Properties

Conductor 1021
Order 170
Real No
Primitive Yes
Parity Even
Orbit Label 1021.s

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[4]
 
pari: [g,chi] = znchar(Mod(4,1021))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1021
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 170
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.s
Orbit index = 19

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 ]
 

\(\chi_{1021}(4,\cdot)\) \(\chi_{1021}(36,\cdot)\) \(\chi_{1021}(42,\cdot)\) \(\chi_{1021}(48,\cdot)\) \(\chi_{1021}(49,\cdot)\) \(\chi_{1021}(56,\cdot)\) \(\chi_{1021}(64,\cdot)\) \(\chi_{1021}(79,\cdot)\) \(\chi_{1021}(85,\cdot)\) \(\chi_{1021}(187,\cdot)\) \(\chi_{1021}(202,\cdot)\) \(\chi_{1021}(213,\cdot)\) \(\chi_{1021}(234,\cdot)\) \(\chi_{1021}(273,\cdot)\) \(\chi_{1021}(278,\cdot)\) \(\chi_{1021}(312,\cdot)\) \(\chi_{1021}(314,\cdot)\) \(\chi_{1021}(319,\cdot)\) \(\chi_{1021}(324,\cdot)\) \(\chi_{1021}(339,\cdot)\) \(\chi_{1021}(364,\cdot)\) \(\chi_{1021}(375,\cdot)\) \(\chi_{1021}(378,\cdot)\) \(\chi_{1021}(382,\cdot)\) \(\chi_{1021}(415,\cdot)\) \(\chi_{1021}(441,\cdot)\) \(\chi_{1021}(452,\cdot)\) \(\chi_{1021}(460,\cdot)\) \(\chi_{1021}(504,\cdot)\) \(\chi_{1021}(530,\cdot)\) ...

Values on generators

\(10\) → \(e\left(\frac{111}{170}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{73}{170}\right)\)\(e\left(\frac{5}{17}\right)\)\(e\left(\frac{73}{85}\right)\)\(e\left(\frac{19}{85}\right)\)\(e\left(\frac{123}{170}\right)\)\(e\left(\frac{113}{170}\right)\)\(e\left(\frac{49}{170}\right)\)\(e\left(\frac{10}{17}\right)\)\(e\left(\frac{111}{170}\right)\)\(e\left(\frac{38}{85}\right)\)
value at  e.g. 2

Related number fields

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