Properties

Conductor 805
Order 44
Real no
Primitive no
Minimal yes
Parity even
Orbit label 4025.cd

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[118]
 
pari: [g,chi] = znchar(Mod(118,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 805
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 44
Real = no
sage: chi.is_primitive()
 
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
 
Primitive = no
Minimal = yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = even
Orbit label = 4025.cd
Orbit index = 56

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 ]
 

\(\chi_{4025}(118,\cdot)\) \(\chi_{4025}(307,\cdot)\) \(\chi_{4025}(468,\cdot)\) \(\chi_{4025}(657,\cdot)\) \(\chi_{4025}(818,\cdot)\) \(\chi_{4025}(832,\cdot)\) \(\chi_{4025}(993,\cdot)\) \(\chi_{4025}(1007,\cdot)\) \(\chi_{4025}(1168,\cdot)\) \(\chi_{4025}(1182,\cdot)\) \(\chi_{4025}(1343,\cdot)\) \(\chi_{4025}(2582,\cdot)\) \(\chi_{4025}(2743,\cdot)\) \(\chi_{4025}(3107,\cdot)\) \(\chi_{4025}(3268,\cdot)\) \(\chi_{4025}(3282,\cdot)\) \(\chi_{4025}(3443,\cdot)\) \(\chi_{4025}(3807,\cdot)\) \(\chi_{4025}(3968,\cdot)\) \(\chi_{4025}(3982,\cdot)\)

Values on generators

\((2577,1151,3501)\) → \((-i,-1,e\left(\frac{8}{11}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{17}{44}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{13}{22}\right)\)\(e\left(\frac{27}{44}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{35}{44}\right)\)\(e\left(\frac{41}{44}\right)\)\(e\left(\frac{9}{11}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{44})\)