Properties

Conductor 8041
Order 210
Real No
Primitive Yes
Parity Even
Orbit Label 8041.ez

Related objects

Learn more about

Show commands for: SageMath / Pari/GP
sage: from dirichlet_conrey import DirichletGroup_conrey # requires nonstandard Sage package to be installed
 
sage: H = DirichletGroup_conrey(8041)
 
sage: chi = H[288]
 
pari: [g,chi] = znchar(Mod(288,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 210
Real = No
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 8041.ez
Orbit index = 130

Galois orbit

sage: chi.sage_character().galois_orbit()
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

\(\chi_{8041}(288,\cdot)\) \(\chi_{8041}(458,\cdot)\) \(\chi_{8041}(492,\cdot)\) \(\chi_{8041}(679,\cdot)\) \(\chi_{8041}(1019,\cdot)\) \(\chi_{8041}(1223,\cdot)\) \(\chi_{8041}(1359,\cdot)\) \(\chi_{8041}(1410,\cdot)\) \(\chi_{8041}(1920,\cdot)\) \(\chi_{8041}(1954,\cdot)\) \(\chi_{8041}(2141,\cdot)\) \(\chi_{8041}(2481,\cdot)\) \(\chi_{8041}(2549,\cdot)\) \(\chi_{8041}(3280,\cdot)\) \(\chi_{8041}(3297,\cdot)\) \(\chi_{8041}(3416,\cdot)\) \(\chi_{8041}(3603,\cdot)\) \(\chi_{8041}(4011,\cdot)\) \(\chi_{8041}(4028,\cdot)\) \(\chi_{8041}(4045,\cdot)\) \(\chi_{8041}(4232,\cdot)\) \(\chi_{8041}(4419,\cdot)\) \(\chi_{8041}(4606,\cdot)\) \(\chi_{8041}(4759,\cdot)\) \(\chi_{8041}(4776,\cdot)\) \(\chi_{8041}(4793,\cdot)\) \(\chi_{8041}(4963,\cdot)\) \(\chi_{8041}(5150,\cdot)\) \(\chi_{8041}(5337,\cdot)\) \(\chi_{8041}(5473,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{1}{10}\right),-1,e\left(\frac{11}{42}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{6}{35}\right)\)\(e\left(\frac{59}{105}\right)\)\(e\left(\frac{12}{35}\right)\)\(e\left(\frac{47}{105}\right)\)\(e\left(\frac{11}{15}\right)\)\(e\left(\frac{11}{30}\right)\)\(e\left(\frac{18}{35}\right)\)\(e\left(\frac{13}{105}\right)\)\(e\left(\frac{13}{21}\right)\)\(e\left(\frac{19}{21}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{105})\)