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Properties

Label 5733.fb
Modulus $5733$
Conductor $819$
Order $12$
Real no
Primitive no
Minimal no
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5733, base_ring=CyclotomicField(12)) M = H._module chi = DirichletCharacter(H, M([4,2,1])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(1354,5733)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(5733\)
Conductor: \(819\)
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 819.fa
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
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: 12.12.21792013086393181607025441573.4

Characters in Galois orbit

Character \(-1\) \(1\) \(2\) \(4\) \(5\) \(8\) \(10\) \(11\) \(16\) \(17\) \(19\) \(20\)
\(\chi_{5733}(1354,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(i\) \(i\) \(1\) \(e\left(\frac{7}{12}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(i\) \(-i\)
\(\chi_{5733}(3118,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(-i\) \(-i\) \(1\) \(e\left(\frac{1}{12}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(-i\) \(i\)
\(\chi_{5733}(3400,\cdot)\) \(1\) \(1\) \(i\) \(-1\) \(-i\) \(-i\) \(1\) \(e\left(\frac{5}{12}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-i\) \(i\)
\(\chi_{5733}(3841,\cdot)\) \(1\) \(1\) \(-i\) \(-1\) \(i\) \(i\) \(1\) \(e\left(\frac{11}{12}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(i\) \(-i\)