Properties

Label 2760.1793
Modulus $2760$
Conductor $345$
Order $4$
Real no
Primitive no
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2760, base_ring=CyclotomicField(4))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,2,3,2]))
 
pari: [g,chi] = znchar(Mod(1793,2760))
 

Basic properties

Modulus: \(2760\)
Conductor: \(345\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{345}(68,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2760.bv

\(\chi_{2760}(137,\cdot)\) \(\chi_{2760}(1793,\cdot)\)

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: \(\mathbb{Q}(i)\)
Fixed field: 4.0.595125.1

Values on generators

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

First values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(29\)\(31\)\(37\)\(41\)\(43\)
\( \chi_{ 2760 }(1793, a) \) \(-1\)\(1\)\(i\)\(1\)\(i\)\(-i\)\(1\)\(1\)\(1\)\(i\)\(-1\)\(-i\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 2760 }(1793,a) \;\) at \(\;a = \) e.g. 2