↑

Properties

Label 4483.1083
Modulus $4483$
Conductor $4483$
Order $1494$
Real no
Primitive yes
Minimal yes
Parity odd

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the Dirichlet character
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4483, base_ring=CyclotomicField(1494)) M = H._module chi = DirichletCharacter(H, M([1349]))
 
Copy content gp:[g,chi] = znchar(Mod(1083, 4483))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4483.1083");
 

Basic properties

Modulus: \(4483\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(4483\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(1494\)
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 4483.n

\(\chi_{4483}(3,\cdot)\) \(\chi_{4483}(8,\cdot)\) \(\chi_{4483}(13,\cdot)\) \(\chi_{4483}(30,\cdot)\) \(\chi_{4483}(41,\cdot)\) \(\chi_{4483}(43,\cdot)\) \(\chi_{4483}(46,\cdot)\) \(\chi_{4483}(53,\cdot)\) \(\chi_{4483}(61,\cdot)\) \(\chi_{4483}(71,\cdot)\) \(\chi_{4483}(80,\cdot)\) \(\chi_{4483}(91,\cdot)\) \(\chi_{4483}(97,\cdot)\) \(\chi_{4483}(116,\cdot)\) \(\chi_{4483}(117,\cdot)\) \(\chi_{4483}(125,\cdot)\) \(\chi_{4483}(130,\cdot)\) \(\chi_{4483}(134,\cdot)\) \(\chi_{4483}(143,\cdot)\) \(\chi_{4483}(147,\cdot)\) \(\chi_{4483}(148,\cdot)\) \(\chi_{4483}(189,\cdot)\) \(\chi_{4483}(193,\cdot)\) \(\chi_{4483}(231,\cdot)\) \(\chi_{4483}(243,\cdot)\) \(\chi_{4483}(247,\cdot)\) \(\chi_{4483}(282,\cdot)\) \(\chi_{4483}(297,\cdot)\) \(\chi_{4483}(300,\cdot)\) \(\chi_{4483}(301,\cdot)\) ...

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: $\Q(\zeta_{747})$
Fixed field: Number field defined by a degree 1494 polynomial (not computed)

Values on generators

\(2\) → \(e\left(\frac{1349}{1494}\right)\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\( \chi_{ 4483 }(1083, a) \) \(-1\)\(1\)\(e\left(\frac{1349}{1494}\right)\)\(e\left(\frac{155}{498}\right)\)\(e\left(\frac{602}{747}\right)\)\(e\left(\frac{1369}{1494}\right)\)\(e\left(\frac{160}{747}\right)\)\(e\left(\frac{143}{249}\right)\)\(e\left(\frac{353}{498}\right)\)\(e\left(\frac{155}{249}\right)\)\(e\left(\frac{68}{83}\right)\)\(e\left(\frac{179}{249}\right)\)
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)
 
\( \chi_{ 4483 }(1083,a) \;\) at \(\;a = \) e.g. 2