Properties

Conductor 115
Order 44
Real No
Primitive No
Parity Even
Orbit Label 4025.cc

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[43]
 
pari: [g,chi] = znchar(Mod(43,4025))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 115
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
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 4025.cc
Orbit index = 55

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 ]
 

\(\chi_{4025}(43,\cdot)\) \(\chi_{4025}(57,\cdot)\) \(\chi_{4025}(218,\cdot)\) \(\chi_{4025}(582,\cdot)\) \(\chi_{4025}(743,\cdot)\) \(\chi_{4025}(757,\cdot)\) \(\chi_{4025}(918,\cdot)\) \(\chi_{4025}(1282,\cdot)\) \(\chi_{4025}(1443,\cdot)\) \(\chi_{4025}(2682,\cdot)\) \(\chi_{4025}(2843,\cdot)\) \(\chi_{4025}(2857,\cdot)\) \(\chi_{4025}(3018,\cdot)\) \(\chi_{4025}(3032,\cdot)\) \(\chi_{4025}(3193,\cdot)\) \(\chi_{4025}(3207,\cdot)\) \(\chi_{4025}(3368,\cdot)\) \(\chi_{4025}(3557,\cdot)\) \(\chi_{4025}(3718,\cdot)\) \(\chi_{4025}(3907,\cdot)\)

Inducing primitive character

\(\chi_{115}(43,\cdot)\)

Values on generators

\((2577,1151,3501)\) → \((-i,1,e\left(\frac{5}{22}\right))\)

Values

-1123468911121316
\(1\)\(1\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{39}{44}\right)\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{27}{44}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{1}{22}\right)\)\(e\left(\frac{13}{44}\right)\)\(e\left(\frac{19}{44}\right)\)\(e\left(\frac{9}{11}\right)\)
value at  e.g. 2

Related number fields

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