Properties

Conductor 1007
Order 468
Real No
Primitive Yes
Parity Even
Orbit Label 1007.bi

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(1007)
 
sage: chi = H[79]
 
pari: [g,chi] = znchar(Mod(79,1007))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1007
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 468
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 = 1007.bi
Orbit index = 35

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 ]
 

\(\chi_{1007}(2,\cdot)\) \(\chi_{1007}(3,\cdot)\) \(\chi_{1007}(14,\cdot)\) \(\chi_{1007}(21,\cdot)\) \(\chi_{1007}(22,\cdot)\) \(\chi_{1007}(32,\cdot)\) \(\chi_{1007}(33,\cdot)\) \(\chi_{1007}(34,\cdot)\) \(\chi_{1007}(41,\cdot)\) \(\chi_{1007}(48,\cdot)\) \(\chi_{1007}(51,\cdot)\) \(\chi_{1007}(67,\cdot)\) \(\chi_{1007}(71,\cdot)\) \(\chi_{1007}(72,\cdot)\) \(\chi_{1007}(79,\cdot)\) \(\chi_{1007}(86,\cdot)\) \(\chi_{1007}(98,\cdot)\) \(\chi_{1007}(108,\cdot)\) \(\chi_{1007}(109,\cdot)\) \(\chi_{1007}(124,\cdot)\) \(\chi_{1007}(127,\cdot)\) \(\chi_{1007}(128,\cdot)\) \(\chi_{1007}(147,\cdot)\) \(\chi_{1007}(154,\cdot)\) \(\chi_{1007}(162,\cdot)\) \(\chi_{1007}(167,\cdot)\) \(\chi_{1007}(173,\cdot)\) \(\chi_{1007}(181,\cdot)\) \(\chi_{1007}(185,\cdot)\) \(\chi_{1007}(186,\cdot)\) ...

Values on generators

\((743,267)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{25}{52}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{95}{468}\right)\)\(e\left(\frac{263}{468}\right)\)\(e\left(\frac{95}{234}\right)\)\(e\left(\frac{71}{468}\right)\)\(e\left(\frac{179}{234}\right)\)\(e\left(\frac{5}{78}\right)\)\(e\left(\frac{95}{156}\right)\)\(e\left(\frac{29}{234}\right)\)\(e\left(\frac{83}{234}\right)\)\(e\left(\frac{43}{78}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{468})\)