Properties

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

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[89]
 
pari: [g,chi] = znchar(Mod(89,6042))
 

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.ck
Orbit index = 63

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 ]
 

\(\chi_{6042}(89,\cdot)\) \(\chi_{6042}(155,\cdot)\) \(\chi_{6042}(203,\cdot)\) \(\chi_{6042}(281,\cdot)\) \(\chi_{6042}(395,\cdot)\) \(\chi_{6042}(413,\cdot)\) \(\chi_{6042}(545,\cdot)\) \(\chi_{6042}(599,\cdot)\) \(\chi_{6042}(611,\cdot)\) \(\chi_{6042}(629,\cdot)\) \(\chi_{6042}(713,\cdot)\) \(\chi_{6042}(725,\cdot)\) \(\chi_{6042}(755,\cdot)\) \(\chi_{6042}(839,\cdot)\) \(\chi_{6042}(1001,\cdot)\) \(\chi_{6042}(1181,\cdot)\) \(\chi_{6042}(1229,\cdot)\) \(\chi_{6042}(1427,\cdot)\) \(\chi_{6042}(1553,\cdot)\) \(\chi_{6042}(1637,\cdot)\) \(\chi_{6042}(1667,\cdot)\) \(\chi_{6042}(1685,\cdot)\) \(\chi_{6042}(1865,\cdot)\) \(\chi_{6042}(1883,\cdot)\) \(\chi_{6042}(1997,\cdot)\) \(\chi_{6042}(2027,\cdot)\) \(\chi_{6042}(2111,\cdot)\) \(\chi_{6042}(2219,\cdot)\) \(\chi_{6042}(2321,\cdot)\) \(\chi_{6042}(2453,\cdot)\) ...

Inducing primitive character

\(\chi_{3021}(89,\cdot)\)

Values on generators

\((2015,4771,2281)\) → \((-1,e\left(\frac{5}{18}\right),e\left(\frac{9}{13}\right))\)

Values

-11571113172325293135
\(1\)\(1\)\(e\left(\frac{113}{234}\right)\)\(e\left(\frac{14}{39}\right)\)\(e\left(\frac{77}{78}\right)\)\(e\left(\frac{1}{234}\right)\)\(e\left(\frac{47}{234}\right)\)\(e\left(\frac{1}{18}\right)\)\(e\left(\frac{113}{117}\right)\)\(e\left(\frac{8}{117}\right)\)\(e\left(\frac{1}{78}\right)\)\(e\left(\frac{197}{234}\right)\)
value at  e.g. 2

Related number fields

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