Properties

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

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[7]
 
pari: [g,chi] = znchar(Mod(7,4033))
 

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.ec
Orbit index = 107

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 ]
 

\(\chi_{4033}(7,\cdot)\) \(\chi_{4033}(49,\cdot)\) \(\chi_{4033}(342,\cdot)\) \(\chi_{4033}(349,\cdot)\) \(\chi_{4033}(625,\cdot)\) \(\chi_{4033}(626,\cdot)\) \(\chi_{4033}(675,\cdot)\) \(\chi_{4033}(811,\cdot)\) \(\chi_{4033}(969,\cdot)\) \(\chi_{4033}(1070,\cdot)\) \(\chi_{4033}(1644,\cdot)\) \(\chi_{4033}(1661,\cdot)\) \(\chi_{4033}(2401,\cdot)\) \(\chi_{4033}(2750,\cdot)\) \(\chi_{4033}(3305,\cdot)\) \(\chi_{4033}(3457,\cdot)\) \(\chi_{4033}(3561,\cdot)\) \(\chi_{4033}(3929,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{8}{9}\right),e\left(\frac{10}{27}\right))\)

Values

-11234567891011
\(1\)\(1\)\(1\)\(e\left(\frac{10}{27}\right)\)\(1\)\(e\left(\frac{16}{27}\right)\)\(e\left(\frac{10}{27}\right)\)\(e\left(\frac{7}{27}\right)\)\(1\)\(e\left(\frac{20}{27}\right)\)\(e\left(\frac{16}{27}\right)\)\(e\left(\frac{11}{27}\right)\)
value at  e.g. 2

Related number fields

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