Properties

Conductor 1003
Order 464
Real No
Primitive No
Parity Even
Orbit Label 6018.bk

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[31]
pari: [g,chi] = znchar(Mod(31,6018))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1003
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 464
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.bk
Orbit index = 37

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 ]

\(\chi_{6018}(31,\cdot)\) \(\chi_{6018}(37,\cdot)\) \(\chi_{6018}(61,\cdot)\) \(\chi_{6018}(73,\cdot)\) \(\chi_{6018}(91,\cdot)\) \(\chi_{6018}(97,\cdot)\) \(\chi_{6018}(109,\cdot)\) \(\chi_{6018}(211,\cdot)\) \(\chi_{6018}(283,\cdot)\) \(\chi_{6018}(301,\cdot)\) \(\chi_{6018}(313,\cdot)\) \(\chi_{6018}(337,\cdot)\) \(\chi_{6018}(367,\cdot)\) \(\chi_{6018}(385,\cdot)\) \(\chi_{6018}(397,\cdot)\) \(\chi_{6018}(415,\cdot)\) \(\chi_{6018}(445,\cdot)\) \(\chi_{6018}(469,\cdot)\) \(\chi_{6018}(505,\cdot)\) \(\chi_{6018}(541,\cdot)\) \(\chi_{6018}(571,\cdot)\) \(\chi_{6018}(583,\cdot)\) \(\chi_{6018}(601,\cdot)\) \(\chi_{6018}(673,\cdot)\) \(\chi_{6018}(691,\cdot)\) \(\chi_{6018}(703,\cdot)\) \(\chi_{6018}(721,\cdot)\) \(\chi_{6018}(745,\cdot)\) \(\chi_{6018}(751,\cdot)\) \(\chi_{6018}(775,\cdot)\) ...

Inducing primitive character

\(\chi_{1003}(31,\cdot)\)

Values on generators

\((4013,1771,1123)\) → \((1,e\left(\frac{9}{16}\right),e\left(\frac{49}{58}\right))\)

Values

-11571113192325293135
\(1\)\(1\)\(e\left(\frac{409}{464}\right)\)\(e\left(\frac{183}{464}\right)\)\(e\left(\frac{27}{464}\right)\)\(e\left(\frac{31}{116}\right)\)\(e\left(\frac{227}{232}\right)\)\(e\left(\frac{51}{464}\right)\)\(e\left(\frac{177}{232}\right)\)\(e\left(\frac{449}{464}\right)\)\(e\left(\frac{213}{464}\right)\)\(e\left(\frac{8}{29}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{464})\)