Properties

Conductor 547
Order 273
Real no
Primitive no
Minimal yes
Parity even
Orbit label 6017.bx

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[34]
 
pari: [g,chi] = znchar(Mod(34,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 547
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 273
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 6017.bx
Orbit index = 50

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 ]
 

\(\chi_{6017}(34,\cdot)\) \(\chi_{6017}(56,\cdot)\) \(\chi_{6017}(67,\cdot)\) \(\chi_{6017}(78,\cdot)\) \(\chi_{6017}(111,\cdot)\) \(\chi_{6017}(122,\cdot)\) \(\chi_{6017}(144,\cdot)\) \(\chi_{6017}(155,\cdot)\) \(\chi_{6017}(166,\cdot)\) \(\chi_{6017}(177,\cdot)\) \(\chi_{6017}(188,\cdot)\) \(\chi_{6017}(210,\cdot)\) \(\chi_{6017}(276,\cdot)\) \(\chi_{6017}(287,\cdot)\) \(\chi_{6017}(452,\cdot)\) \(\chi_{6017}(529,\cdot)\) \(\chi_{6017}(540,\cdot)\) \(\chi_{6017}(551,\cdot)\) \(\chi_{6017}(562,\cdot)\) \(\chi_{6017}(705,\cdot)\) \(\chi_{6017}(738,\cdot)\) \(\chi_{6017}(749,\cdot)\) \(\chi_{6017}(760,\cdot)\) \(\chi_{6017}(848,\cdot)\) \(\chi_{6017}(859,\cdot)\) \(\chi_{6017}(914,\cdot)\) \(\chi_{6017}(947,\cdot)\) \(\chi_{6017}(1002,\cdot)\) \(\chi_{6017}(1024,\cdot)\) \(\chi_{6017}(1046,\cdot)\) ...

Values on generators

\((3830,2190)\) → \((1,e\left(\frac{76}{273}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{76}{273}\right)\)\(e\left(\frac{3}{7}\right)\)\(e\left(\frac{152}{273}\right)\)\(e\left(\frac{227}{273}\right)\)\(e\left(\frac{193}{273}\right)\)\(e\left(\frac{184}{273}\right)\)\(e\left(\frac{76}{91}\right)\)\(e\left(\frac{6}{7}\right)\)\(e\left(\frac{10}{91}\right)\)\(e\left(\frac{269}{273}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{273})\)