Properties

Conductor 4025
Order 660
Real No
Primitive Yes
Parity Even
Orbit Label 4025.do

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[3]
 
pari: [g,chi] = znchar(Mod(3,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4025
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 660
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.do
Orbit index = 93

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 ]
 

\(\chi_{4025}(3,\cdot)\) \(\chi_{4025}(12,\cdot)\) \(\chi_{4025}(52,\cdot)\) \(\chi_{4025}(73,\cdot)\) \(\chi_{4025}(87,\cdot)\) \(\chi_{4025}(108,\cdot)\) \(\chi_{4025}(117,\cdot)\) \(\chi_{4025}(173,\cdot)\) \(\chi_{4025}(187,\cdot)\) \(\chi_{4025}(192,\cdot)\) \(\chi_{4025}(213,\cdot)\) \(\chi_{4025}(248,\cdot)\) \(\chi_{4025}(262,\cdot)\) \(\chi_{4025}(278,\cdot)\) \(\chi_{4025}(292,\cdot)\) \(\chi_{4025}(348,\cdot)\) \(\chi_{4025}(353,\cdot)\) \(\chi_{4025}(397,\cdot)\) \(\chi_{4025}(423,\cdot)\) \(\chi_{4025}(453,\cdot)\) \(\chi_{4025}(472,\cdot)\) \(\chi_{4025}(537,\cdot)\) \(\chi_{4025}(542,\cdot)\) \(\chi_{4025}(558,\cdot)\) \(\chi_{4025}(577,\cdot)\) \(\chi_{4025}(633,\cdot)\) \(\chi_{4025}(647,\cdot)\) \(\chi_{4025}(698,\cdot)\) \(\chi_{4025}(703,\cdot)\) \(\chi_{4025}(717,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{7}{20}\right),e\left(\frac{1}{6}\right),e\left(\frac{8}{11}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{91}{660}\right)\)\(e\left(\frac{167}{660}\right)\)\(e\left(\frac{91}{330}\right)\)\(e\left(\frac{43}{110}\right)\)\(e\left(\frac{91}{220}\right)\)\(e\left(\frac{167}{330}\right)\)\(e\left(\frac{134}{165}\right)\)\(e\left(\frac{349}{660}\right)\)\(e\left(\frac{73}{220}\right)\)\(e\left(\frac{91}{165}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{660})\)