Properties

Label 6001.324
Modulus $6001$
Conductor $353$
Order $88$
Real no
Primitive no
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([0,83]))
 
pari: [g,chi] = znchar(Mod(324,6001))
 

Basic properties

Modulus: \(6001\)
Conductor: \(353\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(88\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from \(\chi_{353}(324,\cdot)\)
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 

Galois orbit 6001.df

\(\chi_{6001}(324,\cdot)\) \(\chi_{6001}(426,\cdot)\) \(\chi_{6001}(698,\cdot)\) \(\chi_{6001}(817,\cdot)\) \(\chi_{6001}(834,\cdot)\) \(\chi_{6001}(1038,\cdot)\) \(\chi_{6001}(1140,\cdot)\) \(\chi_{6001}(1344,\cdot)\) \(\chi_{6001}(1395,\cdot)\) \(\chi_{6001}(1429,\cdot)\) \(\chi_{6001}(1480,\cdot)\) \(\chi_{6001}(1684,\cdot)\) \(\chi_{6001}(1786,\cdot)\) \(\chi_{6001}(1990,\cdot)\) \(\chi_{6001}(2007,\cdot)\) \(\chi_{6001}(2126,\cdot)\) \(\chi_{6001}(2398,\cdot)\) \(\chi_{6001}(2500,\cdot)\) \(\chi_{6001}(2908,\cdot)\) \(\chi_{6001}(3469,\cdot)\) \(\chi_{6001}(3486,\cdot)\) \(\chi_{6001}(3639,\cdot)\) \(\chi_{6001}(3707,\cdot)\) \(\chi_{6001}(3724,\cdot)\) \(\chi_{6001}(3792,\cdot)\) \(\chi_{6001}(3894,\cdot)\) \(\chi_{6001}(4234,\cdot)\) \(\chi_{6001}(4268,\cdot)\) \(\chi_{6001}(4319,\cdot)\) \(\chi_{6001}(4506,\cdot)\) ...

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

\((2825,3180)\) → \((1,e\left(\frac{83}{88}\right))\)

Values

\(-1\)\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)\(7\)\(8\)\(9\)\(10\)\(11\)
\(1\)\(1\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{83}{88}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{39}{88}\right)\)\(e\left(\frac{5}{8}\right)\)\(e\left(\frac{3}{8}\right)\)\(e\left(\frac{1}{22}\right)\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{1}{8}\right)\)\(e\left(\frac{13}{22}\right)\)
value at e.g. 2

Related number fields

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