Properties

Conductor 4001
Order 200
Real No
Primitive No
Parity Even
Orbit Label 8002.q

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[5]
 
pari: [g,chi] = znchar(Mod(5,8002))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4001
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 = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 8002.q
Orbit index = 17

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 ]
 

\(\chi_{8002}(5,\cdot)\) \(\chi_{8002}(79,\cdot)\) \(\chi_{8002}(125,\cdot)\) \(\chi_{8002}(261,\cdot)\) \(\chi_{8002}(347,\cdot)\) \(\chi_{8002}(357,\cdot)\) \(\chi_{8002}(509,\cdot)\) \(\chi_{8002}(637,\cdot)\) \(\chi_{8002}(731,\cdot)\) \(\chi_{8002}(761,\cdot)\) \(\chi_{8002}(803,\cdot)\) \(\chi_{8002}(821,\cdot)\) \(\chi_{8002}(857,\cdot)\) \(\chi_{8002}(863,\cdot)\) \(\chi_{8002}(919,\cdot)\) \(\chi_{8002}(923,\cdot)\) \(\chi_{8002}(931,\cdot)\) \(\chi_{8002}(997,\cdot)\) \(\chi_{8002}(1005,\cdot)\) \(\chi_{8002}(1349,\cdot)\) \(\chi_{8002}(1477,\cdot)\) \(\chi_{8002}(1717,\cdot)\) \(\chi_{8002}(1769,\cdot)\) \(\chi_{8002}(1895,\cdot)\) \(\chi_{8002}(1975,\cdot)\) \(\chi_{8002}(2067,\cdot)\) \(\chi_{8002}(2251,\cdot)\) \(\chi_{8002}(2431,\cdot)\) \(\chi_{8002}(2581,\cdot)\) \(\chi_{8002}(3021,\cdot)\) ...

Inducing primitive character

\(\chi_{4001}(5,\cdot)\)

Values on generators

\(3\) → \(e\left(\frac{59}{200}\right)\)

Values

-113579111315171921
\(1\)\(1\)\(e\left(\frac{59}{200}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{13}{50}\right)\)\(e\left(\frac{59}{100}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{19}{50}\right)\)\(e\left(\frac{79}{200}\right)\)\(e\left(\frac{29}{200}\right)\)\(e\left(\frac{29}{50}\right)\)\(e\left(\frac{111}{200}\right)\)
value at  e.g. 2

Related number fields

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