Properties

Conductor 1340
Order 132
Real No
Primitive No
Parity Odd
Orbit Label 4020.dr

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[7]
 
pari: [g,chi] = znchar(Mod(7,4020))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1340
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 132
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.dr
Orbit index = 96

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 ]
 

\(\chi_{4020}(7,\cdot)\) \(\chi_{4020}(247,\cdot)\) \(\chi_{4020}(367,\cdot)\) \(\chi_{4020}(463,\cdot)\) \(\chi_{4020}(487,\cdot)\) \(\chi_{4020}(547,\cdot)\) \(\chi_{4020}(727,\cdot)\) \(\chi_{4020}(787,\cdot)\) \(\chi_{4020}(883,\cdot)\) \(\chi_{4020}(1123,\cdot)\) \(\chi_{4020}(1183,\cdot)\) \(\chi_{4020}(1267,\cdot)\) \(\chi_{4020}(1543,\cdot)\) \(\chi_{4020}(1687,\cdot)\) \(\chi_{4020}(1723,\cdot)\) \(\chi_{4020}(1783,\cdot)\) \(\chi_{4020}(1843,\cdot)\) \(\chi_{4020}(1927,\cdot)\) \(\chi_{4020}(1963,\cdot)\) \(\chi_{4020}(1987,\cdot)\) \(\chi_{4020}(2023,\cdot)\) \(\chi_{4020}(2347,\cdot)\) \(\chi_{4020}(2443,\cdot)\) \(\chi_{4020}(2527,\cdot)\) \(\chi_{4020}(2587,\cdot)\) \(\chi_{4020}(2647,\cdot)\) \(\chi_{4020}(2743,\cdot)\) \(\chi_{4020}(2767,\cdot)\) \(\chi_{4020}(2827,\cdot)\) \(\chi_{4020}(3043,\cdot)\) ...

Inducing primitive character

\(\chi_{1340}(7,\cdot)\)

Values on generators

\((2011,2681,3217,1141)\) → \((-1,1,i,e\left(\frac{23}{66}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{101}{132}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{49}{132}\right)\)\(e\left(\frac{73}{132}\right)\)\(e\left(\frac{16}{33}\right)\)\(e\left(\frac{1}{132}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{29}{33}\right)\)\(e\left(\frac{11}{12}\right)\)\(e\left(\frac{31}{66}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{132})\)