Properties

Conductor 4025
Order 165
Real No
Primitive Yes
Parity Even
Orbit Label 4025.dc

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(4025)
 
sage: chi = H[16]
 
pari: [g,chi] = znchar(Mod(16,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4025
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 165
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 = 4025.dc
Orbit index = 81

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 ]
 

\(\chi_{4025}(16,\cdot)\) \(\chi_{4025}(81,\cdot)\) \(\chi_{4025}(121,\cdot)\) \(\chi_{4025}(156,\cdot)\) \(\chi_{4025}(186,\cdot)\) \(\chi_{4025}(256,\cdot)\) \(\chi_{4025}(261,\cdot)\) \(\chi_{4025}(331,\cdot)\) \(\chi_{4025}(361,\cdot)\) \(\chi_{4025}(466,\cdot)\) \(\chi_{4025}(541,\cdot)\) \(\chi_{4025}(606,\cdot)\) \(\chi_{4025}(611,\cdot)\) \(\chi_{4025}(646,\cdot)\) \(\chi_{4025}(716,\cdot)\) \(\chi_{4025}(786,\cdot)\) \(\chi_{4025}(821,\cdot)\) \(\chi_{4025}(886,\cdot)\) \(\chi_{4025}(956,\cdot)\) \(\chi_{4025}(961,\cdot)\) \(\chi_{4025}(991,\cdot)\) \(\chi_{4025}(1061,\cdot)\) \(\chi_{4025}(1066,\cdot)\) \(\chi_{4025}(1131,\cdot)\) \(\chi_{4025}(1136,\cdot)\) \(\chi_{4025}(1166,\cdot)\) \(\chi_{4025}(1271,\cdot)\) \(\chi_{4025}(1306,\cdot)\) \(\chi_{4025}(1346,\cdot)\) \(\chi_{4025}(1411,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{1}{3}\right),e\left(\frac{4}{11}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{98}{165}\right)\)\(e\left(\frac{91}{165}\right)\)\(e\left(\frac{31}{165}\right)\)\(e\left(\frac{8}{55}\right)\)\(e\left(\frac{43}{55}\right)\)\(e\left(\frac{17}{165}\right)\)\(e\left(\frac{133}{165}\right)\)\(e\left(\frac{122}{165}\right)\)\(e\left(\frac{49}{55}\right)\)\(e\left(\frac{62}{165}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{165})\)