Properties

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

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([7,0,1]))
 
pari: [g,chi] = znchar(Mod(101,4410))
 

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.dg
Orbit index = 85

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 ]
 

\(\chi_{4410}(101,\cdot)\) \(\chi_{4410}(131,\cdot)\) \(\chi_{4410}(731,\cdot)\) \(\chi_{4410}(761,\cdot)\) \(\chi_{4410}(1361,\cdot)\) \(\chi_{4410}(2021,\cdot)\) \(\chi_{4410}(2621,\cdot)\) \(\chi_{4410}(2651,\cdot)\) \(\chi_{4410}(3251,\cdot)\) \(\chi_{4410}(3281,\cdot)\) \(\chi_{4410}(3881,\cdot)\) \(\chi_{4410}(3911,\cdot)\)

Values on generators

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

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{5}{42}\right)\)\(e\left(\frac{5}{42}\right)\)\(e\left(\frac{2}{21}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{31}{42}\right)\)\(e\left(\frac{25}{42}\right)\)\(-1\)\(e\left(\frac{16}{21}\right)\)\(e\left(\frac{4}{21}\right)\)\(e\left(\frac{17}{21}\right)\)
value at  e.g. 2

Related number fields

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