Properties

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

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[36]
pari: [g,chi] = znchar(Mod(36,4033))

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.hd
Orbit index = 186

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 ]

\(\chi_{4033}(36,\cdot)\) \(\chi_{4033}(628,\cdot)\) \(\chi_{4033}(850,\cdot)\) \(\chi_{4033}(1368,\cdot)\) \(\chi_{4033}(1664,\cdot)\) \(\chi_{4033}(1775,\cdot)\) \(\chi_{4033}(2145,\cdot)\) \(\chi_{4033}(2700,\cdot)\) \(\chi_{4033}(2737,\cdot)\) \(\chi_{4033}(2922,\cdot)\) \(\chi_{4033}(3181,\cdot)\) \(\chi_{4033}(3255,\cdot)\) \(\chi_{4033}(3440,\cdot)\) \(\chi_{4033}(3588,\cdot)\) \(\chi_{4033}(3625,\cdot)\) \(\chi_{4033}(3699,\cdot)\) \(\chi_{4033}(3810,\cdot)\) \(\chi_{4033}(3921,\cdot)\)

Values on generators

\((1963,2295)\) → \((-1,e\left(\frac{1}{54}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{26}{27}\right)\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{49}{54}\right)\)\(e\left(\frac{14}{27}\right)\)\(e\left(\frac{20}{27}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{25}{27}\right)\)\(e\left(\frac{25}{54}\right)\)\(e\left(\frac{29}{54}\right)\)
value at  e.g. 2

Related number fields

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