Properties

Modulus 6017
Conductor 6017
Order 390
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6017.by

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(6017)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([117,85]))
 
pari: [g,chi] = znchar(Mod(1460,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 6017
Conductor = 6017
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 390
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.by
Orbit index = 51

Galois orbit

sage: chi.galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{6017}(83,\cdot)\) \(\chi_{6017}(106,\cdot)\) \(\chi_{6017}(128,\cdot)\) \(\chi_{6017}(145,\cdot)\) \(\chi_{6017}(222,\cdot)\) \(\chi_{6017}(314,\cdot)\) \(\chi_{6017}(316,\cdot)\) \(\chi_{6017}(348,\cdot)\) \(\chi_{6017}(426,\cdot)\) \(\chi_{6017}(536,\cdot)\) \(\chi_{6017}(798,\cdot)\) \(\chi_{6017}(855,\cdot)\) \(\chi_{6017}(877,\cdot)\) \(\chi_{6017}(965,\cdot)\) \(\chi_{6017}(998,\cdot)\) \(\chi_{6017}(1040,\cdot)\) \(\chi_{6017}(1047,\cdot)\) \(\chi_{6017}(1073,\cdot)\) \(\chi_{6017}(1196,\cdot)\) \(\chi_{6017}(1239,\cdot)\) \(\chi_{6017}(1316,\cdot)\) \(\chi_{6017}(1339,\cdot)\) \(\chi_{6017}(1410,\cdot)\) \(\chi_{6017}(1460,\cdot)\) \(\chi_{6017}(1520,\cdot)\) \(\chi_{6017}(1630,\cdot)\) \(\chi_{6017}(1667,\cdot)\) \(\chi_{6017}(1700,\cdot)\) \(\chi_{6017}(1724,\cdot)\) \(\chi_{6017}(1949,\cdot)\) ...

Values on generators

\((3830,2190)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{17}{78}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{101}{195}\right)\)\(e\left(\frac{9}{10}\right)\)\(e\left(\frac{7}{195}\right)\)\(e\left(\frac{83}{390}\right)\)\(e\left(\frac{163}{390}\right)\)\(e\left(\frac{107}{195}\right)\)\(e\left(\frac{36}{65}\right)\)\(e\left(\frac{4}{5}\right)\)\(e\left(\frac{19}{26}\right)\)\(e\left(\frac{73}{78}\right)\)
value at  e.g. 2

Related number fields

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