Properties

Conductor 1007
Order 78
Real No
Primitive No
Parity Even
Orbit Label 6042.by

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[7]
 
pari: [g,chi] = znchar(Mod(7,6042))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1007
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 78
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.by
Orbit index = 51

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 ]
 

\(\chi_{6042}(7,\cdot)\) \(\chi_{6042}(163,\cdot)\) \(\chi_{6042}(961,\cdot)\) \(\chi_{6042}(1831,\cdot)\) \(\chi_{6042}(1945,\cdot)\) \(\chi_{6042}(2743,\cdot)\) \(\chi_{6042}(2785,\cdot)\) \(\chi_{6042}(2899,\cdot)\) \(\chi_{6042}(3085,\cdot)\) \(\chi_{6042}(3541,\cdot)\) \(\chi_{6042}(3697,\cdot)\) \(\chi_{6042}(3769,\cdot)\) \(\chi_{6042}(4039,\cdot)\) \(\chi_{6042}(4225,\cdot)\) \(\chi_{6042}(4495,\cdot)\) \(\chi_{6042}(4567,\cdot)\) \(\chi_{6042}(4681,\cdot)\) \(\chi_{6042}(4723,\cdot)\) \(\chi_{6042}(4795,\cdot)\) \(\chi_{6042}(5179,\cdot)\) \(\chi_{6042}(5251,\cdot)\) \(\chi_{6042}(5521,\cdot)\) \(\chi_{6042}(5635,\cdot)\) \(\chi_{6042}(5749,\cdot)\)

Inducing primitive character

\(\chi_{1007}(7,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((1,e\left(\frac{1}{3}\right),e\left(\frac{7}{26}\right))\)

Values

-11571113172325293135
\(1\)\(1\)\(e\left(\frac{77}{78}\right)\)\(e\left(\frac{10}{13}\right)\)\(e\left(\frac{8}{13}\right)\)\(e\left(\frac{5}{39}\right)\)\(e\left(\frac{1}{39}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{38}{39}\right)\)\(e\left(\frac{2}{39}\right)\)\(e\left(\frac{23}{26}\right)\)\(e\left(\frac{59}{78}\right)\)
value at  e.g. 2

Related number fields

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