Properties

Label 6001.222
Modulus $6001$
Conductor $353$
Order $22$
Real no
Primitive no
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([0,17]))
 
pari: [g,chi] = znchar(Mod(222,6001))
 

Basic properties

Modulus: \(6001\)
Conductor: \(353\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(22\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{353}(222,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6001.bw

\(\chi_{6001}(222,\cdot)\) \(\chi_{6001}(919,\cdot)\) \(\chi_{6001}(1225,\cdot)\) \(\chi_{6001}(1548,\cdot)\) \(\chi_{6001}(2449,\cdot)\) \(\chi_{6001}(2568,\cdot)\) \(\chi_{6001}(2840,\cdot)\) \(\chi_{6001}(3299,\cdot)\) \(\chi_{6001}(4404,\cdot)\) \(\chi_{6001}(5237,\cdot)\)

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

\((2825,3180)\) → \((1,e\left(\frac{17}{22}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{17}{22}\right)\)\(-1\)\(-1\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{6}{11}\right)\)\(-1\)\(e\left(\frac{4}{11}\right)\)
value at e.g. 2

Related number fields

Field of values: \(\Q(\zeta_{11})\)
Fixed field: 22.22.318616903907445618105221556406323103529996534834275553.1