Properties

Label 1600.ba
Modulus $1600$
Conductor $160$
Order $8$
Real no
Primitive no
Minimal no
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1600, base_ring=CyclotomicField(8))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,5,4]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(249,1600))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1600\)
Conductor: \(160\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(8\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 160.z
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{8})\)
Fixed field: 8.8.1342177280000.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\)
\(\chi_{1600}(249,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{1600}(649,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(i\) \(i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{1600}(1049,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(-i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{1600}(1449,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(i\) \(i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\)