Properties

Conductor 731
Order 112
Real No
Primitive No
Parity Even
Orbit Label 8041.eh

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(8041)
 
sage: chi = H[45]
 
pari: [g,chi] = znchar(Mod(45,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 731
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 112
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 8041.eh
Orbit index = 112

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{8041}(45,\cdot)\) \(\chi_{8041}(199,\cdot)\) \(\chi_{8041}(309,\cdot)\) \(\chi_{8041}(419,\cdot)\) \(\chi_{8041}(452,\cdot)\) \(\chi_{8041}(925,\cdot)\) \(\chi_{8041}(991,\cdot)\) \(\chi_{8041}(1145,\cdot)\) \(\chi_{8041}(1200,\cdot)\) \(\chi_{8041}(1255,\cdot)\) \(\chi_{8041}(1365,\cdot)\) \(\chi_{8041}(1618,\cdot)\) \(\chi_{8041}(1673,\cdot)\) \(\chi_{8041}(1728,\cdot)\) \(\chi_{8041}(2564,\cdot)\) \(\chi_{8041}(2674,\cdot)\) \(\chi_{8041}(2817,\cdot)\) \(\chi_{8041}(2883,\cdot)\) \(\chi_{8041}(3037,\cdot)\) \(\chi_{8041}(3257,\cdot)\) \(\chi_{8041}(3356,\cdot)\) \(\chi_{8041}(3565,\cdot)\) \(\chi_{8041}(3730,\cdot)\) \(\chi_{8041}(3763,\cdot)\) \(\chi_{8041}(3983,\cdot)\) \(\chi_{8041}(4236,\cdot)\) \(\chi_{8041}(4511,\cdot)\) \(\chi_{8041}(4566,\cdot)\) \(\chi_{8041}(4984,\cdot)\) \(\chi_{8041}(5039,\cdot)\) ...

Inducing primitive character

\(\chi_{731}(45,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((1,e\left(\frac{7}{16}\right),e\left(\frac{9}{14}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{27}{56}\right)\)\(e\left(\frac{9}{112}\right)\)\(e\left(\frac{27}{28}\right)\)\(e\left(\frac{29}{112}\right)\)\(e\left(\frac{9}{16}\right)\)\(e\left(\frac{5}{16}\right)\)\(e\left(\frac{25}{56}\right)\)\(e\left(\frac{9}{56}\right)\)\(e\left(\frac{83}{112}\right)\)\(e\left(\frac{5}{112}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{112})\)