Properties

Conductor 4025
Order 330
Real No
Primitive Yes
Parity Even
Orbit Label 4025.dl

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[19]
 
pari: [g,chi] = znchar(Mod(19,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4025
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 330
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.dl
Orbit index = 90

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 ]
 

\(\chi_{4025}(19,\cdot)\) \(\chi_{4025}(89,\cdot)\) \(\chi_{4025}(129,\cdot)\) \(\chi_{4025}(159,\cdot)\) \(\chi_{4025}(194,\cdot)\) \(\chi_{4025}(264,\cdot)\) \(\chi_{4025}(304,\cdot)\) \(\chi_{4025}(339,\cdot)\) \(\chi_{4025}(444,\cdot)\) \(\chi_{4025}(479,\cdot)\) \(\chi_{4025}(544,\cdot)\) \(\chi_{4025}(619,\cdot)\) \(\chi_{4025}(654,\cdot)\) \(\chi_{4025}(684,\cdot)\) \(\chi_{4025}(789,\cdot)\) \(\chi_{4025}(894,\cdot)\) \(\chi_{4025}(934,\cdot)\) \(\chi_{4025}(964,\cdot)\) \(\chi_{4025}(1004,\cdot)\) \(\chi_{4025}(1069,\cdot)\) \(\chi_{4025}(1109,\cdot)\) \(\chi_{4025}(1144,\cdot)\) \(\chi_{4025}(1279,\cdot)\) \(\chi_{4025}(1284,\cdot)\) \(\chi_{4025}(1354,\cdot)\) \(\chi_{4025}(1454,\cdot)\) \(\chi_{4025}(1459,\cdot)\) \(\chi_{4025}(1489,\cdot)\) \(\chi_{4025}(1529,\cdot)\) \(\chi_{4025}(1594,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{5}{6}\right),e\left(\frac{15}{22}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{307}{330}\right)\)\(e\left(\frac{7}{165}\right)\)\(e\left(\frac{142}{165}\right)\)\(e\left(\frac{107}{110}\right)\)\(e\left(\frac{87}{110}\right)\)\(e\left(\frac{14}{165}\right)\)\(e\left(\frac{287}{330}\right)\)\(e\left(\frac{149}{165}\right)\)\(e\left(\frac{8}{55}\right)\)\(e\left(\frac{119}{165}\right)\)
value at  e.g. 2

Related number fields

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