Properties

Conductor 4011
Order 114
Real No
Primitive Yes
Parity Even
Orbit Label 4011.bs

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[5]
 
pari: [g,chi] = znchar(Mod(5,4011))
 

Basic properties

sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Conductor = 4011
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Order = 114
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.bs
Orbit index = 45

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 ]
 

\(\chi_{4011}(5,\cdot)\) \(\chi_{4011}(227,\cdot)\) \(\chi_{4011}(341,\cdot)\) \(\chi_{4011}(542,\cdot)\) \(\chi_{4011}(605,\cdot)\) \(\chi_{4011}(698,\cdot)\) \(\chi_{4011}(794,\cdot)\) \(\chi_{4011}(941,\cdot)\) \(\chi_{4011}(1076,\cdot)\) \(\chi_{4011}(1109,\cdot)\) \(\chi_{4011}(1151,\cdot)\) \(\chi_{4011}(1487,\cdot)\) \(\chi_{4011}(1517,\cdot)\) \(\chi_{4011}(1580,\cdot)\) \(\chi_{4011}(1664,\cdot)\) \(\chi_{4011}(1844,\cdot)\) \(\chi_{4011}(1916,\cdot)\) \(\chi_{4011}(1979,\cdot)\) \(\chi_{4011}(2063,\cdot)\) \(\chi_{4011}(2126,\cdot)\) \(\chi_{4011}(2222,\cdot)\) \(\chi_{4011}(2399,\cdot)\) \(\chi_{4011}(2663,\cdot)\) \(\chi_{4011}(2726,\cdot)\) \(\chi_{4011}(2810,\cdot)\) \(\chi_{4011}(3062,\cdot)\) \(\chi_{4011}(3092,\cdot)\) \(\chi_{4011}(3125,\cdot)\) \(\chi_{4011}(3209,\cdot)\) \(\chi_{4011}(3272,\cdot)\) ...

Values on generators

\((2675,2866,2311)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{5}{19}\right))\)

Values

-112458101113161719
\(1\)\(1\)\(e\left(\frac{85}{114}\right)\)\(e\left(\frac{28}{57}\right)\)\(e\left(\frac{47}{57}\right)\)\(e\left(\frac{9}{38}\right)\)\(e\left(\frac{65}{114}\right)\)\(e\left(\frac{23}{114}\right)\)\(e\left(\frac{37}{38}\right)\)\(e\left(\frac{56}{57}\right)\)\(e\left(\frac{7}{57}\right)\)\(e\left(\frac{49}{114}\right)\)
value at  e.g. 2

Related number fields

Field of values \(\Q(\zeta_{57})\)