Properties

Modulus 6048
Conductor 756
Order 18
Real no
Primitive no
Minimal yes
Parity even
Orbit label 6048.ff

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(6048)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([9,0,8,15]))
 
pari: [g,chi] = znchar(Mod(607,6048))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 6048
Conductor = 756
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 18
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 6048.ff
Orbit index = 136

Galois orbit

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

\(\chi_{6048}(607,\cdot)\) \(\chi_{6048}(1375,\cdot)\) \(\chi_{6048}(2623,\cdot)\) \(\chi_{6048}(3391,\cdot)\) \(\chi_{6048}(4639,\cdot)\) \(\chi_{6048}(5407,\cdot)\)

Values on generators

\((4159,3781,3809,2593)\) → \((-1,1,e\left(\frac{4}{9}\right),e\left(\frac{5}{6}\right))\)

Values

-115111317192325293137
\(1\)\(1\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{1}{18}\right)\)\(-1\)\(1\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{1}{3}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{9})\)