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Properties

Label 5593.1381
Modulus $5593$
Conductor $5593$
Order $276$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the Dirichlet character
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5593, base_ring=CyclotomicField(276)) M = H._module chi = DirichletCharacter(H, M([92,207,72]))
 
Copy content gp:[g,chi] = znchar(Mod(1381, 5593))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5593.1381");
 

Basic properties

Modulus: \(5593\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(5593\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(276\)
Copy content comment:Order
 
Copy content sage:chi.multiplicative_order()
 
Copy content gp:charorder(g,chi)
 
Copy content magma:Order(chi);
 
Real: no
Copy content comment:Whether the character is real
 
Copy content sage:chi.multiplicative_order() <= 2
 
Copy content gp:charorder(g,chi) <= 2
 
Copy content magma:Order(chi) le 2;
 
Primitive: yes
Copy content comment:If the character is primitive
 
Copy content sage:chi.is_primitive()
 
Copy content gp:#znconreyconductor(g,chi)==1
 
Copy content magma:IsPrimitive(chi);
 
Minimal: yes
Parity: even
Copy content comment:Parity
 
Copy content sage:chi.is_odd()
 
Copy content gp:zncharisodd(g,chi)
 
Copy content magma:IsOdd(chi);
 

Galois orbit 5593.cn

\(\chi_{5593}(4,\cdot)\) \(\chi_{5593}(72,\cdot)\) \(\chi_{5593}(81,\cdot)\) \(\chi_{5593}(149,\cdot)\) \(\chi_{5593}(191,\cdot)\) \(\chi_{5593}(200,\cdot)\) \(\chi_{5593}(242,\cdot)\) \(\chi_{5593}(310,\cdot)\) \(\chi_{5593}(319,\cdot)\) \(\chi_{5593}(361,\cdot)\) \(\chi_{5593}(429,\cdot)\) \(\chi_{5593}(506,\cdot)\) \(\chi_{5593}(625,\cdot)\) \(\chi_{5593}(667,\cdot)\) \(\chi_{5593}(676,\cdot)\) \(\chi_{5593}(786,\cdot)\) \(\chi_{5593}(863,\cdot)\) \(\chi_{5593}(905,\cdot)\) \(\chi_{5593}(914,\cdot)\) \(\chi_{5593}(956,\cdot)\) \(\chi_{5593}(982,\cdot)\) \(\chi_{5593}(1024,\cdot)\) \(\chi_{5593}(1152,\cdot)\) \(\chi_{5593}(1271,\cdot)\) \(\chi_{5593}(1381,\cdot)\) \(\chi_{5593}(1390,\cdot)\) \(\chi_{5593}(1619,\cdot)\) \(\chi_{5593}(1670,\cdot)\) \(\chi_{5593}(1696,\cdot)\) \(\chi_{5593}(1747,\cdot)\) ...

Copy content comment:Galois orbit
 
Copy content sage:chi.galois_orbit()
 
Copy content gp:order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 
Copy content magma:order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };
 

Related number fields

Field of values: $\Q(\zeta_{276})$
Fixed field: Number field defined by a degree 276 polynomial (not computed)

Values on generators

\((1599,1975,4047)\) → \((e\left(\frac{1}{3}\right),-i,e\left(\frac{6}{23}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(8\)\(9\)\(10\)\(11\)\(12\)
\( \chi_{ 5593 }(1381, a) \) \(1\)\(1\)\(e\left(\frac{119}{138}\right)\)\(e\left(\frac{83}{276}\right)\)\(e\left(\frac{50}{69}\right)\)\(e\left(\frac{187}{276}\right)\)\(e\left(\frac{15}{92}\right)\)\(e\left(\frac{27}{46}\right)\)\(e\left(\frac{83}{138}\right)\)\(e\left(\frac{149}{276}\right)\)\(e\left(\frac{113}{276}\right)\)\(e\left(\frac{7}{276}\right)\)
Copy content comment:Value of chi at x
 
Copy content sage:chi(x)
 
Copy content gp:chareval(g,chi,x) \\\\ x integer, value in Q/Z'
 
Copy content magma:chi(x)
 
\( \chi_{ 5593 }(1381,a) \;\) at \(\;a = \) e.g. 2