Properties

Conductor 2003
Order 154
Real No
Primitive Yes
Parity Odd
Orbit Label 2003.l

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(2003)
 
sage: chi = H[50]
 
pari: [g,chi] = znchar(Mod(50,2003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2003
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 154
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 = Odd
Orbit label = 2003.l
Orbit index = 12

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 ]
 

\(\chi_{2003}(50,\cdot)\) \(\chi_{2003}(65,\cdot)\) \(\chi_{2003}(99,\cdot)\) \(\chi_{2003}(111,\cdot)\) \(\chi_{2003}(124,\cdot)\) \(\chi_{2003}(199,\cdot)\) \(\chi_{2003}(207,\cdot)\) \(\chi_{2003}(210,\cdot)\) \(\chi_{2003}(214,\cdot)\) \(\chi_{2003}(234,\cdot)\) \(\chi_{2003}(245,\cdot)\) \(\chi_{2003}(257,\cdot)\) \(\chi_{2003}(273,\cdot)\) \(\chi_{2003}(329,\cdot)\) \(\chi_{2003}(371,\cdot)\) \(\chi_{2003}(397,\cdot)\) \(\chi_{2003}(459,\cdot)\) \(\chi_{2003}(566,\cdot)\) \(\chi_{2003}(628,\cdot)\) \(\chi_{2003}(648,\cdot)\) \(\chi_{2003}(726,\cdot)\) \(\chi_{2003}(756,\cdot)\) \(\chi_{2003}(757,\cdot)\) \(\chi_{2003}(797,\cdot)\) \(\chi_{2003}(814,\cdot)\) \(\chi_{2003}(847,\cdot)\) \(\chi_{2003}(870,\cdot)\) \(\chi_{2003}(935,\cdot)\) \(\chi_{2003}(1015,\cdot)\) \(\chi_{2003}(1059,\cdot)\) ...

Values on generators

\(5\) → \(e\left(\frac{103}{154}\right)\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{5}{22}\right)\)\(e\left(\frac{32}{77}\right)\)\(e\left(\frac{5}{11}\right)\)\(e\left(\frac{103}{154}\right)\)\(e\left(\frac{9}{14}\right)\)\(e\left(\frac{41}{154}\right)\)\(e\left(\frac{15}{22}\right)\)\(e\left(\frac{64}{77}\right)\)\(e\left(\frac{69}{77}\right)\)\(e\left(\frac{17}{22}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{77})\)