Properties

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

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[37]
 
pari: [g,chi] = znchar(Mod(37,8041))
 

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.fc
Orbit index = 133

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 ]
 

\(\chi_{8041}(37,\cdot)\) \(\chi_{8041}(80,\cdot)\) \(\chi_{8041}(295,\cdot)\) \(\chi_{8041}(394,\cdot)\) \(\chi_{8041}(566,\cdot)\) \(\chi_{8041}(609,\cdot)\) \(\chi_{8041}(652,\cdot)\) \(\chi_{8041}(768,\cdot)\) \(\chi_{8041}(940,\cdot)\) \(\chi_{8041}(983,\cdot)\) \(\chi_{8041}(1026,\cdot)\) \(\chi_{8041}(1082,\cdot)\) \(\chi_{8041}(1125,\cdot)\) \(\chi_{8041}(1340,\cdot)\) \(\chi_{8041}(1456,\cdot)\) \(\chi_{8041}(1499,\cdot)\) \(\chi_{8041}(1714,\cdot)\) \(\chi_{8041}(1813,\cdot)\) \(\chi_{8041}(2028,\cdot)\) \(\chi_{8041}(2071,\cdot)\) \(\chi_{8041}(2187,\cdot)\) \(\chi_{8041}(2402,\cdot)\) \(\chi_{8041}(2445,\cdot)\) \(\chi_{8041}(2458,\cdot)\) \(\chi_{8041}(2544,\cdot)\) \(\chi_{8041}(2759,\cdot)\) \(\chi_{8041}(2832,\cdot)\) \(\chi_{8041}(2918,\cdot)\) \(\chi_{8041}(2931,\cdot)\) \(\chi_{8041}(3133,\cdot)\) ...

Values on generators

\((6580,2366,562)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{1}{16}\right),e\left(\frac{1}{6}\right))\)

Values

-11234567891012
\(1\)\(1\)\(e\left(\frac{23}{40}\right)\)\(e\left(\frac{199}{240}\right)\)\(e\left(\frac{3}{20}\right)\)\(e\left(\frac{67}{240}\right)\)\(e\left(\frac{97}{240}\right)\)\(e\left(\frac{221}{240}\right)\)\(e\left(\frac{29}{40}\right)\)\(e\left(\frac{79}{120}\right)\)\(e\left(\frac{41}{48}\right)\)\(e\left(\frac{47}{48}\right)\)
value at  e.g. 2

Related number fields

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