Properties

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

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[69]
pari: [g,chi] = znchar(Mod(69,4033))

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.jz
Orbit index = 260

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 ]

\(\chi_{4033}(69,\cdot)\) \(\chi_{4033}(167,\cdot)\) \(\chi_{4033}(316,\cdot)\) \(\chi_{4033}(449,\cdot)\) \(\chi_{4033}(483,\cdot)\) \(\chi_{4033}(503,\cdot)\) \(\chi_{4033}(531,\cdot)\) \(\chi_{4033}(648,\cdot)\) \(\chi_{4033}(753,\cdot)\) \(\chi_{4033}(819,\cdot)\) \(\chi_{4033}(890,\cdot)\) \(\chi_{4033}(1169,\cdot)\) \(\chi_{4033}(1236,\cdot)\) \(\chi_{4033}(1238,\cdot)\) \(\chi_{4033}(1393,\cdot)\) \(\chi_{4033}(1685,\cdot)\) \(\chi_{4033}(1700,\cdot)\) \(\chi_{4033}(1905,\cdot)\) \(\chi_{4033}(2128,\cdot)\) \(\chi_{4033}(2333,\cdot)\) \(\chi_{4033}(2348,\cdot)\) \(\chi_{4033}(2640,\cdot)\) \(\chi_{4033}(2795,\cdot)\) \(\chi_{4033}(2797,\cdot)\) \(\chi_{4033}(2864,\cdot)\) \(\chi_{4033}(3143,\cdot)\) \(\chi_{4033}(3214,\cdot)\) \(\chi_{4033}(3280,\cdot)\) \(\chi_{4033}(3385,\cdot)\) \(\chi_{4033}(3502,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{5}{36}\right),e\left(\frac{85}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(1\)\(e\left(\frac{29}{54}\right)\)\(1\)\(e\left(\frac{1}{108}\right)\)\(e\left(\frac{29}{54}\right)\)\(e\left(\frac{25}{27}\right)\)\(1\)\(e\left(\frac{2}{27}\right)\)\(e\left(\frac{1}{108}\right)\)\(e\left(\frac{53}{108}\right)\)
value at  e.g. 2

Related number fields

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