↑

Properties

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

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(896, base_ring=CyclotomicField(32)) M = H._module chi = DirichletCharacter(H, M([16,9,16])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(27,896)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

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

Related number fields

Field of values: \(\Q(\zeta_{32})\)
Fixed field: 32.32.104303243075213755167445035578915122359095224799654955003407693930037248.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\)
\(\chi_{896}(27,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{896}(83,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{896}(139,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{896}(195,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{896}(251,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{896}(307,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{896}(363,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{896}(419,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{896}(475,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{896}(531,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{896}(587,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{896}(643,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{896}(699,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{896}(755,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{896}(811,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{896}(867,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\)