Properties

Label 28900.23119
Modulus $28900$
Conductor $1700$
Order $10$
Real no
Primitive no
Minimal no
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(28900, base_ring=CyclotomicField(10))
 
M = H._module
 
chi = DirichletCharacter(H, M([5,9,5]))
 
pari: [g,chi] = znchar(Mod(23119,28900))
 

Basic properties

Modulus: \(28900\)
Conductor: \(1700\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(10\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{1700}(1019,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 28900.bh

\(\chi_{28900}(5779,\cdot)\) \(\chi_{28900}(11559,\cdot)\) \(\chi_{28900}(17339,\cdot)\) \(\chi_{28900}(23119,\cdot)\)

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: \(\Q(\zeta_{5})\)
Fixed field: 10.0.1109263281250000000000.3

Values on generators

\((14451,24277,23701)\) → \((-1,e\left(\frac{9}{10}\right),-1)\)

First values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(19\)\(21\)\(23\)\(27\)\(29\)
\( \chi_{ 28900 }(23119, a) \) \(-1\)\(1\)\(e\left(\frac{3}{10}\right)\)\(-1\)\(e\left(\frac{3}{5}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{3}{10}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 28900 }(23119,a) \;\) at \(\;a = \) e.g. 2