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Properties

Label 663.bv
Modulus $663$
Conductor $221$
Order $12$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(663, base_ring=CyclotomicField(12)) M = H._module chi = DirichletCharacter(H, M([0,4,9])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(55,663)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(663\)
Conductor: \(221\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(12\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 221.x
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{12})\)
Fixed field: 12.12.96735773996756764337.1

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(7\) \(8\) \(10\) \(11\) \(14\) \(16\) \(19\)
\(\chi_{663}(55,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(e\left(\frac{11}{12}\right)\) \(-1\) \(e\left(\frac{7}{12}\right)\) \(e\left(\frac{7}{12}\right)\) \(-i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{663}(217,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(i\) \(e\left(\frac{1}{12}\right)\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{5}{12}\right)\) \(i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{663}(412,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(e\left(\frac{7}{12}\right)\) \(-1\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{11}{12}\right)\) \(-i\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{663}(523,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\) \(i\) \(e\left(\frac{5}{12}\right)\) \(-1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{12}\right)\) \(i\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{6}\right)\)