Properties

Label 2304.47
Modulus $2304$
Conductor $576$
Order $48$
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(2304)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([24,33,8]))
 
pari: [g,chi] = znchar(Mod(47,2304))
 

Basic properties

Modulus: \(2304\)
Conductor: \(576\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(48\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{576}(227,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2304.bp

\(\chi_{2304}(47,\cdot)\) \(\chi_{2304}(239,\cdot)\) \(\chi_{2304}(335,\cdot)\) \(\chi_{2304}(527,\cdot)\) \(\chi_{2304}(623,\cdot)\) \(\chi_{2304}(815,\cdot)\) \(\chi_{2304}(911,\cdot)\) \(\chi_{2304}(1103,\cdot)\) \(\chi_{2304}(1199,\cdot)\) \(\chi_{2304}(1391,\cdot)\) \(\chi_{2304}(1487,\cdot)\) \(\chi_{2304}(1679,\cdot)\) \(\chi_{2304}(1775,\cdot)\) \(\chi_{2304}(1967,\cdot)\) \(\chi_{2304}(2063,\cdot)\) \(\chi_{2304}(2255,\cdot)\)

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

\((1279,2053,1793)\) → \((-1,e\left(\frac{11}{16}\right),e\left(\frac{1}{6}\right))\)

Values

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

Related number fields

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