Properties

Conductor 1005
Order 132
Real No
Primitive No
Parity Even
Orbit Label 4020.dk

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[17]
 
pari: [g,chi] = znchar(Mod(17,4020))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 1005
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.dk
Orbit index = 89

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 ]
 

\(\chi_{4020}(17,\cdot)\) \(\chi_{4020}(77,\cdot)\) \(\chi_{4020}(173,\cdot)\) \(\chi_{4020}(257,\cdot)\) \(\chi_{4020}(317,\cdot)\) \(\chi_{4020}(437,\cdot)\) \(\chi_{4020}(473,\cdot)\) \(\chi_{4020}(557,\cdot)\) \(\chi_{4020}(773,\cdot)\) \(\chi_{4020}(797,\cdot)\) \(\chi_{4020}(977,\cdot)\) \(\chi_{4020}(1193,\cdot)\) \(\chi_{4020}(1253,\cdot)\) \(\chi_{4020}(1277,\cdot)\) \(\chi_{4020}(1373,\cdot)\) \(\chi_{4020}(1433,\cdot)\) \(\chi_{4020}(1493,\cdot)\) \(\chi_{4020}(1577,\cdot)\) \(\chi_{4020}(1673,\cdot)\) \(\chi_{4020}(1997,\cdot)\) \(\chi_{4020}(2033,\cdot)\) \(\chi_{4020}(2057,\cdot)\) \(\chi_{4020}(2093,\cdot)\) \(\chi_{4020}(2177,\cdot)\) \(\chi_{4020}(2237,\cdot)\) \(\chi_{4020}(2297,\cdot)\) \(\chi_{4020}(2333,\cdot)\) \(\chi_{4020}(2477,\cdot)\) \(\chi_{4020}(2753,\cdot)\) \(\chi_{4020}(2837,\cdot)\) ...

Inducing primitive character

\(\chi_{1005}(17,\cdot)\)

Values on generators

\((2011,2681,3217,1141)\) → \((1,-1,i,e\left(\frac{32}{33}\right))\)

Values

-117111317192329313741
\(1\)\(1\)\(e\left(\frac{73}{132}\right)\)\(e\left(\frac{47}{66}\right)\)\(e\left(\frac{23}{132}\right)\)\(e\left(\frac{107}{132}\right)\)\(e\left(\frac{13}{66}\right)\)\(e\left(\frac{53}{132}\right)\)\(e\left(\frac{2}{3}\right)\)\(e\left(\frac{19}{33}\right)\)\(e\left(\frac{7}{12}\right)\)\(e\left(\frac{59}{66}\right)\)
value at  e.g. 2

Related number fields

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