Properties

Conductor 1021
Order 85
Real No
Primitive Yes
Parity Even
Orbit Label 1021.q

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(1021)
sage: chi = H[78]
pari: [g,chi] = znchar(Mod(78,1021))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 1021
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 85
Real = No
sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
Primitive = Yes
sage: chi.is_odd()
pari: zncharisodd(g,chi)
Parity = Even
Orbit label = 1021.q
Orbit index = 17

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 ]

\(\chi_{1021}(12,\cdot)\) \(\chi_{1021}(14,\cdot)\) \(\chi_{1021}(16,\cdot)\) \(\chi_{1021}(71,\cdot)\) \(\chi_{1021}(73,\cdot)\) \(\chi_{1021}(78,\cdot)\) \(\chi_{1021}(91,\cdot)\) \(\chi_{1021}(104,\cdot)\) \(\chi_{1021}(108,\cdot)\) \(\chi_{1021}(113,\cdot)\) \(\chi_{1021}(115,\cdot)\) \(\chi_{1021}(125,\cdot)\) \(\chi_{1021}(126,\cdot)\) \(\chi_{1021}(144,\cdot)\) \(\chi_{1021}(147,\cdot)\) \(\chi_{1021}(168,\cdot)\) \(\chi_{1021}(192,\cdot)\) \(\chi_{1021}(196,\cdot)\) \(\chi_{1021}(224,\cdot)\) \(\chi_{1021}(235,\cdot)\) \(\chi_{1021}(237,\cdot)\) \(\chi_{1021}(253,\cdot)\) \(\chi_{1021}(255,\cdot)\) \(\chi_{1021}(256,\cdot)\) \(\chi_{1021}(262,\cdot)\) \(\chi_{1021}(275,\cdot)\) \(\chi_{1021}(302,\cdot)\) \(\chi_{1021}(310,\cdot)\) \(\chi_{1021}(316,\cdot)\) \(\chi_{1021}(335,\cdot)\) ...

Values on generators

\(10\) → \(e\left(\frac{14}{85}\right)\)

Values

-11234567891011
\(1\)\(1\)\(e\left(\frac{72}{85}\right)\)\(e\left(\frac{8}{17}\right)\)\(e\left(\frac{59}{85}\right)\)\(e\left(\frac{27}{85}\right)\)\(e\left(\frac{27}{85}\right)\)\(e\left(\frac{2}{85}\right)\)\(e\left(\frac{46}{85}\right)\)\(e\left(\frac{16}{17}\right)\)\(e\left(\frac{14}{85}\right)\)\(e\left(\frac{54}{85}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{85})\)