Properties

Conductor 8027
Order 1276
Real No
Primitive Yes
Parity Even
Orbit Label 8027.bq

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(8027)
 
sage: chi = H[10]
 
pari: [g,chi] = znchar(Mod(10,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 1276
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 = 8027.bq
Orbit index = 43

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 ]
 

\(\chi_{8027}(10,\cdot)\) \(\chi_{8027}(11,\cdot)\) \(\chi_{8027}(21,\cdot)\) \(\chi_{8027}(28,\cdot)\) \(\chi_{8027}(38,\cdot)\) \(\chi_{8027}(53,\cdot)\) \(\chi_{8027}(61,\cdot)\) \(\chi_{8027}(65,\cdot)\) \(\chi_{8027}(79,\cdot)\) \(\chi_{8027}(102,\cdot)\) \(\chi_{8027}(103,\cdot)\) \(\chi_{8027}(182,\cdot)\) \(\chi_{8027}(203,\cdot)\) \(\chi_{8027}(218,\cdot)\) \(\chi_{8027}(222,\cdot)\) \(\chi_{8027}(247,\cdot)\) \(\chi_{8027}(251,\cdot)\) \(\chi_{8027}(270,\cdot)\) \(\chi_{8027}(291,\cdot)\) \(\chi_{8027}(296,\cdot)\) \(\chi_{8027}(297,\cdot)\) \(\chi_{8027}(310,\cdot)\) \(\chi_{8027}(314,\cdot)\) \(\chi_{8027}(339,\cdot)\) \(\chi_{8027}(341,\cdot)\) \(\chi_{8027}(343,\cdot)\) \(\chi_{8027}(355,\cdot)\) \(\chi_{8027}(359,\cdot)\) \(\chi_{8027}(360,\cdot)\) \(\chi_{8027}(387,\cdot)\) ...

Values on generators

\((350,5935)\) → \((e\left(\frac{3}{22}\right),e\left(\frac{105}{116}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{227}{1276}\right)\)\(e\left(\frac{457}{638}\right)\)\(e\left(\frac{227}{638}\right)\)\(e\left(\frac{115}{319}\right)\)\(e\left(\frac{1141}{1276}\right)\)\(e\left(\frac{303}{1276}\right)\)\(e\left(\frac{681}{1276}\right)\)\(e\left(\frac{138}{319}\right)\)\(e\left(\frac{687}{1276}\right)\)\(e\left(\frac{301}{1276}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{1276})\)