Properties

Label 28900.3467
Modulus $28900$
Conductor $1700$
Order $20$
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(20))
 
M = H._module
 
chi = DirichletCharacter(H, M([10,13,10]))
 
pari: [g,chi] = znchar(Mod(3467,28900))
 

Basic properties

Modulus: \(28900\)
Conductor: \(1700\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(20\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1700}(67,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 28900.bv

\(\chi_{28900}(3467,\cdot)\) \(\chi_{28900}(4623,\cdot)\) \(\chi_{28900}(9247,\cdot)\) \(\chi_{28900}(10403,\cdot)\) \(\chi_{28900}(15027,\cdot)\) \(\chi_{28900}(16183,\cdot)\) \(\chi_{28900}(21963,\cdot)\) \(\chi_{28900}(26587,\cdot)\)

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: \(\Q(\zeta_{20})\)
Fixed field: 20.20.6152325135647583007812500000000000000000000.1

Values on generators

\((14451,24277,23701)\) → \((-1,e\left(\frac{13}{20}\right),-1)\)

First values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(19\)\(21\)\(23\)\(27\)\(29\)
\( \chi_{ 28900 }(3467, a) \) \(1\)\(1\)\(e\left(\frac{11}{20}\right)\)\(i\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{13}{20}\right)\)\(e\left(\frac{4}{5}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 28900 }(3467,a) \;\) at \(\;a = \) e.g. 2