Properties

Conductor 6027
Order 140
Real No
Primitive Yes
Parity Even
Orbit Label 6027.dz

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[20]
 
pari: [g,chi] = znchar(Mod(20,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 140
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.dz
Orbit index = 104

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 ]
 

\(\chi_{6027}(20,\cdot)\) \(\chi_{6027}(62,\cdot)\) \(\chi_{6027}(125,\cdot)\) \(\chi_{6027}(251,\cdot)\) \(\chi_{6027}(377,\cdot)\) \(\chi_{6027}(566,\cdot)\) \(\chi_{6027}(692,\cdot)\) \(\chi_{6027}(818,\cdot)\) \(\chi_{6027}(923,\cdot)\) \(\chi_{6027}(986,\cdot)\) \(\chi_{6027}(1112,\cdot)\) \(\chi_{6027}(1238,\cdot)\) \(\chi_{6027}(1427,\cdot)\) \(\chi_{6027}(1553,\cdot)\) \(\chi_{6027}(1679,\cdot)\) \(\chi_{6027}(1742,\cdot)\) \(\chi_{6027}(1784,\cdot)\) \(\chi_{6027}(1847,\cdot)\) \(\chi_{6027}(1973,\cdot)\) \(\chi_{6027}(2099,\cdot)\) \(\chi_{6027}(2288,\cdot)\) \(\chi_{6027}(2414,\cdot)\) \(\chi_{6027}(2540,\cdot)\) \(\chi_{6027}(2603,\cdot)\) \(\chi_{6027}(2708,\cdot)\) \(\chi_{6027}(2834,\cdot)\) \(\chi_{6027}(2960,\cdot)\) \(\chi_{6027}(3149,\cdot)\) \(\chi_{6027}(3275,\cdot)\) \(\chi_{6027}(3401,\cdot)\) ...

Values on generators

\((4019,493,2794)\) → \((-1,e\left(\frac{13}{14}\right),e\left(\frac{17}{20}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{26}{35}\right)\)\(e\left(\frac{17}{35}\right)\)\(e\left(\frac{9}{70}\right)\)\(e\left(\frac{8}{35}\right)\)\(e\left(\frac{61}{70}\right)\)\(e\left(\frac{27}{140}\right)\)\(e\left(\frac{139}{140}\right)\)\(e\left(\frac{34}{35}\right)\)\(e\left(\frac{107}{140}\right)\)\(e\left(\frac{3}{20}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{140})\)