Properties

Label 6001.24
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([242,141]))
 
pari: [g,chi] = znchar(Mod(24,6001))
 

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.et

\(\chi_{6001}(24,\cdot)\) \(\chi_{6001}(54,\cdot)\) \(\chi_{6001}(62,\cdot)\) \(\chi_{6001}(107,\cdot)\) \(\chi_{6001}(114,\cdot)\) \(\chi_{6001}(139,\cdot)\) \(\chi_{6001}(143,\cdot)\) \(\chi_{6001}(150,\cdot)\) \(\chi_{6001}(193,\cdot)\) \(\chi_{6001}(224,\cdot)\) \(\chi_{6001}(227,\cdot)\) \(\chi_{6001}(235,\cdot)\) \(\chi_{6001}(419,\cdot)\) \(\chi_{6001}(504,\cdot)\) \(\chi_{6001}(555,\cdot)\) \(\chi_{6001}(601,\cdot)\) \(\chi_{6001}(602,\cdot)\) \(\chi_{6001}(619,\cdot)\) \(\chi_{6001}(640,\cdot)\) \(\chi_{6001}(649,\cdot)\) \(\chi_{6001}(743,\cdot)\) \(\chi_{6001}(751,\cdot)\) \(\chi_{6001}(762,\cdot)\) \(\chi_{6001}(839,\cdot)\) \(\chi_{6001}(853,\cdot)\) \(\chi_{6001}(964,\cdot)\) \(\chi_{6001}(979,\cdot)\) \(\chi_{6001}(996,\cdot)\) \(\chi_{6001}(997,\cdot)\) \(\chi_{6001}(1064,\cdot)\) ...

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

\((2825,3180)\) → \((e\left(\frac{11}{16}\right),e\left(\frac{141}{352}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{31}{352}\right)\)\(e\left(\frac{7}{11}\right)\)\(e\left(\frac{75}{352}\right)\)\(e\left(\frac{13}{32}\right)\)\(e\left(\frac{7}{32}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{31}{176}\right)\)\(e\left(\frac{17}{32}\right)\)\(e\left(\frac{149}{176}\right)\)
value at e.g. 2

Related number fields

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