Properties

Conductor 4011
Order 570
Real No
Primitive Yes
Parity Even
Orbit Label 4011.cj

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[44]
 
pari: [g,chi] = znchar(Mod(44,4011))
 

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 = Even
Orbit label = 4011.cj
Orbit index = 62

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 ]
 

\(\chi_{4011}(44,\cdot)\) \(\chi_{4011}(53,\cdot)\) \(\chi_{4011}(74,\cdot)\) \(\chi_{4011}(95,\cdot)\) \(\chi_{4011}(116,\cdot)\) \(\chi_{4011}(137,\cdot)\) \(\chi_{4011}(179,\cdot)\) \(\chi_{4011}(212,\cdot)\) \(\chi_{4011}(233,\cdot)\) \(\chi_{4011}(254,\cdot)\) \(\chi_{4011}(284,\cdot)\) \(\chi_{4011}(296,\cdot)\) \(\chi_{4011}(305,\cdot)\) \(\chi_{4011}(317,\cdot)\) \(\chi_{4011}(359,\cdot)\) \(\chi_{4011}(380,\cdot)\) \(\chi_{4011}(401,\cdot)\) \(\chi_{4011}(410,\cdot)\) \(\chi_{4011}(443,\cdot)\) \(\chi_{4011}(473,\cdot)\) \(\chi_{4011}(494,\cdot)\) \(\chi_{4011}(506,\cdot)\) \(\chi_{4011}(527,\cdot)\) \(\chi_{4011}(557,\cdot)\) \(\chi_{4011}(569,\cdot)\) \(\chi_{4011}(620,\cdot)\) \(\chi_{4011}(662,\cdot)\) \(\chi_{4011}(674,\cdot)\) \(\chi_{4011}(683,\cdot)\) \(\chi_{4011}(704,\cdot)\) ...

Values on generators

\((2675,2866,2311)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{173}{190}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{131}{570}\right)\)\(e\left(\frac{131}{285}\right)\)\(e\left(\frac{79}{114}\right)\)\(e\left(\frac{131}{190}\right)\)\(e\left(\frac{263}{285}\right)\)\(e\left(\frac{13}{57}\right)\)\(e\left(\frac{93}{95}\right)\)\(e\left(\frac{262}{285}\right)\)\(e\left(\frac{37}{570}\right)\)\(e\left(\frac{329}{570}\right)\)
value at  e.g. 2

Related number fields

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