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Properties

Label 5795.2894
Modulus $5795$
Conductor $5795$
Order $90$
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(5795, base_ring=CyclotomicField(90)) M = H._module chi = DirichletCharacter(H, M([45,70,27]))
 
Copy content gp:[g,chi] = znchar(Mod(2894, 5795))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5795.2894");
 

Basic properties

Modulus: \(5795\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(5795\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(90\)
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 5795.ks

\(\chi_{5795}(149,\cdot)\) \(\chi_{5795}(454,\cdot)\) \(\chi_{5795}(479,\cdot)\) \(\chi_{5795}(529,\cdot)\) \(\chi_{5795}(674,\cdot)\) \(\chi_{5795}(784,\cdot)\) \(\chi_{5795}(834,\cdot)\) \(\chi_{5795}(1089,\cdot)\) \(\chi_{5795}(2004,\cdot)\) \(\chi_{5795}(2284,\cdot)\) \(\chi_{5795}(2589,\cdot)\) \(\chi_{5795}(2664,\cdot)\) \(\chi_{5795}(2809,\cdot)\) \(\chi_{5795}(2894,\cdot)\) \(\chi_{5795}(2969,\cdot)\) \(\chi_{5795}(3114,\cdot)\) \(\chi_{5795}(3274,\cdot)\) \(\chi_{5795}(3809,\cdot)\) \(\chi_{5795}(4139,\cdot)\) \(\chi_{5795}(4189,\cdot)\) \(\chi_{5795}(4444,\cdot)\) \(\chi_{5795}(4944,\cdot)\) \(\chi_{5795}(5249,\cdot)\) \(\chi_{5795}(5554,\cdot)\)

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: $\Q(\zeta_{45})$
Fixed field: Number field defined by a degree 90 polynomial

Values on generators

\((4637,306,856)\) → \((-1,e\left(\frac{7}{9}\right),e\left(\frac{3}{10}\right))\)

First values

\(a\) \(-1\)\(1\)\(2\)\(3\)\(4\)\(6\)\(7\)\(8\)\(9\)\(11\)\(12\)\(13\)
\( \chi_{ 5795 }(2894, a) \) \(1\)\(1\)\(e\left(\frac{26}{45}\right)\)\(e\left(\frac{37}{90}\right)\)\(e\left(\frac{7}{45}\right)\)\(e\left(\frac{89}{90}\right)\)\(e\left(\frac{13}{15}\right)\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{37}{45}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{7}{18}\right)\)
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)
 
\( \chi_{ 5795 }(2894,a) \;\) at \(\;a = \) e.g. 2