Properties

Conductor 6027
Order 168
Real No
Primitive Yes
Parity Even
Orbit Label 6027.ee

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(6027)
 
sage: chi = H[44]
 
pari: [g,chi] = znchar(Mod(44,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 168
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6027.ee
Orbit index = 109

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 ]
 

\(\chi_{6027}(44,\cdot)\) \(\chi_{6027}(137,\cdot)\) \(\chi_{6027}(191,\cdot)\) \(\chi_{6027}(284,\cdot)\) \(\chi_{6027}(506,\cdot)\) \(\chi_{6027}(536,\cdot)\) \(\chi_{6027}(653,\cdot)\) \(\chi_{6027}(683,\cdot)\) \(\chi_{6027}(905,\cdot)\) \(\chi_{6027}(1052,\cdot)\) \(\chi_{6027}(1367,\cdot)\) \(\chi_{6027}(1397,\cdot)\) \(\chi_{6027}(1514,\cdot)\) \(\chi_{6027}(1544,\cdot)\) \(\chi_{6027}(1766,\cdot)\) \(\chi_{6027}(1859,\cdot)\) \(\chi_{6027}(1913,\cdot)\) \(\chi_{6027}(2006,\cdot)\) \(\chi_{6027}(2228,\cdot)\) \(\chi_{6027}(2258,\cdot)\) \(\chi_{6027}(2375,\cdot)\) \(\chi_{6027}(2405,\cdot)\) \(\chi_{6027}(2720,\cdot)\) \(\chi_{6027}(2867,\cdot)\) \(\chi_{6027}(3089,\cdot)\) \(\chi_{6027}(3119,\cdot)\) \(\chi_{6027}(3236,\cdot)\) \(\chi_{6027}(3266,\cdot)\) \(\chi_{6027}(3488,\cdot)\) \(\chi_{6027}(3581,\cdot)\) ...

Values on generators

\((4019,493,2794)\) → \((-1,e\left(\frac{4}{21}\right),e\left(\frac{3}{8}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{17}{84}\right)\)\(e\left(\frac{17}{42}\right)\)\(e\left(\frac{23}{84}\right)\)\(e\left(\frac{17}{28}\right)\)\(e\left(\frac{10}{21}\right)\)\(e\left(\frac{41}{168}\right)\)\(e\left(\frac{51}{56}\right)\)\(e\left(\frac{17}{21}\right)\)\(e\left(\frac{107}{168}\right)\)\(e\left(\frac{1}{24}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{168})\)