Properties

Conductor 4020
Order 22
Real No
Primitive Yes
Parity Odd
Orbit Label 4020.ci

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[119]
 
pari: [g,chi] = znchar(Mod(119,4020))
 

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 = Odd
Orbit label = 4020.ci
Orbit index = 61

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 ]
 

\(\chi_{4020}(119,\cdot)\) \(\chi_{4020}(179,\cdot)\) \(\chi_{4020}(539,\cdot)\) \(\chi_{4020}(779,\cdot)\) \(\chi_{4020}(1259,\cdot)\) \(\chi_{4020}(1919,\cdot)\) \(\chi_{4020}(2219,\cdot)\) \(\chi_{4020}(2819,\cdot)\) \(\chi_{4020}(2939,\cdot)\) \(\chi_{4020}(3779,\cdot)\)

Values on generators

\((2011,2681,3217,1141)\) → \((-1,-1,-1,e\left(\frac{7}{22}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{7}{22}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{6}{11}\right)\)\(e\left(\frac{4}{11}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{9}{22}\right)\)\(-1\)\(e\left(\frac{5}{11}\right)\)\(-1\)\(e\left(\frac{4}{11}\right)\)
value at  e.g. 2

Related number fields

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