Properties

Conductor 8027
Order 3828
Real No
Primitive Yes
Parity Even
Orbit Label 8027.bu

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[7]
 
pari: [g,chi] = znchar(Mod(7,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 3828
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.bu
Orbit index = 47

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 ]
 

\(\chi_{8027}(7,\cdot)\) \(\chi_{8027}(30,\cdot)\) \(\chi_{8027}(33,\cdot)\) \(\chi_{8027}(34,\cdot)\) \(\chi_{8027}(40,\cdot)\) \(\chi_{8027}(43,\cdot)\) \(\chi_{8027}(44,\cdot)\) \(\chi_{8027}(63,\cdot)\) \(\chi_{8027}(74,\cdot)\) \(\chi_{8027}(84,\cdot)\) \(\chi_{8027}(89,\cdot)\) \(\chi_{8027}(90,\cdot)\) \(\chi_{8027}(97,\cdot)\) \(\chi_{8027}(99,\cdot)\) \(\chi_{8027}(107,\cdot)\) \(\chi_{8027}(112,\cdot)\) \(\chi_{8027}(113,\cdot)\) \(\chi_{8027}(120,\cdot)\) \(\chi_{8027}(129,\cdot)\) \(\chi_{8027}(132,\cdot)\) \(\chi_{8027}(134,\cdot)\) \(\chi_{8027}(149,\cdot)\) \(\chi_{8027}(152,\cdot)\) \(\chi_{8027}(159,\cdot)\) \(\chi_{8027}(166,\cdot)\) \(\chi_{8027}(172,\cdot)\) \(\chi_{8027}(175,\cdot)\) \(\chi_{8027}(176,\cdot)\) \(\chi_{8027}(195,\cdot)\) \(\chi_{8027}(199,\cdot)\) ...

Values on generators

\((350,5935)\) → \((e\left(\frac{19}{22}\right),e\left(\frac{67}{348}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{3521}{3828}\right)\)\(e\left(\frac{1577}{1914}\right)\)\(e\left(\frac{1607}{1914}\right)\)\(e\left(\frac{304}{957}\right)\)\(e\left(\frac{949}{1276}\right)\)\(e\left(\frac{1181}{3828}\right)\)\(e\left(\frac{969}{1276}\right)\)\(e\left(\frac{620}{957}\right)\)\(e\left(\frac{303}{1276}\right)\)\(e\left(\frac{1041}{1276}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{3828})\)