Properties

Modulus 4410
Conductor 2205
Order 84
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4410.ep

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4410)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([14,21,76]))
 
pari: [g,chi] = znchar(Mod(317,4410))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4410
Conductor = 2205
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 = 4410.ep
Orbit index = 120

Galois orbit

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{4410}(317,\cdot)\) \(\chi_{4410}(347,\cdot)\) \(\chi_{4410}(443,\cdot)\) \(\chi_{4410}(473,\cdot)\) \(\chi_{4410}(947,\cdot)\) \(\chi_{4410}(977,\cdot)\) \(\chi_{4410}(1073,\cdot)\) \(\chi_{4410}(1103,\cdot)\) \(\chi_{4410}(1577,\cdot)\) \(\chi_{4410}(1607,\cdot)\) \(\chi_{4410}(1703,\cdot)\) \(\chi_{4410}(2207,\cdot)\) \(\chi_{4410}(2237,\cdot)\) \(\chi_{4410}(2363,\cdot)\) \(\chi_{4410}(2837,\cdot)\) \(\chi_{4410}(2867,\cdot)\) \(\chi_{4410}(2963,\cdot)\) \(\chi_{4410}(2993,\cdot)\) \(\chi_{4410}(3467,\cdot)\) \(\chi_{4410}(3593,\cdot)\) \(\chi_{4410}(3623,\cdot)\) \(\chi_{4410}(4127,\cdot)\) \(\chi_{4410}(4223,\cdot)\) \(\chi_{4410}(4253,\cdot)\)

Values on generators

\((3431,2647,1081)\) → \((e\left(\frac{1}{6}\right),i,e\left(\frac{19}{21}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{79}{84}\right)\)\(e\left(\frac{31}{84}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{27}{28}\right)\)\(e\left(\frac{20}{21}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{17}{84}\right)\)\(e\left(\frac{17}{42}\right)\)\(e\left(\frac{71}{84}\right)\)
value at  e.g. 2

Related number fields

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