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Properties

Label 40393.18296
Modulus $40393$
Conductor $40393$
Order $186$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

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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(40393, base_ring=CyclotomicField(186)) M = H._module chi = DirichletCharacter(H, M([155,109]))
 
Copy content gp:[g,chi] = znchar(Mod(18296, 40393))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("40393.18296");
 

Basic properties

Modulus: \(40393\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(40393\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(186\)
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 40393.dh

\(\chi_{40393}(987,\cdot)\) \(\chi_{40393}(1700,\cdot)\) \(\chi_{40393}(1866,\cdot)\) \(\chi_{40393}(2165,\cdot)\) \(\chi_{40393}(3602,\cdot)\) \(\chi_{40393}(3974,\cdot)\) \(\chi_{40393}(4687,\cdot)\) \(\chi_{40393}(5823,\cdot)\) \(\chi_{40393}(8520,\cdot)\) \(\chi_{40393}(9709,\cdot)\) \(\chi_{40393}(11558,\cdot)\) \(\chi_{40393}(12550,\cdot)\) \(\chi_{40393}(12581,\cdot)\) \(\chi_{40393}(12902,\cdot)\) \(\chi_{40393}(13739,\cdot)\) \(\chi_{40393}(13801,\cdot)\) \(\chi_{40393}(14700,\cdot)\) \(\chi_{40393}(16828,\cdot)\) \(\chi_{40393}(17087,\cdot)\) \(\chi_{40393}(18068,\cdot)\) \(\chi_{40393}(18296,\cdot)\) \(\chi_{40393}(18606,\cdot)\) \(\chi_{40393}(19184,\cdot)\) \(\chi_{40393}(19339,\cdot)\) \(\chi_{40393}(19463,\cdot)\) \(\chi_{40393}(20590,\cdot)\) \(\chi_{40393}(22791,\cdot)\) \(\chi_{40393}(23473,\cdot)\) \(\chi_{40393}(23597,\cdot)\) \(\chi_{40393}(24299,\cdot)\) ...

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: $\Q(\zeta_{93})$
Fixed field: Number field defined by a degree 186 polynomial (not computed)

Values on generators

\((2607,33884)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{109}{186}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\( \chi_{ 40393 }(18296, a) \) \(1\)\(1\)\(e\left(\frac{29}{93}\right)\)\(e\left(\frac{10}{93}\right)\)\(e\left(\frac{58}{93}\right)\)\(e\left(\frac{103}{186}\right)\)\(e\left(\frac{13}{31}\right)\)\(e\left(\frac{11}{62}\right)\)\(e\left(\frac{29}{31}\right)\)\(e\left(\frac{20}{93}\right)\)\(e\left(\frac{161}{186}\right)\)\(e\left(\frac{92}{93}\right)\)
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)
 
\( \chi_{ 40393 }(18296,a) \;\) at \(\;a = \) e.g. 2