Properties

Conductor 8041
Order 70
Real No
Primitive Yes
Parity Even
Orbit Label 8041.du

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[16]
 
pari: [g,chi] = znchar(Mod(16,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 70
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.du
Orbit index = 99

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 ]
 

\(\chi_{8041}(16,\cdot)\) \(\chi_{8041}(322,\cdot)\) \(\chi_{8041}(1325,\cdot)\) \(\chi_{8041}(1478,\cdot)\) \(\chi_{8041}(2209,\cdot)\) \(\chi_{8041}(2634,\cdot)\) \(\chi_{8041}(2787,\cdot)\) \(\chi_{8041}(2940,\cdot)\) \(\chi_{8041}(3008,\cdot)\) \(\chi_{8041}(3518,\cdot)\) \(\chi_{8041}(4096,\cdot)\) \(\chi_{8041}(4249,\cdot)\) \(\chi_{8041}(4470,\cdot)\) \(\chi_{8041}(4691,\cdot)\) \(\chi_{8041}(4827,\cdot)\) \(\chi_{8041}(5201,\cdot)\) \(\chi_{8041}(5439,\cdot)\) \(\chi_{8041}(5558,\cdot)\) \(\chi_{8041}(5932,\cdot)\) \(\chi_{8041}(6153,\cdot)\) \(\chi_{8041}(6884,\cdot)\) \(\chi_{8041}(6901,\cdot)\) \(\chi_{8041}(7615,\cdot)\) \(\chi_{8041}(7632,\cdot)\)

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{2}{5}\right),-1,e\left(\frac{4}{7}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{29}{35}\right)\)\(e\left(\frac{19}{70}\right)\)\(e\left(\frac{23}{35}\right)\)\(e\left(\frac{27}{70}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{3}{10}\right)\)\(e\left(\frac{17}{35}\right)\)\(e\left(\frac{19}{35}\right)\)\(e\left(\frac{3}{14}\right)\)\(e\left(\frac{13}{14}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{35})\)