Properties

Conductor 8027
Order 33
Real No
Primitive Yes
Parity Even
Orbit Label 8027.r

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[924]
 
pari: [g,chi] = znchar(Mod(924,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 33
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.r
Orbit index = 18

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 ]
 

\(\chi_{8027}(924,\cdot)\) \(\chi_{8027}(1273,\cdot)\) \(\chi_{8027}(1622,\cdot)\) \(\chi_{8027}(1867,\cdot)\) \(\chi_{8027}(1971,\cdot)\) \(\chi_{8027}(2216,\cdot)\) \(\chi_{8027}(2565,\cdot)\) \(\chi_{8027}(2914,\cdot)\) \(\chi_{8027}(3367,\cdot)\) \(\chi_{8027}(3716,\cdot)\) \(\chi_{8027}(4310,\cdot)\) \(\chi_{8027}(4659,\cdot)\) \(\chi_{8027}(4763,\cdot)\) \(\chi_{8027}(5112,\cdot)\) \(\chi_{8027}(5706,\cdot)\) \(\chi_{8027}(6055,\cdot)\) \(\chi_{8027}(6159,\cdot)\) \(\chi_{8027}(6857,\cdot)\) \(\chi_{8027}(7102,\cdot)\) \(\chi_{8027}(7800,\cdot)\)

Values on generators

\((350,5935)\) → \((e\left(\frac{2}{11}\right),e\left(\frac{1}{3}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{23}{33}\right)\)\(e\left(\frac{19}{33}\right)\)\(e\left(\frac{13}{33}\right)\)\(e\left(\frac{28}{33}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{26}{33}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{5}{33}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{7}{11}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{33})\)