Properties

Label 1800.901
Modulus $1800$
Conductor $8$
Order $2$
Real yes
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1800, base_ring=CyclotomicField(2))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,1,0,0]))
 
pari: [g,chi] = znchar(Mod(901,1800))
 

Basic properties

Modulus: \(1800\)
Conductor: \(8\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(2\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: no, induced from \(\chi_{8}(5,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 1800.k

\(\chi_{1800}(901,\cdot)\)

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: \(\Q(\sqrt{2}) \)

Values on generators

\((1351,901,1001,577)\) → \((1,-1,1,1)\)

Values

\(a\) \(-1\)\(1\)\(7\)\(11\)\(13\)\(17\)\(19\)\(23\)\(29\)\(31\)\(37\)\(41\)
\( \chi_{ 1800 }(901, a) \) \(1\)\(1\)\(1\)\(-1\)\(-1\)\(1\)\(-1\)\(1\)\(-1\)\(1\)\(-1\)\(1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 1800 }(901,a) \;\) at \(\;a = \) e.g. 2