Properties

Conductor 473
Order 42
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4730.cg

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[1781]
 
pari: [g,chi] = znchar(Mod(1781,4730))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 473
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 42
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.cg
Orbit index = 59

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 ]
 

\(\chi_{4730}(241,\cdot)\) \(\chi_{4730}(571,\cdot)\) \(\chi_{4730}(1121,\cdot)\) \(\chi_{4730}(1781,\cdot)\) \(\chi_{4730}(2221,\cdot)\) \(\chi_{4730}(2441,\cdot)\) \(\chi_{4730}(2771,\cdot)\) \(\chi_{4730}(3101,\cdot)\) \(\chi_{4730}(3211,\cdot)\) \(\chi_{4730}(3431,\cdot)\) \(\chi_{4730}(3761,\cdot)\) \(\chi_{4730}(4201,\cdot)\)

Values on generators

\((947,431,1981)\) → \((1,-1,e\left(\frac{29}{42}\right))\)

Values

-1137913171921232729
\(1\)\(1\)\(e\left(\frac{29}{42}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{8}{21}\right)\)\(e\left(\frac{25}{42}\right)\)\(e\left(\frac{31}{42}\right)\)\(e\left(\frac{13}{21}\right)\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{1}{21}\right)\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{17}{21}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{21})\)