Properties

Conductor 1007
Order 78
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 1007.z

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(1007)
 
sage: chi = H[486]
 
pari: [g,chi] = znchar(Mod(486,1007))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1007
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 78
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 = even
Orbit label = 1007.z
Orbit index = 26

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 ]
 

\(\chi_{1007}(7,\cdot)\) \(\chi_{1007}(11,\cdot)\) \(\chi_{1007}(64,\cdot)\) \(\chi_{1007}(144,\cdot)\) \(\chi_{1007}(163,\cdot)\) \(\chi_{1007}(197,\cdot)\) \(\chi_{1007}(216,\cdot)\) \(\chi_{1007}(467,\cdot)\) \(\chi_{1007}(486,\cdot)\) \(\chi_{1007}(520,\cdot)\) \(\chi_{1007}(539,\cdot)\) \(\chi_{1007}(600,\cdot)\) \(\chi_{1007}(653,\cdot)\) \(\chi_{1007}(676,\cdot)\) \(\chi_{1007}(695,\cdot)\) \(\chi_{1007}(714,\cdot)\) \(\chi_{1007}(729,\cdot)\) \(\chi_{1007}(748,\cdot)\) \(\chi_{1007}(767,\cdot)\) \(\chi_{1007}(771,\cdot)\) \(\chi_{1007}(824,\cdot)\) \(\chi_{1007}(885,\cdot)\) \(\chi_{1007}(938,\cdot)\) \(\chi_{1007}(961,\cdot)\)

Values on generators

\((743,267)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{17}{26}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{25}{78}\right)\)\(e\left(\frac{61}{78}\right)\)\(e\left(\frac{25}{39}\right)\)\(e\left(\frac{31}{78}\right)\)\(e\left(\frac{4}{39}\right)\)\(e\left(\frac{2}{13}\right)\)\(e\left(\frac{25}{26}\right)\)\(e\left(\frac{22}{39}\right)\)\(e\left(\frac{28}{39}\right)\)\(e\left(\frac{12}{13}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{39})\)