Properties

Conductor 4025
Order 330
Real No
Primitive Yes
Parity Odd
Orbit Label 4025.dh

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[11]
 
pari: [g,chi] = znchar(Mod(11,4025))
 

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 = Odd
Orbit label = 4025.dh
Orbit index = 86

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 ]
 

\(\chi_{4025}(11,\cdot)\) \(\chi_{4025}(86,\cdot)\) \(\chi_{4025}(191,\cdot)\) \(\chi_{4025}(221,\cdot)\) \(\chi_{4025}(291,\cdot)\) \(\chi_{4025}(296,\cdot)\) \(\chi_{4025}(366,\cdot)\) \(\chi_{4025}(396,\cdot)\) \(\chi_{4025}(431,\cdot)\) \(\chi_{4025}(471,\cdot)\) \(\chi_{4025}(536,\cdot)\) \(\chi_{4025}(571,\cdot)\) \(\chi_{4025}(641,\cdot)\) \(\chi_{4025}(681,\cdot)\) \(\chi_{4025}(711,\cdot)\) \(\chi_{4025}(746,\cdot)\) \(\chi_{4025}(816,\cdot)\) \(\chi_{4025}(856,\cdot)\) \(\chi_{4025}(891,\cdot)\) \(\chi_{4025}(996,\cdot)\) \(\chi_{4025}(1031,\cdot)\) \(\chi_{4025}(1096,\cdot)\) \(\chi_{4025}(1171,\cdot)\) \(\chi_{4025}(1206,\cdot)\) \(\chi_{4025}(1236,\cdot)\) \(\chi_{4025}(1341,\cdot)\) \(\chi_{4025}(1446,\cdot)\) \(\chi_{4025}(1486,\cdot)\) \(\chi_{4025}(1516,\cdot)\) \(\chi_{4025}(1556,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{2}{3}\right),e\left(\frac{9}{22}\right))\)

Values

-1123468911121316
\(-1\)\(1\)\(e\left(\frac{157}{165}\right)\)\(e\left(\frac{134}{165}\right)\)\(e\left(\frac{149}{165}\right)\)\(e\left(\frac{42}{55}\right)\)\(e\left(\frac{47}{55}\right)\)\(e\left(\frac{103}{165}\right)\)\(e\left(\frac{49}{330}\right)\)\(e\left(\frac{118}{165}\right)\)\(e\left(\frac{51}{55}\right)\)\(e\left(\frac{133}{165}\right)\)
value at  e.g. 2

Related number fields

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