Properties

Conductor 2012
Order 502
Real No
Primitive No
Parity Even
Orbit Label 4024.p

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[15]
 
pari: [g,chi] = znchar(Mod(15,4024))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2012
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 = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 4024.p
Orbit index = 16

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 ]
 

\(\chi_{4024}(15,\cdot)\) \(\chi_{4024}(31,\cdot)\) \(\chi_{4024}(55,\cdot)\) \(\chi_{4024}(71,\cdot)\) \(\chi_{4024}(87,\cdot)\) \(\chi_{4024}(103,\cdot)\) \(\chi_{4024}(111,\cdot)\) \(\chi_{4024}(119,\cdot)\) \(\chi_{4024}(127,\cdot)\) \(\chi_{4024}(135,\cdot)\) \(\chi_{4024}(151,\cdot)\) \(\chi_{4024}(159,\cdot)\) \(\chi_{4024}(167,\cdot)\) \(\chi_{4024}(191,\cdot)\) \(\chi_{4024}(215,\cdot)\) \(\chi_{4024}(239,\cdot)\) \(\chi_{4024}(247,\cdot)\) \(\chi_{4024}(279,\cdot)\) \(\chi_{4024}(287,\cdot)\) \(\chi_{4024}(295,\cdot)\) \(\chi_{4024}(303,\cdot)\) \(\chi_{4024}(311,\cdot)\) \(\chi_{4024}(319,\cdot)\) \(\chi_{4024}(327,\cdot)\) \(\chi_{4024}(335,\cdot)\) \(\chi_{4024}(359,\cdot)\) \(\chi_{4024}(375,\cdot)\) \(\chi_{4024}(391,\cdot)\) \(\chi_{4024}(399,\cdot)\) \(\chi_{4024}(407,\cdot)\) ...

Inducing primitive character

\(\chi_{2012}(15,\cdot)\)

Values on generators

\((1007,2013,2017)\) → \((-1,1,e\left(\frac{157}{502}\right))\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{145}{502}\right)\)\(e\left(\frac{157}{502}\right)\)\(e\left(\frac{199}{502}\right)\)\(e\left(\frac{145}{251}\right)\)\(e\left(\frac{319}{502}\right)\)\(e\left(\frac{196}{251}\right)\)\(e\left(\frac{151}{251}\right)\)\(e\left(\frac{311}{502}\right)\)\(e\left(\frac{156}{251}\right)\)\(e\left(\frac{172}{251}\right)\)
value at  e.g. 2

Related number fields

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