Properties

Conductor 2009
Order 168
Real No
Primitive No
Parity Even
Orbit Label 6027.eb

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[208]
 
pari: [g,chi] = znchar(Mod(208,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2009
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 = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6027.eb
Orbit index = 106

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 ]
 

\(\chi_{6027}(208,\cdot)\) \(\chi_{6027}(355,\cdot)\) \(\chi_{6027}(577,\cdot)\) \(\chi_{6027}(670,\cdot)\) \(\chi_{6027}(724,\cdot)\) \(\chi_{6027}(817,\cdot)\) \(\chi_{6027}(1039,\cdot)\) \(\chi_{6027}(1069,\cdot)\) \(\chi_{6027}(1186,\cdot)\) \(\chi_{6027}(1216,\cdot)\) \(\chi_{6027}(1438,\cdot)\) \(\chi_{6027}(1531,\cdot)\) \(\chi_{6027}(1585,\cdot)\) \(\chi_{6027}(1678,\cdot)\) \(\chi_{6027}(1900,\cdot)\) \(\chi_{6027}(2047,\cdot)\) \(\chi_{6027}(2299,\cdot)\) \(\chi_{6027}(2392,\cdot)\) \(\chi_{6027}(2446,\cdot)\) \(\chi_{6027}(2539,\cdot)\) \(\chi_{6027}(2761,\cdot)\) \(\chi_{6027}(2791,\cdot)\) \(\chi_{6027}(2908,\cdot)\) \(\chi_{6027}(2938,\cdot)\) \(\chi_{6027}(3160,\cdot)\) \(\chi_{6027}(3307,\cdot)\) \(\chi_{6027}(3622,\cdot)\) \(\chi_{6027}(3652,\cdot)\) \(\chi_{6027}(3769,\cdot)\) \(\chi_{6027}(3799,\cdot)\) ...

Inducing primitive character

\(\chi_{2009}(208,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((1,e\left(\frac{11}{42}\right),e\left(\frac{3}{8}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{47}{84}\right)\)\(e\left(\frac{5}{42}\right)\)\(e\left(\frac{71}{84}\right)\)\(e\left(\frac{19}{28}\right)\)\(e\left(\frac{17}{42}\right)\)\(e\left(\frac{101}{168}\right)\)\(e\left(\frac{15}{56}\right)\)\(e\left(\frac{5}{21}\right)\)\(e\left(\frac{155}{168}\right)\)\(e\left(\frac{13}{24}\right)\)
value at  e.g. 2

Related number fields

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