Properties

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

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[461]
 
pari: [g,chi] = znchar(Mod(461,6027))
 

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.dj
Orbit index = 88

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 ]
 

\(\chi_{6027}(461,\cdot)\) \(\chi_{6027}(713,\cdot)\) \(\chi_{6027}(797,\cdot)\) \(\chi_{6027}(1574,\cdot)\) \(\chi_{6027}(1595,\cdot)\) \(\chi_{6027}(1658,\cdot)\) \(\chi_{6027}(2183,\cdot)\) \(\chi_{6027}(2435,\cdot)\) \(\chi_{6027}(2456,\cdot)\) \(\chi_{6027}(2519,\cdot)\) \(\chi_{6027}(3044,\cdot)\) \(\chi_{6027}(3296,\cdot)\) \(\chi_{6027}(3317,\cdot)\) \(\chi_{6027}(3905,\cdot)\) \(\chi_{6027}(4157,\cdot)\) \(\chi_{6027}(4178,\cdot)\) \(\chi_{6027}(4241,\cdot)\) \(\chi_{6027}(4766,\cdot)\) \(\chi_{6027}(5018,\cdot)\) \(\chi_{6027}(5039,\cdot)\) \(\chi_{6027}(5102,\cdot)\) \(\chi_{6027}(5627,\cdot)\) \(\chi_{6027}(5900,\cdot)\) \(\chi_{6027}(5963,\cdot)\)

Values on generators

\((4019,493,2794)\) → \((-1,e\left(\frac{13}{14}\right),e\left(\frac{1}{5}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{59}{70}\right)\)\(e\left(\frac{24}{35}\right)\)\(e\left(\frac{29}{35}\right)\)\(e\left(\frac{37}{70}\right)\)\(e\left(\frac{47}{70}\right)\)\(e\left(\frac{17}{70}\right)\)\(e\left(\frac{59}{70}\right)\)\(e\left(\frac{13}{35}\right)\)\(e\left(\frac{11}{35}\right)\)\(e\left(\frac{3}{10}\right)\)
value at  e.g. 2

Related number fields

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