Properties

Conductor 1021
Order 85
Real No
Primitive Yes
Parity Even
Orbit Label 1021.q

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[115]
 
pari: [g,chi] = znchar(Mod(115,1021))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1021
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 85
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.q
Orbit index = 17

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 ]
 

\(\chi_{1021}(12,\cdot)\) \(\chi_{1021}(14,\cdot)\) \(\chi_{1021}(16,\cdot)\) \(\chi_{1021}(71,\cdot)\) \(\chi_{1021}(73,\cdot)\) \(\chi_{1021}(78,\cdot)\) \(\chi_{1021}(91,\cdot)\) \(\chi_{1021}(104,\cdot)\) \(\chi_{1021}(108,\cdot)\) \(\chi_{1021}(113,\cdot)\) \(\chi_{1021}(115,\cdot)\) \(\chi_{1021}(125,\cdot)\) \(\chi_{1021}(126,\cdot)\) \(\chi_{1021}(144,\cdot)\) \(\chi_{1021}(147,\cdot)\) \(\chi_{1021}(168,\cdot)\) \(\chi_{1021}(192,\cdot)\) \(\chi_{1021}(196,\cdot)\) \(\chi_{1021}(224,\cdot)\) \(\chi_{1021}(235,\cdot)\) \(\chi_{1021}(237,\cdot)\) \(\chi_{1021}(253,\cdot)\) \(\chi_{1021}(255,\cdot)\) \(\chi_{1021}(256,\cdot)\) \(\chi_{1021}(262,\cdot)\) \(\chi_{1021}(275,\cdot)\) \(\chi_{1021}(302,\cdot)\) \(\chi_{1021}(310,\cdot)\) \(\chi_{1021}(316,\cdot)\) \(\chi_{1021}(335,\cdot)\) ...

Values on generators

\(10\) → \(e\left(\frac{3}{85}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{64}{85}\right)\)\(e\left(\frac{9}{17}\right)\)\(e\left(\frac{43}{85}\right)\)\(e\left(\frac{24}{85}\right)\)\(e\left(\frac{24}{85}\right)\)\(e\left(\frac{49}{85}\right)\)\(e\left(\frac{22}{85}\right)\)\(e\left(\frac{1}{17}\right)\)\(e\left(\frac{3}{85}\right)\)\(e\left(\frac{48}{85}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{85})\)