↑

Properties

Label 1280.bo
Modulus $1280$
Conductor $640$
Order $32$
Real no
Primitive no
Minimal no
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1280, base_ring=CyclotomicField(32)) M = H._module chi = DirichletCharacter(H, M([0,3,16])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(9,1280)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1280\)
Conductor: \(640\)
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: no, induced from 640.bo
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: no
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: 32.32.478904856520590268236983445984471619880855975682375680000000000000000.1

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\)
\(\chi_{1280}(9,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{32}\right)\)
\(\chi_{1280}(89,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{17}{32}\right)\)
\(\chi_{1280}(169,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{23}{32}\right)\)
\(\chi_{1280}(249,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{29}{32}\right)\)
\(\chi_{1280}(329,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{32}\right)\)
\(\chi_{1280}(409,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{9}{32}\right)\)
\(\chi_{1280}(489,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{32}\right)\)
\(\chi_{1280}(569,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{21}{32}\right)\)
\(\chi_{1280}(649,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{27}{32}\right)\)
\(\chi_{1280}(729,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{1}{32}\right)\)
\(\chi_{1280}(809,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{32}\right)\)
\(\chi_{1280}(889,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{13}{32}\right)\)
\(\chi_{1280}(969,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{19}{32}\right)\)
\(\chi_{1280}(1049,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{25}{32}\right)\)
\(\chi_{1280}(1129,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{31}{32}\right)\)
\(\chi_{1280}(1209,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{5}{32}\right)\)