Properties

Label 896.bn
Modulus $896$
Conductor $128$
Order $32$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(896, base_ring=CyclotomicField(32))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,27,0]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(29,896))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(896\)
Conductor: \(128\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(32\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 128.k
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{32})\)
Fixed field: \(\Q(\zeta_{128})^+\)

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\)
\(\chi_{896}(29,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{896}(85,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{896}(141,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{896}(197,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{896}(253,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{896}(309,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{896}(365,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{896}(421,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{896}(477,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{896}(533,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{896}(589,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{896}(645,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{896}(701,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{896}(757,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{896}(813,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{896}(869,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{16}\right)\)