Properties

Conductor 1021
Order 204
Real No
Primitive Yes
Parity Odd
Orbit Label 1021.t

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[19]
 
pari: [g,chi] = znchar(Mod(19,1021))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1021
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 204
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 = Odd
Orbit label = 1021.t
Orbit index = 20

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 ]
 

\(\chi_{1021}(19,\cdot)\) \(\chi_{1021}(57,\cdot)\) \(\chi_{1021}(58,\cdot)\) \(\chi_{1021}(88,\cdot)\) \(\chi_{1021}(97,\cdot)\) \(\chi_{1021}(107,\cdot)\) \(\chi_{1021}(136,\cdot)\) \(\chi_{1021}(148,\cdot)\) \(\chi_{1021}(174,\cdot)\) \(\chi_{1021}(200,\cdot)\) \(\chi_{1021}(215,\cdot)\) \(\chi_{1021}(229,\cdot)\) \(\chi_{1021}(242,\cdot)\) \(\chi_{1021}(264,\cdot)\) \(\chi_{1021}(291,\cdot)\) \(\chi_{1021}(295,\cdot)\) \(\chi_{1021}(308,\cdot)\) \(\chi_{1021}(311,\cdot)\) \(\chi_{1021}(321,\cdot)\) \(\chi_{1021}(334,\cdot)\) \(\chi_{1021}(376,\cdot)\) \(\chi_{1021}(407,\cdot)\) \(\chi_{1021}(408,\cdot)\) \(\chi_{1021}(412,\cdot)\) \(\chi_{1021}(421,\cdot)\) \(\chi_{1021}(443,\cdot)\) \(\chi_{1021}(444,\cdot)\) \(\chi_{1021}(476,\cdot)\) \(\chi_{1021}(488,\cdot)\) \(\chi_{1021}(499,\cdot)\) ...

Values on generators

\(10\) → \(e\left(\frac{113}{204}\right)\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{31}{68}\right)\)\(e\left(\frac{19}{34}\right)\)\(e\left(\frac{31}{34}\right)\)\(e\left(\frac{5}{51}\right)\)\(e\left(\frac{1}{68}\right)\)\(e\left(\frac{41}{68}\right)\)\(e\left(\frac{25}{68}\right)\)\(e\left(\frac{2}{17}\right)\)\(e\left(\frac{113}{204}\right)\)\(e\left(\frac{44}{51}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{204})\)