Properties

Conductor 3021
Order 156
Real No
Primitive No
Parity Odd
Orbit Label 6042.cf

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[65]
 
pari: [g,chi] = znchar(Mod(65,6042))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 3021
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 156
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.cf
Orbit index = 58

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 ]
 

\(\chi_{6042}(65,\cdot)\) \(\chi_{6042}(179,\cdot)\) \(\chi_{6042}(563,\cdot)\) \(\chi_{6042}(677,\cdot)\) \(\chi_{6042}(1019,\cdot)\) \(\chi_{6042}(1091,\cdot)\) \(\chi_{6042}(1133,\cdot)\) \(\chi_{6042}(1205,\cdot)\) \(\chi_{6042}(1433,\cdot)\) \(\chi_{6042}(1661,\cdot)\) \(\chi_{6042}(1775,\cdot)\) \(\chi_{6042}(1889,\cdot)\) \(\chi_{6042}(2045,\cdot)\) \(\chi_{6042}(2117,\cdot)\) \(\chi_{6042}(2159,\cdot)\) \(\chi_{6042}(2231,\cdot)\) \(\chi_{6042}(2387,\cdot)\) \(\chi_{6042}(2459,\cdot)\) \(\chi_{6042}(2615,\cdot)\) \(\chi_{6042}(2729,\cdot)\) \(\chi_{6042}(2801,\cdot)\) \(\chi_{6042}(2843,\cdot)\) \(\chi_{6042}(3029,\cdot)\) \(\chi_{6042}(3071,\cdot)\) \(\chi_{6042}(3185,\cdot)\) \(\chi_{6042}(3371,\cdot)\) \(\chi_{6042}(3413,\cdot)\) \(\chi_{6042}(3599,\cdot)\) \(\chi_{6042}(3713,\cdot)\) \(\chi_{6042}(3755,\cdot)\) ...

Inducing primitive character

\(\chi_{3021}(65,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{19}{52}\right))\)

Values

-11571113172325293135
\(-1\)\(1\)\(e\left(\frac{53}{156}\right)\)\(e\left(\frac{3}{26}\right)\)\(e\left(\frac{9}{13}\right)\)\(e\left(\frac{47}{78}\right)\)\(e\left(\frac{32}{39}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{53}{78}\right)\)\(e\left(\frac{11}{78}\right)\)\(e\left(\frac{29}{52}\right)\)\(e\left(\frac{71}{156}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{156})\)