Properties

Label 896.bs
Modulus $896$
Conductor $896$
Order $96$
Real no
Primitive yes
Minimal yes
Parity odd

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Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(896, base_ring=CyclotomicField(96))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([48,63,64]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(11,896))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(896\)
Conductor: \(896\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(96\)
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: $\Q(\zeta_{96})$
Fixed field: Number field defined by a degree 96 polynomial

First 31 of 32 characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(5\) \(9\) \(11\) \(13\) \(15\) \(17\) \(19\) \(23\) \(25\)
\(\chi_{896}(11,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{47}{48}\right)\)
\(\chi_{896}(51,\cdot)\) \(-1\) \(1\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{13}{48}\right)\)
\(\chi_{896}(67,\cdot)\) \(-1\) \(1\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{41}{48}\right)\)
\(\chi_{896}(107,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{7}{48}\right)\)
\(\chi_{896}(123,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{35}{48}\right)\)
\(\chi_{896}(163,\cdot)\) \(-1\) \(1\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{1}{48}\right)\)
\(\chi_{896}(179,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{29}{48}\right)\)
\(\chi_{896}(219,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{43}{48}\right)\)
\(\chi_{896}(235,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{23}{48}\right)\)
\(\chi_{896}(275,\cdot)\) \(-1\) \(1\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{37}{48}\right)\)
\(\chi_{896}(291,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{17}{48}\right)\)
\(\chi_{896}(331,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{31}{48}\right)\)
\(\chi_{896}(347,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{11}{48}\right)\)
\(\chi_{896}(387,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{25}{48}\right)\)
\(\chi_{896}(403,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{5}{48}\right)\)
\(\chi_{896}(443,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{19}{48}\right)\)
\(\chi_{896}(459,\cdot)\) \(-1\) \(1\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{47}{48}\right)\)
\(\chi_{896}(499,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{13}{48}\right)\)
\(\chi_{896}(515,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{41}{48}\right)\)
\(\chi_{896}(555,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{7}{48}\right)\)
\(\chi_{896}(571,\cdot)\) \(-1\) \(1\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{35}{48}\right)\)
\(\chi_{896}(611,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{1}{48}\right)\)
\(\chi_{896}(627,\cdot)\) \(-1\) \(1\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{29}{48}\right)\)
\(\chi_{896}(667,\cdot)\) \(-1\) \(1\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{24}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{43}{48}\right)\)
\(\chi_{896}(683,\cdot)\) \(-1\) \(1\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{24}\right)\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{23}{48}\right)\)
\(\chi_{896}(723,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{11}{24}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{37}{48}\right)\)
\(\chi_{896}(739,\cdot)\) \(-1\) \(1\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{24}\right)\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{17}{48}\right)\)
\(\chi_{896}(779,\cdot)\) \(-1\) \(1\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{17}{24}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{31}{48}\right)\)
\(\chi_{896}(795,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{13}{24}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{11}{48}\right)\)
\(\chi_{896}(835,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{23}{24}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{25}{48}\right)\)
\(\chi_{896}(851,\cdot)\) \(-1\) \(1\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{19}{24}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{5}{48}\right)\)