Properties

Conductor 215
Order 84
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4730.da

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[177]
 
pari: [g,chi] = znchar(Mod(177,4730))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 215
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.da
Orbit index = 79

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 ]
 

\(\chi_{4730}(177,\cdot)\) \(\chi_{4730}(243,\cdot)\) \(\chi_{4730}(287,\cdot)\) \(\chi_{4730}(463,\cdot)\) \(\chi_{4730}(507,\cdot)\) \(\chi_{4730}(793,\cdot)\) \(\chi_{4730}(837,\cdot)\) \(\chi_{4730}(1123,\cdot)\) \(\chi_{4730}(1233,\cdot)\) \(\chi_{4730}(1277,\cdot)\) \(\chi_{4730}(1453,\cdot)\) \(\chi_{4730}(1783,\cdot)\) \(\chi_{4730}(2047,\cdot)\) \(\chi_{4730}(2223,\cdot)\) \(\chi_{4730}(2377,\cdot)\) \(\chi_{4730}(2927,\cdot)\) \(\chi_{4730}(2993,\cdot)\) \(\chi_{4730}(3323,\cdot)\) \(\chi_{4730}(3587,\cdot)\) \(\chi_{4730}(3873,\cdot)\) \(\chi_{4730}(4027,\cdot)\) \(\chi_{4730}(4247,\cdot)\) \(\chi_{4730}(4533,\cdot)\) \(\chi_{4730}(4577,\cdot)\)

Values on generators

\((947,431,1981)\) → \((i,1,e\left(\frac{25}{42}\right))\)

Values

-1137913171921232729
\(1\)\(1\)\(e\left(\frac{29}{84}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{29}{42}\right)\)\(e\left(\frac{67}{84}\right)\)\(e\left(\frac{73}{84}\right)\)\(e\left(\frac{17}{21}\right)\)\(e\left(\frac{3}{7}\right)\)\(e\left(\frac{23}{84}\right)\)\(e\left(\frac{1}{28}\right)\)\(e\left(\frac{19}{21}\right)\)
value at  e.g. 2

Related number fields

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