Properties

Conductor 4000
Order 200
Real No
Primitive Yes
Parity Odd
Orbit Label 4000.cz

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[797]
 
pari: [g,chi] = znchar(Mod(797,4000))
 

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
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 4000.cz
Orbit index = 78

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 ]
 

\(\chi_{4000}(53,\cdot)\) \(\chi_{4000}(77,\cdot)\) \(\chi_{4000}(133,\cdot)\) \(\chi_{4000}(213,\cdot)\) \(\chi_{4000}(237,\cdot)\) \(\chi_{4000}(317,\cdot)\) \(\chi_{4000}(373,\cdot)\) \(\chi_{4000}(397,\cdot)\) \(\chi_{4000}(453,\cdot)\) \(\chi_{4000}(477,\cdot)\) \(\chi_{4000}(533,\cdot)\) \(\chi_{4000}(613,\cdot)\) \(\chi_{4000}(637,\cdot)\) \(\chi_{4000}(717,\cdot)\) \(\chi_{4000}(773,\cdot)\) \(\chi_{4000}(797,\cdot)\) \(\chi_{4000}(853,\cdot)\) \(\chi_{4000}(877,\cdot)\) \(\chi_{4000}(933,\cdot)\) \(\chi_{4000}(1013,\cdot)\) \(\chi_{4000}(1037,\cdot)\) \(\chi_{4000}(1117,\cdot)\) \(\chi_{4000}(1173,\cdot)\) \(\chi_{4000}(1197,\cdot)\) \(\chi_{4000}(1253,\cdot)\) \(\chi_{4000}(1277,\cdot)\) \(\chi_{4000}(1333,\cdot)\) \(\chi_{4000}(1413,\cdot)\) \(\chi_{4000}(1437,\cdot)\) \(\chi_{4000}(1517,\cdot)\) ...

Values on generators

\((2751,2501,1377)\) → \((1,e\left(\frac{3}{8}\right),e\left(\frac{97}{100}\right))\)

Values

-1137911131719212327
\(-1\)\(1\)\(e\left(\frac{183}{200}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{83}{100}\right)\)\(e\left(\frac{119}{200}\right)\)\(e\left(\frac{91}{200}\right)\)\(e\left(\frac{31}{100}\right)\)\(e\left(\frac{17}{200}\right)\)\(e\left(\frac{23}{200}\right)\)\(e\left(\frac{8}{25}\right)\)\(e\left(\frac{149}{200}\right)\)
value at  e.g. 2

Related number fields

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