Properties

Conductor 3009
Order 58
Real No
Primitive No
Parity Even
Orbit Label 6018.x

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[101]
pari: [g,chi] = znchar(Mod(101,6018))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 3009
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 58
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.x
Orbit index = 24

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 ]

\(\chi_{6018}(101,\cdot)\) \(\chi_{6018}(305,\cdot)\) \(\chi_{6018}(509,\cdot)\) \(\chi_{6018}(917,\cdot)\) \(\chi_{6018}(1223,\cdot)\) \(\chi_{6018}(1427,\cdot)\) \(\chi_{6018}(1529,\cdot)\) \(\chi_{6018}(1631,\cdot)\) \(\chi_{6018}(1835,\cdot)\) \(\chi_{6018}(2039,\cdot)\) \(\chi_{6018}(2345,\cdot)\) \(\chi_{6018}(2651,\cdot)\) \(\chi_{6018}(2753,\cdot)\) \(\chi_{6018}(2855,\cdot)\) \(\chi_{6018}(3059,\cdot)\) \(\chi_{6018}(3161,\cdot)\) \(\chi_{6018}(3263,\cdot)\) \(\chi_{6018}(3365,\cdot)\) \(\chi_{6018}(3671,\cdot)\) \(\chi_{6018}(3773,\cdot)\) \(\chi_{6018}(3875,\cdot)\) \(\chi_{6018}(3977,\cdot)\) \(\chi_{6018}(4079,\cdot)\) \(\chi_{6018}(4691,\cdot)\) \(\chi_{6018}(4793,\cdot)\) \(\chi_{6018}(5303,\cdot)\) \(\chi_{6018}(5711,\cdot)\) \(\chi_{6018}(5813,\cdot)\)

Inducing primitive character

\(\chi_{3009}(101,\cdot)\)

Values on generators

\((4013,1771,1123)\) → \((-1,-1,e\left(\frac{11}{58}\right))\)

Values

-11571113192325293135
\(1\)\(1\)\(e\left(\frac{4}{29}\right)\)\(e\left(\frac{53}{58}\right)\)\(e\left(\frac{43}{58}\right)\)\(e\left(\frac{31}{58}\right)\)\(e\left(\frac{6}{29}\right)\)\(e\left(\frac{49}{58}\right)\)\(e\left(\frac{8}{29}\right)\)\(e\left(\frac{9}{29}\right)\)\(e\left(\frac{23}{29}\right)\)\(e\left(\frac{3}{58}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{29})\)