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Properties

Label 16268.43
Modulus $16268$
Conductor $16268$
Order $574$
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(16268, base_ring=CyclotomicField(574)) M = H._module chi = DirichletCharacter(H, M([287,82,497]))
 
Copy content gp:[g,chi] = znchar(Mod(43, 16268))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("16268.43");
 

Basic properties

Modulus: \(16268\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(16268\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(574\)
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 16268.bx

\(\chi_{16268}(15,\cdot)\) \(\chi_{16268}(43,\cdot)\) \(\chi_{16268}(71,\cdot)\) \(\chi_{16268}(155,\cdot)\) \(\chi_{16268}(211,\cdot)\) \(\chi_{16268}(239,\cdot)\) \(\chi_{16268}(267,\cdot)\) \(\chi_{16268}(323,\cdot)\) \(\chi_{16268}(351,\cdot)\) \(\chi_{16268}(379,\cdot)\) \(\chi_{16268}(435,\cdot)\) \(\chi_{16268}(603,\cdot)\) \(\chi_{16268}(631,\cdot)\) \(\chi_{16268}(743,\cdot)\) \(\chi_{16268}(771,\cdot)\) \(\chi_{16268}(799,\cdot)\) \(\chi_{16268}(827,\cdot)\) \(\chi_{16268}(967,\cdot)\) \(\chi_{16268}(1051,\cdot)\) \(\chi_{16268}(1135,\cdot)\) \(\chi_{16268}(1219,\cdot)\) \(\chi_{16268}(1247,\cdot)\) \(\chi_{16268}(1303,\cdot)\) \(\chi_{16268}(1443,\cdot)\) \(\chi_{16268}(1499,\cdot)\) \(\chi_{16268}(1583,\cdot)\) \(\chi_{16268}(1611,\cdot)\) \(\chi_{16268}(1639,\cdot)\) \(\chi_{16268}(1695,\cdot)\) \(\chi_{16268}(1751,\cdot)\) ...

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: $\Q(\zeta_{287})$
Fixed field: Number field defined by a degree 574 polynomial (not computed)

Values on generators

\((8135,10293,7057)\) → \((-1,e\left(\frac{1}{7}\right),e\left(\frac{71}{82}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(23\)\(25\)
\( \chi_{ 16268 }(43, a) \) \(1\)\(1\)\(e\left(\frac{565}{574}\right)\)\(e\left(\frac{299}{574}\right)\)\(e\left(\frac{278}{287}\right)\)\(e\left(\frac{571}{574}\right)\)\(e\left(\frac{221}{574}\right)\)\(e\left(\frac{145}{287}\right)\)\(e\left(\frac{17}{287}\right)\)\(e\left(\frac{8}{41}\right)\)\(e\left(\frac{505}{574}\right)\)\(e\left(\frac{12}{287}\right)\)
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)
 
\( \chi_{ 16268 }(43,a) \;\) at \(\;a = \) e.g. 2