Properties

Label 6240.947
Modulus $6240$
Conductor $6240$
Order $24$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6240, base_ring=CyclotomicField(24))
 
M = H._module
 
chi = DirichletCharacter(H, M([12,21,12,6,14]))
 
pari: [g,chi] = znchar(Mod(947,6240))
 

Basic properties

Modulus: \(6240\)
Conductor: \(6240\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(24\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6240.ou

\(\chi_{6240}(947,\cdot)\) \(\chi_{6240}(1163,\cdot)\) \(\chi_{6240}(2867,\cdot)\) \(\chi_{6240}(3083,\cdot)\) \(\chi_{6240}(4067,\cdot)\) \(\chi_{6240}(4283,\cdot)\) \(\chi_{6240}(5987,\cdot)\) \(\chi_{6240}(6203,\cdot)\)

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

Related number fields

Field of values: \(\Q(\zeta_{24})\)
Fixed field: Number field defined by a degree 24 polynomial

Values on generators

\((1951,2341,2081,2497,5761)\) → \((-1,e\left(\frac{7}{8}\right),-1,i,e\left(\frac{7}{12}\right))\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 6240 }(947, a) \) \(1\)\(1\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{11}{24}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{1}{24}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{23}{24}\right)\)\(-i\)\(e\left(\frac{5}{24}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{19}{24}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 6240 }(947,a) \;\) at \(\;a = \) e.g. 2