Properties

Conductor 1343
Order 52
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4029.bz

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4029)
 
sage: chi = H[64]
 
pari: [g,chi] = znchar(Mod(64,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1343
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 52
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4029.bz
Orbit index = 52

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{4029}(64,\cdot)\) \(\chi_{4029}(166,\cdot)\) \(\chi_{4029}(259,\cdot)\) \(\chi_{4029}(574,\cdot)\) \(\chi_{4029}(778,\cdot)\) \(\chi_{4029}(931,\cdot)\) \(\chi_{4029}(1237,\cdot)\) \(\chi_{4029}(1381,\cdot)\) \(\chi_{4029}(1432,\cdot)\) \(\chi_{4029}(1645,\cdot)\) \(\chi_{4029}(1942,\cdot)\) \(\chi_{4029}(1993,\cdot)\) \(\chi_{4029}(2155,\cdot)\) \(\chi_{4029}(2197,\cdot)\) \(\chi_{4029}(2299,\cdot)\) \(\chi_{4029}(2707,\cdot)\) \(\chi_{4029}(2911,\cdot)\) \(\chi_{4029}(3064,\cdot)\) \(\chi_{4029}(3277,\cdot)\) \(\chi_{4029}(3328,\cdot)\) \(\chi_{4029}(3370,\cdot)\) \(\chi_{4029}(3778,\cdot)\) \(\chi_{4029}(3838,\cdot)\) \(\chi_{4029}(3889,\cdot)\)

Values on generators

\((2687,3556,3163)\) → \((1,i,e\left(\frac{4}{13}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{19}{26}\right)\)\(e\left(\frac{6}{13}\right)\)\(e\left(\frac{17}{52}\right)\)\(e\left(\frac{3}{52}\right)\)\(e\left(\frac{5}{26}\right)\)\(e\left(\frac{3}{52}\right)\)\(e\left(\frac{35}{52}\right)\)\(e\left(\frac{6}{13}\right)\)\(e\left(\frac{41}{52}\right)\)\(e\left(\frac{12}{13}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{52})\)