Properties

Label 2176.dv
Modulus $2176$
Conductor $2176$
Order $32$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2176, base_ring=CyclotomicField(32))
 
M = H._module
 
chi = DirichletCharacter(H, M([16,15,8]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(115,2176))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(2176\)
Conductor: \(2176\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(32\)
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: \(\Q(\zeta_{32})\)
Fixed field: 32.0.1065376921891826694498186101801476972105263426181534166450452088549139595121406884446208.2

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(7\) \(9\) \(11\) \(13\) \(15\) \(19\) \(21\) \(23\)
\(\chi_{2176}(115,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{2176}(123,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{2176}(387,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{2176}(395,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{2176}(659,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{2176}(667,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{2176}(931,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{2176}(939,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{7}{16}\right)\)
\(\chi_{2176}(1203,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{13}{16}\right)\)
\(\chi_{2176}(1211,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{3}{16}\right)\)
\(\chi_{2176}(1475,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{9}{16}\right)\)
\(\chi_{2176}(1483,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{15}{16}\right)\)
\(\chi_{2176}(1747,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{5}{16}\right)\)
\(\chi_{2176}(1755,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{11}{16}\right)\)
\(\chi_{2176}(2019,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{1}{16}\right)\)
\(\chi_{2176}(2027,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{7}{16}\right)\)