Properties

Label 6001.19
Modulus $6001$
Conductor $6001$
Order $176$
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([154,35]))
 
pari: [g,chi] = znchar(Mod(19,6001))
 

Basic properties

Modulus: \(6001\)
Conductor: \(6001\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(176\)
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.ed

\(\chi_{6001}(19,\cdot)\) \(\chi_{6001}(144,\cdot)\) \(\chi_{6001}(189,\cdot)\) \(\chi_{6001}(240,\cdot)\) \(\chi_{6001}(314,\cdot)\) \(\chi_{6001}(315,\cdot)\) \(\chi_{6001}(376,\cdot)\) \(\chi_{6001}(383,\cdot)\) \(\chi_{6001}(400,\cdot)\) \(\chi_{6001}(451,\cdot)\) \(\chi_{6001}(518,\cdot)\) \(\chi_{6001}(525,\cdot)\) \(\chi_{6001}(586,\cdot)\) \(\chi_{6001}(784,\cdot)\) \(\chi_{6001}(858,\cdot)\) \(\chi_{6001}(875,\cdot)\) \(\chi_{6001}(892,\cdot)\) \(\chi_{6001}(961,\cdot)\) \(\chi_{6001}(967,\cdot)\) \(\chi_{6001}(977,\cdot)\) \(\chi_{6001}(1012,\cdot)\) \(\chi_{6001}(1018,\cdot)\) \(\chi_{6001}(1029,\cdot)\) \(\chi_{6001}(1097,\cdot)\) \(\chi_{6001}(1124,\cdot)\) \(\chi_{6001}(1430,\cdot)\) \(\chi_{6001}(1437,\cdot)\) \(\chi_{6001}(1511,\cdot)\) \(\chi_{6001}(1539,\cdot)\) \(\chi_{6001}(1715,\cdot)\) ...

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

\((2825,3180)\) → \((e\left(\frac{7}{8}\right),e\left(\frac{35}{176}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{19}{22}\right)\)\(e\left(\frac{13}{176}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{145}{176}\right)\)\(e\left(\frac{15}{16}\right)\)\(e\left(\frac{5}{16}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{13}{88}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{5}{88}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{176})$
Fixed field: Number field defined by a degree 176 polynomial