Properties

Conductor 4029
Order 208
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4029.cs

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[62]
 
pari: [g,chi] = znchar(Mod(62,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4029
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 208
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.cs
Orbit index = 71

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 ]
 

\(\chi_{4029}(62,\cdot)\) \(\chi_{4029}(65,\cdot)\) \(\chi_{4029}(125,\cdot)\) \(\chi_{4029}(131,\cdot)\) \(\chi_{4029}(143,\cdot)\) \(\chi_{4029}(146,\cdot)\) \(\chi_{4029}(176,\cdot)\) \(\chi_{4029}(245,\cdot)\) \(\chi_{4029}(275,\cdot)\) \(\chi_{4029}(299,\cdot)\) \(\chi_{4029}(326,\cdot)\) \(\chi_{4029}(362,\cdot)\) \(\chi_{4029}(368,\cdot)\) \(\chi_{4029}(380,\cdot)\) \(\chi_{4029}(413,\cdot)\) \(\chi_{4029}(482,\cdot)\) \(\chi_{4029}(539,\cdot)\) \(\chi_{4029}(575,\cdot)\) \(\chi_{4029}(605,\cdot)\) \(\chi_{4029}(617,\cdot)\) \(\chi_{4029}(653,\cdot)\) \(\chi_{4029}(719,\cdot)\) \(\chi_{4029}(776,\cdot)\) \(\chi_{4029}(836,\cdot)\) \(\chi_{4029}(857,\cdot)\) \(\chi_{4029}(887,\cdot)\) \(\chi_{4029}(890,\cdot)\) \(\chi_{4029}(1010,\cdot)\) \(\chi_{4029}(1013,\cdot)\) \(\chi_{4029}(1049,\cdot)\) ...

Values on generators

\((2687,3556,3163)\) → \((-1,e\left(\frac{7}{16}\right),e\left(\frac{10}{13}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{73}{104}\right)\)\(e\left(\frac{21}{52}\right)\)\(e\left(\frac{79}{208}\right)\)\(e\left(\frac{121}{208}\right)\)\(e\left(\frac{11}{104}\right)\)\(e\left(\frac{17}{208}\right)\)\(e\left(\frac{181}{208}\right)\)\(e\left(\frac{47}{52}\right)\)\(e\left(\frac{59}{208}\right)\)\(e\left(\frac{21}{26}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{208})\)