Properties

Conductor 800
Order 40
Real no
Primitive no
Minimal no
Parity even
Orbit label 4000.by

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(4000)
 
sage: chi = H[43]
 
pari: [g,chi] = znchar(Mod(43,4000))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 800
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 40
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = no
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4000.by
Orbit index = 51

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 ]
 

\(\chi_{4000}(43,\cdot)\) \(\chi_{4000}(707,\cdot)\) \(\chi_{4000}(843,\cdot)\) \(\chi_{4000}(1107,\cdot)\) \(\chi_{4000}(1243,\cdot)\) \(\chi_{4000}(1507,\cdot)\) \(\chi_{4000}(1643,\cdot)\) \(\chi_{4000}(1907,\cdot)\) \(\chi_{4000}(2043,\cdot)\) \(\chi_{4000}(2707,\cdot)\) \(\chi_{4000}(2843,\cdot)\) \(\chi_{4000}(3107,\cdot)\) \(\chi_{4000}(3243,\cdot)\) \(\chi_{4000}(3507,\cdot)\) \(\chi_{4000}(3643,\cdot)\) \(\chi_{4000}(3907,\cdot)\)

Values on generators

\((2751,2501,1377)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{19}{20}\right))\)

Values

-1137911131719212327
\(1\)\(1\)\(e\left(\frac{1}{40}\right)\)\(-1\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{33}{40}\right)\)\(e\left(\frac{17}{40}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{39}{40}\right)\)\(e\left(\frac{21}{40}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{3}{40}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{40})\)