Properties

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

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[140]
 
pari: [g,chi] = znchar(Mod(140,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4029
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 = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4029.bx
Orbit index = 50

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 ]
 

\(\chi_{4029}(140,\cdot)\) \(\chi_{4029}(191,\cdot)\) \(\chi_{4029}(251,\cdot)\) \(\chi_{4029}(659,\cdot)\) \(\chi_{4029}(701,\cdot)\) \(\chi_{4029}(752,\cdot)\) \(\chi_{4029}(965,\cdot)\) \(\chi_{4029}(1118,\cdot)\) \(\chi_{4029}(1322,\cdot)\) \(\chi_{4029}(1730,\cdot)\) \(\chi_{4029}(1832,\cdot)\) \(\chi_{4029}(1874,\cdot)\) \(\chi_{4029}(2036,\cdot)\) \(\chi_{4029}(2087,\cdot)\) \(\chi_{4029}(2384,\cdot)\) \(\chi_{4029}(2597,\cdot)\) \(\chi_{4029}(2648,\cdot)\) \(\chi_{4029}(2792,\cdot)\) \(\chi_{4029}(3098,\cdot)\) \(\chi_{4029}(3251,\cdot)\) \(\chi_{4029}(3455,\cdot)\) \(\chi_{4029}(3770,\cdot)\) \(\chi_{4029}(3863,\cdot)\) \(\chi_{4029}(3965,\cdot)\)

Values on generators

\((2687,3556,3163)\) → \((-1,-i,e\left(\frac{15}{26}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{4}{13}\right)\)\(e\left(\frac{8}{13}\right)\)\(e\left(\frac{1}{52}\right)\)\(e\left(\frac{43}{52}\right)\)\(e\left(\frac{12}{13}\right)\)\(e\left(\frac{17}{52}\right)\)\(e\left(\frac{51}{52}\right)\)\(e\left(\frac{8}{13}\right)\)\(e\left(\frac{7}{52}\right)\)\(e\left(\frac{3}{13}\right)\)
value at  e.g. 2

Related number fields

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