Properties

Label 6001.14
Modulus $6001$
Conductor $6001$
Order $352$
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([198,263]))
 
pari: [g,chi] = znchar(Mod(14,6001))
 

Basic properties

Modulus: \(6001\)
Conductor: \(6001\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(352\)
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.es

\(\chi_{6001}(14,\cdot)\) \(\chi_{6001}(40,\cdot)\) \(\chi_{6001}(71,\cdot)\) \(\chi_{6001}(90,\cdot)\) \(\chi_{6001}(141,\cdot)\) \(\chi_{6001}(148,\cdot)\) \(\chi_{6001}(173,\cdot)\) \(\chi_{6001}(190,\cdot)\) \(\chi_{6001}(199,\cdot)\) \(\chi_{6001}(250,\cdot)\) \(\chi_{6001}(333,\cdot)\) \(\chi_{6001}(384,\cdot)\) \(\chi_{6001}(422,\cdot)\) \(\chi_{6001}(449,\cdot)\) \(\chi_{6001}(581,\cdot)\) \(\chi_{6001}(632,\cdot)\) \(\chi_{6001}(673,\cdot)\) \(\chi_{6001}(703,\cdot)\) \(\chi_{6001}(754,\cdot)\) \(\chi_{6001}(821,\cdot)\) \(\chi_{6001}(840,\cdot)\) \(\chi_{6001}(864,\cdot)\) \(\chi_{6001}(925,\cdot)\) \(\chi_{6001}(947,\cdot)\) \(\chi_{6001}(1032,\cdot)\) \(\chi_{6001}(1234,\cdot)\) \(\chi_{6001}(1252,\cdot)\) \(\chi_{6001}(1270,\cdot)\) \(\chi_{6001}(1286,\cdot)\) \(\chi_{6001}(1297,\cdot)\) ...

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

\((2825,3180)\) → \((e\left(\frac{9}{16}\right),e\left(\frac{263}{352}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{109}{352}\right)\)\(e\left(\frac{9}{11}\right)\)\(e\left(\frac{241}{352}\right)\)\(e\left(\frac{23}{32}\right)\)\(e\left(\frac{5}{32}\right)\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{109}{176}\right)\)\(e\left(\frac{3}{32}\right)\)\(e\left(\frac{135}{176}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{352})$
Fixed field: Number field defined by a degree 352 polynomial