Properties

Conductor 3021
Order 468
Real No
Primitive No
Parity Even
Orbit Label 6042.ct

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[101]
 
pari: [g,chi] = znchar(Mod(101,6042))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 3021
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 468
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 = Even
Orbit label = 6042.ct
Orbit index = 72

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 ]
 

\(\chi_{6042}(5,\cdot)\) \(\chi_{6042}(35,\cdot)\) \(\chi_{6042}(101,\cdot)\) \(\chi_{6042}(137,\cdot)\) \(\chi_{6042}(161,\cdot)\) \(\chi_{6042}(215,\cdot)\) \(\chi_{6042}(233,\cdot)\) \(\chi_{6042}(245,\cdot)\) \(\chi_{6042}(251,\cdot)\) \(\chi_{6042}(263,\cdot)\) \(\chi_{6042}(359,\cdot)\) \(\chi_{6042}(389,\cdot)\) \(\chi_{6042}(443,\cdot)\) \(\chi_{6042}(479,\cdot)\) \(\chi_{6042}(491,\cdot)\) \(\chi_{6042}(503,\cdot)\) \(\chi_{6042}(557,\cdot)\) \(\chi_{6042}(575,\cdot)\) \(\chi_{6042}(605,\cdot)\) \(\chi_{6042}(617,\cdot)\) \(\chi_{6042}(671,\cdot)\) \(\chi_{6042}(701,\cdot)\) \(\chi_{6042}(707,\cdot)\) \(\chi_{6042}(803,\cdot)\) \(\chi_{6042}(815,\cdot)\) \(\chi_{6042}(821,\cdot)\) \(\chi_{6042}(845,\cdot)\) \(\chi_{6042}(899,\cdot)\) \(\chi_{6042}(935,\cdot)\) \(\chi_{6042}(959,\cdot)\) ...

Inducing primitive character

\(\chi_{3021}(101,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((-1,e\left(\frac{7}{9}\right),e\left(\frac{21}{52}\right))\)

Values

-11571113172325293135
\(1\)\(1\)\(e\left(\frac{433}{468}\right)\)\(e\left(\frac{25}{78}\right)\)\(e\left(\frac{10}{39}\right)\)\(e\left(\frac{68}{117}\right)\)\(e\left(\frac{37}{117}\right)\)\(e\left(\frac{29}{36}\right)\)\(e\left(\frac{199}{234}\right)\)\(e\left(\frac{35}{117}\right)\)\(e\left(\frac{155}{156}\right)\)\(e\left(\frac{115}{468}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{468})\)