↑

Properties

Label 836352.yf
Modulus $836352$
Conductor $139392$
Order $5280$
Real no
Primitive no
Minimal no
Parity even

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the Dirichlet character orbit
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(836352, base_ring=CyclotomicField(5280)) M = H._module chi = DirichletCharacter(H, M([2640,2145,4400,4512])) chi.galois_orbit()
 
Copy content gp:[g,chi] = znchar(Mod(71, 836352)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("836352.71"); order := Order(chi); { chi^k : k in [1..order-1] | GCD(k,order) eq 1 };
 

Basic properties

Modulus: \(836352\)
Copy content comment:Modulus
 
Copy content sage:chi.modulus()
 
Copy content gp:g[1][1]
 
Copy content magma:Modulus(chi);
 
Conductor: \(139392\)
Copy content comment:Conductor
 
Copy content sage:chi.conductor()
 
Copy content gp:znconreyconductor(g,chi)
 
Copy content magma:Conductor(chi);
 
Order: \(5280\)
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 139392.or
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: no
Parity: even
Copy content comment:Parity
 
Copy content sage:chi.is_odd()
 
Copy content gp:zncharisodd(g,chi)
 
Copy content magma:IsOdd(chi);
 

Related number fields

Field of values: $\Q(\zeta_{5280})$
Copy content comment:Field of values of chi
 
Copy content sage:CyclotomicField(chi.multiplicative_order())
 
Copy content gp:nfinit(polcyclo(charorder(g,chi)))
 
Copy content magma:CyclotomicField(Order(chi));
 
Fixed field: Number field defined by a degree 5280 polynomial (not computed)
Copy content comment:Fixed field
 
Copy content sage:chi.fixed_field()
 

First 2 of 1280 characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\) \(35\)
\(\chi_{836352}(71,\cdot)\) \(1\) \(1\) \(e\left(\frac{4273}{5280}\right)\) \(e\left(\frac{2317}{2640}\right)\) \(e\left(\frac{367}{5280}\right)\) \(e\left(\frac{329}{440}\right)\) \(e\left(\frac{1357}{1760}\right)\) \(e\left(\frac{91}{528}\right)\) \(e\left(\frac{1633}{2640}\right)\) \(e\left(\frac{1739}{5280}\right)\) \(e\left(\frac{599}{660}\right)\) \(e\left(\frac{1209}{1760}\right)\)
\(\chi_{836352}(1367,\cdot)\) \(1\) \(1\) \(e\left(\frac{2011}{5280}\right)\) \(e\left(\frac{2239}{2640}\right)\) \(e\left(\frac{709}{5280}\right)\) \(e\left(\frac{403}{440}\right)\) \(e\left(\frac{1039}{1760}\right)\) \(e\left(\frac{265}{528}\right)\) \(e\left(\frac{2011}{2640}\right)\) \(e\left(\frac{5273}{5280}\right)\) \(e\left(\frac{53}{660}\right)\) \(e\left(\frac{403}{1760}\right)\)