Properties

Conductor 2009
Order 140
Real No
Primitive No
Parity Even
Orbit Label 6027.dx

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[43]
 
pari: [g,chi] = znchar(Mod(43,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2009
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 140
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.dx
Orbit index = 102

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 ]
 

\(\chi_{6027}(43,\cdot)\) \(\chi_{6027}(169,\cdot)\) \(\chi_{6027}(484,\cdot)\) \(\chi_{6027}(610,\cdot)\) \(\chi_{6027}(799,\cdot)\) \(\chi_{6027}(841,\cdot)\) \(\chi_{6027}(904,\cdot)\) \(\chi_{6027}(1156,\cdot)\) \(\chi_{6027}(1345,\cdot)\) \(\chi_{6027}(1597,\cdot)\) \(\chi_{6027}(1660,\cdot)\) \(\chi_{6027}(1702,\cdot)\) \(\chi_{6027}(1891,\cdot)\) \(\chi_{6027}(2017,\cdot)\) \(\chi_{6027}(2332,\cdot)\) \(\chi_{6027}(2458,\cdot)\) \(\chi_{6027}(2521,\cdot)\) \(\chi_{6027}(2563,\cdot)\) \(\chi_{6027}(2626,\cdot)\) \(\chi_{6027}(2752,\cdot)\) \(\chi_{6027}(2878,\cdot)\) \(\chi_{6027}(3067,\cdot)\) \(\chi_{6027}(3193,\cdot)\) \(\chi_{6027}(3319,\cdot)\) \(\chi_{6027}(3424,\cdot)\) \(\chi_{6027}(3487,\cdot)\) \(\chi_{6027}(3613,\cdot)\) \(\chi_{6027}(3739,\cdot)\) \(\chi_{6027}(3928,\cdot)\) \(\chi_{6027}(4054,\cdot)\) ...

Inducing primitive character

\(\chi_{2009}(43,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((1,e\left(\frac{1}{7}\right),e\left(\frac{13}{20}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{43}{70}\right)\)\(e\left(\frac{8}{35}\right)\)\(e\left(\frac{31}{70}\right)\)\(e\left(\frac{59}{70}\right)\)\(e\left(\frac{2}{35}\right)\)\(e\left(\frac{93}{140}\right)\)\(e\left(\frac{121}{140}\right)\)\(e\left(\frac{16}{35}\right)\)\(e\left(\frac{3}{140}\right)\)\(e\left(\frac{17}{20}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{140})\)