Properties

Conductor 3021
Order 234
Real No
Primitive No
Parity Even
Orbit Label 6042.cm

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[59]
 
pari: [g,chi] = znchar(Mod(59,6042))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 3021
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 234
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.cm
Orbit index = 65

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 ]
 

\(\chi_{6042}(29,\cdot)\) \(\chi_{6042}(59,\cdot)\) \(\chi_{6042}(143,\cdot)\) \(\chi_{6042}(269,\cdot)\) \(\chi_{6042}(431,\cdot)\) \(\chi_{6042}(515,\cdot)\) \(\chi_{6042}(623,\cdot)\) \(\chi_{6042}(857,\cdot)\) \(\chi_{6042}(941,\cdot)\) \(\chi_{6042}(965,\cdot)\) \(\chi_{6042}(971,\cdot)\) \(\chi_{6042}(983,\cdot)\) \(\chi_{6042}(1067,\cdot)\) \(\chi_{6042}(1085,\cdot)\) \(\chi_{6042}(1097,\cdot)\) \(\chi_{6042}(1283,\cdot)\) \(\chi_{6042}(1421,\cdot)\) \(\chi_{6042}(1541,\cdot)\) \(\chi_{6042}(1649,\cdot)\) \(\chi_{6042}(1739,\cdot)\) \(\chi_{6042}(1895,\cdot)\) \(\chi_{6042}(1967,\cdot)\) \(\chi_{6042}(2105,\cdot)\) \(\chi_{6042}(2237,\cdot)\) \(\chi_{6042}(2255,\cdot)\) \(\chi_{6042}(2339,\cdot)\) \(\chi_{6042}(2369,\cdot)\) \(\chi_{6042}(2423,\cdot)\) \(\chi_{6042}(2447,\cdot)\) \(\chi_{6042}(2561,\cdot)\) ...

Inducing primitive character

\(\chi_{3021}(59,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((-1,e\left(\frac{1}{18}\right),e\left(\frac{9}{26}\right))\)

Values

-11571113172325293135
\(1\)\(1\)\(e\left(\frac{77}{117}\right)\)\(e\left(\frac{7}{39}\right)\)\(e\left(\frac{19}{78}\right)\)\(e\left(\frac{137}{234}\right)\)\(e\left(\frac{121}{234}\right)\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{37}{117}\right)\)\(e\left(\frac{43}{117}\right)\)\(e\left(\frac{10}{39}\right)\)\(e\left(\frac{98}{117}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{117})\)