Properties

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

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[13]
 
pari: [g,chi] = znchar(Mod(13,4024))
 

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.o
Orbit index = 15

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 ]
 

\(\chi_{4024}(13,\cdot)\) \(\chi_{4024}(21,\cdot)\) \(\chi_{4024}(61,\cdot)\) \(\chi_{4024}(69,\cdot)\) \(\chi_{4024}(77,\cdot)\) \(\chi_{4024}(85,\cdot)\) \(\chi_{4024}(117,\cdot)\) \(\chi_{4024}(141,\cdot)\) \(\chi_{4024}(173,\cdot)\) \(\chi_{4024}(189,\cdot)\) \(\chi_{4024}(197,\cdot)\) \(\chi_{4024}(205,\cdot)\) \(\chi_{4024}(229,\cdot)\) \(\chi_{4024}(237,\cdot)\) \(\chi_{4024}(253,\cdot)\) \(\chi_{4024}(285,\cdot)\) \(\chi_{4024}(293,\cdot)\) \(\chi_{4024}(301,\cdot)\) \(\chi_{4024}(317,\cdot)\) \(\chi_{4024}(325,\cdot)\) \(\chi_{4024}(373,\cdot)\) \(\chi_{4024}(389,\cdot)\) \(\chi_{4024}(397,\cdot)\) \(\chi_{4024}(413,\cdot)\) \(\chi_{4024}(421,\cdot)\) \(\chi_{4024}(429,\cdot)\) \(\chi_{4024}(445,\cdot)\) \(\chi_{4024}(469,\cdot)\) \(\chi_{4024}(493,\cdot)\) \(\chi_{4024}(509,\cdot)\) ...

Values on generators

\((1007,2013,2017)\) → \((1,-1,e\left(\frac{62}{251}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{17}{502}\right)\)\(e\left(\frac{375}{502}\right)\)\(e\left(\frac{61}{251}\right)\)\(e\left(\frac{17}{251}\right)\)\(e\left(\frac{439}{502}\right)\)\(e\left(\frac{65}{502}\right)\)\(e\left(\frac{196}{251}\right)\)\(e\left(\frac{142}{251}\right)\)\(e\left(\frac{21}{502}\right)\)\(e\left(\frac{139}{502}\right)\)
value at  e.g. 2

Related number fields

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