Properties

Conductor 6027
Order 420
Real No
Primitive Yes
Parity Even
Orbit Label 6027.er

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[5]
 
pari: [g,chi] = znchar(Mod(5,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6027
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 = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6027.er
Orbit index = 122

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 ]
 

\(\chi_{6027}(5,\cdot)\) \(\chi_{6027}(131,\cdot)\) \(\chi_{6027}(143,\cdot)\) \(\chi_{6027}(185,\cdot)\) \(\chi_{6027}(248,\cdot)\) \(\chi_{6027}(320,\cdot)\) \(\chi_{6027}(446,\cdot)\) \(\chi_{6027}(500,\cdot)\) \(\chi_{6027}(572,\cdot)\) \(\chi_{6027}(635,\cdot)\) \(\chi_{6027}(677,\cdot)\) \(\chi_{6027}(689,\cdot)\) \(\chi_{6027}(740,\cdot)\) \(\chi_{6027}(866,\cdot)\) \(\chi_{6027}(941,\cdot)\) \(\chi_{6027}(992,\cdot)\) \(\chi_{6027}(1004,\cdot)\) \(\chi_{6027}(1046,\cdot)\) \(\chi_{6027}(1181,\cdot)\) \(\chi_{6027}(1235,\cdot)\) \(\chi_{6027}(1307,\cdot)\) \(\chi_{6027}(1361,\cdot)\) \(\chi_{6027}(1433,\cdot)\) \(\chi_{6027}(1496,\cdot)\) \(\chi_{6027}(1601,\cdot)\) \(\chi_{6027}(1676,\cdot)\) \(\chi_{6027}(1727,\cdot)\) \(\chi_{6027}(1802,\cdot)\) \(\chi_{6027}(1853,\cdot)\) \(\chi_{6027}(1865,\cdot)\) ...

Values on generators

\((4019,493,2794)\) → \((-1,e\left(\frac{29}{42}\right),e\left(\frac{11}{20}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{79}{105}\right)\)\(e\left(\frac{53}{105}\right)\)\(e\left(\frac{131}{210}\right)\)\(e\left(\frac{9}{35}\right)\)\(e\left(\frac{79}{210}\right)\)\(e\left(\frac{323}{420}\right)\)\(e\left(\frac{117}{140}\right)\)\(e\left(\frac{1}{105}\right)\)\(e\left(\frac{383}{420}\right)\)\(e\left(\frac{7}{60}\right)\)
value at  e.g. 2

Related number fields

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