Properties

Label 6001.81
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([22,1]))
 
pari: [g,chi] = znchar(Mod(81,6001))
 

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.cu

\(\chi_{6001}(81,\cdot)\) \(\chi_{6001}(225,\cdot)\) \(\chi_{6001}(242,\cdot)\) \(\chi_{6001}(336,\cdot)\) \(\chi_{6001}(361,\cdot)\) \(\chi_{6001}(370,\cdot)\) \(\chi_{6001}(625,\cdot)\) \(\chi_{6001}(727,\cdot)\) \(\chi_{6001}(735,\cdot)\) \(\chi_{6001}(1143,\cdot)\) \(\chi_{6001}(1339,\cdot)\) \(\chi_{6001}(1704,\cdot)\) \(\chi_{6001}(1942,\cdot)\) \(\chi_{6001}(2129,\cdot)\) \(\chi_{6001}(2427,\cdot)\) \(\chi_{6001}(2554,\cdot)\) \(\chi_{6001}(2580,\cdot)\) \(\chi_{6001}(2665,\cdot)\) \(\chi_{6001}(2733,\cdot)\) \(\chi_{6001}(2741,\cdot)\) \(\chi_{6001}(3166,\cdot)\) \(\chi_{6001}(3175,\cdot)\) \(\chi_{6001}(3209,\cdot)\) \(\chi_{6001}(3353,\cdot)\) \(\chi_{6001}(3498,\cdot)\) \(\chi_{6001}(3532,\cdot)\) \(\chi_{6001}(3591,\cdot)\) \(\chi_{6001}(3974,\cdot)\) \(\chi_{6001}(4042,\cdot)\) \(\chi_{6001}(4127,\cdot)\) ...

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

\((2825,3180)\) → \((i,e\left(\frac{1}{88}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{23}{88}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{67}{88}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{23}{44}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{19}{44}\right)\)
value at e.g. 2

Related number fields

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