Properties

Conductor 1007
Order 468
Real No
Primitive No
Parity Even
Orbit Label 6042.cq

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[67]
 
pari: [g,chi] = znchar(Mod(67,6042))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1007
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.cq
Orbit index = 69

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 ]
 

\(\chi_{6042}(67,\cdot)\) \(\chi_{6042}(79,\cdot)\) \(\chi_{6042}(109,\cdot)\) \(\chi_{6042}(127,\cdot)\) \(\chi_{6042}(181,\cdot)\) \(\chi_{6042}(193,\cdot)\) \(\chi_{6042}(337,\cdot)\) \(\chi_{6042}(421,\cdot)\) \(\chi_{6042}(451,\cdot)\) \(\chi_{6042}(469,\cdot)\) \(\chi_{6042}(535,\cdot)\) \(\chi_{6042}(565,\cdot)\) \(\chi_{6042}(667,\cdot)\) \(\chi_{6042}(697,\cdot)\) \(\chi_{6042}(763,\cdot)\) \(\chi_{6042}(775,\cdot)\) \(\chi_{6042}(781,\cdot)\) \(\chi_{6042}(793,\cdot)\) \(\chi_{6042}(889,\cdot)\) \(\chi_{6042}(1009,\cdot)\) \(\chi_{6042}(1021,\cdot)\) \(\chi_{6042}(1039,\cdot)\) \(\chi_{6042}(1093,\cdot)\) \(\chi_{6042}(1105,\cdot)\) \(\chi_{6042}(1135,\cdot)\) \(\chi_{6042}(1207,\cdot)\) \(\chi_{6042}(1231,\cdot)\) \(\chi_{6042}(1237,\cdot)\) \(\chi_{6042}(1267,\cdot)\) \(\chi_{6042}(1333,\cdot)\) ...

Inducing primitive character

\(\chi_{1007}(67,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((1,e\left(\frac{17}{18}\right),e\left(\frac{15}{52}\right))\)

Values

-11571113172325293135
\(1\)\(1\)\(e\left(\frac{313}{468}\right)\)\(e\left(\frac{55}{78}\right)\)\(e\left(\frac{5}{78}\right)\)\(e\left(\frac{151}{234}\right)\)\(e\left(\frac{77}{234}\right)\)\(e\left(\frac{5}{36}\right)\)\(e\left(\frac{79}{234}\right)\)\(e\left(\frac{38}{117}\right)\)\(e\left(\frac{107}{156}\right)\)\(e\left(\frac{175}{468}\right)\)
value at  e.g. 2

Related number fields

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