Properties

Conductor 4025
Order 660
Real No
Primitive Yes
Parity Odd
Orbit Label 4025.dq

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[2]
 
pari: [g,chi] = znchar(Mod(2,4025))
 

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 = Odd
Orbit label = 4025.dq
Orbit index = 95

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 ]
 

\(\chi_{4025}(2,\cdot)\) \(\chi_{4025}(58,\cdot)\) \(\chi_{4025}(72,\cdot)\) \(\chi_{4025}(123,\cdot)\) \(\chi_{4025}(128,\cdot)\) \(\chi_{4025}(142,\cdot)\) \(\chi_{4025}(163,\cdot)\) \(\chi_{4025}(177,\cdot)\) \(\chi_{4025}(233,\cdot)\) \(\chi_{4025}(242,\cdot)\) \(\chi_{4025}(303,\cdot)\) \(\chi_{4025}(312,\cdot)\) \(\chi_{4025}(317,\cdot)\) \(\chi_{4025}(338,\cdot)\) \(\chi_{4025}(347,\cdot)\) \(\chi_{4025}(403,\cdot)\) \(\chi_{4025}(417,\cdot)\) \(\chi_{4025}(422,\cdot)\) \(\chi_{4025}(473,\cdot)\) \(\chi_{4025}(478,\cdot)\) \(\chi_{4025}(487,\cdot)\) \(\chi_{4025}(492,\cdot)\) \(\chi_{4025}(508,\cdot)\) \(\chi_{4025}(522,\cdot)\) \(\chi_{4025}(578,\cdot)\) \(\chi_{4025}(583,\cdot)\) \(\chi_{4025}(627,\cdot)\) \(\chi_{4025}(648,\cdot)\) \(\chi_{4025}(653,\cdot)\) \(\chi_{4025}(662,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{1}{20}\right),e\left(\frac{1}{3}\right),e\left(\frac{1}{11}\right))\)

Values

-1123468911121316
\(-1\)\(1\)\(e\left(\frac{593}{660}\right)\)\(e\left(\frac{91}{660}\right)\)\(e\left(\frac{263}{330}\right)\)\(e\left(\frac{2}{55}\right)\)\(e\left(\frac{153}{220}\right)\)\(e\left(\frac{91}{330}\right)\)\(e\left(\frac{157}{165}\right)\)\(e\left(\frac{617}{660}\right)\)\(e\left(\frac{49}{220}\right)\)\(e\left(\frac{98}{165}\right)\)
value at  e.g. 2

Related number fields

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