Properties

Conductor 1003
Order 58
Real No
Primitive No
Parity Even
Orbit Label 6018.bb

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[169]
pari: [g,chi] = znchar(Mod(169,6018))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1003
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.bb
Orbit index = 28

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 ]

\(\chi_{6018}(169,\cdot)\) \(\chi_{6018}(271,\cdot)\) \(\chi_{6018}(373,\cdot)\) \(\chi_{6018}(475,\cdot)\) \(\chi_{6018}(577,\cdot)\) \(\chi_{6018}(883,\cdot)\) \(\chi_{6018}(985,\cdot)\) \(\chi_{6018}(1087,\cdot)\) \(\chi_{6018}(1189,\cdot)\) \(\chi_{6018}(1393,\cdot)\) \(\chi_{6018}(1495,\cdot)\) \(\chi_{6018}(1597,\cdot)\) \(\chi_{6018}(1903,\cdot)\) \(\chi_{6018}(2209,\cdot)\) \(\chi_{6018}(2413,\cdot)\) \(\chi_{6018}(2617,\cdot)\) \(\chi_{6018}(2719,\cdot)\) \(\chi_{6018}(2821,\cdot)\) \(\chi_{6018}(3025,\cdot)\) \(\chi_{6018}(3331,\cdot)\) \(\chi_{6018}(3739,\cdot)\) \(\chi_{6018}(3943,\cdot)\) \(\chi_{6018}(4147,\cdot)\) \(\chi_{6018}(4453,\cdot)\) \(\chi_{6018}(4555,\cdot)\) \(\chi_{6018}(4963,\cdot)\) \(\chi_{6018}(5473,\cdot)\) \(\chi_{6018}(5575,\cdot)\)

Inducing primitive character

\(\chi_{1003}(169,\cdot)\)

Values on generators

\((4013,1771,1123)\) → \((1,-1,e\left(\frac{16}{29}\right))\)

Values

-11571113192325293135
\(1\)\(1\)\(e\left(\frac{47}{58}\right)\)\(e\left(\frac{25}{58}\right)\)\(e\left(\frac{17}{58}\right)\)\(e\left(\frac{24}{29}\right)\)\(e\left(\frac{28}{29}\right)\)\(e\left(\frac{45}{58}\right)\)\(e\left(\frac{18}{29}\right)\)\(e\left(\frac{55}{58}\right)\)\(e\left(\frac{31}{58}\right)\)\(e\left(\frac{7}{29}\right)\)
value at  e.g. 2

Related number fields

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