Properties

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

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[182]
pari: [g,chi] = znchar(Mod(182,4033))

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.dx
Orbit index = 102

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 ]

\(\chi_{4033}(182,\cdot)\) \(\chi_{4033}(514,\cdot)\) \(\chi_{4033}(789,\cdot)\) \(\chi_{4033}(860,\cdot)\) \(\chi_{4033}(996,\cdot)\) \(\chi_{4033}(1006,\cdot)\) \(\chi_{4033}(1329,\cdot)\) \(\chi_{4033}(1439,\cdot)\) \(\chi_{4033}(1529,\cdot)\) \(\chi_{4033}(1561,\cdot)\) \(\chi_{4033}(1607,\cdot)\) \(\chi_{4033}(1792,\cdot)\) \(\chi_{4033}(2051,\cdot)\) \(\chi_{4033}(2338,\cdot)\) \(\chi_{4033}(2734,\cdot)\) \(\chi_{4033}(3786,\cdot)\) \(\chi_{4033}(3820,\cdot)\) \(\chi_{4033}(3931,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{2}{9}\right),e\left(\frac{14}{27}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{20}{27}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{14}{27}\right)\)\(e\left(\frac{14}{27}\right)\)\(e\left(\frac{23}{27}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{13}{27}\right)\)\(e\left(\frac{8}{27}\right)\)\(e\left(\frac{19}{27}\right)\)
value at  e.g. 2

Related number fields

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