Properties

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

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[39]
pari: [g,chi] = znchar(Mod(39,4033))

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.jx
Orbit index = 258

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 ]

\(\chi_{4033}(39,\cdot)\) \(\chi_{4033}(200,\cdot)\) \(\chi_{4033}(351,\cdot)\) \(\chi_{4033}(597,\cdot)\) \(\chi_{4033}(607,\cdot)\) \(\chi_{4033}(612,\cdot)\) \(\chi_{4033}(912,\cdot)\) \(\chi_{4033}(1127,\cdot)\) \(\chi_{4033}(1149,\cdot)\) \(\chi_{4033}(1243,\cdot)\) \(\chi_{4033}(1278,\cdot)\) \(\chi_{4033}(1430,\cdot)\) \(\chi_{4033}(1475,\cdot)\) \(\chi_{4033}(1515,\cdot)\) \(\chi_{4033}(1536,\cdot)\) \(\chi_{4033}(1758,\cdot)\) \(\chi_{4033}(1800,\cdot)\) \(\chi_{4033}(1956,\cdot)\) \(\chi_{4033}(2077,\cdot)\) \(\chi_{4033}(2233,\cdot)\) \(\chi_{4033}(2275,\cdot)\) \(\chi_{4033}(2497,\cdot)\) \(\chi_{4033}(2518,\cdot)\) \(\chi_{4033}(2558,\cdot)\) \(\chi_{4033}(2603,\cdot)\) \(\chi_{4033}(2755,\cdot)\) \(\chi_{4033}(2790,\cdot)\) \(\chi_{4033}(2884,\cdot)\) \(\chi_{4033}(2906,\cdot)\) \(\chi_{4033}(3121,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{1}{36}\right),e\left(\frac{11}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{1}{54}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{41}{108}\right)\)\(e\left(\frac{23}{27}\right)\)\(e\left(\frac{26}{27}\right)\)\(-1\)\(e\left(\frac{1}{27}\right)\)\(e\left(\frac{23}{108}\right)\)\(e\left(\frac{31}{108}\right)\)
value at  e.g. 2

Related number fields

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