Properties

Conductor 6017
Order 130
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6017.bp

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(6017)
 
sage: chi = H[28]
 
pari: [g,chi] = znchar(Mod(28,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6017
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 130
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = yes
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 6017.bp
Orbit index = 42

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 ]
 

\(\chi_{6017}(28,\cdot)\) \(\chi_{6017}(30,\cdot)\) \(\chi_{6017}(72,\cdot)\) \(\chi_{6017}(107,\cdot)\) \(\chi_{6017}(172,\cdot)\) \(\chi_{6017}(194,\cdot)\) \(\chi_{6017}(310,\cdot)\) \(\chi_{6017}(501,\cdot)\) \(\chi_{6017}(585,\cdot)\) \(\chi_{6017}(744,\cdot)\) \(\chi_{6017}(833,\cdot)\) \(\chi_{6017}(1124,\cdot)\) \(\chi_{6017}(1201,\cdot)\) \(\chi_{6017}(1348,\cdot)\) \(\chi_{6017}(1404,\cdot)\) \(\chi_{6017}(1669,\cdot)\) \(\chi_{6017}(1679,\cdot)\) \(\chi_{6017}(1713,\cdot)\) \(\chi_{6017}(1927,\cdot)\) \(\chi_{6017}(2142,\cdot)\) \(\chi_{6017}(2218,\cdot)\) \(\chi_{6017}(2295,\cdot)\) \(\chi_{6017}(2360,\cdot)\) \(\chi_{6017}(2382,\cdot)\) \(\chi_{6017}(2763,\cdot)\) \(\chi_{6017}(2807,\cdot)\) \(\chi_{6017}(2932,\cdot)\) \(\chi_{6017}(2989,\cdot)\) \(\chi_{6017}(3021,\cdot)\) \(\chi_{6017}(3236,\cdot)\) ...

Values on generators

\((3830,2190)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{5}{26}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{6}{65}\right)\)\(e\left(\frac{7}{10}\right)\)\(e\left(\frac{12}{65}\right)\)\(e\left(\frac{3}{130}\right)\)\(e\left(\frac{103}{130}\right)\)\(e\left(\frac{7}{65}\right)\)\(e\left(\frac{18}{65}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{3}{26}\right)\)\(e\left(\frac{23}{26}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{65})\)