(1277,\cdot)\)

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

\((127,1093,449,577)\) → \((1,e\left(\frac{1}{16}\right),-1,e\left(\frac{5}{6}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\(1\)\(1\)\(e\left(\frac{35}{48}\right)\)\(e\left(\frac{7}{48}\right)\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{29}{48}\right)\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{11}{24}\right)\)\(e\left(\frac{3}{16}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{11}{48}\right)\)
value at e.g. 2

Related number fields

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