Properties

Label 6001.121
Modulus $6001$
Conductor $6001$
Order $88$
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([77,30]))
 
pari: [g,chi] = znchar(Mod(121,6001))
 

Basic properties

Modulus: \(6001\)
Conductor: \(6001\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(88\)
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.cz

\(\chi_{6001}(121,\cdot)\) \(\chi_{6001}(162,\cdot)\) \(\chi_{6001}(474,\cdot)\) \(\chi_{6001}(671,\cdot)\) \(\chi_{6001}(740,\cdot)\) \(\chi_{6001}(852,\cdot)\) \(\chi_{6001}(971,\cdot)\) \(\chi_{6001}(995,\cdot)\) \(\chi_{6001}(1063,\cdot)\) \(\chi_{6001}(1147,\cdot)\) \(\chi_{6001}(1205,\cdot)\) \(\chi_{6001}(1266,\cdot)\) \(\chi_{6001}(1324,\cdot)\) \(\chi_{6001}(1447,\cdot)\) \(\chi_{6001}(1800,\cdot)\) \(\chi_{6001}(1997,\cdot)\) \(\chi_{6001}(2083,\cdot)\) \(\chi_{6001}(2467,\cdot)\) \(\chi_{6001}(2535,\cdot)\) \(\chi_{6001}(2559,\cdot)\) \(\chi_{6001}(2678,\cdot)\) \(\chi_{6001}(2790,\cdot)\) \(\chi_{6001}(2820,\cdot)\) \(\chi_{6001}(2888,\cdot)\) \(\chi_{6001}(3143,\cdot)\) \(\chi_{6001}(3368,\cdot)\) \(\chi_{6001}(3409,\cdot)\) \(\chi_{6001}(3721,\cdot)\) \(\chi_{6001}(3748,\cdot)\) \(\chi_{6001}(4054,\cdot)\) ...

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

\((2825,3180)\) → \((e\left(\frac{7}{8}\right),e\left(\frac{15}{44}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{7}{44}\right)\)\(e\left(\frac{19}{88}\right)\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{63}{88}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{21}{44}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{7}{8}\right)\)\(e\left(\frac{51}{88}\right)\)
value at e.g. 2

Related number fields

Field of values: $\Q(\zeta_{88})$
Fixed field: Number field defined by a degree 88 polynomial