Properties

Conductor 8027
Order 319
Real No
Primitive Yes
Parity Even
Orbit Label 8027.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(8027)
 
sage: chi = H[31]
 
pari: [g,chi] = znchar(Mod(31,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 319
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.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 ]
 

\(\chi_{8027}(31,\cdot)\) \(\chi_{8027}(41,\cdot)\) \(\chi_{8027}(110,\cdot)\) \(\chi_{8027}(118,\cdot)\) \(\chi_{8027}(210,\cdot)\) \(\chi_{8027}(234,\cdot)\) \(\chi_{8027}(257,\cdot)\) \(\chi_{8027}(269,\cdot)\) \(\chi_{8027}(280,\cdot)\) \(\chi_{8027}(285,\cdot)\) \(\chi_{8027}(289,\cdot)\) \(\chi_{8027}(301,\cdot)\) \(\chi_{8027}(312,\cdot)\) \(\chi_{8027}(380,\cdot)\) \(\chi_{8027}(416,\cdot)\) \(\chi_{8027}(577,\cdot)\) \(\chi_{8027}(583,\cdot)\) \(\chi_{8027}(606,\cdot)\) \(\chi_{8027}(623,\cdot)\) \(\chi_{8027}(629,\cdot)\) \(\chi_{8027}(634,\cdot)\) \(\chi_{8027}(650,\cdot)\) \(\chi_{8027}(653,\cdot)\) \(\chi_{8027}(662,\cdot)\) \(\chi_{8027}(671,\cdot)\) \(\chi_{8027}(729,\cdot)\) \(\chi_{8027}(739,\cdot)\) \(\chi_{8027}(765,\cdot)\) \(\chi_{8027}(786,\cdot)\) \(\chi_{8027}(808,\cdot)\) ...

Values on generators

\((350,5935)\) → \((e\left(\frac{3}{11}\right),e\left(\frac{13}{29}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{317}{319}\right)\)\(e\left(\frac{6}{319}\right)\)\(e\left(\frac{315}{319}\right)\)\(e\left(\frac{10}{319}\right)\)\(e\left(\frac{4}{319}\right)\)\(e\left(\frac{69}{319}\right)\)\(e\left(\frac{313}{319}\right)\)\(e\left(\frac{12}{319}\right)\)\(e\left(\frac{8}{319}\right)\)\(e\left(\frac{277}{319}\right)\)
value at  e.g. 2

Related number fields

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