Properties

Conductor 201
Order 66
Real No
Primitive No
Parity Even
Orbit Label 4020.da

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[41]
 
pari: [g,chi] = znchar(Mod(41,4020))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 201
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.da
Orbit index = 79

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 ]
 

\(\chi_{4020}(41,\cdot)\) \(\chi_{4020}(101,\cdot)\) \(\chi_{4020}(221,\cdot)\) \(\chi_{4020}(281,\cdot)\) \(\chi_{4020}(701,\cdot)\) \(\chi_{4020}(1001,\cdot)\) \(\chi_{4020}(1301,\cdot)\) \(\chi_{4020}(1481,\cdot)\) \(\chi_{4020}(1721,\cdot)\) \(\chi_{4020}(1841,\cdot)\) \(\chi_{4020}(1961,\cdot)\) \(\chi_{4020}(2021,\cdot)\) \(\chi_{4020}(2201,\cdot)\) \(\chi_{4020}(2261,\cdot)\) \(\chi_{4020}(2741,\cdot)\) \(\chi_{4020}(3161,\cdot)\) \(\chi_{4020}(3401,\cdot)\) \(\chi_{4020}(3461,\cdot)\) \(\chi_{4020}(3821,\cdot)\) \(\chi_{4020}(4001,\cdot)\)

Inducing primitive character

\(\chi_{201}(41,\cdot)\)

Values on generators

\((2011,2681,3217,1141)\) → \((1,-1,1,e\left(\frac{53}{66}\right))\)

Values

-117111317192329313741
\(1\)\(1\)\(e\left(\frac{31}{66}\right)\)\(e\left(\frac{29}{33}\right)\)\(e\left(\frac{17}{66}\right)\)\(e\left(\frac{59}{66}\right)\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{65}{66}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{49}{66}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{2}{33}\right)\)
value at  e.g. 2

Related number fields

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