Properties

Conductor 2011
Order 2010
Real No
Primitive Yes
Parity Odd
Orbit Label 2011.p

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[28]
 
pari: [g,chi] = znchar(Mod(28,2011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 2011
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 2010
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.p
Orbit index = 16

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 ]
 

\(\chi_{2011}(3,\cdot)\) \(\chi_{2011}(7,\cdot)\) \(\chi_{2011}(11,\cdot)\) \(\chi_{2011}(12,\cdot)\) \(\chi_{2011}(17,\cdot)\) \(\chi_{2011}(18,\cdot)\) \(\chi_{2011}(19,\cdot)\) \(\chi_{2011}(26,\cdot)\) \(\chi_{2011}(28,\cdot)\) \(\chi_{2011}(29,\cdot)\) \(\chi_{2011}(35,\cdot)\) \(\chi_{2011}(39,\cdot)\) \(\chi_{2011}(40,\cdot)\) \(\chi_{2011}(42,\cdot)\) \(\chi_{2011}(50,\cdot)\) \(\chi_{2011}(61,\cdot)\) \(\chi_{2011}(62,\cdot)\) \(\chi_{2011}(66,\cdot)\) \(\chi_{2011}(69,\cdot)\) \(\chi_{2011}(73,\cdot)\) \(\chi_{2011}(79,\cdot)\) \(\chi_{2011}(82,\cdot)\) \(\chi_{2011}(86,\cdot)\) \(\chi_{2011}(90,\cdot)\) \(\chi_{2011}(93,\cdot)\) \(\chi_{2011}(98,\cdot)\) \(\chi_{2011}(99,\cdot)\) \(\chi_{2011}(102,\cdot)\) \(\chi_{2011}(107,\cdot)\) \(\chi_{2011}(108,\cdot)\) ...

Values on generators

\(3\) → \(e\left(\frac{287}{2010}\right)\)

Values

-11234567891011
\(-1\)\(1\)\(e\left(\frac{395}{402}\right)\)\(e\left(\frac{287}{2010}\right)\)\(e\left(\frac{194}{201}\right)\)\(e\left(\frac{214}{1005}\right)\)\(e\left(\frac{42}{335}\right)\)\(e\left(\frac{29}{2010}\right)\)\(e\left(\frac{127}{134}\right)\)\(e\left(\frac{287}{1005}\right)\)\(e\left(\frac{131}{670}\right)\)\(e\left(\frac{139}{2010}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{1005})\)