Properties

Label 1088.bw
Modulus $1088$
Conductor $1088$
Order $16$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1088, base_ring=CyclotomicField(16))
 
M = H._module
 
chi = DirichletCharacter(H, M([8,7,14]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(19,1088))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1088\)
Conductor: \(1088\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(16\)
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)
 

Related number fields

Field of values: \(\Q(\zeta_{16})\)
Fixed field: 16.0.101778150989126822408855042987257078218752.4

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(19\) \(21\) \(23\)
\(\chi_{1088}(19,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(-i\)
\(\chi_{1088}(315,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(i\)
\(\chi_{1088}(331,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(-1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(i\)
\(\chi_{1088}(355,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(-1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(-i\)
\(\chi_{1088}(563,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(-1\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(-1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(-i\)
\(\chi_{1088}(859,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(-1\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(-1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(i\)
\(\chi_{1088}(875,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(-1\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(-1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(i\)
\(\chi_{1088}(899,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(-1\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(-1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(-i\)