Properties

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

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[56]
pari: [g,chi] = znchar(Mod(56,4033))

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.hz
Orbit index = 208

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 ]

\(\chi_{4033}(56,\cdot)\) \(\chi_{4033}(59,\cdot)\) \(\chi_{4033}(72,\cdot)\) \(\chi_{4033}(91,\cdot)\) \(\chi_{4033}(314,\cdot)\) \(\chi_{4033}(494,\cdot)\) \(\chi_{4033}(498,\cdot)\) \(\chi_{4033}(832,\cdot)\) \(\chi_{4033}(957,\cdot)\) \(\chi_{4033}(967,\cdot)\) \(\chi_{4033}(975,\cdot)\) \(\chi_{4033}(1051,\cdot)\) \(\chi_{4033}(1189,\cdot)\) \(\chi_{4033}(1352,\cdot)\) \(\chi_{4033}(1428,\cdot)\) \(\chi_{4033}(1556,\cdot)\) \(\chi_{4033}(1578,\cdot)\) \(\chi_{4033}(1811,\cdot)\) \(\chi_{4033}(2222,\cdot)\) \(\chi_{4033}(2455,\cdot)\) \(\chi_{4033}(2477,\cdot)\) \(\chi_{4033}(2605,\cdot)\) \(\chi_{4033}(2681,\cdot)\) \(\chi_{4033}(2844,\cdot)\) \(\chi_{4033}(2982,\cdot)\) \(\chi_{4033}(3058,\cdot)\) \(\chi_{4033}(3066,\cdot)\) \(\chi_{4033}(3076,\cdot)\) \(\chi_{4033}(3201,\cdot)\) \(\chi_{4033}(3535,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{35}{36}\right),e\left(\frac{103}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{47}{54}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{91}{108}\right)\)\(e\left(\frac{11}{54}\right)\)\(e\left(\frac{7}{27}\right)\)\(1\)\(e\left(\frac{20}{27}\right)\)\(e\left(\frac{19}{108}\right)\)\(e\left(\frac{35}{108}\right)\)
value at  e.g. 2

Related number fields

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