Properties

Label 6048.3553
Modulus $6048$
Conductor $189$
Order $9$
Real no
Primitive no
Minimal yes
Parity even

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([0,0,2,6]))
 
pari: [g,chi] = znchar(Mod(3553,6048))
 

Basic properties

Modulus: \(6048\)
Conductor: \(189\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(9\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{189}(151,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6048.du

\(\chi_{6048}(1537,\cdot)\) \(\chi_{6048}(1633,\cdot)\) \(\chi_{6048}(3553,\cdot)\) \(\chi_{6048}(3649,\cdot)\) \(\chi_{6048}(5569,\cdot)\) \(\chi_{6048}(5665,\cdot)\)

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

\((4159,3781,3809,2593)\) → \((1,1,e\left(\frac{2}{9}\right),e\left(\frac{2}{3}\right))\)

Values

\(-1\)\(1\)\(5\)\(11\)\(13\)\(17\)\(19\)\(23\)\(25\)\(29\)\(31\)\(37\)
\(1\)\(1\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{7}{9}\right)\)\(1\)\(1\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{2}{3}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{9})\)
Fixed field: 9.9.3691950281939241.2