Properties

Conductor 4024
Order 502
Real No
Primitive Yes
Parity Even
Orbit Label 4024.j

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(4024)
 
sage: chi = H[19]
 
pari: [g,chi] = znchar(Mod(19,4024))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4024
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 502
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 4024.j
Orbit index = 10

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 ]
 

\(\chi_{4024}(19,\cdot)\) \(\chi_{4024}(35,\cdot)\) \(\chi_{4024}(51,\cdot)\) \(\chi_{4024}(107,\cdot)\) \(\chi_{4024}(115,\cdot)\) \(\chi_{4024}(123,\cdot)\) \(\chi_{4024}(139,\cdot)\) \(\chi_{4024}(163,\cdot)\) \(\chi_{4024}(171,\cdot)\) \(\chi_{4024}(179,\cdot)\) \(\chi_{4024}(187,\cdot)\) \(\chi_{4024}(195,\cdot)\) \(\chi_{4024}(203,\cdot)\) \(\chi_{4024}(211,\cdot)\) \(\chi_{4024}(227,\cdot)\) \(\chi_{4024}(235,\cdot)\) \(\chi_{4024}(251,\cdot)\) \(\chi_{4024}(259,\cdot)\) \(\chi_{4024}(267,\cdot)\) \(\chi_{4024}(307,\cdot)\) \(\chi_{4024}(315,\cdot)\) \(\chi_{4024}(331,\cdot)\) \(\chi_{4024}(347,\cdot)\) \(\chi_{4024}(371,\cdot)\) \(\chi_{4024}(395,\cdot)\) \(\chi_{4024}(403,\cdot)\) \(\chi_{4024}(411,\cdot)\) \(\chi_{4024}(419,\cdot)\) \(\chi_{4024}(451,\cdot)\) \(\chi_{4024}(459,\cdot)\) ...

Values on generators

\((1007,2013,2017)\) → \((-1,-1,e\left(\frac{237}{502}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{163}{251}\right)\)\(e\left(\frac{244}{251}\right)\)\(e\left(\frac{51}{502}\right)\)\(e\left(\frac{75}{251}\right)\)\(e\left(\frac{208}{251}\right)\)\(e\left(\frac{21}{502}\right)\)\(e\left(\frac{156}{251}\right)\)\(e\left(\frac{57}{502}\right)\)\(e\left(\frac{447}{502}\right)\)\(e\left(\frac{377}{502}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{251})\)