Properties

Conductor 3021
Order 234
Real No
Primitive No
Parity Odd
Orbit Label 6042.cj

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[17]
 
pari: [g,chi] = znchar(Mod(17,6042))
 

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 = Odd
Orbit label = 6042.cj
Orbit index = 62

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 ]
 

\(\chi_{6042}(17,\cdot)\) \(\chi_{6042}(131,\cdot)\) \(\chi_{6042}(149,\cdot)\) \(\chi_{6042}(329,\cdot)\) \(\chi_{6042}(347,\cdot)\) \(\chi_{6042}(377,\cdot)\) \(\chi_{6042}(461,\cdot)\) \(\chi_{6042}(587,\cdot)\) \(\chi_{6042}(785,\cdot)\) \(\chi_{6042}(833,\cdot)\) \(\chi_{6042}(1013,\cdot)\) \(\chi_{6042}(1175,\cdot)\) \(\chi_{6042}(1259,\cdot)\) \(\chi_{6042}(1289,\cdot)\) \(\chi_{6042}(1301,\cdot)\) \(\chi_{6042}(1385,\cdot)\) \(\chi_{6042}(1403,\cdot)\) \(\chi_{6042}(1415,\cdot)\) \(\chi_{6042}(1469,\cdot)\) \(\chi_{6042}(1601,\cdot)\) \(\chi_{6042}(1619,\cdot)\) \(\chi_{6042}(1733,\cdot)\) \(\chi_{6042}(1811,\cdot)\) \(\chi_{6042}(1859,\cdot)\) \(\chi_{6042}(1925,\cdot)\) \(\chi_{6042}(2039,\cdot)\) \(\chi_{6042}(2057,\cdot)\) \(\chi_{6042}(2213,\cdot)\) \(\chi_{6042}(2285,\cdot)\) \(\chi_{6042}(2495,\cdot)\) ...

Inducing primitive character

\(\chi_{3021}(17,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((-1,e\left(\frac{5}{9}\right),e\left(\frac{5}{26}\right))\)

Values

-11571113172325293135
\(-1\)\(1\)\(e\left(\frac{50}{117}\right)\)\(e\left(\frac{1}{39}\right)\)\(e\left(\frac{25}{78}\right)\)\(e\left(\frac{46}{117}\right)\)\(e\left(\frac{229}{234}\right)\)\(e\left(\frac{1}{9}\right)\)\(e\left(\frac{100}{117}\right)\)\(e\left(\frac{185}{234}\right)\)\(e\left(\frac{53}{78}\right)\)\(e\left(\frac{53}{117}\right)\)
value at  e.g. 2

Related number fields

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