Properties

Modulus 6017
Conductor 6017
Order 910
Real no
Primitive yes
Minimal yes
Parity even
Orbit label 6017.cf

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([819,295]))
 
pari: [g,chi] = znchar(Mod(138,6017))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Modulus = 6017
Conductor = 6017
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 910
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.cf
Orbit index = 58

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 ]
 

\(\chi_{6017}(8,\cdot)\) \(\chi_{6017}(68,\cdot)\) \(\chi_{6017}(79,\cdot)\) \(\chi_{6017}(94,\cdot)\) \(\chi_{6017}(101,\cdot)\) \(\chi_{6017}(105,\cdot)\) \(\chi_{6017}(138,\cdot)\) \(\chi_{6017}(151,\cdot)\) \(\chi_{6017}(156,\cdot)\) \(\chi_{6017}(173,\cdot)\) \(\chi_{6017}(226,\cdot)\) \(\chi_{6017}(238,\cdot)\) \(\chi_{6017}(244,\cdot)\) \(\chi_{6017}(255,\cdot)\) \(\chi_{6017}(270,\cdot)\) \(\chi_{6017}(299,\cdot)\) \(\chi_{6017}(332,\cdot)\) \(\chi_{6017}(338,\cdot)\) \(\chi_{6017}(343,\cdot)\) \(\chi_{6017}(380,\cdot)\) \(\chi_{6017}(382,\cdot)\) \(\chi_{6017}(393,\cdot)\) \(\chi_{6017}(398,\cdot)\) \(\chi_{6017}(447,\cdot)\) \(\chi_{6017}(457,\cdot)\) \(\chi_{6017}(503,\cdot)\) \(\chi_{6017}(512,\cdot)\) \(\chi_{6017}(523,\cdot)\) \(\chi_{6017}(578,\cdot)\) \(\chi_{6017}(602,\cdot)\) ...

Values on generators

\((3830,2190)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{59}{182}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{102}{455}\right)\)\(e\left(\frac{19}{70}\right)\)\(e\left(\frac{204}{455}\right)\)\(e\left(\frac{571}{910}\right)\)\(e\left(\frac{451}{910}\right)\)\(e\left(\frac{314}{455}\right)\)\(e\left(\frac{306}{455}\right)\)\(e\left(\frac{19}{35}\right)\)\(e\left(\frac{155}{182}\right)\)\(e\left(\frac{131}{182}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{455})\)