Properties

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

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[144]
pari: [g,chi] = znchar(Mod(144,4033))

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.eb
Orbit index = 106

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 ]

\(\chi_{4033}(144,\cdot)\) \(\chi_{4033}(157,\cdot)\) \(\chi_{4033}(416,\cdot)\) \(\chi_{4033}(451,\cdot)\) \(\chi_{4033}(571,\cdot)\) \(\chi_{4033}(663,\cdot)\) \(\chi_{4033}(784,\cdot)\) \(\chi_{4033}(921,\cdot)\) \(\chi_{4033}(1311,\cdot)\) \(\chi_{4033}(1640,\cdot)\) \(\chi_{4033}(1751,\cdot)\) \(\chi_{4033}(2476,\cdot)\) \(\chi_{4033}(2713,\cdot)\) \(\chi_{4033}(3401,\cdot)\) \(\chi_{4033}(3568,\cdot)\) \(\chi_{4033}(3622,\cdot)\) \(\chi_{4033}(3670,\cdot)\) \(\chi_{4033}(4005,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{2}{27}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{8}{27}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{11}{27}\right)\)\(e\left(\frac{2}{27}\right)\)\(e\left(\frac{20}{27}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{16}{27}\right)\)\(e\left(\frac{5}{27}\right)\)\(e\left(\frac{22}{27}\right)\)
value at  e.g. 2

Related number fields

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