Properties

Label 4608.bw
Modulus $4608$
Conductor $1152$
Order $96$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4608, base_ring=CyclotomicField(96))
 
M = H._module
 
chi = DirichletCharacter(H, M([48,33,16]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(47,4608))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4608\)
Conductor: \(1152\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(96\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 1152.bs
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: no
Parity: even
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 \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{4608}(47,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{4608}(239,\cdot)\) \(1\) \(1\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{4608}(335,\cdot)\) \(1\) \(1\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{4608}(527,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{4608}(623,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{4608}(815,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{4608}(911,\cdot)\) \(1\) \(1\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{4608}(1103,\cdot)\) \(1\) \(1\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{4608}(1199,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{4608}(1391,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{4608}(1487,\cdot)\) \(1\) \(1\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{4608}(1679,\cdot)\) \(1\) \(1\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{4608}(1775,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{4608}(1967,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{4608}(2063,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{4608}(2255,\cdot)\) \(1\) \(1\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{4608}(2351,\cdot)\) \(1\) \(1\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{4608}(2543,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{4608}(2639,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{96}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{41}{96}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{4608}(2831,\cdot)\) \(1\) \(1\) \(e\left(\frac{91}{96}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{37}{96}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{4608}(2927,\cdot)\) \(1\) \(1\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{1}{96}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{29}{48}\right)\) \(e\left(\frac{31}{96}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{4608}(3119,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{53}{96}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{1}{48}\right)\) \(e\left(\frac{11}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{4608}(3215,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{23}{48}\right)\) \(e\left(\frac{79}{96}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{49}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{4608}(3407,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{43}{48}\right)\) \(e\left(\frac{35}{96}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{29}{96}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{4608}(3503,\cdot)\) \(1\) \(1\) \(e\left(\frac{89}{96}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{71}{96}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{31}{48}\right)\) \(e\left(\frac{41}{48}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{4608}(3695,\cdot)\) \(1\) \(1\) \(e\left(\frac{61}{96}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{67}{96}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{4608}(3791,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{96}\right)\) \(e\left(\frac{35}{48}\right)\) \(e\left(\frac{43}{96}\right)\) \(e\left(\frac{17}{96}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{85}{96}\right)\) \(e\left(\frac{1}{12}\right)\)
\(\chi_{4608}(3983,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{96}\right)\) \(e\left(\frac{7}{48}\right)\) \(e\left(\frac{95}{96}\right)\) \(e\left(\frac{13}{96}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{65}{96}\right)\) \(e\left(\frac{5}{12}\right)\)
\(\chi_{4608}(4079,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{17}{48}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{19}{48}\right)\) \(e\left(\frac{5}{48}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{7}{12}\right)\)
\(\chi_{4608}(4271,\cdot)\) \(1\) \(1\) \(e\left(\frac{73}{96}\right)\) \(e\left(\frac{37}{48}\right)\) \(e\left(\frac{77}{96}\right)\) \(e\left(\frac{55}{96}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{25}{48}\right)\) \(e\left(\frac{83}{96}\right)\) \(e\left(\frac{11}{12}\right)\)
\(\chi_{4608}(4367,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{96}\right)\) \(e\left(\frac{47}{48}\right)\) \(e\left(\frac{7}{96}\right)\) \(e\left(\frac{5}{96}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{13}{48}\right)\) \(e\left(\frac{11}{48}\right)\) \(e\left(\frac{25}{96}\right)\) \(e\left(\frac{1}{12}\right)\)