Properties

Conductor 2365
Order 84
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4730.db

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(4730)
 
sage: chi = H[153]
 
pari: [g,chi] = znchar(Mod(153,4730))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2365
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 84
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 = 4730.db
Orbit index = 80

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 ]
 

\(\chi_{4730}(153,\cdot)\) \(\chi_{4730}(197,\cdot)\) \(\chi_{4730}(483,\cdot)\) \(\chi_{4730}(703,\cdot)\) \(\chi_{4730}(857,\cdot)\) \(\chi_{4730}(1143,\cdot)\) \(\chi_{4730}(1407,\cdot)\) \(\chi_{4730}(1737,\cdot)\) \(\chi_{4730}(1803,\cdot)\) \(\chi_{4730}(2353,\cdot)\) \(\chi_{4730}(2507,\cdot)\) \(\chi_{4730}(2683,\cdot)\) \(\chi_{4730}(2947,\cdot)\) \(\chi_{4730}(3277,\cdot)\) \(\chi_{4730}(3453,\cdot)\) \(\chi_{4730}(3497,\cdot)\) \(\chi_{4730}(3607,\cdot)\) \(\chi_{4730}(3893,\cdot)\) \(\chi_{4730}(3937,\cdot)\) \(\chi_{4730}(4223,\cdot)\) \(\chi_{4730}(4267,\cdot)\) \(\chi_{4730}(4443,\cdot)\) \(\chi_{4730}(4487,\cdot)\) \(\chi_{4730}(4553,\cdot)\)

Values on generators

\((947,431,1981)\) → \((-i,-1,e\left(\frac{20}{21}\right))\)

Values

-1137913171921232729
\(1\)\(1\)\(e\left(\frac{17}{84}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{17}{42}\right)\)\(e\left(\frac{19}{84}\right)\)\(e\left(\frac{37}{84}\right)\)\(e\left(\frac{2}{21}\right)\)\(e\left(\frac{11}{14}\right)\)\(e\left(\frac{41}{84}\right)\)\(e\left(\frac{17}{28}\right)\)\(e\left(\frac{1}{21}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{84})\)