Properties

Conductor 1005
Order 22
Real No
Primitive No
Parity Odd
Orbit Label 4020.ck

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[89]
 
pari: [g,chi] = znchar(Mod(89,4020))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1005
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 = No
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Odd
Orbit label = 4020.ck
Orbit index = 63

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 ]
 

\(\chi_{4020}(89,\cdot)\) \(\chi_{4020}(149,\cdot)\) \(\chi_{4020}(509,\cdot)\) \(\chi_{4020}(1349,\cdot)\) \(\chi_{4020}(1469,\cdot)\) \(\chi_{4020}(2069,\cdot)\) \(\chi_{4020}(2369,\cdot)\) \(\chi_{4020}(3029,\cdot)\) \(\chi_{4020}(3509,\cdot)\) \(\chi_{4020}(3749,\cdot)\)

Inducing primitive character

\(\chi_{1005}(89,\cdot)\)

Values on generators

\((2011,2681,3217,1141)\) → \((1,-1,-1,e\left(\frac{10}{11}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{9}{22}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{17}{22}\right)\)\(e\left(\frac{2}{11}\right)\)\(e\left(\frac{1}{11}\right)\)\(e\left(\frac{5}{11}\right)\)\(-1\)\(e\left(\frac{8}{11}\right)\)\(-1\)\(e\left(\frac{15}{22}\right)\)
value at  e.g. 2

Related number fields

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