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Properties

Label 4783.23
Modulus $4783$
Conductor $4783$
Order $797$
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(4783, base_ring=CyclotomicField(1594)) M = H._module chi = DirichletCharacter(H, M([194]))
 
Copy content gp:[g,chi] = znchar(Mod(23, 4783))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4783.23");
 

Basic properties

Modulus: \(4783\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(4783\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(797\)
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 4783.e

\(\chi_{4783}(8,\cdot)\) \(\chi_{4783}(9,\cdot)\) \(\chi_{4783}(15,\cdot)\) \(\chi_{4783}(21,\cdot)\) \(\chi_{4783}(23,\cdot)\) \(\chi_{4783}(25,\cdot)\) \(\chi_{4783}(26,\cdot)\) \(\chi_{4783}(35,\cdot)\) \(\chi_{4783}(37,\cdot)\) \(\chi_{4783}(49,\cdot)\) \(\chi_{4783}(51,\cdot)\) \(\chi_{4783}(61,\cdot)\) \(\chi_{4783}(64,\cdot)\) \(\chi_{4783}(66,\cdot)\) \(\chi_{4783}(72,\cdot)\) \(\chi_{4783}(73,\cdot)\) \(\chi_{4783}(76,\cdot)\) \(\chi_{4783}(81,\cdot)\) \(\chi_{4783}(83,\cdot)\) \(\chi_{4783}(85,\cdot)\) \(\chi_{4783}(93,\cdot)\) \(\chi_{4783}(110,\cdot)\) \(\chi_{4783}(119,\cdot)\) \(\chi_{4783}(120,\cdot)\) \(\chi_{4783}(131,\cdot)\) \(\chi_{4783}(135,\cdot)\) \(\chi_{4783}(154,\cdot)\) \(\chi_{4783}(155,\cdot)\) \(\chi_{4783}(158,\cdot)\) \(\chi_{4783}(168,\cdot)\) ...

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: $\Q(\zeta_{797})$
Fixed field: Number field defined by a degree 797 polynomial (not computed)

Values on generators

\(6\) → \(e\left(\frac{97}{797}\right)\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\( \chi_{ 4783 }(23, a) \) \(1\)\(1\)\(e\left(\frac{427}{797}\right)\)\(e\left(\frac{467}{797}\right)\)\(e\left(\frac{57}{797}\right)\)\(e\left(\frac{344}{797}\right)\)\(e\left(\frac{97}{797}\right)\)\(e\left(\frac{104}{797}\right)\)\(e\left(\frac{484}{797}\right)\)\(e\left(\frac{137}{797}\right)\)\(e\left(\frac{771}{797}\right)\)\(e\left(\frac{241}{797}\right)\)
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)
 
\( \chi_{ 4783 }(23,a) \;\) at \(\;a = \) e.g. 2