Properties

Label 4608.bv
Modulus $4608$
Conductor $256$
Order $64$
Real no
Primitive no
Minimal no
Parity odd

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4608, base_ring=CyclotomicField(64))
 
M = H._module
 
chi = DirichletCharacter(H, M([32,43,0]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(55,4608))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4608\)
Conductor: \(256\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(64\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 256.n
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: $\Q(\zeta_{64})$
Fixed field: Number field defined by a degree 64 polynomial

First 31 of 32 characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{4608}(55,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{4608}(199,\cdot)\) \(-1\) \(1\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{4608}(343,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{4608}(487,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{4608}(631,\cdot)\) \(-1\) \(1\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{4608}(775,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{4608}(919,\cdot)\) \(-1\) \(1\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{4608}(1063,\cdot)\) \(-1\) \(1\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{4608}(1207,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{4608}(1351,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{4608}(1495,\cdot)\) \(-1\) \(1\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{4608}(1639,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{4608}(1783,\cdot)\) \(-1\) \(1\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{4608}(1927,\cdot)\) \(-1\) \(1\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{4608}(2071,\cdot)\) \(-1\) \(1\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{4608}(2215,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{4608}(2359,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{4608}(2503,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{4608}(2647,\cdot)\) \(-1\) \(1\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{4608}(2791,\cdot)\) \(-1\) \(1\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{4608}(2935,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{4608}(3079,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{4608}(3223,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{4608}(3367,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{4608}(3511,\cdot)\) \(-1\) \(1\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{4608}(3655,\cdot)\) \(-1\) \(1\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{4608}(3799,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{4608}(3943,\cdot)\) \(-1\) \(1\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{4608}(4087,\cdot)\) \(-1\) \(1\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{4608}(4231,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{4608}(4375,\cdot)\) \(-1\) \(1\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{3}{8}\right)\)