↑

Properties

Label 1472.275
Modulus $1472$
Conductor $1472$
Order $16$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the Dirichlet character
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1472, base_ring=CyclotomicField(16)) M = H._module chi = DirichletCharacter(H, M([8,7,8]))
 
Copy content gp:[g,chi] = znchar(Mod(275, 1472))
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1472.275");
 

Basic properties

Modulus: \(1472\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(1472\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(16\)
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 1472.u

\(\chi_{1472}(91,\cdot)\) \(\chi_{1472}(275,\cdot)\) \(\chi_{1472}(459,\cdot)\) \(\chi_{1472}(643,\cdot)\) \(\chi_{1472}(827,\cdot)\) \(\chi_{1472}(1011,\cdot)\) \(\chi_{1472}(1195,\cdot)\) \(\chi_{1472}(1379,\cdot)\)

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: \(\Q(\zeta_{16})\)
Fixed field: 16.16.47336086032831043196344263117897728.1

Values on generators

\((1151,645,833)\) → \((-1,e\left(\frac{7}{16}\right),-1)\)

First values

\(a\) \(-1\)\(1\)\(3\)\(5\)\(7\)\(9\)\(11\)\(13\)\(15\)\(17\)\(19\)\(21\)
\( \chi_{ 1472 }(275, a) \) \(1\)\(1\)\(e\left(\frac{13}{16}\right)\)\(e\left(\frac{15}{16}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{3}{16}\right)\)\(e\left(\frac{9}{16}\right)\)\(-i\)\(-i\)\(e\left(\frac{1}{16}\right)\)\(e\left(\frac{3}{16}\right)\)
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)
 
\( \chi_{ 1472 }(275,a) \;\) at \(\;a = \) e.g. 2