Properties

Conductor 79
Order 39
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4029.bs

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[256]
 
pari: [g,chi] = znchar(Mod(256,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 79
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 39
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.bs
Orbit index = 45

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 ]
 

\(\chi_{4029}(256,\cdot)\) \(\chi_{4029}(358,\cdot)\) \(\chi_{4029}(562,\cdot)\) \(\chi_{4029}(664,\cdot)\) \(\chi_{4029}(715,\cdot)\) \(\chi_{4029}(919,\cdot)\) \(\chi_{4029}(1021,\cdot)\) \(\chi_{4029}(1072,\cdot)\) \(\chi_{4029}(1225,\cdot)\) \(\chi_{4029}(1582,\cdot)\) \(\chi_{4029}(1684,\cdot)\) \(\chi_{4029}(1735,\cdot)\) \(\chi_{4029}(1837,\cdot)\) \(\chi_{4029}(2296,\cdot)\) \(\chi_{4029}(2500,\cdot)\) \(\chi_{4029}(2857,\cdot)\) \(\chi_{4029}(2959,\cdot)\) \(\chi_{4029}(3112,\cdot)\) \(\chi_{4029}(3265,\cdot)\) \(\chi_{4029}(3367,\cdot)\) \(\chi_{4029}(3469,\cdot)\) \(\chi_{4029}(3520,\cdot)\) \(\chi_{4029}(3571,\cdot)\) \(\chi_{4029}(3724,\cdot)\)

Values on generators

\((2687,3556,3163)\) → \((1,1,e\left(\frac{16}{39}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{25}{39}\right)\)\(e\left(\frac{11}{39}\right)\)\(e\left(\frac{17}{39}\right)\)\(e\left(\frac{29}{39}\right)\)\(e\left(\frac{12}{13}\right)\)\(e\left(\frac{1}{13}\right)\)\(e\left(\frac{35}{39}\right)\)\(e\left(\frac{37}{39}\right)\)\(e\left(\frac{5}{13}\right)\)\(e\left(\frac{22}{39}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{39})\)