Properties

Conductor 349
Order 29
Real No
Primitive No
Parity Even
Orbit Label 8027.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(8027)
 
sage: chi = H[415]
 
pari: [g,chi] = znchar(Mod(415,8027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 349
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 29
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 = 8027.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 ]
 

\(\chi_{8027}(415,\cdot)\) \(\chi_{8027}(967,\cdot)\) \(\chi_{8027}(1427,\cdot)\) \(\chi_{8027}(1979,\cdot)\) \(\chi_{8027}(2002,\cdot)\) \(\chi_{8027}(2025,\cdot)\) \(\chi_{8027}(2416,\cdot)\) \(\chi_{8027}(2531,\cdot)\) \(\chi_{8027}(2692,\cdot)\) \(\chi_{8027}(3267,\cdot)\) \(\chi_{8027}(3658,\cdot)\) \(\chi_{8027}(3957,\cdot)\) \(\chi_{8027}(4049,\cdot)\) \(\chi_{8027}(4578,\cdot)\) \(\chi_{8027}(4647,\cdot)\) \(\chi_{8027}(5199,\cdot)\) \(\chi_{8027}(5406,\cdot)\) \(\chi_{8027}(5498,\cdot)\) \(\chi_{8027}(5567,\cdot)\) \(\chi_{8027}(6234,\cdot)\) \(\chi_{8027}(6349,\cdot)\) \(\chi_{8027}(6510,\cdot)\) \(\chi_{8027}(6556,\cdot)\) \(\chi_{8027}(6855,\cdot)\) \(\chi_{8027}(7269,\cdot)\) \(\chi_{8027}(7292,\cdot)\) \(\chi_{8027}(7614,\cdot)\) \(\chi_{8027}(7982,\cdot)\)

Inducing primitive character

\(\chi_{349}(66,\cdot)\)

Values on generators

\((350,5935)\) → \((1,e\left(\frac{4}{29}\right))\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{4}{29}\right)\)\(e\left(\frac{17}{29}\right)\)\(e\left(\frac{8}{29}\right)\)\(e\left(\frac{9}{29}\right)\)\(e\left(\frac{21}{29}\right)\)\(e\left(\frac{7}{29}\right)\)\(e\left(\frac{12}{29}\right)\)\(e\left(\frac{5}{29}\right)\)\(e\left(\frac{13}{29}\right)\)\(e\left(\frac{26}{29}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{29})\)