Properties

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

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[156]
pari: [g,chi] = znchar(Mod(156,4033))

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.jk
Orbit index = 245

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 ]

\(\chi_{4033}(156,\cdot)\) \(\chi_{4033}(384,\cdot)\) \(\chi_{4033}(399,\cdot)\) \(\chi_{4033}(563,\cdot)\) \(\chi_{4033}(569,\cdot)\) \(\chi_{4033}(584,\cdot)\) \(\chi_{4033}(970,\cdot)\) \(\chi_{4033}(1096,\cdot)\) \(\chi_{4033}(1229,\cdot)\) \(\chi_{4033}(1318,\cdot)\) \(\chi_{4033}(1457,\cdot)\) \(\chi_{4033}(1540,\cdot)\) \(\chi_{4033}(1577,\cdot)\) \(\chi_{4033}(1688,\cdot)\) \(\chi_{4033}(1694,\cdot)\) \(\chi_{4033}(1895,\cdot)\) \(\chi_{4033}(1975,\cdot)\) \(\chi_{4033}(2006,\cdot)\) \(\chi_{4033}(2027,\cdot)\) \(\chi_{4033}(2058,\cdot)\) \(\chi_{4033}(2138,\cdot)\) \(\chi_{4033}(2339,\cdot)\) \(\chi_{4033}(2345,\cdot)\) \(\chi_{4033}(2456,\cdot)\) \(\chi_{4033}(2493,\cdot)\) \(\chi_{4033}(2576,\cdot)\) \(\chi_{4033}(2715,\cdot)\) \(\chi_{4033}(2804,\cdot)\) \(\chi_{4033}(2937,\cdot)\) \(\chi_{4033}(3063,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{1}{12}\right),e\left(\frac{17}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{19}{54}\right)\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{95}{108}\right)\)\(e\left(\frac{11}{27}\right)\)\(e\left(\frac{26}{27}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{19}{27}\right)\)\(e\left(\frac{101}{108}\right)\)\(e\left(\frac{61}{108}\right)\)
value at  e.g. 2

Related number fields

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