Properties

Conductor 1021
Order 17
Real No
Primitive Yes
Parity Even
Orbit Label 1021.j

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(1021)
 
sage: chi = H[9]
 
pari: [g,chi] = znchar(Mod(9,1021))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1021
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 17
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 1021.j
Orbit index = 10

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 ]
 

\(\chi_{1021}(9,\cdot)\) \(\chi_{1021}(81,\cdot)\) \(\chi_{1021}(227,\cdot)\) \(\chi_{1021}(340,\cdot)\) \(\chi_{1021}(435,\cdot)\) \(\chi_{1021}(479,\cdot)\) \(\chi_{1021}(507,\cdot)\) \(\chi_{1021}(521,\cdot)\) \(\chi_{1021}(605,\cdot)\) \(\chi_{1021}(729,\cdot)\) \(\chi_{1021}(737,\cdot)\) \(\chi_{1021}(778,\cdot)\) \(\chi_{1021}(852,\cdot)\) \(\chi_{1021}(876,\cdot)\) \(\chi_{1021}(994,\cdot)\) \(\chi_{1021}(1018,\cdot)\)

Values on generators

\(10\) → \(e\left(\frac{9}{17}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{5}{17}\right)\)\(e\left(\frac{16}{17}\right)\)\(e\left(\frac{10}{17}\right)\)\(e\left(\frac{4}{17}\right)\)\(e\left(\frac{4}{17}\right)\)\(e\left(\frac{11}{17}\right)\)\(e\left(\frac{15}{17}\right)\)\(e\left(\frac{15}{17}\right)\)\(e\left(\frac{9}{17}\right)\)\(e\left(\frac{8}{17}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{17})\)