Properties

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

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[37]
 
pari: [g,chi] = znchar(Mod(37,4025))
 

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.dr
Orbit index = 96

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 ]
 

\(\chi_{4025}(37,\cdot)\) \(\chi_{4025}(53,\cdot)\) \(\chi_{4025}(67,\cdot)\) \(\chi_{4025}(88,\cdot)\) \(\chi_{4025}(102,\cdot)\) \(\chi_{4025}(158,\cdot)\) \(\chi_{4025}(172,\cdot)\) \(\chi_{4025}(198,\cdot)\) \(\chi_{4025}(212,\cdot)\) \(\chi_{4025}(228,\cdot)\) \(\chi_{4025}(247,\cdot)\) \(\chi_{4025}(263,\cdot)\) \(\chi_{4025}(333,\cdot)\) \(\chi_{4025}(352,\cdot)\) \(\chi_{4025}(373,\cdot)\) \(\chi_{4025}(387,\cdot)\) \(\chi_{4025}(408,\cdot)\) \(\chi_{4025}(452,\cdot)\) \(\chi_{4025}(513,\cdot)\) \(\chi_{4025}(527,\cdot)\) \(\chi_{4025}(548,\cdot)\) \(\chi_{4025}(562,\cdot)\) \(\chi_{4025}(592,\cdot)\) \(\chi_{4025}(613,\cdot)\) \(\chi_{4025}(688,\cdot)\) \(\chi_{4025}(697,\cdot)\) \(\chi_{4025}(723,\cdot)\) \(\chi_{4025}(753,\cdot)\) \(\chi_{4025}(802,\cdot)\) \(\chi_{4025}(842,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{1}{3}\right),e\left(\frac{21}{22}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{17}{660}\right)\)\(e\left(\frac{499}{660}\right)\)\(e\left(\frac{17}{330}\right)\)\(e\left(\frac{43}{55}\right)\)\(e\left(\frac{17}{220}\right)\)\(e\left(\frac{169}{330}\right)\)\(e\left(\frac{41}{330}\right)\)\(e\left(\frac{533}{660}\right)\)\(e\left(\frac{201}{220}\right)\)\(e\left(\frac{17}{165}\right)\)
value at  e.g. 2

Related number fields

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