Properties

Conductor 4001
Order 20
Real No
Primitive No
Parity Even
Orbit Label 8002.h

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(8002)
 
sage: chi = H[6697]
 
pari: [g,chi] = znchar(Mod(6697,8002))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4001
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 20
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 = Even
Orbit label = 8002.h
Orbit index = 8

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 ]
 

\(\chi_{8002}(1305,\cdot)\) \(\chi_{8002}(2931,\cdot)\) \(\chi_{8002}(3185,\cdot)\) \(\chi_{8002}(3849,\cdot)\) \(\chi_{8002}(4153,\cdot)\) \(\chi_{8002}(4817,\cdot)\) \(\chi_{8002}(5071,\cdot)\) \(\chi_{8002}(6697,\cdot)\)

Inducing primitive character

\(\chi_{4001}(2696,\cdot)\)

Values on generators

\(3\) → \(e\left(\frac{7}{20}\right)\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{7}{20}\right)\)\(1\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{7}{10}\right)\)\(-i\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{7}{20}\right)\)\(e\left(\frac{17}{20}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{3}{20}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{20})\)