Properties

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

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[84]
pari: [g,chi] = znchar(Mod(84,4033))

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.hn
Orbit index = 196

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 ]

\(\chi_{4033}(84,\cdot)\) \(\chi_{4033}(137,\cdot)\) \(\chi_{4033}(211,\cdot)\) \(\chi_{4033}(306,\cdot)\) \(\chi_{4033}(322,\cdot)\) \(\chi_{4033}(433,\cdot)\) \(\chi_{4033}(639,\cdot)\) \(\chi_{4033}(972,\cdot)\) \(\chi_{4033}(1173,\cdot)\) \(\chi_{4033}(1453,\cdot)\) \(\chi_{4033}(2209,\cdot)\) \(\chi_{4033}(2267,\cdot)\) \(\chi_{4033}(2785,\cdot)\) \(\chi_{4033}(3192,\cdot)\) \(\chi_{4033}(3282,\cdot)\) \(\chi_{4033}(3562,\cdot)\) \(\chi_{4033}(3726,\cdot)\) \(\chi_{4033}(3985,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{49}{54}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{14}{27}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{8}{27}\right)\)\(e\left(\frac{49}{54}\right)\)\(e\left(\frac{17}{27}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{1}{27}\right)\)\(e\left(\frac{37}{54}\right)\)\(e\left(\frac{17}{54}\right)\)
value at  e.g. 2

Related number fields

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