Properties

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

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[78]
pari: [g,chi] = znchar(Mod(78,4033))

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.hp
Orbit index = 198

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 ]

\(\chi_{4033}(78,\cdot)\) \(\chi_{4033}(669,\cdot)\) \(\chi_{4033}(768,\cdot)\) \(\chi_{4033}(879,\cdot)\) \(\chi_{4033}(1002,\cdot)\) \(\chi_{4033}(1003,\cdot)\) \(\chi_{4033}(1061,\cdot)\) \(\chi_{4033}(1769,\cdot)\) \(\chi_{4033}(1841,\cdot)\) \(\chi_{4033}(2097,\cdot)\) \(\chi_{4033}(2298,\cdot)\) \(\chi_{4033}(2324,\cdot)\) \(\chi_{4033}(2837,\cdot)\) \(\chi_{4033}(3101,\cdot)\) \(\chi_{4033}(3351,\cdot)\) \(\chi_{4033}(3536,\cdot)\) \(\chi_{4033}(3795,\cdot)\) \(\chi_{4033}(3888,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{17}{27}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{17}{18}\right)\)\(e\left(\frac{5}{27}\right)\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{7}{54}\right)\)\(e\left(\frac{7}{54}\right)\)\(e\left(\frac{26}{27}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{10}{27}\right)\)\(e\left(\frac{2}{27}\right)\)\(e\left(\frac{25}{27}\right)\)
value at  e.g. 2

Related number fields

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