Properties

Label 1792.bz
Modulus $1792$
Conductor $896$
Order $96$
Real no
Primitive no
Minimal no
Parity odd

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1792, base_ring=CyclotomicField(96))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,81,16]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(73,1792))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1792\)
Conductor: \(896\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(96\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 896.bv
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: odd
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Related number fields

Field of values: $\Q(\zeta_{96})$
Fixed field: Number field defined by a degree 96 polynomial

First 31 of 32 characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\)
\(\chi_{1792}(73,\cdot)\) \(-1\) \(1\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{17}{48}\right)\)
\(\chi_{1792}(89,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{43}{48}\right)\)
\(\chi_{1792}(185,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{23}{48}\right)\)
\(\chi_{1792}(201,\cdot)\) \(-1\) \(1\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{1}{48}\right)\)
\(\chi_{1792}(297,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{29}{48}\right)\)
\(\chi_{1792}(313,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{7}{48}\right)\)
\(\chi_{1792}(409,\cdot)\) \(-1\) \(1\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{35}{48}\right)\)
\(\chi_{1792}(425,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{13}{48}\right)\)
\(\chi_{1792}(521,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{41}{48}\right)\)
\(\chi_{1792}(537,\cdot)\) \(-1\) \(1\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{19}{48}\right)\)
\(\chi_{1792}(633,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{47}{48}\right)\)
\(\chi_{1792}(649,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{25}{48}\right)\)
\(\chi_{1792}(745,\cdot)\) \(-1\) \(1\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{5}{48}\right)\)
\(\chi_{1792}(761,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{31}{48}\right)\)
\(\chi_{1792}(857,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{11}{48}\right)\)
\(\chi_{1792}(873,\cdot)\) \(-1\) \(1\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{37}{48}\right)\)
\(\chi_{1792}(969,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{17}{48}\right)\)
\(\chi_{1792}(985,\cdot)\) \(-1\) \(1\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{43}{48}\right)\)
\(\chi_{1792}(1081,\cdot)\) \(-1\) \(1\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{23}{48}\right)\)
\(\chi_{1792}(1097,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{1}{48}\right)\)
\(\chi_{1792}(1193,\cdot)\) \(-1\) \(1\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{29}{48}\right)\)
\(\chi_{1792}(1209,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{7}{48}\right)\)
\(\chi_{1792}(1305,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{35}{48}\right)\)
\(\chi_{1792}(1321,\cdot)\) \(-1\) \(1\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{13}{48}\right)\)
\(\chi_{1792}(1417,\cdot)\) \(-1\) \(1\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{41}{48}\right)\)
\(\chi_{1792}(1433,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{19}{48}\right)\)
\(\chi_{1792}(1529,\cdot)\) \(-1\) \(1\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{47}{48}\right)\)
\(\chi_{1792}(1545,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{25}{48}\right)\)
\(\chi_{1792}(1641,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{5}{48}\right)\)
\(\chi_{1792}(1657,\cdot)\) \(-1\) \(1\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{31}{48}\right)\)
\(\chi_{1792}(1753,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{11}{48}\right)\)