Properties

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

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[44]
 
pari: [g,chi] = znchar(Mod(44,4025))
 

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.dn
Orbit index = 92

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 ]
 

\(\chi_{4025}(44,\cdot)\) \(\chi_{4025}(79,\cdot)\) \(\chi_{4025}(109,\cdot)\) \(\chi_{4025}(214,\cdot)\) \(\chi_{4025}(319,\cdot)\) \(\chi_{4025}(359,\cdot)\) \(\chi_{4025}(389,\cdot)\) \(\chi_{4025}(429,\cdot)\) \(\chi_{4025}(494,\cdot)\) \(\chi_{4025}(534,\cdot)\) \(\chi_{4025}(569,\cdot)\) \(\chi_{4025}(704,\cdot)\) \(\chi_{4025}(709,\cdot)\) \(\chi_{4025}(779,\cdot)\) \(\chi_{4025}(879,\cdot)\) \(\chi_{4025}(884,\cdot)\) \(\chi_{4025}(914,\cdot)\) \(\chi_{4025}(954,\cdot)\) \(\chi_{4025}(1019,\cdot)\) \(\chi_{4025}(1054,\cdot)\) \(\chi_{4025}(1164,\cdot)\) \(\chi_{4025}(1194,\cdot)\) \(\chi_{4025}(1229,\cdot)\) \(\chi_{4025}(1234,\cdot)\) \(\chi_{4025}(1339,\cdot)\) \(\chi_{4025}(1479,\cdot)\) \(\chi_{4025}(1509,\cdot)\) \(\chi_{4025}(1514,\cdot)\) \(\chi_{4025}(1579,\cdot)\) \(\chi_{4025}(1584,\cdot)\) ...

Values on generators

\((2577,1151,3501)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{1}{3}\right),e\left(\frac{13}{22}\right))\)

Values

-1123468911121316
\(-1\)\(1\)\(e\left(\frac{247}{330}\right)\)\(e\left(\frac{29}{330}\right)\)\(e\left(\frac{82}{165}\right)\)\(e\left(\frac{46}{55}\right)\)\(e\left(\frac{27}{110}\right)\)\(e\left(\frac{29}{165}\right)\)\(e\left(\frac{17}{330}\right)\)\(e\left(\frac{193}{330}\right)\)\(e\left(\frac{41}{110}\right)\)\(e\left(\frac{164}{165}\right)\)
value at  e.g. 2

Related number fields

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