Properties

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

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[42]
pari: [g,chi] = znchar(Mod(42,4033))

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.jn
Orbit index = 248

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 ]

\(\chi_{4033}(42,\cdot)\) \(\chi_{4033}(50,\cdot)\) \(\chi_{4033}(96,\cdot)\) \(\chi_{4033}(242,\cdot)\) \(\chi_{4033}(274,\cdot)\) \(\chi_{4033}(442,\cdot)\) \(\chi_{4033}(610,\cdot)\) \(\chi_{4033}(614,\cdot)\) \(\chi_{4033}(624,\cdot)\) \(\chi_{4033}(923,\cdot)\) \(\chi_{4033}(1038,\cdot)\) \(\chi_{4033}(1160,\cdot)\) \(\chi_{4033}(1319,\cdot)\) \(\chi_{4033}(1573,\cdot)\) \(\chi_{4033}(1645,\cdot)\) \(\chi_{4033}(1781,\cdot)\) \(\chi_{4033}(1867,\cdot)\) \(\chi_{4033}(1980,\cdot)\) \(\chi_{4033}(2053,\cdot)\) \(\chi_{4033}(2166,\cdot)\) \(\chi_{4033}(2252,\cdot)\) \(\chi_{4033}(2388,\cdot)\) \(\chi_{4033}(2460,\cdot)\) \(\chi_{4033}(2714,\cdot)\) \(\chi_{4033}(2873,\cdot)\) \(\chi_{4033}(2995,\cdot)\) \(\chi_{4033}(3110,\cdot)\) \(\chi_{4033}(3409,\cdot)\) \(\chi_{4033}(3419,\cdot)\) \(\chi_{4033}(3423,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{23}{36}\right),e\left(\frac{41}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{5}{18}\right)\)\(e\left(\frac{19}{54}\right)\)\(e\left(\frac{5}{9}\right)\)\(e\left(\frac{59}{108}\right)\)\(e\left(\frac{17}{27}\right)\)\(e\left(\frac{17}{27}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{19}{27}\right)\)\(e\left(\frac{89}{108}\right)\)\(e\left(\frac{73}{108}\right)\)
value at  e.g. 2

Related number fields

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