Properties

Conductor 8027
Order 638
Real No
Primitive Yes
Parity Even
Orbit Label 8027.bm

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[27]
 
pari: [g,chi] = znchar(Mod(27,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 638
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.bm
Orbit index = 39

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 ]
 

\(\chi_{8027}(27,\cdot)\) \(\chi_{8027}(36,\cdot)\) \(\chi_{8027}(48,\cdot)\) \(\chi_{8027}(64,\cdot)\) \(\chi_{8027}(75,\cdot)\) \(\chi_{8027}(100,\cdot)\) \(\chi_{8027}(121,\cdot)\) \(\chi_{8027}(223,\cdot)\) \(\chi_{8027}(239,\cdot)\) \(\chi_{8027}(261,\cdot)\) \(\chi_{8027}(282,\cdot)\) \(\chi_{8027}(308,\cdot)\) \(\chi_{8027}(376,\cdot)\) \(\chi_{8027}(386,\cdot)\) \(\chi_{8027}(394,\cdot)\) \(\chi_{8027}(397,\cdot)\) \(\chi_{8027}(409,\cdot)\) \(\chi_{8027}(418,\cdot)\) \(\chi_{8027}(441,\cdot)\) \(\chi_{8027}(449,\cdot)\) \(\chi_{8027}(464,\cdot)\) \(\chi_{8027}(588,\cdot)\) \(\chi_{8027}(610,\cdot)\) \(\chi_{8027}(657,\cdot)\) \(\chi_{8027}(715,\cdot)\) \(\chi_{8027}(725,\cdot)\) \(\chi_{8027}(762,\cdot)\) \(\chi_{8027}(767,\cdot)\) \(\chi_{8027}(784,\cdot)\) \(\chi_{8027}(790,\cdot)\) ...

Values on generators

\((350,5935)\) → \((e\left(\frac{2}{11}\right),e\left(\frac{13}{58}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{375}{638}\right)\)\(e\left(\frac{235}{319}\right)\)\(e\left(\frac{56}{319}\right)\)\(e\left(\frac{179}{319}\right)\)\(e\left(\frac{207}{638}\right)\)\(e\left(\frac{301}{638}\right)\)\(e\left(\frac{487}{638}\right)\)\(e\left(\frac{151}{319}\right)\)\(e\left(\frac{95}{638}\right)\)\(e\left(\frac{219}{638}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{319})\)