Properties

Conductor 1007
Order 234
Real No
Primitive No
Parity Odd
Orbit Label 6042.cp

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[91]
 
pari: [g,chi] = znchar(Mod(91,6042))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1007
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 = Odd
Orbit label = 6042.cp
Orbit index = 68

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 ]
 

\(\chi_{6042}(91,\cdot)\) \(\chi_{6042}(223,\cdot)\) \(\chi_{6042}(241,\cdot)\) \(\chi_{6042}(325,\cdot)\) \(\chi_{6042}(355,\cdot)\) \(\chi_{6042}(409,\cdot)\) \(\chi_{6042}(433,\cdot)\) \(\chi_{6042}(547,\cdot)\) \(\chi_{6042}(661,\cdot)\) \(\chi_{6042}(679,\cdot)\) \(\chi_{6042}(751,\cdot)\) \(\chi_{6042}(865,\cdot)\) \(\chi_{6042}(877,\cdot)\) \(\chi_{6042}(907,\cdot)\) \(\chi_{6042}(979,\cdot)\) \(\chi_{6042}(991,\cdot)\) \(\chi_{6042}(1117,\cdot)\) \(\chi_{6042}(1153,\cdot)\) \(\chi_{6042}(1363,\cdot)\) \(\chi_{6042}(1435,\cdot)\) \(\chi_{6042}(1495,\cdot)\) \(\chi_{6042}(1705,\cdot)\) \(\chi_{6042}(1789,\cdot)\) \(\chi_{6042}(1819,\cdot)\) \(\chi_{6042}(1915,\cdot)\) \(\chi_{6042}(1933,\cdot)\) \(\chi_{6042}(1951,\cdot)\) \(\chi_{6042}(2131,\cdot)\) \(\chi_{6042}(2149,\cdot)\) \(\chi_{6042}(2179,\cdot)\) ...

Inducing primitive character

\(\chi_{1007}(91,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((1,e\left(\frac{11}{18}\right),e\left(\frac{19}{26}\right))\)

Values

-11571113172325293135
\(-1\)\(1\)\(e\left(\frac{29}{234}\right)\)\(e\left(\frac{35}{39}\right)\)\(e\left(\frac{28}{39}\right)\)\(e\left(\frac{139}{234}\right)\)\(e\left(\frac{49}{117}\right)\)\(e\left(\frac{13}{18}\right)\)\(e\left(\frac{29}{117}\right)\)\(e\left(\frac{1}{234}\right)\)\(e\left(\frac{11}{39}\right)\)\(e\left(\frac{5}{234}\right)\)
value at  e.g. 2

Related number fields

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