Properties

Label 2304.97
Modulus $2304$
Conductor $288$
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(2304)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,15,16]))
 
pari: [g,chi] = znchar(Mod(97,2304))
 

Basic properties

Modulus: \(2304\)
Conductor: \(288\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(24\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{288}(277,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2304.bg

\(\chi_{2304}(97,\cdot)\) \(\chi_{2304}(481,\cdot)\) \(\chi_{2304}(673,\cdot)\) \(\chi_{2304}(1057,\cdot)\) \(\chi_{2304}(1249,\cdot)\) \(\chi_{2304}(1633,\cdot)\) \(\chi_{2304}(1825,\cdot)\) \(\chi_{2304}(2209,\cdot)\)

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

\((1279,2053,1793)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{2}{3}\right))\)

Values

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

Related number fields

Field of values: \(\Q(\zeta_{24})\)
Fixed field: 24.24.18351423083070806589199715754737431920771072.1