Properties

Label 2304.23
Modulus $2304$
Conductor $1152$
Order $96$
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([48,21,80]))
 
pari: [g,chi] = znchar(Mod(23,2304))
 

Basic properties

Modulus: \(2304\)
Conductor: \(1152\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(96\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1152}(851,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2304.bw

\(\chi_{2304}(23,\cdot)\) \(\chi_{2304}(119,\cdot)\) \(\chi_{2304}(167,\cdot)\) \(\chi_{2304}(263,\cdot)\) \(\chi_{2304}(311,\cdot)\) \(\chi_{2304}(407,\cdot)\) \(\chi_{2304}(455,\cdot)\) \(\chi_{2304}(551,\cdot)\) \(\chi_{2304}(599,\cdot)\) \(\chi_{2304}(695,\cdot)\) \(\chi_{2304}(743,\cdot)\) \(\chi_{2304}(839,\cdot)\) \(\chi_{2304}(887,\cdot)\) \(\chi_{2304}(983,\cdot)\) \(\chi_{2304}(1031,\cdot)\) \(\chi_{2304}(1127,\cdot)\) \(\chi_{2304}(1175,\cdot)\) \(\chi_{2304}(1271,\cdot)\) \(\chi_{2304}(1319,\cdot)\) \(\chi_{2304}(1415,\cdot)\) \(\chi_{2304}(1463,\cdot)\) \(\chi_{2304}(1559,\cdot)\) \(\chi_{2304}(1607,\cdot)\) \(\chi_{2304}(1703,\cdot)\) \(\chi_{2304}(1751,\cdot)\) \(\chi_{2304}(1847,\cdot)\) \(\chi_{2304}(1895,\cdot)\) \(\chi_{2304}(1991,\cdot)\) \(\chi_{2304}(2039,\cdot)\) \(\chi_{2304}(2135,\cdot)\) ...

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

\((1279,2053,1793)\) → \((-1,e\left(\frac{7}{32}\right),e\left(\frac{5}{6}\right))\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{37}{96}\right)\)\(e\left(\frac{1}{48}\right)\)\(e\left(\frac{89}{96}\right)\)\(e\left(\frac{91}{96}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{17}{32}\right)\)\(e\left(\frac{35}{48}\right)\)\(e\left(\frac{37}{48}\right)\)\(e\left(\frac{71}{96}\right)\)\(e\left(\frac{11}{12}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{96})$
Fixed field: Number field defined by a degree 96 polynomial