Properties

Conductor 6017
Order 455
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6017.cb

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(6017)
 
sage: chi = H[64]
 
pari: [g,chi] = znchar(Mod(64,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6017
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 455
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 6017.cb
Orbit index = 54

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 ]
 

\(\chi_{6017}(64,\cdot)\) \(\chi_{6017}(93,\cdot)\) \(\chi_{6017}(114,\cdot)\) \(\chi_{6017}(179,\cdot)\) \(\chi_{6017}(185,\cdot)\) \(\chi_{6017}(212,\cdot)\) \(\chi_{6017}(218,\cdot)\) \(\chi_{6017}(224,\cdot)\) \(\chi_{6017}(240,\cdot)\) \(\chi_{6017}(247,\cdot)\) \(\chi_{6017}(267,\cdot)\) \(\chi_{6017}(268,\cdot)\) \(\chi_{6017}(290,\cdot)\) \(\chi_{6017}(295,\cdot)\) \(\chi_{6017}(311,\cdot)\) \(\chi_{6017}(355,\cdot)\) \(\chi_{6017}(383,\cdot)\) \(\chi_{6017}(399,\cdot)\) \(\chi_{6017}(422,\cdot)\) \(\chi_{6017}(444,\cdot)\) \(\chi_{6017}(449,\cdot)\) \(\chi_{6017}(460,\cdot)\) \(\chi_{6017}(467,\cdot)\) \(\chi_{6017}(482,\cdot)\) \(\chi_{6017}(576,\cdot)\) \(\chi_{6017}(599,\cdot)\) \(\chi_{6017}(631,\cdot)\) \(\chi_{6017}(632,\cdot)\) \(\chi_{6017}(647,\cdot)\) \(\chi_{6017}(696,\cdot)\) ...

Values on generators

\((3830,2190)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{1}{91}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{278}{455}\right)\)\(e\left(\frac{18}{35}\right)\)\(e\left(\frac{101}{455}\right)\)\(e\left(\frac{167}{455}\right)\)\(e\left(\frac{57}{455}\right)\)\(e\left(\frac{151}{455}\right)\)\(e\left(\frac{379}{455}\right)\)\(e\left(\frac{1}{35}\right)\)\(e\left(\frac{89}{91}\right)\)\(e\left(\frac{67}{91}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{455})\)