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Properties

Label 40320.xg
Modulus $40320$
Conductor $896$
Order $32$
Real no
Primitive no
Minimal yes
Parity even

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Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40320, base_ring=CyclotomicField(32)) M = H._module chi = DirichletCharacter(H, M([16,29,0,0,16])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(811,40320)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(40320\)
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: no, induced from 896.bk
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 \(-1\) \(1\) \(11\) \(13\) \(17\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{40320}(811,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{15}{32}\right)\) \(i\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{25}{32}\right)\)
\(\chi_{40320}(3331,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{17}{32}\right)\) \(-i\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{7}{32}\right)\)
\(\chi_{40320}(5851,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{3}{32}\right)\) \(i\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{5}{32}\right)\)
\(\chi_{40320}(8371,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{5}{32}\right)\) \(-i\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{19}{32}\right)\)
\(\chi_{40320}(10891,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{23}{32}\right)\) \(i\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{17}{32}\right)\)
\(\chi_{40320}(13411,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{25}{32}\right)\) \(-i\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{31}{32}\right)\)
\(\chi_{40320}(15931,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{11}{32}\right)\) \(i\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{29}{32}\right)\)
\(\chi_{40320}(18451,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{13}{32}\right)\) \(-i\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{11}{32}\right)\)
\(\chi_{40320}(20971,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{31}{32}\right)\) \(i\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{9}{32}\right)\)
\(\chi_{40320}(23491,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{1}{32}\right)\) \(-i\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{23}{32}\right)\)
\(\chi_{40320}(26011,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{19}{32}\right)\) \(i\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{21}{32}\right)\)
\(\chi_{40320}(28531,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{21}{32}\right)\) \(-i\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{3}{32}\right)\)
\(\chi_{40320}(31051,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{7}{32}\right)\) \(i\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{1}{32}\right)\)
\(\chi_{40320}(33571,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{9}{32}\right)\) \(-i\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{15}{32}\right)\)
\(\chi_{40320}(36091,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{27}{32}\right)\) \(i\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{13}{32}\right)\)
\(\chi_{40320}(38611,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{29}{32}\right)\) \(-i\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{27}{32}\right)\)