Properties

Conductor 4029
Order 624
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4029.cz

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[5]
 
pari: [g,chi] = znchar(Mod(5,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4029
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 624
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.cz
Orbit index = 78

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 ]
 

\(\chi_{4029}(5,\cdot)\) \(\chi_{4029}(11,\cdot)\) \(\chi_{4029}(20,\cdot)\) \(\chi_{4029}(44,\cdot)\) \(\chi_{4029}(92,\cdot)\) \(\chi_{4029}(95,\cdot)\) \(\chi_{4029}(167,\cdot)\) \(\chi_{4029}(194,\cdot)\) \(\chi_{4029}(209,\cdot)\) \(\chi_{4029}(248,\cdot)\) \(\chi_{4029}(269,\cdot)\) \(\chi_{4029}(320,\cdot)\) \(\chi_{4029}(329,\cdot)\) \(\chi_{4029}(335,\cdot)\) \(\chi_{4029}(347,\cdot)\) \(\chi_{4029}(431,\cdot)\) \(\chi_{4029}(437,\cdot)\) \(\chi_{4029}(479,\cdot)\) \(\chi_{4029}(500,\cdot)\) \(\chi_{4029}(524,\cdot)\) \(\chi_{4029}(566,\cdot)\) \(\chi_{4029}(572,\cdot)\) \(\chi_{4029}(584,\cdot)\) \(\chi_{4029}(602,\cdot)\) \(\chi_{4029}(626,\cdot)\) \(\chi_{4029}(641,\cdot)\) \(\chi_{4029}(668,\cdot)\) \(\chi_{4029}(674,\cdot)\) \(\chi_{4029}(677,\cdot)\) \(\chi_{4029}(683,\cdot)\) ...

Values on generators

\((2687,3556,3163)\) → \((-1,e\left(\frac{5}{16}\right),e\left(\frac{31}{39}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{17}{312}\right)\)\(e\left(\frac{17}{156}\right)\)\(e\left(\frac{215}{624}\right)\)\(e\left(\frac{353}{624}\right)\)\(e\left(\frac{17}{104}\right)\)\(e\left(\frac{83}{208}\right)\)\(e\left(\frac{461}{624}\right)\)\(e\left(\frac{43}{156}\right)\)\(e\left(\frac{129}{208}\right)\)\(e\left(\frac{17}{78}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{624})\)