Properties

Conductor 3021
Order 234
Real No
Primitive No
Parity Odd
Orbit Label 6042.cl

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(6042)
 
sage: chi = H[47]
 
pari: [g,chi] = znchar(Mod(47,6042))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 3021
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 234
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 6042.cl
Orbit index = 64

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 ]
 

\(\chi_{6042}(47,\cdot)\) \(\chi_{6042}(119,\cdot)\) \(\chi_{6042}(275,\cdot)\) \(\chi_{6042}(365,\cdot)\) \(\chi_{6042}(473,\cdot)\) \(\chi_{6042}(593,\cdot)\) \(\chi_{6042}(731,\cdot)\) \(\chi_{6042}(917,\cdot)\) \(\chi_{6042}(929,\cdot)\) \(\chi_{6042}(947,\cdot)\) \(\chi_{6042}(1031,\cdot)\) \(\chi_{6042}(1043,\cdot)\) \(\chi_{6042}(1049,\cdot)\) \(\chi_{6042}(1073,\cdot)\) \(\chi_{6042}(1157,\cdot)\) \(\chi_{6042}(1391,\cdot)\) \(\chi_{6042}(1499,\cdot)\) \(\chi_{6042}(1583,\cdot)\) \(\chi_{6042}(1745,\cdot)\) \(\chi_{6042}(1871,\cdot)\) \(\chi_{6042}(1955,\cdot)\) \(\chi_{6042}(1985,\cdot)\) \(\chi_{6042}(2183,\cdot)\) \(\chi_{6042}(2189,\cdot)\) \(\chi_{6042}(2201,\cdot)\) \(\chi_{6042}(2303,\cdot)\) \(\chi_{6042}(2315,\cdot)\) \(\chi_{6042}(2381,\cdot)\) \(\chi_{6042}(2429,\cdot)\) \(\chi_{6042}(2639,\cdot)\) ...

Inducing primitive character

\(\chi_{3021}(47,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((-1,e\left(\frac{4}{9}\right),e\left(\frac{11}{13}\right))\)

Values

-11571113172325293135
\(-1\)\(1\)\(e\left(\frac{89}{234}\right)\)\(e\left(\frac{20}{39}\right)\)\(e\left(\frac{71}{78}\right)\)\(e\left(\frac{62}{117}\right)\)\(e\left(\frac{95}{234}\right)\)\(e\left(\frac{7}{18}\right)\)\(e\left(\frac{89}{117}\right)\)\(e\left(\frac{229}{234}\right)\)\(e\left(\frac{23}{39}\right)\)\(e\left(\frac{209}{234}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{117})\)