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Properties

Label 5963.2543
Modulus $5963$
Conductor $5963$
Order $88$
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(5963, base_ring=CyclotomicField(88)) M = H._module chi = DirichletCharacter(H, M([8,7]))
 
Copy content gp:[g,chi] = znchar(Mod(2543, 5963))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5963.2543");
 

Basic properties

Modulus: \(5963\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(5963\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(88\)
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 5963.fl

\(\chi_{5963}(24,\cdot)\) \(\chi_{5963}(159,\cdot)\) \(\chi_{5963}(308,\cdot)\) \(\chi_{5963}(399,\cdot)\) \(\chi_{5963}(531,\cdot)\) \(\chi_{5963}(617,\cdot)\) \(\chi_{5963}(1203,\cdot)\) \(\chi_{5963}(1220,\cdot)\) \(\chi_{5963}(1498,\cdot)\) \(\chi_{5963}(1898,\cdot)\) \(\chi_{5963}(1965,\cdot)\) \(\chi_{5963}(2019,\cdot)\) \(\chi_{5963}(2139,\cdot)\) \(\chi_{5963}(2184,\cdot)\) \(\chi_{5963}(2287,\cdot)\) \(\chi_{5963}(2543,\cdot)\) \(\chi_{5963}(3230,\cdot)\) \(\chi_{5963}(3323,\cdot)\) \(\chi_{5963}(3575,\cdot)\) \(\chi_{5963}(3814,\cdot)\) \(\chi_{5963}(3833,\cdot)\) \(\chi_{5963}(4176,\cdot)\) \(\chi_{5963}(4243,\cdot)\) \(\chi_{5963}(4347,\cdot)\) \(\chi_{5963}(4380,\cdot)\) \(\chi_{5963}(4481,\cdot)\) \(\chi_{5963}(4504,\cdot)\) \(\chi_{5963}(4819,\cdot)\) \(\chi_{5963}(4833,\cdot)\) \(\chi_{5963}(4839,\cdot)\) ...

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: $\Q(\zeta_{88})$
Fixed field: Number field defined by a degree 88 polynomial

Values on generators

\((5697,537)\) → \((e\left(\frac{1}{11}\right),e\left(\frac{7}{88}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\( \chi_{ 5963 }(2543, a) \) \(-1\)\(1\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{41}{44}\right)\)\(e\left(\frac{87}{88}\right)\)\(e\left(\frac{47}{88}\right)\)\(e\left(\frac{1}{11}\right)\)\(i\)\(e\left(\frac{13}{44}\right)\)\(e\left(\frac{1}{22}\right)\)
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)
 
\( \chi_{ 5963 }(2543,a) \;\) at \(\;a = \) e.g. 2