↑

Properties

Label 5899.1095
Modulus $5899$
Conductor $5899$
Order $2768$
Real no
Primitive yes
Minimal yes
Parity even

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(5899, base_ring=CyclotomicField(2768)) M = H._module chi = DirichletCharacter(H, M([1903,888]))
 
Copy content gp:[g,chi] = znchar(Mod(1095, 5899))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5899.1095");
 

Basic properties

Modulus: \(5899\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(5899\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(2768\)
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 5899.t

\(\chi_{5899}(5,\cdot)\) \(\chi_{5899}(6,\cdot)\) \(\chi_{5899}(7,\cdot)\) \(\chi_{5899}(20,\cdot)\) \(\chi_{5899}(22,\cdot)\) \(\chi_{5899}(23,\cdot)\) \(\chi_{5899}(24,\cdot)\) \(\chi_{5899}(28,\cdot)\) \(\chi_{5899}(37,\cdot)\) \(\chi_{5899}(41,\cdot)\) \(\chi_{5899}(45,\cdot)\) \(\chi_{5899}(54,\cdot)\) \(\chi_{5899}(57,\cdot)\) \(\chi_{5899}(58,\cdot)\) \(\chi_{5899}(62,\cdot)\) \(\chi_{5899}(63,\cdot)\) \(\chi_{5899}(65,\cdot)\) \(\chi_{5899}(78,\cdot)\) \(\chi_{5899}(79,\cdot)\) \(\chi_{5899}(80,\cdot)\) \(\chi_{5899}(88,\cdot)\) \(\chi_{5899}(91,\cdot)\) \(\chi_{5899}(92,\cdot)\) \(\chi_{5899}(96,\cdot)\) \(\chi_{5899}(97,\cdot)\) \(\chi_{5899}(112,\cdot)\) \(\chi_{5899}(122,\cdot)\) \(\chi_{5899}(125,\cdot)\) \(\chi_{5899}(139,\cdot)\) \(\chi_{5899}(141,\cdot)\) ...

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: $\Q(\zeta_{2768})$
Fixed field: Number field defined by a degree 2768 polynomial (not computed)

Values on generators

\((3471,4166)\) → \((e\left(\frac{11}{16}\right),e\left(\frac{111}{346}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\( \chi_{ 5899 }(1095, a) \) \(1\)\(1\)\(e\left(\frac{1309}{1384}\right)\)\(e\left(\frac{1247}{2768}\right)\)\(e\left(\frac{617}{692}\right)\)\(e\left(\frac{835}{2768}\right)\)\(e\left(\frac{1097}{2768}\right)\)\(e\left(\frac{765}{2768}\right)\)\(e\left(\frac{1159}{1384}\right)\)\(e\left(\frac{1247}{1384}\right)\)\(e\left(\frac{685}{2768}\right)\)\(e\left(\frac{201}{2768}\right)\)
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)
 
\( \chi_{ 5899 }(1095,a) \;\) at \(\;a = \) e.g. 2