Properties

Conductor 335
Order 132
Real No
Primitive No
Parity Even
Orbit Label 4020.dl

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[13]
 
pari: [g,chi] = znchar(Mod(13,4020))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 335
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 132
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.dl
Orbit index = 90

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 ]
 

\(\chi_{4020}(13,\cdot)\) \(\chi_{4020}(337,\cdot)\) \(\chi_{4020}(433,\cdot)\) \(\chi_{4020}(517,\cdot)\) \(\chi_{4020}(577,\cdot)\) \(\chi_{4020}(637,\cdot)\) \(\chi_{4020}(733,\cdot)\) \(\chi_{4020}(757,\cdot)\) \(\chi_{4020}(817,\cdot)\) \(\chi_{4020}(1033,\cdot)\) \(\chi_{4020}(1213,\cdot)\) \(\chi_{4020}(1237,\cdot)\) \(\chi_{4020}(1453,\cdot)\) \(\chi_{4020}(1537,\cdot)\) \(\chi_{4020}(1573,\cdot)\) \(\chi_{4020}(1693,\cdot)\) \(\chi_{4020}(1753,\cdot)\) \(\chi_{4020}(1837,\cdot)\) \(\chi_{4020}(1933,\cdot)\) \(\chi_{4020}(1993,\cdot)\) \(\chi_{4020}(2017,\cdot)\) \(\chi_{4020}(2257,\cdot)\) \(\chi_{4020}(2377,\cdot)\) \(\chi_{4020}(2473,\cdot)\) \(\chi_{4020}(2497,\cdot)\) \(\chi_{4020}(2557,\cdot)\) \(\chi_{4020}(2737,\cdot)\) \(\chi_{4020}(2797,\cdot)\) \(\chi_{4020}(2893,\cdot)\) \(\chi_{4020}(3133,\cdot)\) ...

Inducing primitive character

\(\chi_{335}(13,\cdot)\)

Values on generators

\((2011,2681,3217,1141)\) → \((1,1,-i,e\left(\frac{19}{66}\right))\)

Values

-117111317192329313741
\(1\)\(1\)\(e\left(\frac{49}{132}\right)\)\(e\left(\frac{65}{66}\right)\)\(e\left(\frac{95}{132}\right)\)\(e\left(\frac{23}{132}\right)\)\(e\left(\frac{25}{66}\right)\)\(e\left(\frac{41}{132}\right)\)\(e\left(\frac{1}{6}\right)\)\(e\left(\frac{35}{66}\right)\)\(e\left(\frac{1}{12}\right)\)\(e\left(\frac{17}{66}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{132})\)