Properties

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

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[152]
 
pari: [g,chi] = znchar(Mod(152,8041))
 

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.fa
Orbit index = 131

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 ]
 

\(\chi_{8041}(152,\cdot)\) \(\chi_{8041}(169,\cdot)\) \(\chi_{8041}(203,\cdot)\) \(\chi_{8041}(339,\cdot)\) \(\chi_{8041}(526,\cdot)\) \(\chi_{8041}(713,\cdot)\) \(\chi_{8041}(883,\cdot)\) \(\chi_{8041}(900,\cdot)\) \(\chi_{8041}(917,\cdot)\) \(\chi_{8041}(1070,\cdot)\) \(\chi_{8041}(1257,\cdot)\) \(\chi_{8041}(1444,\cdot)\) \(\chi_{8041}(1631,\cdot)\) \(\chi_{8041}(1648,\cdot)\) \(\chi_{8041}(1665,\cdot)\) \(\chi_{8041}(2073,\cdot)\) \(\chi_{8041}(2260,\cdot)\) \(\chi_{8041}(2379,\cdot)\) \(\chi_{8041}(2396,\cdot)\) \(\chi_{8041}(3127,\cdot)\) \(\chi_{8041}(3195,\cdot)\) \(\chi_{8041}(3535,\cdot)\) \(\chi_{8041}(3722,\cdot)\) \(\chi_{8041}(3756,\cdot)\) \(\chi_{8041}(4266,\cdot)\) \(\chi_{8041}(4317,\cdot)\) \(\chi_{8041}(4453,\cdot)\) \(\chi_{8041}(4657,\cdot)\) \(\chi_{8041}(4997,\cdot)\) \(\chi_{8041}(5184,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{3}{5}\right),-1,e\left(\frac{8}{21}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{31}{35}\right)\)\(e\left(\frac{143}{210}\right)\)\(e\left(\frac{27}{35}\right)\)\(e\left(\frac{89}{210}\right)\)\(e\left(\frac{17}{30}\right)\)\(e\left(\frac{1}{30}\right)\)\(e\left(\frac{23}{35}\right)\)\(e\left(\frac{38}{105}\right)\)\(e\left(\frac{13}{42}\right)\)\(e\left(\frac{19}{42}\right)\)
value at  e.g. 2

Related number fields

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