Properties

Conductor 1340
Order 132
Real No
Primitive No
Parity Even
Orbit Label 4020.dn

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[103]
 
pari: [g,chi] = znchar(Mod(103,4020))
 

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 = Even
Orbit label = 4020.dn
Orbit index = 92

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 ]
 

\(\chi_{4020}(103,\cdot)\) \(\chi_{4020}(127,\cdot)\) \(\chi_{4020}(307,\cdot)\) \(\chi_{4020}(523,\cdot)\) \(\chi_{4020}(583,\cdot)\) \(\chi_{4020}(607,\cdot)\) \(\chi_{4020}(703,\cdot)\) \(\chi_{4020}(763,\cdot)\) \(\chi_{4020}(823,\cdot)\) \(\chi_{4020}(907,\cdot)\) \(\chi_{4020}(1003,\cdot)\) \(\chi_{4020}(1327,\cdot)\) \(\chi_{4020}(1363,\cdot)\) \(\chi_{4020}(1387,\cdot)\) \(\chi_{4020}(1423,\cdot)\) \(\chi_{4020}(1507,\cdot)\) \(\chi_{4020}(1567,\cdot)\) \(\chi_{4020}(1627,\cdot)\) \(\chi_{4020}(1663,\cdot)\) \(\chi_{4020}(1807,\cdot)\) \(\chi_{4020}(2083,\cdot)\) \(\chi_{4020}(2167,\cdot)\) \(\chi_{4020}(2227,\cdot)\) \(\chi_{4020}(2467,\cdot)\) \(\chi_{4020}(2563,\cdot)\) \(\chi_{4020}(2623,\cdot)\) \(\chi_{4020}(2803,\cdot)\) \(\chi_{4020}(2863,\cdot)\) \(\chi_{4020}(2887,\cdot)\) \(\chi_{4020}(2983,\cdot)\) ...

Inducing primitive character

\(\chi_{1340}(103,\cdot)\)

Values on generators

\((2011,2681,3217,1141)\) → \((-1,1,-i,e\left(\frac{7}{33}\right))\)

Values

-117111317192329313741
\(1\)\(1\)\(e\left(\frac{17}{132}\right)\)\(e\left(\frac{1}{66}\right)\)\(e\left(\frac{37}{132}\right)\)\(e\left(\frac{43}{132}\right)\)\(e\left(\frac{4}{33}\right)\)\(e\left(\frac{91}{132}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{31}{66}\right)\)\(e\left(\frac{5}{12}\right)\)\(e\left(\frac{8}{33}\right)\)
value at  e.g. 2

Related number fields

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