Properties

Modulus 4410
Conductor 2205
Order 42
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4410.dj

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([7,21,33]))
 
pari: [g,chi] = znchar(Mod(209,4410))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4410
Conductor = 2205
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.dj
Orbit index = 88

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 ]
 

\(\chi_{4410}(209,\cdot)\) \(\chi_{4410}(419,\cdot)\) \(\chi_{4410}(839,\cdot)\) \(\chi_{4410}(1049,\cdot)\) \(\chi_{4410}(1679,\cdot)\) \(\chi_{4410}(2099,\cdot)\) \(\chi_{4410}(2309,\cdot)\) \(\chi_{4410}(2729,\cdot)\) \(\chi_{4410}(3359,\cdot)\) \(\chi_{4410}(3569,\cdot)\) \(\chi_{4410}(3989,\cdot)\) \(\chi_{4410}(4199,\cdot)\)

Values on generators

\((3431,2647,1081)\) → \((e\left(\frac{1}{6}\right),-1,e\left(\frac{11}{14}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{25}{42}\right)\)\(e\left(\frac{16}{21}\right)\)\(e\left(\frac{9}{14}\right)\)\(-1\)\(e\left(\frac{4}{21}\right)\)\(e\left(\frac{13}{42}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{9}{14}\right)\)\(e\left(\frac{13}{21}\right)\)\(e\left(\frac{37}{42}\right)\)
value at  e.g. 2

Related number fields

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