Properties

Conductor 6017
Order 70
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6017.bh

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[365]
 
pari: [g,chi] = znchar(Mod(365,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6017
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
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 6017.bh
Orbit index = 34

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 ]
 

\(\chi_{6017}(365,\cdot)\) \(\chi_{6017}(574,\cdot)\) \(\chi_{6017}(1085,\cdot)\) \(\chi_{6017}(1097,\cdot)\) \(\chi_{6017}(1337,\cdot)\) \(\chi_{6017}(1459,\cdot)\) \(\chi_{6017}(1668,\cdot)\) \(\chi_{6017}(2107,\cdot)\) \(\chi_{6017}(2191,\cdot)\) \(\chi_{6017}(2978,\cdot)\) \(\chi_{6017}(3273,\cdot)\) \(\chi_{6017}(3285,\cdot)\) \(\chi_{6017}(3647,\cdot)\) \(\chi_{6017}(3748,\cdot)\) \(\chi_{6017}(3856,\cdot)\) \(\chi_{6017}(4072,\cdot)\) \(\chi_{6017}(4842,\cdot)\) \(\chi_{6017}(4914,\cdot)\) \(\chi_{6017}(5166,\cdot)\) \(\chi_{6017}(5288,\cdot)\) \(\chi_{6017}(5473,\cdot)\) \(\chi_{6017}(5497,\cdot)\) \(\chi_{6017}(5936,\cdot)\) \(\chi_{6017}(6008,\cdot)\)

Values on generators

\((3830,2190)\) → \((e\left(\frac{1}{10}\right),e\left(\frac{3}{14}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{11}{35}\right)\)\(e\left(\frac{51}{70}\right)\)\(e\left(\frac{22}{35}\right)\)\(e\left(\frac{53}{70}\right)\)\(e\left(\frac{3}{70}\right)\)\(e\left(\frac{27}{35}\right)\)\(e\left(\frac{33}{35}\right)\)\(e\left(\frac{16}{35}\right)\)\(e\left(\frac{1}{14}\right)\)\(e\left(\frac{5}{14}\right)\)
value at  e.g. 2

Related number fields

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