Properties

Conductor 2009
Order 420
Real No
Primitive No
Parity Even
Orbit Label 6027.et

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[46]
 
pari: [g,chi] = znchar(Mod(46,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2009
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 420
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.et
Orbit index = 124

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 ]
 

\(\chi_{6027}(46,\cdot)\) \(\chi_{6027}(121,\cdot)\) \(\chi_{6027}(172,\cdot)\) \(\chi_{6027}(184,\cdot)\) \(\chi_{6027}(289,\cdot)\) \(\chi_{6027}(415,\cdot)\) \(\chi_{6027}(487,\cdot)\) \(\chi_{6027}(541,\cdot)\) \(\chi_{6027}(613,\cdot)\) \(\chi_{6027}(676,\cdot)\) \(\chi_{6027}(718,\cdot)\) \(\chi_{6027}(730,\cdot)\) \(\chi_{6027}(781,\cdot)\) \(\chi_{6027}(856,\cdot)\) \(\chi_{6027}(907,\cdot)\) \(\chi_{6027}(982,\cdot)\) \(\chi_{6027}(1033,\cdot)\) \(\chi_{6027}(1045,\cdot)\) \(\chi_{6027}(1087,\cdot)\) \(\chi_{6027}(1150,\cdot)\) \(\chi_{6027}(1222,\cdot)\) \(\chi_{6027}(1276,\cdot)\) \(\chi_{6027}(1348,\cdot)\) \(\chi_{6027}(1474,\cdot)\) \(\chi_{6027}(1579,\cdot)\) \(\chi_{6027}(1591,\cdot)\) \(\chi_{6027}(1642,\cdot)\) \(\chi_{6027}(1717,\cdot)\) \(\chi_{6027}(1768,\cdot)\) \(\chi_{6027}(1894,\cdot)\) ...

Inducing primitive character

\(\chi_{2009}(46,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((1,e\left(\frac{11}{21}\right),e\left(\frac{11}{20}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{193}{210}\right)\)\(e\left(\frac{88}{105}\right)\)\(e\left(\frac{61}{210}\right)\)\(e\left(\frac{53}{70}\right)\)\(e\left(\frac{22}{105}\right)\)\(e\left(\frac{253}{420}\right)\)\(e\left(\frac{47}{140}\right)\)\(e\left(\frac{71}{105}\right)\)\(e\left(\frac{103}{420}\right)\)\(e\left(\frac{17}{60}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{420})\)