Properties

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

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([28,63,66]))
 
pari: [g,chi] = znchar(Mod(13,4410))
 

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.en
Orbit index = 118

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 ]
 

\(\chi_{4410}(13,\cdot)\) \(\chi_{4410}(223,\cdot)\) \(\chi_{4410}(517,\cdot)\) \(\chi_{4410}(643,\cdot)\) \(\chi_{4410}(727,\cdot)\) \(\chi_{4410}(853,\cdot)\) \(\chi_{4410}(1147,\cdot)\) \(\chi_{4410}(1357,\cdot)\) \(\chi_{4410}(1483,\cdot)\) \(\chi_{4410}(1777,\cdot)\) \(\chi_{4410}(1903,\cdot)\) \(\chi_{4410}(1987,\cdot)\) \(\chi_{4410}(2113,\cdot)\) \(\chi_{4410}(2407,\cdot)\) \(\chi_{4410}(2533,\cdot)\) \(\chi_{4410}(2617,\cdot)\) \(\chi_{4410}(3163,\cdot)\) \(\chi_{4410}(3247,\cdot)\) \(\chi_{4410}(3373,\cdot)\) \(\chi_{4410}(3667,\cdot)\) \(\chi_{4410}(3793,\cdot)\) \(\chi_{4410}(3877,\cdot)\) \(\chi_{4410}(4003,\cdot)\) \(\chi_{4410}(4297,\cdot)\)

Values on generators

\((3431,2647,1081)\) → \((e\left(\frac{1}{3}\right),-i,e\left(\frac{11}{14}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{16}{21}\right)\)\(e\left(\frac{71}{84}\right)\)\(e\left(\frac{11}{28}\right)\)\(1\)\(e\left(\frac{65}{84}\right)\)\(e\left(\frac{41}{42}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{25}{28}\right)\)\(e\left(\frac{19}{42}\right)\)\(e\left(\frac{25}{84}\right)\)
value at  e.g. 2

Related number fields

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