Properties

Label 1280.bw
Modulus $1280$
Conductor $1280$
Order $64$
Real no
Primitive yes
Minimal yes
Parity even

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Show commands: PariGP / SageMath
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1280, base_ring=CyclotomicField(64))
 
M = H._module
 
chi = DirichletCharacter(H, M([0,59,32]))
 
chi.galois_orbit()
 
[g,chi] = znchar(Mod(29,1280))
 
order = charorder(g,chi)
 
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1280\)
Conductor: \(1280\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(64\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
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 \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(23\) \(27\)
\(\chi_{1280}(29,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{19}{64}\right)\)
\(\chi_{1280}(69,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{57}{64}\right)\)
\(\chi_{1280}(109,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{47}{64}\right)\)
\(\chi_{1280}(149,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{53}{64}\right)\)
\(\chi_{1280}(189,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{11}{64}\right)\)
\(\chi_{1280}(229,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{49}{64}\right)\)
\(\chi_{1280}(269,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{39}{64}\right)\)
\(\chi_{1280}(309,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{45}{64}\right)\)
\(\chi_{1280}(349,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{3}{64}\right)\)
\(\chi_{1280}(389,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{41}{64}\right)\)
\(\chi_{1280}(429,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{31}{64}\right)\)
\(\chi_{1280}(469,\cdot)\) \(1\) \(1\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{37}{64}\right)\)
\(\chi_{1280}(509,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{59}{64}\right)\)
\(\chi_{1280}(549,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{13}{64}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{33}{64}\right)\)
\(\chi_{1280}(589,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{23}{64}\right)\)
\(\chi_{1280}(629,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{29}{64}\right)\)
\(\chi_{1280}(669,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{55}{64}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{51}{64}\right)\)
\(\chi_{1280}(709,\cdot)\) \(1\) \(1\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{25}{64}\right)\)
\(\chi_{1280}(749,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{17}{64}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{15}{64}\right)\)
\(\chi_{1280}(789,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{17}{32}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{11}{64}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{21}{64}\right)\)
\(\chi_{1280}(829,\cdot)\) \(1\) \(1\) \(e\left(\frac{57}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{29}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{53}{64}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{43}{64}\right)\)
\(\chi_{1280}(869,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{17}{64}\right)\)
\(\chi_{1280}(909,\cdot)\) \(1\) \(1\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{35}{64}\right)\) \(e\left(\frac{25}{32}\right)\) \(e\left(\frac{7}{64}\right)\)
\(\chi_{1280}(949,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{15}{32}\right)\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{11}{16}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{1}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{13}{64}\right)\)
\(\chi_{1280}(989,\cdot)\) \(1\) \(1\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{7}{32}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{39}{64}\right)\) \(e\left(\frac{37}{64}\right)\) \(e\left(\frac{5}{16}\right)\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{47}{64}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{35}{64}\right)\)
\(\chi_{1280}(1029,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{64}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{3}{32}\right)\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{15}{64}\right)\) \(e\left(\frac{15}{16}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{9}{64}\right)\)
\(\chi_{1280}(1069,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{64}\right)\) \(e\left(\frac{19}{32}\right)\) \(e\left(\frac{21}{32}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{9}{16}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{59}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{63}{64}\right)\)
\(\chi_{1280}(1109,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{1}{32}\right)\) \(e\left(\frac{23}{32}\right)\) \(e\left(\frac{33}{64}\right)\) \(e\left(\frac{51}{64}\right)\) \(e\left(\frac{3}{16}\right)\) \(e\left(\frac{27}{64}\right)\) \(e\left(\frac{25}{64}\right)\) \(e\left(\frac{27}{32}\right)\) \(e\left(\frac{5}{64}\right)\)
\(\chi_{1280}(1149,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{63}{64}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{13}{16}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{7}{64}\right)\) \(e\left(\frac{5}{32}\right)\) \(e\left(\frac{27}{64}\right)\)
\(\chi_{1280}(1189,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{13}{32}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{45}{64}\right)\) \(e\left(\frac{23}{64}\right)\) \(e\left(\frac{7}{16}\right)\) \(e\left(\frac{31}{64}\right)\) \(e\left(\frac{5}{64}\right)\) \(e\left(\frac{31}{32}\right)\) \(e\left(\frac{1}{64}\right)\)
\(\chi_{1280}(1229,\cdot)\) \(1\) \(1\) \(e\left(\frac{61}{64}\right)\) \(e\left(\frac{11}{32}\right)\) \(e\left(\frac{29}{32}\right)\) \(e\left(\frac{43}{64}\right)\) \(e\left(\frac{49}{64}\right)\) \(e\left(\frac{1}{16}\right)\) \(e\left(\frac{41}{64}\right)\) \(e\left(\frac{19}{64}\right)\) \(e\left(\frac{9}{32}\right)\) \(e\left(\frac{55}{64}\right)\)