Properties

Label 3800.949
Modulus $3800$
Conductor $760$
Order $2$
Real yes
Primitive no
Minimal no
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3800, base_ring=CyclotomicField(2))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,1,1,1]))
 
pari: [g,chi] = znchar(Mod(949,3800))
 

Basic properties

Modulus: \(3800\)
Conductor: \(760\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(2\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: yes
Primitive: no, induced from \(\chi_{760}(189,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 3800.b

\(\chi_{3800}(949,\cdot)\)

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: \(\Q\)
Fixed field: \(\Q(\sqrt{-190}) \)

Values on generators

\((951,1901,1977,401)\) → \((1,-1,-1,-1)\)

First values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(17\)\(21\)\(23\)\(27\)\(29\)
\( \chi_{ 3800 }(949, a) \) \(-1\)\(1\)\(-1\)\(-1\)\(1\)\(-1\)\(-1\)\(-1\)\(1\)\(-1\)\(-1\)\(1\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 3800 }(949,a) \;\) at \(\;a = \) e.g. 2