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Properties

Label 2793.2081
Modulus $2793$
Conductor $2793$
Order $126$
Real no
Primitive yes
Minimal yes
Parity even

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(2793, base_ring=CyclotomicField(126)) M = H._module chi = DirichletCharacter(H, M([63,114,119]))
 
Copy content gp:[g,chi] = znchar(Mod(2081, 2793))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2793.2081");
 

Basic properties

Modulus: \(2793\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(2793\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(126\)
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 2793.es

\(\chi_{2793}(86,\cdot)\) \(\chi_{2793}(242,\cdot)\) \(\chi_{2793}(317,\cdot)\) \(\chi_{2793}(326,\cdot)\) \(\chi_{2793}(338,\cdot)\) \(\chi_{2793}(485,\cdot)\) \(\chi_{2793}(515,\cdot)\) \(\chi_{2793}(641,\cdot)\) \(\chi_{2793}(725,\cdot)\) \(\chi_{2793}(737,\cdot)\) \(\chi_{2793}(884,\cdot)\) \(\chi_{2793}(914,\cdot)\) \(\chi_{2793}(1040,\cdot)\) \(\chi_{2793}(1115,\cdot)\) \(\chi_{2793}(1124,\cdot)\) \(\chi_{2793}(1136,\cdot)\) \(\chi_{2793}(1283,\cdot)\) \(\chi_{2793}(1313,\cdot)\) \(\chi_{2793}(1514,\cdot)\) \(\chi_{2793}(1523,\cdot)\) \(\chi_{2793}(1535,\cdot)\) \(\chi_{2793}(1682,\cdot)\) \(\chi_{2793}(1712,\cdot)\) \(\chi_{2793}(1838,\cdot)\) \(\chi_{2793}(1913,\cdot)\) \(\chi_{2793}(1922,\cdot)\) \(\chi_{2793}(1934,\cdot)\) \(\chi_{2793}(2081,\cdot)\) \(\chi_{2793}(2111,\cdot)\) \(\chi_{2793}(2237,\cdot)\) ...

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: $\Q(\zeta_{63})$
Fixed field: Number field defined by a degree 126 polynomial (not computed)

Values on generators

\((932,2110,2206)\) → \((-1,e\left(\frac{19}{21}\right),e\left(\frac{17}{18}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(13\)\(16\)\(17\)\(20\)
\( \chi_{ 2793 }(2081, a) \) \(1\)\(1\)\(e\left(\frac{61}{63}\right)\)\(e\left(\frac{59}{63}\right)\)\(e\left(\frac{107}{126}\right)\)\(e\left(\frac{19}{21}\right)\)\(e\left(\frac{103}{126}\right)\)\(e\left(\frac{1}{42}\right)\)\(e\left(\frac{73}{126}\right)\)\(e\left(\frac{55}{63}\right)\)\(e\left(\frac{71}{126}\right)\)\(e\left(\frac{11}{14}\right)\)
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)
 
\( \chi_{ 2793 }(2081,a) \;\) at \(\;a = \) e.g. 2