Properties

Conductor 2000
Order 100
Real no
Primitive no
Minimal no
Parity odd
Orbit label 4000.cp

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[73]
 
pari: [g,chi] = znchar(Mod(73,4000))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2000
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 100
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 = odd
Orbit label = 4000.cp
Orbit index = 68

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 ]
 

\(\chi_{4000}(73,\cdot)\) \(\chi_{4000}(217,\cdot)\) \(\chi_{4000}(233,\cdot)\) \(\chi_{4000}(377,\cdot)\) \(\chi_{4000}(537,\cdot)\) \(\chi_{4000}(553,\cdot)\) \(\chi_{4000}(697,\cdot)\) \(\chi_{4000}(713,\cdot)\) \(\chi_{4000}(873,\cdot)\) \(\chi_{4000}(1017,\cdot)\) \(\chi_{4000}(1033,\cdot)\) \(\chi_{4000}(1177,\cdot)\) \(\chi_{4000}(1337,\cdot)\) \(\chi_{4000}(1353,\cdot)\) \(\chi_{4000}(1497,\cdot)\) \(\chi_{4000}(1513,\cdot)\) \(\chi_{4000}(1673,\cdot)\) \(\chi_{4000}(1817,\cdot)\) \(\chi_{4000}(1833,\cdot)\) \(\chi_{4000}(1977,\cdot)\) \(\chi_{4000}(2137,\cdot)\) \(\chi_{4000}(2153,\cdot)\) \(\chi_{4000}(2297,\cdot)\) \(\chi_{4000}(2313,\cdot)\) \(\chi_{4000}(2473,\cdot)\) \(\chi_{4000}(2617,\cdot)\) \(\chi_{4000}(2633,\cdot)\) \(\chi_{4000}(2777,\cdot)\) \(\chi_{4000}(2937,\cdot)\) \(\chi_{4000}(2953,\cdot)\) ...

Values on generators

\((2751,2501,1377)\) → \((1,-i,e\left(\frac{91}{100}\right))\)

Values

-1137911131719212327
\(-1\)\(1\)\(e\left(\frac{31}{50}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{6}{25}\right)\)\(e\left(\frac{91}{100}\right)\)\(e\left(\frac{37}{50}\right)\)\(e\left(\frac{43}{100}\right)\)\(e\left(\frac{63}{100}\right)\)\(e\left(\frac{47}{100}\right)\)\(e\left(\frac{71}{100}\right)\)\(e\left(\frac{43}{50}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{100})\)