Properties

Label 2736.341
Modulus $2736$
Conductor $912$
Order $4$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(2736, base_ring=CyclotomicField(4))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,1,2,2]))
 
pari: [g,chi] = znchar(Mod(341,2736))
 

Basic properties

Modulus: \(2736\)
Conductor: \(912\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{912}(341,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 2736.u

\(\chi_{2736}(341,\cdot)\) \(\chi_{2736}(1709,\cdot)\)

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

Related number fields

Field of values: \(\Q(\sqrt{-1}) \)
Fixed field: 4.4.6653952.1

Values on generators

\((1711,2053,1217,1009)\) → \((1,i,-1,-1)\)

Values

\(-1\)\(1\)\(5\)\(7\)\(11\)\(13\)\(17\)\(23\)\(25\)\(29\)\(31\)\(35\)
\(1\)\(1\)\(-i\)\(-1\)\(-i\)\(i\)\(-1\)\(1\)\(-1\)\(-i\)\(-1\)\(i\)
value at e.g. 2