Properties

Modulus 4410
Conductor 245
Order 84
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4410.ek

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([0,63,74]))
 
pari: [g,chi] = znchar(Mod(73,4410))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 4410
Conductor = 245
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.ek
Orbit index = 115

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 ]
 

\(\chi_{4410}(73,\cdot)\) \(\chi_{4410}(397,\cdot)\) \(\chi_{4410}(523,\cdot)\) \(\chi_{4410}(577,\cdot)\) \(\chi_{4410}(703,\cdot)\) \(\chi_{4410}(1027,\cdot)\) \(\chi_{4410}(1153,\cdot)\) \(\chi_{4410}(1333,\cdot)\) \(\chi_{4410}(1657,\cdot)\) \(\chi_{4410}(1837,\cdot)\) \(\chi_{4410}(1963,\cdot)\) \(\chi_{4410}(2287,\cdot)\) \(\chi_{4410}(2413,\cdot)\) \(\chi_{4410}(2467,\cdot)\) \(\chi_{4410}(2593,\cdot)\) \(\chi_{4410}(2917,\cdot)\) \(\chi_{4410}(3043,\cdot)\) \(\chi_{4410}(3097,\cdot)\) \(\chi_{4410}(3223,\cdot)\) \(\chi_{4410}(3673,\cdot)\) \(\chi_{4410}(3727,\cdot)\) \(\chi_{4410}(4177,\cdot)\) \(\chi_{4410}(4303,\cdot)\) \(\chi_{4410}(4357,\cdot)\)

Values on generators

\((3431,2647,1081)\) → \((1,-i,e\left(\frac{37}{42}\right))\)

Values

-1111131719232931374143
\(1\)\(1\)\(e\left(\frac{5}{21}\right)\)\(e\left(\frac{9}{28}\right)\)\(e\left(\frac{65}{84}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{61}{84}\right)\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{79}{84}\right)\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{15}{28}\right)\)
value at  e.g. 2

Related number fields

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