Properties

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

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[2085]
pari: [g,chi] = znchar(Mod(2085,4033))

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.hy
Orbit index = 207

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 ]

\(\chi_{4033}(24,\cdot)\) \(\chi_{4033}(166,\cdot)\) \(\chi_{4033}(168,\cdot)\) \(\chi_{4033}(466,\cdot)\) \(\chi_{4033}(476,\cdot)\) \(\chi_{4033}(701,\cdot)\) \(\chi_{4033}(942,\cdot)\) \(\chi_{4033}(994,\cdot)\) \(\chi_{4033}(1108,\cdot)\) \(\chi_{4033}(1132,\cdot)\) \(\chi_{4033}(1162,\cdot)\) \(\chi_{4033}(1314,\cdot)\) \(\chi_{4033}(1364,\cdot)\) \(\chi_{4033}(1482,\cdot)\) \(\chi_{4033}(1537,\cdot)\) \(\chi_{4033}(1795,\cdot)\) \(\chi_{4033}(1863,\cdot)\) \(\chi_{4033}(1948,\cdot)\) \(\chi_{4033}(2085,\cdot)\) \(\chi_{4033}(2170,\cdot)\) \(\chi_{4033}(2238,\cdot)\) \(\chi_{4033}(2496,\cdot)\) \(\chi_{4033}(2551,\cdot)\) \(\chi_{4033}(2669,\cdot)\) \(\chi_{4033}(2719,\cdot)\) \(\chi_{4033}(2871,\cdot)\) \(\chi_{4033}(2901,\cdot)\) \(\chi_{4033}(2925,\cdot)\) \(\chi_{4033}(3039,\cdot)\) \(\chi_{4033}(3091,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{11}{36}\right),e\left(\frac{97}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(-1\)\(e\left(\frac{35}{54}\right)\)\(1\)\(e\left(\frac{31}{108}\right)\)\(e\left(\frac{4}{27}\right)\)\(e\left(\frac{19}{27}\right)\)\(-1\)\(e\left(\frac{8}{27}\right)\)\(e\left(\frac{85}{108}\right)\)\(e\left(\frac{77}{108}\right)\)
value at  e.g. 2

Related number fields

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