Properties

Conductor 4033
Order 54
Real No
Primitive Yes
Parity Even
Orbit Label 4033.hw

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(4033)
 
sage: chi = H[3]
 
pari: [g,chi] = znchar(Mod(3,4033))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4033
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 54
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 = 4033.hw
Orbit index = 205

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 ]
 

\(\chi_{4033}(3,\cdot)\) \(\chi_{4033}(243,\cdot)\) \(\chi_{4033}(798,\cdot)\) \(\chi_{4033}(844,\cdot)\) \(\chi_{4033}(990,\cdot)\) \(\chi_{4033}(1029,\cdot)\) \(\chi_{4033}(1288,\cdot)\) \(\chi_{4033}(1575,\cdot)\) \(\chi_{4033}(2076,\cdot)\) \(\chi_{4033}(2187,\cdot)\) \(\chi_{4033}(2260,\cdot)\) \(\chi_{4033}(2689,\cdot)\) \(\chi_{4033}(2803,\cdot)\) \(\chi_{4033}(3149,\cdot)\) \(\chi_{4033}(3296,\cdot)\) \(\chi_{4033}(3503,\cdot)\) \(\chi_{4033}(3728,\cdot)\) \(\chi_{4033}(3836,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{13}{18}\right),e\left(\frac{13}{27}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{22}{27}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{11}{54}\right)\)\(e\left(\frac{53}{54}\right)\)\(e\left(\frac{10}{27}\right)\)\(-1\)\(e\left(\frac{17}{27}\right)\)\(e\left(\frac{10}{27}\right)\)\(e\left(\frac{17}{27}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{27})\)