Properties

Conductor 6027
Order 70
Real No
Primitive Yes
Parity Even
Orbit Label 6027.dk

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[209]
 
pari: [g,chi] = znchar(Mod(209,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 70
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6027.dk
Orbit index = 89

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 ]
 

\(\chi_{6027}(209,\cdot)\) \(\chi_{6027}(230,\cdot)\) \(\chi_{6027}(482,\cdot)\) \(\chi_{6027}(1007,\cdot)\) \(\chi_{6027}(1070,\cdot)\) \(\chi_{6027}(1091,\cdot)\) \(\chi_{6027}(1343,\cdot)\) \(\chi_{6027}(1868,\cdot)\) \(\chi_{6027}(1931,\cdot)\) \(\chi_{6027}(1952,\cdot)\) \(\chi_{6027}(2729,\cdot)\) \(\chi_{6027}(2813,\cdot)\) \(\chi_{6027}(3065,\cdot)\) \(\chi_{6027}(3590,\cdot)\) \(\chi_{6027}(3653,\cdot)\) \(\chi_{6027}(3926,\cdot)\) \(\chi_{6027}(4451,\cdot)\) \(\chi_{6027}(4514,\cdot)\) \(\chi_{6027}(4535,\cdot)\) \(\chi_{6027}(4787,\cdot)\) \(\chi_{6027}(5312,\cdot)\) \(\chi_{6027}(5375,\cdot)\) \(\chi_{6027}(5396,\cdot)\) \(\chi_{6027}(5648,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((-1,e\left(\frac{11}{14}\right),e\left(\frac{3}{10}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{51}{70}\right)\)\(e\left(\frac{16}{35}\right)\)\(e\left(\frac{31}{35}\right)\)\(e\left(\frac{13}{70}\right)\)\(e\left(\frac{43}{70}\right)\)\(e\left(\frac{29}{35}\right)\)\(e\left(\frac{8}{35}\right)\)\(e\left(\frac{32}{35}\right)\)\(e\left(\frac{3}{70}\right)\)\(e\left(\frac{1}{5}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{35})\)