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Properties

Label 107911.400
Modulus $107911$
Conductor $107911$
Order $25665$
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(107911, base_ring=CyclotomicField(51330)) M = H._module chi = DirichletCharacter(H, M([27376,48960]))
 
Copy content gp:[g,chi] = znchar(Mod(400, 107911))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("107911.400");
 

Basic properties

Modulus: \(107911\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(107911\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(25665\)
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 107911.ci

\(\chi_{107911}(7,\cdot)\) \(\chi_{107911}(9,\cdot)\) \(\chi_{107911}(19,\cdot)\) \(\chi_{107911}(20,\cdot)\) \(\chi_{107911}(28,\cdot)\) \(\chi_{107911}(41,\cdot)\) \(\chi_{107911}(45,\cdot)\) \(\chi_{107911}(49,\cdot)\) \(\chi_{107911}(51,\cdot)\) \(\chi_{107911}(71,\cdot)\) \(\chi_{107911}(76,\cdot)\) \(\chi_{107911}(80,\cdot)\) \(\chi_{107911}(81,\cdot)\) \(\chi_{107911}(100,\cdot)\) \(\chi_{107911}(107,\cdot)\) \(\chi_{107911}(112,\cdot)\) \(\chi_{107911}(121,\cdot)\) \(\chi_{107911}(133,\cdot)\) \(\chi_{107911}(134,\cdot)\) \(\chi_{107911}(138,\cdot)\) \(\chi_{107911}(143,\cdot)\) \(\chi_{107911}(144,\cdot)\) \(\chi_{107911}(164,\cdot)\) \(\chi_{107911}(169,\cdot)\) \(\chi_{107911}(175,\cdot)\) \(\chi_{107911}(193,\cdot)\) \(\chi_{107911}(196,\cdot)\) \(\chi_{107911}(204,\cdot)\) \(\chi_{107911}(205,\cdot)\) \(\chi_{107911}(206,\cdot)\) ...

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: $\Q(\zeta_{25665})$
Fixed field: Number field defined by a degree 25665 polynomial (not computed)

Values on generators

\((48735,83546)\) → \((e\left(\frac{8}{15}\right),e\left(\frac{1632}{1711}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\( \chi_{ 107911 }(400, a) \) \(1\)\(1\)\(e\left(\frac{6449}{8555}\right)\)\(e\left(\frac{20558}{25665}\right)\)\(e\left(\frac{4343}{8555}\right)\)\(e\left(\frac{2087}{5133}\right)\)\(e\left(\frac{2848}{5133}\right)\)\(e\left(\frac{884}{25665}\right)\)\(e\left(\frac{2237}{8555}\right)\)\(e\left(\frac{15451}{25665}\right)\)\(e\left(\frac{4117}{25665}\right)\)\(e\left(\frac{18109}{25665}\right)\)
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)
 
\( \chi_{ 107911 }(400,a) \;\) at \(\;a = \) e.g. 2