Properties

Label 6001.31
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([198,93]))
 
pari: [g,chi] = znchar(Mod(31,6001))
 

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.eq

\(\chi_{6001}(31,\cdot)\) \(\chi_{6001}(79,\cdot)\) \(\chi_{6001}(108,\cdot)\) \(\chi_{6001}(163,\cdot)\) \(\chi_{6001}(180,\cdot)\) \(\chi_{6001}(192,\cdot)\) \(\chi_{6001}(278,\cdot)\) \(\chi_{6001}(282,\cdot)\) \(\chi_{6001}(296,\cdot)\) \(\chi_{6001}(300,\cdot)\) \(\chi_{6001}(320,\cdot)\) \(\chi_{6001}(398,\cdot)\) \(\chi_{6001}(448,\cdot)\) \(\chi_{6001}(470,\cdot)\) \(\chi_{6001}(500,\cdot)\) \(\chi_{6001}(503,\cdot)\) \(\chi_{6001}(588,\cdot)\) \(\chi_{6001}(589,\cdot)\) \(\chi_{6001}(617,\cdot)\) \(\chi_{6001}(658,\cdot)\) \(\chi_{6001}(669,\cdot)\) \(\chi_{6001}(709,\cdot)\) \(\chi_{6001}(759,\cdot)\) \(\chi_{6001}(802,\cdot)\) \(\chi_{6001}(881,\cdot)\) \(\chi_{6001}(957,\cdot)\) \(\chi_{6001}(974,\cdot)\) \(\chi_{6001}(980,\cdot)\) \(\chi_{6001}(1115,\cdot)\) \(\chi_{6001}(1144,\cdot)\) ...

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

\((2825,3180)\) → \((e\left(\frac{9}{16}\right),e\left(\frac{93}{352}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{291}{352}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{159}{352}\right)\)\(e\left(\frac{1}{32}\right)\)\(e\left(\frac{11}{32}\right)\)\(e\left(\frac{27}{44}\right)\)\(e\left(\frac{115}{176}\right)\)\(e\left(\frac{21}{32}\right)\)\(e\left(\frac{139}{176}\right)\)
value at e.g. 2

Related number fields

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