Properties

Conductor 2009
Order 840
Real No
Primitive No
Parity Even
Orbit Label 6027.ex

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[52]
 
pari: [g,chi] = znchar(Mod(52,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2009
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 840
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.ex
Orbit index = 128

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 ]
 

\(\chi_{6027}(52,\cdot)\) \(\chi_{6027}(94,\cdot)\) \(\chi_{6027}(136,\cdot)\) \(\chi_{6027}(145,\cdot)\) \(\chi_{6027}(157,\cdot)\) \(\chi_{6027}(199,\cdot)\) \(\chi_{6027}(220,\cdot)\) \(\chi_{6027}(229,\cdot)\) \(\chi_{6027}(304,\cdot)\) \(\chi_{6027}(334,\cdot)\) \(\chi_{6027}(376,\cdot)\) \(\chi_{6027}(388,\cdot)\) \(\chi_{6027}(397,\cdot)\) \(\chi_{6027}(439,\cdot)\) \(\chi_{6027}(481,\cdot)\) \(\chi_{6027}(514,\cdot)\) \(\chi_{6027}(544,\cdot)\) \(\chi_{6027}(586,\cdot)\) \(\chi_{6027}(598,\cdot)\) \(\chi_{6027}(628,\cdot)\) \(\chi_{6027}(649,\cdot)\) \(\chi_{6027}(682,\cdot)\) \(\chi_{6027}(691,\cdot)\) \(\chi_{6027}(703,\cdot)\) \(\chi_{6027}(712,\cdot)\) \(\chi_{6027}(745,\cdot)\) \(\chi_{6027}(796,\cdot)\) \(\chi_{6027}(808,\cdot)\) \(\chi_{6027}(850,\cdot)\) \(\chi_{6027}(880,\cdot)\) ...

Inducing primitive character

\(\chi_{2009}(52,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((1,e\left(\frac{1}{42}\right),e\left(\frac{3}{40}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{239}{420}\right)\)\(e\left(\frac{29}{210}\right)\)\(e\left(\frac{143}{420}\right)\)\(e\left(\frac{99}{140}\right)\)\(e\left(\frac{191}{210}\right)\)\(e\left(\frac{149}{840}\right)\)\(e\left(\frac{31}{280}\right)\)\(e\left(\frac{29}{105}\right)\)\(e\left(\frac{59}{840}\right)\)\(e\left(\frac{61}{120}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{840})\)