Properties

Conductor 6017
Order 210
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6017.bu

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[39]
 
pari: [g,chi] = znchar(Mod(39,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6017
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 210
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.bu
Orbit index = 47

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 ]
 

\(\chi_{6017}(39,\cdot)\) \(\chi_{6017}(369,\cdot)\) \(\chi_{6017}(424,\cdot)\) \(\chi_{6017}(534,\cdot)\) \(\chi_{6017}(589,\cdot)\) \(\chi_{6017}(667,\cdot)\) \(\chi_{6017}(734,\cdot)\) \(\chi_{6017}(898,\cdot)\) \(\chi_{6017}(1080,\cdot)\) \(\chi_{6017}(1515,\cdot)\) \(\chi_{6017}(1524,\cdot)\) \(\chi_{6017}(1680,\cdot)\) \(\chi_{6017}(1828,\cdot)\) \(\chi_{6017}(2010,\cdot)\) \(\chi_{6017}(2019,\cdot)\) \(\chi_{6017}(2065,\cdot)\) \(\chi_{6017}(2174,\cdot)\) \(\chi_{6017}(2175,\cdot)\) \(\chi_{6017}(2230,\cdot)\) \(\chi_{6017}(2609,\cdot)\) \(\chi_{6017}(2774,\cdot)\) \(\chi_{6017}(2855,\cdot)\) \(\chi_{6017}(2922,\cdot)\) \(\chi_{6017}(3086,\cdot)\) \(\chi_{6017}(3104,\cdot)\) \(\chi_{6017}(3159,\cdot)\) \(\chi_{6017}(3165,\cdot)\) \(\chi_{6017}(3269,\cdot)\) \(\chi_{6017}(3324,\cdot)\) \(\chi_{6017}(3660,\cdot)\) ...

Values on generators

\((3830,2190)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{13}{42}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{22}{105}\right)\)\(e\left(\frac{69}{70}\right)\)\(e\left(\frac{44}{105}\right)\)\(e\left(\frac{1}{210}\right)\)\(e\left(\frac{41}{210}\right)\)\(e\left(\frac{19}{105}\right)\)\(e\left(\frac{22}{35}\right)\)\(e\left(\frac{34}{35}\right)\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{17}{42}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{105})\)