Properties

Conductor 3009
Order 232
Real No
Primitive No
Parity Even
Orbit Label 6018.bh

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(6018)
 
sage: chi = H[77]
 
pari: [g,chi] = znchar(Mod(77,6018))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 3009
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 232
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 = 6018.bh
Orbit index = 34

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 ]
 

\(\chi_{6018}(77,\cdot)\) \(\chi_{6018}(83,\cdot)\) \(\chi_{6018}(155,\cdot)\) \(\chi_{6018}(161,\cdot)\) \(\chi_{6018}(179,\cdot)\) \(\chi_{6018}(185,\cdot)\) \(\chi_{6018}(365,\cdot)\) \(\chi_{6018}(467,\cdot)\) \(\chi_{6018}(485,\cdot)\) \(\chi_{6018}(563,\cdot)\) \(\chi_{6018}(569,\cdot)\) \(\chi_{6018}(587,\cdot)\) \(\chi_{6018}(689,\cdot)\) \(\chi_{6018}(773,\cdot)\) \(\chi_{6018}(791,\cdot)\) \(\chi_{6018}(797,\cdot)\) \(\chi_{6018}(869,\cdot)\) \(\chi_{6018}(893,\cdot)\) \(\chi_{6018}(899,\cdot)\) \(\chi_{6018}(977,\cdot)\) \(\chi_{6018}(1073,\cdot)\) \(\chi_{6018}(1175,\cdot)\) \(\chi_{6018}(1277,\cdot)\) \(\chi_{6018}(1283,\cdot)\) \(\chi_{6018}(1409,\cdot)\) \(\chi_{6018}(1481,\cdot)\) \(\chi_{6018}(1505,\cdot)\) \(\chi_{6018}(1589,\cdot)\) \(\chi_{6018}(1607,\cdot)\) \(\chi_{6018}(1685,\cdot)\) ...

Inducing primitive character

\(\chi_{3009}(77,\cdot)\)

Values on generators

\((4013,1771,1123)\) → \((-1,e\left(\frac{1}{8}\right),e\left(\frac{43}{58}\right))\)

Values

-11571113192325293135
\(1\)\(1\)\(e\left(\frac{133}{232}\right)\)\(e\left(\frac{167}{232}\right)\)\(e\left(\frac{211}{232}\right)\)\(e\left(\frac{25}{29}\right)\)\(e\left(\frac{107}{116}\right)\)\(e\left(\frac{115}{232}\right)\)\(e\left(\frac{17}{116}\right)\)\(e\left(\frac{205}{232}\right)\)\(e\left(\frac{105}{232}\right)\)\(e\left(\frac{17}{58}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{232})\)