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Properties

Label 4883.698
Modulus $4883$
Conductor $4883$
Order $576$
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(4883, base_ring=CyclotomicField(576)) M = H._module chi = DirichletCharacter(H, M([224,387]))
 
Copy content gp:[g,chi] = znchar(Mod(698, 4883))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4883.698");
 

Basic properties

Modulus: \(4883\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(4883\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(576\)
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 4883.bu

\(\chi_{4883}(22,\cdot)\) \(\chi_{4883}(67,\cdot)\) \(\chi_{4883}(70,\cdot)\) \(\chi_{4883}(117,\cdot)\) \(\chi_{4883}(146,\cdot)\) \(\chi_{4883}(162,\cdot)\) \(\chi_{4883}(165,\cdot)\) \(\chi_{4883}(184,\cdot)\) \(\chi_{4883}(211,\cdot)\) \(\chi_{4883}(222,\cdot)\) \(\chi_{4883}(268,\cdot)\) \(\chi_{4883}(279,\cdot)\) \(\chi_{4883}(280,\cdot)\) \(\chi_{4883}(338,\cdot)\) \(\chi_{4883}(345,\cdot)\) \(\chi_{4883}(352,\cdot)\) \(\chi_{4883}(374,\cdot)\) \(\chi_{4883}(433,\cdot)\) \(\chi_{4883}(447,\cdot)\) \(\chi_{4883}(470,\cdot)\) \(\chi_{4883}(584,\cdot)\) \(\chi_{4883}(602,\cdot)\) \(\chi_{4883}(637,\cdot)\) \(\chi_{4883}(648,\cdot)\) \(\chi_{4883}(660,\cdot)\) \(\chi_{4883}(679,\cdot)\) \(\chi_{4883}(698,\cdot)\) \(\chi_{4883}(725,\cdot)\) \(\chi_{4883}(736,\cdot)\) \(\chi_{4883}(782,\cdot)\) ...

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: $\Q(\zeta_{576})$
Fixed field: Number field defined by a degree 576 polynomial (not computed)

Values on generators

\((515,3858)\) → \((e\left(\frac{7}{18}\right),e\left(\frac{43}{64}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\( \chi_{ 4883 }(698, a) \) \(-1\)\(1\)\(e\left(\frac{23}{36}\right)\)\(e\left(\frac{419}{576}\right)\)\(e\left(\frac{5}{18}\right)\)\(e\left(\frac{101}{576}\right)\)\(e\left(\frac{211}{576}\right)\)\(e\left(\frac{85}{192}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{131}{288}\right)\)\(e\left(\frac{469}{576}\right)\)\(e\left(\frac{17}{48}\right)\)
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)
 
\( \chi_{ 4883 }(698,a) \;\) at \(\;a = \) e.g. 2