Properties

Conductor 6017
Order 195
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6017.bt

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[47]
 
pari: [g,chi] = znchar(Mod(47,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6017
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 195
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.bt
Orbit index = 46

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 ]
 

\(\chi_{6017}(47,\cdot)\) \(\chi_{6017}(136,\cdot)\) \(\chi_{6017}(181,\cdot)\) \(\chi_{6017}(302,\cdot)\) \(\chi_{6017}(445,\cdot)\) \(\chi_{6017}(488,\cdot)\) \(\chi_{6017}(521,\cdot)\) \(\chi_{6017}(643,\cdot)\) \(\chi_{6017}(676,\cdot)\) \(\chi_{6017}(746,\cdot)\) \(\chi_{6017}(764,\cdot)\) \(\chi_{6017}(786,\cdot)\) \(\chi_{6017}(872,\cdot)\) \(\chi_{6017}(949,\cdot)\) \(\chi_{6017}(966,\cdot)\) \(\chi_{6017}(988,\cdot)\) \(\chi_{6017}(1105,\cdot)\) \(\chi_{6017}(1115,\cdot)\) \(\chi_{6017}(1148,\cdot)\) \(\chi_{6017}(1215,\cdot)\) \(\chi_{6017}(1230,\cdot)\) \(\chi_{6017}(1325,\cdot)\) \(\chi_{6017}(1390,\cdot)\) \(\chi_{6017}(1582,\cdot)\) \(\chi_{6017}(1615,\cdot)\) \(\chi_{6017}(1688,\cdot)\) \(\chi_{6017}(1840,\cdot)\) \(\chi_{6017}(1874,\cdot)\) \(\chi_{6017}(2060,\cdot)\) \(\chi_{6017}(2082,\cdot)\) ...

Values on generators

\((3830,2190)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{19}{39}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{56}{195}\right)\)\(e\left(\frac{2}{5}\right)\)\(e\left(\frac{112}{195}\right)\)\(e\left(\frac{79}{195}\right)\)\(e\left(\frac{134}{195}\right)\)\(e\left(\frac{152}{195}\right)\)\(e\left(\frac{56}{65}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{9}{13}\right)\)\(e\left(\frac{38}{39}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{195})\)