Properties

Conductor 6017
Order 182
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6017.bs

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[65]
 
pari: [g,chi] = znchar(Mod(65,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6017
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 182
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.bs
Orbit index = 45

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 ]
 

\(\chi_{6017}(65,\cdot)\) \(\chi_{6017}(87,\cdot)\) \(\chi_{6017}(98,\cdot)\) \(\chi_{6017}(164,\cdot)\) \(\chi_{6017}(252,\cdot)\) \(\chi_{6017}(307,\cdot)\) \(\chi_{6017}(329,\cdot)\) \(\chi_{6017}(362,\cdot)\) \(\chi_{6017}(483,\cdot)\) \(\chi_{6017}(615,\cdot)\) \(\chi_{6017}(626,\cdot)\) \(\chi_{6017}(648,\cdot)\) \(\chi_{6017}(703,\cdot)\) \(\chi_{6017}(791,\cdot)\) \(\chi_{6017}(802,\cdot)\) \(\chi_{6017}(846,\cdot)\) \(\chi_{6017}(879,\cdot)\) \(\chi_{6017}(890,\cdot)\) \(\chi_{6017}(945,\cdot)\) \(\chi_{6017}(1242,\cdot)\) \(\chi_{6017}(1286,\cdot)\) \(\chi_{6017}(1330,\cdot)\) \(\chi_{6017}(1374,\cdot)\) \(\chi_{6017}(1429,\cdot)\) \(\chi_{6017}(1462,\cdot)\) \(\chi_{6017}(1649,\cdot)\) \(\chi_{6017}(1792,\cdot)\) \(\chi_{6017}(1814,\cdot)\) \(\chi_{6017}(1979,\cdot)\) \(\chi_{6017}(2023,\cdot)\) ...

Values on generators

\((3830,2190)\) → \((-1,e\left(\frac{155}{182}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{32}{91}\right)\)\(e\left(\frac{5}{14}\right)\)\(e\left(\frac{64}{91}\right)\)\(e\left(\frac{81}{182}\right)\)\(e\left(\frac{129}{182}\right)\)\(e\left(\frac{20}{91}\right)\)\(e\left(\frac{5}{91}\right)\)\(e\left(\frac{5}{7}\right)\)\(e\left(\frac{145}{182}\right)\)\(e\left(\frac{11}{182}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{91})\)