Properties

Conductor 2011
Order 670
Real No
Primitive Yes
Parity Odd
Orbit Label 2011.n

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(2011)
sage: chi = H[10]
pari: [g,chi] = znchar(Mod(10,2011))

Basic properties

sage: chi.conductor()
pari: znconreyconductor(g,chi)
Conductor = 2011
sage: chi.multiplicative_order()
pari: charorder(g,chi)
Order = 670
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 = Odd
Orbit label = 2011.n
Orbit index = 14

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 ]

\(\chi_{2011}(10,\cdot)\) \(\chi_{2011}(27,\cdot)\) \(\chi_{2011}(44,\cdot)\) \(\chi_{2011}(46,\cdot)\) \(\chi_{2011}(47,\cdot)\) \(\chi_{2011}(48,\cdot)\) \(\chi_{2011}(55,\cdot)\) \(\chi_{2011}(59,\cdot)\) \(\chi_{2011}(68,\cdot)\) \(\chi_{2011}(75,\cdot)\) \(\chi_{2011}(76,\cdot)\) \(\chi_{2011}(85,\cdot)\) \(\chi_{2011}(95,\cdot)\) \(\chi_{2011}(104,\cdot)\) \(\chi_{2011}(112,\cdot)\) \(\chi_{2011}(113,\cdot)\) \(\chi_{2011}(130,\cdot)\) \(\chi_{2011}(140,\cdot)\) \(\chi_{2011}(149,\cdot)\) \(\chi_{2011}(162,\cdot)\) \(\chi_{2011}(166,\cdot)\) \(\chi_{2011}(218,\cdot)\) \(\chi_{2011}(242,\cdot)\) \(\chi_{2011}(244,\cdot)\) \(\chi_{2011}(248,\cdot)\) \(\chi_{2011}(253,\cdot)\) \(\chi_{2011}(257,\cdot)\) \(\chi_{2011}(261,\cdot)\) \(\chi_{2011}(264,\cdot)\) \(\chi_{2011}(267,\cdot)\) ...

Values on generators

\(3\) → \(e\left(\frac{423}{670}\right)\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{91}{134}\right)\)\(e\left(\frac{423}{670}\right)\)\(e\left(\frac{24}{67}\right)\)\(e\left(\frac{166}{335}\right)\)\(e\left(\frac{104}{335}\right)\)\(e\left(\frac{561}{670}\right)\)\(e\left(\frac{5}{134}\right)\)\(e\left(\frac{88}{335}\right)\)\(e\left(\frac{117}{670}\right)\)\(e\left(\frac{471}{670}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{335})\)