Properties

Label 1520.609
Modulus $1520$
Conductor $5$
Order $2$
Real yes
Primitive no
Minimal no
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1520, base_ring=CyclotomicField(2))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,0,1,0]))
 
pari: [g,chi] = znchar(Mod(609,1520))
 

Basic properties

Modulus: \(1520\)
Conductor: \(5\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(2\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: no, induced from \(\chi_{5}(4,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1520.d

\(\chi_{1520}(609,\cdot)\)

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: \(\Q\)
Fixed field: \(\Q(\sqrt{5}) \)

Values on generators

\((191,1141,1217,401)\) → \((1,1,-1,1)\)

Values

\(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(21\)\(23\)\(27\)\(29\)
\(1\)\(1\)\(-1\)\(-1\)\(1\)\(1\)\(-1\)\(-1\)\(1\)\(-1\)\(-1\)\(1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1520 }(609,a) \;\) at \(\;a = \) e.g. 2