Properties

Label 2240.199
Modulus $2240$
Conductor $1120$
Order $24$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2240, base_ring=CyclotomicField(24))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([12,15,12,4]))
 
pari: [g,chi] = znchar(Mod(199,2240))
 

Basic properties

Modulus: \(2240\)
Conductor: \(1120\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(24\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1120}(619,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2240.eu

\(\chi_{2240}(199,\cdot)\) \(\chi_{2240}(439,\cdot)\) \(\chi_{2240}(759,\cdot)\) \(\chi_{2240}(999,\cdot)\) \(\chi_{2240}(1319,\cdot)\) \(\chi_{2240}(1559,\cdot)\) \(\chi_{2240}(1879,\cdot)\) \(\chi_{2240}(2119,\cdot)\)

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{24})\)
Fixed field: 24.24.192925861865498681671181009584199252836352000000000000.1

Values on generators

\((1471,1541,897,1921)\) → \((-1,e\left(\frac{5}{8}\right),-1,e\left(\frac{1}{6}\right))\)

Values

\(-1\)\(1\)\(3\)\(9\)\(11\)\(13\)\(17\)\(19\)\(23\)\(27\)\(29\)\(31\)
\(1\)\(1\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{7}{24}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{17}{24}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{2}{3}\right)\)
value at e.g. 2