Properties

Conductor 8027
Order 132
Real No
Primitive Yes
Parity Even
Orbit Label 8027.be

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[189]
 
pari: [g,chi] = znchar(Mod(189,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 132
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.be
Orbit index = 31

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 ]
 

\(\chi_{8027}(189,\cdot)\) \(\chi_{8027}(373,\cdot)\) \(\chi_{8027}(674,\cdot)\) \(\chi_{8027}(858,\cdot)\) \(\chi_{8027}(1023,\cdot)\) \(\chi_{8027}(1207,\cdot)\) \(\chi_{8027}(1236,\cdot)\) \(\chi_{8027}(1372,\cdot)\) \(\chi_{8027}(1420,\cdot)\) \(\chi_{8027}(1556,\cdot)\) \(\chi_{8027}(1585,\cdot)\) \(\chi_{8027}(1721,\cdot)\) \(\chi_{8027}(1769,\cdot)\) \(\chi_{8027}(1905,\cdot)\) \(\chi_{8027}(2632,\cdot)\) \(\chi_{8027}(2816,\cdot)\) \(\chi_{8027}(2981,\cdot)\) \(\chi_{8027}(3165,\cdot)\) \(\chi_{8027}(3815,\cdot)\) \(\chi_{8027}(3999,\cdot)\) \(\chi_{8027}(4377,\cdot)\) \(\chi_{8027}(4513,\cdot)\) \(\chi_{8027}(4561,\cdot)\) \(\chi_{8027}(4697,\cdot)\) \(\chi_{8027}(4726,\cdot)\) \(\chi_{8027}(4910,\cdot)\) \(\chi_{8027}(5075,\cdot)\) \(\chi_{8027}(5259,\cdot)\) \(\chi_{8027}(5424,\cdot)\) \(\chi_{8027}(5560,\cdot)\) ...

Values on generators

\((350,5935)\) → \((e\left(\frac{1}{22}\right),e\left(\frac{5}{12}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{67}{132}\right)\)\(e\left(\frac{37}{66}\right)\)\(e\left(\frac{1}{66}\right)\)\(e\left(\frac{29}{33}\right)\)\(e\left(\frac{3}{44}\right)\)\(e\left(\frac{103}{132}\right)\)\(e\left(\frac{23}{44}\right)\)\(e\left(\frac{4}{33}\right)\)\(e\left(\frac{17}{44}\right)\)\(e\left(\frac{7}{44}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{132})\)