Properties

Conductor 8041
Order 240
Real No
Primitive Yes
Parity Even
Orbit Label 8041.fd

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[6]
 
pari: [g,chi] = znchar(Mod(6,8041))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 8041
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 240
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.fd
Orbit index = 134

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 ]
 

\(\chi_{8041}(6,\cdot)\) \(\chi_{8041}(79,\cdot)\) \(\chi_{8041}(294,\cdot)\) \(\chi_{8041}(337,\cdot)\) \(\chi_{8041}(380,\cdot)\) \(\chi_{8041}(436,\cdot)\) \(\chi_{8041}(479,\cdot)\) \(\chi_{8041}(651,\cdot)\) \(\chi_{8041}(810,\cdot)\) \(\chi_{8041}(853,\cdot)\) \(\chi_{8041}(1025,\cdot)\) \(\chi_{8041}(1382,\cdot)\) \(\chi_{8041}(1425,\cdot)\) \(\chi_{8041}(1756,\cdot)\) \(\chi_{8041}(1799,\cdot)\) \(\chi_{8041}(1812,\cdot)\) \(\chi_{8041}(1898,\cdot)\) \(\chi_{8041}(2186,\cdot)\) \(\chi_{8041}(2272,\cdot)\) \(\chi_{8041}(2285,\cdot)\) \(\chi_{8041}(2543,\cdot)\) \(\chi_{8041}(2659,\cdot)\) \(\chi_{8041}(2844,\cdot)\) \(\chi_{8041}(2917,\cdot)\) \(\chi_{8041}(3016,\cdot)\) \(\chi_{8041}(3218,\cdot)\) \(\chi_{8041}(3274,\cdot)\) \(\chi_{8041}(3390,\cdot)\) \(\chi_{8041}(3648,\cdot)\) \(\chi_{8041}(3747,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{15}{16}\right),e\left(\frac{2}{3}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{1}{40}\right)\)\(e\left(\frac{193}{240}\right)\)\(e\left(\frac{1}{20}\right)\)\(e\left(\frac{229}{240}\right)\)\(e\left(\frac{199}{240}\right)\)\(e\left(\frac{227}{240}\right)\)\(e\left(\frac{3}{40}\right)\)\(e\left(\frac{73}{120}\right)\)\(e\left(\frac{47}{48}\right)\)\(e\left(\frac{41}{48}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{240})\)