Properties

Label 2760.1241
Modulus $2760$
Conductor $69$
Order $2$
Real yes
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2760, base_ring=CyclotomicField(2))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,1,0,1]))
 
pari: [g,chi] = znchar(Mod(1241,2760))
 

Basic properties

Modulus: \(2760\)
Conductor: \(69\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(2\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: no, induced from \(\chi_{69}(68,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2760.p

\(\chi_{2760}(1241,\cdot)\)

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: \(\Q\)
Fixed field: \(\Q(\sqrt{69}) \)

Values on generators

\((2071,1381,1841,1657,1201)\) → \((1,1,-1,1,-1)\)

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 2760 }(1241, a) \) \(1\)\(1\)\(-1\)\(1\)\(1\)\(1\)\(-1\)\(-1\)\(1\)\(-1\)\(-1\)\(-1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2760 }(1241,a) \;\) at \(\;a = \) e.g. 2