Properties

Conductor 1005
Order 44
Real No
Primitive No
Parity Odd
Orbit Label 4020.cq

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[53]
 
pari: [g,chi] = znchar(Mod(53,4020))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1005
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 = Odd
Orbit label = 4020.cq
Orbit index = 69

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 ]
 

\(\chi_{4020}(53,\cdot)\) \(\chi_{4020}(137,\cdot)\) \(\chi_{4020}(377,\cdot)\) \(\chi_{4020}(713,\cdot)\) \(\chi_{4020}(857,\cdot)\) \(\chi_{4020}(1013,\cdot)\) \(\chi_{4020}(1517,\cdot)\) \(\chi_{4020}(1613,\cdot)\) \(\chi_{4020}(1733,\cdot)\) \(\chi_{4020}(1817,\cdot)\) \(\chi_{4020}(2417,\cdot)\) \(\chi_{4020}(2537,\cdot)\) \(\chi_{4020}(2573,\cdot)\) \(\chi_{4020}(2933,\cdot)\) \(\chi_{4020}(2993,\cdot)\) \(\chi_{4020}(3353,\cdot)\) \(\chi_{4020}(3377,\cdot)\) \(\chi_{4020}(3593,\cdot)\) \(\chi_{4020}(3737,\cdot)\) \(\chi_{4020}(3797,\cdot)\)

Inducing primitive character

\(\chi_{1005}(53,\cdot)\)

Values on generators

\((2011,2681,3217,1141)\) → \((1,-1,-i,e\left(\frac{19}{22}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{27}{44}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{29}{44}\right)\)\(e\left(\frac{23}{44}\right)\)\(e\left(\frac{3}{22}\right)\)\(e\left(\frac{41}{44}\right)\)\(1\)\(e\left(\frac{13}{22}\right)\)\(-i\)\(e\left(\frac{3}{11}\right)\)
value at  e.g. 2

Related number fields

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