Properties

Conductor 4033
Order 27
Real No
Primitive Yes
Parity Even
Orbit Label 4033.du

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[9]
 
pari: [g,chi] = znchar(Mod(9,4033))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4033
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 27
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.du
Orbit index = 99

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 ]
 

\(\chi_{4033}(9,\cdot)\) \(\chi_{4033}(81,\cdot)\) \(\chi_{4033}(266,\cdot)\) \(\chi_{4033}(330,\cdot)\) \(\chi_{4033}(525,\cdot)\) \(\chi_{4033}(1381,\cdot)\) \(\chi_{4033}(1822,\cdot)\) \(\chi_{4033}(2195,\cdot)\) \(\chi_{4033}(2512,\cdot)\) \(\chi_{4033}(2528,\cdot)\) \(\chi_{4033}(2532,\cdot)\) \(\chi_{4033}(2587,\cdot)\) \(\chi_{4033}(2623,\cdot)\) \(\chi_{4033}(2747,\cdot)\) \(\chi_{4033}(3087,\cdot)\) \(\chi_{4033}(3585,\cdot)\) \(\chi_{4033}(3623,\cdot)\) \(\chi_{4033}(3864,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{4}{9}\right),e\left(\frac{26}{27}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{17}{27}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{11}{27}\right)\)\(e\left(\frac{26}{27}\right)\)\(e\left(\frac{20}{27}\right)\)\(1\)\(e\left(\frac{7}{27}\right)\)\(e\left(\frac{20}{27}\right)\)\(e\left(\frac{7}{27}\right)\)
value at  e.g. 2

Related number fields

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