Properties

Conductor 861
Order 60
Real No
Primitive No
Parity Even
Orbit Label 6027.df

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[80]
 
pari: [g,chi] = znchar(Mod(80,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 861
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 60
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.df
Orbit index = 84

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 ]
 

\(\chi_{6027}(80,\cdot)\) \(\chi_{6027}(374,\cdot)\) \(\chi_{6027}(815,\cdot)\) \(\chi_{6027}(1109,\cdot)\) \(\chi_{6027}(1538,\cdot)\) \(\chi_{6027}(1550,\cdot)\) \(\chi_{6027}(2714,\cdot)\) \(\chi_{6027}(2726,\cdot)\) \(\chi_{6027}(3155,\cdot)\) \(\chi_{6027}(3449,\cdot)\) \(\chi_{6027}(3890,\cdot)\) \(\chi_{6027}(4184,\cdot)\) \(\chi_{6027}(4490,\cdot)\) \(\chi_{6027}(4625,\cdot)\) \(\chi_{6027}(5666,\cdot)\) \(\chi_{6027}(5801,\cdot)\)

Inducing primitive character

\(\chi_{861}(80,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{3}{20}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{7}{15}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{1}{5}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{37}{60}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{14}{15}\right)\)\(e\left(\frac{37}{60}\right)\)\(e\left(\frac{11}{60}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{60})\)