Properties

Conductor 8041
Order 120
Real No
Primitive Yes
Parity Even
Orbit Label 8041.em

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[338]
 
pari: [g,chi] = znchar(Mod(338,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 120
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.em
Orbit index = 117

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 ]
 

\(\chi_{8041}(338,\cdot)\) \(\chi_{8041}(695,\cdot)\) \(\chi_{8041}(910,\cdot)\) \(\chi_{8041}(1069,\cdot)\) \(\chi_{8041}(1284,\cdot)\) \(\chi_{8041}(1426,\cdot)\) \(\chi_{8041}(1641,\cdot)\) \(\chi_{8041}(1800,\cdot)\) \(\chi_{8041}(2015,\cdot)\) \(\chi_{8041}(2372,\cdot)\) \(\chi_{8041}(2746,\cdot)\) \(\chi_{8041}(2888,\cdot)\) \(\chi_{8041}(3262,\cdot)\) \(\chi_{8041}(3748,\cdot)\) \(\chi_{8041}(3834,\cdot)\) \(\chi_{8041}(4122,\cdot)\) \(\chi_{8041}(4208,\cdot)\) \(\chi_{8041}(4479,\cdot)\) \(\chi_{8041}(4694,\cdot)\) \(\chi_{8041}(4853,\cdot)\) \(\chi_{8041}(5068,\cdot)\) \(\chi_{8041}(5210,\cdot)\) \(\chi_{8041}(5425,\cdot)\) \(\chi_{8041}(5584,\cdot)\) \(\chi_{8041}(5799,\cdot)\) \(\chi_{8041}(6156,\cdot)\) \(\chi_{8041}(6530,\cdot)\) \(\chi_{8041}(6672,\cdot)\) \(\chi_{8041}(7046,\cdot)\) \(\chi_{8041}(7618,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{3}{10}\right),e\left(\frac{3}{8}\right),e\left(\frac{1}{6}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{113}{120}\right)\)\(e\left(\frac{1}{10}\right)\)\(e\left(\frac{29}{120}\right)\)\(e\left(\frac{119}{120}\right)\)\(e\left(\frac{7}{120}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{53}{60}\right)\)\(e\left(\frac{7}{24}\right)\)\(e\left(\frac{1}{24}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{120})\)