Properties

Conductor 4020
Order 22
Real No
Primitive Yes
Parity Even
Orbit Label 4020.by

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[59]
 
pari: [g,chi] = znchar(Mod(59,4020))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4020
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 22
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 = Even
Orbit label = 4020.by
Orbit index = 51

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 ]
 

\(\chi_{4020}(59,\cdot)\) \(\chi_{4020}(359,\cdot)\) \(\chi_{4020}(1019,\cdot)\) \(\chi_{4020}(1499,\cdot)\) \(\chi_{4020}(1739,\cdot)\) \(\chi_{4020}(2099,\cdot)\) \(\chi_{4020}(2159,\cdot)\) \(\chi_{4020}(2519,\cdot)\) \(\chi_{4020}(3359,\cdot)\) \(\chi_{4020}(3479,\cdot)\)

Values on generators

\((2011,2681,3217,1141)\) → \((-1,-1,-1,e\left(\frac{6}{11}\right))\)

Values

-117111317192329313741
\(1\)\(1\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{19}{22}\right)\)\(e\left(\frac{10}{11}\right)\)\(e\left(\frac{21}{22}\right)\)\(e\left(\frac{17}{22}\right)\)\(-1\)\(e\left(\frac{3}{22}\right)\)\(-1\)\(e\left(\frac{9}{22}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{11})\)