Properties

Conductor 1003
Order 232
Real No
Primitive No
Parity Even
Orbit Label 6018.bi

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(6018)
sage: chi = H[19]
pari: [g,chi] = znchar(Mod(19,6018))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1003
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 232
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 = 6018.bi
Orbit index = 35

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 ]

\(\chi_{6018}(19,\cdot)\) \(\chi_{6018}(25,\cdot)\) \(\chi_{6018}(49,\cdot)\) \(\chi_{6018}(121,\cdot)\) \(\chi_{6018}(127,\cdot)\) \(\chi_{6018}(145,\cdot)\) \(\chi_{6018}(223,\cdot)\) \(\chi_{6018}(253,\cdot)\) \(\chi_{6018}(331,\cdot)\) \(\chi_{6018}(433,\cdot)\) \(\chi_{6018}(529,\cdot)\) \(\chi_{6018}(535,\cdot)\) \(\chi_{6018}(553,\cdot)\) \(\chi_{6018}(559,\cdot)\) \(\chi_{6018}(631,\cdot)\) \(\chi_{6018}(661,\cdot)\) \(\chi_{6018}(733,\cdot)\) \(\chi_{6018}(757,\cdot)\) \(\chi_{6018}(835,\cdot)\) \(\chi_{6018}(841,\cdot)\) \(\chi_{6018}(961,\cdot)\) \(\chi_{6018}(1039,\cdot)\) \(\chi_{6018}(1069,\cdot)\) \(\chi_{6018}(1141,\cdot)\) \(\chi_{6018}(1147,\cdot)\) \(\chi_{6018}(1243,\cdot)\) \(\chi_{6018}(1267,\cdot)\) \(\chi_{6018}(1351,\cdot)\) \(\chi_{6018}(1369,\cdot)\) \(\chi_{6018}(1549,\cdot)\) ...

Inducing primitive character

\(\chi_{1003}(19,\cdot)\)

Values on generators

\((4013,1771,1123)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{19}{29}\right))\)

Values

-11571113192325293135
\(1\)\(1\)\(e\left(\frac{71}{232}\right)\)\(e\left(\frac{97}{232}\right)\)\(e\left(\frac{117}{232}\right)\)\(e\left(\frac{57}{58}\right)\)\(e\left(\frac{17}{116}\right)\)\(e\left(\frac{221}{232}\right)\)\(e\left(\frac{71}{116}\right)\)\(e\left(\frac{167}{232}\right)\)\(e\left(\frac{227}{232}\right)\)\(e\left(\frac{21}{29}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{232})\)