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Properties

Label 10952.355
Modulus $10952$
Conductor $10952$
Order $1332$
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(10952, base_ring=CyclotomicField(1332)) M = H._module chi = DirichletCharacter(H, M([666,666,391]))
 
Copy content gp:[g,chi] = znchar(Mod(355, 10952))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("10952.355");
 

Basic properties

Modulus: \(10952\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(10952\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(1332\)
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 10952.cq

\(\chi_{10952}(19,\cdot)\) \(\chi_{10952}(35,\cdot)\) \(\chi_{10952}(59,\cdot)\) \(\chi_{10952}(91,\cdot)\) \(\chi_{10952}(131,\cdot)\) \(\chi_{10952}(163,\cdot)\) \(\chi_{10952}(187,\cdot)\) \(\chi_{10952}(203,\cdot)\) \(\chi_{10952}(227,\cdot)\) \(\chi_{10952}(235,\cdot)\) \(\chi_{10952}(283,\cdot)\) \(\chi_{10952}(291,\cdot)\) \(\chi_{10952}(315,\cdot)\) \(\chi_{10952}(331,\cdot)\) \(\chi_{10952}(355,\cdot)\) \(\chi_{10952}(387,\cdot)\) \(\chi_{10952}(427,\cdot)\) \(\chi_{10952}(459,\cdot)\) \(\chi_{10952}(483,\cdot)\) \(\chi_{10952}(499,\cdot)\) \(\chi_{10952}(523,\cdot)\) \(\chi_{10952}(531,\cdot)\) \(\chi_{10952}(579,\cdot)\) \(\chi_{10952}(587,\cdot)\) \(\chi_{10952}(611,\cdot)\) \(\chi_{10952}(627,\cdot)\) \(\chi_{10952}(651,\cdot)\) \(\chi_{10952}(683,\cdot)\) \(\chi_{10952}(723,\cdot)\) \(\chi_{10952}(755,\cdot)\) ...

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: $\Q(\zeta_{1332})$
Fixed field: Number field defined by a degree 1332 polynomial (not computed)

Values on generators

\((8215,5477,9585)\) → \((-1,-1,e\left(\frac{391}{1332}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(21\)
\( \chi_{ 10952 }(355, a) \) \(1\)\(1\)\(e\left(\frac{115}{666}\right)\)\(e\left(\frac{1307}{1332}\right)\)\(e\left(\frac{19}{666}\right)\)\(e\left(\frac{115}{333}\right)\)\(e\left(\frac{5}{222}\right)\)\(e\left(\frac{539}{1332}\right)\)\(e\left(\frac{205}{1332}\right)\)\(e\left(\frac{253}{1332}\right)\)\(e\left(\frac{365}{1332}\right)\)\(e\left(\frac{67}{333}\right)\)
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)
 
\( \chi_{ 10952 }(355,a) \;\) at \(\;a = \) e.g. 2