Properties

Label 6001.43
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([22,19]))
 
pari: [g,chi] = znchar(Mod(43,6001))
 

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.dh

\(\chi_{6001}(43,\cdot)\) \(\chi_{6001}(76,\cdot)\) \(\chi_{6001}(93,\cdot)\) \(\chi_{6001}(223,\cdot)\) \(\chi_{6001}(508,\cdot)\) \(\chi_{6001}(553,\cdot)\) \(\chi_{6001}(756,\cdot)\) \(\chi_{6001}(859,\cdot)\) \(\chi_{6001}(903,\cdot)\) \(\chi_{6001}(960,\cdot)\) \(\chi_{6001}(1369,\cdot)\) \(\chi_{6001}(1453,\cdot)\) \(\chi_{6001}(1494,\cdot)\) \(\chi_{6001}(1498,\cdot)\) \(\chi_{6001}(1504,\cdot)\) \(\chi_{6001}(1579,\cdot)\) \(\chi_{6001}(1596,\cdot)\) \(\chi_{6001}(1613,\cdot)\) \(\chi_{6001}(1719,\cdot)\) \(\chi_{6001}(1885,\cdot)\) \(\chi_{6001}(1946,\cdot)\) \(\chi_{6001}(1953,\cdot)\) \(\chi_{6001}(1991,\cdot)\) \(\chi_{6001}(2093,\cdot)\) \(\chi_{6001}(2100,\cdot)\) \(\chi_{6001}(2157,\cdot)\) \(\chi_{6001}(2327,\cdot)\) \(\chi_{6001}(2406,\cdot)\) \(\chi_{6001}(2433,\cdot)\) \(\chi_{6001}(2480,\cdot)\) ...

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

\((2825,3180)\) → \((e\left(\frac{1}{8}\right),e\left(\frac{19}{176}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{41}{176}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{173}{176}\right)\)\(e\left(\frac{11}{16}\right)\)\(e\left(\frac{1}{16}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{41}{88}\right)\)\(e\left(\frac{7}{16}\right)\)\(e\left(\frac{31}{88}\right)\)
value at e.g. 2

Related number fields

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