Properties

Label 1200.107
Modulus $1200$
Conductor $240$
Order $4$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1200, base_ring=CyclotomicField(4))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([2,1,2,1]))
 
pari: [g,chi] = znchar(Mod(107,1200))
 

Basic properties

Modulus: \(1200\)
Conductor: \(240\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{240}(107,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1200.z

\(\chi_{1200}(107,\cdot)\) \(\chi_{1200}(1043,\cdot)\)

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: 4.0.2304000.1

Values on generators

\((751,901,401,577)\) → \((-1,i,-1,i)\)

Values

\(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\(-1\)\(1\)\(i\)\(i\)\(-1\)\(-i\)\(-i\)\(i\)\(-i\)\(-1\)\(-1\)\(1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1200 }(107,a) \;\) at \(\;a = \) e.g. 2