Properties

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

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[57]
pari: [g,chi] = znchar(Mod(57,4033))

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.jj
Orbit index = 244

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 ]

\(\chi_{4033}(57,\cdot)\) \(\chi_{4033}(283,\cdot)\) \(\chi_{4033}(422,\cdot)\) \(\chi_{4033}(486,\cdot)\) \(\chi_{4033}(644,\cdot)\) \(\chi_{4033}(721,\cdot)\) \(\chi_{4033}(883,\cdot)\) \(\chi_{4033}(1018,\cdot)\) \(\chi_{4033}(1034,\cdot)\) \(\chi_{4033}(1387,\cdot)\) \(\chi_{4033}(1404,\cdot)\) \(\chi_{4033}(1423,\cdot)\) \(\chi_{4033}(1502,\cdot)\) \(\chi_{4033}(1596,\cdot)\) \(\chi_{4033}(1726,\cdot)\) \(\chi_{4033}(1900,\cdot)\) \(\chi_{4033}(1904,\cdot)\) \(\chi_{4033}(1922,\cdot)\) \(\chi_{4033}(2111,\cdot)\) \(\chi_{4033}(2129,\cdot)\) \(\chi_{4033}(2133,\cdot)\) \(\chi_{4033}(2307,\cdot)\) \(\chi_{4033}(2437,\cdot)\) \(\chi_{4033}(2531,\cdot)\) \(\chi_{4033}(2610,\cdot)\) \(\chi_{4033}(2629,\cdot)\) \(\chi_{4033}(2646,\cdot)\) \(\chi_{4033}(2999,\cdot)\) \(\chi_{4033}(3015,\cdot)\) \(\chi_{4033}(3150,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{25}{36}\right),e\left(\frac{19}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{11}{54}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{37}{108}\right)\)\(e\left(\frac{25}{27}\right)\)\(e\left(\frac{7}{27}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{11}{27}\right)\)\(e\left(\frac{7}{108}\right)\)\(e\left(\frac{47}{108}\right)\)
value at  e.g. 2

Related number fields

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