Properties

Conductor 8027
Order 116
Real No
Primitive Yes
Parity Even
Orbit Label 8027.bb

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[321]
 
pari: [g,chi] = znchar(Mod(321,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 116
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.bb
Orbit index = 28

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 ]
 

\(\chi_{8027}(321,\cdot)\) \(\chi_{8027}(482,\cdot)\) \(\chi_{8027}(528,\cdot)\) \(\chi_{8027}(597,\cdot)\) \(\chi_{8027}(1057,\cdot)\) \(\chi_{8027}(1126,\cdot)\) \(\chi_{8027}(1149,\cdot)\) \(\chi_{8027}(1402,\cdot)\) \(\chi_{8027}(1448,\cdot)\) \(\chi_{8027}(1494,\cdot)\) \(\chi_{8027}(1563,\cdot)\) \(\chi_{8027}(1724,\cdot)\) \(\chi_{8027}(1908,\cdot)\) \(\chi_{8027}(1931,\cdot)\) \(\chi_{8027}(2115,\cdot)\) \(\chi_{8027}(2276,\cdot)\) \(\chi_{8027}(2345,\cdot)\) \(\chi_{8027}(2391,\cdot)\) \(\chi_{8027}(2437,\cdot)\) \(\chi_{8027}(2690,\cdot)\) \(\chi_{8027}(2713,\cdot)\) \(\chi_{8027}(2782,\cdot)\) \(\chi_{8027}(3242,\cdot)\) \(\chi_{8027}(3311,\cdot)\) \(\chi_{8027}(3357,\cdot)\) \(\chi_{8027}(3518,\cdot)\) \(\chi_{8027}(3886,\cdot)\) \(\chi_{8027}(4001,\cdot)\) \(\chi_{8027}(4484,\cdot)\) \(\chi_{8027}(4576,\cdot)\) ...

Values on generators

\((350,5935)\) → \((-1,e\left(\frac{81}{116}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{81}{116}\right)\)\(e\left(\frac{9}{58}\right)\)\(e\left(\frac{23}{58}\right)\)\(e\left(\frac{22}{29}\right)\)\(e\left(\frac{99}{116}\right)\)\(e\left(\frac{33}{116}\right)\)\(e\left(\frac{11}{116}\right)\)\(e\left(\frac{9}{29}\right)\)\(e\left(\frac{53}{116}\right)\)\(e\left(\frac{19}{116}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{116})\)