Properties

Label 2176.cq
Modulus $2176$
Conductor $544$
Order $16$
Real no
Primitive no
Minimal no
Parity odd

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2176, base_ring=CyclotomicField(16))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,2,1]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(241,2176))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2176\)
Conductor: \(544\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(16\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 544.by
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{16})\)
Fixed field: 16.0.13200596365472076270679746481196367872.3

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(19\) \(21\) \(23\)
\(\chi_{2176}(241,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{2176}(657,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{2176}(721,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{2176}(881,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{2176}(1457,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{2176}(1489,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{2176}(1553,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{2176}(1841,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{16}\right)\)