Properties

Conductor 2009
Order 280
Real No
Primitive No
Parity Even
Orbit Label 6027.em

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[13]
 
pari: [g,chi] = znchar(Mod(13,6027))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2009
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 = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6027.em
Orbit index = 117

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 ]
 

\(\chi_{6027}(13,\cdot)\) \(\chi_{6027}(34,\cdot)\) \(\chi_{6027}(76,\cdot)\) \(\chi_{6027}(181,\cdot)\) \(\chi_{6027}(265,\cdot)\) \(\chi_{6027}(475,\cdot)\) \(\chi_{6027}(559,\cdot)\) \(\chi_{6027}(580,\cdot)\) \(\chi_{6027}(622,\cdot)\) \(\chi_{6027}(643,\cdot)\) \(\chi_{6027}(727,\cdot)\) \(\chi_{6027}(790,\cdot)\) \(\chi_{6027}(874,\cdot)\) \(\chi_{6027}(895,\cdot)\) \(\chi_{6027}(937,\cdot)\) \(\chi_{6027}(958,\cdot)\) \(\chi_{6027}(1042,\cdot)\) \(\chi_{6027}(1252,\cdot)\) \(\chi_{6027}(1336,\cdot)\) \(\chi_{6027}(1441,\cdot)\) \(\chi_{6027}(1483,\cdot)\) \(\chi_{6027}(1504,\cdot)\) \(\chi_{6027}(1546,\cdot)\) \(\chi_{6027}(1588,\cdot)\) \(\chi_{6027}(1651,\cdot)\) \(\chi_{6027}(1693,\cdot)\) \(\chi_{6027}(1735,\cdot)\) \(\chi_{6027}(1756,\cdot)\) \(\chi_{6027}(1798,\cdot)\) \(\chi_{6027}(1819,\cdot)\) ...

Inducing primitive character

\(\chi_{2009}(13,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((1,e\left(\frac{11}{14}\right),e\left(\frac{31}{40}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{81}{140}\right)\)\(e\left(\frac{11}{70}\right)\)\(e\left(\frac{117}{140}\right)\)\(e\left(\frac{103}{140}\right)\)\(e\left(\frac{29}{70}\right)\)\(e\left(\frac{211}{280}\right)\)\(e\left(\frac{267}{280}\right)\)\(e\left(\frac{11}{35}\right)\)\(e\left(\frac{61}{280}\right)\)\(e\left(\frac{19}{40}\right)\)
value at  e.g. 2

Related number fields

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