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Properties

Label 11593.40
Modulus $11593$
Conductor $11593$
Order $1656$
Real no
Primitive yes
Minimal yes
Parity odd

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(11593, base_ring=CyclotomicField(1656)) M = H._module chi = DirichletCharacter(H, M([1141]))
 
Copy content gp:[g,chi] = znchar(Mod(40, 11593))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("11593.40");
 

Basic properties

Modulus: \(11593\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(11593\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(1656\)
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: odd
Copy content comment:Parity
 
Copy content sage:chi.is_odd()
 
Copy content gp:zncharisodd(g,chi)
 
Copy content magma:IsOdd(chi);
 

Galois orbit 11593.bq

\(\chi_{11593}(11,\cdot)\) \(\chi_{11593}(30,\cdot)\) \(\chi_{11593}(40,\cdot)\) \(\chi_{11593}(83,\cdot)\) \(\chi_{11593}(93,\cdot)\) \(\chi_{11593}(114,\cdot)\) \(\chi_{11593}(124,\cdot)\) \(\chi_{11593}(152,\cdot)\) \(\chi_{11593}(197,\cdot)\) \(\chi_{11593}(226,\cdot)\) \(\chi_{11593}(253,\cdot)\) \(\chi_{11593}(255,\cdot)\) \(\chi_{11593}(258,\cdot)\) \(\chi_{11593}(263,\cdot)\) \(\chi_{11593}(267,\cdot)\) \(\chi_{11593}(290,\cdot)\) \(\chi_{11593}(340,\cdot)\) \(\chi_{11593}(344,\cdot)\) \(\chi_{11593}(356,\cdot)\) \(\chi_{11593}(375,\cdot)\) \(\chi_{11593}(423,\cdot)\) \(\chi_{11593}(500,\cdot)\) \(\chi_{11593}(509,\cdot)\) \(\chi_{11593}(539,\cdot)\) \(\chi_{11593}(564,\cdot)\) \(\chi_{11593}(594,\cdot)\) \(\chi_{11593}(603,\cdot)\) \(\chi_{11593}(611,\cdot)\) \(\chi_{11593}(662,\cdot)\) \(\chi_{11593}(671,\cdot)\) ...

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: $\Q(\zeta_{1656})$
Fixed field: Number field defined by a degree 1656 polynomial (not computed)

Values on generators

\(5\) → \(e\left(\frac{1141}{1656}\right)\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\( \chi_{ 11593 }(40, a) \) \(-1\)\(1\)\(e\left(\frac{395}{828}\right)\)\(e\left(\frac{263}{414}\right)\)\(e\left(\frac{395}{414}\right)\)\(e\left(\frac{1141}{1656}\right)\)\(e\left(\frac{31}{276}\right)\)\(e\left(\frac{1}{828}\right)\)\(e\left(\frac{119}{276}\right)\)\(e\left(\frac{56}{207}\right)\)\(e\left(\frac{275}{1656}\right)\)\(e\left(\frac{1471}{1656}\right)\)
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)
 
\( \chi_{ 11593 }(40,a) \;\) at \(\;a = \) e.g. 2