Properties

Label 28900.19401
Modulus $28900$
Conductor $17$
Order $4$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(28900, base_ring=CyclotomicField(4))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,0,3]))
 
pari: [g,chi] = znchar(Mod(19401,28900))
 

Basic properties

Modulus: \(28900\)
Conductor: \(17\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(4\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{17}(4,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 28900.o

\(\chi_{28900}(14701,\cdot)\) \(\chi_{28900}(19401,\cdot)\)

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: \(\mathbb{Q}(i)\)
Fixed field: 4.4.4913.1

Values on generators

\((14451,24277,23701)\) → \((1,1,-i)\)

First values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(19\)\(21\)\(23\)\(27\)\(29\)
\( \chi_{ 28900 }(19401, a) \) \(1\)\(1\)\(-i\)\(i\)\(-1\)\(i\)\(1\)\(-1\)\(1\)\(i\)\(i\)\(-i\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 28900 }(19401,a) \;\) at \(\;a = \) e.g. 2