Properties

Conductor 6003
Order 132
Real No
Primitive Yes
Parity Even
Orbit Label 6003.ct

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(6003)
 
sage: chi = H[157]
 
pari: [g,chi] = znchar(Mod(157,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6003
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 = Yes
sage: chi.is_odd()
 
pari: zncharisodd(g,chi)
 
Parity = Even
Orbit label = 6003.ct
Orbit index = 72

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 ]
 

\(\chi_{6003}(157,\cdot)\) \(\chi_{6003}(481,\cdot)\) \(\chi_{6003}(592,\cdot)\) \(\chi_{6003}(655,\cdot)\) \(\chi_{6003}(916,\cdot)\) \(\chi_{6003}(940,\cdot)\) \(\chi_{6003}(1003,\cdot)\) \(\chi_{6003}(1114,\cdot)\) \(\chi_{6003}(1201,\cdot)\) \(\chi_{6003}(1525,\cdot)\) \(\chi_{6003}(1699,\cdot)\) \(\chi_{6003}(1723,\cdot)\) \(\chi_{6003}(1786,\cdot)\) \(\chi_{6003}(1897,\cdot)\) \(\chi_{6003}(1960,\cdot)\) \(\chi_{6003}(2158,\cdot)\) \(\chi_{6003}(2245,\cdot)\) \(\chi_{6003}(2482,\cdot)\) \(\chi_{6003}(2767,\cdot)\) \(\chi_{6003}(2941,\cdot)\) \(\chi_{6003}(3004,\cdot)\) \(\chi_{6003}(3028,\cdot)\) \(\chi_{6003}(3202,\cdot)\) \(\chi_{6003}(3352,\cdot)\) \(\chi_{6003}(3526,\cdot)\) \(\chi_{6003}(3724,\cdot)\) \(\chi_{6003}(3787,\cdot)\) \(\chi_{6003}(3874,\cdot)\) \(\chi_{6003}(4246,\cdot)\) \(\chi_{6003}(4594,\cdot)\) ...

Values on generators

\((668,3133,4555)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{15}{22}\right),i)\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{125}{132}\right)\)\(e\left(\frac{59}{66}\right)\)\(e\left(\frac{28}{33}\right)\)\(e\left(\frac{19}{66}\right)\)\(e\left(\frac{37}{44}\right)\)\(e\left(\frac{35}{44}\right)\)\(e\left(\frac{95}{132}\right)\)\(e\left(\frac{47}{66}\right)\)\(e\left(\frac{31}{132}\right)\)\(e\left(\frac{26}{33}\right)\)
value at  e.g. 2

Related number fields

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