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Properties

Label 24854.3401
Modulus $24854$
Conductor $12427$
Order $119$
Real no
Primitive no
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(24854, base_ring=CyclotomicField(238)) M = H._module chi = DirichletCharacter(H, M([42,68]))
 
Copy content gp:[g,chi] = znchar(Mod(3401, 24854))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("24854.3401");
 

Basic properties

Modulus: \(24854\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(12427\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(119\)
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: no, induced from \(\chi_{12427}(3401,\cdot)\)
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 24854.bu

\(\chi_{24854}(35,\cdot)\) \(\chi_{24854}(477,\cdot)\) \(\chi_{24854}(613,\cdot)\) \(\chi_{24854}(919,\cdot)\) \(\chi_{24854}(987,\cdot)\) \(\chi_{24854}(1225,\cdot)\) \(\chi_{24854}(1497,\cdot)\) \(\chi_{24854}(1939,\cdot)\) \(\chi_{24854}(2075,\cdot)\) \(\chi_{24854}(2381,\cdot)\) \(\chi_{24854}(2449,\cdot)\) \(\chi_{24854}(2687,\cdot)\) \(\chi_{24854}(2959,\cdot)\) \(\chi_{24854}(3401,\cdot)\) \(\chi_{24854}(3537,\cdot)\) \(\chi_{24854}(3843,\cdot)\) \(\chi_{24854}(3911,\cdot)\) \(\chi_{24854}(4149,\cdot)\) \(\chi_{24854}(4421,\cdot)\) \(\chi_{24854}(4863,\cdot)\) \(\chi_{24854}(4999,\cdot)\) \(\chi_{24854}(5305,\cdot)\) \(\chi_{24854}(5373,\cdot)\) \(\chi_{24854}(5611,\cdot)\) \(\chi_{24854}(5883,\cdot)\) \(\chi_{24854}(6325,\cdot)\) \(\chi_{24854}(6461,\cdot)\) \(\chi_{24854}(6767,\cdot)\) \(\chi_{24854}(6835,\cdot)\) \(\chi_{24854}(7073,\cdot)\) ...

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: $\Q(\zeta_{119})$
Fixed field: Number field defined by a degree 119 polynomial (not computed)

Values on generators

\((10407,14451)\) → \((e\left(\frac{3}{17}\right),e\left(\frac{2}{7}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(19\)\(21\)\(23\)
\( \chi_{ 24854 }(3401, a) \) \(1\)\(1\)\(e\left(\frac{55}{119}\right)\)\(e\left(\frac{66}{119}\right)\)\(e\left(\frac{6}{17}\right)\)\(e\left(\frac{110}{119}\right)\)\(e\left(\frac{75}{119}\right)\)\(e\left(\frac{87}{119}\right)\)\(e\left(\frac{2}{119}\right)\)\(e\left(\frac{107}{119}\right)\)\(e\left(\frac{97}{119}\right)\)\(e\left(\frac{110}{119}\right)\)
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)
 
\( \chi_{ 24854 }(3401,a) \;\) at \(\;a = \) e.g. 2