Properties

Conductor 59
Order 29
Real No
Primitive No
Parity Even
Orbit Label 6018.u

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[205]
pari: [g,chi] = znchar(Mod(205,6018))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 59
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 29
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.u
Orbit index = 21

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 ]

\(\chi_{6018}(205,\cdot)\) \(\chi_{6018}(307,\cdot)\) \(\chi_{6018}(715,\cdot)\) \(\chi_{6018}(1225,\cdot)\) \(\chi_{6018}(1327,\cdot)\) \(\chi_{6018}(1939,\cdot)\) \(\chi_{6018}(2041,\cdot)\) \(\chi_{6018}(2143,\cdot)\) \(\chi_{6018}(2245,\cdot)\) \(\chi_{6018}(2347,\cdot)\) \(\chi_{6018}(2653,\cdot)\) \(\chi_{6018}(2755,\cdot)\) \(\chi_{6018}(2857,\cdot)\) \(\chi_{6018}(2959,\cdot)\) \(\chi_{6018}(3163,\cdot)\) \(\chi_{6018}(3265,\cdot)\) \(\chi_{6018}(3367,\cdot)\) \(\chi_{6018}(3673,\cdot)\) \(\chi_{6018}(3979,\cdot)\) \(\chi_{6018}(4183,\cdot)\) \(\chi_{6018}(4387,\cdot)\) \(\chi_{6018}(4489,\cdot)\) \(\chi_{6018}(4591,\cdot)\) \(\chi_{6018}(4795,\cdot)\) \(\chi_{6018}(5101,\cdot)\) \(\chi_{6018}(5509,\cdot)\) \(\chi_{6018}(5713,\cdot)\) \(\chi_{6018}(5917,\cdot)\)

Inducing primitive character

\(\chi_{59}(28,\cdot)\)

Values on generators

\((4013,1771,1123)\) → \((1,1,e\left(\frac{10}{29}\right))\)

Values

-11571113192325293135
\(1\)\(1\)\(e\left(\frac{2}{29}\right)\)\(e\left(\frac{6}{29}\right)\)\(e\left(\frac{18}{29}\right)\)\(e\left(\frac{15}{29}\right)\)\(e\left(\frac{3}{29}\right)\)\(e\left(\frac{5}{29}\right)\)\(e\left(\frac{4}{29}\right)\)\(e\left(\frac{19}{29}\right)\)\(e\left(\frac{26}{29}\right)\)\(e\left(\frac{8}{29}\right)\)
value at  e.g. 2

Related number fields

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