Properties

Conductor 4033
Order 108
Real No
Primitive Yes
Parity Odd
Orbit Label 4033.ja

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[2009]
pari: [g,chi] = znchar(Mod(2009,4033))

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 = Odd
Orbit label = 4033.ja
Orbit index = 235

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 ]

\(\chi_{4033}(11,\cdot)\) \(\chi_{4033}(159,\cdot)\) \(\chi_{4033}(212,\cdot)\) \(\chi_{4033}(418,\cdot)\) \(\chi_{4033}(825,\cdot)\) \(\chi_{4033}(878,\cdot)\) \(\chi_{4033}(1100,\cdot)\) \(\chi_{4033}(1269,\cdot)\) \(\chi_{4033}(1322,\cdot)\) \(\chi_{4033}(1359,\cdot)\) \(\chi_{4033}(1380,\cdot)\) \(\chi_{4033}(1454,\cdot)\) \(\chi_{4033}(1470,\cdot)\) \(\chi_{4033}(1565,\cdot)\) \(\chi_{4033}(1692,\cdot)\) \(\chi_{4033}(1840,\cdot)\) \(\chi_{4033}(1877,\cdot)\) \(\chi_{4033}(2009,\cdot)\) \(\chi_{4033}(2358,\cdot)\) \(\chi_{4033}(2416,\cdot)\) \(\chi_{4033}(2675,\cdot)\) \(\chi_{4033}(2765,\cdot)\) \(\chi_{4033}(2823,\cdot)\) \(\chi_{4033}(3008,\cdot)\) \(\chi_{4033}(3082,\cdot)\) \(\chi_{4033}(3119,\cdot)\) \(\chi_{4033}(3246,\cdot)\) \(\chi_{4033}(3283,\cdot)\) \(\chi_{4033}(3431,\cdot)\) \(\chi_{4033}(3653,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{17}{108}\right))\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{29}{36}\right)\)\(e\left(\frac{23}{27}\right)\)\(e\left(\frac{11}{18}\right)\)\(e\left(\frac{7}{54}\right)\)\(e\left(\frac{71}{108}\right)\)\(e\left(\frac{26}{27}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{19}{27}\right)\)\(e\left(\frac{101}{108}\right)\)\(e\left(\frac{7}{108}\right)\)
value at  e.g. 2

Related number fields

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