Properties

Conductor 503
Order 251
Real No
Primitive No
Parity Even
Orbit Label 4024.i

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[9]
 
pari: [g,chi] = znchar(Mod(9,4024))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 503
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 251
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 4024.i
Orbit index = 9

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 ]
 

\(\chi_{4024}(9,\cdot)\) \(\chi_{4024}(25,\cdot)\) \(\chi_{4024}(33,\cdot)\) \(\chi_{4024}(49,\cdot)\) \(\chi_{4024}(73,\cdot)\) \(\chi_{4024}(81,\cdot)\) \(\chi_{4024}(97,\cdot)\) \(\chi_{4024}(113,\cdot)\) \(\chi_{4024}(121,\cdot)\) \(\chi_{4024}(129,\cdot)\) \(\chi_{4024}(145,\cdot)\) \(\chi_{4024}(161,\cdot)\) \(\chi_{4024}(169,\cdot)\) \(\chi_{4024}(177,\cdot)\) \(\chi_{4024}(185,\cdot)\) \(\chi_{4024}(201,\cdot)\) \(\chi_{4024}(225,\cdot)\) \(\chi_{4024}(233,\cdot)\) \(\chi_{4024}(249,\cdot)\) \(\chi_{4024}(257,\cdot)\) \(\chi_{4024}(265,\cdot)\) \(\chi_{4024}(273,\cdot)\) \(\chi_{4024}(281,\cdot)\) \(\chi_{4024}(289,\cdot)\) \(\chi_{4024}(297,\cdot)\) \(\chi_{4024}(329,\cdot)\) \(\chi_{4024}(361,\cdot)\) \(\chi_{4024}(393,\cdot)\) \(\chi_{4024}(401,\cdot)\) \(\chi_{4024}(433,\cdot)\) ...

Inducing primitive character

\(\chi_{503}(9,\cdot)\)

Values on generators

\((1007,2013,2017)\) → \((1,1,e\left(\frac{156}{251}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{240}{251}\right)\)\(e\left(\frac{156}{251}\right)\)\(e\left(\frac{113}{251}\right)\)\(e\left(\frac{229}{251}\right)\)\(e\left(\frac{26}{251}\right)\)\(e\left(\frac{17}{251}\right)\)\(e\left(\frac{145}{251}\right)\)\(e\left(\frac{82}{251}\right)\)\(e\left(\frac{75}{251}\right)\)\(e\left(\frac{102}{251}\right)\)
value at  e.g. 2

Related number fields

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