Properties

Conductor 4033
Order 36
Real No
Primitive Yes
Parity Even
Orbit Label 4033.fw

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[235]
pari: [g,chi] = znchar(Mod(235,4033))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 4033
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 36
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.fw
Orbit index = 153

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 ]

\(\chi_{4033}(235,\cdot)\) \(\chi_{4033}(631,\cdot)\) \(\chi_{4033}(1167,\cdot)\) \(\chi_{4033}(1798,\cdot)\) \(\chi_{4033}(1855,\cdot)\) \(\chi_{4033}(1943,\cdot)\) \(\chi_{4033}(2090,\cdot)\) \(\chi_{4033}(2178,\cdot)\) \(\chi_{4033}(2235,\cdot)\) \(\chi_{4033}(2866,\cdot)\) \(\chi_{4033}(3402,\cdot)\) \(\chi_{4033}(3798,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{11}{36}\right),e\left(\frac{31}{36}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{7}{9}\right)\)\(e\left(\frac{17}{36}\right)\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{2}{9}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{4}{9}\right)\)\(e\left(\frac{31}{36}\right)\)\(e\left(\frac{23}{36}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{36})\)