Properties

Conductor 2000
Order 100
Real No
Primitive No
Parity Odd
Orbit Label 4000.cm

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[71]
 
pari: [g,chi] = znchar(Mod(71,4000))
 

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
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 4000.cm
Orbit index = 65

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 ]
 

\(\chi_{4000}(71,\cdot)\) \(\chi_{4000}(231,\cdot)\) \(\chi_{4000}(311,\cdot)\) \(\chi_{4000}(391,\cdot)\) \(\chi_{4000}(471,\cdot)\) \(\chi_{4000}(631,\cdot)\) \(\chi_{4000}(711,\cdot)\) \(\chi_{4000}(791,\cdot)\) \(\chi_{4000}(871,\cdot)\) \(\chi_{4000}(1031,\cdot)\) \(\chi_{4000}(1111,\cdot)\) \(\chi_{4000}(1191,\cdot)\) \(\chi_{4000}(1271,\cdot)\) \(\chi_{4000}(1431,\cdot)\) \(\chi_{4000}(1511,\cdot)\) \(\chi_{4000}(1591,\cdot)\) \(\chi_{4000}(1671,\cdot)\) \(\chi_{4000}(1831,\cdot)\) \(\chi_{4000}(1911,\cdot)\) \(\chi_{4000}(1991,\cdot)\) \(\chi_{4000}(2071,\cdot)\) \(\chi_{4000}(2231,\cdot)\) \(\chi_{4000}(2311,\cdot)\) \(\chi_{4000}(2391,\cdot)\) \(\chi_{4000}(2471,\cdot)\) \(\chi_{4000}(2631,\cdot)\) \(\chi_{4000}(2711,\cdot)\) \(\chi_{4000}(2791,\cdot)\) \(\chi_{4000}(2871,\cdot)\) \(\chi_{4000}(3031,\cdot)\) ...

Inducing primitive character

\(\chi_{2000}(571,\cdot)\)

Values on generators

\((2751,2501,1377)\) → \((-1,i,e\left(\frac{18}{25}\right))\)

Values

-1137911131719212327
\(-1\)\(1\)\(e\left(\frac{29}{100}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{29}{50}\right)\)\(e\left(\frac{47}{100}\right)\)\(e\left(\frac{83}{100}\right)\)\(e\left(\frac{14}{25}\right)\)\(e\left(\frac{21}{100}\right)\)\(e\left(\frac{49}{100}\right)\)\(e\left(\frac{8}{25}\right)\)\(e\left(\frac{87}{100}\right)\)
value at  e.g. 2

Related number fields

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