Properties

Conductor 6027
Order 280
Real No
Primitive Yes
Parity Even
Orbit Label 6027.ep

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[29]
 
pari: [g,chi] = znchar(Mod(29,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6027
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 280
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.ep
Orbit index = 120

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 ]
 

\(\chi_{6027}(29,\cdot)\) \(\chi_{6027}(71,\cdot)\) \(\chi_{6027}(134,\cdot)\) \(\chi_{6027}(176,\cdot)\) \(\chi_{6027}(218,\cdot)\) \(\chi_{6027}(239,\cdot)\) \(\chi_{6027}(281,\cdot)\) \(\chi_{6027}(302,\cdot)\) \(\chi_{6027}(386,\cdot)\) \(\chi_{6027}(470,\cdot)\) \(\chi_{6027}(596,\cdot)\) \(\chi_{6027}(680,\cdot)\) \(\chi_{6027}(764,\cdot)\) \(\chi_{6027}(827,\cdot)\) \(\chi_{6027}(848,\cdot)\) \(\chi_{6027}(890,\cdot)\) \(\chi_{6027}(995,\cdot)\) \(\chi_{6027}(1037,\cdot)\) \(\chi_{6027}(1100,\cdot)\) \(\chi_{6027}(1142,\cdot)\) \(\chi_{6027}(1163,\cdot)\) \(\chi_{6027}(1247,\cdot)\) \(\chi_{6027}(1331,\cdot)\) \(\chi_{6027}(1457,\cdot)\) \(\chi_{6027}(1541,\cdot)\) \(\chi_{6027}(1625,\cdot)\) \(\chi_{6027}(1646,\cdot)\) \(\chi_{6027}(1688,\cdot)\) \(\chi_{6027}(1709,\cdot)\) \(\chi_{6027}(1751,\cdot)\) ...

Values on generators

\((4019,493,2794)\) → \((-1,e\left(\frac{3}{7}\right),e\left(\frac{7}{40}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{27}{140}\right)\)\(e\left(\frac{27}{70}\right)\)\(e\left(\frac{109}{140}\right)\)\(e\left(\frac{81}{140}\right)\)\(e\left(\frac{34}{35}\right)\)\(e\left(\frac{47}{280}\right)\)\(e\left(\frac{159}{280}\right)\)\(e\left(\frac{27}{35}\right)\)\(e\left(\frac{277}{280}\right)\)\(e\left(\frac{23}{40}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{280})\)