Properties

Conductor 3021
Order 468
Real No
Primitive No
Parity Odd
Orbit Label 6042.cs

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[41]
 
pari: [g,chi] = znchar(Mod(41,6042))
 

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 = Odd
Orbit label = 6042.cs
Orbit index = 71

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 ]
 

\(\chi_{6042}(41,\cdot)\) \(\chi_{6042}(71,\cdot)\) \(\chi_{6042}(167,\cdot)\) \(\chi_{6042}(173,\cdot)\) \(\chi_{6042}(185,\cdot)\) \(\chi_{6042}(257,\cdot)\) \(\chi_{6042}(287,\cdot)\) \(\chi_{6042}(299,\cdot)\) \(\chi_{6042}(383,\cdot)\) \(\chi_{6042}(485,\cdot)\) \(\chi_{6042}(497,\cdot)\) \(\chi_{6042}(509,\cdot)\) \(\chi_{6042}(527,\cdot)\) \(\chi_{6042}(641,\cdot)\) \(\chi_{6042}(737,\cdot)\) \(\chi_{6042}(773,\cdot)\) \(\chi_{6042}(827,\cdot)\) \(\chi_{6042}(851,\cdot)\) \(\chi_{6042}(869,\cdot)\) \(\chi_{6042}(887,\cdot)\) \(\chi_{6042}(1055,\cdot)\) \(\chi_{6042}(1079,\cdot)\) \(\chi_{6042}(1115,\cdot)\) \(\chi_{6042}(1169,\cdot)\) \(\chi_{6042}(1193,\cdot)\) \(\chi_{6042}(1199,\cdot)\) \(\chi_{6042}(1211,\cdot)\) \(\chi_{6042}(1307,\cdot)\) \(\chi_{6042}(1313,\cdot)\) \(\chi_{6042}(1343,\cdot)\) ...

Inducing primitive character

\(\chi_{3021}(41,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((-1,e\left(\frac{13}{18}\right),e\left(\frac{45}{52}\right))\)

Values

-11571113172325293135
\(-1\)\(1\)\(e\left(\frac{341}{468}\right)\)\(e\left(\frac{35}{78}\right)\)\(e\left(\frac{14}{39}\right)\)\(e\left(\frac{89}{234}\right)\)\(e\left(\frac{44}{117}\right)\)\(e\left(\frac{25}{36}\right)\)\(e\left(\frac{107}{234}\right)\)\(e\left(\frac{137}{234}\right)\)\(e\left(\frac{61}{156}\right)\)\(e\left(\frac{83}{468}\right)\)
value at  e.g. 2

Related number fields

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