Properties

Modulus 4410
Conductor 245
Order 28
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4410.cv

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([0,7,22]))
 
pari: [g,chi] = znchar(Mod(307,4410))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4410
Conductor = 245
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 28
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.cv
Orbit index = 74

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 ]
 

\(\chi_{4410}(307,\cdot)\) \(\chi_{4410}(433,\cdot)\) \(\chi_{4410}(937,\cdot)\) \(\chi_{4410}(1063,\cdot)\) \(\chi_{4410}(1693,\cdot)\) \(\chi_{4410}(2197,\cdot)\) \(\chi_{4410}(2323,\cdot)\) \(\chi_{4410}(2827,\cdot)\) \(\chi_{4410}(2953,\cdot)\) \(\chi_{4410}(3457,\cdot)\) \(\chi_{4410}(3583,\cdot)\) \(\chi_{4410}(4087,\cdot)\)

Values on generators

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

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{3}{7}\right)\)\(e\left(\frac{19}{28}\right)\)\(e\left(\frac{25}{28}\right)\)\(1\)\(e\left(\frac{17}{28}\right)\)\(e\left(\frac{9}{14}\right)\)\(-1\)\(e\left(\frac{11}{28}\right)\)\(e\left(\frac{11}{14}\right)\)\(e\left(\frac{13}{28}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{28})\)