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Properties

Label 24843.2150
Modulus $24843$
Conductor $24843$
Order $364$
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(24843, base_ring=CyclotomicField(364)) M = H._module chi = DirichletCharacter(H, M([182,52,329]))
 
Copy content gp:[g,chi] = znchar(Mod(2150, 24843))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("24843.2150");
 

Basic properties

Modulus: \(24843\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(24843\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(364\)
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 24843.hl

\(\chi_{24843}(8,\cdot)\) \(\chi_{24843}(281,\cdot)\) \(\chi_{24843}(512,\cdot)\) \(\chi_{24843}(554,\cdot)\) \(\chi_{24843}(827,\cdot)\) \(\chi_{24843}(1058,\cdot)\) \(\chi_{24843}(1100,\cdot)\) \(\chi_{24843}(1331,\cdot)\) \(\chi_{24843}(1604,\cdot)\) \(\chi_{24843}(1646,\cdot)\) \(\chi_{24843}(1877,\cdot)\) \(\chi_{24843}(1919,\cdot)\) \(\chi_{24843}(2150,\cdot)\) \(\chi_{24843}(2192,\cdot)\) \(\chi_{24843}(2423,\cdot)\) \(\chi_{24843}(2738,\cdot)\) \(\chi_{24843}(2969,\cdot)\) \(\chi_{24843}(3011,\cdot)\) \(\chi_{24843}(3242,\cdot)\) \(\chi_{24843}(3515,\cdot)\) \(\chi_{24843}(3557,\cdot)\) \(\chi_{24843}(3830,\cdot)\) \(\chi_{24843}(4061,\cdot)\) \(\chi_{24843}(4103,\cdot)\) \(\chi_{24843}(4334,\cdot)\) \(\chi_{24843}(4376,\cdot)\) \(\chi_{24843}(4649,\cdot)\) \(\chi_{24843}(4880,\cdot)\) \(\chi_{24843}(4922,\cdot)\) \(\chi_{24843}(5153,\cdot)\) ...

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: $\Q(\zeta_{364})$
Fixed field: Number field defined by a degree 364 polynomial (not computed)

Values on generators

\((8282,1522,3382)\) → \((-1,e\left(\frac{1}{7}\right),e\left(\frac{47}{52}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(4\)\(5\)\(8\)\(10\)\(11\)\(16\)\(17\)\(19\)\(20\)
\( \chi_{ 24843 }(2150, a) \) \(1\)\(1\)\(e\left(\frac{43}{364}\right)\)\(e\left(\frac{43}{182}\right)\)\(e\left(\frac{283}{364}\right)\)\(e\left(\frac{129}{364}\right)\)\(e\left(\frac{163}{182}\right)\)\(e\left(\frac{113}{364}\right)\)\(e\left(\frac{43}{91}\right)\)\(e\left(\frac{3}{91}\right)\)\(-i\)\(e\left(\frac{5}{364}\right)\)
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)
 
\( \chi_{ 24843 }(2150,a) \;\) at \(\;a = \) e.g. 2