Properties

Conductor 1007
Order 39
Real No
Primitive No
Parity Even
Orbit Label 6042.bs

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(6042)
 
sage: chi = H[49]
 
pari: [g,chi] = znchar(Mod(49,6042))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1007
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 39
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 = 6042.bs
Orbit index = 45

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 ]
 

\(\chi_{6042}(49,\cdot)\) \(\chi_{6042}(121,\cdot)\) \(\chi_{6042}(505,\cdot)\) \(\chi_{6042}(577,\cdot)\) \(\chi_{6042}(619,\cdot)\) \(\chi_{6042}(733,\cdot)\) \(\chi_{6042}(805,\cdot)\) \(\chi_{6042}(1075,\cdot)\) \(\chi_{6042}(1261,\cdot)\) \(\chi_{6042}(1531,\cdot)\) \(\chi_{6042}(1603,\cdot)\) \(\chi_{6042}(1759,\cdot)\) \(\chi_{6042}(2215,\cdot)\) \(\chi_{6042}(2401,\cdot)\) \(\chi_{6042}(2515,\cdot)\) \(\chi_{6042}(2557,\cdot)\) \(\chi_{6042}(3355,\cdot)\) \(\chi_{6042}(3469,\cdot)\) \(\chi_{6042}(4339,\cdot)\) \(\chi_{6042}(5137,\cdot)\) \(\chi_{6042}(5293,\cdot)\) \(\chi_{6042}(5593,\cdot)\) \(\chi_{6042}(5707,\cdot)\) \(\chi_{6042}(5821,\cdot)\)

Inducing primitive character

\(\chi_{1007}(49,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{7}{13}\right))\)

Values

-11571113172325293135
\(1\)\(1\)\(e\left(\frac{38}{39}\right)\)\(e\left(\frac{7}{13}\right)\)\(e\left(\frac{3}{13}\right)\)\(e\left(\frac{10}{39}\right)\)\(e\left(\frac{2}{39}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{37}{39}\right)\)\(e\left(\frac{4}{39}\right)\)\(e\left(\frac{10}{13}\right)\)\(e\left(\frac{20}{39}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{39})\)