Properties

Conductor 4029
Order 104
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4029.ci

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(4029)
 
sage: chi = H[2507]
 
pari: [g,chi] = znchar(Mod(2507,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4029
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 104
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.ci
Orbit index = 61

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 ]
 

\(\chi_{4029}(185,\cdot)\) \(\chi_{4029}(308,\cdot)\) \(\chi_{4029}(410,\cdot)\) \(\chi_{4029}(491,\cdot)\) \(\chi_{4029}(614,\cdot)\) \(\chi_{4029}(644,\cdot)\) \(\chi_{4029}(665,\cdot)\) \(\chi_{4029}(689,\cdot)\) \(\chi_{4029}(848,\cdot)\) \(\chi_{4029}(926,\cdot)\) \(\chi_{4029}(1175,\cdot)\) \(\chi_{4029}(1199,\cdot)\) \(\chi_{4029}(1226,\cdot)\) \(\chi_{4029}(1256,\cdot)\) \(\chi_{4029}(1358,\cdot)\) \(\chi_{4029}(1436,\cdot)\) \(\chi_{4029}(1562,\cdot)\) \(\chi_{4029}(1607,\cdot)\) \(\chi_{4029}(1613,\cdot)\) \(\chi_{4029}(1844,\cdot)\) \(\chi_{4029}(1913,\cdot)\) \(\chi_{4029}(2066,\cdot)\) \(\chi_{4029}(2123,\cdot)\) \(\chi_{4029}(2150,\cdot)\) \(\chi_{4029}(2174,\cdot)\) \(\chi_{4029}(2270,\cdot)\) \(\chi_{4029}(2303,\cdot)\) \(\chi_{4029}(2348,\cdot)\) \(\chi_{4029}(2507,\cdot)\) \(\chi_{4029}(2678,\cdot)\) ...

Values on generators

\((2687,3556,3163)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{5}{26}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{1}{52}\right)\)\(e\left(\frac{1}{26}\right)\)\(e\left(\frac{57}{104}\right)\)\(e\left(\frac{7}{104}\right)\)\(e\left(\frac{3}{52}\right)\)\(e\left(\frac{59}{104}\right)\)\(e\left(\frac{99}{104}\right)\)\(e\left(\frac{1}{26}\right)\)\(e\left(\frac{9}{104}\right)\)\(e\left(\frac{1}{13}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{104})\)