Properties

Label 3072.ba
Modulus $3072$
Conductor $768$
Order $64$
Real no
Primitive no
Minimal no
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3072, base_ring=CyclotomicField(64))
 
M = H._module
 
chi = DirichletCharacter(H, M([32,43,32]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(47,3072))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3072\)
Conductor: \(768\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(64\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 768.ba
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: $\Q(\zeta_{64})$
Fixed field: Number field defined by a degree 64 polynomial

First 31 of 32 characters in Galois orbit

Character \(-1\) \(1\) \(5\) \(7\) \(11\) \(13\) \(17\) \(19\) \(23\) \(25\) \(29\) \(31\)
\(\chi_{3072}(47,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{3072}(143,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{3072}(239,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{3072}(335,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{3072}(431,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{3072}(527,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{3072}(623,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{3072}(719,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{3072}(815,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{3072}(911,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{3072}(1007,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{3072}(1103,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{3072}(1199,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{3072}(1295,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{3072}(1391,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{3072}(1487,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{3072}(1583,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{3072}(1679,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{3072}(1775,\cdot)\) \(1\) \(1\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{3072}(1871,\cdot)\) \(1\) \(1\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{3072}(1967,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{3072}(2063,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{3072}(2159,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{3072}(2255,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{3072}(2351,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{3072}(2447,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{3072}(2543,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{3}{8}\right)\)
\(\chi_{3072}(2639,\cdot)\) \(1\) \(1\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{1}{8}\right)\)
\(\chi_{3072}(2735,\cdot)\) \(1\) \(1\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{7}{8}\right)\)
\(\chi_{3072}(2831,\cdot)\) \(1\) \(1\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{5}{8}\right)\)
\(\chi_{3072}(2927,\cdot)\) \(1\) \(1\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{3}{8}\right)\)