Properties

Conductor 4011
Order 570
Real No
Primitive Yes
Parity Odd
Orbit Label 4011.ci

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(4011)
 
sage: chi = H[23]
 
pari: [g,chi] = znchar(Mod(23,4011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4011
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 570
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 = 4011.ci
Orbit index = 61

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 ]
 

\(\chi_{4011}(2,\cdot)\) \(\chi_{4011}(23,\cdot)\) \(\chi_{4011}(65,\cdot)\) \(\chi_{4011}(86,\cdot)\) \(\chi_{4011}(128,\cdot)\) \(\chi_{4011}(149,\cdot)\) \(\chi_{4011}(158,\cdot)\) \(\chi_{4011}(170,\cdot)\) \(\chi_{4011}(200,\cdot)\) \(\chi_{4011}(242,\cdot)\) \(\chi_{4011}(263,\cdot)\) \(\chi_{4011}(326,\cdot)\) \(\chi_{4011}(338,\cdot)\) \(\chi_{4011}(347,\cdot)\) \(\chi_{4011}(422,\cdot)\) \(\chi_{4011}(485,\cdot)\) \(\chi_{4011}(515,\cdot)\) \(\chi_{4011}(590,\cdot)\) \(\chi_{4011}(599,\cdot)\) \(\chi_{4011}(632,\cdot)\) \(\chi_{4011}(641,\cdot)\) \(\chi_{4011}(653,\cdot)\) \(\chi_{4011}(767,\cdot)\) \(\chi_{4011}(779,\cdot)\) \(\chi_{4011}(788,\cdot)\) \(\chi_{4011}(809,\cdot)\) \(\chi_{4011}(842,\cdot)\) \(\chi_{4011}(872,\cdot)\) \(\chi_{4011}(884,\cdot)\) \(\chi_{4011}(893,\cdot)\) ...

Values on generators

\((2675,2866,2311)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{67}{95}\right))\)

Values

-112458101113161719
\(-1\)\(1\)\(e\left(\frac{113}{570}\right)\)\(e\left(\frac{113}{285}\right)\)\(e\left(\frac{49}{114}\right)\)\(e\left(\frac{113}{190}\right)\)\(e\left(\frac{179}{285}\right)\)\(e\left(\frac{89}{114}\right)\)\(e\left(\frac{94}{95}\right)\)\(e\left(\frac{226}{285}\right)\)\(e\left(\frac{541}{570}\right)\)\(e\left(\frac{106}{285}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{285})\)