Properties

Conductor 335
Order 66
Real No
Primitive No
Parity Even
Orbit Label 4020.cz

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[49]
 
pari: [g,chi] = znchar(Mod(49,4020))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 335
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.cz
Orbit index = 78

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 ]
 

\(\chi_{4020}(49,\cdot)\) \(\chi_{4020}(169,\cdot)\) \(\chi_{4020}(289,\cdot)\) \(\chi_{4020}(529,\cdot)\) \(\chi_{4020}(709,\cdot)\) \(\chi_{4020}(1009,\cdot)\) \(\chi_{4020}(1309,\cdot)\) \(\chi_{4020}(1729,\cdot)\) \(\chi_{4020}(1789,\cdot)\) \(\chi_{4020}(1909,\cdot)\) \(\chi_{4020}(1969,\cdot)\) \(\chi_{4020}(2029,\cdot)\) \(\chi_{4020}(2209,\cdot)\) \(\chi_{4020}(2569,\cdot)\) \(\chi_{4020}(2629,\cdot)\) \(\chi_{4020}(2869,\cdot)\) \(\chi_{4020}(3289,\cdot)\) \(\chi_{4020}(3769,\cdot)\) \(\chi_{4020}(3829,\cdot)\) \(\chi_{4020}(4009,\cdot)\)

Inducing primitive character

\(\chi_{335}(49,\cdot)\)

Values on generators

\((2011,2681,3217,1141)\) → \((1,1,-1,e\left(\frac{23}{33}\right))\)

Values

-117111317192329313741
\(1\)\(1\)\(e\left(\frac{35}{66}\right)\)\(e\left(\frac{4}{33}\right)\)\(e\left(\frac{49}{66}\right)\)\(e\left(\frac{7}{66}\right)\)\(e\left(\frac{32}{33}\right)\)\(e\left(\frac{1}{66}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{25}{33}\right)\)\(e\left(\frac{5}{6}\right)\)\(e\left(\frac{31}{33}\right)\)
value at  e.g. 2

Related number fields

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