Properties

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

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[52]
pari: [g,chi] = znchar(Mod(52,4033))

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.if
Orbit index = 214

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 ]

\(\chi_{4033}(52,\cdot)\) \(\chi_{4033}(165,\cdot)\) \(\chi_{4033}(205,\cdot)\) \(\chi_{4033}(357,\cdot)\) \(\chi_{4033}(425,\cdot)\) \(\chi_{4033}(446,\cdot)\) \(\chi_{4033}(668,\cdot)\) \(\chi_{4033}(698,\cdot)\) \(\chi_{4033}(723,\cdot)\) \(\chi_{4033}(745,\cdot)\) \(\chi_{4033}(1023,\cdot)\) \(\chi_{4033}(1129,\cdot)\) \(\chi_{4033}(1152,\cdot)\) \(\chi_{4033}(1271,\cdot)\) \(\chi_{4033}(1441,\cdot)\) \(\chi_{4033}(1532,\cdot)\) \(\chi_{4033}(1794,\cdot)\) \(\chi_{4033}(2013,\cdot)\) \(\chi_{4033}(2020,\cdot)\) \(\chi_{4033}(2239,\cdot)\) \(\chi_{4033}(2501,\cdot)\) \(\chi_{4033}(2592,\cdot)\) \(\chi_{4033}(2762,\cdot)\) \(\chi_{4033}(2881,\cdot)\) \(\chi_{4033}(2904,\cdot)\) \(\chi_{4033}(3010,\cdot)\) \(\chi_{4033}(3288,\cdot)\) \(\chi_{4033}(3310,\cdot)\) \(\chi_{4033}(3335,\cdot)\) \(\chi_{4033}(3365,\cdot)\) ...

Values on generators

\((1963,2295)\) → \((e\left(\frac{13}{36}\right),e\left(\frac{73}{108}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{8}{9}\right)\)\(e\left(\frac{29}{54}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{73}{108}\right)\)\(e\left(\frac{23}{54}\right)\)\(e\left(\frac{16}{27}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{2}{27}\right)\)\(e\left(\frac{61}{108}\right)\)\(e\left(\frac{101}{108}\right)\)
value at  e.g. 2

Related number fields

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