Properties

Label 28900.1523
Modulus $28900$
Conductor $28900$
Order $1360$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(28900, base_ring=CyclotomicField(1360))
 
M = H._module
 
chi = DirichletCharacter(H, M([680,748,575]))
 
pari: [g,chi] = znchar(Mod(1523,28900))
 

Basic properties

Modulus: \(28900\)
Conductor: \(28900\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(1360\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 28900.fn

\(\chi_{28900}(23,\cdot)\) \(\chi_{28900}(163,\cdot)\) \(\chi_{28900}(167,\cdot)\) \(\chi_{28900}(267,\cdot)\) \(\chi_{28900}(283,\cdot)\) \(\chi_{28900}(363,\cdot)\) \(\chi_{28900}(483,\cdot)\) \(\chi_{28900}(547,\cdot)\) \(\chi_{28900}(623,\cdot)\) \(\chi_{28900}(703,\cdot)\) \(\chi_{28900}(787,\cdot)\) \(\chi_{28900}(823,\cdot)\) \(\chi_{28900}(847,\cdot)\) \(\chi_{28900}(887,\cdot)\) \(\chi_{28900}(947,\cdot)\) \(\chi_{28900}(963,\cdot)\) \(\chi_{28900}(1127,\cdot)\) \(\chi_{28900}(1163,\cdot)\) \(\chi_{28900}(1183,\cdot)\) \(\chi_{28900}(1187,\cdot)\) \(\chi_{28900}(1227,\cdot)\) \(\chi_{28900}(1303,\cdot)\) \(\chi_{28900}(1383,\cdot)\) \(\chi_{28900}(1467,\cdot)\) \(\chi_{28900}(1503,\cdot)\) \(\chi_{28900}(1523,\cdot)\) \(\chi_{28900}(1527,\cdot)\)

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: $\Q(\zeta_{1360})$
Fixed field: Number field defined by a degree 1360 polynomial (not computed)

Values on generators

\((14451,24277,23701)\) → \((-1,e\left(\frac{11}{20}\right),e\left(\frac{115}{272}\right))\)

First values

\(a\) \(-1\)\(1\)\(3\)\(7\)\(9\)\(11\)\(13\)\(19\)\(21\)\(23\)\(27\)\(29\)
\( \chi_{ 28900 }(1523, a) \) \(-1\)\(1\)\(e\left(\frac{1051}{1360}\right)\)\(e\left(\frac{213}{272}\right)\)\(e\left(\frac{371}{680}\right)\)\(e\left(\frac{33}{1360}\right)\)\(e\left(\frac{27}{85}\right)\)\(e\left(\frac{217}{680}\right)\)\(e\left(\frac{189}{340}\right)\)\(e\left(\frac{1133}{1360}\right)\)\(e\left(\frac{433}{1360}\right)\)\(e\left(\frac{1291}{1360}\right)\)
sage: chi.jacobi_sum(n)
 
\( \chi_{ 28900 }(1523,a) \;\) at \(\;a = \) e.g. 2