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Properties

Label 12095.192
Modulus $12095$
Conductor $12095$
Order $1160$
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(12095, base_ring=CyclotomicField(1160)) M = H._module chi = DirichletCharacter(H, M([290,319,1120]))
 
Copy content gp:[g,chi] = znchar(Mod(192, 12095))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("12095.192");
 

Basic properties

Modulus: \(12095\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(12095\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(1160\)
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 12095.eg

\(\chi_{12095}(7,\cdot)\) \(\chi_{12095}(12,\cdot)\) \(\chi_{12095}(63,\cdot)\) \(\chi_{12095}(88,\cdot)\) \(\chi_{12095}(108,\cdot)\) \(\chi_{12095}(112,\cdot)\) \(\chi_{12095}(138,\cdot)\) \(\chi_{12095}(192,\cdot)\) \(\chi_{12095}(212,\cdot)\) \(\chi_{12095}(257,\cdot)\) \(\chi_{12095}(263,\cdot)\) \(\chi_{12095}(293,\cdot)\) \(\chi_{12095}(317,\cdot)\) \(\chi_{12095}(343,\cdot)\) \(\chi_{12095}(357,\cdot)\) \(\chi_{12095}(363,\cdot)\) \(\chi_{12095}(382,\cdot)\) \(\chi_{12095}(417,\cdot)\) \(\chi_{12095}(422,\cdot)\) \(\chi_{12095}(462,\cdot)\) \(\chi_{12095}(498,\cdot)\) \(\chi_{12095}(518,\cdot)\) \(\chi_{12095}(548,\cdot)\) \(\chi_{12095}(567,\cdot)\) \(\chi_{12095}(593,\cdot)\) \(\chi_{12095}(602,\cdot)\) \(\chi_{12095}(678,\cdot)\) \(\chi_{12095}(723,\cdot)\) \(\chi_{12095}(727,\cdot)\) \(\chi_{12095}(753,\cdot)\) ...

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: $\Q(\zeta_{1160})$
Fixed field: Number field defined by a degree 1160 polynomial (not computed)

Values on generators

\((9677,4721,3896)\) → \((i,e\left(\frac{11}{40}\right),e\left(\frac{28}{29}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\( \chi_{ 12095 }(192, a) \) \(1\)\(1\)\(e\left(\frac{53}{145}\right)\)\(e\left(\frac{35}{232}\right)\)\(e\left(\frac{106}{145}\right)\)\(e\left(\frac{599}{1160}\right)\)\(e\left(\frac{411}{1160}\right)\)\(e\left(\frac{14}{145}\right)\)\(e\left(\frac{35}{116}\right)\)\(e\left(\frac{1117}{1160}\right)\)\(e\left(\frac{1023}{1160}\right)\)\(e\left(\frac{839}{1160}\right)\)
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)
 
\( \chi_{ 12095 }(192,a) \;\) at \(\;a = \) e.g. 2