Properties

Conductor 861
Order 120
Real No
Primitive No
Parity Even
Orbit Label 6027.dw

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(6027)
 
sage: chi = H[116]
 
pari: [g,chi] = znchar(Mod(116,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 861
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 120
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 = 6027.dw
Orbit index = 101

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 ]
 

\(\chi_{6027}(116,\cdot)\) \(\chi_{6027}(263,\cdot)\) \(\chi_{6027}(275,\cdot)\) \(\chi_{6027}(422,\cdot)\) \(\chi_{6027}(557,\cdot)\) \(\chi_{6027}(704,\cdot)\) \(\chi_{6027}(716,\cdot)\) \(\chi_{6027}(1010,\cdot)\) \(\chi_{6027}(1586,\cdot)\) \(\chi_{6027}(1733,\cdot)\) \(\chi_{6027}(1880,\cdot)\) \(\chi_{6027}(1892,\cdot)\) \(\chi_{6027}(2039,\cdot)\) \(\chi_{6027}(2186,\cdot)\) \(\chi_{6027}(2762,\cdot)\) \(\chi_{6027}(3056,\cdot)\) \(\chi_{6027}(3068,\cdot)\) \(\chi_{6027}(3215,\cdot)\) \(\chi_{6027}(3350,\cdot)\) \(\chi_{6027}(3497,\cdot)\) \(\chi_{6027}(3509,\cdot)\) \(\chi_{6027}(3656,\cdot)\) \(\chi_{6027}(3791,\cdot)\) \(\chi_{6027}(4085,\cdot)\) \(\chi_{6027}(4538,\cdot)\) \(\chi_{6027}(4685,\cdot)\) \(\chi_{6027}(4832,\cdot)\) \(\chi_{6027}(4967,\cdot)\) \(\chi_{6027}(5114,\cdot)\) \(\chi_{6027}(5261,\cdot)\) ...

Inducing primitive character

\(\chi_{861}(116,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{19}{40}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{11}{60}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{17}{60}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{71}{120}\right)\)\(e\left(\frac{29}{40}\right)\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{101}{120}\right)\)\(e\left(\frac{73}{120}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{120})\)