Properties

Conductor 67
Order 66
Real No
Primitive No
Parity Odd
Orbit Label 4020.cv

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[61]
 
pari: [g,chi] = znchar(Mod(61,4020))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 67
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.cv
Orbit index = 74

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 ]
 

\(\chi_{4020}(61,\cdot)\) \(\chi_{4020}(481,\cdot)\) \(\chi_{4020}(721,\cdot)\) \(\chi_{4020}(781,\cdot)\) \(\chi_{4020}(1141,\cdot)\) \(\chi_{4020}(1321,\cdot)\) \(\chi_{4020}(1381,\cdot)\) \(\chi_{4020}(1441,\cdot)\) \(\chi_{4020}(1561,\cdot)\) \(\chi_{4020}(1621,\cdot)\) \(\chi_{4020}(2041,\cdot)\) \(\chi_{4020}(2341,\cdot)\) \(\chi_{4020}(2641,\cdot)\) \(\chi_{4020}(2821,\cdot)\) \(\chi_{4020}(3061,\cdot)\) \(\chi_{4020}(3181,\cdot)\) \(\chi_{4020}(3301,\cdot)\) \(\chi_{4020}(3361,\cdot)\) \(\chi_{4020}(3541,\cdot)\) \(\chi_{4020}(3601,\cdot)\)

Inducing primitive character

\(\chi_{67}(61,\cdot)\)

Values on generators

\((2011,2681,3217,1141)\) → \((1,1,1,e\left(\frac{7}{66}\right))\)

Values

-117111317192329313741
\(-1\)\(1\)\(e\left(\frac{29}{66}\right)\)\(e\left(\frac{17}{66}\right)\)\(e\left(\frac{1}{66}\right)\)\(e\left(\frac{26}{33}\right)\)\(e\left(\frac{2}{33}\right)\)\(e\left(\frac{32}{33}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{65}{66}\right)\)\(e\left(\frac{1}{3}\right)\)\(e\left(\frac{41}{66}\right)\)
value at  e.g. 2

Related number fields

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