Properties

Conductor 1343
Order 624
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4029.cy

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[7]
 
pari: [g,chi] = znchar(Mod(7,4029))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1343
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 = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4029.cy
Orbit index = 77

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 ]
 

\(\chi_{4029}(7,\cdot)\) \(\chi_{4029}(28,\cdot)\) \(\chi_{4029}(37,\cdot)\) \(\chi_{4029}(82,\cdot)\) \(\chi_{4029}(109,\cdot)\) \(\chi_{4029}(133,\cdot)\) \(\chi_{4029}(139,\cdot)\) \(\chi_{4029}(142,\cdot)\) \(\chi_{4029}(193,\cdot)\) \(\chi_{4029}(211,\cdot)\) \(\chi_{4029}(226,\cdot)\) \(\chi_{4029}(232,\cdot)\) \(\chi_{4029}(235,\cdot)\) \(\chi_{4029}(244,\cdot)\) \(\chi_{4029}(265,\cdot)\) \(\chi_{4029}(346,\cdot)\) \(\chi_{4029}(364,\cdot)\) \(\chi_{4029}(379,\cdot)\) \(\chi_{4029}(430,\cdot)\) \(\chi_{4029}(448,\cdot)\) \(\chi_{4029}(454,\cdot)\) \(\chi_{4029}(469,\cdot)\) \(\chi_{4029}(481,\cdot)\) \(\chi_{4029}(517,\cdot)\) \(\chi_{4029}(556,\cdot)\) \(\chi_{4029}(583,\cdot)\) \(\chi_{4029}(592,\cdot)\) \(\chi_{4029}(601,\cdot)\) \(\chi_{4029}(607,\cdot)\) \(\chi_{4029}(619,\cdot)\) ...

Values on generators

\((2687,3556,3163)\) → \((1,e\left(\frac{11}{16}\right),e\left(\frac{53}{78}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{107}{312}\right)\)\(e\left(\frac{107}{156}\right)\)\(e\left(\frac{353}{624}\right)\)\(e\left(\frac{359}{624}\right)\)\(e\left(\frac{3}{104}\right)\)\(e\left(\frac{189}{208}\right)\)\(e\left(\frac{11}{624}\right)\)\(e\left(\frac{133}{156}\right)\)\(e\left(\frac{191}{208}\right)\)\(e\left(\frac{29}{78}\right)\)
value at  e.g. 2

Related number fields

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