Properties

Conductor 4020
Order 44
Real No
Primitive Yes
Parity Odd
Orbit Label 4020.co

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(4020)
 
sage: chi = H[107]
 
pari: [g,chi] = znchar(Mod(107,4020))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4020
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 = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 4020.co
Orbit index = 67

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 ]
 

\(\chi_{4020}(107,\cdot)\) \(\chi_{4020}(143,\cdot)\) \(\chi_{4020}(263,\cdot)\) \(\chi_{4020}(863,\cdot)\) \(\chi_{4020}(947,\cdot)\) \(\chi_{4020}(1067,\cdot)\) \(\chi_{4020}(1163,\cdot)\) \(\chi_{4020}(1667,\cdot)\) \(\chi_{4020}(1823,\cdot)\) \(\chi_{4020}(1967,\cdot)\) \(\chi_{4020}(2303,\cdot)\) \(\chi_{4020}(2543,\cdot)\) \(\chi_{4020}(2627,\cdot)\) \(\chi_{4020}(2903,\cdot)\) \(\chi_{4020}(2963,\cdot)\) \(\chi_{4020}(3107,\cdot)\) \(\chi_{4020}(3323,\cdot)\) \(\chi_{4020}(3347,\cdot)\) \(\chi_{4020}(3707,\cdot)\) \(\chi_{4020}(3767,\cdot)\)

Values on generators

\((2011,2681,3217,1141)\) → \((-1,-1,i,e\left(\frac{3}{11}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{1}{44}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{41}{44}\right)\)\(e\left(\frac{9}{44}\right)\)\(e\left(\frac{8}{11}\right)\)\(e\left(\frac{17}{44}\right)\)\(1\)\(e\left(\frac{7}{22}\right)\)\(i\)\(e\left(\frac{21}{22}\right)\)
value at  e.g. 2

Related number fields

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