Properties

Conductor 6003
Order 231
Real No
Primitive Yes
Parity Even
Orbit Label 6003.dc

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[16]
 
pari: [g,chi] = znchar(Mod(16,6003))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 6003
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 231
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.dc
Orbit index = 81

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 ]
 

\(\chi_{6003}(16,\cdot)\) \(\chi_{6003}(25,\cdot)\) \(\chi_{6003}(49,\cdot)\) \(\chi_{6003}(52,\cdot)\) \(\chi_{6003}(94,\cdot)\) \(\chi_{6003}(169,\cdot)\) \(\chi_{6003}(223,\cdot)\) \(\chi_{6003}(256,\cdot)\) \(\chi_{6003}(400,\cdot)\) \(\chi_{6003}(430,\cdot)\) \(\chi_{6003}(538,\cdot)\) \(\chi_{6003}(547,\cdot)\) \(\chi_{6003}(616,\cdot)\) \(\chi_{6003}(625,\cdot)\) \(\chi_{6003}(634,\cdot)\) \(\chi_{6003}(745,\cdot)\) \(\chi_{6003}(790,\cdot)\) \(\chi_{6003}(808,\cdot)\) \(\chi_{6003}(832,\cdot)\) \(\chi_{6003}(877,\cdot)\) \(\chi_{6003}(886,\cdot)\) \(\chi_{6003}(922,\cdot)\) \(\chi_{6003}(952,\cdot)\) \(\chi_{6003}(1039,\cdot)\) \(\chi_{6003}(1051,\cdot)\) \(\chi_{6003}(1060,\cdot)\) \(\chi_{6003}(1093,\cdot)\) \(\chi_{6003}(1156,\cdot)\) \(\chi_{6003}(1267,\cdot)\) \(\chi_{6003}(1300,\cdot)\) ...

Values on generators

\((668,3133,4555)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{4}{11}\right),e\left(\frac{1}{7}\right))\)

Values

-11245781011131416
\(1\)\(1\)\(e\left(\frac{124}{231}\right)\)\(e\left(\frac{17}{231}\right)\)\(e\left(\frac{194}{231}\right)\)\(e\left(\frac{67}{231}\right)\)\(e\left(\frac{47}{77}\right)\)\(e\left(\frac{29}{77}\right)\)\(e\left(\frac{118}{231}\right)\)\(e\left(\frac{230}{231}\right)\)\(e\left(\frac{191}{231}\right)\)\(e\left(\frac{34}{231}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{231})\)