Properties

Conductor 4000
Order 200
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 4000.da

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[29]
 
pari: [g,chi] = znchar(Mod(29,4000))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4000
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 200
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 = 4000.da
Orbit index = 79

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 ]
 

\(\chi_{4000}(29,\cdot)\) \(\chi_{4000}(69,\cdot)\) \(\chi_{4000}(109,\cdot)\) \(\chi_{4000}(189,\cdot)\) \(\chi_{4000}(229,\cdot)\) \(\chi_{4000}(269,\cdot)\) \(\chi_{4000}(309,\cdot)\) \(\chi_{4000}(389,\cdot)\) \(\chi_{4000}(429,\cdot)\) \(\chi_{4000}(469,\cdot)\) \(\chi_{4000}(509,\cdot)\) \(\chi_{4000}(589,\cdot)\) \(\chi_{4000}(629,\cdot)\) \(\chi_{4000}(669,\cdot)\) \(\chi_{4000}(709,\cdot)\) \(\chi_{4000}(789,\cdot)\) \(\chi_{4000}(829,\cdot)\) \(\chi_{4000}(869,\cdot)\) \(\chi_{4000}(909,\cdot)\) \(\chi_{4000}(989,\cdot)\) \(\chi_{4000}(1029,\cdot)\) \(\chi_{4000}(1069,\cdot)\) \(\chi_{4000}(1109,\cdot)\) \(\chi_{4000}(1189,\cdot)\) \(\chi_{4000}(1229,\cdot)\) \(\chi_{4000}(1269,\cdot)\) \(\chi_{4000}(1309,\cdot)\) \(\chi_{4000}(1389,\cdot)\) \(\chi_{4000}(1429,\cdot)\) \(\chi_{4000}(1469,\cdot)\) ...

Values on generators

\((2751,2501,1377)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{31}{50}\right))\)

Values

-1137911131719212327
\(1\)\(1\)\(e\left(\frac{93}{200}\right)\)\(e\left(\frac{9}{20}\right)\)\(e\left(\frac{93}{100}\right)\)\(e\left(\frac{199}{200}\right)\)\(e\left(\frac{161}{200}\right)\)\(e\left(\frac{19}{25}\right)\)\(e\left(\frac{157}{200}\right)\)\(e\left(\frac{183}{200}\right)\)\(e\left(\frac{47}{100}\right)\)\(e\left(\frac{79}{200}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{200})\)