Properties

Conductor 4029
Order 156
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4029.cp

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[47]
 
pari: [g,chi] = znchar(Mod(47,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4029
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 156
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.cp
Orbit index = 68

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 ]
 

\(\chi_{4029}(47,\cdot)\) \(\chi_{4029}(149,\cdot)\) \(\chi_{4029}(344,\cdot)\) \(\chi_{4029}(353,\cdot)\) \(\chi_{4029}(455,\cdot)\) \(\chi_{4029}(548,\cdot)\) \(\chi_{4029}(1007,\cdot)\) \(\chi_{4029}(1016,\cdot)\) \(\chi_{4029}(1109,\cdot)\) \(\chi_{4029}(1160,\cdot)\) \(\chi_{4029}(1169,\cdot)\) \(\chi_{4029}(1220,\cdot)\) \(\chi_{4029}(1262,\cdot)\) \(\chi_{4029}(1271,\cdot)\) \(\chi_{4029}(1373,\cdot)\) \(\chi_{4029}(1475,\cdot)\) \(\chi_{4029}(1619,\cdot)\) \(\chi_{4029}(1628,\cdot)\) \(\chi_{4029}(1772,\cdot)\) \(\chi_{4029}(1781,\cdot)\) \(\chi_{4029}(1823,\cdot)\) \(\chi_{4029}(1883,\cdot)\) \(\chi_{4029}(1925,\cdot)\) \(\chi_{4029}(2129,\cdot)\) \(\chi_{4029}(2180,\cdot)\) \(\chi_{4029}(2240,\cdot)\) \(\chi_{4029}(2282,\cdot)\) \(\chi_{4029}(2444,\cdot)\) \(\chi_{4029}(2486,\cdot)\) \(\chi_{4029}(2588,\cdot)\) ...

Values on generators

\((2687,3556,3163)\) → \((-1,i,e\left(\frac{59}{78}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{1}{39}\right)\)\(e\left(\frac{2}{39}\right)\)\(e\left(\frac{101}{156}\right)\)\(e\left(\frac{131}{156}\right)\)\(e\left(\frac{1}{13}\right)\)\(e\left(\frac{35}{52}\right)\)\(e\left(\frac{107}{156}\right)\)\(e\left(\frac{28}{39}\right)\)\(e\left(\frac{45}{52}\right)\)\(e\left(\frac{4}{39}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{156})\)