Properties

Conductor 268
Order 66
Real No
Primitive No
Parity Even
Orbit Label 4020.dh

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[31]
 
pari: [g,chi] = znchar(Mod(31,4020))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 268
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 66
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.dh
Orbit index = 86

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 ]
 

\(\chi_{4020}(31,\cdot)\) \(\chi_{4020}(331,\cdot)\) \(\chi_{4020}(631,\cdot)\) \(\chi_{4020}(811,\cdot)\) \(\chi_{4020}(1051,\cdot)\) \(\chi_{4020}(1171,\cdot)\) \(\chi_{4020}(1291,\cdot)\) \(\chi_{4020}(1351,\cdot)\) \(\chi_{4020}(1531,\cdot)\) \(\chi_{4020}(1591,\cdot)\) \(\chi_{4020}(2071,\cdot)\) \(\chi_{4020}(2491,\cdot)\) \(\chi_{4020}(2731,\cdot)\) \(\chi_{4020}(2791,\cdot)\) \(\chi_{4020}(3151,\cdot)\) \(\chi_{4020}(3331,\cdot)\) \(\chi_{4020}(3391,\cdot)\) \(\chi_{4020}(3451,\cdot)\) \(\chi_{4020}(3571,\cdot)\) \(\chi_{4020}(3631,\cdot)\)

Inducing primitive character

\(\chi_{268}(31,\cdot)\)

Values on generators

\((2011,2681,3217,1141)\) → \((-1,1,1,e\left(\frac{47}{66}\right))\)

Values

-117111317192329313741
\(1\)\(1\)\(e\left(\frac{29}{33}\right)\)\(e\left(\frac{17}{33}\right)\)\(e\left(\frac{35}{66}\right)\)\(e\left(\frac{19}{33}\right)\)\(e\left(\frac{41}{66}\right)\)\(e\left(\frac{29}{66}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{32}{33}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{49}{66}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{33})\)