↑

Properties

Label 2580.11
Modulus $2580$
Conductor $516$
Order $14$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2580, base_ring=CyclotomicField(14)) M = H._module chi = DirichletCharacter(H, M([7,7,0,10]))
 
Copy content pari:[g,chi] = znchar(Mod(11,2580))
 

Basic properties

Modulus: \(2580\)
Conductor: \(516\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(14\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{516}(11,\cdot)\)
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Galois orbit 2580.by

\(\chi_{2580}(11,\cdot)\) \(\chi_{2580}(551,\cdot)\) \(\chi_{2580}(1091,\cdot)\) \(\chi_{2580}(1331,\cdot)\) \(\chi_{2580}(2111,\cdot)\) \(\chi_{2580}(2171,\cdot)\)

Copy content sage:chi.galois_orbit()
 
Copy content pari:order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Related number fields

Field of values: \(\Q(\zeta_{7})\)
Fixed field: Number field defined by a degree 14 polynomial

Values on generators

\((1291,1721,517,1981)\) → \((-1,-1,1,e\left(\frac{5}{7}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 2580 }(11, a) \) \(1\)\(1\)\(-1\)\(e\left(\frac{3}{7}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{9}{14}\right)\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{3}{7}\right)\)\(e\left(\frac{11}{14}\right)\)\(e\left(\frac{11}{14}\right)\)\(1\)\(e\left(\frac{11}{14}\right)\)
Copy content sage:chi.jacobi_sum(n)
 
\( \chi_{ 2580 }(11,a) \;\) at \(\;a = \) e.g. 2