Properties

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

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[18]
pari: [g,chi] = znchar(Mod(18,4033))

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.ig
Orbit index = 215

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 ]

\(\chi_{4033}(18,\cdot)\) \(\chi_{4033}(79,\cdot)\) \(\chi_{4033}(98,\cdot)\) \(\chi_{4033}(224,\cdot)\) \(\chi_{4033}(313,\cdot)\) \(\chi_{4033}(389,\cdot)\) \(\chi_{4033}(535,\cdot)\) \(\chi_{4033}(587,\cdot)\) \(\chi_{4033}(705,\cdot)\) \(\chi_{4033}(1021,\cdot)\) \(\chi_{4033}(1256,\cdot)\) \(\chi_{4033}(1456,\cdot)\) \(\chi_{4033}(1461,\cdot)\) \(\chi_{4033}(1467,\cdot)\) \(\chi_{4033}(1539,\cdot)\) \(\chi_{4033}(1611,\cdot)\) \(\chi_{4033}(1707,\cdot)\) \(\chi_{4033}(1909,\cdot)\) \(\chi_{4033}(2124,\cdot)\) \(\chi_{4033}(2326,\cdot)\) \(\chi_{4033}(2422,\cdot)\) \(\chi_{4033}(2494,\cdot)\) \(\chi_{4033}(2566,\cdot)\) \(\chi_{4033}(2572,\cdot)\) \(\chi_{4033}(2577,\cdot)\) \(\chi_{4033}(2777,\cdot)\) \(\chi_{4033}(3012,\cdot)\) \(\chi_{4033}(3328,\cdot)\) \(\chi_{4033}(3446,\cdot)\) \(\chi_{4033}(3498,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{17}{36}\right),e\left(\frac{53}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{43}{54}\right)\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{17}{108}\right)\)\(e\left(\frac{13}{54}\right)\)\(e\left(\frac{20}{27}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{16}{27}\right)\)\(e\left(\frac{65}{108}\right)\)\(e\left(\frac{97}{108}\right)\)
value at  e.g. 2

Related number fields

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