Properties

Label 6001.168
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([33,60]))
 
pari: [g,chi] = znchar(Mod(168,6001))
 

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.cy

\(\chi_{6001}(168,\cdot)\) \(\chi_{6001}(213,\cdot)\) \(\chi_{6001}(331,\cdot)\) \(\chi_{6001}(450,\cdot)\) \(\chi_{6001}(519,\cdot)\) \(\chi_{6001}(648,\cdot)\) \(\chi_{6001}(722,\cdot)\) \(\chi_{6001}(842,\cdot)\) \(\chi_{6001}(1001,\cdot)\) \(\chi_{6001}(1181,\cdot)\) \(\chi_{6001}(1634,\cdot)\) \(\chi_{6001}(1743,\cdot)\) \(\chi_{6001}(1862,\cdot)\) \(\chi_{6001}(1987,\cdot)\) \(\chi_{6001}(2134,\cdot)\) \(\chi_{6001}(2286,\cdot)\) \(\chi_{6001}(2331,\cdot)\) \(\chi_{6001}(2593,\cdot)\) \(\chi_{6001}(2637,\cdot)\) \(\chi_{6001}(2684,\cdot)\) \(\chi_{6001}(2960,\cdot)\) \(\chi_{6001}(2990,\cdot)\) \(\chi_{6001}(3119,\cdot)\) \(\chi_{6001}(3313,\cdot)\) \(\chi_{6001}(3698,\cdot)\) \(\chi_{6001}(3861,\cdot)\) \(\chi_{6001}(3980,\cdot)\) \(\chi_{6001}(4105,\cdot)\) \(\chi_{6001}(4214,\cdot)\) \(\chi_{6001}(4252,\cdot)\) ...

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

\((2825,3180)\) → \((e\left(\frac{3}{8}\right),e\left(\frac{15}{22}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{3}{44}\right)\)\(e\left(\frac{5}{88}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{49}{88}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{5}{44}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{47}{88}\right)\)
value at e.g. 2

Related number fields

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