Properties

Label 6001.84
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([44,19]))
 
pari: [g,chi] = znchar(Mod(84,6001))
 

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.de

\(\chi_{6001}(84,\cdot)\) \(\chi_{6001}(645,\cdot)\) \(\chi_{6001}(662,\cdot)\) \(\chi_{6001}(815,\cdot)\) \(\chi_{6001}(883,\cdot)\) \(\chi_{6001}(900,\cdot)\) \(\chi_{6001}(968,\cdot)\) \(\chi_{6001}(1070,\cdot)\) \(\chi_{6001}(1410,\cdot)\) \(\chi_{6001}(1444,\cdot)\) \(\chi_{6001}(1495,\cdot)\) \(\chi_{6001}(1682,\cdot)\) \(\chi_{6001}(1733,\cdot)\) \(\chi_{6001}(1767,\cdot)\) \(\chi_{6001}(2107,\cdot)\) \(\chi_{6001}(2209,\cdot)\) \(\chi_{6001}(2277,\cdot)\) \(\chi_{6001}(2294,\cdot)\) \(\chi_{6001}(2362,\cdot)\) \(\chi_{6001}(2515,\cdot)\) \(\chi_{6001}(2532,\cdot)\) \(\chi_{6001}(3093,\cdot)\) \(\chi_{6001}(3501,\cdot)\) \(\chi_{6001}(3603,\cdot)\) \(\chi_{6001}(3875,\cdot)\) \(\chi_{6001}(3994,\cdot)\) \(\chi_{6001}(4011,\cdot)\) \(\chi_{6001}(4215,\cdot)\) \(\chi_{6001}(4317,\cdot)\) \(\chi_{6001}(4521,\cdot)\) ...

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

\((2825,3180)\) → \((-1,e\left(\frac{19}{88}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{63}{88}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{19}{88}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{5}{11}\right)\)
value at e.g. 2

Related number fields

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