Properties

Conductor 1021
Order 68
Real no
Primitive yes
Minimal yes
Parity odd
Orbit label 1021.p

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[471]
 
pari: [g,chi] = znchar(Mod(471,1021))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1021
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 68
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = odd
Orbit label = 1021.p
Orbit index = 16

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 ]
 

\(\chi_{1021}(13,\cdot)\) \(\chi_{1021}(32,\cdot)\) \(\chi_{1021}(39,\cdot)\) \(\chi_{1021}(96,\cdot)\) \(\chi_{1021}(101,\cdot)\) \(\chi_{1021}(112,\cdot)\) \(\chi_{1021}(117,\cdot)\) \(\chi_{1021}(155,\cdot)\) \(\chi_{1021}(157,\cdot)\) \(\chi_{1021}(288,\cdot)\) \(\chi_{1021}(303,\cdot)\) \(\chi_{1021}(336,\cdot)\) \(\chi_{1021}(351,\cdot)\) \(\chi_{1021}(392,\cdot)\) \(\chi_{1021}(465,\cdot)\) \(\chi_{1021}(471,\cdot)\) \(\chi_{1021}(550,\cdot)\) \(\chi_{1021}(556,\cdot)\) \(\chi_{1021}(629,\cdot)\) \(\chi_{1021}(670,\cdot)\) \(\chi_{1021}(685,\cdot)\) \(\chi_{1021}(718,\cdot)\) \(\chi_{1021}(733,\cdot)\) \(\chi_{1021}(864,\cdot)\) \(\chi_{1021}(866,\cdot)\) \(\chi_{1021}(904,\cdot)\) \(\chi_{1021}(909,\cdot)\) \(\chi_{1021}(920,\cdot)\) \(\chi_{1021}(925,\cdot)\) \(\chi_{1021}(982,\cdot)\) ...

Values on generators

\(10\) → \(e\left(\frac{13}{68}\right)\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{45}{68}\right)\)\(e\left(\frac{21}{34}\right)\)\(e\left(\frac{11}{34}\right)\)\(e\left(\frac{9}{17}\right)\)\(e\left(\frac{19}{68}\right)\)\(e\left(\frac{31}{68}\right)\)\(e\left(\frac{67}{68}\right)\)\(e\left(\frac{4}{17}\right)\)\(e\left(\frac{13}{68}\right)\)\(e\left(\frac{1}{17}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{68})\)