Properties

Label 2183.1014
Modulus $2183$
Conductor $2183$
Order $1044$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2183, base_ring=CyclotomicField(1044)) M = H._module chi = DirichletCharacter(H, M([377,450]))
 
Copy content pari:[g,chi] = znchar(Mod(1014,2183))
 

Basic properties

Modulus: \(2183\)
Conductor: \(2183\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(1044\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: yes
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 2183.bi

\(\chi_{2183}(2,\cdot)\) \(\chi_{2183}(13,\cdot)\) \(\chi_{2183}(18,\cdot)\) \(\chi_{2183}(24,\cdot)\) \(\chi_{2183}(32,\cdot)\) \(\chi_{2183}(39,\cdot)\) \(\chi_{2183}(42,\cdot)\) \(\chi_{2183}(50,\cdot)\) \(\chi_{2183}(52,\cdot)\) \(\chi_{2183}(54,\cdot)\) \(\chi_{2183}(55,\cdot)\) \(\chi_{2183}(56,\cdot)\) \(\chi_{2183}(61,\cdot)\) \(\chi_{2183}(69,\cdot)\) \(\chi_{2183}(72,\cdot)\) \(\chi_{2183}(89,\cdot)\) \(\chi_{2183}(91,\cdot)\) \(\chi_{2183}(92,\cdot)\) \(\chi_{2183}(93,\cdot)\) \(\chi_{2183}(96,\cdot)\) \(\chi_{2183}(98,\cdot)\) \(\chi_{2183}(106,\cdot)\) \(\chi_{2183}(109,\cdot)\) \(\chi_{2183}(113,\cdot)\) \(\chi_{2183}(124,\cdot)\) \(\chi_{2183}(126,\cdot)\) \(\chi_{2183}(128,\cdot)\) \(\chi_{2183}(129,\cdot)\) \(\chi_{2183}(131,\cdot)\) \(\chi_{2183}(150,\cdot)\) ...

Copy content sage:chi.galois_orbit()
 
Copy content pari:order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: $\Q(\zeta_{1044})$
Fixed field: Number field defined by a degree 1044 polynomial (not computed)

Values on generators

\((1889,297)\) → \((e\left(\frac{13}{36}\right),e\left(\frac{25}{58}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\( \chi_{ 2183 }(1014, a) \) \(1\)\(1\)\(e\left(\frac{827}{1044}\right)\)\(e\left(\frac{491}{522}\right)\)\(e\left(\frac{305}{522}\right)\)\(e\left(\frac{931}{1044}\right)\)\(e\left(\frac{85}{116}\right)\)\(e\left(\frac{82}{261}\right)\)\(e\left(\frac{131}{348}\right)\)\(e\left(\frac{230}{261}\right)\)\(e\left(\frac{119}{174}\right)\)\(e\left(\frac{53}{87}\right)\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 2183 }(1014,a) \;\) at \(\;a = \) e.g. 2