Properties

Modulus 4410
Conductor 441
Order 42
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4410.dx

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([35,0,25]))
 
pari: [g,chi] = znchar(Mod(311,4410))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4410
Conductor = 441
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 = 4410.dx
Orbit index = 102

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 ]
 

\(\chi_{4410}(311,\cdot)\) \(\chi_{4410}(551,\cdot)\) \(\chi_{4410}(941,\cdot)\) \(\chi_{4410}(1181,\cdot)\) \(\chi_{4410}(1571,\cdot)\) \(\chi_{4410}(1811,\cdot)\) \(\chi_{4410}(2201,\cdot)\) \(\chi_{4410}(2441,\cdot)\) \(\chi_{4410}(2831,\cdot)\) \(\chi_{4410}(3071,\cdot)\) \(\chi_{4410}(3701,\cdot)\) \(\chi_{4410}(4091,\cdot)\)

Values on generators

\((3431,2647,1081)\) → \((e\left(\frac{5}{6}\right),1,e\left(\frac{25}{42}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{9}{14}\right)\)\(e\left(\frac{13}{42}\right)\)\(e\left(\frac{8}{21}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{11}{14}\right)\)\(e\left(\frac{23}{42}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{1}{21}\right)\)\(e\left(\frac{2}{21}\right)\)\(e\left(\frac{19}{21}\right)\)
value at  e.g. 2

Related number fields

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