Properties

Conductor 804
Order 66
Real No
Primitive No
Parity Odd
Orbit Label 4020.de

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[11]
 
pari: [g,chi] = znchar(Mod(11,4020))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 804
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 = Odd
Orbit label = 4020.de
Orbit index = 83

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 ]
 

\(\chi_{4020}(11,\cdot)\) \(\chi_{4020}(191,\cdot)\) \(\chi_{4020}(251,\cdot)\) \(\chi_{4020}(731,\cdot)\) \(\chi_{4020}(1151,\cdot)\) \(\chi_{4020}(1391,\cdot)\) \(\chi_{4020}(1451,\cdot)\) \(\chi_{4020}(1811,\cdot)\) \(\chi_{4020}(1991,\cdot)\) \(\chi_{4020}(2051,\cdot)\) \(\chi_{4020}(2111,\cdot)\) \(\chi_{4020}(2231,\cdot)\) \(\chi_{4020}(2291,\cdot)\) \(\chi_{4020}(2711,\cdot)\) \(\chi_{4020}(3011,\cdot)\) \(\chi_{4020}(3311,\cdot)\) \(\chi_{4020}(3491,\cdot)\) \(\chi_{4020}(3731,\cdot)\) \(\chi_{4020}(3851,\cdot)\) \(\chi_{4020}(3971,\cdot)\)

Inducing primitive character

\(\chi_{804}(11,\cdot)\)

Values on generators

\((2011,2681,3217,1141)\) → \((-1,-1,1,e\left(\frac{59}{66}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{49}{66}\right)\)\(e\left(\frac{65}{66}\right)\)\(e\left(\frac{47}{66}\right)\)\(e\left(\frac{29}{66}\right)\)\(e\left(\frac{1}{33}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{17}{33}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{29}{33}\right)\)
value at  e.g. 2

Related number fields

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