Properties

Conductor 287
Order 120
Real No
Primitive No
Parity Even
Orbit Label 6027.dt

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[19]
 
pari: [g,chi] = znchar(Mod(19,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 287
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.dt
Orbit index = 98

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 ]
 

\(\chi_{6027}(19,\cdot)\) \(\chi_{6027}(313,\cdot)\) \(\chi_{6027}(766,\cdot)\) \(\chi_{6027}(913,\cdot)\) \(\chi_{6027}(1060,\cdot)\) \(\chi_{6027}(1195,\cdot)\) \(\chi_{6027}(1342,\cdot)\) \(\chi_{6027}(1489,\cdot)\) \(\chi_{6027}(1942,\cdot)\) \(\chi_{6027}(2236,\cdot)\) \(\chi_{6027}(2371,\cdot)\) \(\chi_{6027}(2518,\cdot)\) \(\chi_{6027}(2530,\cdot)\) \(\chi_{6027}(2677,\cdot)\) \(\chi_{6027}(2812,\cdot)\) \(\chi_{6027}(2959,\cdot)\) \(\chi_{6027}(2971,\cdot)\) \(\chi_{6027}(3265,\cdot)\) \(\chi_{6027}(3841,\cdot)\) \(\chi_{6027}(3988,\cdot)\) \(\chi_{6027}(4135,\cdot)\) \(\chi_{6027}(4147,\cdot)\) \(\chi_{6027}(4294,\cdot)\) \(\chi_{6027}(4441,\cdot)\) \(\chi_{6027}(5017,\cdot)\) \(\chi_{6027}(5311,\cdot)\) \(\chi_{6027}(5323,\cdot)\) \(\chi_{6027}(5470,\cdot)\) \(\chi_{6027}(5605,\cdot)\) \(\chi_{6027}(5752,\cdot)\) ...

Inducing primitive character

\(\chi_{287}(19,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{9}{40}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{31}{60}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{7}{60}\right)\)\(e\left(\frac{11}{20}\right)\)\(e\left(\frac{19}{30}\right)\)\(e\left(\frac{1}{120}\right)\)\(e\left(\frac{19}{40}\right)\)\(e\left(\frac{1}{15}\right)\)\(e\left(\frac{31}{120}\right)\)\(e\left(\frac{23}{120}\right)\)
value at  e.g. 2

Related number fields

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