Properties

Conductor 4033
Order 108
Real No
Primitive Yes
Parity Even
Orbit Label 4033.jl

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[6]
pari: [g,chi] = znchar(Mod(6,4033))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4033
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 108
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.jl
Orbit index = 246

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 ]

\(\chi_{4033}(6,\cdot)\) \(\chi_{4033}(228,\cdot)\) \(\chi_{4033}(265,\cdot)\) \(\chi_{4033}(290,\cdot)\) \(\chi_{4033}(450,\cdot)\) \(\chi_{4033}(475,\cdot)\) \(\chi_{4033}(487,\cdot)\) \(\chi_{4033}(598,\cdot)\) \(\chi_{4033}(672,\cdot)\) \(\chi_{4033}(968,\cdot)\) \(\chi_{4033}(1079,\cdot)\) \(\chi_{4033}(1338,\cdot)\) \(\chi_{4033}(1474,\cdot)\) \(\chi_{4033}(1486,\cdot)\) \(\chi_{4033}(1585,\cdot)\) \(\chi_{4033}(1659,\cdot)\) \(\chi_{4033}(1918,\cdot)\) \(\chi_{4033}(2004,\cdot)\) \(\chi_{4033}(2029,\cdot)\) \(\chi_{4033}(2115,\cdot)\) \(\chi_{4033}(2374,\cdot)\) \(\chi_{4033}(2448,\cdot)\) \(\chi_{4033}(2547,\cdot)\) \(\chi_{4033}(2559,\cdot)\) \(\chi_{4033}(2695,\cdot)\) \(\chi_{4033}(2954,\cdot)\) \(\chi_{4033}(3065,\cdot)\) \(\chi_{4033}(3361,\cdot)\) \(\chi_{4033}(3435,\cdot)\) \(\chi_{4033}(3546,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((-i,e\left(\frac{1}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{5}{18}\right)\)\(e\left(\frac{53}{54}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{103}{108}\right)\)\(e\left(\frac{7}{27}\right)\)\(e\left(\frac{10}{27}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{26}{27}\right)\)\(e\left(\frac{25}{108}\right)\)\(e\left(\frac{29}{108}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{108})\)