Properties

Label 6001.21
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([66,25]))
 
pari: [g,chi] = znchar(Mod(21,6001))
 

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.cv

\(\chi_{6001}(21,\cdot)\) \(\chi_{6001}(285,\cdot)\) \(\chi_{6001}(421,\cdot)\) \(\chi_{6001}(633,\cdot)\) \(\chi_{6001}(931,\cdot)\) \(\chi_{6001}(948,\cdot)\) \(\chi_{6001}(1067,\cdot)\) \(\chi_{6001}(1441,\cdot)\) \(\chi_{6001}(1721,\cdot)\) \(\chi_{6001}(1849,\cdot)\) \(\chi_{6001}(1874,\cdot)\) \(\chi_{6001}(1959,\cdot)\) \(\chi_{6001}(2027,\cdot)\) \(\chi_{6001}(2410,\cdot)\) \(\chi_{6001}(2469,\cdot)\) \(\chi_{6001}(2503,\cdot)\) \(\chi_{6001}(2648,\cdot)\) \(\chi_{6001}(2792,\cdot)\) \(\chi_{6001}(2826,\cdot)\) \(\chi_{6001}(2835,\cdot)\) \(\chi_{6001}(3260,\cdot)\) \(\chi_{6001}(3268,\cdot)\) \(\chi_{6001}(3336,\cdot)\) \(\chi_{6001}(3421,\cdot)\) \(\chi_{6001}(3447,\cdot)\) \(\chi_{6001}(3574,\cdot)\) \(\chi_{6001}(3872,\cdot)\) \(\chi_{6001}(4059,\cdot)\) \(\chi_{6001}(4297,\cdot)\) \(\chi_{6001}(4662,\cdot)\) ...

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

\((2825,3180)\) → \((-i,e\left(\frac{25}{88}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{3}{88}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{47}{88}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{3}{11}\right)\)\(e\left(\frac{3}{44}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{13}{44}\right)\)
value at e.g. 2

Related number fields

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