Properties

Label 6001.270
Modulus $6001$
Conductor $6001$
Order $88$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more about

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(6001)
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([33,31]))
 
pari: [g,chi] = znchar(Mod(270,6001))
 

Basic properties

Modulus: \(6001\)
Conductor: \(6001\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(88\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6001.cw

\(\chi_{6001}(270,\cdot)\) \(\chi_{6001}(280,\cdot)\) \(\chi_{6001}(332,\cdot)\) \(\chi_{6001}(342,\cdot)\) \(\chi_{6001}(529,\cdot)\) \(\chi_{6001}(689,\cdot)\) \(\chi_{6001}(767,\cdot)\) \(\chi_{6001}(978,\cdot)\) \(\chi_{6001}(1521,\cdot)\) \(\chi_{6001}(1674,\cdot)\) \(\chi_{6001}(1681,\cdot)\) \(\chi_{6001}(1736,\cdot)\) \(\chi_{6001}(2229,\cdot)\) \(\chi_{6001}(2439,\cdot)\) \(\chi_{6001}(2463,\cdot)\) \(\chi_{6001}(2473,\cdot)\) \(\chi_{6001}(2599,\cdot)\) \(\chi_{6001}(2780,\cdot)\) \(\chi_{6001}(2892,\cdot)\) \(\chi_{6001}(2983,\cdot)\) \(\chi_{6001}(3018,\cdot)\) \(\chi_{6001}(3109,\cdot)\) \(\chi_{6001}(3221,\cdot)\) \(\chi_{6001}(3402,\cdot)\) \(\chi_{6001}(3528,\cdot)\) \(\chi_{6001}(3538,\cdot)\) \(\chi_{6001}(3562,\cdot)\) \(\chi_{6001}(3772,\cdot)\) \(\chi_{6001}(4265,\cdot)\) \(\chi_{6001}(4320,\cdot)\) ...

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

Values on generators

\((2825,3180)\) → \((e\left(\frac{3}{8}\right),e\left(\frac{31}{88}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{1}{22}\right)\)\(e\left(\frac{8}{11}\right)\)\(-i\)\(1\)\(e\left(\frac{3}{44}\right)\)\(e\left(\frac{5}{11}\right)\)\(-i\)\(e\left(\frac{67}{88}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{88})$
Fixed field: Number field defined by a degree 88 polynomial