Properties

Modulus 4033
Conductor 4033
Order 54
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4033.hi

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4033)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([6,35]))
 
pari: [g,chi] = znchar(Mod(1718,4033))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4033
Conductor = 4033
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 54
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4033.hi
Orbit index = 191

Galois orbit

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{4033}(12,\cdot)\) \(\chi_{4033}(292,\cdot)\) \(\chi_{4033}(847,\cdot)\) \(\chi_{4033}(959,\cdot)\) \(\chi_{4033}(974,\cdot)\) \(\chi_{4033}(978,\cdot)\) \(\chi_{4033}(1085,\cdot)\) \(\chi_{4033}(1718,\cdot)\) \(\chi_{4033}(1884,\cdot)\) \(\chi_{4033}(2486,\cdot)\) \(\chi_{4033}(2636,\cdot)\) \(\chi_{4033}(2754,\cdot)\) \(\chi_{4033}(2819,\cdot)\) \(\chi_{4033}(2895,\cdot)\) \(\chi_{4033}(3080,\cdot)\) \(\chi_{4033}(3548,\cdot)\) \(\chi_{4033}(3633,\cdot)\) \(\chi_{4033}(3697,\cdot)\)

Values on generators

\((1963,2295)\) → \((e\left(\frac{1}{9}\right),e\left(\frac{35}{54}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{16}{27}\right)\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{22}{27}\right)\)\(e\left(\frac{35}{54}\right)\)\(e\left(\frac{13}{27}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{5}{27}\right)\)\(e\left(\frac{47}{54}\right)\)\(e\left(\frac{7}{54}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{27})\)